Further Titles of Interest S.M. Roberts
Catalysts for Fine Chemical Synthesis V 5 – Regio and Stereo-controlled Oxidations and Reductions 2007 ISBN 0-470-09022-7
M. Beller, C. Bolm (Eds)
Transition Metals for Organic Synthesis. Building Blocks and Fine Chemicals Building Blocks and Fine Chemicals 2004 ISBN 3-527-306137
G. Dyker (Ed.)
Handbook of C-H Transformations Applications in Organic Synthesis 2005 ISBN 3-527-310746
H. Yamamoto, K. Oshima (Eds.)
Main Group Metals in Organic Synthesis 2004 ISBN 3-527-305084
G. A. Olah, . Molnr
Hydrocarbon Chemistry 2003 ISBN 0-471-417823
Hydrogen-Transfer Reactions Edited by James T. Hynes, Judith P. Klinman, Hans-Heinrich Limbach, Richard L. Schowen
Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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Hydrogen-Transfer Reactions
Edited by James T. Hynes, Judith P. Klinman, Hans-Heinrich Limbach, Richard L. Schowen
The Editors Prof. James T. Hynes Department of Chemistry and Biochemistry University of Colorado Boulder, CO 80309-0215 USA Prof. Judith P. Klinman Departments of Chemistry and Molecular and Cell Biology University of California Berkeley, CA 94720-1460 USA Dpartement de Chimie Ecole Normale Suprieure 24 rue Lhomond 75231 Paris France Prof. Hans-Heinrich Limbach Institut fr Chemie und Biochemie Freie Universitt Berlin Takustrasse 3 14195 Berlin Germany Prof. Richard L. Schowen Departments of Chemistry, Molecular Biosciences, and Pharmaceutical Chemistry University of Kansas Lawrence, KS 66047 USA Cover The cover picture is derived artistically from the potential-energy profile for the dynamic equilibrium of water molecules in the hydration layer of a protein (see A. Douhal’s chapter in volume 1) and the three-dimensional vibrational wavefunctions for reactants, transition state, and products in a hydride-transfer reaction (see the chapter by S.J. Benkovic and S. HammesSchiffer in volume 4).
&
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Printed in the Federal Republic of Germany. Printed on acid-free paper. ISBN:
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V
Foreword The Remarkable Phenomena of Hydrogen Transfer Ahmed H. Zewail* California Institute of Technology Pasadena, CA 91125, USA
Life would not exist without the making and breaking of chemical bonds - chemical reactions. Among the most elementary and significant of all reactions is the transfer of a hydrogen atom or a hydrogen ion (proton). Besides being a fundamental process involving the smallest of all atoms, such reactions form the basis of general phenomena in physical, chemical, and biological changes. Thus, there is a wide-ranging scope of studies of hydrogen transfer reactions and their role in determining properties and behaviors across different areas of molecular sciences. Remarkably, this transfer of a small particle appears deceptively simple, but is in fact complex in its nature. For the most part, the dynamics cannot be described by a classical picture and the process involves more than one nuclear motion. For example, the transfer may occur by tunneling through a reaction barrier and a quantum description is necessary; the hydrogen is not isolated as it is part of a chemical bond and in many cases the nature of the bond, “covalent” and/or “ionic” in Pauling’s valence bond description, is difficult to characterize; and the description of atom movement, although involving the local hydrogen bond, must take into account the coupling to other coordinates. In the modern age of quantum chemistry, much has been done to characterize the rate of transfer in different systems and media, and the strength of the bond and degree of charge localization. The intermediate bonding strength, directionality, and specificity are unique features of this bond. * The author is currently the Linus Pauling Chair Professor of chemistry and physics and the Director of the Physical Biology Center for Ultrafast Science & Technology and the National Science Foundation Laboratory for Molecular Sciences at Caltech in Pasadena, California, USA. He was awarded the 1999 Nobel Prize in Chemistry. Email: [email protected] Fax: 626.792.8456 Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
VI
Foreword
The supreme example for the unique role in specificity and rates comes from life’s genetic information, where the hydrogen bond determines the complementarities of G with C and A with T and the rate of hydrogen transfer controls genetic mutations. Moreover, the not-too-weak, not-too-strong strength of the bond allows for special “mobility” and for the potent hydrophobic/hydrophilic interactions. Life’s matrix, liquid water, is one such example. The making and breaking of the hydrogen bond occurs on the picosecond time scale and the process is essential to keeping functional the native structures of DNA and proteins, and their recognition of other molecules, such as drugs. At interfaces, water can form ordered structures and with its amphiphilic character, utilizing either hydrogen or oxygen for bonding, determines many properties at the nanometer scale. Hydrogen transfer can also be part of biological catalysis. In enzyme reactions, a huge complex structure is involved in bringing this small particle of hydrogen into the right place at the right time so that the reaction can be catalytically enhanced, with rates orders of magnitude larger than those in solution. The molecular theatre for these reactions is that of a very complex energy landscape, but with guided bias for specificity and selectivity in function. Control of reactivity at the active site has now reached the frontier of research in “catalytic antibody”, and one of the most significant achievements in chemical synthesis, using heterogeneous catalysis, has been the design of site-selective reaction control. Both experiments and theory join in the studies of hydrogen transfer reactions. In general, the approach is of two categories. The first involves the study of prototypical but well-defined molecular systems, either under isolated (microscopic) conditions or in complexes or clusters (mesoscopic) with the solvent, in the gas phase or molecular beams. Such studies over the past three decades have provided unprecedented resolution of the elementary processes involved in isolated molecules and en route to the condensed phase. Examples include the discovery of a “magic solvent number” for acid-base reactions, the elucidation of motions involved in double proton transfer, and the dynamics of acid dissociation in finitesized clusters. For these systems, theory is nearly quantitative, especially as more accurate electronic structure and molecular dynamics computations become available. The other category of study focuses on the nature of the transfer in the condensed phase and in biological systems. Here, it is not perhaps beneficial to consider every atom of a many-body complex system. Instead, the objective is hopefully to project the key electronic and nuclear forces which are responsible for behavior. With this perspective, approximate, but predictive, theories have a much more valuable outreach in applications than those simulating or computing bonding and motion of all atoms. Computer simulations are important, but for such systems they should be a tool of guidance to formulate a predictive theory. Similarly for experiments, the most significant ones are those that dissect complexity and provide lucid pictures of the key and relevant processes. Progress has been made in these areas of study, but challenges remain. For example, the problem of vibrational energy redistribution in large molecules, although critical to the description of rates, statistical or not, and to the separation
Foreword
of intra and intermolecular pathways, has not been solved analytically, even in an approximate but predictive formulation. Another problem of significance concerns the issue of the energy landscape of complex reactions, and the question is: what determines specificity and selectivity? This series edited by prominent players in the field is a testimony to the advances and achievements made over the past several decades. The diversity of topics covered is impressive: from isolated molecular systems, to clusters and confined geometries, and to condensed media; from organics to inorganics; from zeolites to surfaces; and, for biological systems, from proteins (including enzymes) to assemblies exhibiting conduction and other phenomena. The fundamentals are addressed by the most advanced theories of transition state, tunneling, Kramers’ friction, Marcus’ electron transfer, Grote-Hynes reaction dynamics, and free energy landscapes. Equally covered are state-of-the-art techniques and tools introduced for studies in this field and including ultrafast methods of femtochemistry and femtobiology, Raman and infrared, isotope probes, magnetic resonance, and electronic structure and MD simulations. These volumes are a valuable addition to a field that continues to impact diverse areas of molecular sciences. The field is rigorous and vigorous as it still challenges the minds of many with the fascination of how the physics of the smallest of all atoms plays in diverse applications, not only in chemistry, but also in life sciences. Our gratitude is to the Editors and Authors for this compilation of articles with new knowledge in a field still pregnant with challenges and opportunities. Pasadena, California August, 2006
Ahmed Zewail
VII
IX
Contents Foreword Preface
V XXXVII
Preface to Volumes 1 and 2 XXXIX List of Contributors to Volumes 1 and 2
XLI
I
Physical and Chemical Aspects, Parts I–III
Part I
Hydrogen Transfer in Isolated Hydrogen Bonded Molecules, Complexes and Clusters 1
1
Coherent Proton Tunneling in Hydrogen Bonds of Isolated Molecules: Malonaldehyde and Tropolone Richard L. Redington
3
1.1 1.2 1.3 1.4 1.5
Introduction 3 Coherent Tunneling Splitting Phenomena in Malonaldehyde Coherent Tunneling Phenomena in Tropolone 13 Tropolone Derivatives 26 Concluding Remarks 27 Acknowledgments 28 References 29
2
Coherent Proton Tunneling in Hydrogen Bonds of Isolated Molecules: Carboxylic Dimers 33 Martina Havenith
2.1 2.2 2.3 2.4 2.4.1
Introduction 33 Quantum Tunneling versus Classical Over Barrier Reactions Carboxylic Dimers 35 Benzoic Acid Dimer 38 Introduction 38
5
34
Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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Contents
2.4.2 2.4.3 2.4.4 2.5 2.5.1 2.5.2 2.5.3 2.5.4 2.5.5 2.5.6 2.6
Determination of the Structure 38 Barriers and Splittings 39 Infrared Vibrational Spectroscopy 41 Formic Acid Dimer 42 Introduction 42 Determination of the Structure 42 Tunneling Path 43 Barriers and Tunneling Splittings 44 Infrared Vibrational Spectroscopy 45 Coherent Proton Transfer in Formic Acid Dimer Conclusion 49 References 50
3
Gas Phase Vibrational Spectroscopy of Strong Hydrogen Bonds Knut R. Asmis, Daniel M. Neumark, and Joel M. Bowman
3.1 3.2 3.2.1 3.2.2 3.2.3 3.2.4 3.3 3.3.1 3.3.2 3.3.2.1 3.3.2.2 3.4
Introduction 53 Methods 55 Vibrational Spectroscopy of Gas Phase Ions 55 Experimental Setup 56 Potential Energy Surfaces 58 Vibrational Calculations 59 Selected Systems 60 Bihalide Anions 60 The Protonated Water Dimer (H2O_H_OH2)+ Experiments 65 Calculations 70 Outlook 75 Acknowledgments 76 References 77
4
Laser-driven Ultrafast Hydrogen Transfer Dynamics Oliver Khn and Leticia Gonzlez
4.1 4.2 4.3 4.3.1 4.3.2 4.4
Introduction 79 Theory 80 Laser Control 83 Laser-driven Intramolecular Hydrogen Transfer 83 Laser-driven H-Bond Breaking 90 Conclusions and Outlook 100 Acknowledgments 101 References 101
46
65
79
53
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Part II
Hydrogen Transfer in Condensed Phases
5
Proton Transfer from Alkane Radical Cations to Alkanes Jan Ceulemans
5.1 5.2 5.3 5.4 5.5 5.6 5.7
Introduction 108 Electronic Absorption of Alkane Radical Cations 108 Paramagnetic Properties of Alkane Radical Cations 109 The Brønsted Acidity of Alkane Radical Cations 110 The r-Basicity of Alkanes 112 Powder EPR Spectra of Alkyl Radicals 114 Symmetric Proton Transfer from Alkane Radical Cations to Alkanes: An Experimental Study in c-Irradiated n-Alkane Nanoparticles Embedded in a Cryogenic CCl3F Matrix 117 Mechanism of the Radiolytic Process 117 Physical State of Alkane Aggregates in CCl3F 118 Evidence for Proton-donor and Proton-acceptor Site Selectivity in the Symmetric Proton Transfer from Alkane Radical Cations to Alkane Molecules 121 Proton-donor Site Selectivity 121 Proton-acceptor Site Selectivity 122 Comparison with Results on Proton Transfer and “Deprotonation” in Other Systems 124 Asymmetric Proton Transfer from Alkane Radical Cations to Alkanes: An Experimental Study in c-Irradiated Mixed Alkane Crystals 125 Mechanism of the Radiolytic Process 125 Evidence for Proton-donor and Proton-acceptor Site Selectivity in the Asymmetric Proton Transfer from Alkane Radical Cations to Alkanes 128 References 131
5.7.1 5.7.2 5.7.3
5.7.3.1 5.7.3.2 5.7.4 5.8 5.8.1 5.8.2
105 107
6
Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids 135 Hans-Heinrich Limbach
6.1 6.2 6.2.1 6.2.2 6.2.3 6.2.4
Introduction 136 Theoretical 138 Coherent vs. Incoherent Tunneling 138 The Bigeleisen Theory 140 Hydrogen Bond Compression Assisted H-transfer 141 Reduction of a Two-dimensional to a One-dimensional Tunneling Model 143 The Bell–Limbach Tunneling Model 146 Concerted Multiple Hydrogen Transfer 151 Multiple Stepwise Hydrogen Transfer 152 HH-transfer 153
6.2.5 6.2.6 6.2.7 6.2.7.1
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Contents
6.2.7.2 6.2.7.3 6.2.8 6.3 6.3.1 6.3.1.1 6.3.1.2 6.3.1.3 6.3.1.4 6.3.1.5 6.3.1.6 6.3.1.7 6.3.2 6.3.2.1 6.3.2.2 6.3.2.3 6.4
Degenerate Stepwise HHH-transfer 159 Degenerate Stepwise HHHH-transfer 161 Hydrogen Transfers Involving Pre-equilibria 165 Applications 168 H-transfers Coupled to Minor Heavy Atom Motions 174 Symmetric Porphyrins and Porphyrin Analogs 174 Unsymmetrically Substituted Porphyrins 181 Hydroporphyrins 184 Intramolecular Single and Stepwise Double Hydrogen Transfer in H-bonds of Medium Strength 185 Dependence on the Environment 187 Intermolecular Multiple Hydrogen Transfer in H-bonds of Medium Strength 188 Dependence of the Barrier on Molecular Structure 193 H-transfers Coupled to Major Heavy Atom Motions 197 H-transfers Coupled to Conformational Changes 197 H-transfers Coupled to Conformational Changes and Hydrogen Bond Pre-equilibria 203 H-transfers in Complex Systems 212 Conclusions 216 Acknowledgments 217 References 217
7
Intra- and Intermolecular Proton Transfer and Related Processes in Confined Cyclodextrin Nanostructures 223 Abderrazzak Douhal
7.1 7.2
Introduction and Concept of Femtochemistry in Nanocavities 223 Overview of the Photochemistry and Photophysics of Cyclodextrin Complexes 224 Picosecond Studies of Proton Transfer in Cyclodextrin Complexes 225 1¢-Hydroxy,2¢-acetonaphthone 225 1-Naphthol and 1-Aminopyrene 228 Femtosecond Studies of Proton Transfer in Cyclodextrin Complexes 230 Coumarins 460 and 480 230 Bound and Free Water Molecules 231 2-(2¢-Hydroxyphenyl)-4-methyloxazole 236 Orange II 239 Concluding Remarks 240 Acknowledgment 241 References 241
7.3 7.3.1 7.3.2 7.4 7.4.1 7.4.2 7.5.3 7.5.4 7.6
Contents
8
Tautomerization in Porphycenes Jacek Waluk
8.1 8.2 8.2.1 8.2.2 8.2.3 8.2.4
Introduction 245 Tautomerization in the Ground Electronic State 247 Structural Data 247 NMR Studies of Tautomerism 251 Supersonic Jet Studies 253 The Nonsymmetric Case: 2,7,12,17-Tetra-n-propyl-9acetoxyporphycene 256 Calculations 258 Tautomerization in the Lowest Excited Singlet State 258 Tautomerization as a Tool to Determine Transition Moment Directions in Low Symmetry Molecules 260 Determination of Tautomerization Rates from Anisotropy Measurements 262 Tautomerization in the Lowest Excited Triplet State 265 Tautomerization in Single Molecules of Porphycene 266 Summary 267 Acknowledgments 268 References 269
8.2.5 8.3 8.3.1 8.3.2 8.4 8.5 8.6
245
9
Proton Dynamics in Hydrogen-bonded Crystals Mikhail V. Vener
9.1 9.2
Introduction 273 Tentative Study of Proton Dynamics in Crystals with Quasi-linear H-bonds 274 A Model 2D Hamiltonian 275 Specific Features of H-bonded Crystals with a Quasi-symmetric O_H_O Fragment 277 Proton Transfer Assisted by a Low-frequency Mode Excitation 279 Crystals with Moderate H-bonds 280 Crystals with Strong H-bonds 283 Limitations of the Model 2D Treatment 284 Vibrational Spectra of H-bonded Crystals: IR versus INS 285 DFT Calculations with Periodic Boundary Conditions 286 Evaluation of the Vibrational Spectra Using Classical MD Simulations 287 Effects of Crystalline Environment on Strong H-bonds: the H5O2+ Ion 288 The Structure and Harmonic Frequencies 288 The PES of the O_H_O Fragment 291 Anharmonic INS and IR Spectra 293
9.2.1 9.2.2 9.2.3 9.2.3.1 9.2.3.2 9.2.3.3 9.2.4 9.3 9.3.1 9.3.2 9.3.2.1 9.3.2.2 9.3.2.3
273
XIII
XIV
Contents
9.4
Conclusions 296 Acknowledgments 297 References 217
Part III
Hydrogen Transfer in Polar Environments
10
Theoretical Aspects of Proton Transfer Reactions in a Polar Environment 303 Philip M. Kiefer and James T. Hynes
10.1 10.2 10.2.1 10.2.2 10.2.3 10.2.3.1 10.2.3.2 10.2.3.3 10.2.3.4 10.2.3.5 10.2.4 10.3 10.3.1
Introduction 303 Adiabatic Proton Transfer 309 General Picture 309 Adiabatic Proton Transfer Free Energy Relationship (FER) 315 Adiabatic Proton Transfer Kinetic Isotope Effects 320 KIE Arrhenius Behavior 321 KIE Magnitude and Variation with Reaction Asymmetry 321 Swain–Schaad Relationship 323 Further Discussion of Nontunneling Kinetic Isotope Effects 323 Transition State Geometric Structure in the Adiabatic PT Picture 324 Temperature Solvent Polarity Effects 325 Nonadiabatic Tunneling’ Proton Transfer 326 General Nonadiabatic Proton Transfer Perspective and Rate Constant 327 Nonadiabatic Proton Transfer Kinetic Isotope Effects 333 Kinetic Isotope Effect Magnitude and Variation with Reaction Asymmetry 333 Temperature Behavior 337 Swain–Schaad Relationship 340 Concluding Remarks 341 Acknowledgments 343 References 345
10.3.2 10.3.2.1 10.3.2.2 10.3.2.3 10.4
301
11
Direct Observation of Nuclear Motion during Ultrafast Intramolecular Proton Transfer 349 Stefan Lochbrunner, Christian Schriever, and Eberhard Riedle
11.1 11.2 11.3 11.3.1 11.3.2 11.3.3 11.3.4 11.4 11.4.1
Introduction 349 Time-resolved Absorption Measurements 352 Spectral Signatures of Ultrafast ESIPT 353 Characteristic Features of the Transient Absorption 354 Analysis 356 Ballistic Wavepacket Motion 357 Coherently Excited Vibrations in Product Modes 359 Reaction Mechanism 362 Reduction of Donor–Acceptor Distance by Skeletal Motions
362
Contents
11.4.2 11.4.3 11.4.4 11.4.5 11.4.6 11.5 11.6
Multidimensional ESIPT Model 363 Micro-irreversibility 365 Topology of the PES and Turns in the Reaction Path 366 Comparison with Ground State Hydrogen Transfer Dynamics 368 Internal Conversion 368 Reaction Path Specific Wavepacket Dynamics in Double Proton Transfer Molecules 370 Conclusions 372 Acknowledgment 373 References 373
12
Solvent Assisted Photoacidity Dina Pines and Ehud Pines
12.1 12.2 12.2.1 12.2.2
Introduction 377 Photoacids, Photoacidity and Frster Cycle 378 Photoacids and Photobases 378 Use of the Frster Cycle to Estimate the Photoacidity of Photoacids 379 Direct Methods for Determining the Photoacidity of Photoacids 387 Evidence for the General Validity of the Frster Cycle and the K*a Scale 389 Evidence for the General Validity of the Frster Cycle Based on Timeresolved and Steady State Measurements of Excited-state Proton Transfer of Photoacids 389 Evidence Based on Free Energy Correlations 393 Factors Affecting Photoacidity 397 General Considerations 397 Comparing the Solvent Effect on the Photoacidities of Neutral and Cationic Photoacids 398 The Effect of Substituents on the Photoacidity of Aromatic Alcohols 400 Solvent Assisted Photoacidity: The 1La, 1Lb Paradigm 404 Summary 410 Acknowledgments 411 References 411
12.2.3 12.3 12.3.1
12.3.2 12.4 12.4.1 12.4.2 12.4.3 12.5 12.6
377
13
Design and Implementation of “Super” Photoacids Laren M. Tolbert and Kyril M. Solntsev
13.1 13.2 13.2.1 13.2.2 13.2.3 13.3 13.3.1
Introduction 417 Excited-state Proton Transfer (ESPT) 420 1-Naphthol vs. 2-Naphthol 420 “Super” Photoacids 422 Fluorinated Phenols 426 Nature of the Solvent 426 Hydrogen Bonding and Solvatochromism in Super Photoacids
417
426
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13.3.2 13.3.3 13.3.4 13.3.5 13.4 13.4.1 13.5
Dynamics in Water and Mixed Solvents 427 Dynamics in Nonaqueous Solvents 428 ESPT in the Gas Phase 431 Stereochemistry 433 ESPT in Biological Systems 433 The Green Fluorescent Protein (GFP) or “ESPT in a Box” 435 Conclusions 436 Acknowledgments 436 References 437
Foreword Preface
V XXXVII
Preface to Volumes 1 and 2 XXXIX List of Contributors to Volumes 1 and 2
XLI
I
Physical and Chemical Aspects, Parts IV–VII
Part IV
Hydrogen Transfer in Protic Systems
14
Bimolecular Proton Transfer in Solution Erik T. J. Nibbering and Ehud Pines
14.1 14.2 14.3 14.4
Intermolecular Proton Transfer in the Liquid Phase 443 Photoacids as Ultrafast Optical Triggers for Proton Transfer 445 Proton Recombination and Acid–Base Neutralization 448 Reaction Dynamics Probing with Vibrational Marker Modes 449 Acknowledgment 455 References 455
15
Coherent Low-frequency Motions in Condensed Phase Hydrogen Bonding and Transfer 459 Thomas Elsaesser
15.1 15.2 15.3
Introduction 459 Vibrational Excitations of Hydrogen Bonded Systems 460 Low-frequency Wavepacket Dynamics of Hydrogen Bonds in the Electronic Ground State 463 Intramolecular Hydrogen Bonds 463 Hydrogen Bonded Dimers 466 Low-frequency Motions in Excited State Hydrogen Transfer 471 Conclusions 475 Acknowledgments 476 References 476
15.3.1 15.3.2 15.4 15.5
441 443
Contents
16
Proton-Coupled Electron Transfer: Theoretical Formulation and Applications 479 Sharon Hammes-Schiffer
16.1 16.2 16.2.1 16.2.2 16.2.3 16.2.3.1 16.2.3.2 16.3 16.3.1 16.3.2 16.4
Introduction 479 Theoretical Formulation for PCET 480 Fundamental Concepts 480 Proton Donor–Acceptor Motion 483 Dynamical Effects 485 Dielectric Continuum Representation of the Environment Molecular Representation of the Environment 490 Applications 492 PCET in Solution 492 PCET in a Protein 498 Conclusions 500 Acknowledgments 500 References 501
17
The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer in Model Systems 503 Justin M. Hodgkiss, Joel Rosenthal, and Daniel G. Nocera
17.1 17.1.1 17.1.2 17.1.2.1 17.1.2.2 17.2 17.2.1 17.2.2 17.2.3 17.2.4 17.3 17.3.1 17.3.2 17.3.2.1 17.3.2.2 17.4 17.4.1 17.4.2 17.5 17.6
Introduction 503 Formulation of HAT as a PCET Reaction 504 Scope of Chapter 507 Unidirectional PCET 508 Bidirectional PCET 508 Methods of HAT and PCET Study 509 Free Energy Correlations 510 Solvent Dependence 511 Deuterium Kinetic Isotope Effects 511 Temperature Dependence 512 Unidirectional PCET 512 Type A: Hydrogen Abstraction 512 Type B: Site Differentiated PCET 523 PCET across Symmetric Hydrogen Bonding Interfaces 523 PCET across Polarized Hydrogen Bonding Interfaces 527 Bidirectional PCET 537 Type C: Non-Specific 3-Point PCET 538 Type D: Site-Specified 3-Point PCET 543 The Different Types of PCET in Biology 548 Application of Emerging Ultrafast Spectroscopy to PCET 554 Acknowledgment 556 References 556
486
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Part V
Hydrogen Transfer in Organic and Organometallic Reactions
18
Formation of Hydrogen-bonded Carbanions as Intermediates in Hydron Transfer between Carbon and Oxygen 565 Heinz F. Koch
18.1 18.2 18.3
Proton Transfer from Carbon Acids to Methoxide Ion 565 Proton Transfer from Methanol to Carbanion Intermediates Proton Transfer Associated with Methoxide Promoted Dehydrohalogenation Reactions 576 Conclusion 580 References 581
18.4
563
573
19
Theoretical Simulations of Free Energy Relationships in Proton Transfer 583 Ian H. Williams
19.1 19.2 19.2.1 19.2.2 19.3 19.3.1 19.4
Introduction 583 Qualitative Models for FERs 584 What is Meant by “Reaction Coordinate”? 588 The Brønsted a as a Measure of TS Structure 589 FERs from MO Calculations of PESs 590 Energies and Transition States 590 FERs from VB Studies of Free Energy Changes for PT in Condensed Phases 597 Concluding Remarks 600 References 600
19.5
20
The Extraordinary Dynamic Behavior and Reactivity of Dihydrogen and Hydride in the Coordination Sphere of Transition Metals 603 Gregory J. Kubas
20.1 20.1.1 20.1.2 20.1.2 20.1.3 20.1.4 20.2 20.2.1 20.3
Introduction 603 Structure, Bonding, and Activation of Dihydrogen Complexes 603 Extraordinary Dynamics of Dihydrogen Complexes 606 Vibrational Motion of Dihydrogen Complexes 608 Elongated Dihydrogen Complexes 609 Cleavage of the H–H Bond in Dihydrogen Complexes 610 H2 Rotation in Dihydrogen Complexes 615 Determination of the Barrier to Rotation of Dihydrogen 616 NMR Studies of H2 Activation, Dynamics, and Transfer Processes 617 Solution NMR 617 Solid State NMR of H2 Complexes 621
20.3.1 20.3.2
Contents
20.4 20.4.1 20.4.2 20.5
Intramolecular Hydrogen Rearrangement and Exchange 623 Extremely Facile Hydrogen Transfer in IrXH2(H2)(PR3)2 and Other Systems 627 Quasielastic Neutron Scattering Studies of H2 Exchange with cisHydrides 632 Summary 633 Acknowledgments 634 References 634
21
Dihydrogen Transfer and Symmetry: The Role of Symmetry in the Chemistry of Dihydrogen Transfer in the Light of NMR Spectroscopy 639 Gerd Buntkowsky and Hans-Heinrich Limbach
21.1 21.2 21.2.1 21.2.1.1 21.2.1.2 21.2.1.3 21.2.2 21.3 21.3.1
Introduction 639 Tunneling and Chemical Kinetics 641 The Role of Symmetry in Chemical Exchange Reactions 641 Coherent Tunneling 642 The Density Matrix 648 The Transition from Coherent to Incoherent Tunneling 649 Incoherent Tunneling and the Bell Model 653 Symmetry Effects on NMR Lineshapes of Hydration Reactions 655 Analytical Solution for the Lineshape of PHIP Spectra Without Exchange 657 Experimental Examples of PHIP Spectra 662 PHIP under ALTADENA Conditions 662 PHIP Studies of Stereoselective Reactions 662 13 C-PHIP-NMR 664 Effects of Chemical Exchange on the Lineshape of PHIP Spectra 665 Symmetry Effects on NMR Lineshapes of Intramolecular Dihydrogen Exchange Reactions 670 Experimental Examples 670 Slow Tunneling Determined by 1H Liquid State NMR Spectroscopy 671 Slow to Intermediate Tunneling Determined by 2 H Solid State NMR 671 Intermediate to Fast Tunneling Determined by 2 H Solid State NMR 673 Fast Tunneling Determined by Incoherent Neutron Scattering 675 Kinetic Data Obtained from the Experiments 675 Ru-D2 Complex 676 W(PCy)3(CO)3 (g-H2 ) Complex 677 Summary and Conclusion 678 Acknowledgments 679 References 679
21.3.2 21.3.2.1 21.3.2.2 21.3.2.3 21.3.3 21.4 21.4.1 21.4.1.1 21.4.1.2 21.4.1.3 21.4.1.4 21.4.2 21.4.2.1 21.4.2.2 21.5
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Part VI
Proton Transfer in Solids and Surfaces
22
Proton Transfer in Zeolites Joachim Sauer
22.1 22.2 22.3 22.4 22.5 22.6 22.7
Introduction – The Active Sites of Acidic Zeolite Catalysts 685 Proton Transfer to Substrate Molecules within Zeolite Cavities 686 Formation of NH4+ ions on NH3 adsorption 688 Methanol Molecules and Dimers in Zeolites 691 Water Molecules and Clusters in Zeolites 694 Proton Jumps in Hydrated and Dry Zeolites 700 Stability of Carbenium Ions in Zeolites 703 References 706
23
Proton Conduction in Fuel Cells Klaus-Dieter Kreuer
23.1 23.2 23.3
Introduction 709 Proton Conducting Electrolytes and Their Application in Fuel Cells 710 Long-range Proton Transport of Protonic Charge Carriers in Homogeneous Media 714 Proton Conduction in Aqueous Environments 715 Phosphoric Acid 719 Heterocycles (Imidazole) 720 Confinement and Interfacial Effects 723 Hydrated Acidic Polymers 723 Adducts of Basic Polymers with Oxo-acids 727 Separated Systems with Covalently Bound Proton Solvents 728 Concluding Remarks 731 Acknowledgment 733 References 733
23.3.1 23.3.2 23.3.3 23.4 23.4.1 23.4.2 23.4.3 23.5
683
685
709
24
Proton Diffusion in Ice Bilayers Katsutoshi Aoki
24.1 24.1.1 24.1.2 24.1.3 24.2 24.2.1 24.2.2 24.2.3 24.2.4 24.3 24.3.1
Introduction 737 Phase Diagram and Crystal Structure of Ice 737 Molecular and Protonic Diffusion 739 Protonic Diffusion at High Pressure 740 Experimental Method 741 Diffusion Equation 741 High Pressure Measurement 742 Infrared Reflection Spectra 743 Thermal Activation of Diffusion Motion 744 Spectral Analysis of the Diffusion Process 745 Protonic Diffusion 745
737
Contents
24.3.2 24.3.3 24.4
Molecular Diffusion 746 Pressure Dependence of Protonic Diffusion Coefficient 747 Summary 749 References 749
25
Hydrogen Transfer on Metal Surfaces Klaus Christmann
25.1 25.2
Introduction 751 The Principles of the Interaction of Hydrogen with Surfaces: Terms and Definitions 755 The Transfer of Hydrogen on Metal Surfaces 761 Hydrogen Surface Diffusion on Homogeneous Metal Surfaces 761 Hydrogen Surface Diffusion and Transfer on Heterogeneous Metal Surfaces 771 Alcohol and Water on Metal Surfaces: Evidence of H Bond Formation and H Transfer 775 Alcohols on Metal Surfaces 775 Water on Metal Surfaces 778 Conclusion 783 Acknowledgments 783 References 783
25.3 25.3.1 25.3.2 25.4 25.4.1 25.4.2 25.5
751
26
Hydrogen Motion in Metals 787 Rolf Hempelmann and Alexander Skripov
26.1 26.2 26.2.1 26.2.2 26.2.3 26.2.4 26.3 26.4 26.4.1 26.4.2 26.4.3 26.5 26.5.1 26.5.2 26.5.3
Survey 787 Experimental Methods 788 Anelastic Relaxation 788 Nuclear Magnetic Resonance 790 Quasielastic Neutron Scattering 792 Other Methods 795 Experimental Results on Diffusion Coefficients 796 Experimental Results on Hydrogen Jump Diffusion Mechanisms 801 Binary Metal–Hydrogen Systems 802 Hydrides of Alloys and Intermetallic Compounds 804 Hydrogen in Amorphous Metals 810 Quantum Motion of Hydrogen 812 Hydrogen Tunneling in Nb Doped with Impurities 814 Hydrogen Tunneling in a-MnHx 817 Rapid Low-temperature Hopping of Hydrogen in a-ScHx(Dx) and TaV2Hx(Dx) 821 Concluding Remarks 825 Acknowledgment 825 References 826
26.6
XXI
XXII
Contents
Part VII
Special Features of Hydrogen-Transfer Reactions 831
27
Variational Transition State Theory in the Treatment of Hydrogen Transfer Reactions 833 Donald G. Truhlar and Bruce C. Garrett
27.1 27.2 27.2.1 27.2.2 27.3 27.3.1 27.3.2 27.3.3 27.4
Introduction 833 Incorporation of Quantum Mechanical Effects in VTST 835 Adiabatic Theory of Reactions 837 Quantum Mechanical Effects on Reaction Coordinate Motion 840 H-atom Transfer in Bimolecular Gas-phase Reactions 843 H + H2 and Mu + H2 843 Cl + HBr 849 Cl + CH4 853 Intramolecular Hydrogen Transfer in Unimolecular Gas-phase Reactions 857 Intramolecular H-transfer in 1,3-Pentadiene 858 1,2-Hydrogen Migration in Methylchlorocarbene 860 Liquid-phase and Enzyme-catalyzed Reactions 860 Separable Equilibrium Solvation 862 Equilibrium Solvation Path 864 Nonequilibrium Solvation Path 864 Potential-of-mean-force Method 865 Ensemble-averaged Variational Transition State Theory 865 Examples of Condensed-phase Reactions 867 H + Methanol 867 Xylose Isomerase 868 Dihydrofolate Reductase 868 Another Perspective 869 Concluding Remarks 869 Acknowledgments 871 References 871
27.4.1 27.4.2 27.5 27.5.1 27.5.2 27.5.3 27.5.4 27.5.5 27.6 27.6.1 27.6.2 27.6.3 27.7 27.8
28
Quantum Mechanical Tunneling of Hydrogen Atoms in Some Simple Chemical Systems 875 K. U. Ingold
28.1 28.2 28.2.1 28.2.1.1 28.2.1.2 28.2.2 28.2.2.1 28.2.2.2 28.2.2.3
Introduction 875 Unimolecular Reactions 876 Isomerization of Sterically Hindered Phenyl Radicals 876 2,4,6-Tri–tert–butylphenyl 876 Other Sterically Hindered Phenyl Radicals 881 Inversion of Nonplanar, Cyclic, Carbon-Centered Radicals 883 Cyclopropyl and 1-Methylcyclopropyl Radicals 883 The Oxiranyl Radical 884 The Dioxolanyl Radical 886
Contents
28.2.2.4 28.3 28.3.1 28.3.2
Summary 887 Bimolecular Reactions 887 H-Atom Abstraction by Methyl Radicals in Organic Glasses 887 H-Atom Abstraction by Bis(trifluoromethyl) Nitroxide in the Liquid Phase 890 References 892
29
Multiple Proton Transfer: From Stepwise to Concerted 895 Zorka Smedarchina, Willem Siebrand, and Antonio Fernndez-Ramos
29.1 29.2 29.3 29.4 29.5 29.6 29.7 29.8 29.9 29.10 29.11
Introduction 895 Basic Model 897 Approaches to Proton Tunneling Dynamics 904 Tunneling Dynamics for Two Reaction Coordinates 908 Isotope Effects 914 Dimeric Formic Acid and Related Dimers 918 Other Dimeric Systems 922 Intramolecular Double Proton Transfer 926 Proton Conduits 932 Transfer of More Than Two Protons 939 Conclusion 940 Acknowledgment 943 References 943
Foreword Preface
V XXXVII
Preface to Volumes 3 and 4 XXXIX List of Contributors to Volumes 3 and 4
XLI
II
Biological Aspects, Parts I–II
Part I
Models for Biological Hydrogen Transfer
1
Proton Transfer to and from Carbon in Model Reactions Tina L. Amyes and John P. Richard
1.1 1.2
Introduction 949 Rate and Equilibrium Constants for Carbon Deprotonation in Water 949 Rate Constants for Carbanion Formation 951 Rate Constants for Carbanion Protonation 953 Protonation by Hydronium Ion 953
1.2.1 1.2.2 1.2.2.1
947 949
XXIII
XXIV
Contents
1.2.2.2 1.2.2.3 1.2.3 1.3 1.4 1.4.1 1.4.2 1.4.2.1 1.4.2.2 1.5 1.5.1 1.5.2 1.6
Protonation by Buffer Acids 954 Protonation by Water 955 The Burden Borne by Enzyme Catalysts 955 Substituent Effects on Equilibrium Constants for Deprotonation of Carbon 957 Substituent Effects on Rate Constants for Proton Transfer at Carbon 958 The Marcus Equation 958 Marcus Intrinsic Barriers for Proton Transfer at Carbon 960 Hydrogen Bonding 960 Resonance Effects 961 Small Molecule Catalysis of Proton Transfer at Carbon 965 General Base Catalysis 966 Electrophilic Catalysis 967 Comments on Enzymatic Catalysis of Proton Transfer 970 Acknowledgment 970 References 971
2
General Acid–Base Catalysis in Model Systems Anthony J. Kirby
2.1 2.1.1 2.1.2 2.1.3 2.2 2.2.1 2.2.2 2.2.3 2.2.3.1 2.2.3.2 2.3 2.3.1 2.3.2 2.3.2.1 2.3.3 2.3.4
Introduction 975 Kinetics 975 Mechanism 977 Kinetic Equivalence 979 Structural Requirements and Mechanism 981 General Acid Catalysis 982 Classical General Base Catalysis 983 General Base Catalysis of Cyclization Reactions 984 Nucleophilic Substitution 984 Ribonuclease Models 985 Intramolecular Reactions 987 Introduction 987 Efficient Intramolecular General Acid–Base Catalysis 988 Aliphatic Systems 991 Intramolecular General Acid Catalysis of Nucleophilic Catalysis 993 Intramolecular General Acid Catalysis of Intramolecular Nucleophilic Catalysis 998 Intramolecular General Base Catalysis 999 Proton Transfers to and from Carbon 1000 Intramolecular General Acid Catalysis 1002 Intramolecular General Base Catalysis 1004 Simple Enzyme Models 1006 Hydrogen Bonding, Mechanism and Reactivity 1007 References 1010
2.3.5 2.4 2.4.1 2.4.2 2.4.3 2.5
975
Contents
3
Hydrogen Atom Transfer in Model Reactions 1013 Christian Schneich
3.1 3.2 3.3 3.3.1 3.3.2 3.4 3.4.1 3.4.1.1 3.4.1.2 3.4.2 3.5
Introduction 1013 Oxygen-centered Radicals 1013 Nitrogen-dentered Radicals 1017 Generation of Aminyl and Amidyl Radicals 1017 Reactions of Aminyl and Amidyl Radicals 1018 Sulfur-centered Radicals 1019 Thiols and Thiyl Radicals 1020 Hydrogen Transfer from Thiols 1020 Hydrogen Abstraction by Thiyl Radicals 1023 Sulfide Radical Cations 1029 Conclusion 1032 Acknowledgment 1032 References 1032
4
Model Studies of Hydride-transfer Reactions Richard L. Schowen
4.1 4.1.1 4.1.2 4.1.3 4.1.4 4.2 4.2.1 4.2.2 4.2.3 4.3 4.3.1 4.3.2 4.4 4.4.1 4.4.2 4.4.3 4.4.4
Introduction 1037 Nicotinamide Coenzymes: Basic Features 1038 Flavin Coenzymes: Basic Features 1039 Quinone Coenzymes: Basic Features 1039 Matters Not Treated in This Chapter 1039 The Design of Suitable Model Reactions 1040 The Anchor Principle of Jencks 1042 The Proximity Effect of Bruice 1044 Environmental Considerations 1045 The Role of Model Reactions in Mechanistic Enzymology 1045 Kinetic Baselines for Estimations of Enzyme Catalytic Power 1045 Mechanistic Baselines and Enzymic Catalysis 1047 Models for Nicotinamide-mediated Hydrogen Transfer 1048 Events in the Course of Formal Hydride Transfer 1048 Electron-transfer Reactions and H-atom-transfer Reactions 1049 Hydride-transfer Mechanisms in Nicotinamide Models 1052 Transition-state Structure in Hydride Transfer: The Kreevoy Model 1054 Quantum Tunneling in Model Nicotinamide-mediated Hydride Transfer 1060 Intramolecular Models for Nicotinamide-mediated Hydride Transfer 1061 Summary 1063 Models for Flavin-mediated Hydride Transfer 1064 Differences between Flavin Reactions and Nicotinamide Reactions 1064
4.4.5 4.4.6 4.4.7 4.5 4.5.1
1037
XXV
XXVI
Contents
4.5.2 4.6 4.7 4.8
The Hydride-transfer Process in Model Systems 1065 Models for Quinone-mediated Reactions 1068 Summary and Conclusions 1071 Appendix: The Use of Model Reactions to Estimate Enzyme Catalytic Power 1071 References 1074
5
Acid–Base Catalysis in Designed Peptides Lars Baltzer
5.1 5.1.1 5.1.2 5.1.3 5.2 5.2.1 5.2.2 5.2.3 5.2.4
Designed Polypeptide Catalysts 1079 Protein Design 1080 Catalyst Design 1083 Designed Catalysts 1085 Catalysis of Ester Hydrolysis 1089 Design of a Folded Polypeptide Catalyst for Ester Hydrolysis 1089 The HisH+-His Pair 1091 Reactivity According to the Brnsted Equation 1093 Cooperative Nucleophilic and General-acid Catalysis in Ester Hydrolysis 1094 Why General-acid Catalysis? 1095 Limits of Activity in Surface Catalysis 1096 Optimal Organization of His Residues for Catalysis of Ester Hydrolysis 1097 Substrate and Transition State Binding 1098 His Catalysis in Re-engineered Proteins 1099 Computational Catalyst Design 1100 Ester Hydrolysis 1101 Triose Phosphate Isomerase Activity by Design 1101 Enzyme Design 1102 References 1102
5.2.5 5.3 5.3.1 5.3.2 5.3.3 5.4 5.4.1 5.4.2 5.5
1079
Part II
General Aspects of Biological Hydrogen Transfer
6
Enzymatic Catalysis of Proton Transfer at Carbon Atoms John A. Gerlt
6.1 6.2
Introduction 1107 The Kinetic Problems Associated with Proton Abstraction from Carbon 1108 Marcus Formalism for Proton Transfer 1110 DGo, the Thermodynamic Barrier 1111 DG‡int, the Intrinsic Kinetic Barrier 1112 Structural Strategies for Reduction of DGo 1114 Proposals for Understanding the Rates of Proton Transfer 1114 Short Strong Hydrogen Bonds 1115
6.2.1 6.2.2 6.2.3 6.3 6.3.1 6.3.2
1105 1107
Contents
6.3.3 6.3.4 6.4 6.4.1 6.4.2 6.4.3 6.4.4 6.5
Electrostatic Stabilization of Enolate Anion Intermediates 1115 Experimental Measure of Differential Hydrogen Bond Strengths 1116 Experimental Paradigms for Enzyme-catalyzed Proton Abstraction from Carbon 1118 Triose Phosphate Isomerase 1118 Ketosteroid Isomerase 1125 Enoyl-CoA Hydratase (Crotonase) 1127 Mandelate Racemase and Enolase 1131 Summary 1134 References 1135
7
Multiple Hydrogen Transfers in Enzyme Action 1139 M. Ashley Spies and Michael D. Toney
7.1 7.2 7.2.1 7.2.2 7.2.3 7.2.4 7.2.5 7.2.6 7.3 7.4 7.4.1 7.4.2 7.4.3 7.4.4 7.5 7.6
Introduction 1139 Cofactor-Dependent with Activated Substrates 1139 Alanine Racemase 1139 Broad Specificity Amino Acid Racemase 1151 Serine Racemase 1152 Mandelate Racemase 1152 ATP-Dependent Racemases 1154 Methylmalonyl-CoA Epimerase 1156 Cofactor-Dependent with Unactivated Substrates 1157 Cofactor-Independent with Activated Substrates 1157 Proline Racemase 1157 Glutamate Racemase 1161 DAP Epimerase 1162 Sugar Epimerases 1165 Cofactor-Independent with Unactivated Substrates 1165 Summary 1166 References 1167
8
Computer Simulations of Proton Transfer in Proteins and Solutions Sonja Braun-Sand, Mats H. M. Olsson, Janez Mavri, and Arieh Warshel
8.1 8.2
Introduction 1171 Simulating PT Reactions by the EVB and other QM/MM Methods 1171 Simulating the Fluctuations of the Environment and Nuclear Quantum Mechanical Effects 1177 The EVB as a Basis for LFER of PT Reactions 1185 Demonstrating the Applicability of the Modified Marcus’ Equation 1188 General Aspects of Enzymes that Catalyze PT Reactions 1194 Dynamics, Tunneling and Related Nuclear Quantum Mechanical Effects 1195
8.3 8.4 8.5 8.6 8.7
1171
XXVII
XXVIII
Contents
8.8
Concluding Remarks 1198 Acknowledgements 1199 Abbreviations 1199 References 1200
Foreword Preface
V XXXVII
Preface to Volumes 3 and 4 XXXIX List of Contributors to Volumes 3 and 4
XLI
II
Biological Aspects, Parts III–V
Part III
Quantum Tunneling and Protein Dynamics
9
The Quantum Kramers Approach to Enzymatic Hydrogen Transfer – Protein Dynamics as it Couples to Catalysis 1209 Steven D. Schwartz
9.1 9.2 9.3 9.3.1 9.3.2
Introduction 1209 The Derivation of the Quantum Kramers Method 1210 Promoting Vibrations and the Dynamics of Hydrogen Transfer Promoting Vibrations and The Symmetry of Coupling 1213 Promoting Vibrations – Corner Cutting and the Masking of KIEs 1215 Hydrogen Transfer and Promoting Vibrations – Alcohol Dehydrogenase 1217 Promoting Vibrations and the Kinetic Control of Enzymes – Lactate Dehydrogenase 1223 The Quantum Kramers Model and Proton Coupled Electron Transfer 1231 Promoting Vibrations and Electronic Polarization 1233 Conclusions 1233 Acknowledgment 1234 References 1234
9.4 9.5 9.6 9.7 9.8
1207
10
Nuclear Tunneling in the Condensed Phase: Hydrogen Transfer in Enzyme Reactions 1241 Michael J. Knapp, Matthew Meyer, and Judith P. Klinman
10.1 10.2 10.3
Introduction 1241 Enzyme Kinetics: Extracting Chemistry from Complexity 1242 Methodology for Detecting Nonclassical H-Transfers 1245
1213
Contents
10.3.1 10.3.1.1 10.3.1.2 10.3.2 10.3.2.1 10.3.2.2 10.3.3 10.3.3.1 10.3.3.2 10.3.3.3 10.3.3.4 10.4 10.4.1 10.4.2 10.4.3 10.4.4 10.5 10.5.1 10.5.1.1 10.5.1.2 10.5.2 10.5.2.1 10.5.2.2 10.5.3 10.5.3.1 10.5.3.2 10.6
Bond Stretch KIE Model: Zero-point Energy Effects 1245 Primary Kinetic Isotope Effects 1246 Secondary Kinetic Isotope Effects 1247 Methods to Measure Kinetic Isotope Effects 1247 Noncompetitive Kinetic Isotope Effects: kcat or kcat/KM 1247 Competitive Kinetic Isotope Effects: kcat/KM 1248 Diagnostics for Nonclassical H-Transfer 1249 The Magnitude of Primary KIEs: kH/kD > 8 at Room Temperature 1249 Discrepant Predictions of Transition-state Structure and Inflated Secondary KIEs 1251 Exponential Breakdown: Rule of the Geometric Mean and Swain–Schaad Relationships 1252 Variable Temperature KIEs: AH/AD >> 1 or AH/AD << 1 1254 Concepts and Theories Regarding Hydrogen Tunneling 1256 Conceptual View of Tunneling 1256 Tunnel Corrections to Rates: Static Barriers 1258 Fluctuating Barriers: Reproducing Temperature Dependences 1260 Overview 1264 Experimental Systems 1265 Hydride Transfers 1265 Alcohol Dehydrogenases 1265 Glucose Oxidase 1270 Amine Oxidases 1273 Bovine Serum Amine Oxidase 1273 Monoamine Oxidase B 1275 Hydrogen Atom (H.) Transfers 1276 Soybean Lipoxygense-1 1276 Peptidylglycine a-Hydroxylating Monooxygenase (PHM) and Dopamine b-Monooxygenase (DbM) 1279 Concluding Comments 1280 References 1281
11
Multiple-isotope Probes of Hydrogen Tunneling W. Phillip Huskey
11.1 11.2 11.2.1 11.2.2 11.3 11.3.1 11.3.2 11.3.3
Introduction 1285 Background: H/D Isotope Effects as Probes of Tunneling 1287 One-frequency Models 1287 Temperature Dependence of Isotope Effects 1289 Swain–Schaad Exponents: H/D/T Rate Comparisons 1290 Swain–Schaad Limits in the Absence of Tunneling 1291 Swain–Schaad Exponents for Tunneling Systems 1292 Swain–Schaad Exponents from Computational Studies that Include Tunneling 1293
1285
XXIX
XXX
Contents
11.3.4 11.3.5 11.4 11.4.1 11.4.2 11.4.3 11.5 11.5.1 11.5.2 11.5.3 11.6
12
12.1 12.1.1 12.1.2 12.1.2.1 12.1.2.2 12.1.2.3 12.1.2.4 12.1.2.5 12.2 12.3 12.3.1 12.3.1.1 12.3.1.2 12.3.2 12.3.2.1 12.3.2.2 12.3.3 12.3.3.1 12.3.3.2 12.3.3.3 12.3.4 12.3.4.1 12.3.4.2
Swain–Schaad Exponents for Secondary Isotope Effects 1294 Effects of Mechanistic Complexity on Swain–Schaad Exponents 1294 Rule of the Geometric Mean: Isotope Effects on Isotope Effects 1297 RGM Breakdown from Intrinsic Nonadditivity 1298 RGM Breakdown from Isotope-sensitive Effective States 1300 RGM Breakdown as Evidence for Tunneling 1303 Saunders’ Exponents: Mixed Multiple Isotope Probes 1304 Experimental Considerations 1304 Separating Swain–Schaad and RGM Effects 1304 Effects of Mechanistic Complexity on Mixed Isotopic Exponents 1306 Concluding Remarks 1306 References 1307 Current Issues in Enzymatic Hydrogen Transfer from Carbon: Tunneling and Coupled Motion from Kinetic Isotope Effect Studies Amnon Kohen
1311
Introduction 1311 Enzymatic H-transfer – Open Questions 1311 Terminology and Definitions 1312 Catalysis 1312 Tunneling 1313 Dynamics 1313 Coupling and Coupled Motion 1314 Kinetic Isotope Effects (KIEs) 1315 The H-transfer Step in Enzyme Catalysis 1316 Probing H-transfer in Complex Systems 1318 The Swain–Schaad Relationship 1318 The Semiclassical Relationship of Reaction Rates of H, D and T 1318 Effects of Tunneling and Kinetic Complexity on EXP 1319 Primary Swain–Schaad Relationship 1320 Intrinsic Primary KIEs 1320 Experimental Examples Using Intrinsic Primary KIEs 1322 Secondary Swain–Schaad Relationship 1323 Mixed Labeling Experiments as Probes for Tunneling and Primary–Secondary Coupled Motion 1323 Upper Semiclassical Limit for Secondary Swain–Schaad Relationship 1324 Experimental Examples Using 2 Swain–Schaad Exponents 1325 Temperature Dependence of Primary KIEs 1326 Temperature Dependence of Reaction Rates and KIEs 1326 KIEs on Arrhenius Activation Factors 1327
Contents
12.3.4.3 12.4 12.4.1 12.4.2 12.5
Experimental Examples Using Isotope Effects on Arrhenius Activation Factors 1328 Theoretical Models for H-transfer and Dynamic Effects in Enzymes 1331 Phenomenological “Marcus-like Models” 1332 MM/QM Models and Simulations 1334 Concluding Comments 1334 Acknowledgments 1335 References 1335
13
Hydrogen Tunneling in Enzyme-catalyzed Hydrogen Transfer: Aspects from Flavoprotein Catalysed Reactions 1341 Jaswir Basran, Parvinder Hothi, Laura Masgrau, Michael J. Sutcliffe, and Nigel S. Scrutton
13.1 13.2
Introduction 1341 Stopped-flow Methods to Access the Half-reactions of Flavoenzymes 1343 Interpreting Temperature Dependence of Isotope Effects in Terms of H-Tunneling 1343 H-Tunneling in Morphinone Reductase and Pentaerythritol Tetranitrate Reductase 1347 Reductive Half-reaction in MR and PETN Reductase 1348 Oxidative Half-reaction in MR 1349 H-Tunneling in Flavoprotein Amine Dehydrogenases: Heterotetrameric Sarcosine Oxidase and Engineering Gated Motion in Trimethylamine Dehydrogenase 1350 Heterotetrameric Sarcosine Oxidase 1351 Trimethylamine Dehydrogenase 1351 Mechanism of Substrate Oxidation in Trimethylamine Dehydrogenase 1351 H-Tunneling in Trimethylamine Dehydrogenase 1353 Concluding Remarks 1356 Acknowledgments 1357 References 1357
13.3 13.4 13.4.1 13.4.2 13.5
13.5.1 13.5.2 13.5.2.1 13.5.2.2 13.6
14
Hydrogen Exchange Measurements in Proteins 1361 Thomas Lee, Carrie H. Croy, Katheryn A. Resing, and Natalie G. Ahn
14.1 14.1.1 14.1.2 14.1.3 14.2 14.2.1
Introduction 1361 Hydrogen Exchange in Unstructured Peptides 1361 Hydrogen Exchange in Native Proteins 1363 Hydrogen Exchange and Protein Motions 1364 Methods and Instrumentation 1365 Hydrogen Exchange Measured by Nuclear Magnetic Resonance (NMR) Spectroscopy 1365
XXXI
XXXII
Contents
14.2.2 14.2.3 14.3 14.3.1 14.3.2 14.3.3 14.3.4 14.3.5 14.3.6 14.4
Hydrogen Exchange Measured by Mass Spectrometry 1367 Hydrogen Exchange Measured by Fourier-transform Infrared (FT-IR) Spectroscopy 1369 Applications of Hydrogen Exchange to Study Protein Conformations and Dynamics 1371 Protein Folding 1371 Protein–Protein, Protein–DNA Interactions 1374 Macromolecular Complexes 1378 Protein–Ligand Interactions 1379 Allostery 1381 Protein Dynamics 1382 Future Developments 1386 References 1387
15
Spectroscopic Probes of Hydride Transfer Activation by Enzymes Robert Callender and Hua Deng
15.1 15.2 15.2.1 15.2.1.1
Introduction 1393 Substrate Activation for Hydride Transfer 1395 Substrate C–O Bond Activation 1395 Hydrogen Bond Formation with the C–O Bond of Pyruvate in LDH 1395 Hydrogen Bond Formation with the C–O Bond of Substrate in LADH 1397 Substrate C–N Bond Activation 1398 N5 Protonation of 7,8-Dihydrofolate in DHFR 1398 NAD(P) Cofactor Activation for Hydride Transfer by Enzymes 1401 Ring Puckering of Reduced Nicotinamide and Hydride Transfer 1401 Effects of the Carboxylamide Orientation on the Hydride Transfer 1403 Spectroscopic Signatures of “Entropic Activation” of Hydride Transfer 1404 Activation of CH bonds in NAD(P)+ or NAD(P)H 1405 Dynamics of Protein Catalysis and Hydride Transfer Activation 1406 The Approach to the Michaelis Complex: the Binding of Ligands 1407 Dynamics of Enzymic Bound Substrate–Product Interconversion 1410 Acknowledgments 1412 Abbreviations 1412 References 1412
15.2.1.2 15.2.2 15.2.2.1 15.3 15.3.1 15.3.2 15.3.3 15.3.4 15.4 15.4.1 15.4.2
1393
Contents
Part IV
Hydrogen Transfer in the Action of Specific Enzyme Systems 1417
16
Hydrogen Transfer in the Action of Thiamin Diphosphate Enzymes Gerhard Hbner, Ralph Golbik, and Kai Tittmann
16.1 16.2
Introduction 1419 The Mechanism of the C2-H Deprotonation of Thiamin Diphosphate in Enzymes 1421 Deprotonation Rate of the C2-H of Thiamin Diphosphate in Pyruvate Decarboxylase 1422 Deprotonation Rate of the C2-H of Thiamin Diphosphate in Transketolase from Saccharomyces cerevisiae 1424 Deprotonation Rate of the C2-H of Thiamin Diphosphate in the Pyruvate Dehydrogenase Multienzyme Complex from Escherichia coli 1425 Deprotonation Rate of the C2-H of Thiamin Diphosphate in the Phosphate-dependent Pyruvate Oxidase from Lactobacillus plantarum 1425 Suggested Mechanism of the C2-H Deprotonation of Thiamin Diphosphate in Enzymes 1427 Proton Transfer Reactions during Enzymic Thiamin Diphosphate Catalysis 1428 Hydride Transfer in Thiamin Diphosphate-dependent Enzymes 1432 References 1436
16.2.1 16.2.2 16.2.3
16.2.4
16.2.5 16.3 16.4
17
Dihydrofolate Reductase: Hydrogen Tunneling and Protein Motion Stephen J. Benkovic and Sharon Hammes-Schiffer
17.1 17.1.1 17.1.2 17.2 17.2.1 17.2.2 17.3 17.4
Reaction Chemistry and Catalysis 1439 Hydrogen Tunneling 1441 Kinetic Analysis 1443 Structural Features of DHFR 1443 The Active Site of DHFR 1444 Role of Interloop Interactions in DHFR Catalysis 1446 Enzyme Motion in DHFR Catalysis 1447 Conclusions 1452 References 1452
18
Proton Transfer During Catalysis by Hydrolases Ross L. Stein
18.1 18.1.1 18.1.2 18.1.2.1
Introduction 1455 Classification of Hydrolases 1455 Mechanistic Strategies in Hydrolase Chemistry 1456 Heavy Atom Rearrangement and Kinetic Mechanism 1457
1455
1419
1439
XXXIII
XXXIV
Contents
18.1.2.2 18.1.3 18.2 18.2.1 18.2.2 18.2.2.1 18.2.2.2 18.3 18.3.1 18.3.2 18.3.2.1 18.3.2.2 18.4 18.4.1 18.4.2
Proton Bridging and the Stabilization of Chemical Transition States 1458 Focus and Organization of Chapter 1458 Proton Abstraction – Activation of Water or Amino Acid Nucleophiles 1459 Activation of Nucleophile – First Step of Double Displacement Mechanisms 1459 Activation of Active-site Water 1462 Double-displacement Mechanisms – Second Step 1462 Single Displacement Mechanisms 1464 Proton Donation – Stabilization of Intermediates or Leaving Groups 1466 Proton Donation to Stabilize Formation of Intermediates 1466 Proton Donation to Facilitate Leaving Group Departure 1467 Double-displacement Mechanisms 1467 Single-displacement Mechanisms 1468 Proton Transfer in Physical Steps of Hydrolase-catalyzed Reactions 1468 Product Release 1468 Protein Conformational Changes 1469 References 1469
19
Hydrogen Atom Transfers in B12 Enzymes 1473 Ruma Banerjee, Donald G. Truhlar, Agnieszka Dybala-Defratyka, and Piotr Paneth
19.1 19.2 19.3 19.4
Introduction to B12 Enzymes 1473 Overall Reaction Mechanisms of Isomerases 1475 Isotope Effects in B12 Enzymes 1478 Theoretical Approaches to Mechanisms of H-transfer in B12 Enzymes 1480 Free Energy Profile for Cobalt–Carbon Bond Cleavage and H-atom Transfer Steps 1487 Model Reactions 1488 Summary 1489 Acknowledgments 1489 References 1489
19.5 19.6 19.7
Part V
Proton Conduction in Biology
20
Proton Transfer at the Protein/Water Interface Menachem Gutman and Esther Nachliel
20.1 20.2 20.2.1
Introduction 1499 The Membrane/Protein Surface as a Special Environment 1501 The Effect of Dielectric Boundary 1501
1497 1499
Contents
20.2.2 20.2.2.1 20.2.2.2 20.3 20.4 20.5 20.5.1 20.5.1.1 20.5.1.2 20.5.2 20.6 20.7 20.8
The Ordering of the Water by the Surface 1501 The Effect of Water on the Rate of Proton Dissociation 1502 The Effect of Water Immobilization on the Diffusion of a Proton 1503 The Electrostatic Potential Near the Surface 1504 The Effect of the Geometry on the Bulk-surface Proton Transfer Reaction 1505 Direct Measurements of Proton Transfer at an Interface 1509 A Model System: Proton Transfer Between Adjacent Sites on Fluorescein 1509 The Rate Constants of Proton Transfer Between Nearby Sites 1509 Proton Transfer Inside the Coulomb Cage 1511 Direct Measurements of Proton Transfer Between Bulk and Surface Groups 1514 Proton Transfer at the Surface of a Protein 1517 The Dynamics of Ions at an Interface 1518 Concluding Remarks 1522 Acknowledgments 1522 References 1522 Index
1527
XXXV
XXXVII
Preface
As one of the simplest of chemical reactions, pervasive on this highly aqueous planet populated by highly aqueous organisms, yet still imperfectly understood, the transfer of hydrogen as a subject of scientific attention seems hardly to require defense. This claim is supported by the readiness with which the editors of this series of four volumes on Hydrogen-transfer Reactions accepted the suggestion that they organize a group of their most active and talented colleagues to survey the subject from viewpoints beginning in physics and extending into biology. Furthermore, forty-nine authors and groups of authors acceded, with alacrity and grace, to the request to contribute and have then supplied the articles that make up these volumes. Our scheme of organization involved an initial division into physical and chemical aspects on the one hand, and biological aspects on the other hand (and one might well have said biochemical and biological aspects). In current science, such a division may provide an element of convenience but no-one would seriously claim the segregation to be either easy or entirely meaningful. We have accordingly felt quite entitled to place a number of articles rather arbitrarily in one or the other category. It is nevertheless our hope that readers may find the division adequate to help in the use of the volumes. It will be apparent that the division of space between the two categories is unequal, the physical and chemical aspects occupying considerably more pages than the biological aspects, but our judgment is that this distribution of space is proper to the subjects treated. For example, many of the treatments of fundamental principles and broadly applicable techniques were classified under physical and chemical aspects. But they have powerful implications for the understanding and use of the matters treated under biological aspects. Within each of these two broad disciplinary categories, we have organized the subject by beginning with the simple and proceeding toward the complex. Thus the physical and chemical aspects appear as two volumes, volume1 on simple systems and volume 2 on complex systems. Similarly, the biological aspects appear as volume 3 on simple systems and volume 4 on complex systems. Volume 1 then begins with isolated molecules, complexes, and clusters, then treats condensed-phase molecules, complexes, and crystals, and finally reaches Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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treatments of molecules in polar environments and in electronic excited states. Volume 2 reaches higher levels of complexity in protic systems with bimolecular reactions in solution, coupling of proton transfer to low-frequency motions and proton-coupled electron transfer, then organic and organometallic reactions, and hydrogen-transfer reactions in solids and on surfaces. Thereafter articles on quantum tunneling and appropriate theories of hydrogen transfer complete the treatment of physical and chemical aspects. Volume 3 begins with simple model (i.e., non-enzymic) reactions for protontransfer, both to and from carbon and among electronegative atoms, hydrogenatom transfer, and hydride transfer, as well as the extension to small, synthetic peptides. It is completed by treatments of how enzymes activate C-H bonds, multiple hydrogen transfer reactions in enzymes, and theoretical models. Volume 4 moves then into enzymic reactions and a thorough consideration of quantum tunneling and protein dynamics, one of the most vigorous areas of study in biological hydrogen transfer, then considers several specific enzyme systems of high interest, and is completed by the treatment of proton conduction in biological systems. While we do not claim any sort of comprehensive coverage of this large subject, we believe the reader will find a representative treatment, written by accomplished and respected experts, of most of the matters currently considered important for an understanding of hydrogen-transfer reactions. I am enormously grateful to James T. (Casey) Hynes and Hans-Heinrich Limbach, who saw to the high quality of the volumes on the physical and chemical aspects, and to Judith Klinman, who gave me a nearly free pass as her co-editor of the volumes on biological aspects. We are all grateful indeed to the authors who contributed their wisdom and eloquence to these volumes. It has been a very great pleasure to be assisted, encouraged, and supported at every turn by the outstanding staff of VCH-Wiley in Weinheim, particularly (in alphabetical order) Ms. Nele Denzau, Dr. Renate Dtzer, Dr. Tim Kersebohm, Dr. Elke Maase, Ms. Claudia Zschernitz, and – of course – Dr. Peter Glitz. Lawrence, Kansas, USA, September 2006
Richard L. Schowen
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Preface to Volumes 1 and 2
These volumes together address the subject of the physical and chemical aspects of hydrogen transfer, volume 1 focusing on comparatively simple systems and volume 2 treating relatively more complex ones. Volume 1 comprises three parts, commencing with Part I, dealing with hydrogen transfers of polyatomic molecules and complexes in relatively isolated conditions. In the first three contributions, the transfer is a coherent tunneling process rather than a rate process, characterized by “tunnel splittings” or delocalized hydrogen nuclei, for which electronic and vibrational spectroscopies are common and potent tools. The molecular systems discussed are malonaldehyde and tropolone (Redington, Ch. 1), carboxylic acid dimers (Havenith, Ch. 2) and strongly hydrogen-bonded systems such as (H2O...H...OH2)+ (Asmis, Neumark and Bauman, Ch. 3). Khn and Gonzales (Ch. 4) consider theoretically the more active role of infrared radiation in controlling hydrogen dissociation dynamics in e.g. OHF–. The five contributions of Part II focus on condensed matter. If the barriers are large, the hydrogen transfer becomes a rate process which may involve incoherent tunneling. Ceulemans (Ch. 5) examines proton abstraction by alkanes from strongly acidic alkane radical cations in inert matrices. Limbach (Ch. 5) follows the kinetics of single and multiple hydrogen and deuteron transfers in liquids and solids via NMR. Optical methods are applied by Douhal (Ch. 6) to systems embedded in a nanocavity, and embedded in liquids and polymer matrices by Waluk (Ch. 7), with a contrast to coherent hydrogen transfer in supersonic jets. Finally, Vener (Ch. 9) compares theory and experiment for anharmonic vibrations of strong hydrogen bonds in crystals. Part III, comprising four chapters, commences the examination of hydrogen transfer – here proton transfer – in polar environments. The strong electrostatic proton-environment interaction guarantees incoherent rate phenomena. Kiefer and Hynes (Ch. 10) lay out the theoretical description for such reactions. The next three chapters exploit the greatly enhanced acidity of aromatic acids in the excited electronic state. Lochbrunner, Schriever and Riedle (Ch. 11) focus on the role of the motion of the groups between which the proton transfers, Pines and Pines (Ch. 12) thoroughly examine the insight to be gained from Frster cycle and free Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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energy analyses, while Tolbert and Solnstev (Ch. 13) pursue related themes for “super” photoacids in the concluding chapter of volume 1. Volume 2 opens with Part IV dealing with hydrogen transfer in protic systems. Generally, a larger number of solvent molecules is involved, and hence multiple protons may be transferred. The first two chapters elucidate molecular details of proton transfer in solution via ultrafast infrared spectroscopy. Nibbering and Pines (Ch. 14) examine the transfer between acid-base pairs for the acid in the excited electronic state, while Elsaesser (Ch. 15) discusses coherent low frequency motions coupled to related proton transfers as well as in hydrogen-bonded complexes. The final two chapters in Part IV deal with proton transfer coupled to electron transfer, with Hammes-Schiffer (Ch. 16) expounding and illustrating the theory for these, while Hodgkiss, Rosenthal and Nocera (Ch. 17) discuss these reactions with a special emphasis on the connection to hydrogen atom transfer. Part V, consisting of four chapters, opens with a discussion of the kinetics and mechanisms of proton abstraction from carbon in organic systems by Koch (Ch. 18) and then turns to a presentation by Williams (Ch. 19) on free energy relationships for proton transfer, as informed by various theoretical approaches. The final two chapters are devoted to hydrogen and dihydrogen mobility in the coordination sphere of transition metal complexes, where the transition from coherent to incoherent H-tunneling can be observed, with a review of the field given by Kubas in Ch. 20 and a discussion of insights from NMR studies presented by Buntkowsky and Limbach in Ch. 21. In the first three of the five chapters of Part VI, hydrogen transfer is examined in assorted complex solids of importance in various applications: zeolites by Sauer in Ch. 22, fuel cells by Kreuer in Ch. 23 and ice bilayers by Aoki in Ch. 24. Attention is then turned to hydrogen transfer at metal surfaces in Ch. 25 by Christmann and in metals in Ch. 26 by Hempelmann and Skripov. Volume 2 concludes in Part VII with contributions on the variational transition state theory approach to hydrogen transfer in various contexts (Truhlar and Garrett, Ch. 27), on experimental evidence of hydrogen atom tunneling in simple systems (Ingold, Ch. 28), and finally on a theoretical perspective for multiple hydrogen transfers (Smedarchina, Siebrand and Fernndez-Ramos, Ch. 29). JTH acknowledges the support of grant CHE-0417570 from the US National Science Foundation. HHL thanks the Deutsche Forschungsgemeinschaft, Bonn, and the Fonds der Chemischen Industrie, Frankfurt, for financial support. Boulder and Paris, September 2006 Berlin, September 2006
James T. Hynes Hans-Heinrich Limbach
XXXIX
Preface to Volumes 3 and 4
These volumes together address the rather enormous subject of hydrogen transfer in biological systems, volume 3 presenting the role of relatively simple systems in the understanding of hydrogen transfer while volume 4 considers complex systems, for the most part enzymes. Volume 3 contains two parts that treat basic concepts and systems not limited to a single enzyme or class of enzymes in their significance. Part I consists of five chapters on the chemistry of the transfer of hydrogen in biological model systems: as a proton to and from carbon (Amyes and Richard, Ch. 1); as a proton in acidbase catalysis; i.e., largely among electronegative atoms (Kirby, Ch. 2); as a hydrogen atom (Schneich, Ch. 3); as a hydride ion (Schowen, Ch..4); as a proton in acid-base catalysis in designed peptides (Baltzer, Ch. 5). Part II is composed of three chapters on generally significant features of biological hydrogen-transfer reactions: in enzyme-catalyzed proton transfer from carbon (Gerlt, Ch. 6); in multiple proton transfers in enzymic systems (Spies and Toney, Ch. 7); and in computer simulations of enzymic hydrogen transfer (Braun-Sand, Olsson, Mavri, and Warshel, Ch. 8). Volume 4, consisting of three parts, then proceeds to studies in enzyme and protein systems that for the most part serve well as paradigms for broader groups in which hydrogen transfer is important. Part III brings together seven chapters on the subject of quantum tunneling in enzymic hydrogen-transfer and its relationship to protein motions. A relative new theoretical approach is described by Schwartz (Ch. 9), leading into a general consideration of the existing evidence and its significance for the tunneling/dynamics nexus (Knapp, Meyer, and Klinman, Ch. 10), and articles by Huskey (Ch. 11) on the importance of multiple-isotope labeling for characterization of tunneling phenomena, by Kohen on kinetic isotope effects (Ch.12) and by Basran, Hothi, Masgrau, Sutcliffe, and Scrutton on the opportunities afforded by flavoprotein systems (Ch. 13). This part is closed by articles on two important experimental approaches, isotope exchange with solvent as a probe of protein motion (Lee, Croy, Resing, and Ahn, Ch. 14) and resonance Raman spectroscopy as a probe of active-site dynamical properties (Callender and Deng, Ch. 15). Part IV brings into focus several central examples of important enzyme classes: thiamin-dependent enzymes (Ch. 16 by Hbner, Golbik, and Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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Tittmann), dihydrofolate reductase (Ch. 17 by Benkovic and Hammes-Schiffer), hydrolases (Ch. 18 by Stein), and vitamin B12 enzymes (Ch. 19 by Banerjee, Truhlar, Dybala-Defratyka, and Paneth). The volume is the closed by a onechapter Part V on proton conduction in biology, in which Gutman and Nachliel (Ch. 20) treat the subject of proton conductance at protein surfaces and interfacial regions. JPK acknowledges the support of grant MCB 0446395 from the US National Science Foundation and of grant GM 025765 from the US National Institutes of Health. Berkeley, California, USA, September 2006 Lawrence, Kansas, USA, September 2006
Judith P. Klinman Richard L. Schowen
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List of Contributors to Volumes 1 and 2 Katsutoshi Aoki Synchroton Radiation Research Center Kansai Research Establishment Japan Atomic Energy Research Institute Kouto 1-1-1 Mikazuki-cho Sayo-gun Hyogo Japan Knut R. Asmis Department of Molecular Physics Fritz-Haber-Institut der Max-PlanckGesellschaft Faradayweg 4–6 14195 Berlin Germany Joel M. Bowman Department of Chemistry and Cherry L. Emerson Center for Scientific Computation Emory University Dickey Drive Atlanta, GA 30322 USA
Gerd Buntkowsky Department of Chemistry FSU Jena Helmholtzweg 4 07743 Jena Germany Jan Ceulemans Department of Chemistry K.U. Leuven Celestijnenlaan 200-F 3001 Leuven Belgium Klaus Christmann Institut fr Chemie und Biochemie Physikalische und Theoretische Chemie Freie Universitt Berlin Takustrasse 3 14195 Berlin Germany Abderrazzak Douhal Departamento de Qu mica F sca Secci n de Qu micas Facultad de Ciencias del Medio Ambiente Universidad de Castillo-La Mancha Avda. Carlos III S.N. 45071 Toledo Spain
Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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List of Contributors to Volumes 1 and 2
Thomas Elsaesser Max-Born-Institut fr Nichtlineare Optik und Kurzzeitspektroskopie Max-Born-Strasse 2A 12489 Berlin Germany Antonio Fernndez-Ramos Department of Physical Chemistry Faculty of Chemistry University of Santiago de Compostela 15706 Santiago de Compostela Spain Bruce C. Garrett Chemical Sciences Division Pacific Northwest National Laboratory Richland, WA 99352 USA Leticia Gonzlez Institut fr Chemie und Biochemie Freie Universitt Berlin Takustrasse 3 14195 Berlin Germany Sharon Hammes-Schiffer Department of Chemistry 104 Chemistry Building Pennsylvania State University University Park, PA 16802-4615 USA Rolf Hempelmann Institute of Physical Chemistry Saarland University 66123 Saarbrcken Germany
Justin Hodgkiss Department of Chemistry Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 02139-4307 USA James T. Hynes Department of Chemistry and Biochemistry Pacific Northwest National Laboratory University of Colorado Boulder, CO 80309-0215 USA and Ecole Normale Suprieure CNRS UMR 8640 PASTEUR Dpartement de Chimie 24, rue Lhomond 75231 Paris France Keith U. Ingold National Research Council Ottawa, ON K1A 0R6 Canada Philip M. Kiefer Department of Chemistry and Biochemistry University of Colorado Boulder, CO 80309-0215 USA and Ecole Normale Suprieure CNRS UMR 8640 PASTEUR Dpartement de Chimie 24, rue Lhomond 75231 Paris France
List of Contributors to Volumes 1 and 2
Heinz F. Koch Department of Chemistry Ithaca College Ithaca, NY 14850 USA
Daniel M. Neumark Department of Chemistry University of California Berkeley, CA 94702 USA
Klaus-Dieter Kreuer Max-Planck-Institut fr Festkrperforschung Heisenbergstrasse 1 70569 Stuttgart Germany
Erik T. J. Nibbering Max-Born-Institut fr nichtlineare Optik und Kurzzeitspektroskopie Max-Born-Strasse 2A 12489 Berlin Germany
Gregory J. Kubas Los Alamos National Laboratory Chemistry Division MS J514 Los Alamos, NM 87545 USA
Daniel G. Nocera Department of Chemistry Massachusetts Institute of Technology 77 Massachusetts Cambridge, MA 02139-4307 USA
Oliver Khn Institut fr Chemie und Biochemie Freie Universitt Berlin Takustrasse 3 14195 Berlin Germany
Dina Pines Department of Chemistry Ben-Gurion University of the Negev P.O.B. 653 Beer Sheva 84105 Israel
Hans-Heinrich Limbach Institut fr Chemie und Biochemie Freie Universitt Berlin Takustrasse 3 14195 Berlin Germany
Ehud Pines Department of Chemistry Ben-Gurion University of the Negev P.O.B. 653 Beer Sheva 84105 Israel
Stefan Lochbrunner Department of Physics Ludwig Maximillians University Oettingenstrasse 67 80538 Mnchen Germany
Richard L. Redington Department of Chemistry and Biochemistry Texas Tech University Mail Stop 1061 Lubbock, TX 79409 USA
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Eberhard Riedle Department of Physics Ludwig Maximilians University Oettingenstrasse 67 80538 Mnchen Germany Joel Rosenthal Department of Chemistry Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 02139-4307 USA Joachim Sauer Institut fr Chemie Humboldt-Universitt zu Berlin Unter den Linden 6 10099 Berlin Germany C. Schriever Department of Physics Ludwig Maximilians University Oettingenstrasse 67 80538 Mnchen Germany
Zorka Smedarchina Steacie Institute for Molecular Sciences National Research Council of Canada Ottawa, K1A 0R6 Canada Kyril M. Solntsev School of Chemistry and Biochemistry Georgia Institute of Technology Atlanta, GA 30332-0400 USA Laren M. Tolbert School of Chemistry and Biochemistry Georgia Institute of Technology Atlanta, GA 30332-0400 USA Donald G. Truhlar Department of Chemistry University of Minnesota Minneapolis, MN 55455-0431 USA
Mikhail V. Vener Department of Quantum Chemistry Mendeleev University of Chemical Technology Willem Siebrand Miusskaya Sq. 9 Steacie Institute for Molecular Sciences Moscow 125047 National Research Council of Canada Russia Vorontsova pole 10 Ottawa, K1A 0R6 Jacek Waluk Canada Institute of Physical Chemistry Polish Academy of Sciences Alexander Skripov Kasprzaka 44/52 Institute of Metal Physics 01-224 Warsaw Urals Branch of the Academy of Poland Sciences Ekaterinburg 620219 Ian H. Williams Russia Department of Chemistry University of Bath Bath BA2 7AY UK
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List of Contributors to Volumes 3 and 4 Natalie G. Ahn Department of Chemistry and Biochemistry Howard Hughes Medical Institute University of Colorado Boulder, CO 80309-0215 USA Tina L. Amyes Department of Chemistry University at Buffalo SUNY Buffalo, NY 14260-3000 USA Lars Baltzer Department of Chemistry Uppsala University Box 599 75124 Uppsala Sweden
Stephen J. Benkovic Department of Chemistry 104 Chemistry Building, Pennsylvania State University University Park, PA 16802 USA Sonja Braun-Sand University of Southern California Department of Chemistry 3620 McClintock Avenue, SGM 418 Los Angeles, CA 90089-1062 USA Robert Callender Department of Biochemistry Albert Einstein College of Medicine 1300 Morris Park Avenue Bronx, NY 10461 USA
Ruma Banerjee Biochemistry Department University of Nebraska Lincoln, NE 68588-0664 USA
Carrie H. Croy Department of Chemistry and Biochemistry Howard Hughes Medical Institute University of Colorado Boulder, CO 80309-0215 USA
Jaswir Basran Department of Biochemistry University of Leicester University Road Leicester LE1 7RH UK
Hua Deng Department of Biochemistry Albert Einstein College of Medicine 1300 Morris Park Avenue Bronx, NY 10461 USA
Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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Agnieszka Dybala-Defratyka Faculty of Chemistry Technical University of Lodz 90-924 Lodz Poland John A. Gerlt University of Illinois, Urbana-Champaign Departments of Biochemistry and Chemistry 600 South Mathews Avenue Urbana, IL 61801 USA Ralph Golbik Institute of Biochemistry Martin Luther University Halle-Wittenberg Kurt-Mothes-Strasse 3 06120 Halle/Saale Germany Menachem Gutman Laser Laboratory for Fast Reactions in Biology Department of Biochemistry George S. Wise Faculty of Life Sciences Tel Aviv University Tel Aviv 69978 Israel Sharon Hammes-Schiffer Department of Chemistry 104 Chemistry Building Pennsylvania State University University Park, PA 16802 USA Parvinder Hothi Faculty of Life Sciences and Manchester Interdisciplinary Biocentre University of Manchester 131 Princess Street Manchester M1 7ND UK
¨bner Gerhard Hu Institute of Biochemistry Martin Luther University Halle-Wittenberg Kurt-Mothes-Strasse 3 06120 Halle/Saale Germany W. Phillip Huskey Department of Chemistry Rutgers University – Newark 73 Warren Street Newark, NJ 07102 USA Anthony J. Kirby University Chemical Laboratory Cambridge CB2 1EW UK Judith P. Klinman Departments of Chemistry and Molecular and Cell Biology University of California Berkeley, CA 94720-1460 USA Michael J. Knapp Department of Chemistry 710 N. Pleasant Street University of Massachusetts Amherst, MA 01003-9336 USA Amnon Kohen Department of Chemistry University of Iowa Iowa City, IA 52242 USA Thomas Lee Department of Chemistry and Biochemistry Howard Hughes Medical Institute University of Colorado Boulder, CO 80309-0215 USA
List of Contributors to Volumes 3 and 4
Laura Masgrau School of Chemical Engineering and Analytical Science Manchester Interdisciplinary Biocentre University of Manchester 131 Princess Street Manchester M1 7ND UK Janez Mavri National Institute of Chemistry P.O.B. 660 Hajarihova 19 SI-1001 Ljubljana Slovenia Matthew Meyer Merced School of Natural Sciences University of California P.O. Box 2039 Merced, CA 95344 USA Esther Nachliel Laser Laboratory for Fast Reactions in Biology Department of Biochemistry George S. Wise Faculty of Life Sciences Tel Aviv University Tel Aviv 69978 Israel Mats H. M. Olsson University of Southern California Department of Chemistry 3620 McClintock Avenue, SGM 418 Los Angeles, CA 90089-1062 USA Piotr Paneth Faculty of Chemistry Technical University of Lodz 90-924 Lodz Poland
Katheryn A. Resing Department of Chemistry and Biochemistry Howard Hughes Medical Institute University of Colorado Boulder, CO 80309-0215 USA John P. Richard Department of Chemistry University at Buffalo SUNY Buffalo, NY 14260-3000 USA Christian Scho¨neich Department of Pharmaceutical Chemistry University of Kansas 2095 Constant Avenue Lawrence, KS 66047 USA Richard L. Schowen Departments of Chemistry, Molecular Biosciences, and Pharmaceutical Chemistry University of Kansas Lawrence, KS 66047 USA Steven D. Schwartz Departments of Biophysics and Biochemistry Seaver Center for Bioinformatics Albert Einstein College of Medicine Bronx, New York USA Nigel S. Scrutton Faculty of Life Sciences and Manchester Interdisciplinary Biocentre University of Manchester 131 Princess Street Manchester M1 7ND UK
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Michael Ashley Spies Department of Biochemistry University of Illinois 600 South Mathews Avenue Urbana, IL 61801 USA Ross L. Stein Laboratory for Drug Discovery in Neurodegeneration Harvard Center for Neurodegeneration and Repair Department of Neurology Harvard Medical School 65 Landsdowne Street, Fourth Floor Cambridge, MA 02129 USA Michael J. Sutcliffe School of Chemical Engineering and Analytical Science Manchester Interdisciplinary Biocentre University of Manchester 131 Princess Street Manchester M1 7ND UK
Kai Tittmann Martin Luther University Halle-Wittenberg Institute of Biochemistry Kurt-Mothes-Strasse 3 06120 Halle/Saale Germany Michael D. Toney Department of Chemistry University of California, Davis 1-Shields Avenue Davis, CA 96616 USA Donald G. Truhlar Chemistry Department University of Minnesota Minneapolis, MN 55455-0431 USA Arieh Warshel University of Southern California Department of Chemistry 3620 McClintock Avenue, SGM 418 Los Angeles, CA 90089-1062 USA
1
I
Physical and Chemical Aspects
Part I Hydrogen Transfer in Isolated Hydrogen Bonded Molecules, Complexes and Clusters
This first part is devoted to hydrogen transfers in small isolated molecular systems in the gas phase and jet streams. Coherent proton tunneling in malonaldehyde and tropolone in the electronic ground- and excited states is reviewed in Ch. 1 by Redington. These splittings, first observed by E. B. Wilson for malonaldehyde, depend on the vibrational and the electronic state. Often, only the difference of tunnel splittings between the initial and final spectrocopic state can be observed. In the case of formic acid dimers, however, the ground state splittings could be observed (Ch. 2 by Havenith). The challenge for the theoretical chemist is to reproduce experimental tunnel splittings from first principles. For this purpose, not only the Schrdinger equation for electrons but also for the nuclei has to be solved. Various theories are reviewed, e.g. the theory of Benderskii and of Wjcik which take multidimensional tunneling into account. Malonaldehyde and tropolone exhibit hydrogen bonds of medium strength, releatively large barriers and OH-stretching frequencies and small tunnel splittings of the order of a few wave numbers or smaller. The results of novel gas phase vibrational spectroscopic experiments of strong hydrogen bonded systems such as bihalide anions, (H2O··H··OH2)+ and (HO··H··OH) – etc. are reviewed by Asmis, Neumark, Bauman (Ch.3). These ions exhibit either low-barrier hydrogen bonds where tunnel splittings become larger than the barrier heights or nobarrier hydrogen bonds. The goal is to describe the proton motion by calculation of the strongly anharmonic vibrations from first principles. This task is a prerequisite before the well-known IR continua observed by Zundel in condensed matter will be really understood. In Ch. 4, Khn and Gonzlez deals with the theory of ultrafast hydrogen transfer dynamics driven by tailored IR laser pulses. For small systems such as OHFpulse schemes can be devised, which either lead to a breaking of the OH or of the HF bond. For multidimensional hydrogen bond dynamics in medium sized moleHydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
2
cules anharmonic coupling and intramolecular vibrational energy redistribution constitute a serious challenge to any control attempt. The situation may be improved in alternative control schemes involving a properly timed UV excitation.
3
1 Coherent Proton Tunneling in Hydrogen Bonds of Isolated Molecules: Malonaldehyde and Tropolone Richard L. Redington
1.1 Introduction
A series of articles reporting temperature dependent H and D isotope effects on the rates of certain enzymatic H transfer reactions show there is quantum tunneling by the H in these systems [1–7]. Theoretical considerations [4, 6, 7] infer vibrations within the enzyme–substrate complex, especially within the enzyme protein, develop transient geometrical configurations fomenting the tunneling process. Details of the promoting vibrations are still speculative, but it seems clear they work through transient reshaping of the potential energy surface (PES) barrier region, its width, energy maximum, overall contour, to provide “gated” impetus to H tunneling and to product escape. Molecules hosting coherent H tunneling activity in the presence of complex vibrational structure are of immediate interest in the above context. They provide sharp data points probing specific vibrational couplings along the large amplitude tunneling coordinate, and they probe portions of the PES topography in detail. Studies on isotopomers and close chemical congeners provide clusters of data points reflecting systematic changes of the dynamical behavior. In this chapter research on the coherent tunneling properties of malonaldehyde, tropolone, and tropolone derivatives is surveyed. These are among the few currently known 10– 15 atom molecules showing clear-cut spectral doublet structures signifying coherent tunneling properties. Interestingly, the equal double-minimum global PESs for these molecules, notably for S0 tropolone, are also poised for demonstrations of tunneling activity by the heavy atoms. The presence of H tunneling in some enzymatic systems is newly recognized; tunneling processes by heavy atoms such as C, N, and O may also prove consequential. Zuev et al. [8] recently published low temperature rate data and theoretical-computational results showing the tunneling of C atom from a single quantum state during the ring expansion isomerization of 1-methycyclobutylfluorocarbene.
Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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1 Coherent Proton Tunneling in Hydrogen Bonds
As illustrated in Fig. 1.1, the tautomerizations of tropolone (TRN, C7H6O2) and malonaldehyde (MA, C3H4O2) involve an O_HO fi OH_O transfer accompanied by shifts of the skeletal atom positions as the bond characters interchange. Spectroscopic experiments performed on low pressure gaseous samples of TRN and MA experience minimal disruptive interactions with the environment, and spectral doublet structures observed for both molecules unequivocally reveal coherent quantum tunneling. MA has 21 and TRN has 39 internal coordinates available for coupling into their tunneling processes. MA, with a developing experimental base [9–21], holds a computational edge over TRN which currently stands alone in its size group for its catalog of spectroscopic tunneling structures [22–39]. With 15 atoms TRN is reasonably expected to model elements of the intramolecular dynamical behavior occurring in much larger molecules, and it is amenable to high level experimental and theoretical studies. The topography of its PES has saddle-point (SP) energy barriers just low enough, and tautomer-to-tautomer heavy atom excursions that are just short enough, to produce numerous resolvable vibrational state-specific coherent tunneling splittings. They are also observed in the 2H [40, 41] and 18O [39, 42, 43] isotopomers of gaseous TRN, and in simple chemical derivatives [44–57]. The numerous van der Waals complexes of tropolone are not discussed in this chapter. The rotation–contortion–vibration electronic states of the nonrigid TRN and MA molecules are classified according to the G4 molecular symmetry group using the permutation-inversion operations E, P, i, and P* [58]. The G4 group is iso-
A
O
H
O
O
H
H
H
H
00+
S1
∆
S1 0
B H7
H H
H H
000
O
1 1
H
O
H O H
H
H9 H8
O
H
H O H6
H
-
0 0+
S0
∆S00
Figure 1.1 Symbolic representation of equal double-well potential energy functions for (A) tropolone and (B) malonaldehyde in the S0 ground and lowest S1 singlet electronic states. The spectral doublet of the S1–S0 zero-point transitions is shown. The doublet separation is (H11 – 000) = |D0S1 – D0S0 |.
H
1.2 Coherent Tunneling Splitting Phenomena in Malonaldehyde
morphic to the C2v point group and the energy states are conventionally labeled using the a1, a2, b1, and b2 irreducible representations of C2v. The spectra observed for tropolone are complicated by many overlaps of the tunneling doubled fundamental, overtone, combination, and hot band vibrational transitions – the latter abundant at 25 C. Many of the vibrational states are coupled by anharmonic resonance interactions affecting transition intensities more strongly than frequencies, and perturbing tunneling doublets [39]. The Schrdinger equation for a particle moving in a symmetrical one-dimensional (1D) double-well potential energy function (PEF) is readily solved for the lower energy levels and wavefunctions. The time-dependent wavefunctions produce probability density functions which coherently oscillate at a constant frequency between the two wells. In one’s dreams multidimensional coordinate spaces of real molecules separate into simple 1D equations, and discovering the most effective real life coordinate separations and the most pertinent regions of the PES topography for complex molecules requires access to as much diverse and discriminating experimental information as possible. The status of research on coherent tunneling in the S0 and S1 electronic states of malonaldehyde and tropolone is discussed in Sections 1.2 and 1.3, respectively, with observations for several TRN derivatives sketched in Section 1.4, and a summary given in Section 1.5.
1.2 Coherent Tunneling Splitting Phenomena in Malonaldehyde
In 1976 Wilson’s group published the first of several [9–12] studies on the microwave spectroscopy of the C, H, and O isotopomers of MA. These established its internally H bonded geometry, equal double-minimum nature of the PES, and coherent quantum tunneling activity. Their conclusions concerning the value of the zero-point (ZP) tunneling splitting, D0, from precise observations of tunneling–rotation transitions were supported by their early far-infrared spectral measurements in the 20 cm–1 region. Subsequent precision studies in this wavelength region by Firth et al. [17] and by Baba et al. [14] showed D0 = 21.583 cm–1 for MA in its S0 ground electronic state. Baughcum et al. [10] reported D0[MA(OD)] = 2.915(4) cm–1 for the symmetrical MA(D6D7D9) isotopomer (see atom numbering in Fig. 1.1), and slightly smaller values for nine other MA(OD) isotopomers, six of them incorporating 13C or 18O atoms. ZP tunneling splitting values for MA in excited electronic states have proved elusive. Seliskar and Hoffman [20] reported vibronic spectral structure for the ~ 1B1 ‹ X ~ 1A1 (p*–n) [S1‹S0] absorption near 354 nm to have a spectral weak A doublet separation (DS) of 7 cm–1. Arias et al. [21] applied the absorbance-based degenerate four-wave mixing (DFWM) spectroscopic method to the S1 ‹ S0 transition. With higher intrinsic spectral resolution, and spectral clarification arising through the reduction of signal due to hot band transitions that is inherent in this nonlinear spectroscopic technique, they found DS = |D0S1 – D0S0 | ~ 19 cm–1, to place the ffi 1B1 zero-point tunneling splitting value at D0S1 ~ 2.5 cm–1. The 19 cm–1
5
1 Coherent Proton Tunneling in Hydrogen Bonds
DS value appears for the members of a 185 cm–1 vibronic progression, but details of the doublings for other vibrational states have not yet been reported. The strong quenching of D0S1 relative to D0S0 suggests the p*‹n promotion increases the energy maximum and/or width of the effective PEF barrier [21]. Infrared spectra of gaseous MA and its deuterium isotopomers were reported at medium resolution by Seliskar and Hoffman [16] and by Smith et al. [15] and an overview at 1 cm–1 resolution is provided by Duan and Luckhaus [19]. At these modest resolutions the observed transition profiles include isolated PQR rotational envelopes as well as Q branch regions with multiple peaks suggesting doublets and probable hot band structures. Figure 1.2 is taken from Smith et al. [15] and shows peaks resolved in the 200–300 cm–1 region. Peaks #20 and #26 were assigned as representing the m15 (nominal O_O stretch) and m21 (out-ofplane skeletal deformation) fundamentals, respectively [15, 59, 60], with no specific tunneling doublet or hot band assignments made. No evidence for the presence of resolved spectral tunneling doublets was reported by Firth et al. [17] for Ar-isolated MA or by Chiavassa et al. [18] in their IR studies of MA isotopomers isolated
TRANSMITTANCE (%)
6
18 29
19
22
27 28
30
23 24 21 20
25 26
DS15
DS21 280
250 cm-1
220
Figure 1.2 Infrared spectrum of MA(OH) in the 200–300 cm–1 region due to Smith et al. [15]. Spectral doublet separations DS21 and DS15 replace the single-peak assignments m15 = peak 20 and m21 = peak 26.
1.2 Coherent Tunneling Splitting Phenomena in Malonaldehyde
in Ar, Kr, and Xe matrices. Smith et al. [15] proposed a vibrational assignment for MA on the basis of their IR spectra for H and D isotopomers, comparative spectra for other substances, and a valence force field. Tayyari and Milani-Nejad [59] reassigned many fundamentals with the guidance of MP2/6-31G*//MP2/6-31G*(sp and p on H) computations performed on MA, MA(D6D8), and MA(D7D9). Alparone and Millefiori [60] affirmed the assignment through vibrational self-consistent field (VSCF) and correlation-corrected-VSCF computations introducing anharmonicities to estimate the fundamental isotopomer spectra. Duan and Luckhaus [19] made a major experimental advance by using a Pb-salt diode laser to measure rotational transitions for m6 in jet-cooled samples prepared by seeding MA into He carrier gas with expansion through a pulsed slit nozzle. The clarified spectrum allowed the origin for the m6+ ‹ m0+ (type A) tunneling doublet component to be evaluated as 1594.08983(26) cm–1. Further, the determination of 12 rotation and centrifugal distortion constants provides comparisons for corresponding ZP state constants determined by Baba et al. [14]. The analysis of weak IR transitions produced a selection of parameters for the m6–‹m0– tunneling doublet component, to yield the remarkably small DS = D6 – D0 = –0.03 cm–1 value for the m6 fundamental (mC=O + in-phase (iph) mC=C + dCOH [60]). Duan and Luckhaus suggested the tunneling enhancing effect of symmetrical C=C— C=O motion may be cancelled by the tunneling damping effect of concomitant COH angle widening, and they noted the challenge to theoretical treatments of the tunneling dynamics in MA provided by this accurate new experimental result. While Smith et al. [15] eschewed the assignment of tunneling doublets, Seliskar and Hoffman [16] noted the Q branch doublet separations implying DS20 = 6.3 cm–1 for m20 at 384 cm–1 (out-of-plane ring deformation) and DS14 = 5.8 cm–1 for m14 at 512 cm–1 (in-plane ring deformation). These DSV = |DV – D0| values suggest the upper state tunneling splittings D20 = 15.3 or 27.9 cm–1 and D14 = 15.8 or 27.4 cm–1. At 1 cm–1 resolution [19] there is a single sharp Q peak for m6, and a single sharp Q peak for m19 = 766 cm–1. Isolated PQR envelopes with sharp Q spikes [19] reasonably imply DV ~ D0 for m10 at 1260 cm–1, m8 at 1346 cm–1, and m7 at 1452 cm–1. To extract DV values from Fig. 1.2 the cluster of peaks to the blue of ~270 cm–1 (dotted line) is observed to be qualitatively similar to peaks shown for m20 in the 370–410 cm–1 region (Fig. 7 of Ref. [15]). Assigning peak #20 = 282.2 cm–1 and #21 = 279.3 cm–1 as the sharp Q spikes of type C absorption profiles for the doublet components of the out-of-plane – i.e. m21 instead of m15 – vibration yields DS21 = |D21 – D0| = 2.9 cm–1, D21 = 18.7 or 24.5 cm–1, and m21 = –1 12(282.2+279.3) = 280.8 cm–1. The value m 21 = 277.5 cm is computed from the CC-VSCF treatment of Alparone and Millefiori [60] and the calculated minus observed value difference of –1.2% is similar to the –1.6% value found for m20. The cluster of peaks in Fig. 1.2 to the red of ~270 cm–1 divide into similar groups with peaks #23 to #26, separated by 17.1 cm–1, and peaks #27 to #30, separated by 16.6 cm–1, spanning the high and low frequency groups, respectively. One of the two central peaks in each group is probably due to a type A Q spike of the Y polarized transition dipole, and the other probably to a hot band Q spike. The outer peaks are attributed to apparent band heads in the P and R branches.
7
8
1 Coherent Proton Tunneling in Hydrogen Bonds
Pending further data, the doublet component origins are represented using peaks #24 and #25 as 12(260.7 + 256.8) = 258.8 cm–1 and peaks #28 and #29 as –1 12(231.9 + 228.5) = 230.2 cm–1. Then DS 15 = |D15 – D0| = 28.6 cm yielding D15 = 7.0 or 50.2 cm–1, and m15 = 244.5 cm–1. The CC-VSCF computed estimate [60] for m15 is 267.2 cm–1, a value 9.3% higher than m15 = 244.5 cm–1. For the original assignment the differences are 277.5 – 252 = 25.5 (10.1%) and 267.2 – 282 = –14.8 cm–1 (–5.2%). The experimentally based DV values for nine fundamentals are listed in column 3 of Table 1.1 and approximate descriptions of the vibrations by Alparone and Millefiori [60], whose computations fit the observed IR spectrum to 2 or 3%, are listed in the right-most column. In column 4 the DV/D0 ratios are listed next to theoretical ratios [61–64] discussed below. Of the nine experimental values only the four lower frequency skeletal displacements – two in-plane and two out-ofplane – appear to significantly impact the tunneling process. Experimental splittings remain unknown for the vibrations dominated by motion of the tunneling H (that is the mOH, dCOH, and cOH internal coordinates). The mOH stretching vibration is anharmonically coupled to many nearby overtone and combination vibrations and its doublet separation is concealed in the broad IR absorption profile. The vibrational compositions in Table 1.1 show that the fundamentals containing the cOH torsion and dCOG bending coordinates are strongly mixed with other internal coordinates. Carrington and Miller [65] using 2D and Shida et al. [66] using 3D quantum chemical reaction surface models produced the first of many extant theoretical estimates for D0 and vibrational state specific splittings DV for MA. The differences of 2D and 3D computations are very noticeable and they are the exclusive topic of a recent article by Yagi et al. [67]. The theoretical approaches to MA vary from extensions of the cited early work, to that on full multidimensional instanton computations by Smedarchina et al. [68], to work on new techniques such as the short time propagation method being tested by Giese and Khn [69]. DoÐlic and Khn [70] studied modes in the OHO fragment in 4D computation. Tautermann et al. [71] developed an improved semiclassical method for determining the optimized multidimensional tunneling path between the straight line and minimum energy path routes. The ZP corrected PES was constructed using low-level energy points calculated using B3LYP/6-31G(d) density functional theory (DFT) methodology and this PES was then scaled to match a few high level G3(MP2) reference points. The procedure produced computed D0 values for (HF)2, MA, and TRN that were each in good agreement with experiment. PES features are now routinely computed using quantum chemistry methods that must necessarily include estimates for the electron correlation energy. The computed SP energy values depend strongly on the level of theory used, as exemplified by the range 10.34 kcal mol–1 (RHF/6-31G**) to 2.86 kcal/mol [B3LYP/6311+G(2d,p)] reported by Benderskii et al. [61]. Barone and Adamo [72] proposed 4.3 kcal mol–1 as the best value for the SP barrier for MA on the basis of high level comparative studies. Sadhukhan et al. [73] reported 3.9 kcal mol–1 for CCSD(T)/ cc-pVDZ computation.
1.2 Coherent Tunneling Splitting Phenomena in Malonaldehyde
Yagi et al. [74] determined an ab initio PES for MA, based on 698 reference points in the full 21D vibrational space, in work made possible through the use of a modified Shepard interpolation method. For this PES they estimated D0 = 13.9 cm–1 by using the semiclassical trajectory method proposed by Makri and Miller [75]. The D0 value can also be calculated using exact quantum dynamics methods, and Coutinho-Neto et al. [76] computed D0 using the diffusion Monte Carlo based projection operator imaginary time spectral evolution method to obtain D0 = 25.7 – 0.3 cm–1. The multiconfigurational time-dependent Hartree approach yielded D0 = 25 cm–1 to about 10% accuracy. These results establish an independent benchmark comparison for the various semiclassical results. Mil’nikov and Nakamura [77] reformulated instanton theory to allow “practical” computations of multidimensional tunneling splittings which, with some refinements, was applied [78] to the 21D PES to obtain D0 = 30.7 cm–1. The reformulated instanton theory introduces a variational procedure to minimize the classical action functional determining the instanton trajectory. Few iterations of the procedure are required to converge an initial approximate trajectory into the instanton. Because the required quantum chemical PES computations are focused on the instanton region of the PES, relatively few points (energy, gradient, Hessian) are required. The method allows the instanton obtained from a low level PES to be the starting point for determining the instanton generated from a higher level PES [77, 78]. Mil’nikov et al. [78] could address MA – with full 21D consideration – using ab initio PESs obtained at high levels of quantum chemistry. The new theoretical development produces smooth instanton paths (unlike results found for the PES obtained through the Shepard interpolation procedure). The reduced quantum chemistry work load allowed the variational instanton method to determine D0 = 16.4 cm–1 for MA at the CCSD(T)/ (aug-)pVDZ level of PES computation. With recognition that full computation using the (aug-)cc-pVTZ basis would require more than 5 years of CPU time because of the Hessian calculation, a partial computation with the instanton preexponential B and S1 factors transferred from MP2/cc-pVDZ computations yielded D0 = 21.2 cm–1 – very near the 21.6 cm–1 experimental result. Similarly, D0[MA(OD)] = 3.0 cm–1 was calculated with 2.9 cm–1 observed. Mil’nikhov et al. [78] estimate the error in the computed D0 value for MA to be at most 10%. This work re-emphasizes the sensitivity of the D0 computation to the PES determination, while taking advantage of the lower sensitivity of the B and S1 pre-exponential factor computations to the quantum chemical method. The developmental work [77] included the demonstration that the utilized multidimensional path integral method and the multidimensional Wentzel–Kramers–Brillouin (WKB) method yield equivalent results. The variational instanton method has not yet been applied to the tunneling splittings of vibrational excited states of MA. Benderskii et al. [61] developed a theory called the perturbative instanton approach (PIA) which they applied to MA in full 21D treatment. An important feature of their work is the expression of the carefully partitioned and symmetrized Hamiltonian in expansions using dimensionless variables including a semiclassical parameter called c. The c value allows scaling of the tunneling
9
1028
16
0.32 2.32
7.0[b] 50.2
245[a]
14
15
1260
10 0.73 1.27
1358
9
15.8[b] 27.4
1346
8
~1.00
~21.6
512
1452
7
1.000
21.55
~1.00
1594
6
~21.6
1655
5
1.00
Obs.[c] 21.6
~1.00
2856
1
21.583
DV [b]
Observed
~21.6
21.583
mV [a]
ZP
Mode[a] (V)
0.96
1.56
0.91
1.76
1.26
23.3
1.10
0.80
1.03
2.96
1.00
Bend.[d] 21.6
2.45
1.11
1.26[e]
1.06
1.10
1.56
1.00
Sew.[e] 21.8
0.30
0.79
1.47
2.14
1.49
1.31
1.03
1.14
0.89
7.89
1.00
Meyer[ f ] 22.0
DV/D0 ratios
0.21
3.26
0.76
0.61
1.05
6.63
0.76
0.79
1.11
1.00
Tew[g] 38
1.20
5.20
1.93
1.53
1.53
1.40
1.87
0.73
1.60
1.00
Tew[g] 15
Tab. 1.1 Comparisons of observed and computed fundamental tunneling splitting ratios DV/D0 for malonaldehyde.
cCH7 + cCH9
mO_O mO_O
dRING dRING
dCH7 + dOH + mC–O
dCH9 + dOH + mC–O
dOH + dCH9 + mC=O + iph mC=C
dCH7 + dCH8 + mC–C
mC=O + iph mC=C + dOH
mC=O + oph mC=C
mOH + mCH7
Approx. description[a]
10
1 Coherent Proton Tunneling in Hydrogen Bonds
0.83
1.05
1.04
0.73
0.86
Bend.[d] 21.6
0.91
1.08
Sew.[e] 21.8
0.67
1.08
1.06
0.72
0.89
Meyer[ f ] 22.0
DV/D0 ratios
0.53
0.87
0.92
0.39
0.58
Tew[g] 38
1.47
1.47
1.60
1.13, 0.67
0.27
Tew[g] 15
cRING cRING
cRING cRING
cCH8
cOH + oph cCH7
cOH + iph cCH7 + cCH9
Approx. description[a]
a Mode numbers, observed frequencies, and descriptions (oph = out of phase; iph = in phase) are from Table 1 of Ref. [60] – except reassigned frequencies for m15 and m21. Computed frequencies [d,e,f,g] do not exactly match the observed values. b IR data from Refs. [15,19]. Indeterminate doublet splittings DSV = | DV – D0| give two choices for the tunneling splittings DV. c ZP tunneling splittings D0 (cm–1) are included in the DV/D0 headings. d Benderskii et al. [61]. D8/D0 = 23.3 because of resonance interaction. D0 is fit to the exact experimental value. e Sewell et al. [62]. Vibrations from the utilized PES correlate poorly with the observed midrange vibrations. The 1.26 ratio correlates with dOH type mode with 1452 cm–1 frequency. f Meyer and Ha [63]. g Tew et al. [64]. The D0 = 38 and 15 cm–1 columns are for harmonic and anharmonic valleys, respectively. The 1358 and 1346 cm–1 vibrations are labeled m8 and m9, respectively, by Tew et al.
0.87 1.13
18.7[b] 24.5
281[a]
21
0.71 1.29
15.3[b] 27.9
20
384
766
19
Obs.[c] 21.6
~1.00
873
18
DV [b]
Observed
~21.6
981
mV [a]
17
Mode[a] (V)
1.2 Coherent Tunneling Splitting Phenomena in Malonaldehyde 11
12
1 Coherent Proton Tunneling in Hydrogen Bonds
splitting D0 and SP barrier height, which are quite sensitive to c, as well as spectral densities and other quantities that are relatively insensitive to c. The selected PES was scaled with c chosen to duplicate the experimental D0 = 21.6 cm–1 splitting. The resulting SP energy is 4.30 kcal mol–1 – the same value chosen by Barone and Adamo [72] as the best value for MA on the basis of their comparative quantum chemical computations. Conversely, choosing c to reproduce this ab initio SP energy value yields the observed D0 splitting. The full 21D vibrational spectrum and 21 DV values were computed in the PIA. In column 5 of Table 1.1 a selection of the resulting DV/D0 ratios are listed for comparison with columns containing the available experimental values and results from other computational procedures. At this stage, the appreciable dispersion of the computed PES topologies, vibrational spectra, and tunneling splitting values favors comparison of the results through ratios. Benderskii et al. [61] present a detailed description of the dynamics calculated for MA and several isotopomers. They refer to m8, observed at 1346 cm–1, as the tunneling coordinate with m1 (OH stretching) and m15 (O_O stretching) designated as promoting modes. The very large (500 cm–1) computed splitting obtained for m8 is attributed to a resonance interaction with m1 – also stated to be resonantly coupled with two nearby CH stretching modes with computed tunneling splittings above 100 cm–1. The values D8/D0 = 23.3, D3/D0 = 7.55, and D2/D0 = 5.89 are by far the largest ratios arising in this study. Column 6 of Table 1.1 presents several DV/D0 ratios obtained from the full 21D classical trajectory/WKB computations of Sewell et al. [62]. The utilized PES is based on the 1983 valence force field, and early vibrational assignments of Smith et al. [15] – some of which differ from later work [59, 60]. Many of the computed splitting ratios are therefore not entered in Table 1.1. The PES was given Morse functions for the bond stretching coordinates. At 10.0 kcal mol–1 the SP energy is very high but the barrier is noticeably narrow in its upper reaches. The computed ZP tunneling splitting is D0 = 21.8 cm–1, fortuitously close to the 21.6 cm–1 observed value. The DV/D0 ratios listed in column 6 are those with the closest agreement to current understanding of the vibrational structure and, for whatever reason, they follow the lead of D0 by showing quite good agreement with the experimental results. Full 21D computations were produced using direct quantum chemical methods by Meyer and Ha [63] and by Tew et al. [64, 79]. Meyer and Ha developed a reference reaction path model applied using a PES with the SP barrier of 3.27 kcal mol–1. They obtained D0 = 22.0 cm–1 for MA(OH), 3.8 cm–1 for MA(OD), and values for all 21 DV splittings. Some of the resulting DV/D0 ratios are listed in column 7 of Table 1.1, where it is seen that a large splitting is predicted for m1 (OH stretching) and that damping of the ZP splitting is predicted for the low frequency H transfer coordinate m15 (O_O stretching). The largest ratios are D1/D0 = 7.89, D10/D0 = 2.14, and D13/D0 = 1.66. DV values for several modes are significantly larger than suggested by the experimental data. Tew et al. developed an internal coordinate reaction path Hamiltonian allowing the usual division of coordinates: a single large amplitude motion with 20 orthogonal normal modes. In their work the energy levels are solved by matrix diagonalization (that is, by variational con-
1.3 Coherent Tunneling Phenomena in Tropolone
figuration interaction computations that were performed on three increasingly inclusive approximations for the Hamiltonian.) They initially [79] applied the method to MA using a PES determined by DFT. This work was followed [64] by an article concentrating on the use of PESs determined using the MP2 approximation for electron correlation energies because of convergence inadequacies arising through the use of DFT. In columns 8 and 9 of Table 1.1 the listing of computed DV/D0 ratios is obtained from results for the highest level Hamiltonians using a computed harmonic PES valley (D0 = 38 cm–1, column 8) and a computed anharmonic PES valley (D0 = 15 cm–1, column 9). It is noted that the computations for the harmonic valley predict quenching of the ZP tunneling on exciting m20 or m21, while for the anharmonic valley the computations predict enhancement instead. For the harmonic valley the three largest ratios are D8/D0 = 6.63, D15/D0 = 3.26, and D13/D0 = 2.82. For the anharmonic valley they are D15/D0 = 5.20, D13/D0 = 2.00, and D14/D0 = 1.93. Good convergence was obtained for the lower vibrational frequencies but converged DV splittings could not be obtained for the OH/CH stretching frequencies.
1.3 Coherent Tunneling Phenomena in Tropolone
The first experimental evidence for coherent tunneling in the moderately large molecules of interest in this chapter was reported for TRN in 1972 by Alves and Hollas [22]. Vibronic absorption bands of gaseous TRN(OH) and TRN(OD) in the 370 nm region were recorded at relatively high spectral resolution to clearly show rovibronic fine structures with peak spacings of ~ 0.1 cm–1. Observed band head peaks were systematically paired as spectral doublets [22, 23] with separations both larger and smaller than the value of 18.93 cm–1 determined for the ZP origin doublet. This important work on gaseous tropolone showed that readily measured coherent tunneling processes occur over at least the lower 700 cm–1 range of vibrational excited states in the ffi 1B2 (S1) electronic state and it stimulated many experimental and theoretical studies on this system. For TRN(OH) Alves and Hollas assigned the ZP doublet transitions labeled 000 + (0 –0+) and H11 (0––0–) in Fig. 1.3 and determined their origins to be 27017.54 and 27036.47 cm–1, respectively. The spectral doublet separation is DS = |D0S1 – D0S0 | = 18.93 cm–1; for TRN(OD) they found DS = 2.2 cm–1. Independent data are required to determine the individual D0S1 and D0S0 values, and Alves and Hollas were limited to recognizing that D0S1 is 18.93 cm–1 larger than D0S0 . In 1999 Tanaka et al. [32] used microwave spectroscopy to determine that (rounded to three digits) D0S0 = 0.974 cm–1 for gaseous tropolone. The untruncated ZP splitting, D0S0 = 29193.788(26) MHz, was determined using a single interaction parameter with six rotational and centrifugal distortion constants each for the symmetric (0+) and antisymmetric (0–) tunneling states. Stark effect measurements on the 32,1 ‹ 22,0 and 32,2 ‹ 22,1 rotational transitions show the average dipole moments of gaseous tropolone along the Z (longitudinal) axis in these rotational
13
14
1 Coherent Proton Tunneling in Hydrogen Bonds
Figure 1.3 Vibrational state-specific doublets observed in the S1–S0 fluorescence excitation spectrum of jet-cooled TRN(OH) by Sekiya et al. [31].
states are 3.428(50) D for 0+ and 3.438(50) D for 0–. The analogous dipole moment component for MA is 2.59 D [10]. The microwave study verified beyond any doubt that tropolone possesses a symmetrical double-minimum PES in its S0 electronic state, that the molecule undergoes coherent state-specific rotation-tunneling transitions, and that there are small but measurable differences between rotational constants of the 0+ and 0– states. The node in the 0– tunneling wavefunction may cause the inequality A+ = 2743.0931(54) > A– = 2742.7181(114) MHz [32]. A few years after Alves and Hollas studied the vibronic absorption spectrum of gaseous tropolone in a 1 m cell at room temperature, the application of pulsed UV laser spectroscopy to gaseous samples cooled in pulsed molecular beams became possible. Passing the carrier gas over tropolone crystals loaded into a pulsed nozzle at 45 C produces excellent samples with rotational temperatures ~ 3 K and vibrational temperatures ~ 15 K. The initial works were by Tomioka et al. [26], Redington et al. [28], and Sekiya et al. [30]. With the elimination of hot bands and with rotational envelopes reduced to widths of about 2 cm–1 [28, 29], the S1–S0 fluorescence excitation spectrum is greatly simplified compared with the 25 C absorption spectrum. In the best resolved fluorescence excitation data the ZP origin doublet components show peaks with central dips which, taken as the band origins, yield DS = 18.90 cm–1, in good agreement with the value reported by Alves and Hollas. The most recent publications on the S1–S0 transition of TRN(OH) are by Bracamonte and Vacarro [37, 38], who applied their polarization resolved DFWM spectroscopy method [37] to TRN vapor at its room temperature sublimation pressure. This remarkable nonlinear spectroscopic method simplifies the spectrum by allowing Q branch (DJ = 0) transitions to be observed with greatly diminished R and P branch (DJ = – 1) signal and, with rotation of a polarization element, vice versa. This selective nonlinear optical technique also produces a large reduction in the signal generated by hot bands, as noted in the above discussion for MA. How-
1.3 Coherent Tunneling Phenomena in Tropolone
ever, with optical saturation the hot band Q branch signals are sufficiently strong that some of their band origins could be approximated [38]. With the S0 ground state rotational parameters known from the work of Tanaka et al. [32], the S1 state parameters, including the coherent tunneling splitting value D0S1 = 19.846(25) cm–1, were accurately determined by Bracamante and Vaccaro [38]. The extra large inertial defects DI0+S1 = –0.802(86) and DI0–S1 = –0.882(89) amu 2 led them to conclude that the geometry of tropolone in the S1 electronic state is slightly nonplanar. Tropolone is easily deuterated and the S1–S0 fluorescence excitation spectrum of jet-cooled TRN(OD) was reported by Sekiya et al. [40]. The observed doublet separation, DS = 2 cm–1, is near the 2.2 cm–1 value reported by Alves and Hollis [22], and about 10% of the value observed for TRN(OH). Presently the only available experimental estimate for the ZP tunneling splitting of S0 TRN(OD) is D0S0 £0.17 cm–1 [80] obtained using a chloroform solvent and NMR spectroscopy to measure the deuteron spin–lattice relaxation time. The S1–S0 fluorescence excitation and dispersed fluorescence spectra of TRN(OH) and TRN(OD) isolated in Ne matrices at ~ 3.5 K were studied by Rossetti and Brus [25] using UV pulsed laser excitation. Low temperature Ne matrixisolation sampling is advantageous because, in principle, the sample monomers are dispersed in identical trapping sites resulting in a single sharp peak very near the gas-phase origin for each spectral transition. Rossetti and Brus found that the S1–S0 band origin transitions are doublets with the separations DS = 21–2 cm–1 for TRN(OH) and DS = 7–1 cm–1 for TRN(OD). These values are larger than the gas phase values by 2–2 cm–1 for TRN(OH) and 5–1 cm–1 for TRN(OD). According to theory [81], coupling a tunneling system to a bath of harmonic oscillators produces a damping of the tunneling splittings. The increased spectral doublet separations observed for Ne-isolated tropolone are explainable [82] through the interaction of nonplanar S1 tropolone with an asymmetric Ne matrix trapping site. The large observed inertial defects [38], and molecular orbital (MO) computations reported by Wjcik et al. [83], suggest the geometry of tropolone is probably slightly nonplanar in the S1 state. For discussion it is assumed to be deformed towards a boat shape. (In the crystal state S0 tropolone is boat-shaped with folding angles of 1 or 2 [84]). Tautomerization inverts the concavity of the TRN geometry to, for example, uncradle an initially cradled Ne atom in the asymmetric trapping site. The small reorientation of the TRN position causes minimal disturbance of the trapping site configuration, but it produces an offset between energy minima of the two tautomer configurations to distinguish the behavior of planar S0 and slightly nonplanar S1 tropolone in an asymmetric Ne matrix trapping site. Hameka and de la Vega [85] presented a theoretical description of the ZP energy levels and probability density functions for a particle in a slightly asymmetric double-well PEF. They analyzed the model behavior in terms of two basic parameters: d (the energy offset between the two PEF minima), and D (the tunneling splitting that occurs for the limiting equal double-well PEF – namely at d = 0). Equations presented by Hameka and de la Vega are easily combined [39, 82] into the equation (asD)2 = d2 + D2, where asD is the splitting of the ZP energy levels in the PEF.
15
16
1 Coherent Proton Tunneling in Hydrogen Bonds
Except for the small nonplanarity of S1 TRN, the S0 and S1 geometries, Ne matrix trapping sites, and (probably) fundamental tautomerization processes of TRN(OH) and TRN(OD) are similar. For gaseous TRN in the S0 and S1 states the PEF is symmetrical so that d = 0 and D = D0 = asD. The observed IR and UV spectral data for Ne-isolated TRN suggest d ~ 0 for TRN in the S0 state, and d = 7–1 cm–1 for TRN in the S1 state. The latter value accounts for the comparative spectral doublet behavior of the S1–S0 origin bands of Ne-isolated and gaseous TRN(OH) and TRN(OD). The spectral data also suggest that the Ne trapping site environment damps the D tunneling splitting values by an amount d taken to be the same for the S0 and S1 states of both isotopomers (if d > DV, the DV value is fully quenched). Dampings 1£d£2.5 cm–1 therefore completely quench the TRN(OH) splitting D0S0 = 0.974 cm–1, but only mildly damp D0S1 = 19.864 cm–1. The value d = 2.5 cm–1 is the maximum value consistent with error bars of the observed spectral doublets. The modeling computations of Makri and Miller [81] show that if a specific tunneling system is coupled to a high bath frequency the system tunneling splitting is only slightly damped, whereas if the coupling is to a low bath frequency the damping is strong. An analogous situation is to compare dampings generated by the couplings of a specific bath frequency to different tunneling systems, say high barrier system A with splitting D0 and low barrier system B with splitting 10D0. Compared to the bath oscillator the parameters of system A would be high [that is, relative to them the bath frequency would be low (say below the barrier) with strong damping of the splitting]. Similarly, the parameters of system B would be low [that is, relative to them the bath frequency would be high (say above the barrier) with weak damping of the splitting]. A specific Ne trapping site, with its fixed distribution of vibrational frequencies, can thus be envisioned as strongly damping (percentage wise) a tunneling system with a small D0 value (D0S0 of TRN), and weakly damping (percentage wise) a tunneling system with a large D0 value (D0S1 of TRN). Fluorescence excitation [43] and IR absorption [39] spectra of 16,16TRN(OH), 16,18TRN(OH), and 18,18TRN(OH) show that an asymmetric double-well PES occurs for gaseous 16,18TRN in the S0 and S1 electronic states. This is due to unequal anharmonic vibrational energy contributions to the effective PES at the limiting 16OH_18O and 16O_H18O tautomer configurations. The lowered symmetry of 16,18TRN(OH) facilitates the observation of four (rather than two) fluorescence excitation transitions [43]. Combination differences of the observed transitions show the ZP levels of 16,18TRN(OH) are separated by 1.7 cm–1 in the S0 state [compared to D0S0 = 0.974 cm–1 for 16,16TRN(OH)]. The fluorescence excitation spectra of jet-cooled TRN(OH) and TRN(OD) show vibrational transitions in the S1 state reaching to about 700 cm–1. The lowest frequency fundamental of TRN(OH) occurs at 39 cm–1 in the S1 state, and at 110 cm–1 in the S0 state. The MO-computed normal coordinate for the S0 state suggests primary OCCO/skeletal twisting, rather than wagging, character. If its true nature is torsional, it should be identified as m19 (a2) rather than as m26 (b1). The low frequency values reflect the competition between drives favoring planar
1.3 Coherent Tunneling Phenomena in Tropolone
geometry (the internal H bond and p resonance interactions), and drives favoring nonplanar geometry (the relaxation of heptacyclic ring strain, and of cis OCCO alignment). The fluorescence excitation spectrum of jet-cooled TRN(OH) as presented by Sekiya et al. [31] is shown in Fig. 1.3. A series of vibrational state-specific tunneling doublets (labeled 260V) are seen to proceed to the blue of the S1–S0 origin doublet. These involve even numbered vibrational excitations of the 39 cm–1 mode in the S1 state. The spectral doublet separations, 7.23, 4.72, 3.51, _ cm–1, are strongly damped from the 18.90 cm–1 value for the origin band. The figure also shows vibrationally enhanced doublet separations for m13 (414.66, 446.7 cm–1) and m14 (295.82, 326.41 cm–1) [28–31], which are a1 skeletal deformation fundamentals with strong components of O_O stretching. The above vibrational state-specific doublet separations for the S1 state are collected in column 3 Table 1.2, where they are compared with theoretical splittings computed by Wjcik et al. [83] as noted below. Many of the spectral doublet separations observed for S1 state vibrations are large and easily measured and, in principle, dispersion of the fluorescence excited from the S1 states allows many S0 vibrational states to be probed. The individual doublet components of the S1–S0 origin or other sufficiently strongly fluorescent doublet component can be excited with laser pulses to generate fluorescence transitions of the same parity terminating on S0 vibrational states. Values for the frequencies of m13, m14, and other fundamental and excited state transitions are assigned [27, 31], but most S0 state tunneling splittings DV cannot be determined from the extant fluorescence data. Alves et al. [27] published a large body of dispersed single vibronic level fluorescence spectra excited from doublet components of gaseous tropolone at room temperature by a UV laser with a 1 cm–1 band width. The dispersed fluorescence spectra access many high lying S0 state vibrations that may be basically unobservable to direct IR absorption spectroscopy. This work added greatly to understanding of the vibrational spectra in the S1 and S0 electronic states – especially concerning the lowest frequency modes. Turning to spectral doublings observed in the IR spectra of TRN(OH) and TRN(OD), it was found that samples isolated in Ne matrices produce many more transitions than there are fundamental vibrations [24]. Of these, ten pairs of lines were originally assigned as apparent spectral doublets, but in later experimental and computational research [34, 86] virtually all of the extraneous lines were assignable as binary, and some ternary, overtone and combination transitions. Relative absorption intensities suggest the anharmonic resonance interactions couple many of the vibrational states, and several weak computed fundamentals of TRN(OH) and TRN(OD) have not yet been observed in IR spectroscopic experiments. Spectral tunneling doublet assignments in the Ne matrix data were made only for the OH(OD) stretching (DS = 19[4.8] cm–1) and skeletal contortion (DS = 10.6[9.6] cm–1) fundamentals. The absence of other assignable tunneling doublets in the IR spectra of Ne-isolated TRN is attributed to the above noted total damping of the gas phase coherent tunneling splittings DV < 2.5 cm–1 by couplings to the Ne matrix [82]. In Ar matrices the peaks show shifting, broadening, and sometimes structure relative to the Ne matrix data [24].
17
18
1 Coherent Proton Tunneling in Hydrogen Bonds Table 1.2 Calculated energy splittings (D0S1 ) in cm–1 for the 3D
model potentials for the ffi state of tropolone. (Table VII of Ref. [83].) Band
CIS/6-31++G(d,p)
Exp.
130140
19.6
20
130141
24.2
31
130142
29.0
29
130143
34.0
130144
39.3
131140
20.4
132140
21.2
133140
21.9
134140
22.5
250260
24.4
250261
24.2
250262
24.0
250263
23.8
250264
23.6
250265
23.4
250266
23.3
250267
23.1
250268
22.8
251260
23.9
252260
23.4
253260
22.9
254260
22.5
33
20
8
6
5
2
5
1.3 Coherent Tunneling Phenomena in Tropolone
Vibrations in the S0 state of gaseous TRN(OH) were directly addressed in the 700–3500 cm–1 region using high resolution Fourier transform infrared (FTIR) absorption spectroscopy [35] on samples at 25 C, the sublimation pressure ~0.01 Torr, and optical path length 32 m. Individual rotational transitions of tropolone are not resolved at a spectral resolution of 0.0025 cm–1. However, sharp Q branch peaks arising in rotational contours of the FTIR absorptions mark approximate band origins for the out-of-plane vibrations (type C profiles), and for vibrations with intense transition dipoles paralleling the fictive C2 axis (type A profiles). The observed sharp Q branch spikes led to 32 reported [35] spectral tunneling doublets in the region between 700 and 950 cm–1. Additional doublets were observed at 0.1 cm–1 resolution at frequencies above 950 cm–1, but the details have not yet been reported – exclusive of the CH/OH stretching region which is shown below to have a smooth contour with no resolved spectral doublets [35]. The CCOH torsion fundamental (m22) and two members of an associated progression of hot bands are shown in Fig. 1.4. The doublet separation for m22 is DS22 = |D22 – D0| = 0.90 cm–1. Together with D0 = 0.974 cm–1 for the ZP state, this yields the strongly damped tunneling splitting D22 = 0.074 cm–1 for this fundamental. The transitions in Fig. 1.4 have also been studied for the oxygen isotopomers 16,18TRN(OH) and 18,18TRN(OH) [39]. An analysis including the assumption that 16,16D /16,16D = 18,18D /18,18D for the oxygen isotopomer splittings in the m 22 0 22 0 22 COH torsion and ZP states contributes to first estimates for the isotopomer ZP tunneling splittings 18,18D0 = 0.865 cm–1 and 16,18D0 = 0.920 cm–1. The 18O vibrational isotope shifts of the m22 transitions depend on normal isotopomer reduced mass values near 1.07 amu. In contrast, the 18O isotope dependence of the isotopomer tunneling splittings for m22 correlates with the large reduced mass values of the skeletal contortion fundamental [39]. This unique isotope effect supports the role for skeletal tunneling in the tautomerization process of tropolone in the S0 electronic state.
absorbance
1.5
CCOH torsion
1.0
hot band
contortion (fragment)
hot band
0.5
0.0 740
745
cm -1
Figure 1.4 A 15 cm–1 overview of the high resolution FTIR absorption spectrum of gaseous TRN(OH) at 25 C [35]. The spectral doublets are for the CCOH torsion fundamental and two members of its hot band progres-
750
755
sion. The ultra-narrow spikes are attributed, with other structure, to the high frequency doublet component of the skeletal contortion fundamental.
19
20
1 Coherent Proton Tunneling in Hydrogen Bonds
The OH/CH stretching region around 3100 cm–1 is of obvious importance to a discussion of coherent H tunneling in TRN. Sharp Q peaks are neither predicted nor observed for the OH stretching fundamental, although Fig. 1.5 shows peaks appear in the region. Vibrational assignments [34, 86] were proposed on the basis of (i) gas phase IR spectra at lower frequencies, (ii) moderately high level MO computations, (iii) two-laser fluorescence dip IR spectra (FDIRS) of jet-cooled TRN(OH) and TRN(OD) by Frost et al. [33], (iv) the IR spectra of Ne matrix-isolated samples [24], and (v) the results of independent theoretical computations of the spectral doublet for the OH stretching fundamental. The weak OH stretching fundamental assigned in Fig. 1.5 [3121, 3102 cm–1 in Ne-isolated TRN(OH)] occurs near the five CH stretching fundamentals (overlapped at 3063, 3030 cm–1), with anharmonic resonance couplings to these and many (perhaps all) of the binary overtone and combination states present in the region. The broad gas phase absorption for TRN(OH) closely spans the limits set by these transitions (as
OH stretching tunneling doublet
Tropolone(OH)
Tropolone(OD)
Figure 1.5 Infrared spectra of TRN(OH) and TRN(OD) in the 3100 cm–1 region [34]. In Ne-isolated TRN(OH) the fundamental OH stretching spectral doublet is at 3121 cm–1
and a shoulder at 3102 cm–1. The doublet is not discerned in the gas phase IR absorption profile. The jet-cooled fluorescence dip IR spectra (FDIRS) are due to Frost et al. [33].
1.3 Coherent Tunneling Phenomena in Tropolone
shown in Fig. 3 of Ref. [34].) Hot band absorptions are also present. The assignment of the OD stretching fundamental is 2344.8, 2340 cm–1 for Ne-isolated TRN(OD), with DS = 4.8 cm–1. Because of damping by the Ne matrix, the spectral doublet separations for gaseous TRN(OH) and TRN(OD) would be ~ 2 cm–1 larger than the 19 and 5 cm–1 values observed in Ne-matrix isolation [82]. As noted in Section 1.2 for MA, the vibrational state-specific tunneling dynamics of TRN are addressed using PES features obtained through quantum chemical computations. The results of computing the C2v saddle-point energy barrier maxima [86] for TRN at various levels of theory are shown in Table 1.3. The SP barriers computed using the larger basis sets with second order Møller–Plesset perturbation theory (MP2) for correlation energy are only about one quarter of the values obtained using the restricted Hartree–Fock (RHF) methodology with the 631G(d,p) basis set. Vener et al. [87] addressed the problem of coherent H tunneling in tropolone by approximating solutions to the 2D and 3D Schrdinger equations for the OH_O group using adiabatic separations of the high and low frequency degrees of freedom. The molecular PES was constructed using the 6-31G basis with added polarization functions for some atoms. Self-consistent field (SCF) and configuration interaction singles (CIS) methodologies were used for the S0 and S1 states, respectively. The computed vibrational state-specific tunneling splittings reflect the dynamics of H motion in a double-minimum PES with a high barrier maximum (~ 15.7 kcal mol–1). The computational model produced enhanced tunneling splitting on exciting the O_O stretching coordinate and modest effects on exciting COH bending. Tunneling behavior on the excitation of vibrations beyond the OH_O group was not considered. Smedarchina et al. [88] used a modified semiclassical instanton approach to consider the ZP and excited state tunneling splittings of the S0 and S1 states. PES features were computed at the RHF/6-31G(d,p) level. Scaled by 0.9, the high computed adiabatic barrier reproduced the experimental ZP splitting for S1 tropolone, and the splittings computed for 13 excited vibrational states yielded excellent to poor agreement with experiment. The instanton computations produced a large deuterium isotope effect, as observed. Takada and Nakamura [89] studied S0 tropolone using model 3D analytical PES functions based on coordinates for the OH stretch, a tunneling-promoting nominal O_O stretch, and a low frequency out-of-plane deformation mode. These were parametrized using optimized geometries for the tautomer and SP configurations computed at the MP2/6-31G(d,p) level, with refinement of the critical point energies at the MP4/6-31G(d,p) level. ZP energies for all coordinates, except the three defining the PES, were included using vibrational spectra computed at the MP2/6-31G(d,p) level. Tunneling eigenstates were evaluated by a numerical method. The high value of the C2v SP barrier entering the PES produced good computed agreement with the observed D0S0 = 0.974 cm–1 tunneling splitting. Enhanced tunneling splittings were computed for O_O stretching excitations, with mildly damped splittings for excitations of the out-of-plane mode. In a very similar paper, Wjcik et al. [83] used model 2D and 3D analytical PESs for TRN in the S1 electronic state that were parametrized by data computed at the CIS/6-
21
22
1 Coherent Proton Tunneling in Hydrogen Bonds Tab. 1.3 MO-computed C2v saddle-point potential energies for tropolone [86].
Level
Atoms
Basis
Energy (kcal mol–1)
MP2[a]
COHOC
6-311G(df,pd)
3.64
5CH
6-311G(d,p)
COHOC
6-311G(df,pd)
5CH
6-311G(d,p)
MP3
MP4(DQ)
MP4(SDQ)[b]
MP2
MP2
MP2
COHOC
6-311G(df,pd)
5CH
6-311G(d,p)
COHOC
6-311G(df,pd)
5CH
6-311G(d,p)
C7OHO
6-311G(df,pd)
5H
6-311G(d,p)
COHOC
6-311++G(df,pd)
5CH
6-311G(d,p)
7.12
7.88
6.96
3.64
3.62
OHO
6-311G(2df,2pd)
C7H5
6-311G(d,p)
4.57
MP2
all
6-311G(d,p)
5.02
MP2
all
6-31++G(d,p)
5.57
RHF
all
6-31G(d,p)
15.62
MP2
all
6-31G(d,p)
5.29
MP3
all
6-31G(d,p)
9.22
MP4(DQ)
all
6-31G(d,p)
9.93
MP4(SDQ)
all
6-31G(d,p)
8.86
a MP2/GEN methodology is used for geometry optimizations and harmonic frequency computations. b MP4(SDQ)/GEN methodology is used for points in the PES topography. The G3(MP2) computed SP energy is 7.2 kcal mol–1 [93].
31++G(d,p) level of theory (including the vibrational spectrum for the ZP correction). The tunneling splittings, accurately computed using a variational method, are shown with the experimental splittings for S1 tropolone in Table 1.2 taken from the article.
1.3 Coherent Tunneling Phenomena in Tropolone
Paz et al. [90] used MO-computed energies at modest theoretical levels to parametrize a 2D model PES and obtain tunneling splittings resembling the observed data. As they did for MA, Guo et al. [91] used a semiclassical approach on the tunneling splittings, with trajectory calculations, to compute DV values for all 39 fundamentals of the S0 state of TRN(OH). MO-computations were used to establish the PEF functions. With adjustment of the barrier to give the observed D0 value, the two lowest frequency out-of-plane modes realistically damp the tunneling, several likely modes enhance the tunneling, and the DOH for the OH stretch is 31 cm–1. The scope of the various developing multidimensional theories is general and, while the computations on TRN lag those on MA, inroads on higher dimension computations are being made. Giese and Khn [92] applied a multidimensional reaction surface approach to TRN using 4D and 12D versions of the reaction surface. The 4D surface included reduced normal modes favoring OH stretch, COH bend, the skeletal mode near 750 cm–1 presented [34, 86] as the tautomerization coordinate, and O_O stretching. The 12D model was used to compute IR spectra using the multiconfiguration time-dependent Hartree method. The spectrum provides theoretical justification for the small DOH tunneling splitting value, and for the attribution of the broad OH stretching absorption of gaseous TRN to resonantly coupled binary combination modes as discussed above for Fig. 1.5. This work and investigations described above for TRN –and in the previous section for MA – give prominence to the lowest frequency in-plane mode (nominal O_O stretching) as the H transfer coordinate. As already noted in Section 1.2 Tautermann et al. [71] obtained good agreement with experiment for the ZP splittings of MA. They also successfully applied their semiclassical method for finding the tunneling path to (HF)2 and TRN [93], where the 7.2 kcal mol–1 quantum chemistry barrier for TRN is 50 to 100% lower than the barriers used for the computations on TRN discussed above. It is similar to the MP4/GEN results (footnote b of Table 1.3) used in the following discussion of the tautomerization of S0 TRN that is based on an examination of the computed and spectroscopic data set for TRN(OH) and TRN(OD) [34–36, 86]. MP2/GEN (footnote a in Table 1.3) was used for geometry optimizations and computation of harmonic vibrational spectra, with MP4(SDQ)/GEN refinement of energies at critical points and other PES points of interest. The unscaled MP2/GEN computed vibrational spectra provided insight into sorting of the fundamental vibrations of TRN(OH) and TRN(OD) from the numerous binary (and occasional ternary) overtone and combination transitions resolved in the Ne matrix-isolation IR spectra [24, 34]. Rostkowska et al. [94] recently reported a normal mode analysis for the TRN monomer, and Wjcik et al. [95] studied normal modes of the dimer along with IR and Raman spectra of polycrystalline tropolone. To interpret the observed broadening of the OH absorption, they applied a model coupling the low frequency inter- and intramolecular O_O stretching modes to the OH and OD stretching vibrations. The MP2/GEN optimized minimum energy path (MEP) [86] was found to be very long and to reach C2v geometry at a high energy PES bifurcation point – the source of the energy ridge that divides the tautomers and hosts C2v SP configura-
23
24
1 Coherent Proton Tunneling in Hydrogen Bonds
, Skeletal displacement ∆S(skel), A o
Figure 1.6 Dependence of the 1D potential energy function for OH stretching on the skeletal geometry [86]. PEFs are shown for the localized OH at the tautomer configurations, and for the delocalized H at the intermediate C2v saddle-point configuration of the C7H5O2
skeleton. Plotted as a function of the skeletal displacement DS(skel) (see also Fig. 1.7), the OH stretching eigenvalues E1 and E2 show an avoided crossing symbolized by dots between the levels correlated in the present figure.
tions. At geometries near the tautomer minima the H atom is found to be localized to one O atom as suggested in Fig. 1.6. The figure shows that with contortion of the 14-atom C7H5O2 skeleton to C2v configurations on the energy ridge the OHstretching PEF is transformed into an equal double-minimum function allowing full delocalization of the H atom. The contortional displacement coordinate thus “vibrationally assists” H tunneling in S0 tropolone which, in turn, allows completion of the skeletal tautomerization. The first examinations of this dynamical model are being made at the lowest possible descriptive level: informal adiabatic separation of the fast OH stretching and slow skeletal contortion motions, with quasiharmonic separation of the other 37 vibrations. Despite the disregarded kinetic and potential energy couplings, the informally separated 1D equations allow key features of the tunneling behavior to be outlined and compared with experimental data. The quasiharmonic vibration spectrum is computed at the MP2/GEN level. The 1D OH stretching PEF (Fig. 1.6) is computed using MP4/GEN input points and its vibrational energies are solved numerically. The 1D PEF for the contortion is given quadratic-quartic-Gaussian functionality anchored by MP4/GEN level critical point energies supplemented with the 37 MP2/GEN computed quasiharmonic ZP or excited vibrational energies – and the numerically calculated, geometry-dependent, OH stretching vibrational energy. The Gaussian functionality of the PEF interpolates the vibrational energy contribution between the SP and tautomer geometries. The effective PEF for the tautomerization coordinate depends on the other-coordinate vibrational state. The state-specific ZP contortion levels in the upper and lower vibrational states of the spectroscopic transitions give first estimates for the spectral doublet separations as illustrated for an out-of-plane mode mX in Fig. 1.7.
1.3 Coherent Tunneling Phenomena in Tropolone
νx Vibration X contortion PEF Excited state splitting
νx ZP contortion PEF
Contortion vibration 37
Figure 1.7 Vibrational state-specific effective potential energy functions for the skeletal contortion vibration [86]. Transitions at 754, 743.3 cm–1 for TRN(OH) isolated in a Ne matrix are assigned as the spectral doublet, and D37 is the upper state splitting, of the m37
contortion vibration. The spectral doublet for a vibration mX, for example the CCOH torsion in Fig. 1.4, has the upper state vibrational state-specific tunneling splitting DX. The spectral doublet components have the separation DSX = |DX – D0|.
The model [34–36, 39, 86], labeled the {tunneling skeleton}{tunneling H atom} [TSTH] model for convenience, closely approximates the frequencies and doublet separations of the contortion fundamental as observed in Ne matrix isolation at 754, 743.4 cm–1 for TRN(OH) and 751, 741.4 cm–1 for TRN(OD). Peaks assigned to the higher – but not the lower – frequency component are discerned in the complex IR absorption profiles of gaseous TRN(OH). The observed 18O isotope shifts, 3.3 cm–1 for 16,18TRN(OH) and 6.9 cm–1 for 18,18TRN(OH), are reproduced by the TSTH model. The MP2/GEN isotope shifts for the 754 cm–1 transition, if treated as a quasiharmonic mode, are about twice these values. The contortional reduced mass values are determined as 16,16l = 7.25, 16,18l = 7.32, and 18,18l = 7.37 amu, and these values also correlate the observed 18O effects on the tunneling splittings for the COH torsion fundamental shown for 16,16TRN(OH) in Fig. 1.4. The TSTH model approximates the frequencies and small tunneling splittings of the OH(OD) stretching fundamentals observed in Ne matrix isolation at 3121,
25
26
1 Coherent Proton Tunneling in Hydrogen Bonds
3102 cm–1 for TRN(OH) and 2344.8, 2340 cm–1 for TRN(OD). The successful computation of the OH and OD stretching frequencies depends on a curve-hopping at the major avoided crossing point lying in plots of the OH and OD stretching energies versus contortional displacement. Additional support for the TSTH model is discussed in the articles [34–36, 39, 86]. Spectroscopic experiments pending for tropolone include comprehensive high resolution FTIR spectra for TRN(OD) and its 18O isotopomers – plus extension of the spectral range to the 300 cm–1 region for all TRN isotopomers.
1.4 Tropolone Derivatives
Sekiya and his collaborators [44–48] found spectral doublets in the S1–S0 excitation and dispersed fluorescence spectra of jet-cooled halotropolones that are modifications of the basic coherent tunneling splittings observed for TRN(OH) and TRN(OD). The symmetrical chlorotropolones showed enhancements of the specTab. 1.4 Tunneling splittings (cm–1) in the chlorotropolones and bromotropolones [48].
|Dv ¢ – D0†|
Molecule 000
2602
2604
1401
TRN(OH)
19
7
4
30
5-chloro-TRN(OH)
23
4
£1
21
3,7-dichloro-TRN(OH)
45
7
£1
53
3,5,7-trichloro-TRN(OH)
31
25
12
38
5-bromo-TRN(OH)
16
6
3
13[a]
3,7-dibromo-TRN(OH)
£1 £1
11
TRN(OD)
2
£1
5-chloro-TRN(OD)
2
£1
3,7-dichloro-TRN(OD)
8
1
£1
6
3,5,7-trichloro-TRN(OD)
4
2
2
6
5-bromo-TRN(OD)
2
£1
3,7-dibromo-TRN(OD)
£1
a This 1401 transition is only tentatively assigned.
1.5 Concluding Remarks
tral doublets for the S1–S0 origin bands, while the bromotropolones showed damping. Spectral doublets are absent for the jet-cooled asymmetrical molecules because there is a large asymmetry offset of the energy minima of the double-well PESs [47]. Observations for the ZP, out-of-plane deformation, and nominal O_O stretching spectral doublets are shown in Table 1.4 [48]. The less pronounced consequences on the effective PESs, vibrational spectral doublets, and symmetries arising through the deuteration of the 3-, 4-, and 5- positions have been presented [41, 96]. The couplings between the OH_O and -NH2 groups of the 5-amino-tropolone molecule have been of experimental and theoretical interest [52]. In part this is because the –NH2 in the S0 state may be pyramidal, and in the S1 state it may be planar. The 5-hydroxy-tropolone molecule is planar with an asymmetric doubleminimum PES, and part of its interest resides in the possibility of driving the tropolone tautomerization by laser pumping of the C(5)OH torsion vibration [49, 50, 97]. In the lowest energy configuration the two OH bonds point in opposing directions. Resolved spectral tunneling structures similar to those of the parent TRN(OH) and TRN(OD) molecules are observed for the aforementioned molecules, as well as others: 5-methyl-tropolone [53, 54], isopropyltropolones [55], and 5-phenyl-tropolone [56–57]. The effects of coupling the OH_O coordinates to the methyl internal rotation, or of coupling them to the low frequency phenyl torsional motions, are of interest.
1.5 Concluding Remarks
The zero-point tunneling splittings of S0 malonaldehyde, D0 = 21.583 cm–1, and S0 tropolone, D0 = 0.974 cm–1, plus values for S0 MA isotopomers, are accurately known. The ZP splitting for TRN(OH) in the ffi 1B2 (p*–p), S1, state is 19.846 cm–1 and that for MA(OH) in the ffi 1B1 (p*–n), S1, state is ~ 2.5 cm–1. A sizeable array of less precise vibrational state specific tunneling splittings is known for S0 and S1 TRN(OH). For S0 MA(OH) this type of experimental evidence includes the value D6 = 21.55 cm–1 for m6 at 1594 cm–1, several small doublet separations DSV ~ 0 cm–1 implying DV ~ D0 in the midrange region, and doublet separations DSV = |DV – D0| of several cm–1 for each of the four fundamentals below 600 cm–1. Spectral evidence clearly defining the splitting behavior and couplings for H motions in the OHO group of MA(OH) have not yet been recognized. The IR spectrum of S0 TRN shows clear-cut tunneling doublets in the region below 950 cm–1, evidence for small splittings in the midfrequency range, and DS = 19(5) cm–1 for OH(OD) stretching. All in all, the evidence supporting state-specific coherent tunneling behavior in these molecules is very strong and future experimental work can be expected to provide many accurately measured data points fully amenable to discriminating interpretive models and the discovery of novel intramolecular phenomena. Experimental effort, including overtone and combination spectra, clarifying the dynamical behavior of the OHO modes is a priority
27
28
1 Coherent Proton Tunneling in Hydrogen Bonds
need. The ZP D0 values for the S0 MA and TRN isotopomers are reasonably reproduced by several different semiclassical and ab initio quantum chemical methods – in some cases remarkably well. The extant work shows the ZP tunneling splittings are very sensitive to the quality of the utilized ab initio input PES, and the scatter of results among the method-dependent computed splitting behavior verifies this is true for all energy states. The developments for coordinate systems and coordinate transformations for the kinetic and potential energy operators are well advanced and several full (21D) dimensional computations have been published for MA. The theoretical models use low-dimensioned reaction surface analysis for the large amplitude motions. PES expansions for the remaining orthogonalized, presumably tunneling inert, “bath” modes are truncated at the quadratic, and for some models the quartic, terms. It is important to have accurately computed energy values at distances well out from the expansion points, and the “Morsification” of the stretching coordinate expansions is an approach under examination [98]. Strong promoting modes for H tunneling are found to be sparse. The OH stretching PEF for S0 TRN shown in Fig. 1.6 is an example with pronounced behavior of a type proposed for consideration of an enzyme–substrate complex [99]. Effects of the strong resonance couplings arising in some PES versions [61] are duly noted.
Acknowledgments
The author is very grateful for the help of T. E. Redington with this chapter.
References
References 1 Y. Cha, C. J. Murray, J. P. Klinman,
Science 1989, 243, 1325. 2 T. Jonsson, M. H. Glickman, S. J. Sun, J. P. Klinman, J. Am. Chem. Soc. 1996, 118, 10319. 3 A. Kohen, R. Cannio, S. Bartolucci, J. P. Klinman, Nature 1999, 399, 496. 4 M. J. Knapp, J. P. Klinman, Eur. J. Biochem. 2002, 269, 3113. 5 J. Basran, M. J. Sutcliffe, N. S. Scrutton, Biochemistry 1999, 38, 3218. 6 M. J. Sutcliffe, N. S. Scrutton, Eur. J. Biochem. 2002, 269, 3096. 7 D. Antoniou, S. Caratzoulas, C. Kalyanaraman, J. S. Mincer, S. D. Schwartz, Eur. J. Biochem. 2002, 269, 3103. 8 P. S. Zuev, R. S. Sheridan, T. V. Albu, D. G. Truhlar, D. A. Hrovat, W. T. Borden, Science 2003, 299, 867. 9 W. F. Rowe Jr., R. W. Duerst, E. B. Wilson, J. Am. Chem. Soc. 1976, 98, 4021. 10 S. L. Baughcum, R. W. Duerst, W. F. Rowe, Z. Smith, E. B. Wilson, J. Am Chem. Soc. 1981, 103, 6296. 11 P. Turner, S. L. Baughcum, S. L. Coy, Z. Smith, J. Am. Chem. Soc. 1984, 106, 2265. 12 S. L. Baughcum, Z. Smith, E. B. Wilson, R. W. Duerst, J. Am. Chem. Soc. 1984, 106, 2260. 13 D. W. Firth, K. Beyer, M. A. Dvorak, S. W. Reeve, A. Grushow, K. R. Leopold, J. Chem. Phys. 1991, 94, 1812. 14 T. Baba, T. Tanaka, I. Morino, K. M. T. Yamada, K. Tanaka, J. Chem. Phys. 1999, 110, 4131. 15 Z. Smith, E. B. Wilson, R. W. Duerst, Spectrochim. Acta, Part A 1983, 39, 1117. 16 C. J. Seliskar, R. E. Hoffman, J. Mol. Spectrosc. 1982, 96, 146. 17 D. W. Firth, P. F. Barbara, H. P. Trommsdorff, Chem. Phys. 1989, 136, 349. 18 T. Chiavassa, P. Roubin, L. Pizzala, P. Verlaque, A. Allouche, F. Marinelli, J. Phys. Chem. 1992, 96, 10659. 19 C. Duan, D. Luckhaus, Chem. Phys. Lett. 2004, 391, 129.
20 C. J. Seliskar, R. E. Hoffman, J. Mol.
Spectrosc. 1981, 88, 30. 21 A. A. Arias, T. A. W. Wasserman,
P. H. Vaccaro, J. Chem. Phys. 1997, 107, 5617. 22 A. C. P. Alves, J. M. Hollas, Mol. Phys. 1972, 23, 927. 23 A. C. P. Alves, J. M. Hollas, Mol. Phys. 1973, 25, 1305. 24 R. L. Redington, T. E. Redington, J. Mol. Spectrosc. 1979, 78, 229. 25 R. Rossetti, L. E. Brus, J. Chem. Phys. 1980, 73, 1546. 26 Y. Tomioka, M. Ito, N. Mikami, J. Phys. Chem. 1983, 87, 4401. 27 A. C. P. Alves, J. M. Hollas, H. Musa, T. Ridley, J. Mol. Spectrosc. 1985, 109, 99. 28 R. L. Redington, Y. Chen, G. J. Scherer, R. W. Field, J. Chem. Phys. 1988, 88, 627. 29 R. L. Redington, R. W. Field, Spectrochim. Acta, Part A 1989, 45, 41. 30 H. Sekiya, Y. Nagashima, Y. Nishimura, Bull. Chem. Soc. Jpn. 1989, 62, 3229. 31 H. Sekiya, Y. Nagashima, Y. Nishimura, J. Chem. Phys. 1990, 92, 5761. 32 K. Tanaka, H. Honjo, T. Tanaka, H. Kohguchi, Y. Ohshima, Y. Endo, J. Chem. Phys. 1999, 110, 1969. 33 R. K. Frost, F. C. Hagemeister, C. A. Arrington, T. S. Zwier, K. D. Jordan, J. Chem. Phys. 1996, 105, 2595. 34 R. L. Redington, T. E. Redington, J. M. Montgomery, J. Chem. Phys. 2000, 113, 2304. 35 R. L. Redington, R. L. Sams, J. Phys. Chem. A 2002, 106, 7494. 36 R. L. Redington, R. L. Sams, Chem. Phys. 2002, 283, 135. 37 A. E. Bracamonte, P. H. Vaccaro, J. Chem. Phys. 2003, 119, 997. 38 A. E. Bracamonte, P. H. Vaccaro, J. Chem. Phys. 2004, 120, 4638. 39 R. L. Redington, T. E. Redington, T. A. Blake, R. L. Sams, T. J. Johnson, J. Chem. Phys. 2005, 122, 224311. 40 H. Sekiya, Y. Nagashima, Y. Nishimura, Chem. Phys. Lett. 1989, 160, 581. 41 H. Sekiya, Y. Nagashima, T. Tsuji, Y. Nishimura, A. Mori, H. Takeshita, J. Phys. Chem. 1991, 95, 10311.
29
30
1 Coherent Proton Tunneling in Hydrogen Bonds 42 H. Sekiya, K. Sasaki, Y. Nishimura,
Z.-H. Li, A. Mori, H. Takeshita, Chem. Phys. Lett. 1990, 173, 285. 43 R. L. Redington, T. E. Redington, M. A. Hunter, R. W. Field, J. Chem. Phys. 1990, 92, 6456. 44 H. Sekiya, K. Sasaki, Y. Nishimura, A. Mori, H. Takeshita, Chem. Phys. Lett. 1990, 174, 133. 45 T. Tsuji, H. Sekiya, Y. Nishimura, A. Mori, H. Takeshita, J. Chem. Phys. 1991, 95, 4801. 46 T. Tsuji, H. Sekiya, Y. Nishimura, R. Mori, A. Mori, H. Takeshita, J. Chem. Phys. 1992, 97, 6032. 47 T. Tsuji, H. Sekiya, S. Ito, H. Ujita, M. Habu, A. Mori, H. Takeshita, Y. Nishimura, J. Chem. Phys. 1993, 98, 6571. 48 H. Sekiya, T. Tsuji, S. Ito, A. Mori, H. Takeshita, Y. Nishimura, J. Chem. Phys. 1994, 101, 3464. 49 F. A. Ensminger, J. Plassard, T. S. Zwier, S. Hardinger, J. Chem. Phys. 1995, 102, 5260. 50 R. K. Frost, F. Hagemeister, D. Schleppenbach, G. Laurence, T. S. Zwier, J. Phys. Chem. 1996, 100, 16835. 51 T. Tsuji, H. Hamabe, Y. Hayashi, H. Sekiya, A. Mori, Y. Nishimura, J. Chem. Phys. 1999, 110, 966. 52 F. A. Ensminger, J. Plassard, T. S. Zwier, J. Phys. Chem. 1993, 97, 4344. 53 K. Nishi, H. Sekiya, H. Kawakami, A. Mori, Y. Nishimura, J. Chem. Phys.1998, 109, 1589. 54 K. Nishi, H. Sekiya, H. Kawakami, A. Mori, Y. Nishimura, J. Chem. Phys. 1999, 111, 3961. 55 H. Sekiya, H. Takesue, Y. Nishimura, Z-H. Li, A. Mori, H. Takeshita, J. Chem. Phys. 1990, 92, 2790. 56 T. Tsuji, Y. Hayashi, H. Sekiya, H. Hamabe, Y. Nishimura, H. Kawakami, A. Mori, Chem. Phys. Lett. 1997, 278, 49. 57 T. Tsuji, Y. Hayashi, H. Hamabe, H. Kawakami, A. Mori, Y. Nishimura, H. Sekiya, J. Chem. Phys. 1999, 110, 8485. 58 P. R. Bunker, P. Jensen, Molecular Symmetry and Spectroscopy, 2nd Edn., NRC Research Press, Ottawa 1998.
59 S. F. Tayyari, F. Milani-Nejad, Spectro-
chim. Acta, Part A, 1998, 54, 255. 60 A. Alparone, S. Millefiori, Chem. Phys.
2003, 290, 15. 61 V. A. Benderskii, E. V. Vetoshkin,
I. S. Irgibaeva, H. P. Trommsdorff, Chem. Phys. 2000, 262, 393. 62 T. D. Sewell, Y. Guo, D. L. Thompson, J. Chem. Phys. 1995, 103, 8557. 63 R. Meyer, T.-K Ha, Mol. Phys. 2003, 101, 3263. 64 D. P. Tew, N. C. Handy, S. Carter, Mol. Phys. 2004, 102, 2217. 65 T. Carrington, W. H. Miller, J. Phys. Chem. 1986, 84, 4364. 66 N. Shida, P. F. Barbara, J. E. Almlf, J. Chem. Phys. 1989, 91, 4061. 67 K. Yagi, G. V. Mil’nikov, T. Taketsugu, K. Hirao, H. Nakamura, Chem. Phys. Lett. 2004, 397, 435. 68 Z. Smedarchina, W. Siebrand, M. Z. Zgierski, J. Chem. Phys. 1995, 103, 5326. 69 K. Giese, O. Khn, J. Chem. Phys. 2004, 120, 4107. 70 N. DoÐlic, O. Khn, Z. Phys. Chem. 2003, 217, 1507. 71 C. S. Tautermann, A. F. Voegele, T. Loerting, K. R. Liedl, J. Chem. Phys. 2002, 117, 1962. 72 V. Barone, C. Adamo, J. Chem. Phys. 1996, 105, 11007. 73 S. Sadhukhan, D. Mu oz, C. Adamo, G. E. Scuseria, Chem. Phys. Lett. 1999, 306, 83. 74 K. Yagi, T. Taketsugu, K. Hirao, J. Chem. Phys. 2001, 115, 10647. 75 N. Makri, W. H. Miller, J. Chem. Phys. 1989, 91, 4026. 76 M. D. Coutinho-Neto, A. Viel, U. Manthe, J. Chem. Phys. 2004, 121, 9207. 77 G. V. Mil’nikov, H. Nakamura, J. Chem. Phys. 2001, 115, 6881. 78 G. V. Mil’nikov, K. Yagi, T. Taketsugu, H. Nakamura, K. Hirao, J. Chem. Phys. 2004, 120, 5036. 79 D. P. Tew, N. C. Handy, S. Carter, S. Irle, J. Bowman, Mol. Phys. 2003, 101, 2513. 80 L. M. Jackman, J. C. Trewella, R. C. Haddon, J. Am. Chem. Soc. 1980, 102, 2519. 81 N. Makri, W. H. Miller, J. Chem. Phys. 1987, 86, 1451.
References 82 R. L. Redington, T. E. Redington,
J. Chem. Phys. 2005, 122, 124304. 83 M. J. Wjcik, H. Nakamura, S. Iwata, T. Wiktor, J. Chem. Phys. 2000, 112, 6322 84 H. Shimanouchi, Y. Sasada, Acta. Crystallogr. Sect. B, 1973, 29, 81. 85 H. F. Hameka, J. R. de la Vega, J. Am. Chem. Soc. 1984, 106, 7703. 86 R. L. Redington, J. Chem. Phys. 2000, 113, 2319. 87 M. V. Vener, S. Scheiner, N. D. Sokolov, J. Chem. Phys. 1994, 101, 9755. 88 Z. Smedarchina, W. Siebrand, M. Z. Zgierski, J. Chem. Phys. 1996, 104, 1203. 89 S. Takada, H. Nakamura, J. Chem. Phys. 1995, 102, 3977. 90 J. J. Paz, M. Moreno, J. M. Lluch, J. Chem. Phys. 1995, 103, 353.
91 Y. Guo, T. D. Sewell, D. L. Thompson,
J. Phys. Chem. A 1998, 102, 5040. 92 K. Giese, O. Khn, preprint. 93 C. S. Tautermann, A. F. Voegele,
T. Loerting, K. R. Liedl, J. Chem. Phys. 2002, 117, 1967. 94 H. Rostkowska, L. Lapinski, M. J. Nowak, L. Adamowicz, Int. J. Quant. Chem. 2002, 90, 1163. 95 M. J. Wjcik, M. Boczar, M. Stoma, Int. J. Quant. Chem. 1999, 73, 275. 96 J. J. Paz, M. Moreno, J. M. Lluch, Chem. Phys. 1999, 246, 103. 97 J. J. Nash, T. S. Zwier, K. S. Jordan, J. Chem. Phys. 1995, 102, 5360. 98 R. Burcl, S. Carter, N. C. Handy, Chem. Phys. Lett. 2003, 373, 357. 99 A. Kohen, J. P. Klinman, Chem. Biol. 1999, 6, R191.
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2 Coherent Proton Tunneling in Hydrogen Bonds of Isolated Molecules: Carboxylic Dimers Martina Havenith
2.1 Introduction
Due to the exceptional importance of hydrogen bonds in biology and chemistry the detailed investigation of their structure and dynamics has attracted the attention of several experimental and theoretical groups. Laser spectroscopic measurements and quantum mechanical calculations have led, in recent years, to remarkable progress towards the detailed understanding of important prototype systems such as (NH3)2 [1], (H2O)2 [2], and DNA base pairs [3]. Double hydrogen bonded systems play a crucial role in that they serve as model systems for the understanding of DNA base pairs. Proton transfer is of fundamental interest for biology as well as being a fundamental reaction in chemistry [4, 5]. Moreover, multiple-proton transfer in hydrogen bonded systems is one of the most fundamental processes in biology and chemistry. It governs oxidation– reduction reactions in many chemical and biological reactions [6]. In proton pumping mechanisms of trans membrane proteins protons are transported across the membrane by subsequent proton transfer. These reactions may incorporate strong quantum effects due to the low mass of the proton. The observation of pronounced isotopic effects is taken as an indication of a strong tunneling contribution. In contrast, the classical transmission probability is zero as long as the energy of the particle is lower than the barrier height (V‡) and is equal to 1 if the energy (E) exceeds this. For an ensemble at temperature T this leads to the well known Arrhenius equation for the reaction rate which is proportional to exp (–(E – V‡)/ kT). The transmission will, therefore, depend solely on the barrier height and not on the width or on the exact shape of the transition barrier. Isotopic substitution will shift the zero point energies relative to the transition barrier and will, therefore, lead to a change in the reaction constant. Quantum mechanical tunneling is a result of the wavelike nature of particles which allows transmission through a reaction barrier. The quantum mechanical transmission probability for energies below V‡ is governed by tunneling and reflection at the barrier. The transmission is larger than zero even well below the barrier and will depend crucially on the barrier width. In Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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2 Coherent Proton Tunneling in Hydrogen Bonds of Isolated Molecules: Carboxylic Dimers
the WKB approximation for 1-dim potentials the quantum mechanical transmission coefficient can be approximated by R a pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi PðEÞ ¼ exp 1=" a 2lðVa ðxÞ EÞdx
(1)
with a, Va and E corresponding to the classical turning points, the adiabatic barrier and the energy, respectively. This yields an exponential dependence on the reduced mass characterizing the tunneling motion. The weighting function for the contribution of thermally populated states is described by a Boltzmann distribution ( exp (–E/kT)). When raising the temperature, over barrier processes become more and more feasible, implying that tunneling becomes less important.
2.2 Quantum Tunneling versus Classical Over Barrier Reactions
Recently, a controversial debate has arisen about whether “the optimization of enzyme catalysis may entail the evolutionary implementation of chemical strategies that increase the probability of tunneling and thereby accelerate reaction rates” [7]. Kinetic isotope effect experiments have indicated that hydrogen tunneling plays an important role in many proton and hydride transfer reactions in enzymes [8, 9]. Enzyme catalysis of horse liver alcohol dehydrogenase may be understood by a model of vibrationally enhanced proton transfer tunneling [10]. Furthermore, the double proton transfer reaction in DNA base pairs has been studied in detail and even been hypothesized as a possible source of spontaneous mutation [11–13]. For identification and understanding of the hydrogen transfer mechanism the nature of transfer has been the subject of several studies either supporting [14, 15] or questioning [16] the above hypothesis. Several criteria were raised to test the dominant contribution for enzyme catalyzed reactions [17], such as: 1. The elevated primary isotope kinetic isotope effect (KIE) (with the ratio of the rate constants kH/kD being larger than 8.9 at 20 C) 2. A large difference in the activation energy for the different isotopes 3. A small ratio of the pre-exponential Arrhenius factors (AH/AD<0.7) 4. The Swain Schaad relationship which yields boundaries for the ratios of the rate constants for the primary kinetic isotope effects for H, D and T with deviations being interpreted as evidence of tunneling. However, one has to point out that in a very recent theoretical study by Tautermann et al. [17] all these criteria are found to be inadequate to predict the domi-
2.3 Carboxylic Dimers
nant contribution of tunneling for a small benchmark system such as formic acid dimer. In order to distinguish between the different contributions a comparison with sophisticated theoretical calculations is mandatory. However, it is necessary to test these models on small prototype systems. High resolution gas phase spectroscopy can now provide exact experimental data on proton transfer tunneling and thereby allow a test of tunneling criteria which could be used for more complex systems. Gas phase experiments are ideally suited for this since the perturbations induced by the local environment are completely eliminated, providing an ideal tool for exact measurements. Studies of coherent proton transfer of isolated molecules in the gas phase are able to yield absolute numbers on proton transfer tunneling without being influenced by solvent effects or the interaction of a crystal surrounding. Moreover, high resolution spectroscopy can yield state specific tunneling frequencies. These studies allow direct comparison with the results of ab initio studies and will therefore provide a sensitive test for recently developed theoretical methods. In summary, direct measurements of proton transfer tunneling in double hydrogen bonded dimer complexes in the gas phase are therefore of great interest.
2.3 Carboxylic Dimers
Carboxylic dimer systems are well suited to a study of coherent proton tunneling processes since they provide two identical hydrogen bonds. For the most stable of these, such as formic acid dimer or benzoic acid dimmer, the displacement of the protons can be well described by a double well potential. The barriers are high compared to the zero point energy, since these species are bound by two cooperatively strengthened OH O ¼ C hydrogen bonds. Quantum mechanically, the two protons which are involved in the hydrogen bonds can tunnel, even if the transition barrier is much higher than their kinetic energy. It is a point of discussion whether the coherent proton transfer can be described as a synchronous concerted double proton transfer or whether an asynchronous movement such as a step by step process will give an adequate picture. Most theoretical calculations propose a synchronous concerted proton transfer process for the carboxylic dimers, as is displayed in Fig. 2.1, where the two monomers first approach each other before tunneling can occur. The proton transfer gives rise to a splitting of each rotational–vibrational state into two states (El and Eu) which are separated by DE = hmtunneling with mtunneling describing the tunneling frequency for double proton transfer. Correspondingly, the proton transfer time s is related to the tunneling splitting mtunneling by: s = 1/(2mtunneling) [18]. Spectroscopically, tunneling will manifest itself in a doubling of the observed vibrational–rotational transitions. In the case of finite barriers the wave function
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2 Coherent Proton Tunneling in Hydrogen Bonds of Isolated Molecules: Carboxylic Dimers
of the upper and lower tunneling states can be described by the following wave functions: pffiffiffi pffiffiffi wl= 1/ 2 (wL + wR) and wu= 1/ 2 (wL – wR).
The wave functions wL and wR describe the dimer in one of the double minima (with R and L standing for right or left, respectively). The tunneling splitting DE depends sensitively on the barrier height Vbarrier and on the barrier width. For carboxylic acid dimers the tunneling process cannot be described by a 1-dimensional coordinate but has to be described on a multidimensional potential energy surface. Obviously, the proton is not localized, so the effective barrier and thus the tunneling splitting will depend crucially on the part of the potential surface which has been sampled by the wave function during the optimal tunneling path. In a publication by Tautermann et al. [19], a semiclassical method was used to predict the energy barriers and the tunneling splittings of the numerous carboxylic acid dimers, such as formic acid dimer, benzoic acid dimer, carbamic acid dimer, fluoro acid dimer, carbonic acid dimer, glyoxylic acid dimer, acrylic acid dimer and N,N-dimethyl carbamic acid dimer and their deuterated analogs. The calculated
C2h
D2h
C2h
Figure 2.1 Tunneling motion in carboxylic dimer. The equilibrium structure corresponds to C2h symmetry. In the transition state the dimer resembles D2h symmetry.
2.3 Carboxylic Dimers
barrier heights vary from 6.3 to 8.8 kcal mol–1. The lowest barrier was found for carbamic acid dimer derivatives and the largest for the formic acid dimer, which was explained by a mesomeric stabilization of the transition state being completely missing for the formic acid dimer. For formic acid dimer, benzoic acid dimer, carbamic acid dimer, fluoro acid dimer and N,N-dimethyl carbamic acid dimer the proton transfer occurs from global minimum to global minimum and can be described by a double well potential, such as is displayed in Fig. 2.1. For glyoxylic acid dimer, acrylic acid and carbonic acid dimer the global minimum corresponds to a trans symmetry, as defined by the C2 = O groups for the first two. In the case of a double proton transfer the final configuration differs from the initial structure for these dimers and corresponds to an energetically higher state. Hence, no ground state tunneling splitting is expected. Only the energetically less stable cis conformers are expected to show a detectable tunneling splitting. The calculated tunneling splitting along the most probable tunneling path varies from 0.00053 cm–1 for fluoro acid dimer to 0.13 cm–1 for N,N-dimethyl carbamic acid dimer [19]. The variation was attributed to different barrier heights (smallest for N,N-dimethyl carbamic acid dimer) and, for equal barrier heights such as for formic acid dimer and fluoro acid dimer, to differences in the length of the most probable tunneling path. The most recent calculations on the tunneling dynamics of double proton transfer in formic acid dimer and benzoic acid dimers have been reported by Smedarchina et al. [20]. They used direct dynamics calculations to predict the tunneling splittings of both carboxylic dimers. The corresponding ground state tunneling splitting was predicted to be 441 MHz (0.015 cm–1) for (DCOOH)2 and 1920 MHz (0.064 cm–1) for benzoic acid dimer. The increased splitting in the benzoic acid dimer is attributed to the stronger hydrogen bonding in the benzoic compared to the formic acid dimer. With the tunneling splitting being very small, sophisticated high resolution spectroscopy techniques are required for an exact determination of this fundamental quantity. Whereas microwave spectroscopy has been proven to provide the ultimate frequency resolution, it is not suited to a study of cyclic carboxylic dimers since – due to their inherent symmetry – they have no permanent dipole moment. Therefore, the only spectroscopically accessible transitions are vibration–rotation– tunneling transitions in the infrared spectral region. For aromatic dimers such as benzoic acid dimer electronic–vibrational–rotational–tunneling transitions in the optical or ultraviolet spectral region are also accessible. The exact determination of such a small splitting requires molecular beam techniques. The molecules are cooled in a supersonic expansion which leads to a population distribution among the rotational states corresponding to a Boltzmann distribution with 10–12 K. This leads to a considerable reduction of populated states and thereby to a simplification of the spectrum. In a supersonic expansion we find a considerable decrease in the line width due to the decrease in translational motion, especially when the laser is perpendicular to the expansion direction. The corresponding reduction in Doppler width allows an improved frequency resolution, which will later be shown to be crucial for the success of the experiment.
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2 Coherent Proton Tunneling in Hydrogen Bonds of Isolated Molecules: Carboxylic Dimers
In the following we will present the results for two benchmark systems, the benzoic acid dimer and the formic acid dimer, which have been extensively studied in the past, both experimentally and theoretically. The study of these dimers in the gas phase allows a direct comparison between them.
2.4 Benzoic Acid Dimer 2.4.1 Introduction
Benzoic acid dimer was the first carboxylic dimer to be investigated in detail spectroscopically. The first studies involved the measurements of temperature dependent relaxation times via NMR. Due to the presence of two inherent chromophores it can also be investigated by means of optical spectroscopy. The benzoic acid dimer is stabilized by two hydrogen bonds, with the two monomers being coplanar in the electronic ground state [21]. The proton transfer is shown to strongly couple to the heavy nuclei, implying that the whole benzoic acid frame rearranges itself slightly as the protons tunnel. 2.4.2 Determination of the Structure
X-ray structural studies showed that benzoic acid dimers crystallize in a monoclinic cell with the hydrogens aligned close to the crystallographic c-axis [22]. Time of flight neutron diffraction measurements were carried out by Brougham et al. [23] and these yielded the crystal structure of a deuterated benzoic acid. The structure of the monomer units is assumed to be unchanged upon complexation. Remmers et al. measured the high resolution spectrum of benzoic dimer in the UV excitation spectrum of the S1‹S0 transition and were able to deduce rotational constants for the ground and electronically excited states [24]. When assuming that the monomer structure remains unchanged upon complexation, the value of the intermolecular distance r and the geometry of the two monomers with respect to each other could be deduced. The value of r = 3.622 – 0.147 (r describing the distance from the center of mass of the monomer unit to the center of rotation) was found to be in good agreement with the previously determined O O distance of 3.58 , as was deduced by Brougham et al. [23]. For the ground state a planar linear structure was anticipated. For the excited state a more bent structure was proposed, with the best agreement being for a bending angle of a = 3.4 (with a describing the angle between the longitudinal axis of the dimer and that of the monomer unit) and a reduced intermolecular distance of r = 3.6 . This structural change can be explained by the fact that the electronic excitation reduces the acidity of the monomer so that the two hydrogen bonds will no longer be equivalent [20].
2.4 Benzoic Acid Dimer
2.4.3 Barriers and Splittings
All theoretical studies on benzoic acid dimer underlined the need for a multidimensional potential surface. These studies have investigated the temperature dependence of the transfer process: They included a density matrix model for hydrogen transfer in the benzoic acid dimer, where bath induced vibrational relaxation and dephasing processes are taken into account [25]. Sakun et al. [26] have calculated the temperature dependence of the spin–lattice relaxation time in powdered benzoic acid dimer and shown that low frequency modes assist the proton transfer. At high temperatures the activation energy was found to be 2.3 kcal mol–1. The same assisted proton transfer was found in calculations of the synchronous proton transfer in benzoic acid crystal by Antoniou and Schwarz [27]. It was shown, that for benzoic acid dimer a coupling to the low frequency intramolecular modes will lower the effectively required activation energy. In all these calculations it was found that although the activation energy seems to be rather low, which might support the occurrence of classical over barrier reactions, the actual process is, however, a pure quantum mechanical tunneling process. The benzoic acid dimer has been extensively studied in various condensed phase environments where it experiences an asymmetric local environment. By doping the crystal the inherent asymmetry in the crystal was reduced. However, in general, the crystal structure and the dopant can influence the observed tunneling matrix element. From these experiments the tunneling matrix element of (dye-doped) benzoic acid was determined and was found to be relatively independent of the dopant used [28, 29]. The measured values lie between 8.4 GHz (0.28 cm–1) [28] and 6.56 GHz (0.22 cm–1) [29]. The level structure of a benzoic acid dimer tautomer state of a pair of dimers sandwiching the dye molecule will depend on three parameters: The energy difference between the two tautomer forms in the crystal, the coupling of the two dimers stabilizing the degenerate configuration, and the tunneling matrix element J. In general, all parameters will depend on the specific electronic state. It should be noted that for a free dimer and the splitting will depend only on the tunneling matrix element. In dye- (seleno indigo) doped benzoic acid crystals the energy level structure of a pair of benzoic acid dimers was measured by hole burning spectroscopy [29]. Under the assumption that the tunneling matrix element is independent of the electronic state of the guest a tunneling matrix element of 6.5 – 1.56 GHz for the benzoic acid dimer was deduced, yielding information on the proton transfer tunneling. In 2000 Remmers et al. [24] used the combination of molecular beam techniques and high resolution laser spectroscopy (inherent line width 3 MHz) to obtain the first information on proton transfer tunneling in any isolated gas phase carboxylic acid dimer. They reported the measurement of a high resolution ultraviolet spectrum of benzoic acid dimer in the gas phase. The spectra showed two
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2 Coherent Proton Tunneling in Hydrogen Bonds of Isolated Molecules: Carboxylic Dimers
complete electronic rovibrational spectra with a constant frequency separation of (1107 – 7 MHz) between both sets. The transitions are labeled as a-type (DKa = 0, DKc = 1) transitions, b-type (DKa = 1, DKc = 1) or c-type transitions depending on whether absorption of a photon involved a change in the projection of the angular momentum along the main axes of inertia which are called the a- b- or c-axes. By definition, the moments of inertia are labeled as IA, IB and IC with IA < IB < IC. For carboxylic acid dimers the a-axis corresponds to the intermolecular axis connecting the two monomers. The c-axis corresponds to the out of plane axis. The transition dipole moment lies predominantly along the b-axis, which implies that in the spectrum we find preferentially b-type transitions involving a change in the projection of the angular momentum along the a-axis: DKa = 1. After electronic excitation of one of the monomers to the electronic excited S1 state the symmetry is broken and one expects two asymmetric potential energy surfaces where the electronic excitation takes place in one of the monomers. However, since both monomers are indistinguishable, coupling by an interaction term allows the electronic excitation to be exchanged between the monomers, which leads to two symmetrical potential curves, each consisting of a double well potential. In each double well potential tunneling causes an additional tunneling splitting. As a result, we obtain a potential energy scheme as is indicated in Fig. 2.2 [24]. Allowed transitions require a change of parity. Altogether, we expect to see four transitions; two of them were assigned to correspond to the experimental data. The observed splitting was attributed to the difference between the tunneling splitting in the excited and ground states. In their analysis, Remmers et al. assumed that the splitting in the ground state amounts to 0.22 cm–1 (6500 MHz). This value corresponds to the previously determined tunneling matrix element [29]. The measured value (D = 1107 – 7 MHz), which corresponds to the difference between the tunneling splitting in the ground and excited states, would imply that the ground state tunneling splitting is larger than the splitting in the excited state
(a)
(b)
Figure 2.2 Potential energy surface of benzoic acid dimer. The ground state and electronically excited state are displayed. The potential for excitation of a single monomer (a) and after adiabatic coupling of the potential energy surface (b) are shown. This figure is adapted from Ref. [24].
2.4 Benzoic Acid Dimer
However, in general, it is expected that the tunneling splittings in the electronically excited state will be much larger than the splittings in the ground states. (E.g., in dye-doped crystals splitting in the electronic excited state exceeds the splittings in the ground state by far (35 cm–1 versus < 1 cm–1) [28].) In agreement with this expectation, Tautermann et al. predicted a tunneling splitting of 0.0022 cm–1 (6.6 MHz) for benzoic acid dimer [19]. If we assume this prediction to yield reliable predictions for the ground state of benzoic acid dimer as well (e.g. assume that the tunneling splitting of the ground state of benzoic acid dimer is of the order of 0.0022 cm–1, which is well below experimental resolution in this rather congested spectrum ) the measured splitting would have to be mainly attributed to the tunneling splitting in the excited state, which might far exceed the splitting in the ground state. The measured difference of tunneling splitting of 1107 MHz for the gas phase benzoic acid dimer would then correspond to the splitting in the excited state but would yield no further information on the tunneling splittings in the ground state. However, based upon a direct dynamical calculation, which used a potential surface for benzoic acid dimer at a B3LYP/6-31 + G(d) level [20], Smedarchina et al. suggest that the hydrogen bonding is weaker in the excited state, in agreement with the experimentally observed increase in the intermolecular distance r [24]. This weakening of the bond is expected to yield a decrease in the tunneling splitting. They conclude, therefore, that the measurements are consistent with a splitting dominated by the ground state with a small or negligible contribution from the excited state. In summary, one can state that in order to come to an unambiguous assignment, further high resolution gas phase studies which determine the ground state tunneling splitting independently would be required . 2.4.4 Infrared Vibrational Spectroscopy
Following the study of Remmers et al. a fluorescence dip spectrum of benzoic acid dimer in the gas phase has been reported by Florio et al. [30]. Using this technique, the IR spectra of three isotopomers (the undeuterated, the ring-deuterated and the mixed OH/OD ring deuterated dimer) have been recorded showing a broad substructure in the region of the O–H stretching fundamental. Using a theoretical model they were able to explain the observed features in terms of large anharmonic effects which couple the O–H stretch with combination bands of appropriate symmetry. The resulting band structure is responsible for the wide spread and the observed substructure of the O–H in the region between 2600 and 3100 cm–1. However, the influence of the intermolecular hydrogen bond vibrations in the electronic ground state, which were discussed extensively in the early theoretical papers, were found to result in negligible coupling to the O–H stretch. In a newer study the fluorescence spectrum has been reinvestigated with improved spectral resolution. Accompanying DFT calculations suggested that in the electronically excited state the low frequency modes are mixed extensively with the carboxyl as well as the aromatic ring vibrations [31]. The experimentally
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observed geometry distortion was explained as a change in the acidic character of benzoic acid in the excited state.
2.5 Formic Acid Dimer 2.5.1 Introduction
The smallest organic complex serving as the prototype for multiple-proton transfer is the formic acid dimer. Formic acid dimerizes like all carboxylic acids with two hydrogen bonds forming a planar eight-membered ring between the two monomers (Fig. 2.1). The study of the double proton transfer in the hydrogen bonded dimer of formic acid has therefore attracted the interest of theoreticians for more than 50 years. As discussed before, the tunneling frequency will depend very sensitively on the height and the width of the barrier, which implies that high quality ab initio calculations are required for an exact description of the complete potential surface. 2.5.2 Determination of the Structure
Early theoretical work on FAD was concerned with the dimer equilibrium geometry and the electronic structure (see for example Refs. [32–36]). Ab initio molecular orbital studies on the structure of formic acid dimer in 1984 agreed very well with the experimental structures as determined by electron diffraction [37]. Due to the importance of the double proton transfer of FAD as a key prototype for multiple proton transfer reactions several theoretical studies have been reviewed in the literature [38]. Rotational constants for formic acid dimer were obtained by high resolution spectroscopy of (DCOOH)2 [39] and by femtosecond degenerate four wave mixing experiments in the gas cell at room temperature and under supersonic jet experiments by Matylisky et al. [40]. The best agreement is obtained with the pure ab initio predictions by Neuheusser et al. [33] using MP2 with counterpointwise correction for basis set superposition error and a TZ2P basis set. These calculations predict an O O distance of 2.672 . DFT calculations [41] yield a smaller O O distance of 2.645 with a hence increased B-value. The MP2 calculations by Kim [42] and the extended molecular mechanics calculation slightly overestimated O O (2.707 ) thereby yielding a slightly too small B-value. The same argument holds for the results of the electron diffraction measurements which obtained an O O distance of 2.696 . These values are in reasonable agreement with the rotational constants as predicted by the potential of Yokoyama et al. [43]. They postulated a semiempirical model potential which was set up to reproduce the experimental vibrational frequencies and the bond lengths in the monomers.
2.5 Formic Acid Dimer
If we compare the structure in the MP2-study of Neuheusser with the structure as predicted by DFT [41] we see that they also differ in the position of the inner hydrogen atom (for example the angle COH). The relative changes in the rotational constant upon deuteration agree within (0.1–0.6)% when taking the structure as proposed by Hobza et al. [44]. More specifically : A comparison of the rotational constants for (HCOOH)2 by Matylitsky et al. [40] with the rotational constants from Madeja and Havenith [39] (DCOOH)2 via model structures based upon the results of ab initio calculations [44] yield an agreement within (0.1– 0.6)%. However, both sets of rotational parameters disagree with the structure as deduced by electron diffraction studies [37]. Due to the inherent experimental limitations of the electron diffraction measurements the position of the inner hydrogen is expected to be less well determined. A displacement of the inner H-atom will affect the A rotational constant, which may explain the deviation between the rotational A-constant of the gas phase measurement [39, 40] and the constants as deduced from the diffraction measurements. We suggest that the deviation between the measured rotational constants and the rotational constants as would be predicted from the structure as deduced by electron diffraction can mainly be attributed to a difference in the intermolecular distance (for example O O or O H). More specifically, the experimental changes in the rotational constants upon deuteration do not agree with the changes expected when the structure of the electron diffraction study holds. This confirms that this structure, which was obtained very early, although providing an excellent reference for the gas phase dimer structure at that time, probably suffers from the inherent problem of the exact position of the hydrogen atoms and from averaging effects due to zero point motions. 2.5.3 Tunneling Path
In 1995 Kim reported a direct dynamics calculation [42]. Their actual tunneling path is visualized in Fig. 2.1. During the proton transfer the heavy atoms move first to bring two formic acid monomers closer together, thereby decreasing the barrier for proton transfer. At the transition state the structure of formic acid dimer changes from C2h to D2h symmetry. Proton transfer gives rise to a splitting of each rotational–vibrational state separated by DE = hm. The tunneling splitting DE depends sensitively on the barrier height Vbarrier and on the barrier width. In the work by Shida et al. [45] a synchronous concerted double proton transfer is found to be the major mode of the reaction, which is confirmed in a recent molecular dynamics calculation by Wolf et al. [46]. In his molecular dynamics calculation the time evolution of the potential energy was additionally taken into account. The double proton transfer has also been investigated in a Car-Parinello ab initio molecular mechanics study by Miura et al. [41]. Quantum fluctuations are shown to cause significant deviations from the minimum energy path. While an asynchronous movement of the two protons close to the equilibrium structure was
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stated, synchronous movement becomes relevant on approaching the reaction barrier. However, in the study of Ushiyama and Takatsuka [47] the tunneling was described as a successive step by step process. In a very recent calculation by Markwick et al. targeted molecular dynamics methods were implemented in the framework of Car-Parinello molecular dynamics to study the nature of the double proton transfer [48]. They predict a concerted proton transfer reaction. In the very early stages of this reaction the system enters a vibrationally excited pretransitional state. Whereas in the global minima large amplitude fluctuations have been found in the pretransitional region, the frequency of these fluctuations is found to increase dramatically while the amplitude of the oscillation decreases when approaching the transition state. 2.5.4 Barriers and Tunneling Splittings
The reported tunneling splitting for the proton transfer in the literature covers more than four orders of magnitudes. In 1981 a paper reported double proton transfer times in formic acid dimer between 95 min and 0.3 ns [49]. More recent calculations of transit times for the proton transfer still cover more than four orders of magnitude: Chang et al. predicted a proton transfer tunneling splitting of 0.3 cm–1 corresponding to a proton transfer time of s = 55 ps [36]. In 1991 Shida, Barbara and Almlf used a reaction surface Hamiltonian to predict the proton transfer barrier for FAD [45]. Using MCPF (modified couple pair functionals) they predicted a tunneling splitting of 0.004 cm–1 (s = 4.2 ns). Molecular dynamics calculations by Ushiyama and Takatsuka [47] yielded transfer times of less than 150 fs which is 3–4 orders of magnitude faster than any of the previous calculations. It should be noted that in a paper by Vener et al. [50], using a similar approach to that of Shida et al., a tunneling splitting of 0.3 cm–1 instead of 0.004 cm–1 was calculated. Tautermann et al. [19] predict a ground state tunneling splitting of 0.0022 cm–1 for formic acid dimer (being equal to the predicted ground state tunneling splitting of benzoic acid dimer), when they apply a semiclassical method to determine the ground state tunneling splitting of various carboxylic acid derivative dimers. The energy barriers were calculated using hybrid density functional theory (B3LYP) and compared to the result of a high level method Gaussian theory (MP2). Correspondingly, the effective barrier heights and the proposed tunneling path have also varied extensively in the literature of the last decade: The reported barrier heights include 14 kcal mol–1 [32]; 7.1–9.1 kcal mol–1 [32]; 15.6 kcal mol–1 [36]; 11.8 kcal mol–1 [45]; 8.9 kcal mol–1 calculated [46], 11.5 kcal mol–1 [50] and 8.39 kcal mol–1 [19].
2.5 Formic Acid Dimer
2.5.5 Infrared Vibrational Spectroscopy
Experimentally, a very detailed spectroscopic study of carboxylic acids in the gas phase including various isotopic forms of FAD has been published by Marchal [51]. He recorded FTIR spectra in the region 500–4000 cm–1. IR band centers and relative intensities are reported. One vibrational band at 1740 cm–1 was reported for the C = O asymmetric stretch of FAD. Later, a high resolution study yielded two separate vibrational bands centered at 1738.5 and 1741.5 cm–1 [52]. However, the high density of lines did not allow a definitive assignment in this frequency range. Anomalous isotope effects in the intensities of the (mC=O) band of FAD [51] and Fourier transform (FT) studies of DCOOH [53] indicate a resonance between the C = O asymmetric stretch and combination bands, which considerably complicates the assignment of the gas phase spectrum. For (DCOOH)2 a Raman study including the IR band heads [54] is reported in the literature. There are no spectroscopic studies in the MW region due to the lack of a permanent dipole moment. The first high resolution spectroscopic measurements of FAD with fully resolved rotational–vibrational–tunneling transitions were reported by Madeja and Havenith in 2002 [39]. They measured the C–O vibrational band of (DCOOH)2 which could be analyzed in terms of an asymmetric top rigid rotor Hamiltonian. The vibrational frequency of the C–O stretch in (DCOOH)2 was determined to be 1244.8461(2) cm–1. This deviated considerably from values for the band center as given by Wachs et al. [55] (1231.85 cm–1). Previous measurements include the Raman transition as reported by Bertie et al. (1230 – 2 cm–1) [54] and the value obtained by Millikan and Pitzer (1239 cm–1) [56]. Very recently high resolution studies of (HCOOH)2 in the gas phase have also been carried out by Ortlieb and Havenith, yielding a vibrational frequency of m0 = 1225.35 cm–1. This also deviates significantly from the values of the vibrational band center (1215 cm–1) as given in the paper by Marchal [51]. The discrepancy can be explained by the fact that the vibrational band centers were determined at room temperature. In this case hot bands will contribute considerably to the observed low resolution spectrum and combination bands can also overlap with the fundamental. In consequence, both effects will shift the observed band center compared to the fundamental band. In a paper by Florio et al. [57] a theoretical modeling of the O–H stretch in carboxylic dimers was reported. In general, large anharmonic effects and Fermi coupling result in a complicated band substructure in which the O–H stretch oscillator strength is spread over hundreds of wavenumbers. This can be the reason for the observed substructure of the first excited O–H stretch of 140 cm–1 in the paper by Robertson and Lawrence. Whereas good agreement with the experimentally observed vibrational substructure of the O–H stretching infrared spectrum of benzoic acid dimer [30] was found, the agreement with the experimental cavity ring down spectrum of Ito and Nakanaga [58] was rather disappointing. A complete FTIR spectrum of formic acid in the gas phase recorded in a supersonic jet expan-
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sion with a limited experimental resolution of 0.5 cm–1 was reported by Georges et al. [59]. We further want to mention an infrared matrix isolation study of FAD in argon matrices [60]. The study of Gantenberg et al. indicates the presence of a second structure, besides the cyclic double hydrogen bonded structure, which was identified as an acyclic dimer. The special dimerization process of FAD in ultracold matrices is found to be a more general phenomenon: In 2004 the observation of the same polar acyclic single hydrogen bonded structure was reported in suprafluid liquid helium droplets, establishing the unique cluster growth process at ultracold temperatures [61]. Based upon these experimental results a new alternative dimerization mechanism, in which two formic acid monomers proceed through an acyclic dimer to the cyclic dimer in a stepwise process, has been investigated theoretically and the corresponding barrier and dissociation energy predicted [62]. 2.5.6 Coherent Proton Transfer in Formic Acid Dimer
We will now focus in this subsection on the experimental study providing accurate information on the proton transfer tunneling in isolated carboxylic acid dimers in the gas phase. In an early paper by Robertson and Lawrence [63] the tunneling splitting of the ground state was estimated to be about 6 cm–1. They assumed that the observed fine structure in the first excited O–H stretch of 140 cm–1 is attributed to the transfer tunneling splitting. However, in view of new theoretical studies and the recent experimental results [39], their conclusions were probably based on a misassignment. In order to determine exact quantitative data it is necessary to obtain high resolution spectra of the dimer. Since a resolution of £ 0.001 cm–1 is beyond the scope of FTIR spectrometers, laser spectroscopic techniques were required. This could be achieved in an IR study using sensitive absorption measurements by a lead salt diode laser. In the paper of Madeja and Havenith the observation of 409 lines in the frequency range from 1241.7 to 1250.7 cm–1 was reported. All lines could be assigned to the C–O stretch vibrational band. The splitting due to proton transfer tunneling was fully resolved (see Fig. 2.3). The frequency range from 1241.6 to 1242.6 cm–1 is displayed; it can clearly be seen that each rotational vibrational line is split into two fully resolved tunneling components. For the selection rules a planar structure showing C2h symmetry was anticipated. When assuming a synchronous tunneling motion, the molecular symmetry group corresponds to the permutation-inversion group G8 which is isomorphic to D2h (see Ref. [58] for further details). A detailed characterization of the different symmetries and their spin statistical weights can be found in Refs. [39, 64]. The proton transfer tunneling splittings in the ground and vibrationally excited states can be determined separately by measuring simultaneously two types of
2.5 Formic Acid Dimer
Figure 2.3 Zoomed part of the high resolution infrared spectrum of formic acid dimer showing the experimentally resolved proton transfer splitting. Each rovibrational transition
is split into two, originating from different tunneling components. The expected intensity ratio is 3:1 due to different spin statistical weights. This figure is adapted from Ref. [39].
transitions (a- and b-type transitions) corresponding to distinct relative orientations of the change in angular momentum with respect to the axes of inertia of the molecule. For b-type transitions the selection rules require a change of tunneling state upon vibrational excitation; for a-type transitions upper to upper and lower to lower selection rules hold. By measuring both a- and b-type transitions, the sum and the difference of the tunneling splitting in the ground and vibrationally excited states can obtained simultaneously (see Fig. 2.3). The direction transition dipole moment for the infrared spectrum is given by the dipole derivative of the C–O stretch relative to the different axis of inertia. A quantitative estimation would involve high level ab initio calculations. However, qualitatively the change in the dipole moment during the antisymmetric C–O stretch is expected also to have a projection along the intermolecular axis (a-axis) as well as perpendicular to this (b-axis). No out of plane motions are expected. Both tunneling components with an approximate intensity ratio of 1 / 3 (in agreement with the corresponding spin statistics) were observed in the measurement [39]. Most lines (179) were assigned to b-type transitions from the upper tunneling state in the vibrational ground state to the lower tunneling state in the C–O stretch. Altogether 66 a-type transitions were observed. The a-type transitions were found to be weaker and are centered at the band origin, a frequency region which was experimentally difficult to access. Due to a lack of precise intensity measurements for the weaker a-type transitions it was difficult to assign whether they have to be attributed to transitions starting in the lower or upper tunneling component. In Ref. [39] two possible assignments were discussed which yielded
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the following tunneling splittings in the ground and vibrationally excited state, corresponding to different assignments: For the ground state tunneling splitting either 0.00286(25) or 0.0123(3) cm–1 can be obtained. For the excited state tunneling splitting 0.00999(21) cm–1 or alternatively 0.0031(3) cm–1 is determined. As long as the vibrational coordinate can be completely separated from the tunneling coordinate, the tunneling splitting should be unaffected by the vibrational excitation. Initially [39], it was argued that an acceleration of the proton transfer upon vibrational excitation seems more likely, which favors the value of 0.00286(25) cm–1 for the ground state. This was based upon the fact that the vibrational analysis involves a mean decrease in the distance between the opposite O atoms of the two monomeric units. The reaction barrier height to double proton transfer is lowered, which is expected to decrease the proton transfer time and increase the tunneling splitting. Correspondingly, an enhancement of the tunneling splitting was observed for malonaldehyde when the O–O stretching vibration was excited [48, 65]. Whereas Tautermann et al., with a value of 0.0022 cm–1, confirm the initial assignment, new IR studies in the carbonyl stretching region unambiguously show the second assignment to be correct with a tunneling splitting of 0.0125(3) cm–1 and 0.0031(3) cm–1 for the ground state and vibrationally excited state, respectively [64]. In 2004 and 2005 direct dynamics calculation based on instanton techniques are reported for tunneling splittings in the formic acid dimer and its deuterated isotopomers for the zero-point level and the lowest vibrationally excited level of a non-totally symmetric C–O stretch vibration [20, 66]. The calculated splittings of Smerdarchina et al. are in good agreement with the experimental observations for (DCOOH)2 with the now confirmed reversed assignments. The deceleration upon vibrational excitation is attributed to the anti-symmetric nature of the vibration which handicaps a symmetrical proton transfer. The zero-point tunneling splitting of formic acid dimer is calculated to be 510 MHz, which is a factor of 1.4 larger than the observed splitting. This discrepancy is explained by the tendency of the B3LYP potential to underestimate the barrier height and width. This overestimation of the tunneling splitting would be consistent with the result for benzoic acid dimer: For the free dimer Smedarchina predicts a tunneling splitting of 1920 MHz which is a factor of 1.7 larger than the experimentally observed splitting. The significantly increased tunneling splitting in dye-doped crystals could also be explained. When inducing three symmetric lattice vibrations in the calculations they predict a tunneling splitting of 17 GHz for zero asymmetry, which can be compared with the tunneling matrix element of 8.4 –1 GHz for the indigodoped crystals [66].
2.6 Conclusion
2.6 Conclusion
In conclusion, high resolution spectroscopy allows an exact quantitative measurement of important dynamical processes. We have summarized the results for two benchmark systems: benzoic acid dimer and formic acid dimer. The tunneling motion in carboxylic dimers is shown to be slow compared to the overall rotation, thus confirming the existence of deep local minima in a C2h structure. The proton transfer time of formic acid dimer in the electronic ground state is of the order of ns and can be compared with recent theoretical predictions which covered more than four orders of magnitude. It is interesting to note that, in 2004, one additional example of proton transfer dynamics has been reported which was obtained via high resolution spectroscopy measurements in the gas phase [67]. Roscioli et al. reported the S1‹S0 fluorescence excitation spectrum of 2-hydroxypyridine/2-pyridine dimer, which showed two subbands separated by 527 MHz. The experimentally determined observed splitting is of the same order of magnitude as the corresponding values for benzoic acid dimer (1107 MHz). Similar to the S1‹S0 transition of benzoic acid dimer, these spectra only yield information on the difference between the tunneling splittings in the ground and electronically excited state; the values could not be determined independently. The proton transfer between the two bridging hydrogen atoms is estimated to occur in the order of ns, which is relatively long compared to the predicted values but very similar to the experimental values for formic acid dimer (nsec). High resolution gas phase spectroscopy has now been able to nail down the size of the tunneling splitting for proton transfer in double hydrogen bonded systems. If we come back to the question of whether the current tunneling criteria with enzyme supported reactions show the nature of the proton transfer process, formic acid dimer serves as a crucial test candidate. In the most recent theoretical study of Tautermann et al. it was shown that the tunneling criteria based on the calculated reaction rates for various isotopomers fail to predict tunneling behavior correctly: Instead of unraveling the pure quantum mechanical tunneling behavior of the proton transfer process in formic acid dimer the criteria indicate a classical over barrier process. It would be important to see whether the experimental data confirm these findings. In general, this shows that the measurement of small aggregates in the gas phase can add another aspect to the ongoing “Tunneling Enhancement by Enzyme” discussion. Exact knowledge of the proton transfer in carboxylic dimers constitutes an important step towards the development of theoretical methods. While we have not tested the reliability of theoretical models on simple benchmark systems we probably will not be able to simulate quantitatively proton transfer tunneling in biological systems in the future.
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References 1 D. D. Nelson Jr., G. T. Fraser,
W. Klemperer, Science 1988, 238, 1670. 2 K. Liu, J. D. Gruzan, R. S. Saykally, Science 1996, 271, 929. 3 E. Nir, K. Kleinermanns, M. S. de Vries, Nature 2000, 408, 949. 4 G. A. Jeffrey, W. Saenger, Hydrogen Bonding in Biological Structures, Springer Verlag, Berlin, 1991. 5 H. H. Limbach, J. Manz, Ber. Bunsenges. Phys. Chem. 1998, 102, 289. 6 S. Hammes-Schiffer, J. Chem. Phys. 1996, 105, 2236. 7 B. J. Bahnson, J. P. Klinmann, Methods Enzymol. 1995, 249, 373. 8 A. Kohen, J. P. Klinman, Chem. Biol. 1999, 6, 191. 9 St. Scheiner, Bioenergetics 2000, 1458, 28. 10 B. J. Bahnson, T. D. Colby, J. K. Chin, B. M. Goldstein, J. P. Klinman, Proc. Natl. Acad. Sci. USA, 1997, 94, 12797. 11 P.-O. Ldin, Rev. Mod. Phys. 1963, 35, 724. 12 J. Florian, V. Hrouda, P. Hobza, J. Am. Chem. Soc. 1997, 116, 1457. 13 J. Maranon, A. Fantoni, J. R. Grigera, J. Theor. Biol. 1999, 201, 93. 14 A. Kohen, J. P. Klinmann, Acc. Chem. Res. 1998, 31, 397. 15 S. R. Billeter, S. P. Webb, P. K. Agarwal, T. Iordanov, S. Hammes-Schiffer, J. Am. Chem. Soc. 2001, 123, 11262. 16 K. M. Doll, B. R. Bender, R. G. Finke, J. Am. Chem. Soc. 2003, 125, 10877. 17 Ch. S. Tautermann, M. J. Loferer, A. F. Voegele, K. R. Liedl, J. Chem. Phys. 2004, 120, 11650. 18 J. M. Hollas, High Resolution Spectroscopy, Wiley & Sons, Sussex 1998. 19 Ch. S. Tautermann, A. F. Voegele, K. R. Liedl, J. Chem. Phys. 2004, 120, 631. 20 Z. Smedarchina, A. Fernndez-Ramos, W. Siebrand, J. Chem. Phys. 2005, 122, 134309. 21 S. Nakaoka, N. Hirota, T. Matsuhita, K. Nishimoto, Chem. Phys. Lett. 1982, 92, 498. 22 R. Feld, M. S. Lehmann, K. W. Muir, J. C. Speakmann, Z. Kristallogr. 1981, 157, 215.
23 D. F. Brougham, A. J. Horsewill,
A. Ikram, R. M. Ibberson, P. J. MacDonald, M. Pinter-Krainer, J. Chem. Phys. 1996, 105, 979. 24 K. Remmers, W. L. Meerts, I. Ozier, J. Chem. Phys. 2000, 112, 10890. 25 Ch. Scheurer, P. Saalfrank, Chem. Phys. Lett. 1995, 245, 201. 26 V. P. Sakun, M. V. Vener, N. D. Sokolov, J. Chem. Phys. 1996, 105, 379. 27 D. Antoniou, St. D. Schwarz, J. Chem. Phys. 1998, 109, 2287. 28 A. Oppenlnder, Ch. Rambaud, H. P. Trommsdorff, J. Vial, Chem. Phys., 1989, 136, 335. 29 Ch. Rambaud, H. P. Trommsdorf, Chem. Phys. Lett. 1999, 306, 124. 30 G. M. Florio, E. L. Sibert III, T. S. Zwier, Faraday Discuss. 2001, 118, 315. 31 Ch. K. Nandi, T. Chakraborty, J. Chem. Phys. 2004, 120, 8521. 32 S. Hayashi, J. Umemura, S. Kato, K. Morokuma, J. Phys. Chem. 1984, 88, 1330. 33 Th. Neuheusser, B. A. Hess, Ch. Reutel, E. Weber, J. Phys. Chem. 1994, 98, 6459. 34 C. Mijoule, M. Allavena, J. M. Leclerco, Y. Bouteiller, Chem. Phys. 1986, 109, 207. 35 W. Quian, S. Krimm, J. Phys. Chem. 1998, 102, 659. 36 Y.-T. Chang, Y. Yamaguchi, W. H. Miller, H. F. Schaeffer III, J. Am. Chem. Soc. 1987, 109, 7245. 37 A. Almeningen, O. Bastiansen, T. Motzfeld, Acta Chem. Scand. 1969, 23, 2848. 38 B. S. Jursic, J. Mol. Struct. 1997, 417, 89. 39 F. Madeja, M. Havenith, J. Chem. Phys. 2002, 117, 7162. 40 V. V. Matylitsky, C. Riehn, M. F. Gelin, B. Brutschy, J. Chem. Phys. 2003, 119, 10553. 41 Sh. Miura, M. E. Tuckermann, M. L. Klein, J. Chem. Phys. 1998, 109, 5290. 42 Y. Kim, J. Am. Chem. Soc. 1995, 118, 1522. 43 I. Yokoyama, Y. Miva, K. Madida, J. Am. Chem. Soc. 1991, 113, 6458. 44 J. ChocholouÐov, J. Vacek, P. Hobza, Phys. Chem. Chem. Phys. 2004, 4, 2119.
References 45 N. Shida, P. F. Barbara, J. Almlf,
J. Chem. Phys. 1991, 94, 3633. 46 K. Wolf, A. Simperler, W. Mikenda, Monatsh. Chem. 1999, 130, 1031. 47 H. Ushiyama, K. Takatsuka, J. Chem. Phys. 2001, 115, 5903. 48 Ph. R. C. Markwick, N. L. Doltsinis, D. Marx, J. Chem. Phys. 2005, 122, 54112. 49 A. Agresti, M. Bacci, A. Ranfagni, Chem. Phys. Lett. 1981, 79, 100. 50 M. V. Vener, O. Khn, J. M. Bowman, Chem. Phys. Lett. 2001, 349, 562. 51 Y. Marchal, J. Chem. Phys. 1987, 87, 6344. 52 U. Merker, P. Engels, F. Madeja, M. Havenith, W. Urban, Rev. Sci. Instrum. 1999, 70, 1933. 53 K. L. Goh, P. P. Ong, T. L. Tan, Spectrochim. Acta, Part A 1999, 55, 2601. 54 J. E. Bertie, K. H. Michaelian, H. H. Eysel, D. J. Hager, J. Chem. Phys. 1986, 85, 4479. 55 T. Wachs, D. Borchardt, S. H. Bauer, Spectrochim. Acta, Part A 1987, 43, 965. 56 R. C. Millikan, K. S. Pitzer, J. Am. Chem. Soc. 1958, 80, 3515.
57 G. M. Florio, T. Zwier, E. M. Myshakin,
58 59
60 61
62
63 64 65 66
67
K. D. Jordan, E. L. Sibert III, J. Chem. Phys. 2003, 118, 1735. F. Ito, T. Nakanaga, Chem. Phys. 2002, 277, 163. R. Georges, M. Freytes, D. Hurtmans, I. Kleiner, J. VanderAuwera, M. Herman, Chem. Phys. 2004, 305, 187. M. Gantenberg, M. Halupka, W. Sander, Chem. Eur. J. 2000, 6, 1865. F. Madeja, M. Havenith, K. Nauta, R. E. Miller, J. ChocholouÐov, P. Hobza, J. Chem. Phys. 2004, 120, 10554. N. R. Brinkmann, G. S. Tschumper, G Yau, H. F. Schaefer III, J. Phys. Chem. A 2003, 107, 10208. R. Robertson, M. C. Lawrence, Chem. Phys. 1981, 62, 131. M. Ortlieb, M. Havenith, in preparation. N. Sato, S. Iwata, J. Chem. Phys. 1988, 89, 2932. Z. Smedarchina, A. Fernndez-Ramos, W. Siebrand, Chem. Phys. Lett. 2004, 395, 339 J. R. Roscioli, D. W. Pratt, Z. Smedarchina, W. Siebrand, A. Fernndez-Ramos, J. Chem. Phys. 2004, 120, 11351.
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3 Gas Phase Vibrational Spectroscopy of Strong Hydrogen Bonds Knut R. Asmis, Daniel M. Neumark, and Joel M. Bowman
3.1 Introduction
The hydrogen bond interaction is key to understanding the structure and properties of water, biomolecules, self-assembled nanostructures and molecular crystals. However, much confusion remains about its electronic nature, a combination of van der Waals, electrostatic and covalent contributions, leading to a wide variety of hydrogen bonds with bond strengths ranging from 2 to 40 kcal mol–1. In particular, our understanding of strong, low-barrier hydrogen bonds and their central role in enzyme catalysis [1], biomolecular recognition [2], proton transfer across biomembranes [3] and proton transport in aqueous media [4] remains incomplete. The central aim of this chapter is to outline some recent advances in the research on strongly hydrogen bonded model systems in the gas phase with emphasis on the work from our research groups. Strong hydrogen bonds (A_H_B) are often classified based on their hydrogen bond energy; a typically cited lower limit is >15 kcal mol–1 [5]. Their most prominent physical properties are large NMR downfield chemical shifts and considerably red-shifted hydrogen stretch frequencies. Moreover, the H-atom transfer barrier, a characteristic feature of weak hydrogen bonds A–H_B, is either absent or very small in these systems (at their minimum energy geometry). Consequently, the H-atom in homoconjugated (A = B) strong hydrogen bonds is equally shared by the two heavy atoms forming two identical strong hydrogen bonds. This symmetry is lost in heteroconjugated (A „ B) systems, but the H-atom remains in a more centered position, i.e., the distance between the heavy atoms is smaller than in weaker hydrogen bonded systems. Strong hydrogen bonds can either be lowbarrier, as in (HO_H_OH)–, or single-well, as in (Br_H_I)–, depending on the form of the potential curve along the H-atom exchange coordinate (see Fig. 3.1 and below). Hydrogen bonds are very sensitive to perturbation, due to an intimate interdependence between the heavy atom separation, the H-atom exchange barrier and the position of the light H-atom leading to unusually high proton polarizabilities. Therefore it can prove advantageous to study strong hydrogen bonds in the gas Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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3 Gas Phase Vibrational Spectroscopy of Strong Hydrogen Bonds
(b)
(a) H3 O2
-
-
BrHI
400
10000
350
Zero-point Energy 8000
Potential (cm )
250
-1
-1
Potential (cm )
300
200
150
R = 4.4 bohr 6000
4000
100
R = 3.7 bohr
2000
50
0 -0.6
0
-0.4
-0.2
0
0.2
0.4
0.6
r1 - r2 (bohr)
Figure 3.1 Typical potential energy curves for strong, low-barrier hydrogen bonds. The homoconjugated H3O2– (a) exhibits a (relaxed) symmetric, double-well potential as a function of the difference of the bridging
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
r1 - r2 (bohr)
hydrogen distance with the two oxygen atoms. The heteroconjugated BrHI– (b) is characterized by an asymmetric single-well potential at equilibrium and an asymmetric double well at a larger Br–I– distance.
phase, in the absence of any perturbations from surrounding solvent or host molecules. Standard experimental techniques to study strong hydrogen bonds, including NMR, as well as X-ray and neutron diffraction, are currently limited to condensed phase probes. Gas phase experiments are hindered by low number densities and only vibrational spectroscopy exhibits the required sensitivity and selectivity to perform such studies. Recently, advances in laser technology as well as in computational approaches have allowed significant progress in the study of strongly hydrogen bonded model systems. We first describe these improved experimental and theoretical methods and then discuss experiments and calculations on three prototypical systems containing strong hydrogen bonds: BrHBr–, BrHI– and H5O+2 . These results demonstrate that the vibrational spectroscopy of triatomic systems involving strong hydrogen bonds has now been successfully solved, even when heavy atoms like iodine are involved. However, the study of slightly larger systems, like the protonated water dimer, remains challenging.
3.2 Methods
3.2 Methods 3.2.1 Vibrational Spectroscopy of Gas Phase Ions
Vibrational spectroscopy paired with quantum chemistry currently offers the most direct and generally applicable experimental approach to structural investigation of neutral and charged clusters in the gas phase [6]. Direct absorption measurements based on ion discharge modulation methods [7] can yield high resolution spectra of small and light molecular ions. Problems associated with high discharge temperatures can nowadays be overcome by using pulsed-slit supersonic expansions [8]. However, these types of experiments become increasingly difficult for larger and heavier molecular ions, particularly ion clusters, owing to spectral congestion, lower gas phase number densities and the presence of other absorbing species. Therefore alternative techniques have been developed in which the absorption of photons can be measured indirectly, by way of resonance enhanced photodissociation (or action) spectroscopy. Photodissociation techniques have the advantage that fragment ions can be detected background-free and with nearly 100% detection efficiency. A high selectivity can be achieved through mass selection of parent and fragment ions using appropriate mass filters. An infrared photodissociation (IR-PD) spectrum is measured by irradiating ions with infrared radiation and monitoring the yield of fragment ions as a function of the irradiation wavelength. In order to induce fragmentation the parent ion AB+ (the same line of argumentation holds for negative ions) is required to absorb sufficient energy to overcome the (lowest) dissociation threshold. Once a metastable ro-vibronic state is reached, intramolecular energy redistribution will eventually lead to dissociation, producing a charged and a neutral fragment: nhm
ABþ ! Aþ þ B
(3.1)
As noted before, the dissociation energy of strong hydrogen bonds is roughly 5000 cm–1 or higher, while the fundamentals of the shared H-atom modes are found well below this limit. Process (3.1) therefore requires the absorption of multiple infrared photons. The coherent stepwise multiphoton excitation, where all photons are absorbed in one vibrational ladder, is unfavorable and becomes unrealistic for higher dissociation thresholds, because the laser falls out of resonance owing to the anharmonicity of vibrational potentials. The multiphoton process is better viewed as a sequential absorption of photons enhanced by rapid intramolecular vibrational energy redistribution at higher excitation [9]. Only the first few photons are absorbed in the “discrete” regime, in which a particular mode is excited resonantly. Higher excitation accesses the “quasi-continuum”, in which the density of states is so high that the vibrational energy is rapidly randomized among all vibrational modes of the molecular ion. The ion continues to absorb photons until it has enough energy to dissociate. The transition between the two
55
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3 Gas Phase Vibrational Spectroscopy of Strong Hydrogen Bonds
regimes depends on the vibrational density of states and the strengths of the interactions between vibrational modes. For larger molecular systems, the IR-PD spectrum often resembles the linear absorption spectrum [10]. For smaller systems with less internal degrees of freedom, the relative intensities may be different. However, if the laser fluence is kept at a moderate level, signal is only detected if the laser wavelength is resonant with a fundamental transition, that is, hm
nhm
ABþ ðv ¼ 0Þ ! ABþ ðv ¼ 1Þ ! Aþ þ B
(3.2)
At high laser fluence the probability of directly exciting overtones is enhanced, complicating the interpretation of the IR-PD spectrum [11]. A useful method to avoid multiphoton excitation and measure IR-PD spectra in the linear regime is the messenger atom technique [12]: ABþ Rg ! ðABþ RgÞ ! ABþ þ Rg hm
(3.3)
By forming ion–rare gas atom (Rg) complexes, the dissociation threshold of the system is lowered, generally below the photon energy and these predissociation spectra directly reflect the linear absorption spectrum. This technique has also been used to great effect in anion spectroscopy experiments [13]. The multiphoton dissociation approach remains attractive for systems in which the perturbation of the messenger atom cannot be neglected, or in instruments where rare gas attachment is difficult. IR-PD experiments generally require intense and tunable radiation sources which, for many years, were only commercially available in the wavelength region up to ~4 lm (>2500 cm–1), that is the region of X–H (X = C, N, O, halogen atom) stretches and overtones. The spectral signature of strong hydrogen bonds, however, is found at longer wavelengths. The application of free electron lasers (FELs) to molecular spectroscopy by Meijer and coworkers has bridged this gap [14]. More recently, several groups [15, 16] were able to access the region below 2000 cm–1 with higher energy, narrow bandwidth table-top laser systems, which make use of difference frequency mixing in an AgGaSe2 crystal [17]. Even though the pulse energy in these table-top systems is roughly three orders of magnitude smaller than from FEL sources and generally not sufficient to perform multiphoton absorption experiments, it is enough to photodissociate messenger atom–ion complexes [16]. 3.2.2 Experimental Setup
The experiments described here were performed on a guided ion beam tandem mass spectrometer [18] that was temporarily installed at the free electron laser facility FELIX (free electron laser for infrared experiments, FOM Institute for Plasma Physics, Nieuwegein, The Netherlands) [19]. A schematic of the experimental setup is shown in Fig. 3.2. Ions are generated in the ion source region (not
3.2 Methods
Figure 3.2 Schematic of the guided-ion-beam tandem mass spectrometer used in the present studies [60]. The instrument is housed in
a five-stage differentially pumped vacuum chamber. The FEL radiation is applied collinearly to the axis of the ion trap.
shown) using either a pulsed supersonic jet crossed by a 1 keV electron beam for the bihalide anions or an ion spray source for the protonated water clusters. The ion beam, comprising a distribution of cluster ions of different size, is collimated and compressed in phase space in a gas-filled radio frequency (RF) ion guide and directed into the first quadrupole mass filter. Mass-selected ions are then guided into a temperature-adjustable RF ion trap. The trap consists of a linear RF ion guide and two electrostatic ion lenses contained in a cylindrical housing, which is connected to the cold head of a closed-cycle He cryostat. The cylinder is continuously filled with He (~0.2 mbar). The use of a buffer gas has several advantages: (i) The trap can be operated in a continuous ion-fill-mode. (ii) Trapped ions are collisionally cooled to the ambient temperature (approximately within a few milliseconds). Experiments can currently be performed at temperatures between 14 and 350 K. IR-PD spectra are obtained by photoexcitation of the trapped ions with the pulsed FEL radiation and subsequent monitoring of the fragment ion signal. The FEL generates 5 ls macropulses at a repetition rate of 5 Hz. Each macropulse contains a series of several thousand ~1 ps micropulses with about 1 ns between micropulses. A new measurement cycle is triggered by the previous FEL macropulse. First, the ion trap is filled with mass-selected ions; typically for 150 ms. The trap is then closed and the ions are allowed to thermalize. Directly after FELIX fires, all ions are extracted and the mass-selected ion yield is monitored. This cycle is repeated multiple times, the signal is summed and then the FEL is set to the next wavelength. Overview spectra are measured first, in the region from 5.5 to
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3 Gas Phase Vibrational Spectroscopy of Strong Hydrogen Bonds
18 lm with a step size of 0.1 lm. Spectra with smaller step sizes and longer accumulation times are then measured in those spectral regions where signal is observed. The accuracy of the determined vibrational frequencies is generally within 1% of the central wavelength. The accuracy of the relative depletion intensities is less well defined, mainly due to the non-monotonic variation of the FELIX beam intensity, bandwidth, and waist size with wavelength. We try to minimize these variations and do not correct for them in our spectra. 3.2.3 Potential Energy Surfaces
Rigorous theoretical modeling of IR spectra of hydrogen bonded complexes consists of two parts. The first is the calculation of the potential energy surface and the dipole moment. The second is appropriate dynamics calculations using the potential and dipole moment surfaces. For simulations of the IR spectrum quantum, semi-classical or purely classical dynamics calculations are straightforward to do, in principle, in the weak-field limit. Practically, quantum dynamics calculations can be quite computationally demanding, depending on the number of degrees of freedom. Both aspects of this theoretical modeling are briefly reviewed next, followed by a review of recent applications to BrHI– and H5O+2 . For triatomic molecules, even with heavy atoms, such as BrHI–, it is now straightforward to obtain global potential energy surfaces, based on highly accurate ab initio calculations. One fairly common approach is to obtain the ab initio energies (and dipole moment) on a regular grid of roughly ten points per degree of freedom and to use interpolation, e.g., splines, to obtain the potential between grid points. This approach will be described below for BrHI–. For larger systems, such as H5O+2 , the proton bound water dimer, and H3O2 , mono-hydrated hydroxyl, the grid approach is impractical. For these systems a “scattered” approach has proved successful. In this approach tens of thousands of ab initio calculations are done at configurations of relevance to the dynamics, including stationary points, etc. The ab initio data are then fit using standard least-squares procedures with, however, some important new features of the basis functions. In the least-squares approach the data are represented by the compact expression Vðx1 ; xd Þ ¼
P n¼0
Cn gn ðx1 ; xd Þ
(3.4)
where xi are the variables of the fit, gn are a known set of linearly independent basis functions, and the Cn are coefficients that are determined by the leastsquares procedure. The key to a successful fit to the data is the choice of basis functions and the variables of the fit. Somewhat surprisingly, fitting approaches done prior to our work did not explicitly incorporate permutational symmetry of like atoms into the basis functions. This was done recently in applications to CH+5 [20], H3O2 [21], and H5O+2 [22]. The approach is to use all internuclear distances, ri, as the basic variables and xi is a suitable function of ri. These variables form a closed set under permutation of atoms. Then, symbolically, V is given by
3.2 Methods
Vðx1 ; xd Þ ¼
P i1 id
i
Ci i Sfx1i1 xdd g 1
d
(3.5)
where the symbol S indicates a symmetrization operator so that the symmetrized i monomial S{x1i1 ... xdd } is invariant with respect to any permutation of like nuclei. The approach we actually use is more involved and is described elsewhere [22]. With this new approach we have been able to obtain full-dimensional potentials using high quality ab initio calculations of electronic energies and dipole moments. Some of these results for H5O+2 will be presented below. 3.2.4 Vibrational Calculations
As with potential surfaces, exact vibrational calculations for triatomics are essentially a “solved” problem. There are several numerically equivalent exact approaches that are currently in use. These basically differ in the choice of coordinates. Our recent calculations on BrHI– made use of two such approaches; one used socalled Jacobi coordinates and the other used internal valence coordinates, i.e., the BrH, HI– bond lengths and the BrHI– bond angle. The kinetic energy operator in these coordinates is complex and so we refer the reader to the original literature [23] instead of giving it here. In Jacobi coordinates this operator is much simpler, and the full Hamiltonian for an “ABC” triatomic for a given value of the total nuclear angular momentum J (in a rotating frame) is given by H ¼ TR þ Tr þ
ðJ jÞ2 þ VðR; r; cÞ 2lR2
(3.6)
where R is the distance of one atom, say A, to the center of mass of the diatom, say BC, r is the diatom internuclear distance, c is the angle between the vectors R and r, J is the total nuclear angular momentum operator, j is the diatom angular momentum operator, and V is the full potential. For the BrHI– calculations, reviewed below, codes based on Jacobi coordinates and valence coordinates were used to obtain vibrational energies and wave functions. IR transition intensities were obtained for J = 0 to J ¢ = 1 transitions using the exact wave functions and the ab initio dipole moment. For larger hydrogen-bonded systems, rigorous calculations are far more difficult to carry out, both from the point of view of obtaining full-dimensional potentials and the subsequent quantum vibrational calculations. Reduced dimensionality approaches are therefore often necessary and several chapters in this volume illustrate this approach. With increasing computational power, coupled with some new approaches, it is possible to treat modest sized H-bonded systems in full dimensionality. We have already briefly reviewed the approach we have developed for potentials; for the vibrations we have primarily used the code Multimode (MM). The methods used in MM have been reviewed recently [24 and references therein, 25], and so we only give a very brief overview of the method here. There are two versions of MM. One, that we refer to as “single-reference” MM is based on the exact Watson Hamiltonian, which is the Hamiltonian in rectilinear
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3 Gas Phase Vibrational Spectroscopy of Strong Hydrogen Bonds
mass-weighted normal coordinates. The normal coordinates, as usual, are referenced to a single stationary point, which does not have to be a minimum. For calculations we review below the reference geometry was chosen as a saddle point, not a minimum. The other version of MM, which is much better suited for highly floppy systems, is based on the reaction path Hamiltonian [25]. A key element of both versions is the n-mode representation of the potential. In the single-reference version of MM, the potential in N normal modes is represented as VðQ1 ; QN Þ ¼
X
V ðiÞ ðQi Þ þ
V ð2Þ ðQi ; Qj Þ þ
i„j
i
X
X
X
V ð3Þ ðQi ; Qj ; Qk Þþ
i„j„k
V ð4Þ ðQi ; Qj ; Qk ; Ql Þ þ
(3.7a)
i„j„k„l
For the reaction-path version of MM the potential is given by Vðs; Q1 ; Q2 ; :::Þ ¼V ð0Þ ðsÞ þ X ijk
X
ð1Þ
Vi ðs; Qi Þþ
i ð3Þ Vijk ðs; Qi ; Qj ; Qk Þ
X
ð2Þ
Vij ðs; Qi ; Qj Þþ
ij
þ
X
ð4Þ
Vijkl ðs; Qi ; Qj ; Qk ; Ql Þ þ :::
(3.7b)
ijkl
where the Qi are rectilinear normal modes and s is the large amplitude coordinate. In these representations n is less than N but the sums run over all sets of normal modes. This representation of the potential makes it feasible to perform the highdimensional numerical quadratures, etc. needed to set up the Hamiltonian matrix for diagonalization. In recent applications n is typically 4 or 5 in Eq. (3.7a) and 3 or 4 in Eq. (3.7b). The basis used to construct the Hamiltonian matrix is the set of virtual excitations of an exact vibrational self-consistent field Hamiltonian, typically for the zero-point state. This virtual “CI” approach is denoted “VCI”. Relevant calculations using both versions of MM have been reported for (OH–)H2O [21, 26] and H5O2+ [27, 28] and some very recent results will be presented below. Diffusion Monte Carlo calculations, done by and in collaboration with Anne McCoy have also been done on these systems, however, these are not reviewed in detail here.
3.3 Selected Systems 3.3.1 Bihalide Anions
The bihalide anions XHY–, where X and Y are halogen atoms, are among the simplest systems containing strong hydrogen bonds. In fact, these triatomic systems exhibit some of the strongest hydrogen bonds known, reaching 1.93 eV (44.5 kcal mol–1) in FHF– [29]. All bihalide anions are linear and have D¥h (X=Y)
3.3 Selected Systems
or C¥h (X„Y) symmetry. As a result of the strong three-center bonding, the interatomic distance between the heavy atoms is small, leading to a pronounced redshift of the antisymmetric stretch frequency m3 compared to the vibrational frequency of the diatomic X–H. Unusually low frequencies of the shared proton modes are a characteristic trademark for strong hydrogen bonds in general. The extensive sharing of the H-atom between the two halogen atoms makes these bonds highly susceptible to solvent perturbation [30]. In larger Br–·(HBr)n clusters (n>1), for example, the additional HBr molecules destroy the symmetry of the H-bonds and the H-atom is localized [31]. XHY– anions are also of interest as transition state precursors in negative ion photoelectron spectroscopy experiments [32] and are isoelectronic with the rare gas compounds RgHRg+, which exhibit very similar vibrational spectra [33]. The vibrational spectroscopy of bihalide anions has been studied extensively in cryogenic matrices [34]. This work showed that the hydrogenic stretching frequencies were very low, ranging from 1330 cm–1 in FHF– to 645 cm–1 in IHI–, in contrast to the uncomplexed HX frequencies of 4138 cm–1 in HF and 2309 cm–1 in HI [35]. These studies also indicated that the effects of the matrix on the vibrational frequencies could be significant, providing strong motivation to measure the unperturbed gas phase IR spectra of these bihalide anions. High resolution gas phase IR spectra over narrow frequency ranges have been measured for FHF– and ClHCl– using diode laser absorption [36]. We recently applied a different and more general approach to gas phase ion vibrational spectroscopy. The result was the first broadband infrared spectra in the range from 600 to 1675 cm–1 of a homoconjugated (BrHBr–) and a heteroconjugated (BrHI–) gas phase bihalide anion measured by vibrational predissociation of the corresponding anion–Ar complex [11, 37]. The results of the BrHBr– study [37], together with recent data on BrDBr–, are shown in Fig. 3.3. The spectra were measured by IR-PD of the anion–Ar complex. The addition of a single Ar atom is expected to result in only a minor shift (<5 cm–1) of the m3 frequency compared to bare BrHBr–. The fundamental of the antisymmetric stretch mode m3 is observed at 733 cm–1 and peaks at higher energies are attributed to m3+nm1 combination bands. As expected, the antisymmetric stretch frequency is red-shifted upon deuteration, while the peak spacing, related to the symmetric stretch mode m1, remains nearly unchanged. The ratio of m3(H)/m3(D) is 1.45, slightly larger than the harmonic value of 2 and considerably larger than 1.2–1.3, the value usually quoted for strong hydrogen bonds [38]. The measured peak positions are in excellent agreement with the results from the anharmonic calculations of Del Bene and Jordan [39], indicated by the black bars in Fig. 3.3. They calculated two-dimensional vibrational eigenfunctions and eigenvalues on a high level ab initio potential energy surface for a collinear XHX– system. The relative intensities in our gas phase spectra differ from the previously measured matrix spectra, presumably due to the underlying dissociation dynamics. Nonetheless, the strong relative intensity of the combination bands in both experiments indicate a complete breakdown of the (uncoupled) harmonic oscillator model in these prototypical systems and underline that explicit consid-
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3 Gas Phase Vibrational Spectroscopy of Strong Hydrogen Bonds
(a)
(b)
Figure 3.3 IR-PD spectra of BrHBr–·Ar (a) and BrDBr–·Ar (b) from 620 to 1680 cm–1. The depletion of the parent ion signal is shown (gray trace and gray shaded-area) and compared to the eigenvalues (black bars) from a variational calculation on a two-dimensional CCSD(T)/aug-cc-pVTZ-based potential
energy surface for bare BrHBr– and BrDBr– anions, respectively. The peak assignment is indicated by three numbers which give the vibrational quantum number for each mode (symmetric stretch m1, bend m2, antisymmetric stretch m3).
eration of intermode coupling is needed when calculating vibrational properties of strongly hydrogen bonded systems. The vibrational spectra of the asymmetric bihalides are more complex and their assignment was only recently unraveled [11]. Earlier matrix IR work [40] on BrHI– indicated the presence of two absorbing species, a strongly asymmetric form, referred to as type I, and a more symmetric form (type II), the latter exhibiting a considerably lower H-atom stretch frequency owing to greater delocalization of the hydrogen atom, similar to the symmetric bihalides discussed above. To investigate this possible dual structure, spectra of BrHI– in the gas phase in the region of the bridging hydrogen stretch were recorded. Parent ion depletion spectra for BrHI–·Ar and BrDI–·Ar are shown in Fig. 3.4. Compared to the IR spectra of the symmetric bihalides, these spectra are considerably more complex and their assignment, based on previous calculations [41], was problematic. The two most intense peaks in both spectra correspond closely to the peaks seen in the previous matrix works. Their frequencies exhibit red-shifts when going from the gas phase to the matrix from 12 to 64 cm–1. All these peaks were assigned to the type I structure in the matrix. No peaks assigned to type II anions are observed in the gas phase, but additional peaks are observed in the gas phase spectra. In order to reach a satisfactory assignment of all the peaks observed
3.3 Selected Systems
(a)
(b)
Figure 3.4 IR-PD spectra of BrHI–·Ar (a) and BrDI–·Ar (b). The depletion of the parent ion signal is shown (gray trace and gray shadedarea) and compared to the calculated frequencies and absorption intensities (black bars). Calculations were performed on the
bare BrHI– and BRDI– anions and involved construction of a three-dimensional MRCI/ AVQZ(cpp) potential energy surface, followed by ro-vibrational bound-state variational calculations (see text).
in the gas phase spectra new calculations on an improved potential energy surface had to be performed. Such calculations were recently done. These included a new potential for this anion using multi-reference CI ab initio methods with large basis sets; the details are given elsewhere [11]. Ab initio energies and dipole moment values were obtained at roughly 2300 configurations taken from regular grids. Both the energy and dipole moment were subsequently interpolated using 3d splines. The potential along two cuts of this potential for the collinear geometry are shown in Fig. 3.1. In these plots, the distance between the Br and I–, denoted R, is fixed while the potential is plotted as a function of the difference coordinate r1 – r2 where r1 and r2 are the distances between the H atom and Br and I–, respectively. As seen, for large R the potential has a double-minimum, however, near the global minimum, where R = 3.7 a0, the potential is a single minimum. This surface and the corresponding ab initio dipole moment were used to calculate the IR spectra of BrHI– and BrDI– using two variational codes, one using valence coordinates and one using Jacobi coordinates. The results from the two calculations agree very well, as they should. The comparisons with experiment, given in Fig. 3.4, show
63
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3 Gas Phase Vibrational Spectroscopy of Strong Hydrogen Bonds
very good agreement. This is especially satisfying because there was uncertainty about the assignment of the bands at 920 and 1171 cm–1. The difficulty in making experimental assignments was illuminated and resolved by the calculations, which indicated a strong 2:1 Fermi mixing between the bend and the “asymmetric-stretch” modes. This mixing is depicted in Fig. 3.5 where plots of the corresponding wave functions are given in the upper two panels and plots of “deperturbed” wave functions are given in the lower two panels. The plots are in the Jacobi coordinates r and c described above (and in the figure caption). The ener(b)
0.98
0.98
0.96
0.96
0.94
0.94
cos(γ )
cos(γ)
(a)
0.92
0.92
0.90
0.90
0.88
0.88
0.86
0.86 2
3
4
6
7
2
3
4
(d)
r (bohr)
(c)
0.98
0.98
0.96
0.96
0.94
0.94
cos(γ )
cos(γ)
5
0.92
6
7
6
7
0.92
0.90
0.90
0.88
0.88
0.86
5
r (bohr)
0.86 2
3
4
5
6
7
r (bohr)
Figure 3.5 Contour plots of the eigen functions at 983 cm–1 (a) and 1127 cm–1 (b) and sum (d) and difference of the two (c), representing the pure states of the bending over-
2
3
4
5
r (bohr)
tone and the H-atom stretch modes, respectively, in BrHI–. The plots are two-dimensional slices in the plane defined by rHBr and the Jacobi bending angle c.
3.3 Selected Systems
gies of these two perturbed states are 983 and 1127 cm–1, in very good agreement with experiment. This analysis presents a satisfactory resolution of the assignment issue for these two lines. (A corresponding and completely analogous situation pertains to BrDI– for the two lines at 742 and 980 cm–1.) Also, it was shown that these 2:1 resonances pervade the entire spectrum for both BrHI– and BrDI–. In summary, the gas phase vibrational frequencies observed for BrHI–·Ar and BrDI–·Ar are close to those seen in earlier matrix-isolation experiments and attributed to the type I form of the anion. The calculated vibrational energy levels show remarkable mode mixing between the H-atom stretch and bend modes, resulting in numerous Fermi resonance states, and thus more complex spectra than for the symmetric XH(D)X– bihalide anions. The calculations also suggest a reassignment of the matrix spectra. The matrix features originally attributed to the symmetric type II anion may actually arise from the bend fundamental and/or the associated combination band with the heavy atom stretch, rather than from a second form of the ion (type II) not observed in the gas phase. These results underline the breakdown of the harmonic approximation; mechanical anharmonicities lead to extended mixing of states, evidenced in the IR spectra by pronounced intensity borrowing effects in the form of Fermi resonances. 3.3.2 The Protonated Water Dimer (H2O_H_OH2)+
The protonated water dimer is one of the most prominent ions containing strong hydrogen bonds. It plays a crucial role in the explanation of the unusually high proton mobility in water [42]. Protonated water clusters and H5O+2 in particular have been suggested as proton release groups in bimolecular proton pumps like bacteriorhodopsin [3, 43]. The interpretation of the spectroscopic signature of hydrated protons in liquid water, characterized by a quasi-continuous absorption observed in the IR, has been a long running controversy [44], in particular the attribution of specific bands to the hydrated proton structures H5O+2 and H9O+4 [45]. More recently, ab initio molecular dynamics simulations have shown that the hydrated proton actually forms a fluxional defect in the hydrogen-bonded network with both H5O+2 and H9O+4 occurring only in the sense of limiting structures [4].
3.3.2.1 Experiments For more than 30 years, starting with X-ray diffraction experiments of hydrated crystals [46], H5O+2 has been the subject of extensive theoretical and experimental studies and its spectroscopy remains challenging until today [47 and references therein]. The vibrational spectroscopy of H5O+2 in the gas phase was first studied in the region above 3500 cm–1, the region of the free O–H stretch modes. The groundbreaking IR-PD experiments of Lee and coworkers [48] (see Fig. 3.6) in 1989 support a hydrated-crystal-like, C2 symmetry H2O_H+_OH2 structure, in which the proton is located symmetrically between the two water ligands. These experiments made use of a two-color excitation scheme; the first, tunable laser
65
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3 Gas Phase Vibrational Spectroscopy of Strong Hydrogen Bonds
Figure 3.6 IR-PD spectrum of H5O2+ measured in the region of the monomer O–H stretches. Figure taken from Ref. [48].
was used to probe the linear absorption regime and the second, fixed-frequency laser to overcome the H5O+2 dissociation energy of 31.6 kcal mol–1 (11055 cm–1) via multiphoton absorption [49]. The two bands in Fig. 3.6 were assigned to the symmetric and antisymmetric O–H stretches (either in phase or out of phase) of the two H2O groups. The rotational progression is assigned to a series of Q branches. The observed peak spacing of 11.6 cm–1 is in good agreement with the calculated C2, near symmetric top structure. In a later study [50], performed at considerably higher spectral resolution, more evidence for a very floppy molecule was found. The number of observed rovibrational lines was considerably more than one would expect for a rigid molecule and was speculatively attributed to tunneling splittings caused by large amplitude motion [51]. Interestingly, four (compared to two in Fig. 3.6) O–H stretching bands were observed in the IR-PD spectrum of the H5O+2 ·H2 complex [49]. Based on a comparison with computed vibrational frequencies, it was concluded that the perturbation exerted by H2, which is bound by less than 4 kcal mol–1, is already sufficient to break the symmetry and stabilizes an “asymmetric” H2O_H3O+ structure, for which four O–H bands are predicted. The spectral region containing the shared proton modes, key to characterizing the potential energy surface for proton transfer, lies much lower in energy (<1600 cm–1) and remained experimentally unexplored until 2003. Advances in free electron laser technology can be credited for making the spectral region of strong hydrogen bonds finally accessible to gas phase spectroscopic techniques. These experiments make use of a simpler one-color excitation scheme, in contrast to the two-color approach applied in the Lee experiments. The vibrational spectra of H5O+2 and D5O+2 measured in the region from 620 to 1900 cm–1 using radiation from the free electron laser for infrared experiments FELIX are plotted in Fig. 3.7 [52]. The spectrum of H5O+2 exhibits four main bands, labeled B to E. Upon H–D substitution four bands (B¢–E¢) of similar width but different relative intensities
3.3 Selected Systems
appear red shifted with isotope shifts varying between 1.3 and 1.4. Based on previous theoretical studies, band E was assigned to the bending motion of the terminal water molecules and bands B to D to vibrations predominantly involving the shared proton. The assignment of the shared proton modes to specific vibrational states remains somewhat controversial and will be discussed in more detail together with the most recent calculations below. The observed bands are more than twenty times broader than the bandwidth of the laser radiation (~5–15 cm–1). The increased width could be caused by vibrational hot-bands, but these should be largely eliminated in the spectra because the ions are collisionally cooled prior to interaction with the laser pulse. However, the zero-point motion of the central proton on the extremely flat PES likely extends over an unusually large area, leading to the exploration of a much larger part of
(a)
(b)
Figure 3.7 IR-PD spectra of H5O+2 (a) and D5O+2 (b). The spectra were measured by monitoring the formation of H3O+ and D3O+ as a function of FELIX wavelength (top axis). The spectra are plotted linearly against the photon energy (bottom axis). See Ref. [52] for experimental details.
67
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3 Gas Phase Vibrational Spectroscopy of Strong Hydrogen Bonds
the configurational space than for a typical rigid molecule, even at 0 K. Additionally, the anharmonicity of the shared proton modes is pronounced, leading to strong anharmonic coupling terms and closely related intensity borrowing effects. The result is an increase in the intensity of bands, which are normally weak or forbidden, like combination bands with low-frequency modes in the present case. Alternatively, multiphoton transitions in which two or more photons are resonant with a vibrational transition may contribute [11]. These transitions appear at shifted photon energies (compared to the single photon transition) due to the anharmonicity of the vibrational potential. In this way, a negative anharmonicity may lead to multiphoton transitions that contribute to the high energy tails of bands B and C. Information on the underlying potential energy surface may also be hidden in the structure observed for bands B to D, which we can currently not assign; its spacing is too large to be attributed to rotational transitions of a near symmetric top.
Figure 3.8 IR-PD spectra of HxD5–xO+2 with x = 0 to 5 (top to bottom) in the region of the shared proton (deuteron) modes (see text).
3.3 Selected Systems
Additional information can be gained from the IR-PD spectra of the partially deuterated isomers DxH5–xO+2 (x=0,1,...,5) and these are shown in Fig. 3.8. Fragment ions of different mass are produced upon photodissociation of partially deuterated species and we measured IR-PD spectra for each possible fragment ion mass. We find nearly identical spectra for all fragment ions of a particular parent ion mass, indicating that efficient H/D scrambling occurs, and therefore only representative sum spectra over all fragment ions are shown for each parent ion mass in Fig. 3.8. Efficient intramolecular H/D exchange is made possible by the underlying sequential absorption mechanism in which the cluster ion can absorb photons during the complete duration of a FEL macropulse (~ 5 ms). If the barrier to internal rotation in DxH5–xO+2 ions is smaller than the dissociation limit, efficient intramolecular energy redistribution leads to complete H/D scrambling after sufficient energy is absorbed but before dissociation can occur. The mixed H/D spectra are more congested than the pure spectra, because multiple isomers are present. Nonetheless, some interesting features can be observed. The band at 1500 cm–1, only present in the mixed H/D spectra is assigned to the bending motion of the terminal HDO monomers. The band centered at 770 cm–1 in DH4O+2 is attributed to a shared proton mode of the symmetric H2O_D+_OH2 isomer, red-shifted by 118 cm–1 compared to band B in Fig. 3.7. This band grows in intensity as the degree of deuteration is increased. Interestingly, it also continues to red-shift, from 770 cm–1 in H2O_D+_OH2 to 700 cm–1 in D2O_D+_OD2, indicating significant coupling between this shared proton mode and the modes of the terminal monomers. The intermediate region is more complex and its assignment requires a simulation of the vibrational spectra of the partially deuterated species. Predissociation spectroscopy of argon-tagged H5O+2 [16], which probes the complex in the linear absorption regime, yields a similar but simpler spectrum compared to the multiphoton dissociation spectrum of bare H5O+2 discussed above (see Fig. 3.9). Headrick et al. argue that, unlike for H2 [48], the extent of the Ar perturbation is not sufficient to stabilize the “asymmetric” H2O_H3O+ complex and change its chemical nature, but only leads to a small shift in the vibrational frequencies. Assuming an additive argon perturbation, they show that the 1080 cm–1 band of the H5O+2 ·Ar complex, found at 1140 cm–1 in H5O+2 ·Ar2, is placed close to the maximum of band C (in the multiphoton spectrum) in the bare ion. No feature corresponding to band D is found in the Headrick et al. spectrum. However a peak in this region is found in the recent (multiphoton) IR-PD by Fridgen et al. [53] (see Fig. 3.9) measured at the French free electron laser facilty CLIO [54]. VCI multimode calculations (see Fig. 3.11, later) also predict transitions with significant intensity in this spectral region. Below 1300 cm–1, the spectra measured at FELIX and CLIO do not agree very well; the band maxima at 921 and 1043 cm–1 in the FELIX spectrum coincide with regions of low signal in the CLIO spectrum. Such discrepancies are surprising and can only in part be rationalized by different ion internal temperature distributions, <100 K in the FELIX study vs. room temperature in the CLIO study. More recent Ar- and Ne-
69
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3 Gas Phase Vibrational Spectroscopy of Strong Hydrogen Bonds
Figure 3.9 IR-PD spectra of (a) H5O+2 ·Ar [16], (b) H5O+2 measured at FELIX [52], and (c) H5O+2 measured at CLIO [53].
tagged predissociation spectra extending below 1000 cm–1 [28] are in better agreement overall with the FELIX experiments than with the CLIO experiments.
3.3.2.2 Calculations There have been a number of calculations recently on the vibrations of H5O+2 beyond the harmonic approximation. As noted already, such calculations are essential due to the highly anharmonic nature of these vibrations. Attempts to go beyond the harmonic approximation have been done in reduced dimensionality [27, 56] and also with the additional vibrational adiabatic approximation [56]. These calculations selected the three proton degrees of freedom and the OOstretch as the reduced dimensionality space. While such approaches are better in
3.3 Selected Systems
some respects than harmonic calculations in full dimensionality, they can miss important coupling with the monomer degrees of freedom. This was demonstrated in comparisons of fully coupled 4d and full dimensionality virtual configuration interaction (VCI) calculations [27]. The results of the comparison showed that for some states the reduced dimensionality treatment was quite realistic, but not for the proton anti-symmetric stretch. For that important mode the 4d estimate for the fundamental is nearly 300 cm–1 higher than the full dimensional calculation. The reason for this large difference was traced to the neglect of coupling of that mode to the monomer modes in the 4d calculations. This coupling is large and can be understood simply by noting that as the proton moves towards one monomer and away from the other, the closer monomer takes on H3O+ character while the other monomer takes on H2O character and this clearly introduces monomer coupling into the proton anti-symmetric stretch. The full-dimensional VCI calculations, mentioned above, were done with the single-reference version of Multimode. The calculations used a full-dimensional potential due to Ojamae, Shavitt, and Singer [57], version OSS3(p), and considered all four-mode couplings among the 15 normal modes. Until just recently, this was the only full dimensional potential surface for H5O+2 . In many respects the OSS3(p) potential is quite realistic; however, it is not spectroscopically accurate. A summary of these published vibrational energies of H5O+2 is given in Table 3.1 along with full-dimensionality correlation-consistent vibrational self-consistent field calculations [58] (CC-VSCF), which were restricted to two-mode coupling. All the calculations find the OO-stretch in the range 569–599 cm–1. However, only the 2d+2d calculations predict the fundamental energy of the OH+O-x bend below the asymmetric stretch; they also are alone in predicting the OH+O-y bend at around 1000 cm–1. With regard to the highly interesting OH+O-anti-symmetric stretch, only the VCI/OSS3(p) calculations predict the fundamental below 1000 cm–1. (Based on this prediction, the intense band labeled “B” in Fig. 3.7 was re-assigned [27] as the OH+O-anti-symmetric stretch.) However, for the OH-monomer stretches agreement between the VCI/OSS3(p) calculations and experiment is only fair to poor. This appears to be due primarily to a shortcoming of the OSS3(p) potential. The CC-VSCF/MP2 calculations [58] for these stretches are in somewhat better agreement with experiment; however, not close to “spectroscopic” accuracy. In reviewing published calculations on H5O+2 , it should be noted that diffusion Monte Carlo (DMC) calculations of the zero-point state using the OSS potential [47, 59] and the more recent ab initio potential [22, 28] (see below) have been reported. These calculations clearly indicate the highly delocalized nature of the zero-point state. In recent work, correlation function DMC calculations of the IR spectrum were reported using the OSS3(p) potential [47]. These calculations indicate a quite complex spectrum with much mixing among low-frequency modes. Two states with substantial OH+O-anti-symmetric stretch character were identified at 737 and 870 cm–1. The latter number is fairly close to the 902 cm–1 result for this state obtained in VCI calculations on the same potential energy surface (and shown in Table 3.1).
71
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3 Gas Phase Vibrational Spectroscopy of Strong Hydrogen Bonds Tab. 3.1 Selected vibrational energies (cm–1) of H5O+2
calculated by a variety of methods and experiment for the OH-monomer stretches. “2d+2d” are the adiabatic 4d calculations of Ref. [56], “4d” are the fully coupled 4d calculations of Ref. [27], “CC-VSCF” are the correlationconsistent vibrational self-consistent field calculations of Ref. [58] and “VCI” are the virtual configuration interaction calculations of Ref. [27]. The potential used in these calculations is indicated after the back-slash. Exp[a]
Mode
2d+2d/MP2
4d/OSS3(p)
CC-VSCF/MP2
VCI/OSS3(p)
OO-stretch
587
571
599
569
OH+O-asym st
1158
1185
1209
902
OH+O-x bend
968
1328
1442
1354
OH+O-y bend
1026
1344
1494
1388
OH-monomer1
NA
NA
3579
3320
–
OH-monomer2
NA
NA
3577
3420
3609
OH-monomer3
NA
NA
3593
3470
–
OH-monomer4
NA
NA
3518
3470
3684
Clearly an accurate simulation of the vibrational energies and IR spectrum of H5O+2 requires accurate full-dimensional potential energy and dipole moment surfaces and a full-dimensional treatment of the dynamics. Very recently we reported a new ab initio, full dimensional potential energy surface and dipole moment for H5O+2 [22]. The ab initio calculations were done at the CCSD(T) level of theory with an aug-cc-pVTZ basis for roughly 50 000 configurations. The potential energy surface is a fit to these energies. It is permutationally invariant with respect to like atoms and dissociates properly to H2O + H3O+. It was obtained using the methods briefly reviewed in Section 3.2.3. The variables of the fit are given by xi,j = exp(–ri,j/a) where ri,j are all the internuclear distances and a was fixed at 2.0 a0. The fit is highly precise and the RMS fitting error is shown in Fig. 3.10 as a function of the maximum energy of the data set used in determining the error. As seen, the RMS error is quite small and is roughly 20 cm–1 for total energies up to 40 000 cm–1 above the global minimum. This value of the RMS is not in the range of “spectroscopic” accuracy, i.e., within 1 cm–1; however, it is close to the expected accuracy of the ab initio method used.
3.3 Selected Systems 100
50000
No.Pts
80
40000 60 35000 RMS error
40
-1
RMS Error/cm
No of ab initio points
45000
30000
20
25000
20000 0
20000
40000
60000
E/cm
80000
100000
0 120000
-1
Figure 3.10 The number of configurations and RMS fitting error as a function of the energy cut-off, as explained in the text.
This new potential is highly anharmonic and fluxional with numerous low energy saddle points. Together with Anne McCoy, Stuart Carter and Xinchuan Huang, we have begun large-scale vibrational calculations using the new potential and dipole moment surfaces. These calculations are quite demanding and are being done with the single reference and reaction path versions of Multimode briefly described above and also with the DMC method. Some preliminary results have very recently been reported [28]; however, at present we only have a “rough” IR spectrum based on VCI calculations using the single-reference version of Multimode. This version of the code cannot describe internal torsional motion fully; however it can do crude IR simulations using the exact dipole moment. We present two plots of the calculated 0 K IR spectrum below. The first one, Fig. 3.11, is in the spectral region of the recent IR experiments, shown in Figs. 3.7–3.9. Based on unpublished comparisons of the VCI energies in this region with excited state DMC ones of McCoy we believe the VCI energies in this region are high by roughly 100 cm–1 Thus, we have shifted this VCI spectrum to the red by 100 cm–1. As seen there are peaks in this calculated spectrum that correspond approximately to the experimental spectra shown in Figs. 3.7–3.9. (Note there is only rough agreement among these experimental spectra, as noted already.)
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3 Gas Phase Vibrational Spectroscopy of Strong Hydrogen Bonds
1.2 ν
7
1
Intensity (arb. units)
74
0.8
0.6 ν
11
0.4
ν +ν 2
3
ν +ν 4
ν +ν 4
6
5
0.2
ν
8
Mixed
ν
9
0 1000
1200
1400
1600
1800
2000
-1
ω (cm ) Figure 3.11 0 K IR spectrum obtained using “single-reference” VCI Multimode calculations using the new potential of Ref. [22]. Modes 2–5 are various low-frequency rock, wag and torsion modes, mode 6 is the
OO-stretch, mode 7 is the OH+O-asymmetric stretch, modes 8 and 9 are the OH+O x and y bends, and mode 11 is the asymmetric monomer bends.
The 0 K IR spectrum in the range 3600–3800 cm–1 is shown in Fig. 3.12 and is presented with no energy shift. As seen, the spectrum is fairly complex but does show intensities in qualitative accord with experiment, shown in Fig. 3.6. Our analysis indicates that the relatively intense lines at 3620 cm–1 are the monomer OH-symmetric stretch and those at 3710 cm–1 are the asymmetric stretch. We stress that these are preliminary results and likely not well converged. More accurate DMC and Multimode-reaction path calculations for the four monomer stretches indicate that the single reference energies are 40–100 cm–1 high [28].
3.4 Outlook
1.2
Intensity (arbitrary units)
1
0.8
0.6
0.4
0.2
0 3600
3620
3640
3660
3680
3700
3720
3740
3760
-1
ω (cm ) Figure 3.12 0 K IR spectrum obtained using “single-reference” VCI Multimode calculations using the new potential of Ref. [22].
3.4 Outlook
The vibrational signature of strong hydrogen bonds is found in a spectral region which can be accessed directly with novel radiation sources operating in the midIR. The photodissociation experiments described above all yield spectra without rotational resolution, mainly due to the inherent broad bandwidth of the FELIX radiation. Recent advances in the technology of table top tunable IR lasers are promising and these narrower bandwidth systems have the potential to go beyond this barrier and elucidate the structures of the clusters with considerably more detail based on high resolution spectra. The experiments using FELs should remain interesting, due to the considerably higher pulse energies, different temporal pulse structure and greater tunability available. Multiphoton absorption photodissociation spectra measured at high pulse energies, above the “quasi-linear” regime, contain additional information on the underlying PES that, in principle, could be extracted, if theoretical models could directly simulate the more complex multiphoton absorption processes.
75
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3 Gas Phase Vibrational Spectroscopy of Strong Hydrogen Bonds
The experimental vibrational spectra of strongly hydrogen bonded systems, especially H5O+2 are complex, owing to strong mode-mixing. Their interpretation requires theoretical approaches beyond the harmonic approximation. The calculated spectra for H5O+2 presented here look promising, but more work is needed using better converged calculations and also for non-zero temperature. Calculations for the various isotopomers of H5O+2 are also needed and this will be forthcoming. More challenging will be calculations that directly address the experimental spectra that use either Ar-messenger or multiphoton dissociation techniques.
Acknowledgments
JMB thanks the National Science Foundation and the Office of Naval Research for financial support. He also gratefully acknowledges collaborators Bastiaan Braams, Stuart Carter, Xinchuan Huang and Anne McCoy. KRA and DMN wish to acknowledge contributions from their collaborators Nicholas L. Pivonka, Matthew J. Nee and Andreas Osterwalder at the University of California Berkeley; Ludger Wste, Cristina Kaposta, Mathias Brmmer, Gabriele Santambrogio and Carlos Cibrin Uhalte at the Freie Universitt Berlin and Gerard Meijer and Gert von Helden at the Fritz-Haber-Institut der Max-Planck-Gesellschaft in Berlin. KRA gratefully acknowledges financial support by the German Research Foundation DFG as part of the Collaborative Research Center 546 and the Research Training Group 788, as well as the “Stichting voor Fundamenteel Onderzoek der Materie (FOM)” in providing the required beam time on FELIX and the skillful assistance of the complete FELIX staff. He also thanks Travis Fridgen for supplying a copy of the CLIO spectrum. DMN acknowledges support from the Air Force Office of Scientific Research.
References
References 1 J. Trylska, P. Grochowski,
J. A. McCammon, Protein Sci. 2004, 13, 513–528. 2 C. A. Hunter, Angew. Chem., Int. Ed. 2004, 43, 5310–5324. 3 V. Z. Spassov, H. Luecke, K. Gerwert, D. Bashford, J. Mol. Biol. 2001, 312, 203–219. 4 D. Marx, M. E. Tuckerman, J. Hutter, M. Parinello, Nature 1999, 397, 601. 5 T. Steiner, Angew. Chem., Int. Ed. 2002, 41, 48–76. 6 M. A. Duncan, Int. J. Mass Spectrom. 2000, 200, 545–569; E. J. Bieske, O. Dopfer, Chem. Rev. 2000, 100, 3963– 3998. 7 N. H. Rosenbaum, J. C. Owrutsky, L. M. Tack, R. J. Saykally, J. Chem. Phys. 1986, 84, 5308–5313. 8 S. Davis, M. Frnk, D. Uy, D. J. Nesbitt, Chem. Phys. Lett. 2001, 344, 23–30. 9 S. Mukamel, J. Jortner, J. Chem. Phys. 1976, 65, 5204. 10 J. Oomens, A. G. G. M. Tielens, B. G. Sartakov, G. von Helden, G. Meijer, Astrophysical Journal 2003, 591, 968. 11 M. Nee, C. Kaposta, A. Osterwalder, C. Cibrian Uhalte, T. Xie, A. Kaledin, S. Carter, J. M. Bowman, G. Meijer, D. M. Neumark, K. R. Asmis, J. Chem. Phys. 2004, 121, 7259. 12 M. Okumura, L. I. Yeh, Y. T. Lee, J. Chem. Phys. 1985, 83, 3705–3706. 13 W. H. Robertson, M. A. Johnson, Annu. Rev. Phys. Chem. 2003, 54, 173–213. 14 G. von Helden, I. Holleman, G. M. H. Knippels, A. F. G. van der Meer, G. Meijer, Phys. Rev. Lett. 1997, 79, 5234–5237. 15 M. Gerhards, C. Unterberg, A. Gerlach, Phys. Chem. Chem. Phys. 2002, 4, 5563– 5565; M. Gerhards, Opt. Commun. 2004, 241, 493–497; J. A. Stearns, A. Das, T. S. Zwier, Phys. Chem. Chem. Phys. 2004, 6, 2605–2610. 16 J. M. Headrick, J. C. Bopp, M. A. Johnson, J. Chem. Phys. 2004, 121, 11523–11526. 17 W. R. Bosenberg, D. R. Guyer, J. Opt. Soc. Am. B-Opt. Phys. 1993, 10, 1716.
18 K. R. Asmis, M. Brmmer, C. Kaposta,
G. Santambrogio, G. von Helden, G. Meijer, K. Rademann, L. Wste, Phys. Chem. Chem. Phys. 2002, 4, 1101–1104. 19 G. M. H. Knippels, G. H. C. Vanwerkhoven, E. H. Haselhoff, B. Faatz, D. Oepts, P. W. Vanamersfoort, Nucl. Instrum. Methods A 1995, 358, 308–310; D. Oepts, A. F. G. van der Meer, P. W. van Amersfoort, Infrared Phys. Technol. 1995, 36, 297–308. 20 A. Brown, B. J. Braams, K. Christoffel, Z. Jin, J. M. Bowman, J. Chem. Phys. 2003, 119, 8790–8793; A. B. McCoy, B. J. Braams, A. Brown, X. C. Huang, Z. Jin, J. M. Bowman, J. Phys. Chem. A 2004, 108, 4991–4994. 21 X. C. Huang, B. J. Braams, S. Carter, J. M. Bowman, J. Am. Chem. Soc. 2004, 126, 5042–5043. 22 X. Huang, B. J. Braams, J. M. Bowman, J. Chem. Phys. 2005, 122, 044308. 23 S. Carter, N. C. Handy, C. Puzzarini, R. Tarroni, P. Palmieri, Mol. Phys. 2000, 98, 1697–1712. 24 J. M. Bowman, S. Carter, X. C. Huang, Int. Rev. Phys. Chem. 2003, 22, 533–549; S. Carter, N. C. Handy, J. Chem. Phys. 2000, 113, 987–993; J. M. Bowman, S. Carter, N. C. Handy, in Theory and Applications of Computational Chemistry: The First 40 Years, C. Dykstra, G. Frenking, K, S. Kim, G. E. Scuseria (Eds.). 25 W. H. Miller, N. C. Handy, J. E. Adams, J. Chem. Phys. 1980, 72, 99–112; J. T. Hougen, P. R. Bunker, J. W. C. Johns, J. Mol. Spectrosc. 1970, 34, 136–172. 26 E. G. Diken, J. M. Headrick, J. R. Roscioli, C. Bopp, M. A. Johnson, A. B. McCoy, X. Huang, S. Carter, J. M. Bowman, J. Phys. Chem. A 2005, 109, 571. 27 J. Dai, Z. Bacic, X. Huang, S. Carter, J. M. Bowman, J. Chem. Phys. 2003, 119, 6571–6580. 28 A. B. McCoy, X. Huang, S. Carter, M. Landeweer, J. M. Bowman, J. Chem. Phys. 2005, 122, 061101; N. J. Hammer, E. G. Diken, J. R. Roscioli, E. M. Myshakin, K. D. Jordan, A. B. McCoy, X. Huang, S. Carter,
77
78
3 Gas Phase Vibrational Spectroscopy of Strong Hydrogen Bonds
29 30
31
32 33
34 35
36
37
38 39 40 41
42 43
J. M. Bowman, M. A. Johnson, J. Chem. Phys. 2005, 122, 244301. G. Caldwell, P. Kebarle, Can. J. Chem. 1985, 63, 1399–1406. H. Gomez, G. Meloni, J. Madrid, D. M. Neumark, J. Chem. Phys. 2003, 119, 872–879. N. L. Pivonka, C. Kaposta, G. von Helden, G. Meijer, L. Wste, D. M. Neumark, K. R. Asmis, J. Chem. Phys. 2002, 117, 6493–6499. D. M. Neumark, Acc. Chem. Res. 1993, 26, 33–39. H. Kunttu, J. Seetula, M. Rsnen, V. A. Apkarian, J. Chem. Phys. 1992, 96, 5630–5635. B. S. Ault, Acc. Chem. Res. 1982, 15, 103– 109. D. U. Webb, K. N. Rao, J. Mol. Spectrosc. 1968, 28, 121; D. R. J. Boyd, H. W. Thompson, Spectrochim. Acta 1952, 5, 308. K. Kawaguchi, J. Chem. Phys. 1988, 88, 4186–4189; K. Kawaguchi, E. Hirota, J. Chem. Phys. 1986, 84, 2953–2960; K. Kawaguchi, E. Hirota, J. Chem. Phys. 1987, 87, 6838–6841; K. Kawaguchi, E. Hirota, J. Mol. Struct. 1995, 352, 389– 394. N. L. Pivonka, C. Kaposta, M. Brmmer, G. von Helden, G. Meijer, L. Wste, D. M. Neumark, K. R. Asmis, J. Chem. Phys. 2003, 118, 5275–5278. P. A. Frey, J. Phys. Org. Chem. 2004, 17, 511–520. J. E. Del Bene, M. J. T. Jordan, Spectrochim Acta, Part A 1999, 55, 719–729. C. M. Ellison, B. S. Ault, J. Phys. Chem. 1979, 83, 832–837. A. Kaledin, S. Skokov, J. M. Bowman, K. Morokuma, J. Chem. Phys. 2000, 113, 9479–9487. N. Agmon, Chem. Phys. Lett. 1995, 244, 456–462. R. Rousseau, V. Kleinschmidt, U. W. Schmitt, D. Marx, Phys. Chem. Chem. Phys. 2004, 6, 1848–1859.
44 G. Zundel, Adv. Chem. Phys. 2000, 111,
1–217. 45 N. B. Librovich, V. P. Sakun,
N. D. Sokolov, Chem. Phys. 1979, 39, 351; J. Kim, U. W. Schmitt, J. A. Gruetzmacher, G. A. Voth, N. E. Scherer, J. Chem. Phys. 2002, 116, 737–746. 46 I. Olovsson, J. Chem. Phys. 1968, 49, 1063–1067. 47 X. Huang, H. M. Cho, S. Carter, J. Ojamae, J. M. Bowman, S. J. Singer, J. Phys. Chem. A 2003, 107, 7142–7151; H. M. Choi, S. J. Singer, J. Phys. Chem. A 2004, 108, 8691. 48 L. I. Yeh, J. D. Myers, J. M. Price, Y. T. Lee, J. Chem. Phys. 1989, 91, 7319– 7330. 49 Y. K. Lau, S. Ikuta, P. Kebarle, J. Am. Chem. Soc. 1982, 104, 1462–1469. 50 L. I. Yeh, Y. T. Lee, J. T. Hougen, J. Mol. Spectrosc. 1994, 164, 473–488. 51 D. J. Wales, J. Chem. Phys. 1999, 110, 10403–10409. 52 K. R. Asmis, N. L. Pivonka, G. Santambrogio, M. Brmmer, C. Kaposta, D. M. Neumark, L. Wste, Science 2003, 299, 1375. 53 T. D. Fridgen, T. B. McMahon, L. MacAleese, J. Lemaire, P. Maitre, J. Phys. Chem. A 2004, 108, 9008–9010. 54 R. Prazeres, F. Glotin, C. Insa, D. A. Jaroszynski, J. M. Ortega, Eur. Phys. J. D 1998, 3, 87. 55 M.A. Johnson, personal communication. 56 M. V. Vener, O. Khn, J. Sauer, J. Chem. Phys. 2001, 114, 240–249. 57 L. Ojame, I. Shavitt, S. J. Singer, J. Chem. Phys. 1998, 109, 5547–5564. 58 G. M. Chaban, J. O. Jung, R. B. Gerber, J. Phys. Chem. A 2000, 104, 2772–2779. 59 M. Mella, D. C. Clary, J. Chem. Phys. 2003, 119, 10048–10062. 60 K. R. Asmis, M. Brummer, C. Kaposta, G. Santambrogio, G. von Helden, G. Meijer, K. Rademann, L. Woste, Phys. Chem. Chem. Phys. 2002, 4, 1101–1104.
79
4 Laser-driven Ultrafast Hydrogen Transfer Dynamics Oliver Khn and Leticia Gonzlez
4.1 Introduction
The ground state tunnel splitting in a symmetric double well potential, D0, is associated with a tunneling time of s0 ¼ h=2D0 . If we take the hydrogen transfer (HT) in tropolone [1] as an example we have D0 » 1 cm–1 and therefore s0 » 16:7 ps. This is a rather long time as compared, e.g. with the period of an OH-stretch vibration or with the T1 relaxation time of this vibration in solution [2]. Consequently, to study ultrafast HT in the electronic ground state the dynamics has to be initiated closer to or even above the reaction barrier what could be achieved by an interaction with an IR laser pulse. Of course, this draws on the analogy with electron-vibrational dynamics triggered after almost instantaneous optical excitation and thus switching of the electronic state. Here the driving force for the nuclear wave packet motion after excitation is due to the difference in the electron density which leads, for instance, to the rather rapid reactions observed for excited state HT [3–5]. Building further on this analogy one could think of adiabatically separating the fast OH-stretch dynamics from the slower motions of the molecular frame. This would result in adiabatic potential energy surfaces (PES) for the slow modes in a given state of the OH-stretch mode [6–8]. The HT can then be viewed as a slow mode wave packet moving on the adiabatic potential whose character changes gradually from an OH-stretch excitation localized in the reactant well to an excitation localized in the product well. The first question, which is raised by this simple analogy, concerns the very possibility of exciting slow mode wave packets in a hydrogen bond at all. Taking a different perspective it touches the very issue of interpretation of the notoriously complex IR spectra [9]. In the condensed phase much of this complexity is hidden under bands broadened by the solvent interaction. Hence it was only recently that coherent wave packet motion of a 100 cm–1 hydrogen bond mode could be observed after OH-stretch excitation, although in a system which has only a single minimum potential [10]. Meanwhile coherent low-frequency dynamics has also been observed in a double minimum system (acetic acid dimer) [11]. With this Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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4 Laser-driven Ultrafast Hydrogen Transfer Dynamics
proof-of-principle at hand it is not far-fetched to tackle the goal of making use of the coherence contained in the hydrogen bond wave packet motion to control it by means of tailored IR laser pulses. Influencing reaction pathways by means of designed laser fields is emerging as a powerful tool in femtochemistry and femtobiology [12–14]. In principle both frequency- and time-domain control schemes are being explored. Only the timedomain ultrashort laser pulse control will be discussed in the following since it gives direct access to the dynamics, particularly in the condensed phase where stationary spectra are usually very broad. In view of the importance of H-bonding and HT reactions it would be desirable to have at hand concepts for guiding the H-bond dynamics with laser pulses. Two scenarios for H-bond dynamics will be addressed below: First, IR laser control of HT between different tautomers in the electronic ground state; second, Hbond breaking by combining IR pre-excitation with a second UV pulse which switches the electronic state. In both cases short few-cycle IR pulses will play an important role. We start by outlining the theoretical methods putting emphasis on the determination of potential energy surfaces in Section 4.2. In Section 4.3.1 we demonstrate ultrafast laser driven HT in low-dimensional gas and condensed phase model systems using IR pulses encompassing a few-cycles only. However, turning to realistic multidimensional PES it is further shown that the anharmonicity of the PES for HT severely challenges any straightforward control attempt. In Section 4.3.2 we present results where the IR driven motion is restricted to the vicinity of the PES minimum, but of an anionic species of the type AHB–. Here a second UV pulse can trigger a transition to a neutral PES. Provided that IR and UV pulses are properly timed the H-bond breaks selectively by virtue of the large forces coming along with the removal of an electron. Finally, a summary is given together with some perspectives in Section 4.4.
4.2 Theory
The theoretical description of HT Dynamics requires having at hand a PES and a method for solving the appropriate equations of motion. For few atom systems such as AHB– one can express the PES in terms of bond distances and angles, or if only the bonded motion shall be considered, vibrational normal mode coordinates can be chosen (see, e.g., Ref. [15]). In the latter approach one relies on the fact that any desired geometry can be expressed in terms of displacements along normal mode coordinates. Since these coordinates are defined and thereby biased with respect to a reference geometry, it is to be expected that the representation of the total PES may not be very compact. Thus, the method is not very economical which hampers its application to large systems. Here one could, in principle, resort to the bond distance/bond angle approach with an additional assumption concerning the majority of degrees of freedom (DOF), which are not explicitly
4.2 Theory
treated. They could be either frozen at some reference geometry or relaxed to the minimum subject to the constraints imposed by the explicit coordinates [16–18]. In both cases one makes an assumption concerning the time scales of the explicit and the neglected coordinates. It should be noted, however, that neither approximation can be fully justified. There will always be faster and slower coordinates as compared with the explicit ones. A more rigorous formulation of this concept, which allows the selection of important DOF according to their actual coupling, is provided by reaction path and reaction surface approaches. Here one makes a distinction between one or a few large amplitude reactive coordinate(s) and many orthogonal harmonic vibrational coordinates [19]. In the case of a single reaction coordinate this is usually selected to be the minimum energy intrinsic reaction path [20]. HT reactions, however, are of the heavy–light–heavy type and the one-dimensional (1D) reaction path is known to be sharply curved. Accordingly, the coupling between the reaction coordinate and the orthogonal modes becomes rather strong which merely indicates that this choice of coordinates is not well suited for HT problems. To cope with this issue Miller et al. [21] and later Shida et al. [22] have proposed to use two and three, respectively, large amplitude coordinates to span a reaction surface. Still the majority of coordinates are treated in the harmonic approximation. Specifically, they have considered malonaldehyde and taken into account the two OH distances and the O–O distance as large amplitude coordinates. If one aims to explore the PES this approach is rather illuminating. For dynamics calculations, however, one faces the challenge that due to the curvilinear nature of the coordinates, the kinetic energy operator takes a rather complicated form. This necessitates further approximations such as the adiabatic decoupling between the reaction coordinates and the orthogonal oscillator modes. It is probably because of this difficulty that the approach has not been fully explored for the use in HT reaction dynamics for many years. It has been only recently that interest has been revived and a number of studies focused on this approach [23–26]. As an alternative that solves the kinetic coupling problem, Miller and co-workers suggested an all-Cartesian reaction surface Hamiltonian [27, 28]. Originally this approach partitioned the DOF into atomic coordinates of the reactive particle, such as the H-atom, and orthogonal anharmonic modes of what was called the substrate. If there are N atoms and we have selected NR reactive coordinates there will be NH = 3N – 6 – NR harmonic oscillator coordinates and the reaction surface Hamiltonian reads H¼
NH NH NR p2 X P Pn2 1 X i þ Vðx1 ; . . . ; xNR Þ þ fn ðxÞQn þ Q K ðxÞQn 2 2 m;n¼1 m mn i¼1 2 n¼1
(4.1)
Here Vðx1 ; . . . ; xNR Þ is the potential for the reactive coordinates when the substrate coordinates are either frozen at some reference geometry or relaxed to minimize Vðx1 ; . . . ; xNR Þ. Since in general we are not dealing with a minimum energy configuration, forces fn ðxÞ appear in Eq. (4.1), which act on the normal mode coordinates fQn g. Finally, the last term in Eq. (4.1) contains the force constant matrix Kmn ðxÞ, which is diagonal at that configuration for which the normal modes have
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been defined. Everywhere else there may be a mode coupling due to the motion of the reaction coordinates. The important point here is to notice that Eq. (4.1) does not contain any kinetic energy coupling, only potential energy coupling. Of course, this comes only at the price of not being able to take into account rotations. In that sense “substrate” implies that this approach is well suited when a light particle moves in the field of a surrounding which is almost rigid. Apart from an application to H-atom diffusion in crystalline silicon [29] this approach went essentially unnoticed until we have used it to study the proton transfer in 8-hydroxyimidazo[1,2-a]pyridine [30]. Subsequently, it has been applied to study the H-bond dynamics in phthalic acid monomethylester [31], the HT in salicylaldimine [32], 3-chlorotropolone [33], and 3,7-dichlorotropolone [34]. Very recently we have modified the original reaction surface approach by choosing collective reaction coordinates instead of the H-atom position [35]. This does not alter the allCartesian form of Eq. (4.1) but gives a more compact representation of the PES, which contains the most relevant motions of the heavy atoms already in the reaction coordinates. For the specific application to the HT in tropolone we could show that the reaction plane spanned by these reaction coordinates contains the intrinsic reaction path almost completely, that is, the remaining couplings to the orthogonal harmonic modes are rather modest [35]. The Hamiltonian in Eq. (4.1) has an almost product-like form since the majority of coordinates are treated as harmonic oscillators. This makes it rather suitable for quantum dynamics simulations, either in the time-dependent Hartree approximation [31] or using the more general multi-configuration time-dependent Hartree approach [36, 37]. However, Eq. (4.1) has another advantage in that it directly connects to the system–bath models used in condensed phase dynamics [38]. Here the reactive coordinates and the substrate modes comprise the relevant system and the bath, respectively. Larger molecules may provide their own bath and Eq. (4.1) can be used to calculate an ab initio system–bath Hamiltonian and microscopic relaxation and dephasing rates [33]. Assuming that the frequencies of the bath modes do not depend on the system coordinates one arrives at the system–bath Hamiltonian H ¼ HS þ HB þ HSB ¼
NR 2 X p i
i¼1
2
þ VðxÞ þ
NH NH X 1X ½Pn2 þ x2n Qn2 fn ðxÞQn 2 n¼1 i¼1
(4.2)
Supplementing this equation with an additional set of solvent oscillators one can incorporate a solvent environment. Notice that this does not necessarily imply harmonic solvent motions. In fact the full anharmonicity of the solvent can be accounted for in the context of linear response theory [39] where the interaction is described in terms of an effective harmonic oscillator bath. This allows calculation of relaxation rates from classical molecular dynamics simulations of the force fn ðxÞ exerted by the solvent on the relevant system. This approach has found appli-
4.3 Laser Control
cation, for instance, for HOD in D2O [40, 41] and for the intramolecular hydrogen bond dynamics in phthalic acid monomethyl ester [42]. Equipped with microscopic relaxation rates the dissipative dynamics can be modeled, e.g., by using a quantum master equation [42, 43]. This restricts the applicability to situations where the interaction between relevant system and bath is weak and Markovian [38]. To go beyond this limitation, quantum-classical methods have been developed and applied, e.g., to enzymatic hydride transfer reactions [44].
4.3 Laser Control 4.3.1 Laser-driven Intramolecular Hydrogen Transfer
The conceptionally simplest approach for IR-driven HT, the pump–dump scheme [45], can be illustrated using a one-dimensional double minimum potential as shown in Fig. 4.1. First we notice that the potential is asymmetric which allows one to distinguish between the initial state Wi and the final state Wf of the HT reaction. Initially a pump-pulse excites the system from the localized ground state Wi to a delocalized intermediate state Wb which usually is energetically above the reaction barrier. From there a second pulse dumps the system into the product
Figure 4.1 Illustration of the pump–dump scheme for a slightly asymmetric one-dimensional double minimum potential. In a first step a pump pulse excites the system from the initial state Wi to an above-the-barrier state Wb. From there a second pulse dumps the population into the target state Wf.
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well, thus populating state Wf. The electric field for this above-the-barrier scheme takes the following form P 0 pðt ti Þ cos ðxi tÞ EðtÞ ¼ Ei Hðt ti ÞHðsi þ ti tÞ sin 2 (4.3) si i¼1;2 Here Ei0 is the amplitude, si the duration, and xi the frequency of the ith pulse. This scheme has been applied in Ref. [46] to a generic two-dimensional HT model which incorporated a H-atom reaction coordinate as well as a low-frequency Hbond mode. In a subsequent work [47] the approach has been specified to a simple model of HT in thioacetylacetone. The Hamiltonian was tailored to the form of Eq. (4.1) based on the information available for the stationary points, that is, the energetics as well as the normal modes of vibration. From these data an effective two-dimensional potential was constructed including the H-atom coordinate as well as a coupled harmonic oscillator, which describes the O–S H-bond motion. Although perhaps oversimplified, this model allowed the study of some principle aspects of laser-driven H-bond motion in an asymmetric low-barrier system. A field like Eq. (4.3) with separate and overlapping pulses is capable of giving an almost 100% population transfer. This “above-the-barrier” mechanism is also obtained when using the more sophisticated optimal control theory. Here the laser pulse form is obtained from maximizing the functional (see, e.g., Ref. [48]) ZT J ¼ jhWðTÞjW f ij2 k
dt
E 2 ðtÞ SðtÞ
0
ZT 2RehWðtÞjW f i 0
(4.4)
¶ dthUðtÞj þ i½H dEðtÞjWðtÞi ¶t
where T is the time at which the propagated wave function W(t) should coincide with the target state Wf; U(t) is some auxiliary function and d is the dipole moment. The laser field is influenced by the shape function S(t) as well as by the parameter j, which sets a penalty for high field intensities [49]. Interestingly, upon increasing j the dynamics of the system changes qualitatively. The abovethe-barrier pathway becomes too expensive and a through-the-barrier tunneling pathway becomes operative. Because of its tunneling nature this pathway was coined “Hydrogen subway” in Ref. [50]. Needless to say both mechanisms are going beyond any perturbation theory with respect to the matter-field interaction. Apart from requiring less intense fields the latter scheme has the advantage that during the time evolution highly excited vibrational states are not appreciably populated. Thus, the moving wave packet does not sample the full anharmonicity of the potential surface and might stay localized in a few DOF. The low degree of excitation is also preferable once considering condensed phase dynamics. Here the energy relaxation rates usually scale with the quantum number of the vibrational state [38]. In other words, exciting the system above the barrier would cause not only rapid energy relaxation but also phase relaxation and the means for controlling the dynamics might be lost. Indeed, using a simple system–bath model
4.3 Laser Control
Figure 4.2 (a) Optimal control field for the system shown in Fig. 4.1 for a penalty parameter j = 400 (see Eq. (4.4)). The pulse triggers quantum tunneling between the two lowest states whose populations are shown in (b); for details see also Ref. [50].
like Eq. (4.2) it was shown in Ref. [47] that the tunneling pathway is more effective in a dissipative situation. The pulse forms in the simplest case where only the two lowest states are involved in the through-the-barrier tunneling dynamics are of plateau type; see Fig. 4.2. They serve to compensate for the potential asymmetry (initial rise), facilitate tunneling (plateau phase), and restore the asymmetry to stabilize the products (switch-off phase). It turns out that more realistic few-cycle pulses may realize the same net effect although not in the step-wise fashion as a plateau pulse [47, 51, 52]. In Fig. 4.3 we show such a few-cycle pulse together with the population dynamics of the two lowest states of a double minimum potential adapted to the situation in thioacetylacetone. The time scale of the reaction is dictated by the tunneling time, i.e., the tunnel splitting for the degenerate levels. This implies that with increasing barrier height the ground state tunneling pair is no longer a good candidate for triggering an ultrafast isomerization. In Ref. [53] it was shown that in this case it is advantageous to combine an IR pulse causing vibrational excitation to a higher lying tunneling pair with a subsequent plateau type pulse which establishes the degeneracy of that pair. The influence of the interaction with an environment on the control yield and pathways can be modeled using different strategies. In principle it is possible to determine optimized pulses in the presence of energy and phase relaxation [12,
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4 Laser-driven Ultrafast Hydrogen Transfer Dynamics
Figure 4.3 (a) Few-cycle control field which drives the HT in a one-dimensional model of thioacetylacetone. (b) Population difference between the two lowest states (initial and target state) for the coherent case and different
strengths of the system–bath coupling as expressed by the Kondo parameter n. The dissipative propagation has been performed using a real-time path integral approach; for details see also Ref. [51].
13]. A simpler route studies the relaxation effects with reference to the optimized laser-driven dynamics of the isolated system. The interaction with the environment can be described using the quantum master equation approach (see Section 4.2) [38]. This requires that the coupling is weak and that a Markov approximation for the system–bath dynamics applies. Even if these two conditions are fulfilled, the presence of the rather strong external control field may lead to a modification of the system’s energy spectrum and therefore to time-dependent relaxation rates. This has been investigated in Ref. [54] on the basis of a generalized Fokker–Planck theory. In Fig. 4.4 we show the time dependence of the low lying states of a 1D approximation to the double minimum potential of the HT in thioacetylacetone and of the relaxation rates for transitions between the two lowest levels. The latter clearly show the dependence on the time-dependent transition frequencies. While this extension of the quantum master equation approach is straightforwardly implemented, going beyond the restrictions imposed by perturbation theory and Markov approximation requires a considerable effort. One possibility is given by the real-time path integral approach [55]. This limits the applications to a few level systems coupled to a harmonic bath, but for this class of systems one can perform numerical exact quantum dynamics simulations. In Ref. [51] we have shown that under the conditions of strong system–bath coupling and strong-field driving the
4.3 Laser Control
Figure 4.4 (a) Time-dependent energy levels for the one-dimensional model of thioacetylacetone for a few-cycle driving field similar to Fig. 4.3. In (b) we show the resulting rates
(in units of the coupling strength) for upward (dotted) and downward (solid) population relaxation between the two lowest lying states; for details see Ref. [54].
dynamics is markedly different from what one observes when using the simple quantum master equation theory. Exemplary results are given in Fig. 4.3(b). Upon increasing the system–bath coupling the interplay between driving and relaxation according to the instantaneous spectrum – reflected in the oscillatory population dynamics – leads to a non-vanishing control yield, even for a relatively long laser pulse. So far we have considered one- and two-dimensional model systems in the gas and condensed phases. Although the two-dimensional model of thioacetylacetone has been based on quantum chemistry data, the choice of a single reaction coordinate and a single coupled oscillator has been dictated by the desired simplicity of the model. The question arises whether the concepts, which have been developed for this model, can be transferred to more realistic situations. The requirements on a system have been spelled out already in Ref. [46]: (i) The PES has to be asymmetric to have a clear distinction between initial and final states. (ii) There should be a significant change in the dipole moment upon HT to provide directionality of the excitation. (iii) The barrier height should exceed the reorganization energy difference between the minimum and the transition state of the most strongly coupled oscillator. The reorganization energy of an oscillator in Eq. (4.1) is the energy, which is required to restore the oscillator’s equilibrium position along the reaction coordinate. The last condition is of approximate character and has been motivated by the observation that upon increasing the coupling between the reaction coordinate and the coupled oscillator in a two-dimensional model, the eigenstates are energetically shifted above the barrier and the notion of localized reactant and product states becomes meaningless. A systematic approach to the determination of multidimensional PES for HT reactions is given by the reaction surface Hamiltonian, Eq. (4.1). In Ref. [32] we
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have calculated a reaction surface for the tautomerism in salicylaldimine, a molecule which appeared to be suitable according to points (i) and (ii) above. The inplane coordinates of the hydrogen atom were taken as large amplitude reaction coordinates and out of the remaining coordinates of the scaffold five harmonic oscillator DOF were identified as being strongly coupled. It turns out that the coupling of the OH-stretch fundamental excitation to the other coordinates is substantially reduced upon deuteration. While the time scale for intramolecular energy redistribution has been estimated to be ~700 fs, the OD-stretching vibration shows no appreciable decay but coherent oscillations during the first 5 ps after excitation [56]. In Fig. 4.5 we show the probability distributions of the ground state, as well as a state which is localized in the product well, for deuterated salicylaldimine. Here, the oscillator DOF have been fixed at their minimum position. Although the reorganization energy difference between reactant and product state is appreciable (3112 cm–1) and larger than the barrier height (1940 cm–1), a localized product state exists. In principle, triggering a transition between the two states in Fig. 4.5 using the methods discussed above appears to be feasible. However, we have not yet taken into account the dynamics of the oscillator coordinates. Their effect is most conveniently visualized after introduction of a diabatic basis, ffa ðxÞg, describing the two reactive coordinates for fixed oscillator DOF, i.e. fQ n ¼ 0g: ½Tx þ VðxÞfa ðxÞ ¼ Ea fa ðxÞ
(4.5)
Two of these basis functions are shown in Fig. 4.5. The Hamiltonian Eq. (4.1) can be transformed into this representation which gives (adopting a vector/matrix notation) [32] Hdiab ¼
P2 X þ Ua ðQÞdab þ Vab ðQÞð1 dab Þ jaihbj 2 ab
Figure 4.5 Probability densities for the diabatic ground state and the product state resulting from a reaction surface description of the deuterium transfer in salicylaldimine.
(4.6)
Here x and y give the position of the H-atom and the substrate oscillators are frozen at their equilibrium value (cf. Eq. (4.1)); for details see Ref. [57].
4.3 Laser Control
with the diabatic PES: Ua ðQÞ ¼ Ea faa Q þ 1=2QKaa Q and the state couplings Vab ðQÞ ¼ fab Q þ 1=2QKab Q. A one-dimensional cut of the potential without state coupling along a HT promoting mode having a harmonic frequency of 861 cm–1 is shown in Fig. 4.6 [57]. The potentials corresponding to the two states in Fig. 4.5 are highlighted. Since the localized product state samples rather large forces, which result from distorting the structure from its reactant to the product configuration, the respective potential curve shows the largest shift as compared to the ground state. Consequently, it crosses with, and also couples to, several of the lower lying potential energy curves. Ideally one would like to know whether there is an eigenstate of this seven-dimensional model Hamiltonian that is localized on the product side similarly to Fig. 4.5. The determination of such an eigenstate, however, appeared to be not feasible, as can be appreciated by inspection of Fig. 4.6, which shows multiple curve crossings already for a one-dimensional cut of the potential.
Figure 4.6 One-dimensional cuts through the diabatic PES for the deuterium transfer in salicylaldimine along the substrate mode shown in the right. The thick solid lines indicate the two diabatic states shown in Fig. 4.5; for details see Ref. [57].
Thus instead of aiming at populating an unknown eigenstate, e.g. by exploring different laser pulse parameters, the intention was to find out what the system does after being prepared in a state localized in the product well [57]. In Fig. 4.7 we show the population dynamics of the diabatic states starting with a wave packet, which corresponds to the oscillator ground state of the uncoupled PES (Vab = 0 in Eq.(4.6)) in the diabatic state with a = 10 (see Fig. 4.5). The (field-free) propagation of this initial state yields a rapid decay during the first 50 fs, most notably into the OD-stretching dominated state (a = 3). Interestingly, about 5–10% of the population remains trapped in the initial state during the first picosecond. Recalling the coherent dynamics after excitation of the OD-stretching fundamental and “reversing” the field-free dynamics would now suggest a two-step mechanism for reaction control in this molecule with transitions like
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Figure 4.7 Population dynamics of the ten lowest diabatic states of a seven-dimensional model of the deuterium transfer in salicylaldimine after inital population of the product
hm1
state shown in Fig. 4.5. (Each curve has been offset by (a – 1)*0.25). The vertical line shows the zero level for the initially populated state; for details see Ref. [57].
hm2
a ¼ 1 ! 3 ! 10. Attempts to realize such a scheme have not yet been successful. In this respect one might also wonder whether the preferred relaxation pathway is, at the same time, the optimum excitation pathway. Clearly, answering this question would be a task for optimal control theory. However, the propagation of seven-dimensional wave packets in this strongly coupled system is rather demanding and an implementation of an approach like Eq. (4.4) is out of reach. 4.3.2 Laser-driven H-Bond Breaking
The already mentioned pump–dump scheme has also found application in the control of bond breaking. The pump pulse excites the system vertically from the electronic ground state to another suitable electronic state, from where the wave packet evolves freely following the steepest descent pathway. After some specific time delay, the wave packet arrives at a region of the excited PES appropriate to return the probability amplitude to the electronic ground state at a different nuclear configuration. Assuming that the electronic ground state possesses different channels for dissociation, the dumped wave packet is now biased to dissociate towards a particular target product, altering then the natural branching ratio of the system. Of course, the laser pulses used in this type of application are in the vis/UV frequency region in order to achieve resonant electronic transitions, rather than in the IR as in the previous applications (cf. Section 4.3.1). The interested
4.3 Laser Control
reader can find numerous examples of pump–dump or more generally pump–control schemes intended for photodissociation, e.g. in Refs. [12, 13]. Triatomic systems like FHF– or more generally AHB– – where two different ligands are strongly bound through a H-bond – are good candidates to exercise control of selective bond breaking. In addition, bihalides ions like FHF– and similar XHX– compounds have been employed thoroughly in the field of transition state spectroscopy, a method that probes spectroscopically the transition state of the neutral system by electron photodetachment of the anion [58]. Note that, because these experiments aim at the characterization of the transition state vibrations, they employ nanosecond UV light with a frequency that goes beyond the resonant transition between the anion and neutral surfaces. As shown in Fig. 4.8(a), after photodetachment of the electron, the wave packet created in the neutral surface in the transition state region will divide into two equal branches along the channels XH+X and X+HX, giving rise to the fragments X–H and H–X, respectively. More generally speaking, the wave packet will split into two channels, AH+B and A+HB, with a given branching ratio that is dictated by the topology of the neutral PES or, in other words, determined by the position of the transition state with respect to the minimum of the anion potential. An approach to achieving H-bond fragmentation in a selective manner is shown in Fig. 4.8(b). It consists of using a few-cycle IR pulse followed by a UV laser (a)
e
(b)
-
X + HX
XH + X
X + HX
UV
UV
IR -
XHX
Figure 4.8 In (a) the principle of transition state spectroscopy is shown. A continuous wave UV laser pulse with a frequency exceeding the energy gap between anionic potential (XHX–) and neutral potential (XHX) is employed. After photodetachment of the electron, dissociation will occur equally in the two possible channels: XH+X and X+HX. In (b)
-
XHX
the principle of few-cycle IR + UV pulses is shown. First an ultrashort IR laser pulse creates a wave packet in the anionic state (XHX–) which, at the appropriate time delay, is then excited to the neutral system (XHX). After photodetachment of the electron, dissociation is steered to occur along one single channel.
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pulse. The sequence of these two pulses reminds one of the pump–dump scheme because the first laser pulse – a few-cycle IR laser pulse – creates a wave packet, in the electronic ground state however, and displaces it until a favored nuclear configuration, while the second pulse – the UV pulse – transfers the probability amplitude to the state where dissociation takes place. In contrast to the UV cw light, the combination of few-cycle IR + UV pulses applied to an XHX– system can be optimized to enhance one of the exit channels, e.g. X +HX (compare Fig. 4.8(a) and (b)). The spirit of this control scheme is rather intuitive. A short (si < 100 fs), relatively intense IR laser pulse containing few-cycles is applied to drive the asymmetric stretching vibration of the anion or, equivalently, to force the oscillation of the H-atom between the two heavy end atoms. Each half cycle of the electric field is matched to half of the period of the asymmetric vibration of the H-bond of the system. With each half cycle of the pulse, the oscillating H-atom is pushed further away from its equilibrium position. When the displacement of the H is greatest at one of the turning points, photodetachment of the electron via the UV pulse will create a replica of the wave packet in a domain of the neutral surface far enough from the transition state window as to lead to the dissociation of the pre-excited bond. Needless to add, to make this scheme efficient the UV pulse must be shorter than the vibrational period of the oscillating H-atom. In this cartoon (cf. Fig. 4.8(b)), the reaction coordinate equals the hydrogen stretch and, therefore, the IR frequency equals the asymmetric H-bond stretching. In general, one could expect other degrees of freedom opening channels for competing processes via intramolecular vibration redistribution (IVR), reducing the efficiency of the proposed scheme. Yet, because the hydrogen vibration takes place very fast, we anticipate IVR, e.g. the bending mode, not to seriously influence the main conclusions obtained here. Encouraging examples of few-cycle IR + UV laser control are found in the theoretical work of Henriksen et al. [59, 60] for isotopically substituted ozone 16O16O18O. A laser field (cf. Eq. (4.3)) consisting of one or several half cycle pulses takes the form EðtÞ ¼
P i
Ei0 sin
pðtti Þ si
þf
(4.7)
where the frequency of the IR laser pulse is given by xIR=p/s and the pulse duration s is about half of the vibrational period of the asymmetric stretch of the H-bond. For convenience, the phase f will be set to zero in the following applications. A one half-cycle pulse and a sequence of those are shown in Fig. 4.9(a). Their effect on FHF– is illustrated using a 1D potential in Fig. 4.10. The frequency of the asymmetric stretching vibration in the 1D model of FHF– is 1815 cm–1 and the pulse duration employed is s=10 fs, which is approximately half of the period of the asymmetric stretch, 0.5sas = 9 fs. To measure the displacement of the initial wave function W a ðq; 0Þ ¼ ft¼0 from its equilibrium position we calculate the modulus of the autocorrelation function in the anion potential Va, Panion ¼ jhft¼0 j W a ðt > 0Þij2 as well as the mean position of the H-atom, qas. While the field is switched on, population from t=0 is moved to other vibrational states, creating a
4.3 Laser Control
wave packet, and Panion decreases accordingly from 1 to ca. 0.9 (cf. Fig. 4.9(b)). The wave packet begins oscillating and at t = 9.5 fs the H-atom has reached the turning point at qas » 0.07 (cf. Fig. 4.9(c)). If three half-cycle pulses of similar duration are employed instead of one, the effect is similar to the classical situation of a driven oscillator: the mass is pushed after passing through each turning point and the amplitude of the resulting oscillation increases. Therefore, after three half-cycle pulses, the Panion has decreased to ca. 0.5 and the H-atom has been maximally shifted from the equilibrium position until qas » 0.16 at t = 26.5 fs (see also the corresponding wave functions in Fig. 4.10). One can then anticipate that the prestretched bond in the anion system will break selectively in the neutral system upon photodetachment. In order to visualize competing bond breaking we consider 2D PES. In view of the simplicity of XHX– systems, PES can be constructed in terms of internal coordinates, and because we are interested in the competing
Figure 4.9 One (solid) and three half-cycle pulses (dashed) and their effects on the asymmetric stretching vibration of FHF–. (a) Electric field (in atomic units) versus time (fs). The parameters are E0 = 5.8 10–3 Eh/ea0 and sI = 10. (b) Modulus of the autocor-
relation function of the anionic wave function as defined in text. (c) Time evolution of the mean value of the H-atom driven by the laser field shown in (a). The time at which maximum displacements occur is indicated.
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Figure 4.10 Potential energy curve of the anionic potential of FHF along the asymmetric stretching vibration given by qas = 1/2(R1 – R2), where R1 and R2 are the bond
distances FH and HF. Embedded are the wave functions at t = 0 fs, after one half-cycle pulse at t = 9.5 fs, and after three half-cycle pulses at t = 26.5 fs, have been applied.
Figure 4.11 Selective H-bond breaking in FHF by photodetachment of the anion using fewcycle IR+UV laser pulses. (a)–(d) are sequential snapshots of the wave packet moving in the bound anionic and repulsive neutral
Va and Vn PES, respectively. The coordinates R1 and R2 are the bond distances FH and HF in . (a) t = 0 fs in Va. (b) Maximum displacement of the H-atom at t = 41.5 fs in Va. (c) t = 42 fs in Vn. (d) t = 70 fs in Vn.
4.3 Laser Control
ligand dissociation, the two internal bond distances X–H and H–X are considered in a collinear geometry, that is, the symmetric and asymmetric stretching normal modes are taken into account, whereas bending and rotations are excluded. Figure 4.11 shows the anion Va and neutral Vn PES of FHF. Moreover, we replace the series of three half-cycle pulses by a smooth, switch-on–switch-off sin2-shaped laser field of the type given in Eq. (4.3) and shown in Fig. 4.12(b). The frequency xIR is chosen, as in the 1D model, to equal the H-bond oscillations, which in the 2D case correspond to longer vibrational periods of ca. 1500 cm–1, therefore xIR = 1516 cm–1 (0.188 eV). In Fig. 4.12(b) it can be seen how qas encompasses the maximum amplitude of each half cycle. In passing we note that with increasing displacement of the wave packet its dispersion increases as well. Thus the optimum time delay between the IR and the UV pulse calls for a compromise between maximum displacement and minimum dispersion. As shown in Fig. 4.11(b), at t = 41.5 fs the wave packet remains relatively compact in the anion surface Va and the mean value of qas has reached 0.207 . When the IR pulse achieves maximum displacement, an ultrashort (s = 5 fs) resonant (xUV = 43548 cm–1 = 5.5 eV) sin2-shaped UV pulse is applied to photodetach an electron, preparing the system on the PES of the neutral species. The maximum intensity needed for this selective preparation of the wave packet is ca. I = 3.3 TW cm–2. For a laser pulse of duration s = 5 fs, mildly focused to a diameter of s = 1 mm, this corresponds to a pulse energy of approximately 500 lJ, which can be provided by state of the art laser systems. This few-cycle UV pulse excites the displaced wave packet to a downhill domain of Vn where it evolves predominantly along one dissociation
Figure 4.12 A few-cycle IR and UV pulse and its effect on the FHF system. (a) Electric field (atomic units) versus time (fs). The parameters are E0IR = 7.8 10–3 Eh/ea0, xIR = 1516 cm–1 and sIR = 55 fs for the IR laser pulse
and E0UV = 9.7 10–3 Eh/ea0, xUV = 43548 cm–1 and sUV = 5 fs. (b) Time evolution of the mean value of the H-atom in the anion (solid) and neutral (dotted) driven by the laser field shown in (a).
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channel. After the wave packet is created in Vn dispersion allows a small portion of the wave function to penetrate the non-desired domain (see Fig. 4.11(c, d)), and the branching ratio at t = 42 fs decreases slightly. Nevertheless, the branching ratio (F+HF:FH+F) is increased from its natural value of 50:50 to 75:25 [61]. The present IR+UV scheme then achieves symmetry breaking in the electronic ground state of the anion and subsequent selective bond breaking of the H-bond in the neutral system. The resulting atomic fragment is driven along the preselected bond, which has been stretched by the IR laser, whereas the molecular product is driven in the opposite direction. Although the resulting products, F+HF or FH+F, are chemically indistinguishable, the present laser strategy allows the choice of one or another, such that either the atomic or the molecular fragments are driven in a pre-selected direction while the counterparts are driven in the opposite one. As a consequence, this approach achieves spatial separation of the products [62], in contrast to cw UV lasers; see Fig. 4.13(a, b).
Figure 4.13 Comparison of traditional cw UV or IR+UV laser pulses (a), versus few-cycle IR+UV laser pulses in an oriented ensemble of FHF– molecules (b) or a randomly oriented ensemble (c).
In these wave packet simulations, the molecular axis of the FHF– system is assumed to be aligned along the space-fixed axis Z electric field vector. This assumption involves a maximum interaction of the IR and UV laser pulses with the system. Recalling that the time-dependent interaction potential is given by the scalar product of the electric field vector and the dipole vector, i.e. E 0 ðtÞ l cos h, it is clear that for field polarizations perpendicular to the molecular axis (h = 90) the interaction of the IR laser pulse with the anion vanishes, and for any molecular orientation different from h = 0 or 180 the interaction is less efficient. Consider now an ensemble of randomly oriented FHF– molecules, as in Fig. 4.13(c). Since the UV pulse is tuned to match the energy gap between anion and neutral
4.3 Laser Control
surfaces at the geometry of maximum displacement, but for angles h „ 0 this geometry is never realized, the frequency of the UV pulse is increasingly offresonant with angles from 0 to 90 and consequently the UV pulse no longer efficiently transfers population to the neutral surface. As a result, in going from 0 to 90 the probability of photodetachment decreases from 1 to 0, except for marginal probabilities of photodetachment due to the significant width of the ultrashort UV laser pulse. As documented in Ref. [62], the general trend for angle values increasing from 0 to 90 is the decrease in the probability of dissociating the molecular product to the direction H = h, and the complementary increase in the probability to the direction H = h+180. Both effects contribute to the dissociation of FH and F fragments in exactly opposite directions, thus spatially separating the products [62]. So far the few-cycle IR+UV laser scheme has been discussed in the FHF system for which the PES, anionic and neutral, are symmetric, and therefore the two dissociation channels are energetically equivalent. In passing we note that the isotopomer FDF has also been reviewed in Ref. [63]. Other systems found in the literature, like isotopically substituted ozone [59, 60] and HOD [64, 65] have different reduced masses for the diatomic fragments, hence allowing the observation of two different dissociation dynamics. Nonetheless, in these cases, the PES are also symmetric, implying that the transition state in the neutral PES can be found at the same nuclear configuration as the minimum energy configuration in the anionic PES and that the UV laser pulses are resonant for both dissociation channels. Much more challenging is the case of a chemically asymmetric system. This is the central part of the study performed in Ref. [66] using OHF– as a model system. OHF– responds to the general pattern of a system possessing one H-bond much stronger than the other one. In the absence of pre-excitation photodetachment of OHF– leads predominantly to the O+HF fragments, because the O_H bond is much weaker than the H_F bond. OHF has been the focus of a number of theoretical and experimental studies due to its environmental significance [67]. Neumark has measured the photodetachment spectrum of OHF– (recall Fig. 4.8) [58], challenging theoretical groups to its simulation and comprehension [68–70]. The exoergicity of the reaction OH + FfiO + HF has been well characterized [71]. However, controlling the branching ratio of the system was never previously tackled. In Ref. [66] we raised the question of whether the natural branching ratio can be enhanced to maximize the O + HF products or even reversed to maximize the amount of OH + F products. In Fig. 4.14 we show the ground state vibrational wave function of OHF– (Fig. 4.14(a)) on the neutral PES. Using a UV laser pulse of time duration sUV = 5 fs one obtains a natural branching ratio of 76:24 for O+HF to OH+F products. Let us first consider now the use of few-cycle IR + UV pulses to enhance the breaking of the weaker hydrogen bond, i.e. O_H. As in the FHF–/FHF case, the approach relies on designing an IR laser pulse which achieves maximum extension and compression of the bonds and thus maximum displacement of the wave function from its equilibrium position. At the minimum energy configuration the equilib-
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rium geometry is calculated to be ROH = 1.1 and RHF =1.3 . The frequency of the IR pulse (xIR = 1565 cm–1) is chosen to drive the asymmetric stretching vibration or the motion of the hydrogen between the O and F end atoms. As in previous cases, the time duration of the pulse is chosen sIR= 50 fs, so that the pulse contains a few half-cycle pulses. Each of them excites a superposition of several vibrational eigenstates. After a time delay of 19 fs (see Fig. 4.14(b)) the O_H has been stretched from 1.1 to 1.28 . The UV pulse prepares the wave packet on the neutral surface along the O+HF dissociation channel (see Fig. 4.14(c)) and exclusive O +HF products are obtained. At the end of the propagation the branching ratio is calculated as 97:3 for O+HF:OH+F, thus enhancing the breaking of the weak H-bond O_H (Fig. 4.14(d)). Notice that the wave packet after 60 fs (Fig. 4.14(c)) still remains compact and dispersion is small. Let us now turn to the problem of breaking the stronger H-bond of the system, while leaving the weaker one intact. Since the previous IR laser pulse was designed to drive the asymmetric stretching vibration and create a dynamical wave packet that oscillates with the largest amplitude away from the equilibrium posi-
Figure 4.14 Selective H-bond breaking in OHF by photodetachment of the anion using few-cycle IR+UV laser pulses. The field parameters to maximize the products O+HF are E0IR = 6.2 10–3 Eh/ea0, xIR = 1565 cm–1, sIR = 50 fs, E0UV = 9.7 10–3 Eh/ea0, xUV = 28228 cm–1 and sUV = 5 fs. The field parameters to maximize the products OH+F are E0IR = 9.7 10–3 Eh/ea0, xIR = 1565 cm–1, sIR = 50 fs, E0UV = 15.5 10–3 Eh/ea0, xUV = 52423 cm–1 and sUV = 5 fs. (a) Initial wave function embedded in the anionic potential.
(b) Wave packet in the anion potential after pre-excitation with the few-cycle IR laser pulse at t = 19 fs. (c) Wave packet in the neutral potential after the UV pulse in the neutral potential at t = 60 fs. (d) Branching ratio of the O+HF versus OH+F products. (e) Wave packet in the anion potential after pre-excitation with the few-cycle IR laser pulse at t = 29 fs. (f) Wave packet in the neutral potential after the UV pulse in the neutral potential at t = 60 fs. (g) Branching ratio of the O+HF versus OH+F products.
4.3 Laser Control
tion, the frequency and pulse duration of this pulse are maintained. Because of the asymmetry of the potential the field strength has to be intensified. The key point is that the UV laser pulse has to be fired at the time the bond of interest is maximally stretched. After 29 fs (see Fig. 4.14(e)) the wave packet has reached the opposite turning point, stretching the H_F bond from 1.3 to 1.41 . The new UV pulse not only has a different time delay in comparison with the previous case but also a different frequency, since it has to match the new gap between the anion and neutral PES. Despite the relatively compact form of the wave packet in the anion surface, because the transition state area is considerably flat, as soon as the wave packet is excited to the neutral PES, it spreads noticeably. As seen in Fig. 4.14(f) it begins traveling towards the center of the neutral potential instead of being confined along the dissociation channel OH+F. As a result, the wave packet disperses in both directions losing selectivity. The branching ratio shown in Fig. 4.14(g) shows that most of the 90% selectivity in the OH+F channel gained during the first 30 fs is lost in the next 10 fs. After 100 fs the wave packet density is stable and the branching ratio is steady. The calculated ratio is 57:43 for O+HF versus OH+F. This means that, after all, we have achieved a significant gain in breaking the strong H-bond H_F versus the weak O_H one. The previous results demonstrate that it should be possible to exert control over the H-bond fragmentation using a sequence of few-cycle IR + UV laser pulses. The key steps for the success of such an approach are: (i) the control of the carrier envelope phase f of the IR pulse, and (ii) the perfect timing of the UV pulse with respect to the IR one. Both aspects are related and their importance cannot be overemphasized. Depending on the carrier phase of the IR laser pulse the halfcycle pulses will have maximum amplitude at different times. Because it is the maxima of each of these half-cycle pulses which determine the maximum displacement of the H-atom, the phase inherently imposes the appropriate time delay at which the UV laser pulse should be fired. The successful implementation of these laser schemes in the laboratory requires therefore the reproducible generation of pulses with the same absolute phases. Though not straightforward, it is encouraging to see that in recent years control of the phase of attosecond X-ray [72, 73] as well as few-cycle femtosecond, near-IR (800–1700 nm) lasers (as the ones employed here!) is becoming a reality [74–76]. A phase of p does not shift the peaks of the half-cycle pulses, just changes the sign, or in other words, determines the direction in which the initial wave packet begins oscillating. For asymmetric systems, like OHF–, this indeed plays again an important role in choosing the time delay of the UV laser pulse. Of course the frequency of the UV laser pulse has to match the energy gap between anion and neutral surfaces at the corresponding geometry achieved by the IR laser pulse. This means that, in asymmetric systems, the frequency of the UV pulse optimized to match one exit channel will not, in general, be efficient in achieving population inversion at the other exit channel. The latter issue serves to bring up the role of molecular orientation (or alignment for symmetric systems) in the proposed laser scheme. In the case of FHF it has already been mentioned that even starting from a random ensemble of all pos-
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sible orientations spatial separation of the products can be achieved due to (i) the inefficiency of the IR laser pulse in exciting molecules which are not in the optimum orientation angle (h = 0, i.e. parallel to the molecular axis); and (ii) the offresonant character of the UV laser pulse acting on those molecules which have not been optimally pre-excited with the IR laser pulse [62]. Similar behavior can be expected in OHF, greatly enhanced by the fact that the UV pulses in both channels have very different frequency. Another way to overcome this problem is of course by achieving pre-orientation of the sample before starting the control experiment. The rotational periods of FHF– and OHF– are calculated as 48.6 and 49.6 ps, respectively [77]. Because the symmetry breaking and posterior bond selective photodissociation takes place in less than 100 fs, it is reasonable to assume that the molecule will stay oriented while the laser-driven control takes place.
4.4 Conclusions and Outlook
The manipulation of molecular systems by means of tailored laser pulses has triggered a host of experimental and theoretical efforts. Due to their importance for various processes in chemical and biological systems H- bonds are a particularly attractive target in this respect. However, despite the impressive progress in the experimental control in the optical wavelength range [12, 13], IR-driven reaction dynamics is just becoming reality [78]. In this chapter we have reviewed control schemes for HT reactions in the electronic ground state. It has been demonstrated that for low-dimensional model systems control can be achieved, e.g., by over-thebarrier and through-the-barrier driving. Stepping to more realistic multidimensional models it turned out that control schemes derived for simpler systems may not be transferable. Of course, this does not imply that laser control of H-bond dynamics is not feasible at all. We merely want to point out that most likely for many real (medium-sized organic) systems the anharmonic coupling coming along with the change in the electronic structure upon H-transfer is rather pronounced and therefore a serious challenge to any control attempt. Feedback control in the optical domain has been shown to be a very powerful tool [14] and similar ideas might provide useful when it comes to multidimensional H-bond dynamics. On the other hand, even if the control of a H-transfer reaction might prove too difficult for many systems due to rapid intramolecular vibrational energy redistribution, driving the ground state wave packet away from its minimum position in a controlled manner could give – if combined with nonlinear spectroscopy – valuable information about the anharmonic PES. In the second part of this chapter we have shown that such displaced wave packets could be the first step in an alternative control scheme involving a properly timed UV excitation. In principle this might cause a transition to some electronically excited state and the subsequent excited state H-bond dynamics could be controlled. Here, however, we focused on the transition between an anionic and a
References
neutral PES accompanied by electron photodetachment. For H-bonds of the type AHB– it was demonstrated that selective bond breaking can be controlled. In view of the experimental progress [79, 80] such an IR/UV scheme does not seem to be too far-fetched.
Acknowledgments
The work related to the few-cycle IR plus UV control strategies on FHF and OHF is part of the PhD work of N. Elghobashi. L.G. wishes to thank her for providing the corresponding figures and her continuous enthusiasm. Further we wish to thank N. DoÐlic´ (Zagreb) for her contributions to the “Hydrogen Subway”, M. Petkovic´ who carried out the calculations for salicylaldimine, and Prof. J. Manz (Berlin) for many stimulating discussions and his continuous support. The financial support from the “Graduiertenkolleg” 788, “Hydrogen Bonding and Hydrogen Transfer” and the Sfb450 is also gratefully acknowledged.
References 1 K. Tanaka, H. Honjo, T. Tanaka,
H. Kohguchi, Y. Ohshima, Y. Endo, J. Chem. Phys. 1999, 110, 1969. 2 E. T. J. Nibbering, T. Elsaesser, Chem. Rev. 2004, 104, 1887. 3 T. Elsaesser, in Femtosecond Chemistry, J. Manz, L. Wste (Eds.), Verlag Chemie, Weinheim, 1995, p. 563. 4 A. Douhal, F. Lahmani, A. H. Zewail, Chem. Phys. 1996, 207, 477. 5 S. Lochbrunner, E. Riedle, Rec. Res. Devel. Chem. Phys. 2003, 4, 31. 6 B. I. Stepanov, Nature 1945, 157, 808. 7 N. Sheppard, in Hydrogen Bonding (Ed.: D. Hadzˇi), Pergamon Press, New York, 1957, p. 85. 8 M. V. Basielevsky, M. V. Vener, Russ. Chem. Rev. 2003, 72, 3. 9 S. Bratos, J. C. Leicknam, G. Gallot, H. Ratajcak, in Ultrafast Hydrogen Bonding Dynamics and Proton Transfer Processes in the Condensed Phase, T. Elsaesser, H. J. Bakker (Eds.), Kluwer Academic, Dordrecht, 2002, p. 5. 10 J. Stenger, D. Madsen, J. Dreyer, E. T. J. Nibbering, P. Hamm, T. Elsaesser, J. Phys. Chem. A 2001, 105, 2929.
11 K. Heyne, N. Huse, J. Dreyer,
E. T. J. Nibbering, T. Elsaesser, S. Mukamel, J. Chem. Phys. 2004, 121, 902. 12 S. Rice, M. Zhao, Optical Control of Molecular Dynamcis, John Wiley and Sons, Hoboken, 2000. 13 M. Shapiro, P. Brumer, Principles of Quantum Control of Molecular Processes, John Wiley and Sons, Hoboken, 2003. 14 T. Brixner, G. Gerber, ChemPhysChem 2003, 4, 418. 15 X. Huang, H. M. Cho, S. Carter, L. Ojame, J. Bowman, S. J. Singer, J. Phys. Chem. A 2003, 107, 7142. 16 M. V. Vener, O. Khn, J. Bowman, Chem. Phys. Lett. 2001, 340, 562. 17 M. V. Vener, O. Khn, J. Sauer, J. Chem. Phys. 2001, 114, 240. 18 N. DoÐlic´, O. Khn, Z. Phys. Chem. 2003, 217, 1507. 19 E. Kraka, in Encyclopedia of Computational Chemistry, P. v. Rague-Schleyer (Ed), Wiley, New York, 1998, p. 2437. 20 W. H. Miller, N. C. Handy, J. E. Adams, J. Chem. Phys. 1980, 72, 99. 21 T. Carrington, W. H. Miller, J. Chem. Phys. 1986, 84, 4364.
101
102
4 Laser-driven Ultrafast Hydrogen Transfer Dynamics 22 N. Shida, P. F. Barbara, J. E. Almlf,
J. Chem. Phys. 1989, 91, 4061. 23 B. Fehrensen, D. Luckhaus, M. Quack, Z. Phys. Chem. 1999, 209, 1. 24 R. Meyer, T. K. Ha, Mol. Phys. 2003, 101, 3263. 25 X. Huang, B. J. Braams, S. Carter, J. Bowman, J. Am. Chem. Soc. 2004, 126, 5042. 26 D. Luckhaus, Chem. Phys. 2004, 304, 79. 27 R. Jaquet, W. H. Miller, J. Phys. Chem. 1985, 89, 2139. 28 B. A. Ruf, W. H. Miller, J. Chem. Soc., Faraday Trans. 2 1988, 84, 1523. 29 K. M. Forsythe, N. Makri, J. Chem. Phys. 1998, 6819. 30 H. Naundorf, J. A. Organero, A. Douhal, O. Khn, J. Chem. Phys. 1999, 110, 11286. 31 G. K. Paramonov, H. Naundorf, O. Khn, Eur. Phys. J. D 2001, 14, 205. 32 M. Petkovic´, O. Khn, J. Phys. Chem. A 2003, 107, 8458. 33 R. Xu, Y. J. Yan, O. Khn, Eur. Phys. J. D 2002, 19, 293. 34 K. Giese, D. Lahav, O. Khn, J. Theor. Comput. Chem. 2004, 3, 567. 35 K. Giese, O. Khn, J. Chem. Phys. 2005, 123, 054315. 36 H.-D. Meyer, G. A. Worth, Theor. Chem. Acc. 2003, 109, 251. 37 H. Naundorf, G. A. Worth, H.-D. Meyer, O. Khn, J. Phys. Chem. A 2002, 106, 719. 38 V. May, O. Khn, Charge and Energy Transfer Dynamics in Molecular Systems, 2nd edn., Wiley-VCH, Weinheim, 2004. 39 N. Makri, J. Phys. Chem. B 1999, 103, 2823. 40 R. Rey, J. T. Hynes, J. Chem. Phys. 1996, 104, 2356. 41 C. P. Lawrence, J. L. Skinner, J. Chem. Phys. 2002, 117, 5827. 42 H. Naundorf, O. Khn, Phys. Chem. Chem. Phys. 2003, 5, 79. 43 K. Heyne, E. T. J. Nibbering, T. Elsaesser, M. Petkovic´, O. Khn, J. Phys. Chem. A 2004, 108, 6083. 44 P. K. Agarwal, S. Billeter, S. HammesSchiffer, J. Phys. Chem. B 2002, 106, 3283. 45 M. V. Korolkov, J. Manz, G. K. Paramonov, Adv. Chem. Phys. 1997, 101, 327.
46 N. DoÐlic´, O. Khn, J. Manz, Ber. Bun-
senges. Phys. Chem. 1998, 102, 292. 47 N. DoÐlic´, K. Sundermann, L. Gonzlez,
48 49 50
51 52 53 54 55 56
57 58 59 60 61 62 63 64 65
66 67 68 69
O. M, J. Giraud-Girard, O. Khn, Phys. Chem. Chem. Phys. 1999, 1, 1249. W. Zhu, J. Botina, H. A. Rabitz, J. Chem. Phys. 1998, 108, 1953. K. Sundermann, R. deVivie-Riedle, J. Chem. Phys. 1999, 110, 1896. N. DoÐlic´, O. Khn, J. Manz, K. Sundermann, J. Phys. Chem. A 1998, 102, 9645. O. Khn, Eur. Phys. J. D 1999, 6, 49. N. DoÐlic´, O. Khn, Chem. Phys. 2000, 255, 247. H. Naundorf, K. Sundermann, O. Khn, Chem. Phys. 1999, 240, 163. O. Khn, Y. Zhao, F. Shuang, Y. Yan, J. Chem. Phys. 2000, 112, 6104. W. Sim, N. Makri, Comput. Phys. Commun. 1997, 99, 335. M. Petkovic´, O. Khn, in Ultrafast Molecular Events in Chemistry and Biology, J. T. Hynes, M. M. Martin (Eds.), Elsevier, Amsterdam, 2004, p. 181. M. Petkovic´, O. Khn, Chem. Phys. 2004, 304, 91. D. M. Neumark, Acc. Chem. Res. 1993, 26, 33. B. Amstrup, N. E. Henriksen, J. Chem. Phys. 1992, 97, 8285. B. Amstrup, N. E. Henriksen, J. Chem. Phys. 1996, 105, 9115. N. Elghobashi, L. Gonzlez, J. Manz, J. Chem. Phys. 2004, 120, 8002. N. Elghobashi, J. Manz, Isr. J. Chem. 2003, 43, 293. N. Elghobashi, L. Gonzlez, J. Manz, Z. Phys. Chem. 2003, 217, 1577. M. Machholm, N. E. Henriksen, J. Chem. Phys. 1996, 105, 9115. N. Elghobashi, P. Krause, J. Manz, M. Oppel, Phys. Chem. Chem. Phys. 2003, 5, 4805. N. Elghobashi, L. Gonzlez, Phys. Chem. Chem. Phys. 2004, 6, 4071. R. P. Wayne, Chemistry of Atmospheres, Oxford University Press, Oxford, 2000. R. N. Dixon, H. Tachikawa, Mol. Phys. 1999, 97, 195. L. Gonzlez-Snchez, S. Gmez-Carrasco, A. Aguado, M. Paniaga, M. L. Hernndez, O. Roncero,
References J. M. Alvari o, J. Chem. Phys. 2004, 121, 309. 70 L. Gonzlez-Snchez, S. Gmez-Carrasco, A. Aguado, M. Paniaga, M. L. Hernndez, O. Roncero, J. M. Alvari o, J. Chem. Phys. 2004, 121, 9865. 71 J. J. Sloan, D. G. Watson, J. M. Williamson, J. S. Wright, J. Chem. Phys. 1981, 75, 1190. 72 A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hnsch, F. Krausz, Science 2000, 288, 635. 73 D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stenz, R. S. Windeler, J. L. Hall, S. T. Cundiff, Science 2001, 293, 825. 74 G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, S. DeSilvestri, Nature 2001, 414, 182.
75 M. Nisoli, G. Sansonse, S. Stagira,
S. DeSilvestri, C. Vozzi, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, Phys. Rev. Lett. 2003, 91, 213905. 76 G. Sansonse, C. Vozzi, S. Stagira, M. Pascolini, L. Poletto, P. Villoresi, G. Tondello, S. DeSilvestri, M. Nisoli, Phys. Rev. Lett. 2004, 92, 113904. 77 N. Elghobashi, PhD Thesis, Free University, Berlin, 2005. 78 L. Windhorn, J. S. Yeston, T. Witte, W. Fuß, M. Motzkus, D. Proch, K. L. Kompa, C. B. Moore, J. Chem. Phys. 2003, 119, 641. 79 B. Schenkel, J. Biegert, U. Keller, C. Vozzi, M. Nisoli, G. Sansone, S. Stagira, S. De Silvestri, O. Svelto, Opt. Lett. 2003, 28, 1987. 80 T. M. Fortier, David J. Jones, S. T. Cundiff, Opt. Lett. 2003, 28, 2198.
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Part II Hydrogen Transfer in Condensed Phases
In Ch. 5 Ceulemans reviews the protonation of alkanes in solid matrices by radical cations created by c-radiation, studied by EPR. The protonation does not take place at a particular atom but at a particular C–H or C–C bond, resulting in the formation of a three-center two-electron bond in a carbon-site specific way. Of great importance is the mobility of the matrix which greatly enhances the molecular reactivity. In Ch. 6 Limbach describes the use of NMR for the study of single and multiple hydrogen/deuterium transfers in liquids and solids. Using suitably labeled molecules, rate constants can now be obtained in a large temperature range from the second to the picosecond timescale. Expressions for multiple kinetic isotope effects of double to quadruple hydrogen transfer reactions are derived by formal kinetics and used in combination with the Bell tunneling model modified by Limbach. Thus, Arrhenius curves of single to quadruple hydrogen transfers can be simulated. The detection of stepwise vs. concerted reaction pathways and the role of H-bond compression in H-transfer reactions is discussed. Criteria are developed which allow one to detect hidden pre-equilibria. A number of cases known in the literature are re-analyzed in this sense, and pre-equilibria are proposed as the origin for non-conventional Arrhenius curves which could not explained before with simple tunneling models. In Ch. 7 Douhal examines ultrafast photoinduced proton transfers of dye molecules trapped in nanocavities. The main factors that determine the issue of a created wavepacket in the cage are the structure, the orientation of the guest, the docking and rigidity of the complex, and the polarity of the cage. Water molecules located inside and at both gates of cyclodextrins have special properties reminiscent of biological water. Their restricted dynamics is slower than that found in bulk water. This abnormal behavior plays a key role in many chemical and biological processes. Further nanospaces in membranes, micelles, polymers, lipid vesicles, liquid crystals, sol–gels, dendrimers, proteins, DNA, zeolites and nanotubes are explored. In Ch. 8, Waluk reviews the spectroscopy of porphycenes embedded in supersonic jets, liquids and polymer matrices. Tunnel splittings caused by delocalization of two inner hydrogen atoms is observed for porphycenes in supersonic jets. Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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The barrier to this transfer is higher in the lowest excited singlet state than in the ground state. The transfer mechanism involves a concerted double hydrogen tunneling process, activated by excitation of a low-frequency mode, which modulates the NHN separation. This separation can also be strongly altered by peripheral substitution. In porphycenes with alkyl substituents on the ethylene bridges, the NHN distances become very small. It is shown that the tautomerism of porphycenes can also be monitored on a single-molecule level. Finally, Ch. 9 by Vener is devoted to the proton dynamics in hydrogen bonded crystals. In particular, the effects on the vibrations of systems with low-barrier hydrogen OHO-hydrogen bonds are studied. DFT calculations with and without periodic boundary conditions indicate that the coupling of the proton to the heavy atom coordinate is stronger in crystals as compared to the isolated systems. This coupling accounts for major structural and spectroscopic properties observed experimentally for molecular crystals, e.g. geometric H/D isotope effects, low-frequency shifts of the asymmetric stretch of the O···H··O fragment and large variations for the isotopic frequency ratio.
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5 Proton Transfer from Alkane Radical Cations to Alkanes Jan Ceulemans
Alkane radical cations are very strong Brønsted acids capable of protonating alkanes. Radiation-chemical studies have proven highly successful for the investigation of such proton transfer from alkane radical cations to alkane molecules, using n-alkane nanoparticles embedded in cryogenic CCl3F matrices for the study of symmetric proton transfer (RH.+ + RH fi R. + RH2+) and mixed n-alkane crystals for the study of asymmetric proton transfer (RIH.+ + RIIH fi RI. + RIIH2+). The mechanism of the radiolytic processes involved is discussed in considerable detail. Selectivity with respect to the site of both proton donation and proton acceptance has been studied, using EPR spectroscopy at 77 K for the study of proton donation and gas chromatographic analysis after melting for the study of proton acceptance. The experiments described allow one to conclude that the protondonor site is related very strictly to the structure of the semi-occupied molecular orbital of the parent radical cation, with proton transfer taking place from those C–H bonds that carry appreciable unpaired-electron and positive-hole density. With respect to the site of proton acceptance, it is observed that chemical transformation due to protonation of n-alkanes by alkane radical cations in the systems studied is restricted to C–H bonds at secondary carbon atoms (no chemical transformation resulting from proton transfer to C–C bonds or to C–H bonds at primary carbon atoms). It is argued that the absence of chemical transformation due to C–C protonation has a complex origin in which thermochemical and structural (cage) effects are involved as well as the intrinsic stability of the carbonium ions, but that the absence with respect to protonation of C–H bonds at primary carbon atoms has (in all likelihood) a purely thermochemical origin. As to protonation of n-alkanes at secondary C–H bonds, extensive evidence is presented supporting a marked preference for the penultimate position, with considerably lower (and mutually equal) transfer to the interior sites (intrinsic acceptor-site selectivity). In mixed n-alkane crystals, additional selectivity with respect to the site of proton acceptance results from structural factors in combination with the donor-site selectivity (structurally determined acceptor-site selectivity).
Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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5 Proton Transfer from Alkane Radical Cations to Alkanes
5.1 Introduction
Three major types of cationic species that can be derived from saturated hydrocarbons are alkyl carbenium ions (R+), alkane radical cations (RH.+) and alkyl carbonium ions (RH2+). The term “carbocations” is usually reserved to denote alkyl carbenium and carbonium ions only. Pentacoordinated alkyl carbonium ions (protonated alkanes) are the species that result from protonation of alkane molecules; they are of paramount importance as reactive intermediates/transition states in the initiation of (Brønsted) acid-catalyzed conversions of saturated hydrocarbons. Upon dissociation of alkyl carbonium ions, trivalent alkyl carbenium ions are formed and these are responsible for the further progression of acid-catalyzed conversions of alkanes. Alkyl carbenium ions may also be formed by ionization of neutral alkyl radicals and by proton addition to olefins. In both carbenium and carbonium ions, the positive charge is very much located on a particular part of the cation. Alkane radical cations are the species that result from ionization (electron removal) of neutral alkane molecules. They have both paramagnetic and ionic properties, hence the term radical cations. In alkane radical cations, the unpairedelectron and positive-charge (hole) density is distributed over a large part of the molecular frame in a manner that depends on the carbon chain conformation. As will be amply demonstrated in the present chapter, alkane radical cations are very strong Brønsted acids that are capable of protonating neutral alkanes. As such, they offer an interesting and elegant alternative to superacids for the study of site selectivity in the protonation of alkanes. Most of the information on alkane radical cations and essentially all the information on their ability to protonate alkane molecules has been derived from radiation chemistry, a rather specialized field that involves the study of the chemical effects of ionizing radiation. The radiolytic processes that allow the study of (donor and acceptor) site selectivity in the proton transfer from alkane radical cations to alkane molecules will therefore be discussed in some detail.
5.2 Electronic Absorption of Alkane Radical Cations
Radical cations of saturated hydrocarbons have strong electronic absorptions in the visible and near-infrared region of the spectrum. The strongly colored nature of alkane radical cations is in striking contrast to neutral alkanes that absorb electronically only in the vacuum UV. The electronic absorption of alkane radical cations has been studied in the solid phase by matrix isolation using c-irradiation [1– 3] and in the gas phase by ion cyclotron resonance (ICR) photodissociation in either the steady-state or pulsed mode of operation [4]. Both methods have their specific merits and drawbacks. A major concern in matrix isolation spectroscopy is spectral purity (because of the possible presence of other absorbing species) and
5.3 Paramagnetic Properties of Alkane Radical Cations
elaborate deconvolution techniques have been developed to overcome this problem. With gas phase dissociation spectra the effects of threshold truncation must be taken into account as photon energies must be sufficient for bond cleavage and truncation of the spectra at some wavelength in the red or near-infrared may be problematic. The strong electronic absorption of alkane radical cations is readily understood in molecular orbital terms. Extending down from the highest occupied molecular orbital (HOMO) is a rather closely packed set of valence molecular orbitals, that are clearly displayed in the photoelectron spectra (PES) of neutral alkanes. The electronic absorption of alkane radical cations is due to transitions (induced by photon absorption) of electrons from such lower-lying molecular orbitals to the semi-occupied molecular orbital (SOMO), which is the highest-occupied molecular orbital in the ground-state ion. By illumination within the (broad and largely unstructured) absorption band of alkane radical cations, electronically excited states of alkane radical cations can thus be created in a quite convenient way.
5.3 Paramagnetic Properties of Alkane Radical Cations
Information on the paramagnetic properties of alkane radical cations has been obtained by conventional EPR spectroscopy using matrix isolation [5–8] and by fluorescence detected magnetic resonance (FDMR) spectroscopy [9]. With the former technique, chlorofluorocarbon matrices (such as CCl3F, CCl2FCF2Cl and CCl3CF3) and perfluorocarbon matrices (such as perfluoromethylcyclohexane) as well as SF6 have routinely been used in combination with X- or c-irradiation. With the matrices employed, EPR signals from matrix radicals are anisotropically spread over a wide range (and are consequently very weak) and the paramagnetic absorption of alkane radical cations can be observed without serious interference. FDMR spectroscopy derives its special interest from the fact that it allows the observation of alkane radical cations in irradiated alkane systems. The paramagnetic absorption of alkane radical cations is critically dependent on their conformation. In neat n-alkane crystals, alkane molecules are in the extended all-trans conformation (see Fig. 5.1) and FDMR spectroscopy unequivocally shows that alkane radical cations retain that conformation in such systems. The extended all-trans conformation is also the preferred conformation of many n-alkane radical cations in chlorofluorocarbon and perfluorocarbon matrices. In this conformation, the unpaired electron occupies the planar r molecular orbital and delocalizes over the entire extended chain. Only two C–H bonds (both chainend, one on each side) are in the planar r molecular frame in the extended structure and high unpaired-electron and positive-hole density appears only on these in-plane protons. Alkane radical cations in the extended conformation (as well as in other conformations) are thus r-delocalized paramagnetic species. The associated hyperfine interaction with the two (equivalent) in-plane chain-end protons results in a 1:2:1 three-line (triplet) EPR spectrum. The fact that the hyperfine in-
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Figure 5.1 Extended all-trans and gauche-at-C2 conformers of octane.
teraction is due to two chain-end C–H bonds has unequivocally been demonstrated by experiments using specific deuteration. With increasing chain length, EPR spectra of n-alkane radical cations in the extended conformation become increasingly contracted as the hyperfine interaction decreases due to increased delocalization of the unpaired electron. The major proton hyperfine coupling constants of n-alkane radical cations in the extended conformation show a steady decrease with increasing chain length. A second conformation that is frequently encountered in chlorofluorocarbon matrices is the gauche-at-C2 conformation, which is obtained from the extended conformer by 120 rotation around C2–C3 (see Fig. 5.1). In this conformation, the unpaired electron and positive hole delocalize over the planar part of the C–C skeleton as well as over one in-plane chain-end and penultimate C–H bond (on opposite sides of the radical cation). Other more twisted conformations (such as obtained from the extended conformer by 120 rotation around the penultimate C–C bond as well as around C2–C3, either both clockwise or one clockwise and the other counterclockwise) have also been observed, but they are less common in chlorofluorocarbon matrices. In n-alkanes in the liquid state, many conformers are present and the paramagnetic absorption reflects this by the fact that an unresolved spectrum is observed for the radical cations, resulting from hyperfine coupling with many different protons [10]. As a result of increased delocalization, the line width of such composite spectra decreases with increasing chain length.
5.4 The Brønsted Acidity of Alkane Radical Cations
Alkane radical cations are very strong Brønsted acids and form an acid–base pair with neutral alkyl radicals as conjugate base according to the acid–base halfreaction RH.+ fi R. + H+
(5.1)
5.4 The Brønsted Acidity of Alkane Radical Cations
For n-alkane radical cations, both primary and secondary alkyl radicals may act as conjugate base, depending on the conformation of the radical cation. This is a direct consequence of the fact that the site of proton donation from alkane radical cations is strictly dependent on their electronic structure, that is, a high unpairedelectron and positive-hole density in a particular C–H bond results in proton transfer from that bond (evidence for this is given in Sections 5.7 and 5.8), whereas the electronic structure of the radical cations in turn depends on their conformation. For n-alkane radical cations in the extended conformation, in which the unpaired-electron and positive-hole delocalize over the planar C–C skeleton and two in-plane chain-end C–H bonds (one on each side), proton transfer takes place exclusively from chain-end positions and the corresponding primary alkyl radicals act as conjugate base. For n-alkane radical cations in the gauche-at-
Figure 5.2 Energy diagram relating the proton affinity of neutral alkyl radicals, PA(R.), to the ionization energy of the corresponding alkane, IE(RH), with the bond dissociation energy of the appropriate C–H bond, BDE(C–H), and the ionization energy of atomic hydrogen, IE(H.), as additional parameters.
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C2 conformation, in which the unpaired electron and positive hole delocalize over the planar part of the C–C skeleton as well as over one planar chain-end and penultimate C–H bond, proton transfer can take place from both a terminal and a penultimate position (on opposite sides of the radical cation); in such conformers, primary as well as secondary alkyl radicals act as conjugate base. As is evident from Fig. 5.2, the proton affinity of neutral alkyl radicals, Epa(R.), may be derived from the ionization energy of the corresponding alkane, Ei(RH), the bond dissociation energy of the appropriate C–H bond, Ebd(C–H), and the ionization energy of atomic hydrogen, Ei(H.), according to Eq. (5.2). Epa(R.) = Ebd(C–H) + Ei(H.) – Ei(RH)
(5.2)
Protonation energies of linear primary and secondary alkyl radicals show a steady increase with increasing chain length. This increase is closely associated with the corresponding decrease in ionization energy of the related alkane molecule, which is due to the fact that alkane radical cations are r-delocalized species for which the degree of delocalization of the unpaired-electron and positive-hole density (and the corresponding stabilization) increases with increasing chain length. As such, it is also related to the decrease with increasing chain length of the proton hyperfine coupling constants in the EPR spectra of n-alkane radical cations.
5.5 The r-Basicity of Alkanes
Conventional organic bases (such as amines) are compounds containing heteroatoms on which lone-pair electrons reside. The basicity of organic compounds is not limited, however, to such nonbonding electron systems. It has long been recognized that unsaturated aliphatic as well as aromatic hydrocarbons have a tendency to act as bases in acid–base reactions. The reactivity of olefins, acetylenes and aromatic hydrocarbons toward electrophiles lies in the p-electron donor abilities of the unsaturated double and triple bonds and p-aromatic systems. The addition of a proton to olefinic double bonds results in the formation of alkyl carbenium ions. In the absence of lone-pair and p-electrons, i.e. in the case of saturated aliphatic hydrocarbons, C–H and C–C bonds (both r-bonds) may also act as proton acceptors, as was evidenced by the work of Olah and coworkers on superacids [11–13]; very strong acids are required to protonate saturated hydrocarbons. As will amply be demonstrated in the present chapter, alkane radical cations offer an elegant alternative to superacids for the protonation of alkanes. Protonation of alkanes by alkane radical cations that are derived from the same alkane will be termed “symmetric”; the term “asymmetric proton transfer” will be applied if this condition is not fulfilled. It is to be remarked at this point that the reaction of an alkane with a free proton is a very exothermic process; the non-occurrence of protonation of alkanes by conventional acids is thus due to the fact that the tendency for proton retention of these acids is too strong and not to “lack of appetite” of the
5.5 The r-Basicity of Alkanes
alkane. As a matter of fact, very strong acids may be characterized as “weak” in the sense that they easily give in to the demand for protons by other species. In contrast to conventional organic bases that contain heteroatoms, in which protonation takes place at the heteroatom involving the lone-pair electrons, protonation in alkanes does not take place at a particular atom but at a particular C–H or C–C bond, resulting in the formation of a three-center two-electron bond. The r-basicity of alkanes is based on the general electron-pair donor ability of shared electron pairs in single bonds, in contrast to the donor ability of unshared electron pairs (lone-pair electrons) in conventional organic bases. In C–H protonated alkanes, bonding is provided by a three-center two-electron bond resulting from the overlap of the r-orbital of a hydrogen molecule with an empty sp3 orbital of the appropriate carbon atom. In C–C protonated alkanes, the bonding is due to an overlap of two sp3 orbitals belonging to adjacent carbon atoms and the 1s orbital of atomic hydrogen; this group also contains only two electrons. As a result of electron-density differentiation, protonation takes place on the main lobes of the C–H or C–C bonds (where the major part of the electron density resides) and not on the back lobes, that is, the carbon atoms themselves. It is to be remarked that with the formation of three-center two-electron bonds the octet rule for the carbon atoms involved is not violated; carbon atoms involved in three-center two-electron bonds in alkyl carbonium ions are pentacoordinated but they are not pentavalent. Experimental data on the protonation energies of saturated hydrocarbons are very scarce. A useful experimental approach consists in the determination of the dissociation energy of the carbonium ions by ion-equilibrium measurements, as performed by Kebarle and Hiraoka using high-pressure ion source mass spectrometry [14]. The thermodynamics of the protonation of alkanes and the energetics of pentacoordinated alkyl carbonium ions are not easily accessible experimentally, but they are linked through the dissociation energy of the carbonium ions to the energetics of the corresponding carbenium ions that can more readily be studied experimentally. The approach only works properly for the lowest members of the alkyl carbonium ion series, however. Because of the shortage of direct experimental observations of carbonium ions and of experiments that provide numerical data on their energies, the structure and energy of these species have been extensively studied theoretically. Considerable progress on this has been made in recent years by high-level theoretical calculations allowing the establishment of a r-basicity scale (viz., C–C > tertiary C–H > secondary C–H > primary C–H > CH4) that reflects the thermodynamics of the protonation of the r bonds [15–17]. However, theoretical studies are also largely limited to short-chain (nC £ 4) cations and reliable high-level theoretical calculations on long-chain alkyl carbonium ions still appear difficult to perform.
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5.6 Powder EPR Spectra of Alkyl Radicals
Proton transfer from alkane radical cations to alkane molecules results in the transformation of these cations into neutral alkyl radicals (the conjugate bases). The nature of these radicals is determined by the site of proton donation in the alkane radical cation. Information on the site of proton donation in the proton transfer from alkane radical cations to alkane molecules can thus be derived from EPR spectral analysis of the neutral alkyl radicals formed. To aid the reader in appreciating the results that are presented on this matter below and in understanding related spectra from the literature, a section on the characterization of neutral alkyl radicals by EPR spectroscopy in solid systems is included at this point. Neutral alkyl radicals derived from n-alkanes can be separated into three distinct classes with respect to their EPR spectrum, viz. chain-end (.CH2–CH2–CH2–_), penultimate (CH3–.CH–CH2–_) and interior (_–CH2–.CH–CH2–_). The possibility of cancellation of the anisotropic interactions of a-hydrogens is highly relevant with respect to the powder EPR spectra of alkyl radicals. Such annulment is possible for chain-end radicals, but not for penultimate and interior radicals. In alkyl radicals both the isotropic and anisotropic hyperfine interactions with the aprotons are “extensive”, that is, they affect the paramagnetic absorption to an extent that can clearly be discerned in the powder EPR spectra; in contrast, there is only a large isotropic interaction with the b-protons (anisotropic interactions with the b-protons are much smaller in value). When in 1-alkyl radicals the two a-proton spins are antiparallel, the hyperfine anisotropy largely cancels and relatively sharp intense hyperfine lines result, which are easily discernible in an EPR spectrum. In contrast, all EPR absorption bands of penultimate and interior n-alkyl radicals are strongly anisotropically broadened because cancellation of the anisotropic hyperfine interaction with the a-proton cannot take place. Another specific characteristic of the powder EPR spectrum of 1-alkyl radicals is the outermost transition, which is severely anisotropically broadened because the a-proton spins are parallel and manifests itself in a first-derivative spectrum as a slightly double-humped curve; (more centrally located anisotropic absorptions are not clearly observable due to mutual interference and spectral interference by the “isotropic” lines). Both features (the relatively narrow and largely isotropic lines and the double-humped curve) make the powder EPR spectrum of 1-alkyl radicals easily recognizable. The structure and overall appearance of the powder spectrum of 1-alkyl radicals are apparent from the simulated spectra shown in Fig. 5.3. Experimental information on the powder spectra of authentic chain-end, penultimate and interior alkyl radicals can be obtained from c-irradiated solid cis-decalin-d18 containing appropriate chloro- and bromoalkanes [18]. The EPR spectrum obtained after c-irradiation of neat cis-decalin-d18 consists of a broad unresolved band, which extends over a relatively restricted spectral region as a result of spectral contraction due to deuteration (see Fig. 5.4(a)). The addition of chloro- and bromoalkanes before irradiation results in a considerable distortion of this unre-
5.6 Powder EPR Spectra of Alkyl Radicals
Figure 5.3 Spectrum of 1-alkyl radicals simulated on the basis of hyperfine coupling constants of Ref. [35]. The spectrum is simulated using the Gaussian type lineshape function, with DHms = 0.5 mT; the effect of different linewidths on the outermost anisotropic transition is also shown.
solved absorption and in the appearance of very characteristic additional EPR absorptions in the lateral regions of the spectra. The additional EPR absorptions are solely due to very specific (solute-dependent) alkyl radicals, formed through dissociative electron attachment to the solute chloro- and bromoalkanes. R–X + e– fi R. + X–
(5.3)
Hole trapping by these compounds is excluded because of the low ionization energy of decalin. Chromatographic analyses have shown that alkyl radicals formed by c-irradiation of chloro- and bromoalkanes in cis- and trans-decalin are characteristic for the haloalkane solute and explicitly rule out the occurrence of radical isomerization [19]. The identity of the alkyl radicals observed is thus unambiguously determined by the choice of the chloro- and bromoalkane solutes. The lateral parts of the spectra obtained from c-irradiated cis-decalin-d18 containing 1 mol% 1-, 2and 3-bromooctane, shown in Fig. 5.4(b)–(d), can thus fully be attributed to chainend (RI.), penultimate (RII.) and interior (RIII.) alkyl radicals, respectively. The relatively narrow (largely isotropic) lines and the double-humped curve, that make the powder EPR spectrum of 1-alkyl radicals easily recognizable, are clearly discernible in the lateral parts of the spectrum obtained from c-irradiated cis-decalind18 containing 1 mol% 1-bromooctane (Fig. 5.4(b)). Unambiguous information on the band shape of (the lateral parts of) the EPR absorption of penultimate and interior alkyl radicals is provided by the spectra of c-irradiated cis-decalin-d18 containing 2- and 3-bromooctane (Fig. 5.4(c, d)). As is evident from these spectra, all
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Figure 5.4 First-derivative EPR spectra obtained after c-irradiation of neat cis-decalind18 (a) and of cis-decalin-d18 containing 1 mol% 1-bromooctane (b), 2-bromooctane (c) and 3-bromooctane (d). The dashed
rectangles contain spectral features that are highly typical for chain-end (RI.), penultimate (RII.) and interior (RIII.) alkyl radicals, respectively; d indicates a background absorption.
absorption bands of these radicals are rather broad. The EPR absorption of interior alkyl radicals is less well resolved than that of penultimate alkyl radicals; as a result, equally weighted combinations of the experimental powder spectra of authentic penultimate and interior alkyl radicals rather tend to correspond to the spectrum of penultimate radicals and quite considerable fractions of interior radicals may be “hidden” under the spectrum of penultimate radicals without seriously affecting the composite spectrum. Most importantly, the spectrum of penultimate and interior alkyl radicals extends over a wider spectral region than that of chain-end radicals, making the former detectable in the presence of the latter by careful examination of the region next to the double-humped curve; the overall appearance of convoluted spectra may also provide an indication of the presence of secondary alkyl radicals.
5.7 Symmetric Proton Transfer from Alkane Radical Cations to Alkanes
5.7 Symmetric Proton Transfer from Alkane Radical Cations to Alkanes: An Experimental Study in c-Irradiated n-Alkane Nanoparticles Embedded in a Cryogenic CCl3F Matrix 5.7.1 Mechanism of the Radiolytic Process
Radiolysis of cryogenic trichlorofluoromethane containing a suitable n-alkane as solute has proven very suitable for the study of symmetric proton transfer from alkane radical cations to alkane molecules. At low concentration of the alkane solute (RH) in the binary CCl3F/alkane system, absorption of ionizing radiation mainly occurs by trichlorofluoromethane resulting in its excitation and ionization, CCl3F ~~~fi CCl3F*
(5.4a)
CCl3F ~~~fi CCl3F.+ + e–
(5.4b)
leaving the solute alkane largely unaffected as far as direct interaction with the ionizing radiation is concerned. The solute alkane is thus little involved in the initial “violent” phase of energy deposition by the ionizing radiation, in which massive excess energy is often available that is not conducive to site-selective processes. As a result of long-range electron tunneling, the positive hole is transferred efficiently from trichlorofluoromethane radical cations to the alkane solute, however, resulting in the neat and selective formation of alkane radical cations (without concomitant neutral alkyl radical formation as would be the case in neat alkanes). CCl3F.+ + RH fi CCl3F + RH.+
(5.5)
Though gas phase ionization energies of CCl3F and higher alkanes (such as undecane) are quite different (“evaluated” ionization energies of 11.68 eV and 9.56 eV have been reported [20] for CCl3F and undecane, respectively), the excess energy imparted to solute alkane radical cations is much lower than this difference suggests because of dimer cation formation in irradiated trichlorofluoromethane. The stabilization energy due to (CCl3F)2.+ dimer cation formation is unknown at present, but is likely to be extensive. Similar stabilization of solute alkane radical cations by radical cation adduct formation with CCl3F or by dimer cation formation can be ruled out on the basis of the relative inaccessibility of the semi-occupied molecular orbital (SOMO) in alkane radical cations and (for the adduct formation) by the great difference in ionization energy between CCl3F and the solute alkane. EPR spectra of alkane radical cations in CCl3F are incompatible with both adduct and dimer cation formation. At cryogenic temperatures, alkane radical cations are stable when fully isolated in the CCl3F matrix, because electrons formed in the ionization process react with trichlorofluoromethane by dissociative electron attachment.
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CCl3F + e– fi CCl2F. + Cl–
(5.6)
It is now well established, however, that alkanes form small aggregates in CCl3F, aggregates to which positive-hole transfer still occurs efficiently [21–23]. The degree of aggregation increases with increasing alkane concentration and at a specific concentration increases quite strongly with increasing chain length of the alkane solute. As a result, symmetric proton transfer may take place from solute alkane radical cations to alkane molecules yielding alkyl radicals and protonated alkanes (alkyl carbonium ions). RH.+ + RH fi R. + RH2+
(5.7)
As became apparent from our experiments, only secondary C–H protonation leads to effective chemical transformation in c-irradiated CCl3F/alkanes (see below). As secondary C–H protonated alkanes are characterized by negative dissociation energies, protonation is followed immediately by dissociation of the C–H protonated alkanes into alkyl carbenium ions and molecular hydrogen. RH2+ fi R+ + H2
(5.8)
Upon melting, alkyl carbenium ions react with chloride ions, both species being trapped in the solid system at 77 K. This leads to the formation of isomeric chloroalkanes, with the position of the chlorine atom being indicative for the original site of C–H protonation; the coulombic attraction involved and the high mobility of chloride ions make this neutralization process highly competitive with respect to ion–molecule reactions involving exclusively long-chain species. 5.7.2 Physical State of Alkane Aggregates in CCl3F
Information on the physical state (crystalline versus amorphous) of alkane aggregates in CCl3F can be derived from EPR experiments on c-irradiated odd n-alkanes with nC ‡ 11 in this matrix, by virtue of the dependence of intermolecular radicalsite transfer on the molecular alignment in n-alkane crystals [24]. Odd n-alkanes with nC ‡ 11 have an orthorhombic crystalline structure and with such a mode of packing the nearest neighboring C–H bond (of adjacent molecules) to a primary radical site belongs to a chain-end methyl group, as can be seen in Fig. 5.5. As a result, transformation of primary into secondary alkyl radicals by intermolecular radical-site transfer does not take place in orthorhombic crystals. Alternatively and viewed from a different perspective, if extensive radical transformation in c-irradiated odd n-alkanes with nC ‡ 11 in CCl3F occurs, then this constitutes evidence that the alkane aggregates do not pack according to the orthorhombic crystalline structure. In view of general considerations on the crystallization of n-alkanes, it can be concluded that in such a case they must be amorphous with no specific structure at all.
5.7 Symmetric Proton Transfer from Alkane Radical Cations to Alkanes
Figure 5.5 Structural diagram showing the molecular packing in odd n-alkanes (nC ‡ 11) with an orthorhombic crystalline structure as a projection on a diametrical plane, dc, that forms an angle of 45 with the ac and bc planes of the crystal.
EPR spectra obtained after c-irradiation of undecane at various concentrations in CCl3F are shown in Fig. 5.6. With increasing undecane concentration, the disappearance of undecane radical cations and transformation of primary into secondary undecyl radicals (by intermolecular radical-site transfer) 1-C11H23. + n-C11H24 fi n-C11H24 + sec-C11H23.
(5.9)
are obvious. The most notable changes in the EPR spectra with increasing undecane concentration which indicate this are (i) the appearance of a paramagnetic absorption outside the spectral region of 1-undecyl radicals; (ii) a gradual shift of the 1-undecyl radical spectrum away from the baseline, i.e., it becomes superimposed on a broad and (in first-derivative spectral terms and at the right-hand side of the spectra) consistently negative paramagnetic absorption; (iii) the gradual decrease and disappearance of the spectral absorption attributed to undecane radical cations, i.e., the pseudo-singlet (contracted triplet) denoted RH.+ and (iv) the gradual decrease and disappearance of the spectral absorption due to primary undecyl radicals, i.e., the relatively narrow (largely isotropic) lines and the double-humped curve denoted RI.. The first two spectral changes listed point to the appearance and gradual increase in importance of secondary undecyl radicals. At 4 mol %, it is hard to see even a trace of the spectral characteristics of 1-undecyl radicals that were so prominent at lower concentrations. The transformation of primary into secondary undecyl radicals and the dominance of secondary undecyl radicals at much higher concentrations unequivocally show that, as a rule, undecane aggregates in CCl3F are amorphous and this conclusion can reasonably be extended to all n-alkanes with nC £ 11 for concentrations below about 20 mol%. In the EPR spectra of c-irradiated CCl3F/undecane primary radical features reappear from about 7 mol%, however, and these features
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Figure 5.6 First-derivative EPR spectra obtained after c-irradiation of undecane at various concentrations in CCl3F. Spectral features due to undecane radical cations and primary undecyl radicals are indicated, respectively, by RH.+ and RI.; d indicates a background absorption.
become more prominent at higher undecane concentration (see Fig. 5.6) pointing to the onset and increasing prominence of crystallization. With undecane this is still very restricted, even at high concentration, but with longer n-alkanes (such as tridecane) crystallization is observed at much lower concentrations and becomes quite prominent at high alkane concentration.
5.7 Symmetric Proton Transfer from Alkane Radical Cations to Alkanes
5.7.3 Evidence for Proton-donor and Proton-acceptor Site Selectivity in the Symmetric Proton Transfer from Alkane Radical Cations to Alkane Molecules 5.7.3.1 Proton-donor Site Selectivity
Information on the site of proton donation in the symmetric proton transfer from alkane radical cations to alkane molecules can be derived from the nature of the alkyl radicals formed in c-irradiated CCl3F/n-alkanes at 77 K but only at relatively low alkane concentration, viz. at or around the onset of alkane aggregation and alkyl radical formation [18, 25]. Working around the onset of alkyl radical formation is essential because otherwise all radicals are transformed into the thermodynamically most stable ones by intermolecular radical-site transfer. The most notable result, the EPR spectrum obtained after c-irradiation of CCl3F containing 1.75 mol heptane, is shown in Fig. 5.7. The spectrum mainly consists of a (distorted) triplet due to heptane radical cations in the extended all-trans conformation. In addition to the triplet spectrum, a weak resonance signal that can be attributed to 1-heptyl radicals is observed in the lateral region of the spectrum. The intensity of the lateral heptyl radical absorption increases with increasing heptane concentration, but this increase is accompanied by gradual transformation of primary into secondary heptyl radicals by intermolecular radical-site transfer. The result on c-irradiated CCl3F/heptane characterizes the reaction of (higher) alkane radical cations with alkane molecules unequivocally as proton transfer (hydrogen abstraction would lead to preferential formation of secondary heptyl radicals) and shows that the site of proton donation is related very strictly
Figure 5.7 First-derivative EPR spectrum obtained after c-irradiation at 77 K of 1.75 mol% heptane in CCl3F; d indicates a background absorption.
121
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5 Proton Transfer from Alkane Radical Cations to Alkanes
to the structure of the semi-occupied molecular orbital in the radical cation. The high unpaired-electron and positive-hole density in the in-plane chain-end C–H bonds leads to proton transfer from those sites, giving rise to the selective formation of 1-heptyl radicals. Experiments with n-alkane radical cations in different conformations confirm the relation between electronic structure and site of proton donation. Octane radical cations in CCl3F, for instance, are largely in a gauche-at-C2 conformation obtained by one 120 rotation around C2–C3 in the extended conformer (see Fig. 5.1). Proton transfer results in the formation of secondary as well as primary octyl radicals in this case, as evidenced by the fact that both are present from the very first appearance of octyl radicals with increasing octane concentration in c-irradiated CCl3F/octane. This is again in accordance with the electronic structure, as in the gauche-at-C2 conformation there is large unpaired-electron and positive-hole density in the planar part of the C–C skeleton as well as in one chain-end and one penultimate C–H bond (both in-plane) at opposite sides.
5.7.3.2 Proton-acceptor Site Selectivity Information on the site of proton acceptance in the symmetric proton transfer from alkane radical cations to alkane molecules can be derived from chromatographic analysis of chloroalkanes formed in CCl3F/alkanes after c-irradiation at 77 K and subsequent melting [26, 27]. Because of the amorphous state of alkane aggregates in CCl3F, any acceptor site selectivity observed must be intrinsic in nature. A manifest effect observed upon analysis of chloroalkanes with the same carbon number as the parent alkane is the gradual reduction in the contribution of the chain-end isomer with increasing alkane concentration; data for CCl3F/ decane are shown in Fig. 5.8. The effect is related to the fact that the protonation energy for primary C–H protonation is substantially lower than that for C–C pro-
Figure 5.8 Contribution percentage of 1-chlorodecane to chlorodecane formation and extent of proton transfer from decane radical cations to decane molecules as a function of decane concentration in c-irradiated CCl3F/decane.
5.7 Symmetric Proton Transfer from Alkane Radical Cations to Alkanes
tonation and secondary C–H protonation and provides further evidence for a gradual increase in proton transfer from alkane radical cations to alkane molecules with increasing alkane concentration in c-irradiated CCl3F/alkanes. The extent of proton transfer as a function of decane concentration in CCl3F/decane calculated from these data is shown in Fig. 5.8. The isomeric composition of chloroalkanes at high alkane concentration (extensive proton transfer) unequivocally shows protonation to take place preferentially at the penultimate (rather than at the interior) C–H bonds in n-alkanes, an observation that is supported by thermochemical data. The weaker protonation at the different inner (non-penultimate) C–H bonds in n-alkanes apparently occurs to about the same extent at each bond. A search for 1-chloroalkanes with smaller carbon number than the parent alkane revealed the absence of such products in CCl3F/decane after c-irradiation at 77 K and subsequent melting, providing strong evidence for the absence of chemical transformation due to C–C protonation of n-alkanes by proton transfer from alkane radical cations. Indeed, pentacoordinated alkyl carbonium ions that have the C–C protonated structure can be formed from and dissociate into alkyl carbenium ions and neutral alkanes (a process characterized by positive dissociation energies) and it is quite logical to expect that neutralization with chloride ions will take place accordingly, i.e., with formation of shorter-chain 1-chloroalkanes and alkanes. The absence of chemical transformation due to C–C protonation was originally considered to be purely thermochemical in nature, but now appears to have a more complex origin in which thermochemical and structural (cage) effects are involved as well as the intrinsic stability of the carbonium ions. This relates specifically to (i) the (modest) endothermicity of the proton transfer from alkane radical cations to alkane molecules for both C–H and C–C protonation, (ii) the sign of the dissociation energy with respect to the normal fragmentation of alkyl carbonium ions and (iii) the size of the corresponding fragmentation products. The dissociation energy of C–C protonated alkanes for fragmentation into smaller-sized alkyl carbenium ions and neutral alkanes is positive and the fragmentation products of such a dissociation are held together by the cage effect, effectively preventing the dissociation of C–C protonated alkanes in condensed phases. This, in association with the endothermicity of the proton transfer from alkane radical cations to alkanes, results in the transfer of the proton from C–C protonated alkanes back to the associated alkyl radicals and thus in the absence of chemical transformation due to C–C protonation. In contrast, the dissociation energy of secondary C–H protonated alkanes for fragmentation into alkyl carbenium ions and molecular hydrogen is negative, i.e., the fragments are more stable than the carbonium ion itself, and molecular hydrogen is small enough to escape from the cage in which it is formed. As a result, back transfer of the proton does not occur and chemical transformation due to secondary C–H protonation is observed. The absence of chemical transformation due to primary C–H protonation is, in all likelihood, due to the very absence of such protonation and is, as such, purely thermochemical in nature; (the positive sign of the dissociation energy of primary C–H protonated alkanes for fragmentation into alkyl carbenium ions and molecular hydrogen may be an additional factor in the absence of chemical trans-
123
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5 Proton Transfer from Alkane Radical Cations to Alkanes
formation). It is to be noted that the results imply that no trapped alkyl carbonium ions are present after irradiation of n-alkanes under cryogenic conditions, either neat or in CCl3F matrices in the solid state. The negative sign of the dissociation energy of secondary (and tertiary) C–H protonated alkanes for fragmentation into alkyl carbenium ions and molecular hydrogen follows from high-level theoretical calculations on the energetics of pentacoordinated carbonium ions and simply represents the fact that the enthalpy of formation of the dissociation products is lower than that of the corresponding carbonium ions. Negative dissociation energies are not easily conceived by experimental chemists and cannot readily be determined by ion-equilibrium measurements on the stability of cationic species. When a particular cation is intrinsically unstable, its dissociation energy is intuitively assumed to be (near) zero. This misconception is at the origin of various erroneous representations of the relative order of the energies of C–C and secondary C–H protonation [14, 27]. 5.7.4 Comparison with Results on Proton Transfer and “Deprotonation” in Other Systems
Information on selectivity with respect to the site of proton donation (but not of proton acceptance) in the symmetric proton transfer from alkane radical cations to alkane molecules has been derived from systems other than c-irradiated CCl3F/ alkanes. Two approaches have basically been taken to bring alkane radical cations into contact with alkane molecules in solid systems in order to study their reaction: (i) increasing the temperature of the irradiated system and bringing it to a point where, as a result of diffusion and migration, alkane radical cations disappear and neutral alkyl radicals are formed and (ii) increasing the concentration of the alkane solute to a point where the alkane molecules are not fully isolated and the appearance of neutral alkyl radicals is observed experimentally. Thermal conversion of alkane radical cations into neutral alkyl radicals has been conducted in SF6 and CCl2FCF2Cl and conflicting results have been obtained in these matrices. n-Alkane radical cations (C4–C7) radiolytically produced in SF6 at 77 K exhibit the planar extended structure with no detectable gauche conformers; upon warming above 100 K transformation into 1-alkyl radicals is observed exclusively, as is expected from the unpaired-electron and positive-hole distribution [28]. In sharp contrast, 2-alkyl radicals are selectively formed by thermal conversion in CCl2FCF2Cl, regardless of the conformation of the alkane radical cations [5–8, 29]. This has been assumed to come from prior thermal conversion of extended conformers into gauche-at-C2 conformers, but an alternative explanation based on charge neutralization in CCl2FCF2Cl is far from inconceivable. The thermal conversion of alkane radical cations into neutral alkyl radicals can phenomenologically be termed “deprotonation” and is usually denoted as such in the literature. Different reaction processes may be at the origin of such thermal “deprotonation”. Increasing the temperature of the irradiated system, to a point where diffusion and migration of species takes place, not only brings alkane radical cations into contact with alkane molecules but also with the counter anions trapped in the sys-
5.8 Asymmetric Proton Transfer from Alkane Radical Cations to Alkanes
tem; these have a relatively low concentration, but are attracted to the radical cations by coulombic attraction and (in the case of chloride ions) are much more mobile species than long-chain alkane molecules. The mechanism of thermal conversion is thus considerably less certain than that of concentration studies, in which reaction of the alkane radical cations with alkane molecules is implicated by the increasing alkane concentration. Concentration studies have been conducted in the synthetic zeolites ZSM-5 and Linde-5A [30]. Radical cations of C6 and C8 n-alkanes prepared by irradiation at 4 K in ZSM-5 at low alkane concentration are in the extended all-trans conformation. At high alkane concentration, alkyl radicals were observed with dominant (but not exclusive) formation of the chain-end isomer; the minor formation of secondary alkyl radicals has been attributed to intermolecular radical-site transfer. In Linde-5A only 1-octyl radicals were observed, but no spectrum of octane radical cations was reported in this zeolite.
5.8 Asymmetric Proton Transfer from Alkane Radical Cations to Alkanes: An Experimental Study in c-Irradiated Mixed Alkane Crystals 5.8.1 Mechanism of the Radiolytic Process
Radiolysis of mixed alkane crystals consisting of a lower alkane (RIH), such as pentane, to which relatively low concentrations (about 1 mol%) of a higher alkane (RIIH) and a suitable electron acceptor (for instance CO2 or a chloroalkane) have been added, has proven very suitable for the study of asymmetric proton transfer from alkane radical cations to alkane molecules. Radiation-chemical mechanisms of alkanes are inherently very complex and the discussion will be limited to processes that have some bearing on the concepts discussed. The primary interaction of c-irradiation with systems composed of a lower alkane with 1 mol% of a higher alkane and with a specific chloroalkane or CO2 as solute consists mainly in excitation and ionization of the main component, i.e., the lower alkane. RIH ~~~fi RIH *
(5.10a)
RIH ~~~fi RIH .+ + e–
(5.10b)
Excited alkane molecules may dissociate into alkyl radicals and hydrogen atoms, RIH* fi RI. + H.
(5.11)
or, by molecular dissociation, into the corresponding alkene and molecular hydrogen. Alkane radical cations formed in the ionization process may also carry quite considerable amounts of excitation energy. Indeed, removal by irradiation of an electron in alkanes from lower-lying molecular orbitals results directly in the for-
125
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5 Proton Transfer from Alkane Radical Cations to Alkanes
mation of electronically excited radical cations. These may react by dissociation into alkyl carbenium ions and hydrogen atoms RIH.+* fi RI+ + H.
(5.12)
and by proton transfer to adjacent alkane molecules yielding alkyl carbonium ions and neutral alkyl radicals. RIH.+* + RIH fi RI. + RIH2+
(5.13)
The alkyl carbonium ions formed may dissociate into alkyl carbenium ions and molecular hydrogen or alternatively transfer the proton back to the associated alkyl radicals. Overall, little or no site selectivity is expected in such reactions (5.12) and (5.13). Many of the lower-lying molecular orbitals in neutral alkanes undoubtedly contribute to C–H bonding at various sites in the molecule and electron removal will result in unpaired-electron and positive-hole density at those sites allowing dissociation at and proton transfer from such positions. Because of the high amount of excess energy available, subtle differences in the tendency of (secondary) C–H bonds to act as proton acceptor are also not likely to play a major role in this initial “violent” phase of energy deposition by the ionizing radiation. Neutralization by electrons remains an important process in the radiolysis of alkanes containing chloroalkanes or CO2 as solute. Many of the electrons formed in the ionization process have insufficient energy to escape the Coulomb field of their associated cation and, on returning, neutralize the corresponding radical cations, carbenium ions or carbonium ions (geminate recombination). Part of the electrons formed do not return, however, but react with the chloroalkane solute by dissociative electron attachment, REA–Cl + e– fi REA. + Cl–
(5.14)
or by electron attachment to CO2. CO2 + e– fi CO2.–
(5.15)
By this process, the negative charge becomes trapped in the solid system as a chloride ion or as a CO2 anion. For the study of proton-donor site selectivities, which are conducted by EPR spectroscopy after irradiation at 77 K, the use of CO2 as electron acceptor is to be preferred as the CO2 anion has only a rather narrow central absorption that does not hinder the analysis. Chloroalkanes can be used in such studies if the respective deuterated products are employed. For the study of proton-acceptor site selectivities, which are conducted by gas-chromatographic analysis after warming and melting the sample, chloroalkanes are highly preferred over CO2 as electron acceptor because of the nature of the respective neutralization products. Upon warming and melting, alkyl carbenium ions that are also trapped in the solid system will be neutralized by chloride ions resulting in the formation of chloroalkanes.
5.8 Asymmetric Proton Transfer from Alkane Radical Cations to Alkanes
RI+ + Cl– fi RICl
(5.16)
Despite their low concentration, a non-negligible fraction of molecules of the higher alkane solute will be located in regions where the initial “violent” phase of energy deposition by the ionizing radiation takes place. This will result in the formation and trapping of alkyl carbenium ions of the higher alkane solute. As with the lower alkane matrix, little or no site selectivity is to be expected overall from this process and the corresponding neutralization reaction RII+ + Cl– fi RIICl
(5.17)
is at the origin of a “random” (non-site-selective) formation of chloroalkanes of the higher alkane solute, upon which the site-selective formation (that yields information on proton-acceptor selectivities) is superimposed. Information on proton-donor and proton-acceptor site selectivities in c-irradiated mixed crystals is yielded by processes that are separated from the initial energy deposition in both space and time. A sizable fraction of the loweralkane radical cations formed in the ionization process are not overly excited or become sufficiently deactivated before reacting by fragmentation or proton transfer. At this point, fragmentation is excluded and proton transfer from radical cations that are in their electronic ground state is not at all efficient in neat n-alkane crystals (and microscopic neat parts in n-alkane mixed crystals). Also, as a result of electron scavenging, a number of such cations escape “immediate” neutralization by electrons. The “unreactive” lower-alkane radical cations are not trapped in the solid system, not because they are mobile themselves, but because of positivehole transfer to (electron transfer from) adjacent matrix molecules, resulting in positive-hole migration. RIH .+ + RIH fi RIH + RIH .+
(5.18)
In the inhomogeneous coulombic field generated by the trapped cations and anions formed by irradiation, positive holes will migrate in the direction of trapped anions. When, as a result of this process, a matrix (RIH) radical cation becomes adjacent to a solute (RIIH) molecule, positive-hole transfer to the solute may occur. RIH.+ + RIIH fi RIH + RIIH.+
(5.19)
In addition, proton-transfer reactions take place. In irradiated mixed alkanes the higher-alkane radical cations are trapped next to matrix molecules and part of them react by proton transfer. RIIH.+ + RIH fi RII. + RIH2+
(5.20)
Also, proton transfer from matrix radical cations to solute molecules takes place in competition with positive-hole transfer (reaction (5.19) in the same direction. RIH.+ + RIIH fi RI. + RIIH2+
(5.21)
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5 Proton Transfer from Alkane Radical Cations to Alkanes
Proton transfer from alkane radical cations that are in their electronic ground state is greatly facilitated by the fact that in mixed n-alkane crystals planar chainend C–H bonds, from which proton donation takes place, come into close contact with secondary C–H bonds in adjacent molecules (see the structural diagrams below). In neat n-alkane crystals, there is only close contact with primary C–H bonds that have much lower protonation energies. 5.8.2 Evidence for Proton-donor and Proton-acceptor Site Selectivity in the Asymmetric Proton Transfer from Alkane Radical Cations to Alkanes
Evidence for the occurrence of asymmetric proton transfer in mixed n-alkane crystals has been obtained in close connection with the demonstration of site selectivity in the donor and acceptor processes. Such evidence can only be gathered properly from species that are related to the solute (higher alkane) molecule, because any site selectivity from matrix species is completely wiped out by an overwhelming amount of nonselective processes (see above). With respect to the site of proton donation, proton transfer from solute radical cations to matrix molecules was therefore studied, whereas, with respect to the site of proton acceptance, proton transfer from matrix radical cations to solute molecules was investigated. The site of proton donation in the proton transfer from solute radical cations to matrix molecules has been investigated using c-irradiated pentane-d12 containing 0.5 mol% octane as well as trapped CO2 [31]. Octane radical cations are formed by positive-hole transfer from matrix cations in this system and part of them react by proton transfer to matrix molecules, n-C8H18.+ + n-C5D12 fi 1-C8H17. + n-C5D12H+
(5.22)
while others simply remain trapped in the solid system. The first-derivative EPR spectrum of the system is shown in Fig. 5.9. The EPR spectrum is largely due to deuterated pentyl radicals (this spectrum is narrowed by the deuteration); the very intense and relatively sharp asymmetric feature near the center of the spectrum, with a pseudodoublet structure at the high-field side, is due to CO2.–. The (weak) lateral features can be attributed with certainty to 1-octyl radicals; no secondary octyl radicals are observable in the system. In association with the results of Ichikawa et al., that show that octane radical cations in pentane matrices are in the extended all-trans conformation [32], these data thus confirm the relation between the electronic structure of alkane radical cations and the site of proton donation. With respect to the site of proton acceptance in the proton transfer from matrix radical cations to solute molecules, two systems have been investigated exhaustively, viz. c-irradiated heptane/octane/1-chlorohexane [33] and heptane/ decane/1-chloroheptane [34]. A third system, viz. c-irradiated pentane/decane/ 1-chloropentane has also been studied but in considerably less detail. In the first system, proton transfer takes place from heptane radical cations to octane molecules n-C7H16.+ + n-C8H18 fi 1-C7H15. + 2-C8H19+
(5.23)
5.8 Asymmetric Proton Transfer from Alkane Radical Cations to Alkanes
Figure 5.9 First-derivative EPR spectrum obtained after c-irradiation at 77 K of 0.5 mol% octane in perdeuterated pentane, containing CO2 as electron acceptor.
followed by dissociation and subsequent neutralization of the octyl carbenium ions by chloride ions upon melting. 2-C8H17+ + Cl– fi 2-C8H17Cl
(5.24)
From Fig. 5.10 it is evident that penultimate C–H bonds in octane, which for reasons of energetics have the greatest propensity to act as proton acceptor, are also structurally favored over the interior C–H bonds with respect to proton acceptance from planar chain-end C–H bonds in the heptane radical cations. Both structural and thermodynamic factors thus favor the penultimate position and this translates into a very high selectivity with respect to this site (C2/C3: 5.3, C2/C4: 13.4, at 3 mol%). As a matter of fact, the minor formation of 3- and 4-chlorooctane can (largely) be attributed to random processes related to reaction (5.17). In the heptane/decane/1-chloroheptane system protonation of decane by heptane radical cations n-C7H16.+ + n-C10H22 fi 1-C7H15. + sec-C10H23+
(5.25)
results in the formation of decyl carbonium ions. Selectivity with respect to the site of proton acceptance is studied by analyzing the chlorodecanes formed by dissociation of these cations and subsequent neutralization by chloride ions upon melting of the carbenium ions produced. sec-C10H21+ + Cl– fi sec-C10H21Cl
(5.26)
129
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5 Proton Transfer from Alkane Radical Cations to Alkanes
Figure 5.10 Structural diagram depicting the packing in heptane crystals containing octane molecules in the extended all-trans and gauche-at-C2 conformation. The arrows indicate potential sites for proton transfer from planar chain-end C–H bonds in heptane radical cations to penultimate C–H
bonds in octane molecules (and vice versa heptane versus octane, indicated by d). The nearest approach of planar chain-end C–H bonds in heptane radical cations to penultimate C–H bonds in heptane molecules is indicated by dashed lines.
Information on the accessibility of the different C–H bonds in decane for planar chain-end C–H bonds in heptane radical cations may be derived from the structural diagrams shown in Fig. 5.11 and 5.12. Some of the proton transfers indicated therein may take place from heptane radical cations above as well as below the decane molecule, whereas other transfers have no such alternative, either due to steric hindrance by the gauche methyl group or due to the transfer occurring in the b-plane of the crystal. Competition between different sites for the same planar chain-end C–H bond in heptane radical cations must also be taken into account. From the structural diagrams it can be seen that the C–H bonds at the C4 position in decane are directly accessible to planar chain-end C–H bonds in heptane radical cations, but to a much lesser extent than C–H bonds at the C3 position; C–H bonds at the C5 position in decane are only accessible to a very minor extent. The formation of 5-chlorodecane can (largely) be attributed to random processes associated with reaction (5.17). C–H bonds at the C2 and C3 position in decane are both easily accessible with a clear positive bias towards C3 for the gauche-at-C2 conformer. In stark contrast, the selectivity for the proton transfer to the penultimate position is higher than for the transfer to the C3 position, as can be derived
5.8 Asymmetric Proton Transfer from Alkane Radical Cations to Alkanes
from the isomeric composition of the chlorodecanes. The site selectivity factor (relative to C3) obtained after correction for a yield due to random processes (as defined by the yield of 5-chlorodecane) amounts to 3.29, confirming that the proton transfer in n-alkanes preferentially occurs to the penultimate C–H bonds. In contrast to the situation in CCl3F/decane, the inner (C3 to C5) positions are not protonated to about the same extent. The disparity between the site selectivity for the protonation of the inner positions of decane in heptane versus in CCl3F, as illustrated by the site selectivity factors (heptane/CCl3F; C3:1/1, C4:0.49/1.02, C5:0/0.96), can be attributed to structurally-determined acceptor site selectivity in heptane crystals, i.e., acceptor site selectivity resulting from the donor site selectivity in combination with accessibility differences due to structural factors. In the pentane/decane/1-chloropentane system, proton transfer takes place from pentane radical cations to decane molecules, n-C5H12.+ + n-C10H22 fi 1-C5H11. + 5-C10H23+
(5.27)
followed by dissociation and subsequent neutralization of the decyl carbenium ions by chloride ions upon melting.
Figure 5.11 Structural diagram depicting the packing in heptane crystals containing decane molecules in the extended all-trans conformation. The arrows indicate potential sites for proton transfer from planar chain-end C–H bonds in heptane radical cations to C2, C3
and C4 carbon–hydrogen bonds in decane molecules; points of approach that are deemed irrelevant or of minor importance to the proton-transfer process for structural reasons are indicated by dashed lines.
131
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5 Proton Transfer from Alkane Radical Cations to Alkanes
5-C10H21+ + Cl– fi 5-C10H21Cl
(5.28)
In this system, planar chain-end C–H bonds in pentane radical cations from which proton donation takes place only come into close contact with secondary C– H bonds at the inner (C5) position in decane, as well as with primary C–H bonds; the latter have a much lower protonation energy than secondary C–H bonds, however, and thus cannot compete effectively as acceptor in the protonation process. Experiments show a marked predominance of 5-chlorodecane over more lateral secondary chlorodecanes, in accordance with the restricted accessibility of secondary C–H bonds in decane to planar chain-end C–H bonds in pentane radical cations. Perhaps even more importantly, no substantial preference is observed for the penultimate position relative to the C3 and C4 positions. This shows unequivocally that the preference for the penultimate position in the experiments with other systems described above is not due to the transformation of alkyl carbenium ions by hydride transfer, i.e., reactions such as 5-C10H21+ + n-C10H22 fi n-C10H22 + 2-C10H21+
(5.29)
but instead can be attributed unambiguously to a greater propensity of penultimate than of more interior secondary C–H bonds for proton acceptance.
Figure 5.12 Structural diagram depicting the packing in heptane crystals containing decane molecules in the gauche-at-C2 conformation. The arrows indicate potential sites for proton transfer from planar chain-end C–H bonds in heptane radical cations to C2, C3 and C4
carbon–hydrogen bonds in decane molecules; points of approach that are deemed irrelevant or of minor importance to the proton-transfer process for structural reasons are indicated by dashed lines.
References
References 1 P. W. F. Louwrier, W. H. Hamill, J. Phys. 2
3
4 5 6 7 8 9
10
11 12 13 14 15
16
17
18
Chem. 1970, 74, 1418–1421. G. Wolput, M. Neyens, M. Strobbe, J. Ceulemans, Radiat. Phys. Chem. 1984, 23, 413–418. A. Van den Bosch, M. Strobbe, J. Ceulemans, in Photophysics and Photochemistry above 6 eV, F. Lahmani (Ed.), Elsevier, Amsterdam, 1985, pp. 179–189. R. C. Benz, R. C. Dunbar, J. Am. Chem. Soc. 1979, 101, 6363–6366. K. Toriyama, K. Nunome, M. Iwasaki, J. Phys. Chem. 1981, 85, 2149–2152. K. Toriyama, K. Nunome, M. Iwasaki, J. Chem. Phys. 1982, 77, 5891–5912. M. Lindgren, A. Lund, G. Dolivo, Chem. Phys. 1985, 99, 103–110. G. Dolivo, A. Lund, Z. Naturforsch.a 1985, 40, 52–65. D. W. Werst, M. G. Bakker, A. D. Trifunac, J. Am. Chem. Soc. 1990, 112, 40–50. V. I. Borovkov, V. A. Bagryansky, I. V. Yeletskikh, Y. N. Molin, Mol. Phys. 2002, 100, 1379–1384. G. A. Olah, Y. Halpern, J. Shen, Y. K. Mo, J. Am. Chem. Soc. 1971, 93, 1251–1256. G. A. Olah, Y. Halpern, J. Shen, Y. K. Mo, J. Am. Chem. Soc. 1973, 95, 4960–4970. G. A. Olah, Angew. Chem., Int. Ed. Engl. 1973, 12, 173–254. K. Hiraoka, P. Kebarle, J. Am. Chem. Soc. 1976, 98, 6119–6125. P. M. Esteves, C. J. A. Mota, A. RamrezSols, R. Hernndez-Lamoneda, J. Am. Chem. Soc. 1998, 120, 3213–3219. C. J. A. Mota, P. M. Esteves, A. RamrezSols, R. Hernndez-Lamoneda, J. Am. Chem. Soc. 1997, 119, 5193–5199. P. M. Esteves, G. G. P. Alberto, A. Ramrez-Sols, C. J. A. Mota, J. Phys. Chem. A 2000, 104, 6233–6240. D. Stienlet, J. Ceulemans, J. Phys. Chem. 1992, 96, 8751–8756.
19 D. Stienlet, A. Vervloessem,
J. Ceulemans, J. Chromatogr. 1989, 475, 247–260. 20 P. J. Linstrom, W. G. Mallard, Eds., NIST Chemistry WebBook, NIST Standard Reference Database Number 69, National Institute of Standards and Technology, Gaithersburg MD, 2003. (Accessible at URL: http://webbook. nist.gov/chemistry). 21 G. Luyckx, J. Ceulemans, J. Chem. Soc., Chem. Commun. 1991, 988–989. 22 G. Luyckx, J. Ceulemans, J. Chem. Soc., Faraday Trans. 1991, 87, 3499–3504. 23 G. Luyckx, J. Ceulemans, Radiat. Phys. Chem. 1993, 41, 567–573. 24 D. Stienlet, G. Luyckx, J. Ceulemans, J. Phys. Chem. B 2002, 106, 10873– 10883. 25 D. Stienlet, J. Ceulemans, J. Chem. Soc., Perkin Trans. 2 1992, 1449–1453. 26 A. Demeyer, J. Ceulemans, J. Phys. Chem. A 1997, 101, 3537–3541. 27 A. Demeyer, J. Ceulemans, J. Phys. Chem. A 2000, 104, 4004–4010. 28 K. Toriyama, K. Nunome, M. Iwasaki, J. Phys. Chem. 1986, 90, 6836–6842. 29 G. Dolivo, A. Lund, J. Phys. Chem. 1985, 89, 3977–3984. 30 K. Toriyama, K. Nunome, M. Iwasaki, J. Am. Chem. Soc. 1987, 109, 4496–4500. 31 D. Stienlet, J. Ceulemans, J. Phys. Chem. 1993, 97, 8595–8601. 32 T. Ichikawa, M. Shiotani, N. Ohta, S. Katsumata, J. Phys. Chem. 1989, 93, 3826–3831. 33 A. Demeyer, D. Stienlet, J. Ceulemans, J. Phys. Chem. 1994, 98, 5830–5843. 34 L. Slabbinck, A. Demeyer, J. Ceulemans, J. Chem. Soc., Perkin Trans. 2 2000, 2241–2247. 35 K. Toriyama, M. Iwasaki, M. Fukaya, J. Chem. Soc., Chem. Commun. 1982, 1293–1295.
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6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids Hans-Heinrich Limbach
Overview
In this chapter, Arrhenius curves of selected single and multiple hydrogen transfer reactions for which kinetic data are available over a large temperature range are reviewed. The curves are described by a combination of formal kinetics of reaction networks and the one-dimensional Bell–Limbach tunneling model for each reaction step. The main parameters of this model are the barrier heights and barrier widths of the isotopic reactions, the tunneling masses, the pre-exponential factor and a minimum energy for tunneling to occur. This approach allows one to compare efficiently very different reactions studied in different environments and to prepare the kinetic data for higher-dimensional quantum-mechanical treatments. The first type of reactions discussed is concerned with those where the hydrogen bond geometries of the reacting molecules are well established and where kinetic data of the isotopic reactions are available over a large temperature range. Here, it is possible to study the relation between kinetic isotope effects and chemical structure. Examples are the tautomerism of porphyrin, of the porphyrin anion and related compounds exhibiting intramolecular hydrogen bonds of medium strength, and the solid state tautomerism of pyrazoles and of benzoic acid in cyclic associates. One main result is the finding of pre-exponential factors of the order of kT/h @ 1013 s–1, as expected by transition state theory for vanishing activation entropies. The barriers of multiple H-transfers are found to be larger than those of single H-transfers. The second type of reactions discussed refers mostly to liquid state solutions and involves major heavy atom reorganization. Here, equilibria between reactive and nonor less reactive molecular configurations may play a role. Several cases are discussed where the less reactive forms dominate at low or at high temperature, leading to unusual Arrhenius curves. These cases include examples from small molecule solution chemistry like the base-catalyzed intramolecular H-transfer in diaryltriazene, 2-(2¢-hydroxyphenyl)-benzoxazole, 2-hydroxy-phenoxyl radicals as well as an enzymatic system, thermophilic alcohol dehydrogenase. In the latter case, temperature dependent kinetic isotope effects are interpreted in terms of a transition between two regimes with different temperature independent kinetic isotope effects. Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
6.1 Introduction
Since the introduction of modern spectroscopic and kinetic techniques, H-transfer reactions constitute an active field of research because of their importance in chemistry and physics [1]. As in electron transfer reactions, tunneling plays an important role. However, in contrast to the Marcus theory of electron transfer [2], there is no widely accepted theory of H-transfer available to date. This is because H-transfer can occur in a variety of forms. Proton and hydride transfer are coupled to charge transfer and are strongly affected by solvent phenomena [3]. In contrast, hydrogen atom transfer and multiple proton transfers often take place without net charge transfer. As the electron/heavy atom mass ratios are smaller than 10–4 the tunneling motion of the electron is well separated from heavy atom reorganization. This may not be the case in H-transfers, where heavy atom tunneling may play a role. In contrast to electron transfer, hydrogen bond formation strongly affects the way H is transferred. Only H-transfer in weak and moderately strong hydrogen bonds can be described in terms of rate processes, as for electron transfer; in strong hydrogen bonds protons may no longer experience a barrier of transfer but are localized in the hydrogen bond center [3]. Finally, the three isotopes of hydrogen add to the complexity of H-transfer but also constitute important mechanistic tools. Many different spectroscopic and kinetic techniques have been applied to the study of H-transfer reactions. Among these are dynamic nuclear magnetic resonance techniques. In the past decades it has been shown that NMR is an especially powerful tool for the study of degenerate single and multiple hydrogen transfer reactions in model hydrogen bonded systems embedded in liquid and solids [4]. Traditionally, the dynamic range of NMR was limited to the millisecond timescale but, for H-transfers in the solid state, it has been possible to extend this scale to the micro- to nanosecond timescale. In addition, it has been possible to elucidate multiple kinetic hydrogen isotope effects over large temperature ranges which enables one to detect tunnel effects at low temperatures from the observation of concave Arrhenius curves of the isotopic reactions. These curves can serve as benchmarks in order to check quantum-mechanical theories of rate processes in condensed matter. Kinetic isotope effects of single H-transfers in organic liquids have often been interpreted in terms of a combination of Eyring’s transition state theory [5] and isotope fractionation theory as proposed by Bigeleisen [6]. In this theory, kinetic isotope effects arise mainly from the difference in zero-point energies between the transition and the initial state. However, as has been shown by Bell [7], in hydrogen transfer reactions one has to take into account tunneling through the barrier, as has been mentioned above. His one-dimensional semiclassical “Bell tunneling model” has been very successful for the interpretation of Arrhenius curves of single hydrogen transfers using empirical parameters. The model was developed in times when computers were not available, i.e. was designed for the case of slow proton transfer, mainly hydrogen abstraction from carbon. Typically,
6.1 Introduction
reactions in solution were studied around room temperature over a limited range of temperatures. For these cases, the so-called “Bell tunneling correction” to the Arrhenius curves, elucidated in terms of classical transition state theory, was sufficient and has, therefore, often been taken as synonymous with the “Bell tunneling model”. Full semiclassical tunneling calculations employing modified barriers have been performed by various other authors e.g. Ingold et al. [8], Limbach et al. [9], and Sutcliffe et al. [10]. Other semiclassical models of single proton abstractions have been proposed by Kuznetsov and Ulstrup [11, 12] and modified by Knapp et al. [13] for use in enzyme reactions. Siebrand et al. [14] have proposed a golden rule treatment of H-transfer between the eigenstates of the reactants and products where low-frequency vibrations play an important role varying the heavy atom distances. Various quantum-mechanical theories have been proposed which allow one to calculate isotopic Arrhenius curves from first principles, where tunneling is included. These theories generally start with an ab initio calculation of the reaction surface and use either quantum or statistical rate theories in order to calculate rate constants and kinetic isotope effects. Among these are the “variational transition state theory” of Truhlar [15], the “instanton” approach of Smedarchina et al. [16], or a Redfield-relaxation-type theory as proposed by Meyer et al. [17]. However, these methods require extensive theoretical work and are, generally, not available for the experimentalist in the stage where he needs to simulate his Arrhenius curves. For this stage, empirical tunneling models are important. This is especially true for the case of multiple hydrogen transfer reactions. In a number of papers, Limbach et al. have proposed to use formal kinetics in order to describe multiple kinetic isotope effects of intramolecular [18–23] and intermolecular HH-transfers [24]. This method has been extended to triple [25] and quadruple transfer reactions [26, 27]. In order to solve the problem of multiple particle transfer two limiting cases were considered. The “concerted” transfer refers to the case where several hydrogen and heavy atoms are transferred at the same time in such a way that they can be treated as a single particle. The “stepwise” transfer refers to the case where intermediates are involved. Here, the overall rate constants of the isotopic reactions studied are related using formal kinetics, to those of the individual reaction steps. Each reaction step, consisting of a single or concerted multiple H-transfer, is treated in terms of a tunneling model based on a modified Bell model [9]. In order to avoid possible confusion, this model will be denoted as the “Bell–Limbach” model. We note that the formal kinetic treatment of the stepwise transfer does not need to be combined with this model, but can also be combined with any theory treating a single step. For example, Smedarchina et al. [16] have used this approach in connection with their instanton approach. The Bell–Limbach model is not designed to give definite interpretations of Arrhenius curves of hydrogen transfer reactions which have to come from more sophisticated methods. However, it provides an opportunity to check whether the number of parameters describing a given set of Arrhenius curves matches or exceeds the number of parameters necessary to describe the same set in terms of sums of single Arrhenius exponentials. This check also tells whether it is useful
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6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
to apply a more sophisticated tunnel model containing a larger number of parameters. Finally, the Bell–Limbach model provides a platform which allows one to compare different reactions with each other and to derive general trends important for the kineticist to guide future research. The scope of this chapter is, therefore, (i) to review the Bell–Limbach tunneling model in comparison with other models and its use for describing single steps of multiple hydrogen transfer networks and (ii) to review applications of this approach in a number of cases which have been studied mainly by NMR. A description of the techniques used for the determination of rate constants of Htransfer will not be included in this chapter; readers interested in this problem are referred to a recent review [4].
6.2 Theoretical
In this section first different models of single H-transfer will be reviewed, including primary kinetic H/D isotope effects, where the focus is on the Bell–Limbach model. Then formal kinetics will be used to describe multiple hydrogen transfers and their kinetic isotope effects. 6.2.1 Coherent vs. Incoherent Tunneling
The simplest model proposed to accommodate a degenerate hydrogen transfer process has been derived [28] from the theory of the one-dimensional symmetric double oscillator [29]. As illustrated in Fig. 6.1(a), this model assumes a symmetric double well with delocalized vibrational hydrogen states which are given in approximation as the positive and the negative linear combinations of the corresponding harmonic oscillator states. The energy splitting is hJ, where J can be interpreted as the frequency of coherent hydrogen tunneling of a wave packet created at t = 0, oscillating between the two wells. This type of coherent H tunneling has been verified for small molecules such as malonaldehyde [30], tropolone [31] (Chapt. 1), or formic acid dimer [32] (Chapt. 2) in the gas phase. In contrast, when malonaldehyde is embedded in condensed matter, intermolecular interactions lift the gas phase symmetry of the double well, leading to localized protons [33]. The situation is depicted schematically in Fig. 6.1(b). Here, the one-dimensional double oscillator theory predicts vibrational states with more or less localized proton wavefunctions. In order to arrive at a rate process, more dimensions have to be taken into account. One way is to couple the double oscillator to a bath of harmonic oscillators which will result in vibrational relaxation (VR), taking place on the femtosecond timescale [34]. VR is responsible for the transfer of vibrational energy between the double oscillator and the bath. By VR the localized reactant ground state is converted to higher vibrational states producing a nuclear wave packet. The latter is transferred by tunneling to the product well and deactivated to the product ground
6.2 Theoretical
state. Usually, if VR is fast enough, the H tunneling process can be described in terms of rate constants for the forward and the backward H-transfer. In the liquid state, the effective symmetry of the potential is restored by solvent relaxation (Fig. 6.1(c)). In principle, H-transfer is not restricted to symmetric configurations but can also take place in asymmetric configurations. Hynes et al. [35, see also Chapter 10] have proposed an alternative view which is sketched in Fig. 6.1(d). Here, localized states exhibiting asymmetric single or double wells are first converted by solvent relaxation to a strong symmetric low-barrier hydrogen bond in which the transfer takes place adiabatically before it is completed again by solvent relaxation. In conclusion, in condensed matter coherent tunneling generally becomes incoherent and can then be described by a rate constant instead of a tunnel frequency.
e
a
VR hJ
b
f
VR
c
d
g
SR
Figure 6.1 One-dimensional double oscillator models for hydrogen transfer and dihydrogen exchange under different conditions.
139
140
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
An exception to this rule is, however, the case of exchange of the nuclei of dihydrogen pairs bound to a transition metal center, where the exchange exhibits a barrier. This phenomenon will be sketched only briefly; for further information the reader is referred to Chapter 21 and to a recent minireview [36]. The situation is illustrated for the gas phase in Fig. 6.1(e). The nuclear spins – characterized by arrows – play a decisive role. The lower tunnel state is symmetric with respect to a permutation Ha–Hb « Hb–Ha and the upper state is antisymmetric. Since hydrogen has a nuclear spin 1/2 the lower state has to be coupled with the antisymmetric nuclear spin function ›fl (antiparallel spins) in order to fuIfill the Pauli exclusion principle. In contrast, the upper tunnel state is antisymmetric and has to be combined with the symmetric nuclear spin states ›› (parallel spins), as in the case of o-H2 and p-H2. Thus, interconversion of the delocalized dihydrogen states also involves a nuclear spin conversion which is much slower than VR. Thus, the tunnel splitting hJ can survive even in larger molecules, even on the NMR timescale. In the crystalline solid the barrier of interchange and the value of J may be altered but not the inherent symmetry of the process, Fig. 6.1(f). When placing the molecule in a multitude of different exchanging environments, i.e. in a liquid (Fig. 6.1(g)) solvent relaxation (SR) will lead to an average temperature dependent tunnel splitting as long as nuclear spin conversion is slow. As this chapter focuses on hydrogen transfers in liquids and solids, it will be assumed that the transfer constitutes a rate process which can be described in terms of rate constants, for which the usual rate theories can be applied, in particular those derived from transition state theory. 6.2.2 The Bigeleisen Theory
In the theory of Bigeleisen [6], a combination of the theory of equilibrium isotope effects with Eyrings transition state theory [5], kinetic H/D isotope effects can be expressed by kH Q D Q Hz ¼ kD Q H Q Dz
(6.1)
Here, QH and QD represent the partition functions of the protonated and deuterated initial state and QH‡ and QD‡ those of the transition state. In order to evaluate Eq. (6.1) the vibrational frequencies of the initial and the transition states are needed. Generally, they are calculated using quantum-mechanical ab initio methods in harmonic approximation. The main source of kinetic isotope effects arises then from zero-point energy changes of the protons and deuterons in flight, as has been discussed by Bell [7, 37]. These effects are illustrated for a triatomic model system in Fig. 6.2. There is only a single stretching vibration of AH in the initial state. The transition state exhibits three normal vibrations, an imaginary antisymmetric stretch, a real symmetric stretch (not illustrated), and a real bending vibration. The antisymmetric stretch does not involve any zero-point energy, neither for H nor for D. The symmetric stretch is not isotope sensitive. However,
6.2 Theoretical
transition state
V
H D
Ea
D
A···H···A*
real bending vibration
A···H···A*
EaH
imaginary antisymmetric stretch A···H···A*
real symmetric stretch (not depicted) H D
H D
A
+
H
A*
final state A
H
+
A*
initial state Figure 6.2 Triatomic model of H-transfer illustrating changes in zero-point energies of normal vibrations between the initial and transition states.
the bending vibration contains different zero-point energies for H and for D. Overall, the model predicts a different barrier for H and D transfer, and a kinetic H/D isotope effect of about 6 at room temperature. 6.2.3 Hydrogen Bond Compression Assisted H-transfer
Hydrogen bonding dominates H-transfers from and to oxygen, nitrogen, and fluorine. The barrier of the transfer depends strongly on the hydrogen bond geometry. Unfortunately, a general relation between both is not available to date. In fact, Htransfers in hydrogen bonds constitute a multidimensional problem where many different modes can contribute to the reaction coordinate. Experimentally, it is not easy to identify these modes and to take them into account in simple tunneling models. There is, however, one exception: from an empirical standpoint, hydrogen bond compression has been identified as one important mode which can be taken into account using empirical hydrogen bond correlations which will be described in this section. With any hydrogen bond A–H_B one can normally associate two distances, the A–H distance r1 ” rAH for the diatomic unit AH, and the H_B distance r2 ” rHB for the diatomic unit HB. According to Pauling [38], one can associate with these distances so-called valence bond orders or bond valences, which correspond to the “exponential distances”
141
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
p1 = exp{–(r1–r1)/b1}, p2 = exp{–(r2–r2)/b2}, with p1 + p2 = 1
(6.2)
b1 and b2 are parameters describing the decrease of the bond valences of the AH and the HB units with the corresponding distances. r1 and r2 are the equilibrium distances of the fictive non-hydrogen bonded diatomic molecules AH and HB. If one assumes that the total valence for hydrogen is unity, it follows that the two distances depend on each other, leading to an ensemble of allowed r1 and r2 values representing the “geometric hydrogen bond correlation”. The hydrogen bond angle does not appear in Eq. (6.2). This correlation may be transformed into a correlation between the natural hydrogen bond coordinates q1 = 12(r1 – r2) and q2 = r1 + r2. For a linear hydrogen bond, q1 represents the distance of H from the hydrogen bond center and q2 the distance between atoms A and B. Experimentally, hydrogen bond correlations have been established using X-ray and neutron diffraction crystallography [39], as well as by NMR [40]. Note, however, that correlations of the type of Eq. (6.2) were also used a long time ago in the context of describing the “bond energy bond order conservation” reaction pathway of the H2 + H reaction [41]. A typical geometric hydrogen bond correlation according to Eq. (6.2) derived for NHN-hydrogen bonded systems [42] is depicted in Fig. 6.3. When H is transferred from one heavy atom to the other, q1 increases from negative values to positive values, and q2 goes through a minimum which is located at q1 = 0 for hydrogen bonded systems of the AHA-type and near 0 for those of the AHB-type. This correlation implies that, as an approximation, both proton transfer and hydrogen bonding coordinates can be combined into a single coordinate.
p1 q1 p2 r1 r2 A···················H·········B q2 r2 r1 N·····H···N
r 1 r2 N···H·····N q2= (r1+r2) / Å
142
r1 r2 N··H··N correction
equilibrium
q1= ½ (r1 -r2) / Å
Figure 6.3 Correlation of the hydrogen bond length q2 = r1 + r2 with the proton transfer coordinate q1 = 12(r1 – r2). Solid line: correlation for equilibrium distances calculated with b1 = b2= 0.404 and r1 = r2 = 0.992 . Dotted line: empirical correction for zero-point vibrations. Adapted from Ref. [42].
6.2 Theoretical
The solid correlation line in Fig. 6.3 is calculated by adapting the parameters of Eq. (6.2) to experimental hydrogen bond geometries established by low-temperature neutron diffraction and NMR data. A deviation has been observed between the experimental data and the solid correlation line in the region of strong hydrogen bonds around q1= 0. This effect has been associated with zero-point energy vibrations which are not taken into account in Eq. (6.2), which is valid only for equilibrium geometries. An empirical correction leading to the dotted line in Fig. 6.3 has been proposed [36]. A similar empirical correction has also been proposed for OHN-hydrogen bonds [43]. The shortest possible equilibrium heavy atom distance is given by [39b] (6.3)
q2min = 2(ro – b ln 12)
which leads to the values for symmetric hydrogen bonds listed in Table 6.1. These distances provide interesting references for characterizing transition states of Htransfers obtained by quantum-mechanical calculations. For example, hydride transfer distances between two carbon atoms at the transition state were calculated to be in the range 2.69–2.75 for various enzyme reactions [44]. Table 6.1 Shortest possible heavy atom distances of symmetric
H-bonds predicted by the valence bond order model. ro/
b/
q2min/
OHO
0.95
0.37
2.41
NHN
0.99
0.404
2.53
CHC
1.1
~0.4
~2.75
6.2.4 Reduction of a Two-dimensional to a One-dimensional Tunneling Model
How do the H-bond geometries change during a typical H-transfer process? It is clear that at the minimum value of the heavy atom coordinate q2 only a single geometry is realized, which is consistent with a single well potential for the Hmotion. In contrast, at other geometries, the correlation curve indicates the possibility of double well situations, where the barrier height Ed increases with increasing value of the heavy atom coordinate q2. The situation is illustrated schematically in Fig. 6.4(a) for the case of degenerate H-transfers. One-dimensional cuts V(q1) at different values of q2 through a twodimensional potential surface of a degenerate H-transfer are displayed. The barrier height Ed of the double well describing the H-transfer decreases when q2 is
143
144
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
q2 a
H-bond compression
V(q1)
Ed
0
q1
0
q1
0
q1
b V(q1)
Ed=constant q1
0
q1
0
q1
0
q1
Figure 6.4 (a) One-dimensional cuts V(q1) through a twodimensional potential energy surface of a degenerate H-transfer at different values of q2. (b) Reduction of the two-dimensional double-well potential problem to a one-dimensional Bell model. Adapted from Refs. [9] and [26].
decreased, and eventually a single well configuration is reached. There are only a small number of AH vibrational states available; here, only the vibrational ground states are depicted. As has been pointed out in Ref. [9], such a two-dimensional model can be reduced to a one-dimensional model by setting Ed = constant, as indicated in Fig. 6.4(b) and by assuming a continuous distribution of rapidly interconverting configurations with different values of q2. Such a situation can be reached practically by excitation of low-frequency H-bond vibrations or phonons. The situation of Fig. 6.4(b) can practically be replaced by an inverted parabola as a barrier, with a continuous distribution of vibrational levels on both sides of the barrier. A similar argument holds for non-degenerate H-transfers, as illustrated schematically in Fig. 6.5. Here, the asymmetry of the potential curve, i.e. the difference in the energy between the two wells will disappear in the region of the strongest H-bond compression. In order to evaluate qualitatively the expected kinetic isotope effects one has to discuss (i) zero-point energy (ZPE) changes of H in the transition state as compared to the initial state and (ii) tunnel effects. The expected changes in the zero-point energies of the H transferred are illustrated schematically in Fig. 6.6 for the degenerate case, as proposed by Westheimer [45]. The antisymmetric stretch in the initial state exhibits quite different ZPEs for H and for D as the force constants are large. This vibration becomes imaginary in the transition state, which is assumed here to be located in the minimum of q2 , i.e. the ZPE of the antisymmetric stretch is lost in the transition state. The ZPE of the symmetric stretch in the transition state is small and exhibits little isotope dependence. We note that ZPE is built up in the bending vibration in the
6.2 Theoretical
q2 a
H-bond compression
V(q1)
Ed
Em 0
b V(q1)
q1
0
q1
0
0
q1
0
q1
Ed
Em 0
q1
q1
Figure 6.5 (a) One-dimensional cuts V(q1) through a two-dimensional potential energy surface of a non-degenerate H-transfer at different values of q2. (b) Reduction of the two-dimensional doublewell potential problem to a one-dimensional Bell model. Em refers to a minimum energy for tunneling to occur. antisymmetric stretch
A··H······A
bending
A··H··A
A··H··A
‡ symmetric stretch
EdD
A ·· ··
EdH
H
A··H······B
H
A······H··B
A H
D
q2= (r1+r2) / Å
D
‡ A··H··B q1= ½(r1 -r2)/ Å
Figure 6.6 Hydrogen bond correlation and zero-point vibrations for a degenerate H-transfer.
transition state. Overall, a substantial difference in the effective barriers for the H-transfer and for the D-transfer is expected. Tunneling pathways can occur at larger values of q2, which is expected to remain constant during the tunnel process. As only hydrogen isotopes move at constant q2 the tunneling masses are then 1 for H and 2 for D.
145
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids quasiantisymmetric stretch
A··H······B
quasisymmetric stretch
A··H··B
B
EdD ‡ A··H······B
A······H··B
·· ··
EdH
H
A
H
s mas eling tunn m ∆ m H+
D
q2= (r1+r2) / Å
146
‡ A···H··B q1= ½(r1 -r2)/ Å
Figure 6.7 Hydrogen bond correlation and zero-point vibrations for a non-degenerate H-transfer.
In contrast, if the transfer is non-degenerate, a situation may occur as illustrated in Fig. 6.7. At the transition state there is remaining ZPE in the antisymmetric stretch. This will lead to a decrease in the difference between the effective barriers for H and for D, as has been proposed by Westheimer [45]. This decrease has also been called the “Westheimer-effect” [46]. Tunneling pathways may no longer involve only changes in q1, but also a substantial heavy atom motion. This means that the effective tunneling masses will be increased by an additional mass Dm as illustrated schematically. 6.2.5 The Bell–Limbach Tunneling Model
The simplest tunnel model which allows one to calculate Arrhenius curves of Htransfer reactions is the Bell tunneling model [7] which has been modified in our laboratory [9]. The model has been reviewed recently by Limbach et al. [26]. It is visualized in Fig. 6.8 which will be explained in the following. According to Bell, the probability of a particle passing through or crossing a barrier is given by [7] G ðW Þ ¼
1
(6.4)
1 þ DðWÞ1
where W represents the energy of the particle and D(W) the transmission coefficient, given according to the Wentzel–Kramers–Brillouin approximation [47] by 0 1 0 1 Za¢ Za¢ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 (6.5) DðWÞ ¼ exp@ pdxA ¼ exp@ 2mðVðxÞ W ÞdxA " " a¢
a¢
6.2 Theoretical H meff = 1 + ∆m
D meff = 2 + ∆m
log A ≅ kT/h ≅ 12.6
EdH
EdD
W W
0
-aH
A-H....B
0
Em
x aH
A....H-B A-D.....B A + H-B
-aD
0
Em
A-H + B
aD
0
A.....D-B A + D-B
A-D + B Figure 6.8 Modified Bell tunneling model for H and D transfer. Adapted from Refs. [9] and [26].
p represents the momentum and m the mass of the particle moving in the q1 ” xdirection, and V(x) the potential energy experienced by the particle. ja¢j represents the position of the particle when it enters or leaves the barrier region at energy W. V(0) = Ed represents the energy of the barrier i.e. the “barrier height” and 2a the width of the barrier at the lowest energy where tunneling can occur. Classically G(W)= 0 for W < Ed and G(W)= 1 for W > Ed, but quantum-mechanically G(W) > 0 for W £ Ed and G(W) < 1 for W ‡ Ed. Note here that D is related to the energy splitting of a symmetric double oscillator by [28] DE ¼
hm 1=2 D p
(6.6)
Assuming that the barrier region can be approximated by an inverted parabola it follows that ! x2 a¢2 (6.7) VðxÞ ¼ Ed 1 2 and that W ¼ Ed 1 2 a a It has been shown by Bell [48] that rffiffiffiffiffiffiffi 2p Ed W 1 Ed ; mt ¼ DðW Þ ¼ exp pa 2m hmt
(6.8)
where mt represents a “tunnel frequency”. The fraction of particles in the energy interval dW is given by the Boltzmann law dN expðW=kT ÞdW 1 ¼ R¥ expðW=kT ÞdW ¼ N kT expðW=kT ÞdW
(6.9)
0
The classical integrated reaction probability is then given by Z¥ DN 1 ¼ expðW=kT ÞdW ¼ expðEd =kT Þ N class kT Ed
(6.10)
147
148
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
the quantum mechanical integrated reaction probability by Z¥ DN 1 ¼ GðW ÞexpðW=kT ÞdW N QM kT
(6.11)
0
and the ratio of both quantities by DN N
QM
N
class
Qt ¼ DN
¼
1 kT
R¥
GðW ÞexpðW=kT ÞdW
0
Z¥ ¼
expðEd =kT Þ
G ðW Þ expððEd W Þ=kT ÞdW kT
(6.12)
0
Using an Arrhenius law for the classical temperature dependence it follows that Z¥ G ðW Þ k ¼ kclass Qt ¼ AexpðEd =kTÞ (6.13) expððEd W Þ=kT ÞdW kT 0
Replacing the Boltzmann constant by the gas constant, and introducing a superscript as label for the isotope L = H, D it follows that Z¥ L G ðW Þ exp EdL W =RT dW; L ¼ H; D kL ¼ AL expðEdL =RTÞ (6.14) RT 0
At very high temperatures, the integral becomes unity and one obtains the classical expression kL ¼ AL expðEdL =RTÞ; L ¼ H; D
(6.15)
From Eq. (6.14) one obtains the following expression for the “primary” kinetic isotope effect for the H-transfer as a function of temperature P¼
kH AH Q H expðEdH =RTÞ ¼ D D kD A Q expðEdD =RTÞ
(6.16)
where Q L has been called the “tunnel correction”. This equation has been introduced by Bell [7]. The energy difference De = EdD – EdH describing the losses of zero-point energy between the reactant and the transition state can be calculated using Bigeleisen theory [6]. In the low temperature regime for W = 0 it follows from Eq. (6.8) that 2p2 a pffiffiffiffiffiffiffiffiffiffiffiffi Gð0Þ@Dð0Þ ¼ exp (6.17) 2mEd h Therefore, ffi 2p2 aL qffiffiffiffiffiffiffiffiffiffiffiffiffi 2mL EdL kLo ¼ AL DL ð0Þ ¼ AL exp h
(6.18)
The width of the barrier for the D-transfer can be calculated from Eq. (6.7) and is given by
6.2 Theoretical
sffiffiffiffiffiffiffi EdD H D 2a ¼ 2a EdH
(6.19)
With mH = 1 and mD = 2, the low-temperature rate constant kH 0 is then determined mainly by aH for a given value of EdH . The low-temperature and temperature indeD D pendent kinetic isotope effect kH 0 =k0 is, therefore, determined by Ed which is H obtained experimentally at high temperatures. In other words, k0 =kD 0 and the high-temperature kinetic isotope effects cannot be varied independently of each other, which is not in agreement with experimental data. This effect can be associated with heavy atom tunneling during the H-transfer. The tunneling mass is increased and the low-temperature H/D isotope effect decreased. In order to take heavy atom tunneling into account, the expansion 1=2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P P 2 ffi pffiffiffiffi L rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ða m Þ ¼ ai mi ¼ ðaL Þ2 mL þ a2k mk ¼ aL mL þ Dm (6.20) i
k
is used [9], where Dm ¼
X ak 2 k
aL
mk , L = H, D and k = heavy atoms
(6.21)
D The heavy atom contribution reduces generally the value of kH 0 =k0 . For example, if H during H-tunneling in an OHO-hydrogen bond over 2a = 0.5 both oxygen atoms are displaced, each by 2a = 0.05 , it follows that Dm= 0.32, and the total tunneling mass is 1.32 instead of 1. Equation (6.14) is visualized in Fig. 6.8. Particles of different kinetic energies W, given by a Boltzmann distribution, hit the barrier from the left side, where the probabilities of finding given energies are symbolized by arrows of different length. The arrows on the right side represent the particles which came through the barrier by tunneling. As the tunneling mass of H is smaller than that of D, at a given temperature, the energy for the maximum number of H tunneling through the barrier is smaller than for D. As Limbach et al. have proposed, Eq. (6.14) needs to be modified in a minor way for application in multiple proton transfer reactions [9, 18, 21, 25, 49]. The most important change is to replace the lower integration limit in Eq. (6.13) by a minimum energy Em for tunneling to occur as indicated in Fig. 6.8, i.e. Z¥ L G ðW Þ L L L exp EdL W =RT dW; L ¼ H; D k ¼ A expðEd =RTÞ (6.22) RT Em
This modification is necessary for example, when the reaction pathway involves an intermediate. Tunneling can then take place only at an energy which corresponds to the energy of the intermediate. Then, one can identify Em with the energy Ei of this intermediate. However, Em may also represent a reorganization energy Er necessary for a heavy atom rearrangement preceding the tunneling process. Thus, Em includes the “work term” in Marcus theory of electron transfer [2]. In addition, Em may include the reaction enthalpy DH of a pre-equilibrium to H-transfer as discussed above.
149
150
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
A set of Arrhenius curves calculated using Eq. (6.22) depends then on the following parameters: 1. A single pre-exponential factor A in s–1 is used for all isotopic reactions, i.e. a possible mass dependence [7] is neglected within the margin of error. If solvent reorganization and preequilibria are absent, A is expected to be about 1013 s–1. According to transition state theory, pre-exponential factors are given by kT/h = 1012.6 s–1 for T = 298 K. 2. Em = DH + Er + Ei represents the minimum energy for tunneling to occur as described above and is assumed to be isotope independent. Note that a similar effect on the Arrhenius curves may be obtained by using more complex barrier shapes [10]. 3. EdH is the barrier height for the H-transfer step of interest. Therefore, the sum Em + EdH represents the total barrier height for the H-transfer. 4. 2aH is the barrier width of the inverted parabola used to describe the barrier of the H-transfer at the energy Em. This parameter indicates the tunnel distance of H. 2aD can be approximated by Eq.(6.19). 5. De ¼ EdD EdH represents the increase in the barrier height when H is replaced by D. L ¼ m L þ Dm, L = H, 6. The tunneling masses are given by meff H D D with m ¼ 1 and m ¼ 2. Dm corresponds to the contribution of heavy atom displacements during the tunneling process. In order to illustrate the formalism typical Arrhenius curves of H and D transfer using arbitrary parameters are plotted in Fig. 6.9. From the slope of the curves at high temperature one can obtain the quantities Em + EdH and Em + EdD which were the same in all graphs of Fig. 6.9. Because of the different slopes of the H and the D curve, temperature dependent kinetic H/D isotope effects occur in the hightemperature range, as illustrated by the dotted lines. At low temperatures, parallel Arrhenius curves are expected, exhibiting a slope given by Em. The low-temperature branches are also illustrated by dotted lines. By extrapolation of the low-temD perature branches to high temperatures, the values of kH 0 and of k0 are obtained. According to Eq. (6.18), they provide information about the barrier width 2aH and the heavy atom tunneling extra mass Dm. Let us discuss the effects of 2aH and Dm on the Arrhenius curves. In Fig. 6.9(a) and (b) the H curves are identical, as the product 2aH(1+Dm)1/2 is the same. However, the introduction of an extra tunneling mass of 3 in Fig. 6.9(b) reduces the kinetic isotope effects in the low-temperature regime but not in the high-temperature regime. On the other hand, by comparison of Fig. 6.9(a) with Fig. 6.9(c), or of Fig. 6.9(b) with Fig. 6.9(d), it follows that when a barrier of constant height becomes narrower, the regime of temperature independent kinetic isotope effects is reached at higher temperatures.
6.2 Theoretical
log (k/ s-1)
a
b log A EdH+Em
2aH = 0.8 Å ∆m = 0
2aH = 0.4 Å ∆m = 3
EdD+Em log koH H
H
D
D
log koD Em
c
d 2aH = 0.2 Å ∆m = 3
H
H
D
D
log (k/ s-1)
2aH = 0.4 Å ∆m = 0
103 / K-1 T Figure 6.9 Arrhenius curves of H and D transfer calculated according to the Bell–Limbach tunneling model. Minimum energy for tunneling to occur EdH = 12.55 kJ mol–1, barrier heights EdH = 20.9 kJ mol–1, EdD = 27.2 kJ mol–1, tunnel-
103 / K-1 T ing masses mH=1+ Dm , mD= 2+ Dm . Barrier width 2aD = 2aH(EdD / EdH)1/2 according to Eq. (6.19). koH and koD are the extrapolated ground state tunneling rates as defined in Eq. (6.18).
6.2.6 Concerted Multiple Hydrogen Transfer
Equation (6.22) may not only be used in the case of a single proton transfer but also in the case of concerted multiple proton transfers, according to Fig. 6.10, characterized by a single barrier. Only some minor changes are necessary. 1. De ¼ EdD EdH continues to represent the increase in the barrier height when a given H is replaced by D. For successive replacements of H by D, generally, the so-called “Rule of the Geometric Mean” (RGM) derived for equilibrium isotope effects [6b] is applied, i.e. it is assumed that replacement of each H by D leads to the same increase De of the barrier height EdHD ¼ EdHH þ De; EdDD ¼ EdHH þ 2De; ::::EdDDDD ¼ EdHHHH þ 4De
(6.23)
151
152
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
H D
H D
A-H
A
A
H-A
H
H
A
A
A
A
H
H
A
A H
H
H
H A
A
A
H
A
A
H A
H H
A H
A
H
H
H A
H
A
Figure 6.10 Schematic one-dimensional energy profile of degenerate single-barrier hydron (H, D , T) transfers in coupled networks of 1 to 4 cyclic hydrogen bonds. The hydron transfer can be an over-barrier process or a tunneling process, as indicated by the double arrows in the energy profile. The overbarrier process leads to kinetic isotope effects
A H
A
because of the loss of zero-point energy at the top of the barrier for each proton transferred, as indicated schematically. The tunneling process leads to kinetic isotope effects because of different tunneling masses for the hydrogen isotopes. Reproduced with permission from Ref. [26].
De is symbolized schematically in Fig. 6.10 by the different spacings of H and D levels in the ground state and the transition states. 2. The tunneling mass of a given isotopic reaction is written as P L mi þ Dm meff ¼ i
6.2.7 Multiple Stepwise Hydrogen Transfer
In a number of papers, Limbach et al. have proposed to use formal kinetics in order to describe the case of stepwise HH-transfer [18, 24]. This method has been
6.2 Theoretical
extended to the stepwise triple [25] and quadruple transfer cases [26]. In these papers the Bell–Limbach model was employed for the treatment of each reaction step. We note again that the same equations developed can also be used when each reaction step is described in terms of a first-principle theory. In this section the main results of this research are reviewed only briefly. For a more detailed description the reader is referred to Ref. [26].
6.2.7.1 HH-transfer In Fig. 6.11 is depicted a general scheme of a stepwise HH-transfer reaction between the initial state A and the final state D. B and C are intermediates whose concentration is small. In each reaction step a single H is transferred, the other H is bound. Let us denote the formation of the intermediate as “dissociation” and the backward reaction as “neutralization”. The corresponding free energy reaction profile is illustrated in Fig. 6.11(b).
a
-
dissociation
H X
Y
+
H
kd
B
kn
neutralization
H
H
X
Y
A
D
H
Y
X H
C H +X
b
Y
-
H
Figure 6.11 Degenerate stepwise HH-transfer involving metastable intermediates. (a) Chemical reaction network as base for a description in terms of formal kinetics. (b) Corresponding free energy diagram. Reproduced with permission from Ref. [26].
Using the steady-state approximation it can easily be shown that the rate constant of the interconversion between A and D is given by kAD ¼
k k kAB kBD þ AC CD kBA þ kBD kCA þ kCD
For the isotopic rate constants it follows that
(6.24)
153
154
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids HH kHH AC kCD HH kCA þ kHH CD
HH kHH AB kBD HH kBA þ kHH BD
kDH AD ¼
HD DD kHD kDH kDD kDD kDH kDD AB kBD AB kBD þ HDAC CDDH ; kDD þ DDAC CDDD AD ¼ DD DH HD DD kBA þ kBD kCA þ kCD kBA þ kBD kCA þ kCD
þ
; kHD AD ¼
DH kHD AB kBD HD kBA þ kDH BD
HD kDH AC kCD DH kCA þ kHD CD
kHH AD ¼
þ
(6.25)
The primary and secondary kinetic isotope effects of a given reaction step ij can be written in the form HðLÞ
Pij ¼
kij
DðLÞ
kij
LðHÞ
and Sij ¼
kij
(6.26)
LðDÞ
kij
where the brackets indicate the bound hydrogen. The corresponding isotopic fractionation factor is given by fij ¼
Pji Sji Pij Sij
(6.27)
For the case of degenerate HH-transfers, the following isotopic reaction rate constants have been derived [18a–c, 26] HH kHH AD ¼ kd DH 1 kHD ¼ kHH AD ¼ k d Pd
1 fd S1 n þ Sd 1 fd Sn þ Pd1
(6.28)
DD HH 1 1 kDD AD ¼ kd ¼ kd Pd Sd
The subscript d refers to the dissociation and the subscript n to the neutralization step in Fig. 6.11(a). In the absence of isotopic fractionation fd ¼ 1; Sn ¼ Sd ¼ S; Pn ¼ Pd ¼ P; and Eq. (6.28) simplifies to HH kHH AD ¼ kd
DH HH kHD AD ¼ kAD ¼ kAD
2 2 ¼ kDD AD SþP P1 þ S1
(6.29)
DD HH 1 1 1 1 kDD ¼ kHH AD ¼ kd ¼ kAD P S d P S
and in the absence of secondary isotope effects to HH kHH AD ¼ kd DH HH kHD AD ¼ kAD ¼ kAD
2 2 2 DD ¼ kDD ¼ k AD d 1þP P1 þ 1 P1 þ 1
(6.30)
DD HH 1 1 kDD ¼ kHH AD ¼ kd ¼ kAD P d P
As the bound H does not contribute, the notation can be simplified by setting L kLL d ¼ kd , by dropping the labels for the tautomeric states and by keeping in mind that according to Eq. (6.26)
6.2 Theoretical
P ¼ kH =kD ¼ kHH =kDD
Thus, it follows that kHH ¼ kH kHD ¼ kDH ¼
2kH 2kD ¼ D H H D 1 þ k =k k =k þ 1
(6.31)
kDD ¼ kD ¼ kHH P1 ¼ kH P1
This means that at low temperature where P is large the HD reaction is ca. twice as fast as the DD reaction. Equation (6.31) has been used in connection with the Bell–Limbach tunneling model to describe the stepwise double proton transfer in porphyrins, azophenine, and oxalamidines, as will be discussed in Section 6.3. Smedarchina et al. [16] used the same equations for their quantum-mechanical treatment of the porphyrin tautomerism.
a
X
HH k AD
.
H. E X H
X
.
H F.X H
X
.
H G. X H
X
.
H. H X H
H X
H A
X
-
H
b
X
.
HD DD k AD ≅ 2k AD
H B H
X
H. E X D
X
.
X+
H F.X D
H +X C H X
.
X
H G. X D
H
X
.
H. H X D
H
H X
A
X
c
X
DD k AD
H B D
-X
D
.
D. E X D
X
.
X+
D F.X D
H +X C D
X
.
X
D G. X D
X
D
X D
X
.
D. D X D
D
D X
X
D
X
A
X D
-X
D B D
X+
D +X C D
D
X X
Figure 6.12 Free energy correlation (shown schematically) for the H and D zero-point vibrations for a degenerate stepwise double hydrogen transfer reaction according to Eq. (6.31), where secondary kinetic isotope effects and isotopic fractionation between the initial and the intermediate state were neglected. Adapted from Ref. [18c].
D
X
155
156
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
Equation (6.30) can be visualized in the free energy diagrams shown in Fig. 6.12. Different free energies for different isotopic reactions arise either from zeropoint energy differences or from tunneling contributions. In all isotopic processes there are equivalent pathways via either intermediate B or C. The initial and final states A and D as well as the two intermediates B and C have two bound hydrogen isotopes, leading to three isotopic states of different free energy, containing either mobile HH, HD, or DD isotopes. In contrast, the states where one hydrogen isotope is in flight are characterized by only two isotopic states of different free energy because there is only one bound hydrogen isotope. Note that the term “state with a hydrogen isotope in flight” can be either a conventional transition state or a state where the isotope tunnels from a thermally activated state through the reaction energy barrier. Let us first compare the HH and the DD reaction profiles in Fig. 6.12(a) and (c). Both profiles are symmetric. Therefore, internal return causes the intermediate to react to the product D only with a probability of 12; it returns with the same probability to A. The factor of 12 entering the expression for kHH AD and kDD AD is, however, canceled in Eq. (6.30) because there are two equivalent pathways via B and via C for all isotopic reactions. The DD reaction is slower than the HH reaction because of the loss of zero point energy of the XH/XD stretching vibration in the transition states or because of tunneling. In contrast, the reaction profile of the HD process is asymmetric and the transition states E and G (and F and H) are now no longer equivalent. Therefore, the problem of internal return is absent. If one neglects secondary kinetic isotope effects, the energy necessary to reach the H transition states is similar to that in the HH process and the energy necessary to reach the D transition states is similar to that in the DD case. The D transfer step constitutes, therefore, the rate-limiting step of the reaction. The HD reaction has then the same free energy of activation as the DD reaction; however, since in the HD reaction all molecules that have passed the transition state react DD to products in contrast to the DD reaction, it follows that kHD AD @ 2kAD (Eq. (6.30)). In contrast, for the case of a non-degenerate reaction where A represents the dominant form and B the dominant intermediate it has been shown [19b] that DD DH HH kHD AD @ kAD and kAD ¼ kAD
(6.32)
These results can again be visualized in a free energy diagram as shown in Fig. 6.13. Since the transition states H are higher in energy than G, the pathways symbolized by the dashed lines do not contribute to the reaction rates. These pathways are, therefore, no longer discussed; only the favored pathways characterized by the solid lines that involve the transition states E and G are considered in the following. The true transition state of all isotopic reactions is G. In the latter, the loss of zero-point energy of XD is larger than of XH and hence the DD reaction is slower than the HH reaction. Thus, neglecting secondary kinetic isotope effects, it follows that the DH reaction is as fast as the HH reaction as H is transferred in the rate-limiting step. By contrast, the D isotope is transferred in the rate-limiting step of the HD reaction which exhibits, therefore, similar rate constants to those of the DD reaction.
6.2 Theoretical
a X
.
H. X E Y H
H X
A
H
H
.
F.Y H
X
H B H
Y
X
Y+
H
b X
.
D. X E Y D
A
G. Y H
H +X C H
.
H. H Y H
Y-
H D
X
Y
.
F.Y D
-X
D B D
X
Y+
.
+X
.
Y
X
G. Y D
D C D
.
X
A
d
X
-X
D B H
.
X
H. X E Y D
A
DD HH k AD = k AD /P
X
Y D
≅
.
X
Y
X
H B D
HD k AD
X
Y+
≅
D Y
D
X H
H
F.Y D
D. H Y H
HH k AD
H
.
.
G. Y H
D +X C H
Y+
DH k AD
H Y
D
D
F.Y H
-
D D
.
Y
X
D
D
H
D. H Y D
Y
D. X E Y H
D
H
D
D
c X
HH k AD
D X
.
X
157
.
X
.
G. Y D
H +X C D
H. H Y D
Y-
DD k AD
Figure 6.13 Free energy correlation (shown schematically) for the H and D zero-point vibrations for a non-degenerate stepwise HH-transfer reaction. The secondary kinetic isotope effect S was set to unity. Adapted from Ref. [18c].
Some calculated kinetic isotope effects are illustrated in the Arrhenius diagrams of Fig. 6.14. If the secondary isotope effects were equal to the primary ones, this would mean that both protons are in flight in the rate-limiting step and the double barrier case would reduce to the single barrier case. Then, one would obtain the rule of the geometric mean (RGM) with kHH/kHD = kHD/kDD = P, and the overall isotope effect is kHH/kDD = P2. This result represents in fact a derivation of the RGM for the single barrier case. In the Arrhenius plot of Fig. 6.14(a) the validity of this rule was assumed. However, this rule is valid only in the absence of tunneling and if both proton sites are equivalent. In the presence of tunneling kHH/kHD > kHD/kDD as has been verified previously. In Fig. 6.14(b) the two-barrier or stepwise transfer Arrhenius diagrams are plotted, where it was assumed that the secondary isotope effects of dissociation and neutralization are small, i.e. equal to 1. In addition, absence of isotopic fractionation is assumed, i.e. fd ¼ 1. In this case, kDD/kHH is equal to the kinetic isotope effects Pd ¼ Pn of the dissociation and neutralization steps. When these isotope effects are large, which is the case at low temperatures, kHD/kDD is equal to 2. The statistical factor arises from the fact that in the DD reaction D is transferred in both steps. Therefore, when the intermediate is reached, return to the reactant as well as reaction to the product occurs with equal probability. By contrast, there is no internal return in the HD reaction which exhibits only a single rate-limiting
H D
X D
Y
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
step, i.e. the one in which D is transferred. Note that Eq. (6.30) is valid even in the presence of tunneling. When isotopic fractionation takes place, for example through a strenghtening of the H-bond in the intermediate leading to reduced zero-point energies [50], the factor will be larger than 2, leading to an increase of kHD/kDD as illustrated in Fig. 6.14c. The effect of an increasing reaction asymmetry is illustrated in Fig. 6.14(d)–(f). When the asymmetry is small, the HD and DH processes are almost equally fast, and again characterized by approximately twice the rate constant of the DD process. When the asymmetry becomes larger, the HD curve merges rapidly with the DD curve, and eventually the DH curve with the HH curve.
a
d
HD
HH
log k/s-1
log k/s-1
HH
DH HD
DD
DD
HD DD
c
e log k/s-1
HH
f HH HD DD
103 -1 T /K
Figure 6.14 Arrhenius diagrams of a degenerate double hydron transfer using the following arbitrary parameters: kHH ¼ 1013 expð27:6 kJ mol1 =RTÞ, P ¼ Pd ¼ Pf ¼ expð7 kJ mol1 =RTÞ. (a) Single barrier case. (b) Double barrier case with
log k/s-1
log k/s-1
b
log k/s-1
158
HH DH HD,DD
HH,DH
HD,DD
103 -1 T /K
the H/D fractionation factor of dissociation fd =1. (c) As (b) but with an arbitrary value of fd = ff = exp (–0.92 kJ mol–1 / RT);. Adapted from Ref. [26]. (d) to (f) Effect of increasing asymmetry on the kinetic HH/HD/DH/DD isotope effects.
6.2 Theoretical
Finally, note that the concerted and the stepwise HH-transfer constitute limiting cases and that various intermediate cases are possible. Rauhut et al. [51] have studied “plateau” reactions which are realized when the energy of the intermediate is raised, producing a very wide flat single barrier region which cannot be described in terms of an inverted parabola. Meschede and Limbach [24c] have pointed out that compression of both hydrogen bonds of a double proton transfer system leads eventually to a single barrier situation, even if at large H-bond distances a stepwise reaction mechanism is realized.
6.2.7.2 Degenerate Stepwise HHH-transfer The case of a stepwise triple proton transfer [25] is illustrated in Fig. 6.15. It can take place along different pathways via at least two metastable intermediates. For example, if hydrons {1}, {2} and {3} are transferred one after the other the reac-
kf = kb
A H
kd {1}
+
A
A H
H
010 (2)
A
A
H
+
A {3+}
A
+ A
H
+ 101 (5) H
{1+}
A {2}
H
- A
H
A {1}
111 (7) H
H A
A
-
H 001 (1)
A
{3}
A
A H
kn
H
+
H
H
H
{3}
110 (6)
{3-} {1-}
-
{2}
000 (0) H
A -
A H
A
A H
{2+}
100 (4)
A H
H
-
{2-} A
H A +
011 (3) H
H A
b
a Figure 6.15 Degenerate triple-barrier triple hydron transfer involving two zwitterionic intermediates. A complete transfer consists of a dissociation step, one or more cation or anion “propagation” steps, characterized by the forward and backward rate constants kf = kb, and a neutralization step. These isotope dependent rate constants depend on whether a cation or an anion is propagated.
Cation and anion propagation are included in the brackets indicating the hydron number transferred as a plus or minus sign in the brackets. The rate-limiting step may correspond to the propagation (a) or the dissociation (b). In each step only a single hydron loses zero-point energy at the configuration at the top of the barrier. Adapted from Ref. [26].
159
160
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids Table 6.2 Kinetic isotope effects of degenerate triple proton transfers according to Ref. [9].
KIE kHHD kHHH kHDD kHHH kDDD kHHH
P1= P2= P3=P
–
fd < 1; Pf1 << 1
P–1
1/3(2 +Pd1 )
1/3(1 +fd )
P–2
1/3(1 +2Pd1 )
fd /3
P–3
Pd1
Pf1 fd
tion pathway is 000fi100fi110fi111. As a degenerate reaction is considered the reaction energy profile must be symmetric, leaving only two cases: in the first case the central reaction step is rate-limiting and in the second case the first and third steps, as indicated schematically at the top of Fig. 6.15. The derivation of expressions for the multiple kinetic isotope effects of the triple hydrogen transfer case is analogous to the HH-transfer but more tedious. Therefore, the reader is referrred to refs. [25] and [26]. The main results are included in Table 6.2. As in the case of the HH-transfer, the kinetic isotope effects derived for the stepwise transfers are valid in the presence of tunneling and are independent of the tunneling model used. By contrast, the kinetic isotope effects of the single barrier reaction are affected by tunneling. The Arrhenius curves calculated for a small temperature range without tunneling contributions are illustrated in Fig. 6.16. For the single barrier case (Fig. 6.16(a)) Table 6.2 again predicts the rule of the geometric mean. Now, the overall isotope effect is larger than in the HH case, i.e. kHHH/kDDD = P3, however the individual isotope effects are the same if P is kept constant. In the stepwise triple barrier case with the central propagation as the rate-limiting step the overall isotope effect is given by kHHH/kDDD = Pd. It seems astonishing that the individual isotope effects kHHH/kHHD = 3/2 and kHHH/kHDD = 3 are given only by statistical values when Pd is large (Table 6.2). Thus, the Arrhenius curves of the HHH, HHD and HDD reaction are grouped closely together as illustrated in Fig. 6.16(b). This result can be explained as follows. When the central step is rate-limiting either H is transferred in this step with the probability 1/3 or D with the probability 2/3. The latter D-transfer does not contribute substantially to the overall rate constant, as H is transferred in the central step as fast as in the HHH reaction. Therefore, the HHH/HHD and the HHD/HDD isotope effects are given only by statistical factors. When the propagation is the rate-limiting step (Fig. 6.16(c)) a similar phenomenon occurs. In the HDD reaction there are pathways where H is transferred both in the first and the final rate-limiting steps, e.g. the sequence 000 fi 100 fi 101
6.2 Theoretical
a log k/s-1
HHH HHD HDD DDD
b log k/s-1
HHH HHD HDD
DDD
c log k/s-1
HHH HHD HDD
H D
3x
DDD
103 -1 T /K
Figure 6.16 Arrhenius diagrams of a degenerate triple hydron transfer. For the HHH-transfer an arbitrary Arrhenius law kHHH ¼ 1013 exp ð27:6 kJ mol1 =RTÞ in s–1 was assumed, involving the single proton kinetic isotope effects P ¼ Pd ¼ Pf ¼ expð7 kJ mol1 =RTÞ. (a) Single barrier case. (b) Triple barrier case with the dissociation as rate-limiting step. The rate constants are independent of the fractionation factor fd of the dissociation. (c) Triple barrier case with fd = exp(–0.92 kJ mol–1/RT) and equal rate constants kf = kb for the cation and anion propagation, i.e. a = 1. Reproduced with permission from Ref. [26].
fi 001 fi 011 fi 111. Therefore, also in this case only replacement of the last proton by a deuteron exhibits a non-statistical kinetic isotope effect. However, the HDD process will experience isotopic fractionation of the dissociation process. Moreover, the DDD process is additionally affected by isotopic fractionation.
6.2.7.3 Degenerate Stepwise HHHH-transfer In Ref. [26] three limiting cases were considered, i.e. a single barrier (Fig. 6.10), a double barrier (Fig. 6.17) and a quadruple-barrier reaction pathway (Fig. 6.18). The first process does not involve any intermediate. The second process consists essentially of consecutive double proton transfer steps, where each step involves a single barrier. There are two possibilities, either protons {1, 2} are transferred first, followed by protons {3, 4}, or vice versa, proceeding via the zwitterionic intermediates 1100 or 0011. It is again assumed that the intermediates can be treated as separate species, i.e. that there are no delocalized states involving different potential wells. This assumption will be realized when the barriers are large. Each reaction step is then characterized by an individual rate constant. The process con-
161
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids H
A
kd
A
H
H
kn
A {3,4}
H
H
H A
H
A
A
0000 (0)
H
+
{1,2}
{3,4}
A 1111 (F)
A H
H
A
A-
0011 (3)
H +
A
H A
H
A
H
A-
{1,2}
A
1100 (C)
H
162
A H
Figure 6.17 Degenerate two-barrier quadruple hydron transfer involving a single zwitterionic intermediate. Two hydrons lose zero-point energy in the configuration corresponding to the top of the barrier. Isotopic fractionation fd can occur for the dissociation. Reproduced with permission from Ref. [26].
sists of consecutive single proton transfer steps, corresponding to dissociation (kd), two propagation steps (kf and kb), and a neutralization step (kn). In the propagation steps one of the four protons is transferred and coupled to the transfer of either a positive or a negative charge (cation or anion propagation), indicated by + or – signs. Two possible intermediates, 0101 and 1010 are double zwitterions involving very high energies and are, therefore, neglected. The expected kinetic isotope effects obtained by neglecting secondary kinetic isotope effects are summarized in Table 6.3. The results are visualized in Fig. 6.19, where again a simple Arrhenius law was assumed for the HHHH reaction with the same arbitrary parameters as for the HH and the HHH reactions in Fig. 6.14 and 6.16. In the case of the single-barrier mechanism, all four hydrons are in flight in the transition state. Subsequent replacement of H by D involves similar primary kinetic isotope effects P, leading to equally spaced Arrhenius curves of the isotopic reactions in Fig. 6.19(a), with an overall kinetic isotope effect of kHHHH/kDDDD » P4. This result is analogous to the single-barrier HH and the HHH-transfer cases discussed above. Note that, generally, the transfer of n hydrons is expected to give rise to an overall kinetic isotope effect of Pn [26]. For the two-barrier HHHH case it was assumed that the first and second primary kinetic isotope effects of the double proton transfer in the dissociation steps
6.2 Theoretical
{1-}
{1-}
H
A
A
{4+}
+A
A
A
{3-}
H
Figure 6.18 Degenerate quadruple-barrier quadruple hydron transfer. A complete transfer consists of a dissociation step, two or more propagation steps and a neutralization step. The double-cation–double-anion
H
A
{3} A
H
A
0011 (3)
H A
A {2-}
{2}
A H
{1}
A
0111 (7) A
intermediates 0101 and 1010 are not further taken into account because of their high Couloumb energy. Reproduced with permission from Ref. [26].
Pd1 and Pd2 are equal. fd represents the single H/D fractionation factor of the dissociation step, corresponding to the equilibrium constant of the formal reaction initial state (D) + intermediate state (H) > initial state (H) + intermediate state (D).
A
H
A H
A-
H
{1+} H
+
H
H
-
H
A
A
H
H
A 0001 (1)
A
{4+}
H A
-
1011 (B)
H
-
A
H
0110 (6)
-
H {4}
+
0010 (2)
H
A
H
+A
A
A
{2-}
{4}
H
A
+
A
A
+
-
kn
(6.33)
The results are depicted in Fig. 6.19(b) and (c). Whereas in Fig. 6.19(b) fd =1, in Fig. 6.19(c) it was assumed that fd = exp(–0.92 kJ mol–1/RT) < 1. This fractionation factor takes into account the fact that the zero-point energies of each proton in the intermediate may be reduced due to low-frequency shifts of the proton vibrations, as expected for an increase in the H-bond strength in the intermediate. One observes three groups of Arrhenius curves, i.e. the HHHH curve, the group of the HHHD and the HDHD curves, and the group of the HHDD, HDDD and DDDD curves. Within each group the differences are small. They are further attenuated by isotope fractionation (Fig. 6.19c). The overall kinetic isotope effect, given by kHHHH/kDDDD = Pd2, is typical for a concerted double proton transfer reaction. It is interesting to note that replacement of the first H by D already leads to a
A 1111 (F)
{3-}
H
{3}
A
{4}
1101 (D) A
1010 (A)
A
H
A
A
H
{1+} H
H
A
H
H
H
H
-
A
{3+}
+
+ H {2+}
1001 (9)
H
-
A
{3}
A
A
-
{1} H
H
A 0000 (0)
A 0100 (4)
-
+
H
A
+
A
H
+A
H
1110 (E)
H
A
H
A
{2}
{4-}
H
{2}
H
{4-}
{1}
-
A
-
H
-
A
H
A
A
A
H
H
kd
-
H
A-
A
H
A 1000 (8)
H
+ H
{3+}
H
1100 (C)
H
A
H
H
+ A
{2+}
H
-
+
H
kb
A+
H
A
H A
H
0101 (5)
H
kf
A+
A
H
H
-
163
A H
H A
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
a
d
HHHH
HHHD
HHDD,HDHD
log k/s-1
log k/s-1
HHHH HHHD HHDD,HDHD
HDDD DDDD
HDDD DDDD
b
e
HHDD H D
HHHD HDDD
HHHH HHHD HHDD HDHD
log k/s-1
log k/s-1
HHHH
HDDD
HDHD
DDDD H D
DDDD
f HHHH HHHD HHDD
HDDD
H D
HDHD
DDDD
103 -1 T /K
Figure 6.19 Simulated Arrhenius diagrams of a degenerate quadruple hydron transfer. Arrhenius laws are assumed for the HHHHtransfer. (a) Single-barrier case. (b) Doublebarrier case with fd = 1. (c) Double-barrier case with fd = exp(–0.92 kJ mol–1/RT). (d) Quadruple-barrier case with dissociation as rate-limiting step. (e) Quadruple-barrier
HHHH HHHD HHDD HDHD
log k/s-1
c log k/s-1
164
H D
HDDD DDDD
103 -1 T /K
case with propagation as rate-limiting step, equal cation and anion propagation a = 1 (as indicated by the – signs), fd = ff = exp(–0.92 kJ mol–1/RT). (f) Quadruple-barrier case with propagation as rate-limiting step, only cation propagation a=0 (as indicated by the + signs), fd = ff = exp(–0.92 kJ mol–1/ RT). Adapted from Ref. [26].
substantial isotope effect of kHHHH/kHHHD = Pd/2 when isotopic fractionation is absent. In the quadruple-barrier case one needs to distinguish whether dissociation/ neutralization or propagation are the rate-limiting steps. Furthermore, a parameter a is needed describing the ratio of the forward reaction rate constants of the anion and the cation propagation, i.e. a¼
ki ki f b @ kiþ kiþ b f
(6.34)
6.2 Theoretical
165
Table 6.3 Kinetic isotope effects of degenerate quadruple proton transfers according to Ref. [26].
1 1 Pd1 ¼ Pd2
fd < 1; ff < 1;
fd < 1; ff < 1;
Pf1 << 1; a ¼ 1
Pf1 << 1; a ¼ 0
3 4
1 þ fd 3
1 þ fd 4
Pd2 ð1 þ f2 d Þ
1 2
fd 4
fd 4
P2
Pd1
1 2
fd 2
Pf1 ð1 þ fd ff Þ
P3
Pd2 ð1 þ f1 d Þ
1 4
Pf1 fd ð1 þ ff Þ
Pf1 ð1 þ 3fd þ 2fd ff Þ 4
P4
Pd2
Pd1
Pf1 fd
Pf1 fd
KIE
P1= P2= P3=P
kHHHD kHHHH
P1
Pd1 ð1 þ f1 d Þ
kHHDD kHHHH
P2
kHDHD kHHHH kHDDD kHHHH kDDDD kHHHH
¼ Pd1 << 1
Pd1 << 1
where i–and i+ indicate the transfer of hydron i coupled to the transfer of a negative or positive charge. In Table 6.3 Pf and Pb constitute the kinetic isotope effects of the two propagation steps; fd corresponds to the fractionation factor of the dissociation. When dissociation and neutralization are the rate-limiting steps (Fig. 6.19(d)), an overall kinetic isotope effect of kHHHH/kDDDD = Pd is expected, again typical for a single H-transfer. Surprisingly, only replacement of the last H by D is affected by Pd. As in the stepwise HHH case, this effect arises again from the possibility of reaction pathways involving transfer of H in the rate-limiting steps, even in the HDDD reaction. In the case of the propagation as rate-limiting step, an overall isotope effect of kHHHH =kDDDD ¼ Pf fd is expected. The rate constants of the other isotopic reactions are between the values of kHHHH and kDDDD. In Fig. 6.19(e) it is assumed that both cation and anion propagation exhibit the same rate constants, and in Fig. 6.19(f) it is assumed that anion propagation does not contribute fundamentally to the rate constants. This effect leads to a reduction in kHDHD. 6.2.8 Hydrogen Transfers Involving Pre-equilibria
According to Eigen’s scheme of H-transfer [52] in solution the reaction partners have first to meet in order to react. For an intermolecular H-transfer from AH to B one can write
166
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids K
k
A–H + B Ð A–H_B Ð A_H–B > A + HB
(6.35)
In Eq. (6.35) electrical charges are omitted. k represents the intrinsic forward rate constant. The pre-equilibrium constant is given by K¼
cAB cA cB
(6.36)
where cA and cB represent the concentrations of the reactants AH and B, and cAB the concentration of the reactive complex AHB. The total concentrations are then given by CA = cA + cAB and CB = cB + cAB. The experimentally accessible forward pseudo-first order rate constant is then given by [53] kobs ¼
dCA dðc þ cAB Þ dc kc ¼ A ¼ AB ¼ AB CA dt CA dt CA dt CA
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k ¼ ðCA CB Þ2 K 2 þ 1 þ 2KðCA þ CB Þ þ 1 þ KðCA þ CB Þ 2KCA
(6.37)
Equation (6.37) predicts changes in the apparent reaction order as a function of CA and CB. It can easily be shown that kobs = kKCB for K << 1 and kobs = k for K >> 1
(6.38)
For the case of two proton donors AH of the same kind which exchange two protons in a cyclic dimer (AH)2 the following equation has been derived kAA ¼
i k h pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ 8KCA þ 1 þ 4KCA 4KCA
(6.39)
which can also be obtained from Eq. (6.37) by setting CA = CB and replacing K by 2K [24]. Again, kobs = 2kKCB for K << 1 and kobs = k for K >> 1
(6.40)
Finally, the intramolecular case is interesting, where AH and B are functional groups of the same molecule. The equilibrium constant between the non-reactive form AH + B and the reactive form AHB is given by K¼
cR cNR
(6.41)
With the total concentration C = cNR + cR it follows that cR ¼
KC 1þK
(6.42)
Often, only the sum of the concentrations of NR and R is measured, i.e. the kinetics cannot distinguish between NR and R. As the interconversion between
6.2 Theoretical
NR and R is assumed to be fast, the observed first order or pseudo-first order rate constant is then given by kobs ¼
1 dcR kcR kK ¼ ¼ C dt 1þK C
(6.43)
In the case where K >>1 it follows that kobs ¼k
(6.44)
By contrast, if K << 1 it follows that kobs ¼kK
(6.45)
In other words, the observed rate constants depend in a similar way on the equilibrium constants in the three cases discussed. In order to have an impression of the effects on the Arrhenius curves let us discuss the intramolecular case given by Eq. (6.43). The temperature dependence of the pre-equilibrium constant is given by K =exp(–DH/RT+DS/R)
(6.46)
where DH and DS represent the enthalpy and entropy of the pre-equilibrium. Let us assume a simple Arrhenius law for the intrinsic H-transfer step k¼AexpðEa =RTÞ
(6.47)
with the arbitrary parameters A = 1013 s–1 and Ea = 30 kJ mol–1, represented by the dashed lines in the Arrhenius diagrams of Fig. 6.20. The effective Arrhenius curves calculated using Eq. (6.43) are represented by the solid lines. Figure 6.20(a) depicts the case where the formation of the reactive state involves a negative enthalpy and a negative entropy, as expected for a hydrogen bond association between the reaction partners AH and B. Thus, the reacting state predominates at low temperatures where kobs = k. The true Arrhenius curve is then measured, with normal pre-exponential factors. At high temperatures, however, nonreactive state dominates and kobs = kK. As K << 1 in this region, the observed Arrhenius curves exhibits a convex curvature and unusually small pre-exponential factors. The effective activation energy is given by Ea – |DH|. Figure 6.20(b) depicts the case where the formation of the reactive state involves a positive entropy and enthalpy. Such a case could happen if the reaction partners AH and B are involved in strong interactions with other species. For example, AH could be hydrogen bonded to any proton acceptor, or B to any proton donor, which requires this interaction to be broken before the partners can react. Now, the reacting state predominates at high temperatures and the non-reactive state at low temperatures. Only at high temperatures is the true Arrhenius curve measured, exhibiting a normal pre-exponential factor of about 13. At low temperatures, the
167
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
k → ←
K
B
→ ←
A-H
A-H---B
A---H-B
A
→ ←
B-H
slow
log (kobs/s-1)
a
∆S < 0 ∆H < 0 1 2 3
→ A---H-B A-H---B ←
A-H + B b
→ A---H-B A-H---B ←
log (kobs/s-1)
168
∆S > 0 ∆H > 0 A-H + B
6
5
4
103 / K-1 T Figure 6.20 Arrhenius curves of a H-transfer in the presence of a pre-equilibrium. Arbitrary parameters of the Arrhenius curves in the reactive complex: logA = 13, and Ea = 30 kJ mol–1. Parameters of the formation of the active complex: (1) DH = – 20 kJ mol–1,
DS = – 70 J K–1 mol–1; (2) DH = – 30 kJ mol–1, DS = – 120 J K–1 mol–1; (3) DH = – 40 kJ mol–1, DS = – 170 J K–1 mol–1 ; (4) DH = 10 kJ mol–1, DS = 40 J K–1 mol–1; (5) DH = 30 kJ mol–1, DS = 100 J K–1 mol–1; (6) DH = 50 kJ mol–1, DS = 160 J K–1 mol–1. Adapted from Ref. [53].
observed rate constants are slower than the intrinsic ones, the effective activation energy is given by Ea + |DH|. In addition, the observed pre-exponential factor is unusually large.
6.3 Applications
In this section various hydrogen transfer systems are reviewed for which Arrhenius curves of the different isotopic reactions are available over a large temperature range. Mainly the systems are discussed exhibiting degenerate hydrogen transfers which could be studied by dynamic NMR. The main question is how the reaction properties are related to the molecular structure.
HH/DD 11.5 HH/HD 6.5 HD/DD 1.9 H/D 11.4 D/T 3.4 H/T 39 H/D 16.5 D/T 3 H/T 49.6
–
–
16000
105
1.1105
4.3105
18d, 18e
23b
66b
66b
porphyrin organic solvents/solid state
porphyrin anion organic solvent/solid phosphazene matrix
phthalocyanine a-form solid
phthalocyanine b-form solid
1) Square brackets indicate values published previously.
HH/HD 16 HH/DH 4 HH/DD
5600
18b
tetraphenylporphyrin organic solvents/solid state
KIE298K
k298K / s–1
Ref
System
–
22.7
24.7
29.3
–
–
–
–
26.8
10.0
DH / kJ mol–1
Em / kJ mol–1
Table 6.4 Bell–Limbach tunneling model parameters of various H-transfers1)
–
–
–
–
–
DS / J K–1 mol–1
12.6
12.9
12.6
12.6
12.9
log (A/s–1)
15.5
17.6
34.3
28.7
29.3
Ed / kJ mol–1
1.5
1.5
0 [1.5]
2.5 [1.5]
1.5
Dm / a.m.u.
0.48
0.48
0.87 [0.78]
0.48 [0.68]
0.48
2a /
HD 5.9
HD 5.9
HD 6.5 [7.74] DT 4.2 [3.8]
HD 4.9 [4.95] DT 3.0 [2.2]
HD 5.0
De / kJ mol–1
6.3 Applications 169
–
–
350
4108
tetraphenyliso- 19a bacterio-chlorin organic solvents k2
indigodiimin HH-transfer organic solvent
68
–
4105
tetraphenyliso- 19a bacterio-chlorin organic solvents k1
tetraphenylchlorin organic solvents
17.6
29.3
16.7
33.5
–
–
–
–
–
–
24.3
HH/HD 16 HH/DH 4 HD/DD 1.2 DH/DD 4.5 23.0
DH / kJ mol–1
Em / kJ mol–1
KIE298K
HH/HD 2.6
2870
k298K / s–1
15
19b
20b
BD fi AD
acetylporphyrin organic solvents trans-cis and cistrans step
AC fi AD
Ref
System
–
–
–
–
–
–
DS / J K–1 mol–1
12.6
12.6
12.6
12.6
12.6
12.6
log (A/s–1)
29.7
29.3
26.4
36.8
22.6
31.0
Ed / kJ mol–1
1.5
1.5
1.5
1.5
1.5
1.5
Dm / a.m.u.
0.4
0.6
0.48
0.48
0.48
0.48
2a /
HD 5.9
HD 5.9
HD 5.9
HD 5.9
HD 5.9
HD 5.9
De / kJ mol–1
170
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
–
–
1.8
5107
2.5106
3109
91010
porphycene sol- 70 id state
49
74
74
74
27
DTAA solid state
TTAA solid state
(PhCOOH)2 solid state
(PhCOOH/ PhCOOD) solid state
(PhCOOD)2 solid state
DPBrP crystal
6500
–
2.6109
68
indigodiimin NH2 rotation organic solvent
HH/HD 5 HD/DD 5 HH/DD 25
5.6
17.6
24.7
16.3
Ed / kJ mol–1
3
1.5
1.5
Dm / a.m.u.
11.6
12.65
47.5
12.1
7.5
5.4
2.3
1.8
1.8
1.8
12.6 [12.4] 15.1 [14.2] 3 [3]
12.6
12.6
12.6
log (A/s–1)
11.6
–
–
–
–
–
DS / J K–1 mol–1
HH/HD » 6 (298 K) 1.0 HD/DD 21 (15 K) –
–
–
–
–
DH / kJ mol–1
11.6
0.84
3.4 [2.9]
20.5
5.9
16.7
Em / kJ mol–1
0.84
HH/HD »2.4 (298 K) HH/HD 24 (15 K)
KIE298K
k298K / s–1
Ref
System
0.55
0.44
0.52
0.48
0.17 [0.50]
0.34
0.48
0.48
2a /
HH/HD HD/DD
1.05 [3.0]
HD 1.05
HD 5.9
HD 5.9
De / kJ mol–1
6.3 Applications 171
HH/HD 3.2 HD/DD 1.6
HH/HD 4.1 HD/DD 3.5 HH/DD 14.3
14
75
107
22b
22b
24
oxalamidine OA7 in methylcyclohexane
oxalamidine OA7 in acetonitrile
F-amidine in THF
HH/HD 3.1 HD/DD 1.5
HH/HD 3
1500
HH/HD 4.1 HD/DD 1.4
HHHH/HDLL 3, HDLL/DDLL 4 HDLL/DDLL 4 HHHH/DDDD 12
22a
10000
HHH/HHD 3.8 HHD/HDD 3.7 HDD/DDD 3.4 HHH/DDD 47
tetraphenyloxalamidine in CD2Cl2
27
DPP crystal
990
KIE298K
720
25, 27
DMP crystal
k298K / s–1
azophenine in 21 organic solvents
Ref
System
–
19
5.4
52.7
52.7
44.4
–
–
–
–
–
8.4
27.2
DH / kJ mol–1
Em / kJ mol–1
–
–
–
–
–
–
12.2
12.6
12.6
12.6
12.6
12.6
12.3
DS / log J K–1 mol–1 (A/s–1)
26.4
16.7
27.2
24
30.1
32.5
48.1
Ed / kJ mol–1
1.05
1.5
1.5
1.5
1.5
4
2.8
Dm / a.m.u.
0.55
0.2
0.2
0.42
0.6
0.384
0.43
2a /
HH/HD 3.0 HD/DD 3.0
HD 3.8
HD 2.9
HD 2.5
HD 3.8
HHLL/HDLL 2.7 HDLL/ DDLL 2.7
HHH/HHD 2.7 HHD/HDD 2.7 HDD/DDD 2.7
De / kJ mol–1
172
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
H/D 56
H/D 9.8
H/D 4.8
–
2 107
4109
750
3200
90
1011
2-hydroxyphen- 86 oxyl radical CCl4+ dioxane
85 di-tertbutyl-2hydroxyphenoxyl radical in heptane
9b CH3COOH+ CH3OH in THF
2 CH3COOH+ 9b CH3OH in THF
Thermophilic 91 Dehydrogenase
pure methanol and calix[4]arene
93, 74
HHH/DDD 11.5 HHH/DHH 2.1
HH/HD 5.1 HD/DD 3.1 HH/DD15.5
H/D 18
» 104
8
Ingold radical
H/D 14.5
2109
83
Me-BO
KIE298K
k298K / s–1
Ref
System
0.13
0.0
27.2
16.5
1.26
0.0
4.2
0.293
Em / kJ mol–1
–
96
27.2
16.5
–
21
-19
-9
DH / kJ mol–1
–
326
-34
-42
–
38
-85
-60
DS / J K–1 mol–1
12.4
12.6
12.6 (11)
12.6 (10.4)
12.6
12.6
12.6
12.6
log (A/s–1)
8.8
67.0
33.5
36
23.9
27.2
50.2
19.7
Ed / kJ mol–1
2.8
0
0
0
1
0
1.9
2.1
Dm / a.m.u.
0.49
0.515
0.2
0.44
0.17
0.3
0.34
0.29
2a /
–
0.0
0.25
HH/HD 0.64 HD/DD 0.64
3.3
6.7
6.7
5.44
De / kJ mol–1
6.3 Applications 173
174
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
According to Eigen’s scheme of H-transfer (Eq. (6.35)) it can be divided into two steps, i.e. a diffusion step and an intrinsic H-transfer step in a hydrogen bonded complex. This picture can be specified further, for example by introduction of heavy atom reorganization in the intrinsic H-transfer step, either before or during the actual H-transfer. Therefore, in the first part of this section, intramolecular hydrogen transfers or intermolecular hydrogen transfers in preformed hydrogen bonded complexes in the solid state which are coupled only to minor heavy atom motions are discussed. H-transfers coupled to major heavy atom motions will then be treated in the second part; they include pre-equilibria, hydrogen bond switches, conformational changes, solvent motions etc. For a better comparison, the Arrhenius curves of all hydrogen transfers discussed in this section have been recalculated for this review using the Bell–Limbach tunneling model described in the theoretical section. Some systems have already been presented recently in a mini-review [54]. The parameters used are assembled in Table 6.4. Finally, note that in all cases where hydrogen isotopes are transferred from and to nitrogen the compounds had to be enriched for NMR measurements with the 15N isotope. 6.3.1 H-transfers Coupled to Minor Heavy Atom Motions 6.3.1.1 Symmetric Porphyrins and Porphyrin Analogs The tautomerism of porphyrin and of its analogs is illustrated in Fig. 6.21. Experimental aspects have been reviewed recently by Elguero et al. [55] and theoretical aspects by Maity et al. [56]. The thermal tautomerism of meso-tetraphenylporphyrin (TPP) – which is more soluble than the parent compound porphyrin – was discovered by Storm and Teklu [57] using liquid state 1H NMR. A large kinetic HH/DD isotope effect was observed which was interpreted in terms of a concerted double proton transfer. Hennig et al. [18a, 58] established in the late 70s and early 80s of the last century the intramolecular pathway of the reaction, measured the HH and DD reaction rates and later also the HD rates of TPP over a wide temperature range. The data were interpreted in terms of tunneling. As NMR methods to obtain rate constants were still developing, the low-temperature rate constants were overestimated by Hennig et al. [58] as criticized by Stilbs and Moseley [59]. As a consequence, the methods used were improved and led to a novel NMR pulse sequence based on “magnetization transfer in the rotating frame” [60], referred to later as “CAMELSPIN” [61] and then as “ROESY” [62], one of the most used NMR pulse sequences nowadays. In the late 70s and early 80s, tunneling theories indicated a preference for tunneling in symmetric double wells vs. asymmetric wells, supporting the concerted double proton transfer [63]. Thus, it seemed at that time that tunneling observed experimentally was only compatible with a concerted reaction pathway, supported
6.3 Applications
a
c
b
d
Figure 6.21 Tautomerism of (a) porphyrin, (b) chlorin, (c) isobacteriochlorin and (d) bacteriochlorin. Adapted from Ref. [19a].
by the finding that the two NH-stretches in the ground state of porphyrins are coupled [63]. In a number of papers, a stepwise transfer was proposed by Sarai [64], promoted by specific vibrations of the porphyrin skeleton which lower the N_N distance for H-transfer. In parallel, quantum-mechanical calculations indicated that cis-tautomers represent metastable intermediates, as indicated in Fig. 6.21(a). To our knowledge, the most recent ab initio calculation was published by Maity et al. [65]. Further theoretical progress will be discussed later.
175
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
log (k/s-1)
a
HH HD DD
b log (k/s-1)
176
HH
β α 103 / K-1 T Figure 6.22 Arrhenius curves of the tautomerism of (a) tetraphenylporphyrin in the liquid and solid state [18b] and (b) of the a- and b-forms of solid phthalocyanin [66b]. The Arrhenius curves were calculated using the parameters listed in Table 6.4.
In the meantime, Limbach et al. [58b] showed, for meso-tetraarylporphyrins, that the transfer also takes place in the solid state [58c], but it was found that the degeneracy of the reaction can be lifted by solid state interactions. Thus, the tautomerism of meso-tetratolylporphyrin was found to be degenerate in the solid state, but the tautomerism of triclinic TPP was perturbed in the sense that the transtautomers BD and DB exhibited a larger energy than the trans-tautomers AC and CA (Fig. 6.21(a)). However, by co-crystallization with a small amount of Ni-TPP a tetragonal structure was obtained in which the degeneracy of the tautomerism was restored, as shown by Schlabach et al. [18b]. No difference between the rate constants of the degenerate reactions in the liquid and the solid state could then be observed. Schlabach et al. also published the final set of rate constants for the HH, HD, and the DD tautomerism of TPP depicted in Fig. 6.22(a). The kinetic isotope effects were interpreted in terms of Eq. (6.31) for degenerate stepwise HH-transfers in the absence of isotopic fractionation between initial and intermediate state and of secondary isotope effects, re-written as
kHH ¼ kH ; kHD ¼
2kD 1 þ kD =k
; kDD ¼ kD H
6.3 Applications
(6.48)
Here kH and kD represent the single H-transfer rate constants of the formation of the individual intermediates in Fig. 6.21(a). Equations (6.31) and (6.48) had already been discussed by Limbach et al. [58] but used only after independent confirmation in the cases of azophenine and oxalamidines [21, 22], discussed below. Equation (6.48) was visualized in Fig. 6.12 and 6.14(b). The reaction energy profile of the HH-transfer involves two transition states of equal height. Thus, the product side is reached only with probability 12 as the internal return to the initial state also exhibits the same probability. The same is true for the DD reaction, only the effective barriers are larger. However, the symmetry is destroyed in the HD reaction. The rate-limiting step is the D-transfer which involves the same barrier as the corresponding process of the DD reaction. But as there is only a single barrier of this type in contrast to the DD reaction the HD reaction is about 2 times faster than the DD reaction. The fit of the experimental data to Eq. (6.48) is very satisfactory, as illustrated in Fig. 6.22(a), where the solid lines were recalculated here using the Bell–Limbach model, with the parameters included in Table 6.4. This result also means that there is no substantial decrease in the zero-point energies of the two protons in the cis-intermediate states as compared to the initial and final trans-states, as this would increase the HD/DD isotope effect beyond the value of 2 as was illustrated in Fig. 6.14(c). The solid state tautomerism of solid phthalocyanine was discovered [66a] and studied by Limbach et al. [66b]. As illustrated in Fig. 6.22(b), there are two forms which differ in the arrangement of the central nitrogen atoms. They are arranged in a square in the a- form but in a rectangular way in the b-form [66b]. Thus, the latter contains two weak inner NHN-hydrogen bonds. The reaction rates observed are substantially increased as compared to TPP; the increase is larger for the b-form as compared to the a- form (Fig. 6.22(b)). Kinetic H/D isotope effects have not yet been studied. The difference in the reaction kinetics of the two forms has been explained as follows. The observed tautomerism in the a- form was interpreted with a circular tautomerism as illustrated in Fig. 6.21(a), with similar transfer rates for the formation of all intermediates. However, the observed transfer in the b-form was assigned to a local HH-transfer within the two intramolecular hydrogen bonds which led to an extra increase in the rate constants. The thermal tautomerism of the unsubstituted solid parent compound porphyrin was discovered by Wehrle et al. [18c]. Again, the degeneracy of the tautomerism was not lifted. The HH, HD, DD rate constants in the liquid and the solid state were determined by Braun et al. [18d] leading to the Arrhenius diagram of Fig. 6.23(b). Again, no kinetic liquid–solid state effects could be observed. The motivation of these studies was to elucidate the influence of substituents on the tautomerism and to facilitate the comparison with theoretical studies which are generally performed on the non-substituted parent compound. In fact, although the observed isotopic pattern is similar to that of TPP, it is found that the reaction
177
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
in the parent compound is considerably faster than in TPP, but slower than in phthalocyanine (Table 6.4). These findings indicate that NHN-hydrogen bond compression is necessary for the HH-transfer in porphyrins and its analogs to occur, and that this compression is hindered by substituents in the meso-positions but facilitated by replacement of meso-carbon by meso-nitrogen atoms. As matrix effects on the tautomerism of porphyrin are absent, it is justified to combine the data obtained by NMR with those obtained at low temperatures using optical methods for porphyrin embedded in solid hexane [67], leading to the full Arrhenius diagram depicted in Fig. 6.23(a) [18d]. In contrast, rate constants obtained for substituted and unsubstituted porphyrins should not be included in a single Arrhenius diagram. Before the full Arrhenius diagram is discussed in detail, let us first include the results of a subsequent study of Braun et al. [18e] who measured also the rate constants kHT and kTT using liquid state 3H NMR of tritiated porphyrin dissolved in toluene. In order to discuss the new data it is convenient to convert the rate constants kLL into the rate constants kL using Eq. (6.31) which is naturally valid also
log (k/s-1)
a
HH HD DD
b log (k/s-1)
178
HH DD
HD
103 / K-1 T Figure 6.23 Mixed liquid and solid state Arrhenius diagrams of the HH-transfer of porphyrin, adapted from Ref. [18d].
6.3 Applications
for L = T. The resulting single H/D/T Arrhenius diagram of the porphyrin transcis reaction is depicted in Fig. 6.24. This representation allows comparison with the Arrhenius diagram of the tautomerism of the deprotonated unsubstituted porphyrin anion depicted in Fig. 6.25. The tautomerism of the latter was discovered by Braun et al. [23a], and the rate constants kH were measured for the liquid and the solid state, as well as kD and kT for the liquid state [23b]. Whereas the reaction profile for the anion is symmetric, it is asymmetric for the parent compound, as illustrated schematically in Fig. 6.26. For the parent compound porphyrin, an Arrhenius curve pattern of the type discussed in Fig. 6.9 is observed. Noteworthy is the same low-temperature slope Em of the Arrhenius curves of the HH and DD reaction in Fig. 6.23, i.e. of the H- and D- reaction in Fig. 6.24. Em will be mainly caused by the asymmetry of the reaction profile because at least the energy of the cis-intermediate is required for tunneling to occur, but also the reorganization energy of the ring skeleton will contribute. Note also that the low-temperature kinetic H/D isotope effect is smaller
log (k/s-1)
a
H D T
log (k/s-1)
b
H T
D
103 / K-1 T Figure 6.24 Mixed liquid and solid state Arrhenius diagram of the uphill trans–cis H/D/T-transfer of porphyrin. Data from Ref. [18e].
179
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
log (k/s-1)
a
H D T
b log (k/s-1)
180
H T D
103/ K-1 T Figure 6.25 Mixed liquid and solid state Arrhenius diagram of the tautomerism of the porphyrin anion. Adapted from Ref. [23b].
Em Ecis
Ereorg
Figure 6.26 Potential curves (shown schematically) of the tautomerism of porphyrin and its mono-deprotonated anion. Adapted from Ref. [18e].
6.3 Applications
than predicted from the relatively large barrier difference for H and D evaluated at high temperatures. In order to match this effect a relatively high value of Dm for the heavy atom tunneling contribution had to be used in order to reduce the lowtemperature isotope effect. In contrast, this was not necessary in the case of the porphyrin anion where the transfer is degenerate and where the low-temperature kinetic isotope effects are substantially larger than in the parent compound. Therefore, the much smaller value of Em in the anion is assigned to the reorganization of the porphyrin skeleton preceeding the transfer. As compared to the parent compound, both larger values for the tunneling distance as well as for the differences of the barrier heights of the isotopic reactions are obtained. These findings can be associated with the lack of the reaction asymmetry in the anion, as discussed in the previous section.
6.3.1.2 Unsymmetrically Substituted Porphyrins In subsequent studies the question arose as to how the kinetics of the tautomerism of porphyrins and porphyrin analogs are affected by a reduction in the molecular symmetry arising from the introduction of single substituents. From a theoretical viewpoint, this question was especially interesting as formal kinetics of the stepwise transfers in Fig. 6.21 predict an evolution of the Arrhenius curves as discussed in Fig. 6.14(d)–(f). When the symmetry of the reaction is perturbed, one of the two barriers of the stepwise transfer is increased and the other decreased, as was illustrated in Fig. 6.13. In the HD reaction the D transfer exhibits the larger barrier and becomes rate-limiting, whereas in the DH reaction H is transferred in the rate-limiting step. Therefore, the HD reaction becomes slower and the DH reaction faster until they coincide with the DD and with the HH rates, as illustrated in Fig. 6.14(f). This effect was observed by Schlabach et al. [20] for an unsymmetrically substituted acetylporphyrin (ACP, Fig. 6.27, X=CH3CO) dissolved in CD2Cl2. The thermodynamics and the kinetics of the HH, HD, DH and DD reactions could be studied by NMR. It was observed that the acetyl substituted pyrrole ring exhibits a smaller proton affinity as compared to the other pyrrole rings which are substituted with aliphatic substituents (Fig. 6.28(a)). The equilibrium constant was given by KACfiBD ¼ 1:14 · expð5:82 kJ mol1 =RTÞ
(6.49)
Therefore, reaction pathways involving transition states and intermediates with hydrogen isotopes located on the non-substituted pyrrole rings are favored. The Arrhenius curve pattern of Fig. 6.28(a) corresponds to the intermediate case between those of Fig. 6.14(d) and (e). It was calculated as follows. It was assumed that only the pathway ACfiADfiBD contributes to the reaction rate constants but not ACfiBCfiBD (Fig. 6.21). Thus, only the first terms in Eq. (6.25) needed to be retained. Neglecting secondary isotope effects, the second hydron in the superscripts of the rate constants could be omitted. Using the substitution AfiAC, BfiAC and DfiBD it was shown that
181
182
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
Figure 6.27 Stepwise HH, HD, DH and DD transfer in monosubstituted porphyrins.
kHH ACfiBD ¼
H D kH kD ACfiAD KACfiBD kBDfiAC ACfiAD KACfiBD kBDfiAC ; kDD ACfiBD ¼ D H D kH þ K k k þ K ACfiBD BDfiAC ACfiBD kBDfiAC ACfiAD ACfiAD
(6.50) kHD ACfiBD
H kH K kD kD ACfiAD KACfiBD kBDfiAC ¼ HACfiAD ACfiBD BDfiAC ; kDH ACfiBD ¼ D H kACfiAD þ KACfiBD kD k þ K ACfiBD kBDfiAC BDfiAC ACfiAD
Equation (6.50) expresses the experimental rate constants as a function of the sinH gle H-transfer forward and backward rate constants kH ACfiAD and kBDfiAC of the steps defined in Fig. 6.27. Both reaction steps are now characterized by different tunnel parameters listed in Table 6.4, used to calculate the Arrhenius curves of Fig. 6.28(a). The step ACfiAD involves a slightly larger barrier energy Ed and a slightly larger minimum energy Em for tunneling to occur as compared to step BDfiAD because of the asymmetry of the reaction. From a quantitative standpoint, the tunnel parameters may be subject to changes if data could be observed over a wider temperature range.
6.3 Applications
log (k/s-1)
a
HH DH HD DD
b log (k/s-1)
kAC→DB kAC→BD HH HD
kAC→DB kAC→BD
103 / K-1 T Figure 6.28 Arrhenius diagrams of the HH-transfer (a) in a substituted acetylporphyrin according to Ref. [20] and (b) in meso- tetraphenylisobacteriochlorin (upper curves) [19a] and in meso-tetraphenylchlorin (lower curves) dissolved in organic solvents [19d].
In conclusion, the theory of formal kinetics developed in the theoretical section for the description of stepwise multiple hydrogen transfers is supported by these experiments, at least for cases with weak hydrogen bonds. Thus, in these systems the assumption that each reaction step can be described in terms of a rate process characterized by rate constants is valid. The hydrogen bonds involved are not strong enough and the barriers not small enough that coherent tunneling states with delocalized protons or hydrogen atoms play an important role in this class of compounds.
183
184
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
6.3.1.3 Hydroporphyrins Hydroporphyrins consist of porphyrins where one or more pyrrole rings are hydrogenated. The inner hydrogen atoms of porphyrins and substituted porphyrins resonate around –2 ppm which is typical for a Hckel aromatic 4n+2 electronic p-system. The same was found for the AC and CA tautomers of meso-tetraphenylchlorin (TPC, Fig. 6.28(b)) where a single pyrrole ring is hydrogenated, and for meso-tetraphenylbacteriochlorin (TPBC, Fig. 6.28(b)) exhibiting two hydrogenated rings in trans-arrangement [19a]. Therefore, is was concluded that the two peripheral double bonds of porphyrin and the peripheral double bond of chlorin are not essential for the aromatic electron delocalization pathway, as illustrated in Fig. 6.21. In other words, porphyrin, chlorin and bacteriochlorin represent Hckel systems with 18 p-electrons in the aromatic pathways depicted in Fig. 6.21. In contrast, the chemical shifts of the inner hydrogen atoms of meso-tetraphenylisobacteriochlorin (TPiBC, Fig. 6.21(d)) were shifted substantially to low field, leading to the conclusion that all trans-forms of TPiBC do not represent aromatic 18 p electron systems. The analysis is different for the intermediate states. TPiBC is predicted to form aromatic cis-intermediates CD and DC which are then lowered in energy as compared to the zwitterionic intermediates AB and BA. Thus, Fig. 6.21c predicts the reactions of iso-bacteriochlorin to be faster than those of porphyrin. On the other hand, the aromatic character of bacteriochlorin is lost in the intermediate states, moreover the trans-tautomers BD and DB of bacteriochlorin exhibit a zwitterionic structure. Thus, one should expect a substantial increase in the barrier height of the exchange between AC and CA in bacteriochlorin as compared to porphyrin. These predictions were indeed confirmed experimentally. Schlabach et al. [19b] showed that in the case of TPC the trans-tautomers BD and DB cannot be observed directly by NMR; however, rate constants of the HH and the HD reaction could be obtained for the interconversion between AC and CA. According to an analysis similar to that leading to Eq. (6.25) it was shown that in the case of the HH reaction the observed rate constants are given by HH H DD DD D kHH ACfiCA ¼ kACfiBD ¼ kACfiAD >> kACfiCA ¼ kACfiBD ¼ kACfiAD
(6.51)
It has been shown [19b] that for the HD reaction two pathways are possible exhibiting reaction profiles similar to those of Fig. 6.13(c) and (d). The rate constants of the HD reaction are given by 1 H 1 D 1 H HD kHD ACfiCA ¼ kACfiBD ¼ 2 kACfiAD þ 2 kACfiAD » 2 kACfiAD
(6.52)
This result can also be directly obtained by inspection of Fig. 6.21(b), setting Ha = H and Hb = D: the pathways of the HD reaction are dominated by the steps where D is transferred from ring C to D to A, so that H is transferred from A to B to C. The latter pathway is rate-limiting and exhibits the same rate constant as the corresponding HH reaction. The factor of 12 in Eq. (6.52) arises from the fact that the alternative pathway where D is transferred via ring B is much slower.
6.3 Applications
The corresponding Arrhenius curves obtained are included in the lower part of Fig. 6.28(b). Within the margin of error, the kinetic HH/HD isotope effect of about 2 predicted by Eq. (6.52) was confirmed experimentally. Table 6.4 indicates that both Em and Ed are increased as compared to porphyrin, as expected. The total increase as compared to TPP is about 11 kJ mol–1, an effect which can be attributed to the loss of the aromaticity of TPP in TPC when the tautomerism occurs. For TPBC no intramolecular tautomerism could be observed up to 140 C, indicating that the sum of Em+Ed is larger than about 86 kJ mol–1, assuming a rate constant smaller than 100 s–1 at 140 C as estimated from the linewidths of the 1H signal of the inner protons. Finally, for TPiBC the rate constants of the processes AD « DB and AD « BD (Fig. 6.21(c)) could be measured [19b]. The results are included in the Arrhenius curves of Fig. 6.28(b). The AD « BD reaction is slower than in TPP which is not surprising, as the molecule is not aromatic. By contrast, the AD « DB reaction is substantially faster than in TPP, an effect which has been associated with the formation of the aromatic cis-intermediate. The reaction rates are similar to those of the porphyrin anion. Although only a few rate constants were measured, one can anticipate with the accepted pre-exponential factor of 1012.6 s–1 a substantial concave curvature of the Arrhenius curves, i.e. a tunneling process occurring at much lower energies as compared to TPP. This is again the consequence of a more symmetric reaction profile as compared to TPP because the energy gap between the non-aromatic initial state AC and the aromatic cis-intermediate DC is substantially reduced.
6.3.1.4 Intramolecular Single and Stepwise Double Hydrogen Transfer in H-bonds of Medium Strength When the hydrogen bonds become stronger the hydrogen transfer rates increase as the barriers are lowered. This is the case in a series of compounds discussed in this section. The first system is indigodiimine which exhibits an intramolecular double proton transfer [68] as illustrated in Fig. 6.29(a), together with the corresponding Arrhenius curve (lower line). This process renders the two halves of the molecule equivalent. An even faster NH2 rotation renders all NH protons equivalent. The rate constants were obtained by performing measurements at low temperatures, using a deuterated liquefied freon mixture CDCl3/CDFCl2/ CDF2Cl as NMR solvent [68]. The parameters of the calculated Arrhenius curves are included in Table 6.4 but are not further discussed as kinetic isotope effects were not obtained. The reaction rates are similar in the polycrystalline porphyrin analog dimethyldibenzo-tetraaza[14]annulene (DTAA) [69] representing a 6-membered H-chelate. They are even faster in the porphyrin isomer porphycene (Fig. 6.29(b)) [70] representing a 7-membered H-chelate with an even stronger intramolecular hydrogen bond. Both molecules form two trans-tautomers which are degenerate in the isolated molecules. However, solid state interactions lift this degeneracy. The rate constants of the forward uphill reactions could be measured in the case of DTAA
185
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
log (k/s-1)
a
b log (k/s-1)
186
103 / K-1 T Figure 6.29 Arrhenius diagrams of the tautomerism of (a) indigodiimine [68] dissolved in a CDCl3/CDFCl2/CDF2Cl mixture and of (b) polycrystalline dimethyldibenzotetraaza[14]annulene (DTAA) [69] and of polycrystalline porphycene [70].
using high resolution 15N solid state NMR by a combination of line shape analysis and 15N-T1 longitudinal relaxation time measurements. In the case of porphycene only the latter method could be used, which allows one to obtain rate constants on the micro- to nanosecond timescale. As kinetic isotope effects could not yet be obtained a detailed analysis of the reaction mechanisms was not yet possible. However, the present data seem to be compatible with stepwise HH tunneling processes where the energies of the cis-intermediates govern the Arrhenius curves at low temperatures. In polycrystalline tetramethyldibenzotetraaza[14]annulene (TTAA, Fig. 6.30) a related tautomerism was observed [49]. By a combination of solid state 15N and 2H
6.3 Applications CH3
CH3 H N
N
H N
CH3
CH3 N HN N
CH3
H N
CH3
CH3
log (k/s-1)
CH3
N
H
D
103 / K-1 T Figure 6.30 Arrhenius diagram of single H-transfer in polycrystalline tetramethyldibenzotetraaza[14]annulene (TTAA) according to Ref. [49].
NMR relaxometry rate constants and kinetic H/D isotope effects of the single Htransfer indicated in Fig. 6.30 could be measured. Evidence was found that the transfer is near-degenerate. Concave Arrhenius curves for the H- and the D-reactions were observed over a large temperature range, exhibiting surprisingly small kinetic H/D isotope effects, which were explained in terms of a relatively large heavy atom contribution to tunneling and a small barrier width. The latter arises from the substantially stronger H-bond in TTAA as compared to porphyrin.
6.3.1.5 Dependence on the Environment The question of how intermolecular interactions perturb the symmetry of a degenerate H-transfer was studied as a function of temperature by Wehrle et al. [71] using TTAA dissolved in glassy polystyrene. In all cases, the transfer was found to be faster than the dynamic range of solid state 15N NMR. The latter gave information about the distribution of the equilibrium constants of H-transfer. The results were rationalized in terms of the scenario of Fig. 6.31.
187
188
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
Figure 6.31 Model for the dependence of the proton transfer potential on the environment arising from experimental observations. Adapted from Wehrle et al. [71].
When a molecule exhibiting a symmetric double well for the proton motion in the gas phase is placed in a molecular crystalline environment, the crystal field will induce an energy difference DE between the tautomers. Whereas DE will be the same for all molecules in a crystal, DE will depend, in a disordered system such as a glass, on the local environment, leading to a distribution of DE-values. At the glass point, some environments may become mobile leading to an average value of DEav = 0, whereas other environments still experience non-zero values. Only well above the glass transition is a situation typical for the liquid reached where all molecules exhibit an average value DEav = 0.
6.3.1.6 Intermolecular Multiple Hydrogen Transfer in H-bonds of Medium Strength The double proton transfer in cyclic dimers of crystalline benzoic acid has been studied by various authors using NMR relaxation techniques [72, 73]. For a recent account of this work the reader is referred to the study of Horsewill et al. [74] who published the correlation times of the HH, HD and DD reactions given by 1 x k ¼ k12 þ k21 ; where K ¼ 2 ¼ 12 ¼ expðDE=RTÞ, sc x1 k21 DE = 85 K = 0.36 kJ mol–1
(6.53)
Here, DE represents the energy difference between the two tautomers whose gasphase degeneracy is lifted by solid-state interactions. x1 and x2 represent the molefractions. The resulting Arrhenius diagram where the forward rate constants k12 of Horsewill et al. [74] are plotted as a function of the inverse temperature is depicted in Fig. 6.32. The Arrhenius curves exhibit large concave curvatures as expected for tunneling. Both sc as well as the backward reaction k21 (not plotted) are almost independent of temperature in this regime. The tunnel parameters used to calculate the Arrhenius curves are included in Table 6.4. The values of the minimum energy for tunneling to occur, Em, are slightly larger than the energy difference DE between the two tautomers.
6.3 Applications
log (k12 /s-1)
k12 k21
HH
HD
DD
103 / K-1 T Figure 6.32 Arrhenius curves of the solid state tautomerism of benzoic acid dimers. Data for the HH and HD reactions taken from Ref. [74], and for the DD reaction from Ref. [72c]. The solid lines were calculated using the Bell–Limbach tunneling model with the parameters listed in Table 6.4.
In contrast to the intramolecular HH-transfers discussed above, replacement of each H by D leads to a significant isotope effect. At low temperatures, the HH/ HD and the HD/DD isotope effects are 24 and 21, i.e. quite similar. In contrast, the extrapolated values at room temperature are about 3 and 6. As compared to other systems discussed below, usually, either similar values are obtained as was illustrated in Fig. 6.14(a) or the kinetic HH/HD isotope effects are larger than the HD/DD isotope effects, an effect arising from tunneling. Whereas the HH and the HD curves in Fig. 6.32 calculated for this review could be simulated assuming only the usual slight changes in the tunneling mass, barrier height and of the barrier width, a substantially larger barrier height and also a larger value of the minimum energy for tunneling to occur had to be assumed for the DD reaction. At present, it is tempting to associate this finding with the fact that something special has happened with the deuterated crystals. For this discussion remember that deuteration generally leads to a different position of D with respect to the hydrogen bond center as compared to H, and to an increase in the heavy atom distance. Such differences have been observed recently for acetic acid dimer [75] and other hydrogen bonded systems [40]. This would lead to an additional term which increases the barrier height of the DD transfer. The tautomerism of crystalline pyrazoles which is discussed in the following, is particularly interesting because of the variety of hydrogen bonded complexes
189
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
formed by this type of compounds in the solid state. Depending on the substituents, one finds non-reactive chains or reactive cyclic dimers, trimers or even tetramers in which degenerate HH, HHH, or HHHH-transfers can take place [76, 77] as depicted in Fig. 6.33 to 6.37. In this series, the influence of crystal fields which can lift the gas phase degeneracy of the transfer processes was not observed within the margin of experimental error. The Arrhenius diagram of the degenerate HH/HD/DD transfer in the cyclic dimer of crystalline 3,5-diphenyl-4-bromopyrazole (DPBrP) [27] is depicted in Fig. 6.33. The kinetic HH/HD and HD/DD isotope effects are about 5 at room temperature and are similar, i.e. follow the rule of the geometric mean (RGM) as predicted by Fig. 6.14(a). The total HH/DD isotope effect is about 25. Concave Arrhenius curves indicate tunneling at low temperatures. This finding has been interpreted in terms of a single barrier reaction where all H loose zero-point energy in the transition state. The RGM is also fulfilled in the case of the degenerate HHH-transfer in the cyclic trimer of crystalline state 3,5-dimethylpyrazole (DMP) (Fig. 6.34) [25a]. The individual isotope effects are about 4 at room temperature, and the total isotope effect is around 47, which is typical again for a single-barrier reaction. The barrier height can be varied substantially by removing the bulky methyl groups and by introducing various substituents in the 4-positions as indicated in Fig. 6.35 [25b]. In the next section, the discussion of this effect will be pursued.
log (k/s-1)
190
HH
DD
HD 103/ K-1 T
Figure 6.33 Arrhenius diagram for the double proton and deuteron transfer in solid DPBrP. Adapted from Ref. [27].
6.3 Applications
log (k/s-1)
The kinetics of the HHHH-transfer in the cyclic tetramer of 3,5-diphenyl-4-pyrazole (DPP) has been evaluated recently [27]. The overall kinetic HHHH/DDDD isotope effects were found to be only around 12. This value indicated absence of a single barrier HHHH process where one would expect a larger overall effect. Instead, the Arrhenius pattern depicted in Fig. 6.36 could be explained in terms of a stepwise HH+HH process according to the profile of Fig. 6.17, where two hydrons are transferred in each step, leading to the expected isotope effects depicted in Fig. 6.19(b) and (c). This means that the rate constants of the HHHD and the HDHD reaction are very similar, and also those of the DDHH, DDHD, DDDD reactions. This leads to a very special dependence of the rate constants observed on the deuterium fraction xD in the mobile proton sites. The mole fractions of all isotopologs according to a statistical distribution are depicted in Fig. 6.37(a), and the sums of mole fractions of the relevant species exhibiting similar rate constants in Fig. 6.37(b). It is clear, that practically only three different species and rate constants are observed in this case. Ab initio calculations performed on pyrazole clusters reproduced these findings [78] and indicated a switch from concerted double and triple proton transfers in the cyclic dimer and trimer of pyrazole to a stepwise HH+HH mechanism for the
HHH HHD HDD
DDD 103/ K-1 T Figure 6.34 Arrhenius diagram for the double proton and deuteron transfer in the cyclic trimers of solid DMP. Adapted from Ref. [25a]. The solid curves were calculated using the Bell–Limbach tunneling model as described in the text.
191
log (k/s-1)
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
10
4NO2P 5
4BrP
0
DMP
0
2
4
6
8 103 / K-1 T
10
Figure 6.35 Arrhenius diagram for the triple proton transfers in cyclic trimers solid DMP, 4-nitropyrazole and 4-Br-pyrazole. Adapted from Ref. [25b].
log (k/s-1)
192
HHHH HHHD HDHD DDHH, DDHD DDDD 103 / K-1 T Figure 6.36 Arrhenius diagram for the quadruple proton and deuteron transfer in solid DPP. Adapted from Ref. [27]. The solid curves were calculated using the Bell–Limbach tunneling model.
6.3 Applications
a HHHH
xLLLL
DDDD
HHHD
HDHD
HDDD HHDD
xLLLL
b HHHH
DDHH DDHD DDDD
HHHD HDHD
xD Figure 6.37 Statistical mole fractions of isotopologs (a) and ensembles of isotopologs (b) of the tetrameric DPP. Adapted from Ref. [27].
tetramer, consisting of two consecutive concerted double proton transfers. The concerted mechanism for the dimer was recently confirmed by Rauhut et al. [79]. Finally, note that Horsewill et al. [80] have reported an intramolecular quasidegenerate quadruple HHHH tunneling process between the OH-groups of solid calix[4]arene, exhibiting temperature-independent rate constants. In a later section the discussion of this process will be pursued.
6.3.1.7 Dependence of the Barrier on Molecular Structure In Fig. 6.38(a) are depicted the correlated NHN-hydrogen bond coordinates (Table 6.5) of porphyrin, of TTAA, porphycene, of the pyrazoles discussed in the previous section, as well as the calculated values of the transition states of porphyrin [65] and of its mono-deprotonated anion [81]. Also the data point of the double proton transfer in the cyclic N,N¢-di-(p-F-phenyl)amidine dimer was added, which is discussed in the next section as it involves a hydrogen bond pre-equilibrium and a coupling to the reorientation of the aryl groups.
193
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
Note that all geometries are located on the NHN-hydrogen bond correlation curve of Fig. 6.3, especially the coordinates of the transition states of porphyrin and of its anion, exhibiting values of 2.60 and 2.66 . This means that hydrogen bond compression is the most important heavy atom motion which enables Htransfer; the transition state structures correspond to those expected for the strongest possible NHN-hydrogen bonds, whereas the initial states do not show any sign of hydrogen bonding. The question arises how the intrinsic barrier of the symmetric H-transfer depends on the hydrogen bond geometries. In Fig. 6.38(b), therefore, the experimental values of the total barrier Ed + Em are plotted as a function of q2 (Table 6.5). As a reference, the values of zero for the transition states calculated for porphyrin [65] and for the anion [81] are included. The dotted lines were calculated using the expression Ed + Em = C(q2 – q2min)
(6.54)
with q2min = 2.60 , C = 60 , 240, and 155 kJ mol–1 –1. The calculated curve with the smallest slope reproduces well the experimental data of the H-transfers. The
q2= (r1+r2) /Å
a
r1 r2 N··H······N
r1 r2 N······H··N
1 porphyrin
1,2 5,8 12,13
9 10
2 porphyrin anion
r1 r2 N··H··N
11 7
3 porphyrin TST
4
3
6
4 porphyrin anion TST 5 TTAA 6 porphycene
q1= ½(r1-r2) / Å b
HH
Ed / kJmol-1
194
10 6
11
1
9
9 DMP 10 4NO2P
2
8
11 4BrP 12 DPP
H 5 3
8 DFFA
HHH 13 12
7
7 DPBrP
4
q2= r1+r2 / Å Figure 6.38 (a) Hydrogen bond geometries of various molecular systems containing NHN-hydrogen bonds. (b) Barrier heights of the H-transfers calculated from the Arrhenius curves of the species in (a). The barrier heights of the transition states are set to zero. Values taken from Table 6.5.
13 PMP
81, 18d, 18e
1
2
3
4
5
6
7
porphyrin
porphyrin TST[a]
porphyrin anion
porphyrin anion TST[a]
tetramethyltetraaza[14]annulene TTAA
porphycene
diphenyl-p-bromopyrazole DPBrP
25a, 25b, 27
8
9
10
11
dimethylpyrazole DMP
4-nitropyrazole 4NO2P
4-bromopyrazole 4BrP
diphenylpyrazole DPP
a calculated using ab initio methods.
27
25b
25b
24c, 82b
N,N¢-di-(p-F-phenyl)amidine 12 DFFA
27
70
49
81
81
56
Ref
System
2.874
2.89
2.87
2.98
2.975
2.84
2.63
2.97
2.89
rNN/
1.05
1.05
1.03
1.02
1.03
1.06
1.10
1.03
1.33
1.03
1.28
1.03
r1/
Table 6.5 Selected distances in systems with intra- and intermolecular H-transfers.
1.82
1.82
1,96
1,96
1.94
1.78
1.60
1.94
1.33
2.31
1.32
2.31
r2/
0.42
0.41
0.42
0.48
0.45
0.45
0.25
0.45
0.005
0.64
0.02
0.64
q1/
2.87
2.87
2.89
2.98
2.975
2.84
2.70
2.97
2.66
3.34
2.60
3.34
q2/
32.5
38.0
36.0
48.1
26.4
47.5
24.7
15.1
0
34.3
0
28.7
Ed/kJ mol–1
19.0
7.53
7.52
8.4
5.4
5.6
5.9
3.4
0
10.0
0
22.7
Em /kJ mol–1
6.3 Applications 195
196
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
calculated curve assigned to the HH-transfer is tentative, as there is only a single point (7, DPBrP) which is well established. Its slope is substantially larger than the slope of the H-transfer curve. This may arise from the fact that two bonds instead of one have to be broken and reformed. Point 6 (porphycene) is located on this curve; it is tempting to conclude that the tautomerism of this molecule represents a more or less concerted HH-transfer process. However, point 8 refers to the HH-transfer in cyclic dimers of a diarylamidine (Fig. 6.44–6.46 ) discussed later. This point is located very far from the HH curve. This might indicate that something unusual happens here, for example a mechanism somewhere in between a concerted and a stepwise HH-transfer. It is interesting to note that for a given hydrogen bond geometry, the total barrier increases substantially from the H to the HH reaction, but that the barrier decreases again for a HHH reaction. Points 12 and 13 representing the HHHH reaction in pyrazole tetramers are located close to the HH curve; this is in agreement with the interpretation of consecutive HH+HH reaction. Let us at this point draw some conclusions based on the systems which have been discussed so far. All systems were “simple” in the sense that heavy atom motions were restricted to changes in bond lengths and angles of the molecular skeletons in which the hydrogen bonds are embedded. Major conformational changes or coupling to solvent molecules were not present. Figure 6.39 summarizes the findings schematically. Figure 6.39(a) illustrates hydrogen bond compression during a single H-transfer process according to the hydrogen bond correlation of Fig. 6.3. In the initial and final states, the geometric H/D isotope effects imply a shortening of the covalent bond distance and a lengthening of the hydrogen bond [40]. In the transition state the deuterated system can be somewhat more compressed as compared to the protonated system, because the wavefunction of D is sharper than the wavefunction of H, i.e. D is closer to the H-bond center than H. The barrier height is larger for D than for H. The mechanism of HH-transfer depends on whether the two hydrogen bonds involved are cooperative (Fig. 6.39(b)) or anti-cooperative (Fig. 6.39(c)). In the case of two cooperative H-bonds compression of one bond leads also to a compression of the second bond. Compression of one of two anti-cooperative bonds leads, however, to a lengthening of the other bond. In the case of non-cooperative H-bonds compression of the first bond has no effect on the second bond. When H in one bond is shifted to the H-bond center, assisted by compression of this hydrogen bridge, this compression will also lead to a compression of the second hydrogen bond, which in turn shifts also the hydrogen in this bond to the H-bond center. In other words, cooperative hydrogen bonds seem to favor a concerted or singlebarrier HH-transfer. This may be the case in benzoic acid dimer, porphycene and pyrazole dimers and trimers. By contrast, in the case of anti- or non-cooperative H-bonds, only one H-bond can be suppressed but not the other, and only a single H is transferred, leading to a stepwise motion involving a metastable intermediate. This is the case in porphyrins, phthalocyanins, indigodiimine, tetraaza[14]annulenes. In the next section, other examples will follow.
6.3 Applications
concerted HH-transfer cooperative H-bonds single H -Transfer
a
H
H
H
H
D
b
H H
H
D
H D
D
D
D D
D
H
H
H
D
D
D
c
H
D
stepwise HH-Transfer anticooperative H-bonds H
H
H
H
D
D D
H
H
D
D
D
Figure 6.39 Simplified models of H- and D-substituted hydrogen transfer systems. The boxes containing springs symbolize the symmetries and the compressibilities of the hydrogen bonds. (a) Geometric H/D isotope effects during compression assisted H-transfer in a single hydrogen bond. (b) Geometric
H D D
D
D D
H H
H
H D
D
H
H H
H
D
D
H/D isotope effects during compression assisted concerted HH-transfer in two cooperatively coupled hydrogen bonds. (c) Geometric H/D isotope effects during compression assisted stepwise HH-transfer in two anticooperatively coupled hydrogen bonds.
6.3.2 H-transfers Coupled to Major Heavy Atom Motions
In many H-transfer reactions in solution the reaction centers have first to form a reactive complex from non-reactive configurations or conformations i.e. they require a major molecular mobility. Therefore, it is understandable that complex H-transfers cannot take place in the solid state. In this section, various experimental published cases will be discussed.
6.3.2.1 H-transfers Coupled to Conformational Changes Let us first discuss the intramolecular degenerate double proton transfers in azophenine [21] and in oxalamidines [22a]. By liquid state NMR of the 15N labeled compounds the intramolecular pathways of the transfer processes were established and the rate constants kHH , kHD ¼ kDH and when possible kDD were measured. The Arrhenius diagrams are depicted in Fig. 6.40. In all cases, the reactions
197
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
log (k/s-1)
in solution were suppressed in the solid state, indicating major heavy atom motions in addition to H-bond compression. The kinetic HH/HD/DD isotope effects are given by Eq. (6.48) and are typical for stepwise degenerate reaction mechanisms involving metastable cis-intermediates reached by single H-transfers as illustrated by Fig. 6.11 and 6.12. In a similar case as described above for porphyrin, the observed rate constants kLL could be converted into the rate constants kL of the uphill single H-transfers. kH and kD were then calculated in terms of the Bell–Limbach tunneling model using the parameters included in Table 6.4 and converted back to kLL using Eq.(6.48). The reaction rates of tetraphenyloxalamidine (TPOA) dissolved in CD2Cl2 are only slightly larger than those of azophenine (AP) dissolved in C2D2Cl4. The kinetic isotope effects are larger in the latter; moreover, they depend on temperature, whereas those of TPOA exhibit little temperature dependence. The tautomerism of the bicyclic oxalamidine OA7 is, on the other hand, substantially slower than that of TPOA. In the corresponding 6-membered bicyclic oxalamidine OA6
AP
HH HD DD
OA7
methylcyclohexane
log (k/s-1)
198
HH HD DD
OA7
TPOA
acetonitrile
103 / K-1 T
Figure 6.40 (a) Arrhenius diagrams of the tautomerism of azophenine (AP) dissolved in CD2Cl2 (top, [22a]) and of the seven-membered bicyclic oxalamidine OA7 (bottom) dissolved in methylcyclohexane [22b, 22c]. (b) Arrhenius diagrams of the tautomerism of
tetraphenyloxalamidine (TPOA) dissolved in C2D2Cl4 (top, [18b]) and of OA7 dissolved in acetonitrile (bottom, [22b, 22c]). The solid lines were calculated using the parameters listed in Table 6.4 as described in the text.
6.3 Applications
no double proton transfer was detectable [22c]. On the other hand, the tautomerism of OA7 was substantially faster in acetonitrile (dielectric constant 37.5) as compared to methylcyclohexane (dielectric constant 2.02), as illustrated in Fig. 6.40. These findings supported the formation of a zwitterionic intermediate according to the stepwise mechanism of Fig. 6.11. The small dependence of the kinetic isotope effects on temperature is confirmed for OA7 as the Arrhenius curves of the isotopic reactions are almost parallel. Note that a quantitative discussion of these parameters is difficult as the temperature range of the experimental data was limited. Therefore, the parameter sets obtained are not unique. However, qualitatively, the above findings and the tunnel parameters obtained can be explained in terms of Fig. 6.41. In all cases, the total barrier heights Ed + Em for each single reaction step are the same; in addition, it is assumed that the classical kinetic hydrogen/deuterium isotope effects for the over-barrier reactions are the same. Therefore, in the high temperature regime, the associated Arrhenius curves coincide. However, drastic differences are expected at lower temperatures, when tunneling becomes important. In this region, temperature independent kinetic isotope effects are expected, leading to parallel Arrhenius curves. Tunneling can occur only at energies indicated by the hatched areas. In Fig. 6.41(a) and (d) Em is given by the energy of the intermediate Ei, whereas in Fig. 6.41(b) and (e) an additional reorganization energy Er is required, mainly to compress the Ed
a
d
Ed
Ei
Ed
b
Ei
e
Ed
Er Ei
c
Er Ei
Ei
f
log k
Ed+Em HH HD DD
HH
Em
HD DD
1/T
1/T
Figure 6.41 Visualization of a modified Bell tunneling model for degenerate, stepwise double proton transfers involving an intermediate. A minimum energy Em is required for proton tunneling, which can take place only in the hatched regions. Ed barrier energy. (a) and (d) Em is given by the energy of the
intermediate, Ei . (b) and (e) Em is given by Ei + Er where Er is associated with heavy atom reorganization preceding the proton transfer. (c) and (d) Corresponding Arrhenius curves (shown schematically) calculated in terms of the Bell–Limbach tunneling model. Adapted from Ref. [22c].
199
200
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
hydrogen bond, as discussed in the theoretical section. This hydrogen bond compression may involve additional molecular conformational changes. The corresponding Arrhenius curves are depicted in Fig. 6.41(c) and (d). The large changes in the experimental activation energies in the tautomerism of the oxalamidines and of azophenine, and at the same time the small changes in the kinetic isotope effects indicate then that the main differences arise from different values of Em = Er + Ei. It is plausible that the changes within the oxalamidines are then mainly due to different reorganization energies Er. This hypothesis was confirmed by semi-empirical calculations of various oxalamidines [22d]. The results are visualized in Fig. 6.42. In all cases, a substantial heavy atom reorganization precedes the H-transfer, which is strongly dependent on the chemical structure. This reorganization mainly involves a decrease in the nitrogen–nitrogen distances of the hydrogen bond in which the proton transfer takes place, thus lowering the barrier for the tautomerism. In contrast, in all other cases, hydrogen bond compression is associated with major conformational changes, requiring an additional reorganization energy. In TPOA and azophenine (not shown), H-bond compression is associated with a phenyl group reorientation.
OA
TPOA
OA5
OA6
OA6
syn
anti
OA7
OA7
syn
anti
Figure 6.42 Heavy atom reorganization during the HH-transfer in oxalamidines calculated using the semiempirical PM3MNDO method. Adapted from Ref. [22d].
6.3 Applications
This reorganization is not possible in the solid state, where only single tautomers are formed [21b, 22c]. The bicyclic oxalamidines also require a ring reorganization for H-bond compression to occur, which is smaller for OA7 than for OA5 and OA6, in accordance with experimental findings. For OA6 and OA7 syn- and anticonformations were found, which both exhibited similar energies for the transition states. However, note that the ring reorganization did not involve a barrier leading to a pre-equilibrium for the tunneling step, as indicated in Fig. 6.20. In all cases, the molecular structures do not allow for a simultaneous compression of both hydrogen bonds which would require a very high energy. Therefore, the transfers are stepwise, as indicated by Fig. 6.39(c). The effects of small changes in the molecular structure can be observed in the case of the related diarylamidines which are the nitrogen analogs of formic acid and which represent models for nucleic acids. In tetrahydrofuran, for N,N¢-di-(pF-phenyl)amidine (DFFA) three forms were observed by NMR, a solvated s-cisform and a solvated s-trans-form which is in fast equilibrium with a cyclic dimer in which a HH-transfer takes place [24] as illustrated in Fig. 6.43. Fortunately, at low temperatures, the s-cis- and the s-trans-forms were in slow exchange. The rate constants of the HH, HD and DD reactions were determined by dynamic 1H and 19F NMR as a function of concentration, deuterium fraction in the mobile proton sites and of temperature. The dependence of the observed rate constants of the s-trans-form on concentration is depicted in Fig. 6.44. The solid lines were calculated using Eq. (6.39) from which the rate constants in the dimer as well as the equilibrium constants of the dimer formation could be obtained. The Arrhenius
s-cis
s-trans
solvated
dimer
Figure 6.43 Conformational isomerism, hydrogen bond exchange and HH-transfer in N,N¢-di-(p-F-phenyl)amidine (DFFA) dissolved in tetrahydrofuran (S) according to Ref. [24c].
201
202
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids T = 189.2 K 10000
kobs/s-1
HH
5000
0 400
kobs/s-1
HD
200
0 40
kobs/s-1 20
DD
0 0
0.1
0.2
C/mol l-1
0.3
0.4
Figure 6.44 Pseudo-first order rate constants of the intermolecular HH, HD and DD transfers in cyclic dimers of s-trans-N,N¢-di-(p-Fphenyl)amidine (DFFA) dissolved in tetrahydrofuran as a function of the concentration. The solid lines were calculated using an equilibrium constant of 1.12 L mol–1 of the monomer–dimer equilibrium. Adapted from Ref. [24c].
diagrams obtained are depicted in Fig. 6.45. Two large isotope effects are observed indicating a single barrier reaction according to Fig. 6.14(a). As the rate constants are intrinsic to the dimer, the contribution from the hydrogen bond equilibrium was eliminated from the minimum energy for tunneling to occur, but not contributions from heavy atom rearrangements, in particular from the expected aryl group conformations. For that reason, symmetric diarylamidines with varying substituents in the pposition of the phenyl rings were studied by X-ray crystallography and dynamic solid state 15N NMR [82]. The tendency to form cyclic dimers in the solid state was supported. In most cases, the angles aN and aNH between the phenyl groups and the molecular skeleton at the imino and the amino nitrogen atoms were different for a given molecule; the aryl ring at the imino nitrogen atom was often found to be coplanar with the molecular skeleton, but a substantial angle was observed at the amino nitrogen. This circumstance can be attributed to steric interactions of aromatic o-CH groups and the CH group of the amidine unit. It leads to a large preference for one of the two potentially degenerate tautomers, and suppresses the HH reaction in the solid. A degenerate HH-transfer was observed only in the OCH3 substituted compound, where the two angles were similar but not coplanar with the molecular skeleton. In solution the aryl groups of a cyclic dimer will not, therefore, be the same as lead to an asymmetry of the double well for the HH-transfer, as illustrated in Fig. 6.46. Reorientation of the phenyl groups to angles around 50 will symmetrize the
log (k/s-1)
6.3 Applications
HH HD DD
103 / K-1 T Figure 6.45 Arrhenius diagrams of the tautomerism of DFFA dissolved in THF. Adapted from Ref. [24c].
potential and minimize the barrier height of the HH-transfer. The latter is expected to take place in this configuration. Finally, the process is completed by a reorientation of the aryl groups. This means that the total barrier of the HH reaction in solution within the cyclic dimer will be slightly higher than in the symmetric configuration in the solid state. This is what was indeed observed for the rate constants of the OCH3 substituted diarylamidine in the solid state.
6.3.2.2 H-transfers Coupled to Conformational Changes and Hydrogen Bond Pre-equilibria Replacing the CH unit of diarylamidines with imino nitrogens leads to diaryltriazenes. As illustrated in Fig. 6.46, the aryl groups are found to be coplanar with the triazene unit. A consequence is that an intermolecular steric interaction between aromatic CH arises, which prevents the formation of cyclic dimers. Thus, diaryltriazenes are not able to exchange protons without the help of a catalyst, as has been shown recently [33]. In order to obtain more information about catalytic proton exchange, the base catalyzed transfer of 1,3-bis(4-fluorophenyl)[1,315N ]triazene was studied in more detail using 1H and 19F NMR. As catalysts 2 dimethylamine, trimethylamine and water were studied, using tetrahydrofuran-d8 and methylethylether-d8 as solvents. The latter is liquid down to 130 K.
203
204
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
Figure 6.46 Coupling of the HH-transfer in cyclic dimers of diarylformamidines to the rearrangement of the aryl groups. Adapted from Ref. [82].
6.3 Applications
205
Surprisingly, both dimethylamine and trimethylamine were able to pick up the mobile proton of the triazene at one nitrogen atom and carry it to the other nitrogen atom, resulting in an intramolecular transfer process catalyzed each time by a different base molecule. Even more surprising is that the intramolecular transfer (Fig. 6.47(a)) catalyzed by dimethylamine is faster than the superimposed intermolecular double proton transfer (Fig. 6.47(b)). The kinetic H/D isotope effects are small, especially in the catalysis by trimethylamine, indicating a major heavy atom rearrangement and absence of tunneling. This is because of the high asymmetry of the H-transfer from the triazene to the base. Semi-empirical PM3 and ab initio DFT calculations indicate a reaction pathway via a hydrogen bond switch of the protonated amine representing the transition state, where the imaginary frequency required by the saddle point corresponds to a heavy atom motion, as was illustrated schematically in Fig. 6.7. Tunneling is absent because of the very high tunneling masses involved, corresponding to the mass of the base.
R
R N N
N
H ···
CH3
R
R
b
R
log kB
N
N
N ····· H
N
N
HH HD
R
R
H ····· N
N
+
N ····· H
·· H N N·
R
R
CH3 N
N R N H ···
-
····· H
CH3 H
103 / K-1 T Figure 6.47 (a) Arrhenius diagrams of the intramolecular proton and deuteron transfer in 1,3-bis-(4-fluorophenyl)-[1,3-15N2]triazene dissolved at a concentration of 0.1 mol l–1 in methyl ethyl ether-d8, catalyzed by the bases dimethylamine (0.0028 mol l–1 at xD = 0 and 0.0041 mol l–1 at xD = 0.95) and trimethyl-
CH3 H
CH3
N
N
· N
R
N
CH3
N
····
N H ··· N
CH3
+ H
N
·
N
N
····
-
N
R
H D
log kB
a
amine (0.02 mol l–1 at xD = 0 and xD = 0.96). kB represents the average inverse life times of the base B between two exchange events. (b) Arrhenius diagrams of the intermolecular proton and deuteron transfer of 1,3-bis-(4fluorophenyl)-[1,3-15N2]triazene catalyzed by dimethylamine. Adapted from Ref [33b].
206
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
The Arrhenius curves of all processes exhibit strong convex curvatures. This phenomenon is explained in terms of the hydrogen bond association of the triazene with the added bases, preceding the proton transfer. At low temperatures, all basic molecules form a hydrogen bonded reactive complex with the triazene, and the rate constants observed equal those of the reacting complex. However, at high temperatures, dissociation of the complex occurs, and the temperature dependence of the observed rate constants is affected also by the enthalpy of the hydrogen bond association according to Eqs. (6.37) and (6.46). As tunneling is not involved, the Arrhenius curves are not further discussed. For that the reader is referred to the original literature [53]. Al-Soufi et al. [83] have followed the kinetics of the intramolecular H- and D-transfer between the keto and the enol form of 2-(2¢-hydroxy-4¢-methylphenyl) benzoxazole (MeBO) dissolved in alkanes using optical methods. No dependence of the rate constants on the solvent viscosity could be found. The Arrhenius diagram obtained over a very wide temperature range is depicted in Fig. 6.48. At low temperatures, the very rare regime of temperature-independent rate constants is obtained, exhibiting a very large temperature independent kinetic H/D isotope effect of about 1400. At room temperature, still a quite large effect of about 14.5 is obtained. Al-Soufi et al. [83] mentioned that the experimental pre-exponential factors obtained at high temperature were only about 109 s–1 instead of about 1013 s–1 as expected. Therefore, the Arrhenius curves of this reaction were recalculated here using Eq. (6.43), assuming an equilbrium between a reactive form and a non-reactive form. The parameters are listed in Table 6.2. Because of the large body of data all parameters could be determined. At low temperatures, the intrinsic Arrhenius curves of the H- and the D-transfer, symbolized by the dashed lines, coincide with the observed ones, represented by the solid lines, as kobs = k. However, at high temperature it was assumed that a non-reactive form of the molecule dominates because of its more positive entropy, leading to kobs = kK. Thus, both the observed rate constants and the observed preexponential factors are smaller than expected. Note that, at low temperatures, a very small minimum energy Em for tunneling to occur is found, which refers to the reactive complex. This value could, therefore, be determined in addition to the values of DH and DS of the pre-equilibrium. In other cases, as discussed later, only the sum of DH + Em can be determined. The barrier for the transfer is similar to that found for TTAA. The difference between the barriers for H and D is substantially large, of the order of that found for porphyrin. In addition, a contribution for heavy atom tunneling is observed. At present, one can only speculate about the structure of the postulated nonreactive form. It could be that at low temperatures, the keto form may exhibit a zwitterionic aromatic character, and at high temperature a less polar but quinoid structure. Both structures are normally limiting structures. However, the zwitterionic structure is highly solvated and will exhibit, therefore, a much more negative entropy as compared to the zwitterionic structure. The entropy decrease is expected to be especially large in the case of apolar but polarizable solvents as has been shown by Caldin et al. [84]. Another possibility could be the formation of an
6.3 Applications
H
O
H O
k
log (k/s-1)
N
N
CH 3
CH 3
O
3Keto
O
3Enol
form
form
H
D
103 / K-1 T Figure 6.48 Arrhenius plot of the triplet state tautomerism of 2-( 2¢-hydroxy-4¢-methylphenyl) benzoxazole (Me-BO, upper curve) and its deuterated analog (lower curve) dissolved in alkanes. The kinetic data were taken from Al-Soufi et al. [83]. The solid lines were calculated using the parameters listed in Table 6.4.
enolic conformer exhibiting an intramolecular OHO- instead of an OHN-hydrogen bond. However, further spectroscopic and kinetic measurements are necessary to clarify this problem. Let us now discuss the well-studied case of the isomerization of the 2,4,6-tri-tertbutylphenyl radical to 3,5-di-tert-butylneophyl in apolar organic solvents, depicted in Fig. 6.49 which has been studied by Brunton et al. [8]. Various barrier types were used by these authors for Bell-type semiclassical tunneling calculations. It was shown that an inverted parabola could not give a satisfactory fit. The pre-exponential factors found for other barrier types were of the order of 8 to 12. As depicted in Fig. 6.49, a solution to the problem can be obtained in terms of an equilibrium where again a reactive form dominates at low and a non-reactive form at high temperature, as in the preceding case of Me-BO. In the case of the 2,4,6-tri-tert-butylphenyl radical one may interpret the reactive form with a configuration where the C–H bonds of the methyl groups are pointing in the direction of the aromatic acceptor carbon atom. Such a configuration could have a more negative entropy as compared to the non-reactive forms with unfavorable transfer geometries, dominating at high temperatures. The tunnel parameters used to calculate the Arrhenius curves are included in Table 6.4. No anomaly can be detected; the high barrier can be explained by the little capability for the formation of CHC-hydrogen bonds. Let us discuss now some examples where non-reactive states are present at low temperatures, and reactive states at high temperatures.
207
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
H
H
H H
C
log (k/s-1)
208
H
H C
k
H
D
103 / K-1 T Figure 6.49 Arrhenius curves of the isomerization of the 2,4,6-tri-tert-butylphenyl radical to 3,5-di-tert-butylneophyl in apolar organic solvents. The solid and dashed lines were calculated as described in the text using the parameters listed in Table 6.4. Data from Brunton et al. [8].
The first two examples are the H-transfers in 2-hydroxyphenoxyl radicals which have been studied using dynamic EPR spectroscopy. When 3,6-di-tert-butyl-2hydroxyphenoxyl and its deuterated analog are dissolved in heptane the Arrhenius diagram of Fig. 6.50 was obtained by Bubnov et al. [85]. The kinetic isotope effect is about 10 at room temperature. Setting the pre-exponential factor to 1012.6 (Table 6.4), leads to the concave Arrhenius curve depicted as solid lines. In contrast, Fig. 6.51 depicts the kinetic data of the parent compound 2-hydroxyphenoxyl in CCl4/ CCl3F to which 0.11 mol l–1 dioxane had been added to increase the solubility [86]. Now, a kinetic isotope effect of about 56 is obtained at room temperature. This large difference between both molecules had been noted already some time ago by Limbach et al. [87]. In particular, it was noted that the two Arrhenius curves of the H and the D reaction are almost parallel. Application of the Bell–Limbach tunneling leads to unusually large pre-exponential factors of 1018 s–1. As shown in Fig. 6.20(b) and the parameters of Table 6.4, the use of Eq. (6.43) improves the analysis, although the interpretation is similar to that obtained before. The dashed lines in Fig. 6.51 indicate the intrinsic Arrhenius curve of the transfer, whereas the solid line indicates the one including the pre-equilibrium. The reduction of the rate constants as compared to the di-tert-butyl radical is explained by the formation of a non-reactive species at low temperatures, which is hydrogen bonded to the added dioxane. Thus, for the reaction to occur, the intramolecular H-bonded species has first to be formed, which exhibits a higher energy but also a
6.3 Applications
log (k/s-1)
k
H
D
103 / K-1 T Figure 6.50 Arrhenius curves of the tautomerism of 3,6-ditert-butyl-2-hydroxyphenoxyl dissolved in heptane according to Bubnov et al. [85]. The solid lines were calculated using the parameters listed in Table 6.4.
log (k/s-1)
k
H
D
103 / K-1 T Figure 6.51 Arrhenius curves of the tautomerism of 2-hydroxyphenoxyl dissolved in CCl4/CCl3F/dioxane according to Loth et al. [86]. The solid lines were calculated using the parameters listed in Table 6.4.
209
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
more positive entropy. A comparison of the Arrhenius curves in Fig. 6.20(b) indicates that the desolvated intramolecular H-bonded species is never dominant over the whole temperature range, as the interaction with dioxane is stronger because of the linear intermolecular H-bond, in comparison with the weaker intramolecular H-bond. The larger kinetic H/D isotope effects in the parent radical can be explained in terms of the higher symmetry of the parent radical as compared to the di-tertbutyl radical. In the latter, the methyl groups on both sides of the ring are not ordered, leading to effective asymmetric double well potentials of the H-transfer. These examples show how subtle structural effects can lead to very different H-transfer properties. A related solvent effect was found for the proton exchange between acetic acid and methanol in tetrahydrofuran by Bureiko et al [88] and by Gerritzen et al. [9]. Hydrogen bonding to the solvent prevents the formation of the cyclic complexes in which the proton exchange takes place. Unfortunately, these complexes could not be seen directly. The rate constants were measured as a function of concentra-
log (k/s-1)
a
HH HD DD
b
log (k/s-1)
210
HHH HHD
HDD DDD
103 / K-1 T Figure 6.52 Arrhenius curves of the HH and HHH-transfer between acetic acid and methanol dissolved in tetrahydrofuran. Adapted from Ref. [9].
6.3 Applications
tion. At low concentration a second-order rate law was obtained indicating a HHtransfer in a cyclic 1:1 hydrogen bonded complex between acetic acid and methanol. At higher concentrations, the rate law changed indicating the participation of two acetic acid molecules, i.e. a HHH process. The multiple kinetic isotope effects were measured as a function of the inverse temperature as illustrated in Fig. 6.52. For the double proton transfer two large kinetic HH/HD and HD/DD isotope effects of about 5 and 3 were observed, consistent with the pattern of Fig. 6.14(a) expected for a single barrier process. In the latter, tunneling was not yet included, which leads to the observed deviation from the Rule of the Geometric Mean. Recently, this reaction has been modeled using the instanton approach by Fernndez-Ramos et al. [89]. The Arrhenius curves could be reproduced. The calculated geometries of the initial and the transition state are depicted in Fig. 6.53. In the latter, a proton is shifted towards the oxygen atom of methanol, but it is not completely transferred, rather, a strong hydrogen bond is formed. The Arrhenius diagram of the HHH-transfer in the 2:1 complex is depicted in Fig. 6.52(b). The kinetic isotope effects are similar to those expected for a single barrier process according to Fig. 6.16(a). They exhibit little dependence on temperature, indicating a rather narrow barrier. Unfortunately, the reacting complex could not be observed directly and its structure studied in more detail. Note, however, that this complex represents a model for the catalytic sites of proteases as proposed by Northrop [90].
a
0.97 Å 2.014 Å
1.225 Å
1.341 Å
1.802 Å 0.984 Å
b
1.317 Å 1.125 Å
1.279 Å
1.279 Å
1.125 Å 1.317 Å
Figure 6.53 Structures of the initial state (a) and of the transition state (b) of the 1:1 complex between acetic acid and methanol according to Fernndez-Ramos et al. [89]. The geometries were fully optimized at QCISD (quadratic configuration interaction including single and double substitutions) level of theory.
211
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
6.3.2.3 H-transfers in Complex Systems Although the model systems of the previous section already involved major molecular motions, the latter can be even much more complex in living systems. Here, only two extreme examples are considered, i.e. hydride transfer in an enzyme and proton transfer in pure methanol.
The Case of H-transfer in Thermophilic Alcohol Dehydrogenase (ADH) Firstly, let us discuss the example of a thermophilic alcohol dehydrogenase from Bacillus stearothermophilus (bsADH) studied by Kohen et al. [91, 92]. This enzyme catalyzes the abstraction of a hydride to the nicotinamide cofactor NAD+ as depicted in Fig. 6.54. The Arrhenius diagram is depicted in Fig. 6.54(a); a sudden decrease in the apparent slope and the apparent intercept of the Arrhenius curves is observed around room temperature (Fig. 6.54(b)). The puzzling observation is that the kinetic isotope effects are independent of temperature in the high-temperature regime but dependent on temperature in the low-temperature regime. The solid lines in Fig. 6.54 were calculated recently [54] assuming the simple reaction network of Fig. 6.55. It is assumed that the enzyme adopts two different 6.3.2.3.1
a
H Zn(II)
H
O H
log (kobs/s-1)
(Alcohol)
CONH2 + N
(NAD+) H
D
b log (kobsH/kobsD)
212
103 / K-1 T Figure 6.54 Arrhenius curves (a) and kinetic H/D isotope effects (b) of the intrinsic H-transfer in a thermophilic alcohol dehydrogenase (ADH) according to Kohen et al. [91]. The solid lines were calculated using the parameters listed in Table 6.4.
6.3 Applications A
B
B
→ → ←
A-H
→ ← more reactive state 2
H
-
less reactive state 1
k1
K
A-H---B
k2
→
K
A---H-B
Figure 6.55 Conformational dependent H-transfer in a biomolecule.
states 1 and 2 at equilibrium (K), where 1 is less reactive than 2. In the less reactive state 1, dominating at lower temperatures, the rate constant of H-transfer is given by k1, but in the more reactive state, dominating at higher temperatures, it is given by k2. Assuming again that the H-transfer is slower than the conversions between the states the following expression is obtained by modification of Eq. (6.43), i.e. k¼x1 k1 þ x2 k2 ¼k1
1 K þ k2 1þK 1þK
(6.55)
x1 and x2 correspond to the mole fractions of states 1 and 2 and K is again the equilibrium constant of the formation of state 2 from state 1. According to Table 6.4, state 2 dominates at higher temperatures, in spite of its higher energy, because of its very large positive entropy. This state could be one where the protein has become ideally flexible for proper activity, in contrast to the low-temperature regime. This conclusion is in accordance with the fact that this bsADH was evolved to function at ~65 C and with qualitative suggestions proposed in the past to rationalize the curved Arrhenius plot [91]. The tunnel parameters included in Table 6.4 indicate a ground state tunneling situation at high and at low temperatures, with temperature-independent kinetic isotope effects. The apparent temperature dependence observed at low temperatures is then the result of the transition between the two regimes, but does not arise from intrinsic temperature-dependent kinetic isotope effects. Note that in both states the pre-exponential factor of 1012.6 s–1 employed throughout this study was consistent with the data. The minimum energy for tunneling to occur is larger in the high-temperature state 2, but the barrier height and the barrier width are smaller than in the low temperature state 1. Thus, there seems to be a substantial change in the barrier parameters upon flexibilization of the enzyme at higher temperatures.
The Case of H-transfer in Pure Methanol and Calix[4]arene As a second case of high complexity, let us discuss how protons are exchanged in pure protic liquids. This problem has been studied by Gerritzen et al. [93] who studied the inverse proton lifetimes s1 AH of CH3OH ” AH in the pure liquid and 6.3.2.3.2
213
214
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
of CH3OH present as isotopic impurity in chemically pure CH3OD ” AD as a function of temperature. A mechanism involving the transfer of a small number n of protons in relatively stable cyclic hydrogen bonded intermediates (AH)n according to Fig. 6.10 to 6.18 was discarded. One reason was the finding that the addition of an organic solvent to methanol immediately quenches the proton exchange observed for the pure liquid. This would not be the case if the transfer takes place in cyclic hydrogen bonded intermediates. Therefore, an autoprotolysis mechanism was proposed consisting of dissociation: kd
þ AH þ AH ! A þAH2
(6.56)
kn
k1
þ ! cation propagation AHþ AH þ AH2 2 þAH k2
anion propagation AH þAH ! AH þAH kn
! neutralization A þAHþ AH þ AH 2
(6.57) (6.58) (6.59)
kd
The concentration of methoxonium and methoxide ions in the pure liquid is given by the autoprotolysis constant KH¼
kd ¼c þ c kn AH2 AH
(6.60)
where K H represents the autoprotolysis constant, which is 2.76 10–17 mol2 l–2 at 298 K, i.e. cAHþ2 ¼ cAH ¼ 5.2 10–9 mol l–1 [94]. The autoprotolysis mechanism is immediately suppressed by adding an organic solvent as it reduces the dielectric constant and hence the autoprotolysis constant. The following expression for the inverse proton life times follows from the autoprotolysis mechanism in CH3OH a straightforward way [93] pffiffiffiffiffiffiffi H H H H H þ s1 AH ¼ ðk1 cAH2 þk2 cAH Þ ¼ ðk1 þk2 Þ K
(6.61)
For 1% CH3OH in CH3OD it was shown that pffiffiffiffiffiffiffi H H D s1 AH ðCH3 ODÞ¼ ðk1 ðCH3 ODÞþk2 ðCH3 ODÞÞ K
(6.62)
H and E H be where K D represents the autoprotolysis constant of CH3OD. Let Ea1 a2 and kH the energies of activation describing the temperature dependence of kH 2 . 1 H H By assuming that Ea1 @ Ea2 it follows then from Eq. (6.61) that the effective energy of activation of proton exchange is given by H EaH ¼Ea1 þ
DH H 2
(6.63)
where DHH represents the enthalpy of autoprotolysis of CH3OH. In other words, if the cation and the anion are not created by autoprotolysis but stem from acid
6.3 Applications
and basic impurities, their concentration will be temperature independent and EaH H . When the impurities are, however, removed, E H is substantially is equal to Ea1 a increased. This is indeed observed, as illustrated in the Arrhenius plot of Fig. 6.56(a). The solid lines are given by 1 6:1 s1 AH ðCH3 OHÞ¼ 10 expð28:5 kJmol =RTÞ 1 5:7 s1 AH ðCH3 ODÞ¼ 10 expð29:3 kJmol =RTÞ
The kinetic isotope effects observed are given by [93] rffiffiffiffiffiffiffi H s1 ðkH KH 1 ðCH3 OHÞþk2 ðCH3 OHÞÞ AH ðCH3 OHÞ · = 3.2 at 298 K ¼ H H 1 KD ðk1 ðCH3 ODÞþk2 ðCH3 ODÞÞ sAH ðCH3 ODÞ
(6.64)
(6.65)
This overall kinetic isotope effect represents the product of an average kinetic isotope effect of the two propagation steps times the equilibrium isotope effect of the a
k
log (τAL-1/s-1)
AH +A*H*
AH ≡ CH3OH
k AH+A*D
AD + A*H
b log (k/s-1)
AH* + A*H
AH2+ + AH A− + AH
k1 k2
AH + AH2+ AH + A−
k= k1+ k2
log (k/s-1)
c k= k1+ k2
k12 k21
k= k12 103 -1 /K T
Figure 6.56 Arrhenius curves of (a) proton exchange in pure CH3OH and CH3OD. Adapted from Gerritzen et al. [93]. (b) Arrhenius curves of the elementary proton transfers in methanol calculated from the data of
Fig. 6.56(a) and the known ionization constant. (c) Kinetic data of the HHHH-transfer in solid p-tert-butyl calix[4]arene reported by Horsewill et al. [80] combined with those of Fig. 6.56(a).
215
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6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids
autoprotolysis. The value for water solutions was shown to be K H =K D = 5 at 298 K [95], whereas for methanol solutions a value of 6.5 was predicted [96]. Thus, the average kinetic isotope effect of the propagation is between 1.3 and 1.4. This effect corresponds to the usual isotope ratio expected for the reorientation of CH3OH and CH3OD. Using Eq. (6.61), the inverse life times s1 AH ðCH3 OHÞ were converted into the H ¼ kH ðCH OHÞ þ kH ðCH OHÞ plotted in Fig. 6.56(b) as a function þ k sum kH 3 3 2 2 1 1 of the inverse temperature. The solid line was given by [93] 12:3 10 1 H H kH expð7:7 kJmol1 =RTÞ, kH at 298 K 1 þ k2 ¼ 10 1 þ k2 ¼ 9:3 · 10 s
(6.66)
It follows that DHH @ 40 kJ mol–1. Note that Grunwald et al. [97] measured values of k1 = 8.8 1010 s–1 and k2=1.85 1010 s–1 for buffered solutions; their sum is in very good agreement with the value obtained for pure methanol. H The values of kH 1 þ k2 for water are very close to those of methanol. Using the known dependence of KH as a function of temperature, the proton lifetimes in pure water were estimated [93] 1 9:9 –1 s1 AH ðH2 OÞ¼ 10 expð39 kJmol =RTÞ ¼ 15000 s at 298 K
(6.67)
Thus, proton exchange is faster than in pure methanol because of the larger autoprotolysis constant. For comparison, let us compare the methanol data with those obtained by Horsewill et al. [80] who have reported an intramolecular quadruple proton transfer in the solid state between the four OH groups of solid calix[4]arene. Almost temperature independent rate constants were observed, which are again indicative of tunneling. An Arrhenius curve can be calculated using reasonable parameters (Table 6.4) which can reproduce both the pure methanol and the calix[4]arene data. It would be interesting to know more about the kinetic isotope effects in both systems.
6.4 Conclusions
In this chapter, the Bell–Limbach tunneling model has been applied to describe the Arrhenius curves of a number of single and multiple hydrogen transfer reactions. This model contains a number of parameters which can be obtained by simulation of the Arrhenius curves when enough experimental data are available. It is proposed to describe concerted multiple H-transfers in terms of a single barrier process. Multiple kinetic isotope effects of stepwise transfers can be treated in terms of formal kinetic reaction theory, where in each step one or more protons can be transferred, again in a concerted way. This approach is justified if each step can be described in terms of rate constants. This may not be the case for very strong hydrogen bonds, where H can be delocalized. Each reaction step can be
References
treated as a first approach in terms of the Bell–Limbach or any other tunneling model, or in terms of a more sophisticated quantum-mechanical theory. A main result of the examples discussed above is that pre-exponential factors of H-transfers coupled to only minor heavy atom motions are of the order of kT/h @ 1012.6 s–1, the value predicted by Eyring’s transition state theory for the high-pressure limit [5]. Deviations are then a first and important diagnostic tool for detecting so far unrecognized heavy atom motions and pre-equilibria such as conformational isomerism and hydrogen bond equilibria. Two types of heavy atom motions are considered, i.e. those which precede the H tunnel process and those which take place during the tunnel process. The latter give rise to an increased tunneling mass which reduces kinetic H/D isotope effects arising from tunneling. Thus, this model helps experimentalists to interpret their kinetic data, but does not preclude further quantum-mechanical studies of the hydrogen transfer steps.
Acknowledgements
This research has been supported by the Deutsche Forschungsgemeinschaft, Bonn, and the Fonds der Chemischen Industrie (Frankfurt). I am indebted to Professors Maurice Kreevoy, Minneapolis, Minnesota, USA; R. L. Schowen, Lawrence, Kansas, USA and G. S. Denisov, St. Petersburg, Russian Federation for stimulating discussions over three decades. I also thank Professors G. S. Denisov and R. L. Schowen for carefully reading the manuscript and for their helpful comments.
References 1 E. Caldin, V. Gold (Eds.), Proton Transfer
Reactions, Chapman and Hall: London, 1975. 2 R. A. Marcus, J. Chem. Phys. 1966, 45, 4493–4499. 3 P. Schuster, G. Zundel, C. Sandorfy (Eds.), The Hydrogen Bond, North Holland, Amsterdam, 1976, Vol 1–3. 4 (a) H. H. Limbach, Dynamic NMR Spectroscopy in the Presence of Kinetic Hydrogen/ Deuterium Isotope Effects, in NMR Basic Principles and Progress, Deuterium and Shift Calculation, Springer-Verlag, Heidelberg 1991, Vol. 23, pp. 66–167; (b) H. H. Limbach, Dynamics of Hydrogen Transfer in Liquids and Solids, in Encyclopedia of Nuclear Magnetic Resonance, D. M. Grant, R. K. Harris (Eds.),
Advances in NMR, John Wiley & Sons, Chichester, 2002, Suppl. Vol. 9, pp. 520–531. 5 S. Glasstone, K. J. Laidler, H. Eyring, The Theory of Rate Processes. McGrawHill, New York 1941. 6 (a) J. Bigeleisen, J. Chem. Phys. 1949, 17, 675–678; (b) J. Bigeleisen, J. Chem. Phys. 1955, 23, 2264–2267; (c) L. Melander, W. H. Saunders, Reaction Rates of Isotopic Molecules, Krieger, Malabar, FL, 1987. 7 (a) R. P. Bell, The Proton in Chemistry, 2nd edn. Chapman and HalI, London, 1973; (b) R. P. Bell, The Tunnel Effect, Chapman and Hall, London, 1980. 8 G. Brunton, J. A. Gray, D. Griller, L. R. C. Barclay, K. U. Ingold, J. Am. Chem. Soc. 1978, 100, 4197–4200.
217
218
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids 9 (a) D. Gerritzen, H. H. Limbach,
J. Am. Chem. Soc. 1984, 106, 869–879; (b) H. H. Limbach, W. Seiffert, J. Am. Chem. Soc. 1980, 102, 538–542. 10 J. Basran, S. Patel, M. J. Sutcliffe, N. S. Scrutton, J. Biol. Chem. 2001, 276, 6234–6242. 11 (a) N. Bruniche-Olsen, J. Ulstrup, J. Chem. Soc., Faraday Trans. 1 1979, 75, 205–226; (b) E. D. German, A. M. Kuznetsov, R. R. Dogonadze, J. Chem. Soc., Faraday Trans. 2 1980, 76, 1128–1146. 12 (a) A. M. Kuznetsov, J. Ulstrup, Can. J. Chem. 1999, 77, 1085–1096; (b) A. M. Kuznetsov, J. Ulstrup, Proton Transfer and Proton Conductivity in Condensed Matter Environment. In: Isotope Effects in the Biological and Chemical Sciences, A. Kohen, H. H. Limbach (Eds.) Taylor & Francis, Boca Raton FL, 2005, Ch. 26, pp. 691–724. 13 M. J. Knapp, K. Rickert, J. P. Klinman, J. Am. Chem. Soc. 2002, 124, 3865–3874. 14 (a) W. Siebrand, T. A. Wildman, M. Z. Zgierski, J. Am. Chem. Soc. 1984, 106, 4083–4089; (b) W. Siebrand, T. A. Wildman, M. Z. Zgierski, J. Am. Chem. Soc. 1984, 106, 4089–4096. 15 D. Truhlar, Variational Transition-State Theory and Multidimensional Tunneling for Simple and Complex Reactions in the Gas Phase, Solids, Liquids, and Enzymes, in Ref. [12b], Ch. 22, pp. 579– 620. 16 Z. Smedarchina, W. Siebrand, A. Fernndez-Ramos, Kinetic Isotope Effects in Multiple Proton Transfer, in Ref. [12b], Ch. 22, pp. 521–548. 17 O. Brackhagen, Ch. Scheurer, R. Meyer, H. H. Limbach, Ber. Bunsenges. Phys. Chem. 1998, 102, 303–316. 18 (a) H. H. Limbach, J. Hennig, D. Gerritzen, H. Rumpel, Faraday Discuss., Chem. Soc. 1982, 74, 229–243; (b) M. Schlabach, B. Wehrle, H. Rumpel, J. Braun, G. Scherer, H. H. Limbach, Ber. Bunsenges. Phys. Chem. 1992, 96, 821–833; (c) B. Wehrle, H. H. Limbach, M. Kcher, O. Ermer, E. Vogel, Angew. Chem. 1987, 99, 914–917; Angew. Chem. Int. Ed. Engl. 1987, 26, 934–936; (d) J. Braun, M. Schlabach, B. Wehrle, M. Kcher, E. Vogel, H. H. Limbach, J. Am. Chem. Soc. 1994, 116, 6593–6604;
19
20
21
22
23
24
25
(e) J. Braun, H. H. Limbach, P. G. Williams, H. Morimoto, D. Wemmer, J. Am. Chem. Soc. 1996, 118, 7231–7232. (a) M. Schlabach, H. Rumpel, H. H. Limbach, Angew. Chem. 1989, 101, 84–87; Angew. Chem. Int. Ed. Engl. 1989, 28, 76–79; (b) M. Schlabach, G. Scherer, H. H. Limbach, J. Am. Chem. Soc. 1991, 113, 3550–3558. (a) M. Schlabach, B. Wehrle, H. H. Limbach, E. Bunnenberg, A. Knierzinger, A. Shu, B. R. Tolf, C. Djerassi, J. Am. Chem. Soc. 1986, 108, 3856–3858; (b) M. Schlabach, H. H. Limbach, E. Bunnenberg, A. Shu, B. R. Tolf, C. Djerassi, J. Am. Chem. Soc. 1993, 115, 4554–4565. (a) H. Rumpel, H. H. Limbach, J. Am. Chem. Soc. 1989, 111, 5429–5441; (b) H. Rumpel, H. H. Limbach, G. Zachmann, J. Phys. Chem. 1989, 93, 1812–1818. (a) G. Otting, H. Rumpel, L. Meschede, G. Scherer. H. H. Limbach, Ber. Bunsenges. Phys. Chem. 1986, 90, 1122–1129; (b) G. Scherer, H. H. Limbach, J. Am. Chem. Soc. 1989, 111, 5946–5947; (c) G. Scherer, H. H. Limbach, J. Am. Chem. Soc. 1994, 116, 1230–1239; (d) G. Scherer, H. H. Limbach. Croat. Chem. Acta, 1994, 67, 431–440. (a) J. Braun, C. Hasenfratz, R. Schwesinger, H. H. Limbach, Angew. Chem. 1994, 106, 2302–2304; Angew. Chem. Int. Ed. Engl. 1994, 33, 2215–2217; (b) J. Braun, R. Schwesinger, P. G. Williams, H. Morimoto, D. E. Wemmer, H. H. Limbach, J. Am. Chem. Soc. 1996, 118, 11101–11110. (a) L. Meschede, D. Gerritzen, H. H. Limbach, Ber. Bunsenges. Phys. Chem. 1988, 92, 469–485; (b) H. H. Limbach, L. Meschede, G. Scherer, Z. Naturforsch.a 1989, 44, 459–471; (c) L. Meschede, H. H. Limbach, J. Phys. Chem. 1991, 95, 10267–10280. (a) F. Aguilar-Parrilla, O. Klein, J. Elguero, H. H. Limbach, Ber. Bunsenges. Phys. Chem. 1997, 101, 889–901; (b) O. Klein, M. M. Bonvehi, F. AguilarParrilla, J. Elguero, H. H. Limbach, Isr. J. Chem. 1999, 34, 291–299.
References 26 H. H. Limbach, O. Klein, J. M. Lopez
27
28
29
30
31 32 33
34 35
36
37 38
Del Amo, J. Elguero, Z. Phys. Chem. 2004, 217, 17–49. O. Klein, F. Aguilar-Parrilla, J. M. Lopez, N. Jagerovic, J. Elguero, H. H. Limbach, J. Am. Chem. Soc. 2004, 126, 11718–11732. J. Brickmann, H. Zimmermann, Ber. Bunsenges. Phys. Chem. 1966, 70, 157–165; 1966, 70, 521–524; 1967, 71, 160–1964; J. Brickmann, H. Zimmermann, J.Chem.Phys. 1969, 50, 1608– 1618. P. M. Morse, E. C. G. Stckelberg, Helv. Phys. Acta 1931, 4, 335–354; R. L. Somorjai, D. F. Hornig, J.Phys.Chem. 1962, 36, 1980–1987; J. Laane, Appl. Spectrosc. 1970, 24, 73–80. W. F. Rowe, R. W. Duerst, E. B. Wilson, J. Am. Chem. Soc. 1976, 98, 4021–4023; S. L. Baughcum, R. W. Duerst, W. F.Rowe, Z. Smith, E. B. Wilson, J. Am. Chem. Soc. 1981, 103, 6296–6393; S. L. Baughcum, Z. Smith, E. B. Wilson, R. W. Duerst, J. Am. Chem. Soc. 1984, 106, 2260–2265. R. L. Redington, R. L. Sams, J. Phys. Chem. A 2002, 106, 7494–7511. F. Madeja, M. Havenith, J. Chem. Phys. 2002, 117, 7162–7168. D. W. Firth, P. F. Barbara, H. P. Trommsdorff, Chem.Phys. 1989, 136, 349–360. J. D. McDonald, Annu. Rev. Phys. Chem. 1979, 30, 29–50. D. Borgis, J. T. Hynes, J. Chem. Phys. 1991, 94, 3619–3628; D. Borgis, J. T. Hynes, Chem. Phys. 1993, 170, 315–346. H. H. Limbach, G. Buntkowsky, J. Matthes, S. Grndemann, T. Pery, B. Walaszek, B. Chaudret, Chem. Phys. Chem. 2006, 7, 551–554; G. Buntkowsky, B. Walaszek, A. Adamczyk, Y. Xu, H. H. Limbach, B. Chaudret, Phys. Chem. Chem. Phys. 2006, 8, 1929–1935. R. P. Bell, J. Chem. Soc., Faraday Discuss. 1965, 39, 16–24. (a) L. Pauling, J. Am. Chem. Soc. 1947, 69, 542–553; (b) I. D. Brown, Acta Crystallogr., Sect. B 1992, 48, 553–572.
39 (a) T. Steiner, J. Chem. Soc., Chem. Com-
40
41
42
43
44
45 46 47
48 49
50
51 52 53
mun. 1995, 1331–1332; (b) T. Steiner, J. Phys. Chem. A 1998, 102, 7041–7052; (c) T. Steiner, Angew. Chem. Int. Ed. Engl. 2002, 41, 48-76. H. H. Limbach, G. S. Denisov, N. S. Golubev, Hydrogen Bond Isotope Effects Studied by NMR, in Ref [12b], Ch. 7, pp. 193–252. (a) H. S. Johnston, Gas Phase Reaction Rate Theory. Modern Concepts in Chemistry, The Ronald Press Company, New York 1966; (b) D. G. Truhlar, J. Am. Chem. Soc. 1972, 94, 7584–7586; (c) N. Agmon, Chem. Phys. Lett. 1977, 45, 343–345. H. H. Limbach, M. Pietrzak, H. Benedict, P. M. Tolstoy, N. S. Golubev, G. S. Denisov, J. Mol. Struct. 2004, 706, 115–119. H. H. Limbach, M. Pietrzak, S. Sharif, P. M. Tolstoy, I. G. Shenderovich, S. N. Smirnov, N. S. Golubev, G. S. Denisov, Chem. Eur. J. 2004, 10, 5195–5204. K. F. Wong, T. Selzer, S. J. Benkovic, S. Hammes-Schiffer, Proc. Nat. Acad. Sci. USA 2005, 102, 6807–6812. F. H. Westheimer, Chem. Rev. 1961, 61, 265–273. R. A. More O’Ferrall, Substrate Isotope Effects. in Ref. [1], Ch. 8, pp. 201–262. (a) G. Wentzel, Z. Phys. 1926, 138, 518– 529; (b) H. A. Kramers, Z. Phys. 1926, 39, 828–840; (c) L. Brillouin, C. R. Acad. Sci, 1926, 153, 24–26. Ref. [7a], p. 275. U. Langer, L. Latanowicz, Ch. Hoelger, G. Buntkowsky, H. M. Vieth, H. H. Limbach, Phys. Chem. Chem. Phys. 2001, 3, 1446–1458. S. N. Smirnov, H. Benedict, N. S. Golubev, G. S. Denisov, M. M. Kreevoy, R. L. Schowen, H. H. Limbach, Can. J. Chem. 1999, 77, 943–949. S. Schweiger, G. Rauhut, J. Phys. Chem. A 2003, 107, 9668–9678. M. Eigen, Angew. Chem. Int. Ed. Engl. 1964, 3, 1–23. (a) F. M nnle, H. H. Limbach, Angew. Chem. Int. Ed. Engl. 1996, 35, 441–442; (b) H. H. Limbach, F. M nnle, C. Detering, G. S. Denisov, Chem. Phys. 2005, 319, 69–92.
219
220
6 Single and Multiple Hydrogen/Deuterium Transfer Reactions in Liquids and Solids 54 H. H. Limbach, J. M. Lopez del Amo,
A. Kohen, Philos. Trans. B. 2006, 361, 1399–1415. 55 R. M. Claramunt, J. Elguero, A. R. Katritzky, Adv. Heterocycl. Chem. 2000, 77, 1–50. 56 D. K. Maity, T. N. Truong, J. Porph. Phthal. 2001, 5, 289–299. 57 C. B. Storm, Y. Teklu, J. Am. Chem. Soc. 1974, 94, 1745–1747; C. B. Storm, Y. Teklu, Ann. N. Y. Acad. Sci. 1973, 206, 631–640. 58 (a) J. Hennig, H. H. Limbach, J. Chem. Soc., Faraday Trans.2 1979, 75, 752–766; (b) H. H. Limbach, J. Hennig, R. Kendrick, C. S. Yannoni, J. Am. Chem. Soc. 1984, 106, 4059–4060. 59 P. Stilbs, M. E. Moseley, J. Chem. Soc., Faraday Trans. 2 1980, 76, 729–731. 60 J. Hennig, H. H. Limbach, J. Magn. Reson. 1982, 49, 322–328. 61 A. A. Bothner-By, R. L. Stephens, J. Lee, C. D. Warren, R. W. Jeanloz, J. Am. Chem. Soc. 1984, 106, 811–813. 62 A. Bax, D. G. Davis, J. Magn. Reson. 1985, 63, 207–213. 63 H. H. Limbach, J. Hennig, J. Chem. Phys. 1979, 71, 3120–3124; H. H. Limbach, J. Hennig, J. Stulz, J. Chem. Phys. 1983, 78, 5432–5436 ; H. H. Limbach, J. Chem. Phys. 1984, 80, 5343–5345. 64 A. Sarai, Chem. Phys. Lett. 1981, 83, 50– 54 ; A. Sarai, J. Chem. Phys. 1982, 76, 5554–5563; A. Sarai, J. Chem. Phys. 1984, 80, 5341–5343. 65 D. K. Maity, R. L. Bell, T. N. Truong, J. Am. Chem. Soc. 2000, 122, 897–906. 66 (a) R. D. Kendrick, S. Friedrich, B. Wehrle, H. H. Limbach, C. S. Yannoni, J. Magn. Reson. 1985, 65, 159–161; (b) B. Wehrle, H. H. Limbach, Chem. Phys. 1989, 136, 223–247. 67 T. J. Butenhoff, C. B. Moore, J. Am. Chem. Soc. 1988, 110, 8336–8341. 68 J. D. Thoburn, W. Lttke, C. Iber, H. H. Limbach, J. Am. Chem. Soc. 1996, 118, 12459–12460. 69 C. G. Hoelger, B. Wehrle, H. Benedict, H. H. Limbach, J. Phys. Chem. 1994, 98, 843–851. 70 U. Langer, C. Hoelger, B. Wehrle, L. Latanowicz, E. Vogel, H. H. Limbach, J. Phys. Org. Chem. 2000, 13, 23–34.
71 B. Wehrle, H. Zimmermann,
72
73
74
75
76
77
H. H. Limbach, J. Am. Chem. Soc. 1988, 110, 7014–7024. (a) B. H. Meier, F. Graf, R. R. Ernst, J. Chem. Phys. 1982, 76, 767–774; (b) A. Stckli, B. H. Meier, R. Kreis, R. Meyer, R. R. Ernst, J. Chem. Phys. 1990, 93, 1502–1520; (c) A. Heuer, U. Haeberlen, J. Chem. Phys. 1991, 95, 4201–4124. (a) J. L. Skinner, H. P. Trommsdorff, J. Phys. Chem. A 1988, 89, 897–907; (b) R. Meyer, R. R. Ernst, J. Chem. Phys. 1990, 93, 5518–5532; (c) Y. Kim, J. Am. Chem. Soc. 1996, 118, 1522–1528; (d) Y. Kim, J. Phys. Chem. A 1998, 102, 3025–3036. Q. A. Xue, A. J. Horsewill, M. R. Johnson, H. P. Trommsdorff, J. Chem. Phys. 2004, 120, 11107–11119. P. M. Tolstoy, P. Schah-Mohammedi, S. N. Smirnov, N. S. Golubev, G. S. Denisov, H. H. Limbach, J. Am. Chem. Soc. 2004, 126, 5621–5634. F. Aguilar-Parrilla, G. Scherer, H. H. Limbach, M. C. Foces-Foces, F. H. Cano, J. A. S. Smith, C. Toiron, J. Elguero, J. Am. Chem. Soc. 1992, 114, 9657–9659. (a) A. Baldy, J. Elguero, R. Faure, M. Pierrot, E. J. Vicent, J. Am. Chem. Soc. 1985, 107, 5290–5291; (b) J. A. S. Smith, B. Wehrle, F. Aguilar-Parrilla, H. H. Limbach, M. C. Foces-Foces, F. H. Cano, J. Elguero, A. Baldy, M. Pierrot, M. M. T. Khurshid, J. B. Larcombe-McDouall, J. Am. Chem. Soc. 1989, 111, 7304–7312; (c) F. Aguilar-Parrilla, C. Cativiela, M. D. Diaz de Villegas, J. Elguero, M. C. Foces-Foces, J. I. G. Laureiro, F. H. Cano, H. H. Limbach, J. A. S. Smith, C. Toiron, J. Chem. Soc., Perkin 2 1992, 1737–1742; (d) J. Elguero, G. I. Yranzo, J. Laynez, P. Jim nez, M. Men dez, J. Cataln, J. L. G. De Paz, F. Anvia, R. W. Taft, J. Org. Chem. 1991, 56, 3942; (e) J. Elguero, F. H. Cano, M. C. FocesFoces, A. Llamas-Saiz, H. H. Limbach, F. Aguilar-Parrilla, R. M. Claramunt, C. Lopez, J. Heterocycl. Chem. 1994, 31, 695–700; (f) F. Aguilar-Parrilla, F. M nnle, H. H. Limbach, J. Elguero, N. Jagerovic, Magn. Reson. Chem. 1994,
References 32, 699–702; (g) A. Llamaz-Saiz, M. C. Foces-Foces, F. H. Cano, P. Jimenez, J. Laynez, W. Meutermans, J. Elguero, H. H. Limbach, F. Aguilar-Parrilla, Acta Crystallogr., Sect. B 1994, 50, 746–762; (h) F. Aguilar-Parrilla, H. H. Limbach, M. C. Foces-Foces, F. H. Cano, N. Jagerovic, J. Elguero, J. Org. Chem. 1995, 60, 1965–1970; (i) J. Elguero, N. Jagerovic, M. C. FocesFoces, F. H. Cano, M. V. Roux, F. Aguilar-Parrilla, H. H. Limbach, J. Heterocycl. Chem. 1995, 32, 451–456; (j) C. Lopez, R. M. Claramunt, A. Llamas-Saiz, M. C. Foces-Foces, J. Elguero, I. Sobrados, F. Aguilar-Parrilla, H. H. Limbach, New J. Chem. 1996, 20, 523–536; (k) C. Hoelger, H. H. Limbach, F. Aguilar-Parrilla, J. Elgu ro, O. Weintraub, S. Vega, J. Magn. Res. 1996, A120, 46–55; (l) J. Catalan, J. l. M. Abboud, J. Elguero, Adv. Heterocycl. Chem. 1987, 41, 187; (m) F. Toda, K. Tanaka, M. C. FocesFoces, A. Llamas-Saiz, H. H. Limbach, F. Aguilar-Parrilla, R. M. Claramunt, C. Lopez, J. Elguero, J. Chem. Soc., Chem. Commun. 1993, 1139–1142; (n) F. Aguilar-Parrilla, R. M. Claramunt, C. Lopez, D. Sanz, H. H. Limbach, J. Elguero, J. Phys. Chem. 1994, 98, 8752–6760; (o) C. Foces-Foces, A. Echevarr a, N. Jagerovic, I. Alkorta, J. Elguero, U. Langer, O. Klein, M. Minguet-Bonveh , H. H. Limbach, J. Am. Chem. Soc. 2001, 123, 7898–7906. 78 J. L. G. de Paz, J. Elguero, M. C. FocesFoces, A. Llamas-Saiz, F. AguilarParrilla, O. Klein, H. H. Limbach, J. Chem. Soc. Perkin Trans. 2 1997, 101–109. 79 (a) S. Schweiger, B. Hartke, G. Rauhut, J. Phys. Chem. A 2003, 107, 9668–9878; (b) S. Schweiger, B. Hartke, G. Rauhut, Phys. Chem. Chem. Phys. 2005, 7, 493– 500. 80 D. F. Brougham, R. Caciuffo, A. J. Horsewill, Nature 1999, 397, 241–243. 81 T. Vangberg, A. Ghosh, J. Phys. Chem. B 1997, 101, 1496–1497.
82 (a) F. M nnle, I. Wawer, H. H. Limbach,
Chem. Phys. Lett. 1996, 256, 657–662; (b) R. Anulewicz, I. Wawer, T. M. Krygowski, F. M nnle, H. H. Limbach, J. Am. Chem. Soc. 1997, 119, 12223– 12230. 83 W. Al-Soufi, K. H. Grellmann, B. Nickel, J. Phys. Chem. 1991, 95, 10503–10509. 84 E. F. Caldin, S. Mateo, J. Chem. Soc., Faraday Trans.1 1975, 71, 1876–1904. 85 (a) A. I. Prokofiev, N. N. Bubnov, S. P. Solodnikov, M. I. Kabachnik, Tetrahedron Lett. 1973, 2479–2480; (b) N. N. Bubnov, S. P. Solodnikov, A. I. Prokofiev, M. I. Kabachnik, Russ. Chem. Rev. 1978, 47, 549–571. 86 K. Loth, F. Graf, H. Gnthardt, Chem. Phys. 1976, 13, 95–113. 87 H. H. Limbach, D. Gerritzen, Faraday Discuss. Chem. Soc. 1982, 74, 279–296. 88 S. F. Bureiko, G. S. Denisov, N. S. Golubev, I. Y. Lange, React. Kinet. Catal. Lett. 1979, 11, 35–38. 89 A. Fernndez-Ramos, Z. Smedarchina, J. Rodr guez-Otero, J. Chem. Phys. 2001, 114, 1567–1574. 90 D. B. Northrop, Acc. Chem. Res. 2001, 34, 790–797. 91 A. Kohen, R. Cannio, S. Bartolucci, J. P. Klinman, Nature 1999, 399, 496– 499. 92 A. Kohen, Kinetic Isotope Effects as Probes for Hydrogen Tunneling in Enzyme Catalysis. In Isotope Effects in the Biological and Chemical Sciences, A. Kohen, H. H. Limbach (Eds.) Taylor & Francis, Boca Raton FL 2005, Ch. 28, pp. 743–765. 93 D. Gerritzen, H. H. Limbach, Ber. Bunsenges. Phys. Chem. 1981, 85, 527–535. 94 C. S. Leung and E. Grunwald, J. Phys. Chem. 1970, 74, 696–701. 95 E. J. King, in Physical Chemistry of Organic Solvent Systems, A. Covington, T. Dickinson (Eds.), Plenum Press, New York 1973, Ch. 3, pp. 331–403. 96 V. Gold, S. Grist, J. Chem. Soc. B, 1971, 1665–1670. 97 E. Grunwald, C. F. Jumper, S. Meiboom, J. Am. Chem. Soc. 1963, 84, 4664–4671.
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7 Intra- and Intermolecular Proton Transfer and Related Processes in Confined Cyclodextrin Nanostructures Abderrazzak Douhal
7.1 Introduction and Concept of Femtochemistry in Nanocavities
In this chapter, we discuss the recent progress made in studying intramolecular and intermolecular reactions of proton (or hydrogen atom) transfer using cyclodextrins as host for selected systems undergoing these kinds of photoinduced reaction. The experiments establish the ultrafast nature of proton motion to convert a trapped reactant to a trapped photoproduct. Upon caging a molecule in a molecular pocket (nanochamber), it produces a confined structure with interesting physical and chemical properties. It reduces the degrees of freedom available to the molecule to move along the reaction coordinates, and confines the wavepacket in a small area of propagation [1, 2]. Therefore, by reducing the space for molecular relaxation, it makes the system robust and immune to transferring “damage” or heat over long distances. Following an ultrafast electronic excitation of the embedded guest in a nanochamber, the nascent wavepacket is trapped in a small area of the potential-energy surface (caged wavepacket), and its evolution along this surface and the subsequent relaxation dynamics to other states (or through chemical reactions) will funnel and will be controlled by the restricted confined geometry. The system has open only a few channels to move along the reduced potential-energy surface, and the neighboring water molecules may direct its evolution. A similar situation occurs in semiconductors where the conduction electrons are not only particles but also waves. So, trapped in a confined area, electrons can only have energies dictated by the present wave patterns that will fit in this small region. Therefore, in a similar but easy way, a free electron can then possibly be trapped by a molecule-chamber entity such as cyclodextrins, calixarenes, Cram boxes, zeolites, as has been realized in solution and in finite clusters. Cooling (or vibrational relaxation) due to a fast (picosecond regime) exchange of heat with the environment (caging medium) might be also controlled by changing the nature or the size of the cage. It is well known that the nature of the solvent plays a key role in the issue of a chemical reaction, in bulk solvent and in a cavity. Understanding the ultrafast dynamics for different cages may help one to understand better the cataHydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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lytic mechanism in these cavities, like those involved in enzymes and zeolites. In addition, an interesting phenomenon in studying nanocavity solvation is the slow solvation of water confined in a nanospace such as those offered by cyclodextrins. This special water is reminiscent of that located at the surface of biological molecules [3–23]. Here, we will focus on fast (picosecond regime) and ultrafast (femtosecond regime) dynamics of proton (or H-atom) transfer and related events that may occur before or/and after the atomic rearrangement in selected systems trapped in cyclodextrin cavities. The information is relevant for a better understanding of many systems where confinement is important for reactivity and function. To this end, we first give a short overview of the photochemistry and photophysics of CD complexes.
7.2 Overview of the Photochemistry and Photophysics of Cyclodextrin Complexes
The ability of cyclodextrins (CDs) (Fig. 7.1), oligosaccharides of six, seven, or eight D-glucopyranose (C6H10O5) units (the well known ones are a-, b-, and c-CD with a diameter of ~ 5.7, 8 and 9.5 , respectively), to encapsulate organic and inorganic molecules has led to intensive studies of their inclusion complexes [24–32]. The relatively hydrophobic interior and hydrophilic exterior of their molecular pockets make them suitable hosts for supramolecular chemistry and for studying the spectroscopy and dynamics of several molecular systems [33–75]. Therefore, the hydrophobic nanocavity of such a host offers an opportunity for studying size-controlled nanoenvironment effects like reduced degrees of freedom of the guest and modified coupling to the heat reservoir. Several studies on CD complexes with aromatic molecules using steady-state and nanosecond spectroscopy have been reported. These studies aimed to understand the photophysical and photochemical behavior of organic guests such as fluorescence and phosphorescence enhancement, excimer/exciplex formation, photocleavage, charge and proton transfer, energy hopping, and cis-trans photo-
d
OH
HO O OH
O
n n= d(Å)=
6 5.7 α-CD
7 8.5 β-CD
8 9.5 γ-CD
Figure 7.1 Structures of cyclodextrins (CDs) and approximate values of the largest diameter of their nanocages.
7.3 Picosecond Studies of Proton Transfer in Cyclodextrin Complexes
isomerization. Most of these reports describe the effect of molecular restriction due to the cavity size of the host and protection of the guest (from quenchers such as oxygen molecules and H-bonding interaction with the medium – water) provided by the CD cavity and its low polarity relative to that of water, on the photophysical and photochemical properties of the encapsulated guest. The presence of H-bonding, electron accepting and donating groups, and twisting groups influences the electronic properties of the encapsulated guest. The value of the inclusion equilibrium constant depends on several parameters where H-bonding, polarity, relative size of the guest to that of the cavity, play an important role for the stability of the relative population of the confined system. Both enthalpic and entropic terms determine the energetic balance between the free and encapsulated guest. Some of the studies have reported the formation of higher stochiometries (1:2, 2:1 and 2:2) or even the formation of nanotubes where a large number of CD capsules are involved [3–33, 60–68]. A general rule to predict the effect of CD on the absorption and emission properties of dyes upon encapsulation cannot be found as the static and dynamic interactions are specific to the studied systems and may change markedly in the excited state [44–75].
7.3 Picosecond Studies of Proton Transfer in Cyclodextrin Complexes 7.3.1 1¢-Hydroxy,2¢-acetonaphthone
One of the molecules which shows, upon photoexcitation, an internal proton transfer and a twisting motion in a confined nanostructure of CD is 1¢-hydroxy-2¢acetonaphthone (HAN) (Fig. 7.2A) [2]. HAN has been studied in gas [76–79], liquid [80–82], polymers [80], and in CD nanocavities [82–84]. The excited dye undergoes an ultrafast (less than 30 fs) excited-state intramolecular proton-transfer (ESIPT) reaction followed by a subsequent twisting motion along the C–C bond when the medium allows it (Fig. 7.2A). The formed excited phototautomer, K*, a keto-type structure where the carbonyl group is on the aromatic ring, may experience an internal rotation producing a twisted keto rotamer (KR*). The C–C bond linking the aromatic part to the protonated acetyl group shows double bond character due to the transfer of the proton and electronic charge rearrangement, as suggested by the ground- and excited-state ab initio calculations [85, 86]. In the presence of CD, the stochiometry of the inclusion complex formed depends on the nature and size of the cage. For b- and c-CD, the complex has a 1:1 stochiometry, while for a-CD, the stochiometry is 1:2, HAN:(a-CD)2 (Fig. 7.2B). The spectroscopy and dynamics of the complexes have also been found to depend on the nature of the cage (Fig. 7.3) [83, 84]. Compared to the observation using water or tetrahydrofuran (considered as a solvent with a polarity comparable to that of CD) the following picture has been provided. Due to the small size of the a- and b-CD cages, the rotation of the protonated acetyl group of the guest is
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7 Intra- and Intermolecular Proton Transfer and Related Processes
A
E*
K*
KR*
B
Figure 7.2 (A) Schematic representation of photoinduced proton-transfer reaction in the enol form (E*) and twisting motion in the keto-type (K*) structure to generate the ketorotamer (KR*) of excited 1¢-hydroxy,2¢-acenaphthone (HAN). (B) Illustration of HAN molecule in water and complexed with one or two CD nanocavities.
restricted, giving rise to a stronger K* emission (460 nm). For c-CD, with a larger cage, the conversion of K* to KR* is allowed and the resulting emission is at 500 nm and the phototautomers are more fluorescent due to the protection (from quenching by formation of an H-bond with water and O2) provided by the cage. The lifetime of caged KR* is in the ns regime, in contrast to that of free K* (about 90 ps). That of caged K* is on the sub-ns or ns time scale. Depending on the size of the CD cavity, the protonated acetyl group can be found inside or outside the cage. So, its twisting to produce KR* and thus connecting with nonradiative channels depends on the degree of confinement and stoichiometry of the complex (Fig. 7.3). The reorientation times of the guest and of the guest:host complexes have been examined using emission anisotropy experiments. For 1:1 complexes, the reorientation times are about 70 and 50 ps for b-CD and c-CD, respectively.
Intensity(a.u.)
7.3 Picosecond Studies of Proton Transfer in Cyclodextrin Complexes
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15
20
Time / ns Figure 7.3 Magic-angle emission decays of HAN in water and in the presence of mM of CDs. The inset shows the emission spectra of HAN in water and complexed to CDs [82–84].
Therefore, within a cage of small size (b-CD) the internal molecular rotation in the trapped guest is restricted and its reorientation time is longer. For a larger cage, internal rotation can occur, producing a caged KR* rotamer, in full agreement with the emission spectral position, and fluorescence lifetime (Fig. 7.3). As expected, the overall rotational time of the complex (HAN:CD) increases with the size of the caging entity: 745 ps and 1.1 ns for b-, and c-CD complexes, respectively [83]. For, a-CD complexes (the smallest cavity amongst the CDs) the situation is different as the complexes involve one or two H-bonded linked CD cavities (Fig. 7.2) [84]. Caged and photoproduced K* in 1:1 complexes has an emission lifetime of ~ 90 ps, similar to that of free K* in water, while that found in the 1:2 complex is about 1 ns. For 1:1 complexes, the protonated acetyl group of K* is found outside the CD cavity and it should not experience any restriction for twisting to produce caged KR* (which was observed). For 1:2 complexes, the restriction dictated by the cavity of 2 CD does not allow the formation of KR*, but enhances the ns-emission of caged K*, as it is now protected from quenchers and twisting nonradiative channels. The emission behavior of caged HAN in a-CD led to a 40 nm blue shift (shortest wavelengths) in the time-resolved emission spectra when the gating time increased (Fig. 7.4). The COHCH3 rotation of K* to produce KR* involves an energy gain of about 16 kJ mol–1, close to the energy gap (~ 24 kJ mol–1) between these structures in the gas phase obtained using theoretical calculations [86]. Rotational times of the complexes have also been measured (Fig. 7.4). In pure solvents, like water and tetrahydrofuran, the rotational times are 70 and 35 ps, respectively. These values show the role of H-bonding interactions with the solvent (water) and the involvement of the solvation shell (water) in the friction dynamics of the dye. The rotational time of the caged phototautomers in a-CD cages depends on the emission wavelength and varies from 50 to 180 ps. The global rotational time of the 1:2 complex is almost constant, ~ 950 ps. This value accords with that estimated for two linked CD using the hydrodynamic theory under stick conditions [87]. The variation of the shortest time with the wave-
227
7 Intra- and Intermolecular Proton Transfer and Related Processes 1.0 1 ns
0.2
70 ps
0.5
HAN:H2O
(a.u.)
Intensity
0.3 Anisotropy
228
HAN:(α-CD)2
0.0 440 480 520 560 Wavelength / nm
α- CD (110 mM) φ1 ∼ 130 ps (13 %) φ2 ∼ 950 ps (87 %)
0.1
0.0
THF φ ∼ 35 ps Water φ ∼ 70 ps
0
1 2 Time / ns
3
Figure 7.4 Anisotropy decays of HAN in water, tetrahydrofuran (THF) and in the presence of a-CD. The solid lines are the best fits using a single or a bi-exponential function giving the indicated rotational times. The inset also displays the emission spectra of the inclusion complexes gated at 70 ps and 1 ns [84].
length of emission indicates the existence of several rotamers (or conformers), and thus agrees with the involvement of 1:1 and 1:2 complexes. The result indicates that the size (space domain) of the nanocavity of the host (1 or 2 CD) determines the photodynamics (time domain) from ps to ns regime, and emission spectroscopy (shift by about 40 nm) of the nanostructure. 7.3.2 1-Naphthol and 1-Aminopyrene
While HAN shows an ESIPT reaction between two groups both located on the molecular frame of the dye and does not need solvation for the occurrence of internal proton motion, 1- and 2-naphthol, which are among the most studied aromatic systems, show an excited-state intermolecular proton transfer to the medium (water, alcohols) [88–96]. The produced anionic structure emits at the blue side of the normal form. The effects of CD on the intermolecular proton-transfer reaction from 1-naphthol (1-NP) [97, 98] to water and from water to 1-aminopyrene (1-AP) [98] have been studied by emission spectroscopy. For 1-NP in pure water, the decay of the 360 nm emission band (that of the neutral reactive species leading to the anionic one emitting at the blue side, 460 nm) was fitted with a 36 ps exponential component [98]. In the presence of b-CD, the decay at 370 nm needed two exponential functions with time constants of 700 ps (75%) and 1600 ps (25%) [98]. The average time constant for deprotonation of 1-NP in the presence of b-CD (1:1
7.3 Picosecond Studies of Proton Transfer in Cyclodextrin Complexes
stochiometry) is 930 ps. The difference in the deprotonation times for free (36 ps) and caged (930 ps) guest was interpreted as a signature of different mechanisms for proton transfer reactions from 1-NP to water [98]. The time for deprotonation of the caged 1-NP in other media such as micelles (600 ps, 1900 ps) [78], and polymer-surfactant aggregate (1600 ps, 5300 ps) [99, 100] was found to be much slower (or almost blocked) compared to that of uncomplexed dye [99]. For 1-AP, the rate of the proton-transfer reaction from water to the dye was found to increase upon formation of 1:1 complexes involving b-CD [98]. To explain this observation, the authors suggest using geometrical factors for the confined structures (Fig. 7.5) which influence the dynamics of the proton-transfer reaction. For geometries where the amino group is found near the hydroxy rims of b-CD, the rate of proton transfer is affected by the microenvironment due to the cage and is enhanced by a factor of 2 [98]. This rate is similar to that observed in a mixture of water : simple alcohols with comparable molar ratio to water. For geometries where the amino group is further away from the hydroxy rims, the amino group is then surrounded by water molecules. The rate constant of the protontransfer reaction is not affected by complexation and is similar to that of uncomplexed 1-AP. Under the experimental conditions of the study (dye:CD ratio, pH and ps-time resolution) the authors suggest that the former confinement is favored by a ratio of 1.5:1 [128]. By comparing to the behavior when using ethanol–water mixtures, the authors proposed to model the CD effect on the protontransfer rate constant of 1-NP and of 1-AP by that of suitable homogeneous mixtures of water and organic solvents. However, such a molecular model cannot be realistic as it does not take into account several microscopic differences like those of hydrophobic interactions, solvation of the transition state, the proton jump mechanism once the atom was ejected, diffusion and geminate recombination of the anion and cation, different H-bond networks with different cooperativities, and the different friction factors of both media, to cite a few. It has been found that the lifetime of the H-bond of a water molecule with that of an organized media (polar headgroup of a micelle) is about 13 times longer than that of the water– water H-bond, and 3.5 kcal mol–1 is needed to “liberate” the bound water molecule from the polar head of the micelle [101]. Furthermore, careful analysis of the emission decay of 1-NP in water leads tono exponential behavior [95], and change in dielectric constant [102], solvation time and diffusion should be taken into account, even in organized media [94]. Thus, to understand the origin of the slow component of deprotonation of 1-NP in CD or in organized media, and most
H2N
H2N
Figure 7.5 Proposed confined geometries of 1-aminopyrene:b-CD complexes [98].
229
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7 Intra- and Intermolecular Proton Transfer and Related Processes
probably of other dyes showing slow solvation dynamics (time constant longer than 300 ps or so), one has to take into account several factors influencing the microscopic and heterogeneous solvation, the self motions of the guest and host for an efficient encounter (sub-nanosecond to microsecond regime) and related H-bond networks dynamics [23]. Therefore, the slowest time constant (more than 100 ps) assigned to solvation dynamics might contain strong contributions from the above factors which would not be included in solvation processes in a classical restricted terminology.
7.4 Femtosecond Studies of Proton Transfer in Cyclodextrin Complexes 7.4.1 Coumarins 460 and 480
Coumarins have been the subject of many steady-state and ultrafast studies [103– 113]. They have been also studied in CD cavities for different purposes [26, 113– 122]. For coumarin 480 (C480) and coumarin 460 (C460) in aqueous solutions, the blue shift in the emission spectrum and the increase in the fluorescence lifetimes in the presence of c-CD have been assigned to the formation of an inclusion complex with CD [120–122]. Molecular mechanics calculations for the C460/c-CD complex suggest that the most stable inclusion complex has the carbonyl end of the guest near the narrower, primary-OH end of the host, and the amino end group of C460 near the secondary-OH side of the cavity [122]. The calculations also suggest the formation of an H-bond between the carbonyl group of the guest and two hydroxy groups of the host. The time-dependent Stokes shift of the emission of c-CD:coumarin complexes has been studied [122]. The solvation time of the excited complex ranges from < 50 fs to 1.2 ns, and most of the solvation takes place within 1 ps. The fast component of the solvation decay for both complexes (C480:c-CD and C460:c-CD) is similar to that in bulk water suggesting that the first solvation shell does not dominate the solvent response, and it is mainly due to a collective response of water molecules found near the guest and outside the cavity. However, at longer times the solvation dynamics in c-CD is at least 3 orders of magnitude slower when compared to that observed in water [122]. For C480 : cCD three components of the slow relaxation were observed: 13, 109 and 1200 ps. For C480 : c-CD and C460 : c-CD entities, molecular dynamics simulations suggest the presence of 13 and 16 water molecules, respectively, inside the cavity [122]. These water molecules are symmetrically distributed around the guest, with one molecule of water near the oxygen of the carbonyl group of the guest. The authors suggested that the slower relaxation components may be due to motion of the guest in and out of the restrictive host, fluctuations of the CD ring, or orientation of highly constrained water molecules [122]. A comparable number of water molecules in the first solvation shell of atomic solutes in pure water have been calculated [123].
7.4 Femtosecond Studies of Proton Transfer in Cyclodextrin Complexes
7.4.2 Bound and Free Water Molecules
To get a better insight into the solvation dynamics of coumarin within CD a multishell continuum model and molecular hydrodynamic theory have been used [124]. The theory can explain solvation dynamics having time constants of less than ~ 100 ps or so where the contribution of self-motion of the (large) probe (and of a large host) is still not important in the solvation dynamics of the probe. The theoretical results indicated that the contribution of the translational component is small, while the orientational component governs the polarization relaxation. For a short time scale (1 ps), inclusion of the intermolecular vibrational mode in the dielectric model leads to good agreement between the calculated and experimental solvation time correlation functions [124]. For a longer time scale (more than 100 ps or so), although the theory does not reproduce well the experimental observation, it suggests that the slower component is controlled by the rotational motion which is affected by the freezing of translational modes of water inside the restricting nanocavity. The models used for the simulations cannot describe properly the effects of the CD rings on the solvent dynamical modes [124]. Note also that at least two kinds of water molecules can be found within CD or at the gate and proximity of cyclodextrins: water molecules bound to the hall of the cage where two types of intermolecular H-bond may act due to the H-bond donating and accepting nature of water and CD, and structurally different networks of water molecules in the vicinity of the host. To some extent, this prevents them playing a more important role in the ultrafast solvation dynamics. Comparable situations have been suggested for water at the interface of micelles [2, 14–16, 21– 23, 124]. Two geometrical relaxations are key elements for the H-bonds¢ cooperativity and related solvation: the H-bond coordination of water molecules (the number of water molecules involved in the process) and the O...O distance shrinkage [125]. The number of water molecules trapped inside CD (up to seven molecules for crystalline hydrated b-CD) [126] or bound to the gates is limited and the energy to cooperate is increased when compared to the situation in bulk water. Neutron scattering experiments on b-CD at room temperature [127] showed that the disorder of water molecules inside the cavity is dynamic in nature, and involves jump time constants of about 10–100 ps. The conformational flexibility of the glycopyranoside units and the dynamics of disorder of water can influence the solvation dynamics of CD. Molecular dynamic simulations of water diffusion in CD with different degrees of hydration, and in water, have been performed [128]. The calculations show that water molecules found outside the cavity have access to the main diffusion pathway. The results also suggest that the diffusion constant for transport of water molecules along the main diffusion pathway (0.007 2 ps–1), parallel to the crystallographic axis b is about 1/30 of the value in bulk water at room temperature, and 1/53 at 320 K [128]. The water molecules outside the main diffusion pathway have an easy and fast (ps time scale) access to this channel. Interestingly, no significant change in the diffusion constants and pathways with the relative humidity of crystalline b-CD was found. For the coumarin-480 trapped
231
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7 Intra- and Intermolecular Proton Transfer and Related Processes
in CD, the water molecule H-bonded to the carbonyl group of the coumarin, as suggested by calculations [122], can be involved in an H-bond network formed by water molecules at the gate of the host and may cause intramolecular chargetransfer dynamics leading to slower solvation dynamics. Furthermore, the slow motion of water molecules at both gates of cyclodextrins has been observed for guests able to show excited-state proton-transfer reactions [129]. For 2-naphthol and 7-hydroxyquinoline [129], the change in the proton-transfer rate constant upon encapsulation by CD is clear evidence that the H-bond network at the gates of CD is special and plays a crucial role in reaction and solvation dynamics of the trapped guest. Furthermore, molecular dynamics simulations have shown a nearly 50% decrease in the dielectric constant of water confined in a nanocavity [130]. Such a decrease will influence the electrostatic field around the guest and may therefore cause large changes in its dynamics, especially when the probe suffers significant change in its dipole moment upon electronic excitation as in the case of the coumarins. Indeed, several studies of water involving micelles, biological systems and channels have shown significant decrease in polarity [131–136] and slowing down of the rate constant for the relaxation of water molecules inside these media [137–152]. Water molecules confined in such environments exhibit a larger degree of spatial and orientational order than in the bulk phase with the formation of well defined molecular layers in the vicinity of the cavity or channel surface [137–152]. The water at this special layer (comparable to biological water) plays a crucial role in the activity of many biological molecules such as enzymes, proteins and DNA. The current view of protein–water interactions is associated with a variety of functional roles, some of which are specific to a given system, whereas others are general to all proteins. The water molecules associated with the surface of proteins are in constant exchange with the bulk solvent, and the related nonlinear dynamics plays a key factor in the function and stability: water is a rate-limiting partner in biological and biochemical processes. For recent reviews on this topic, Ref. [7] reviews protein–water interaction in a slow dynamic world; and Ref. [21] reviews femtosecond dynamics of macromolecular hydration where biological water is critical to the stability of the structure and function of the biological system. Using fs resolution, two residence times of water at the surface of two proteins have been reported (Fig. 7.6) [21]. The natural probe tryptophan amino acid was used to follow the dynamics of water at the protein surface. For comparison, the behavior in bulk water was also studied. The experimental result together with the theoretical simulation-dynamical equilibrium in the hydration shell, show the direct relationship between the residence time of water molecules at the surface of proteins and the observed slow component in solvation dynamics. For the two biological systems studied, a “bimodal decay” for the hydration correlation function, with two primary relaxation times was observed: an ultrafast time, typically 1 ps or less, and a longer one typically 15–40 ps (Fig. 7.7) [21]. Both times are related to the residence period of water at the protein surface, and their values depend on the binding energy. Measurement of the OH librational band corresponding to intermolecular motion in nanoscopic pools of water and methanol
7.4 Femtosecond Studies of Proton Transfer in Cyclodextrin Complexes
confined in reverse micelles has been reported [153]. The result shows that the librational band, which has its maximum at 670 cm–1 in the bulk liquids, shifts to lower frequencies and its shape changes considerably as the size of the reverse micelle decreases. A two-state model based on bound and free water fractions of water (or methanol) was used to fit the shape of the librational band [153]. Using large-scale atomistic molecular dynamics simulation, it has been proposed, for an aqueous micelle solution of cesium perfluorooctane, that water molecules at the
A
B
Figure 7.6 (A) An illustration of the dynamic equilibrium of water molecules at the hydration layer of a protein, with bound (1), quasi-free (2) and free water molecules (3). (B) The potential energy for the exchange [21].
233
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7 Intra- and Intermolecular Proton Transfer and Related Processes
interface fall into two categories: bound and free, with a ratio of 9:1 [22]. The water molecules bound to the hall can be further classified on the basis of the number of H-bonds linking them to the polar headgroups of the micelle. The entropy contribution is found to be critical in determining the relative populations of the free and bound water molecules. It has been shown also that the H-bond dynamics of
Figure 7.7 Time-resolved hydration process for the proteins Sublitisin Carlsberg (SC) and Monellin (Mn). The time evolution of the constructed correlation function is shown for the protein SC (top), the Dansyl dye bonded SC (middle), and for the protein Mn (bottom). The inset of each part shows the corresponding time-resolved anisotropy r(t) decay [21].
7.4 Femtosecond Studies of Proton Transfer in Cyclodextrin Complexes
two tagged water molecules bound to the polar heads of a micellar surface is almost 13 times slower than that found in bulk solution. Water molecules can remain bound to the micellar surface for more than 100 ps [22]. In general, interfacial water is energetically more stable than bulk water, and this will affect its ability to translate, and possibly to reorient. The finding may help to explain the origin of the universal slow relaxation at complex aqueous interfaces of several systems where water resides at their surface or interfaces. Using ultrafast optical Kerr effects spectroscopy, the orientational dynamics of liquids (including water) in nanoporous sol–gel glasses has been studied [16]. In the pore, a ~ 3 ps time constant was observed and assigned to orientational relaxation of water in a hydrophobic pore, in agreement with a previous report [17]. At the pore surface, the orientational relaxation time of water was found to be much slower (15–35 ps) and is dependent on the size of the pore (Fig. 7.8). However, for all pore sizes, the water relaxation at the surfaces is faster for hydrophobic sites than for hydrophilic ones. Thus, the nature of the surface (involving hydrophilic or hydrophobic sites) is a key factor in the dynamics of the confined water molecules as it will influence the number of H-bonds involved in the networks. As noted [16], the rate of relaxation at the surfaces depends on the pore diameter, suggesting that water relaxation at these sites is highly cooperative, and may extend out to zones significantly larger than that defined by a single water molecule. An average solvation time of 220 ps for C-480 in a sol–gel glass of pore size 10–20 has been reported [154]. Taking into account the size of the probe and that of the pores, the rotational mobility of the guest should be restricted. Furthermore, the presence of the polar guest inducing an electric field within the pores, and enhancing the local polarization field, should slow down the motion of the trapped water molecules and thus cause a slowing in solvation dynamics of C-480 in the sol–gel matrix. For ethanol in sol–gel glass the average nonexponential behavior of the solvation time of Nile Blue A is about 19 ps and 36 ps within 75 and 50 average pores, respectively [155]. Within a polyacrylamide hydrogel having larger
Figure 7.8 log–log plot (solid lines) of the collective orientational correlation functions Ccoll for water confined in pores of different diameters (inserted number) and power-law fits (dashed lines). Lower and upper traces are for hydrophilic and hydrophobic pores, respectively [16].
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7 Intra- and Intermolecular Proton Transfer and Related Processes
pores, a solvation time shorter than 50 ps has been reported [156]. However, because of the limited time resolution of the ps-technique used, the fast component of the solvation dynamics of the above system is missing, and comparison of the result with those based on ultrafast techniques should be taken with caution. For CD, the water molecules of interest will H-bond with the hydrophilic gate of CD, leading to a decrease in the number of water–water H-bonds, and then to a slower dynamics. Inside the CD capsule, the surface is hydrophobic, but the small number (seven molecules for crystalline b-CDs) of water molecules which might be trapped there does not help to accelerate the caged dynamics, and then slow solvation is observed. In addition, a (polar) guest with strong local electric field may induce important local polarization of the trapped water molecules which decreases their orientational and translational motions, resulting in longer solvation times for confined structures when compared to bulk solutions. 7.5.3 2-(2¢-Hydroxyphenyl)-4-methyloxazole
Noncovalent interactions which govern the ligand-binding process during guest:host complexation have been studied using 2-(2¢-hydroxyphenyl)-4-methyloxazole (HPMO) as a probe (guest) and CD, micelles and human serum albumin (HSA) proteins as hosts (Fig. 7.9) [56–59]. The interest in the HSA protein caging effect
Figure 7.9 Right: X-ray structure of the Human serum albumin (HSA) protein and molecular structure of the used ligand HPMO. Left: Schematic representation of a normal micelle structure (left top); X-ray structure of b-cyclodextrin (left middle), and illustration of a protein–ligand recognition process (left bottom) [58].
7.4 Femtosecond Studies of Proton Transfer in Cyclodextrin Complexes
lies in the important biological function of this protein in body carriers and in the discovery of new drugs and the development of phototherapy [157–159]. The first report on a fs-dynamics study of HMPO in aqueous solutions of CD showed the confinement affect on the ultrafast dynamics of HPOM caged into a b-CD nanocavity (Fig. 7.10) [58]. After an ultrafast intramolecular proton-transfer reaction in the guest, a subsequent twisting motion can take place while the guest is restricted in the nanocavity. The produced keto-type phototautomer emits a large Stokes shifted band (~ 10 000 cm–1), and the wavelength of the maximum emission depends on the caging medium [57]. The blue transient behavior of HPMO in b-CD (430 nm) is different from that observed in 3-methyl pentane (3MP) (420 nm) [56]. Therefore, after the fs-excitation, the excited enol structure suffers a loss of aromaticity in the six-member ring and the electronic charge rapidly redistributes. This constitutes the driving force for the fs-proton transfer from the N...H–O to the N–H...O configuration [57, 160]. The charge redistribution barely changes the direction of the transition moment, as suggested by the ob-
A
530 nm 470 nm
Signal
420 nm 530 nm
B 470 nm 430 nm
0
5
10
15
20
time /ps Figure 7.10 Femtosecond-fluorescence transients gated at different wavelengths for HPMO in (A) 3-methyl pentane and (B) in water solution containing b-CD. The structures of HPMO and the 1:1 complex with b-CD are indicated. The observation wavelengths are inserted [56].
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7 Intra- and Intermolecular Proton Transfer and Related Processes
Figure 7.11 (a) Schematic illustration for direct proton-transfer reaction (trajectory I) and the one involving twisting motion (trajectory II). (b) Potential-energy curves along the reaction coordinate for trajectories I and II with the observed emission as indicated
schematically. The dashed line in (b) at S1 represents the potential energy for the protein environment. Note that rotamers of the nonplanar enol ground state can undergo proton transfer on the upper surface following an initial twist towards planarity [58].
served initial anisotropy (0.34) which is close to the ideal one (0.4) involving a parallel transition. A more detailed study of HPMO in dioxane and in different cavities has been reported [58]. Although the observed patterns of the fs-transients are similar, they have been divided into two groups of time-resolved fluorescence emission transients overlapping at 430 nm. For wavelengths shorter than 430 nm, all the transients show fast decays, while at wavelengths longer than 430 nm, the transient shows rise and decay. To explain the observed behavior, two trajectories of fs-dynamics of the guest have been proposed (Fig. 7.11) [58]. A direct one (I) in which the wavepacket moves quickly along the proton coordinate without any barrier, and a second one (II) where the system evolves along the repulsive potential toward the keto-type structure involving two types of motions: one is the proton motion at earlier times and the other is the twisting motion of the heterocyclic moieties at a later time. This last motion involves an energy barrier, as also predicted by calculations [160], and this will increase upon confinement by CD or by HSA protein, making the time for barrier crossing longer in these cavities. The times for both motions along trajectory II become significantly longer in the cavity of HSA protein. While the barrier crossing dynamics in dioxane occurs in 3 ps, in HSA it depends on the interrogated wavelength: 8, 20, and 37 ps at 415, 420 and 430 nm, respectively [58, 59]. To get more insight into the effect of confinement on the binding between HPMO and the host, time-resolved anisotropy measurements have been carried out [58]. The result (Fig. 7.12) shows a remarkable difference in the anisotropy decays, especially for the HSA protein case. While in dioxane, the rotational time constant (45 ps) is close to the expected one using hydrodynamic theory [58], this time increases with the rigidity of the host (97 ps for a micelle, 154 ps for b-CD
7.4 Femtosecond Studies of Proton Transfer in Cyclodextrin Complexes 0.4
t ~ ns
HSA
Anisotropy
0.3
0.2
t = 154 ps DM- β -CD
t = 97 ps
0.1
t =45 ps
0.0
Micelle p-Dioxane
0
100
200
300
400
Time (ps) Figure 7.12 Femtosecond-resolved fluorescence anisotropy decays of HPMO in Dioxane, normal micelle, DM-b-CD and HAS protein [58]. Note the effect of confinement on the rotational motion of the probe.
and ~ ns for HSA) indicating the increase of confinement. While the orientation relaxation of the guest is almost complete in the micelle after 500 ps, it persists for longer times in CD and HSA protein indicating the slowing down (CD) or absence (HSA) of diffusive orientational motion in these cavities. Proton NMR studies of HPOM in CD solutions suggested that the oxazole ring of the guest is fully inserted into the cavity of the host [58]. Using initial and final anisotropy values, the calculated average change in direction of the transition moment of the guest inside CD is about 30. For HSA, the high value of the initial anisotropy and the lack of any initial ultrafast decay indicate a strong hydrophobic interaction between the guest and the probe, the hindrance of molecular structure relaxation, and the rigidity of the local nanoenvironment where the guest is trapped. The observed result is consistent with X-ray structural studies showing a strong hydrophobic interaction between the ligand’s aromatic ring and the residues located at site I of the HSA protein [61]. 7.5.4 Orange II
A study of the femtosecond dynamics of Orange II (OII) encapsulated by CD has been reported [162]. In the presence of CD, OII only shows the formation of the 1:1 inclusion complex in which the confined structure (mode of penetration of the dye inside the cavity) depends on the nature of the host (Fig. 7.13). For OII:b-CD, the benzenesulfonate moiety is not included in the cavity, while for OII:c-CD, this part is protected by the molecular cage [163, 164]. The transient made from the ultrafast transient lens (UTL) measurements carried out in the absence and presence of b-, and c-CD showed a remarkable slowing down of the long component
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7 Intra- and Intermolecular Proton Transfer and Related Processes
SO3Na
Signal intensity (a.u.)
240
N
OH N
γ -CD
β -CD SO3Naa
N
OH N
0
Time delay (ps)
Figure 7.13 Decays of ultrafast transient lens (UTL) signal of Orange II in neutral water and in the presence of b- and c-CD [162].
in comparison with the dynamics of water solution (Fig. 7.13) [162]. This component changes from 13 ps in water to 28 and 140 ps in b- and c-CD, respectively. The difference was interpreted as a result of the formation of an H-bond between the OH groups of the guest and those of the cyclodextrin glucopyranose unit, hindering the free motion of the guest inside the nanocavity, lengthening the time for the intermediate state to isomerise, and slowing down the cooling process.
7.6 Concluding Remarks
In this chapter, we have examined the effect of the CD nanocavity on the fast and ultrafast events of a molecule trapped inside such a cavity. The results show that the degree of confinement which is reflected by the structure, the orientation of the guest, the docking and rigidity of the complex, and the polarity of the cage are the main factors that determine the issue of a created wavepacket in the cage, and therefore the spectral and dynamical behavior of the guest. Water molecules located inside and at both gates of CD have special properties reminiscent of biological water. Their restricted dynamics is slower than that found in bulk water. This abnormal behavior plays a key role in many chemical and biological processes, and one can consider taking advantage of this relatively slow response to explore new directions for research and potential applications in nano- and biotechnology. Finally, besides the studies of molecules showing proton-transfer reactions in CDs reviewed here, several proton-transfer studies have been carried out using other nanospaces provided by membranes, normal or reverse micelles, polymers, lipid vesicles, liquid crystals, sol–gels, dendrimers, proteins, DNA, zeolites and nanotubes.
References
Acknowledgment
This work was supported by the MEC and the JCCM (Spain) through projects CTQ2005-00114/BQU, MAT-2002-00301and PBI-05-046, respectively.
References 1 Zewail, A. H. J. Phys. Chem. A 2000,
104, 5660. 2 Douhal, A. Chem. Rev. 2004, 104, 1955. 3 Douhal, A. Acc. Chem. Res. 2004, 37, 3496. 4 Nandi, N., Bhattacharyya, K., Bagchi, B. Chem. Rev. 2000, 100, 2013. 5 Ringe, D. Curr. Opin. Struct. Biol. 1995, 5, 825. 6 Teeter, M. M., Yamano, A., Stec, B., Mohanty, U. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 11242. 7 Mattos, C. Trends Biochem. Sci. 2002, 27, 203. 8 Pratt, L. R., Pohorille, A. Chem. Rev. 2002, 102, 2671. 9 Marchi, M., Sterpone, F., Ceccarelli, M. J. Am. Chem. Soc. 2002, 124, 6787. 10 Ruffle, V., Michalarias, I., Li, J., Ford, R. C. J. Am. Chem. Soc. 2002, 124, 565. 11 Sarkar, N., Dutta, A., Das, S., Bhattacharyya, K. J. Phys. Chem. 1996, 100, 15483. 12 Riter, R. E., Willard, D. M., Levinger, N. E. J. Phys. Chem. B 1998, 102, 2705. 13 Mandal, D., Sen, S., Sukul, D., Bhattacharyya, K. J. Phys. Chem. B 2002, 106, 10741. 14 Faeder, J., Ladanyi, B. M. J. Phys. Chem. B 2001, 105, 11148. 15 Levinger, N. E. Science 2002, 298, 1722. 16 Farrer, R. A., Fourkas, J. T. Acc. Chem. Res. 2003, 36, 605. 17 Winkler, K., Lindler, J., Bursing, H., Vohringer, P. J. Chem. Phys. 2000, 113, 4674. 18 Otting, G. in Biological Magnetic Resonance, Ramakrishna, N., Berliner, L. J., (Eds.), Kluwer Academic/Plenum, New York 1999, Vol. 17, p. 485. 19 Nandi, N., Bagchi, B. J. Phys. Chem. B 1997, 101, 10954. 20 Bizzarri, A. R., Cannistraro, S. J. Phys. Chem. B 2002, 106, 6617.
21 Pal, S. K., Peon, J., Bagchi, B., Zewail,
A. H. J. Phys. Chem. B 2002, 106, 12376. 22 Pal, S., Balasubramanian, S., Bagchi, B.
Phys. Rev. E 67, 2003, 61502. 23 Bhattacharyya, K. Acc. Chem. Res. 2003,
36, 95. 24 Thoma, J. A., Stewart, L. in Starch:
Chemistry and Technology; Whistler, R. L., Paschall, E. F. (Eds.), Academic Press, New York 1965, p. 209. 25 Bender, M. L., Komiyama, M. (Eds.), Cyclodextrin Chemistry, Springer-Verlag, New York 1978. 26 Szejtli, J. L. (Ed.), Cyclodextrins and Their Inclusion Complexes, Akademiai Kiado, Budapest 1982. 27 Sjetli, J. L. (Ed.), Cyclodextrin Technology; Kluwer Academic Publishers, Dordrecht, The Netherlands 1988. 28 Wenz, G. Angew. Chem., Int. Ed. Engl. 1994, 33, 803. 29 Szejtli, J. L. in Comprehensive Supramolecular Chemistry, Atwood, J. L., Davies, J. E. D., MacNicol, D. D., Vogtle, (Eds.), Pergamon, New York 1996, Vol. 3. 30 Lehn, J. M. (Ed.) Supramolecular Chemistry: Concepts and Perspectives, VCH Publishers, New York 1995. 31 Balzani, V., Scandolla, F. (Eds.), Supramolecular Chemistry, Ellis Horwood, London 1991. 32 See the special issue of Chem. Rev. 1998, 98, 1743. 33 Bortolus, P., Monti, S. in Advances in Photochemistry, Neckers, D. C., Volman, D. H., von Bunau, G. (Eds.), John Wiley & Sons, New York 1996, Vol. 21, p.1. 34 Nag, A., Dutta, R., Chattopadhyay, N., Bhattacharyya, K. Chem. Phys. Lett. 1989, 157, 83. 35 Flamigni, L. J. Phys. Chem. 1993, 97, 9566.
241
242
7 Intra- and Intermolecular Proton Transfer and Related Processes 36 Monti, S., Kohler, G., Grabner, G.
J. Phys. Chem. 1993, 97, 13011. 37 Nakamura, A., Sato, S., Hamasaki, K., Ueno, A., Toda, F. J. Phys. Chem. 1995, 99, 10952. 38 Turro, N. J., Okubo, T., Weed, G. C. Photochem. Photobiol. 1982, 35, 325. 39 Hamai, S. J. Phys. Chem. 1989, 93, 6527. 40 Catena, G. C., Bright, F. V. Anal. Chem. 1989, 61, 905. 41 Yorozu, T., Hoshino, M., Imamura, M. J. Phys. Chem. 1982, 86, 4426. 42 Street, K. W. Jr., Acree, W. E. Jr. Appl. Spectrosc. 1988, 43 (7), 1315. 43 Agbaria, R. A., Butterfield, M. T., Warner, I. M., J. Phys. Chem. 1996, 10, 17133. 44 Al-Hassan, K. A. Chem. Phys. Lett. 1994, 227, 527. 45 Jiang, Y.-B. J. Photochem. Photobiol. A, Chem. 1995, 88, 109. 46 Hamai, S. J. Phys. Chem. B 1999, 103, 293. 47 Grabner, G., Rechthaler, K., Khler, G., Rotkiewicz, K. J. Phys. Chem. A 2000, 104, 13656. 48 Barros, T. C., Stefaniak, K., Holzwarth, J. F., Bohne, C. J. Phys. Chem. A 1998, 102, 5639. 49 Park, H.-R., Mayer, B., Wolschann, P., Kohler, G. J. Phys. Chem. 1994, 98, 6158. 50 Grabner, G., Monti, S., Marconi, G., Mayer, B., Klein, Ch. Th., Kohler, G. J. Phys. Chem. 1996, 100, 20069. 51 Dondon, R., Frey-Forgues, S. J. Phys. Chem. B 2001, 105, 10715. 52 Pastor, I., Di Martino A., Mendicutti, F. J. Phys. Chem. B 2002, 106, 1995. 53 Matsushita, Y., Suzuki, T., Ichimura, T., Hikida, T. Chem. Phys. 2003, 286, 399. 54 Douhal, A., Amat-Guerri, F., Acua, A. U. Angew. Chem. Int. Ed. Engl. 1997, 36, 1514. 55 Douhal, A. Ber. Bunsenges. Phys. Chem. 1998, 102, 448. 56 Douhal, A., Fiebig, T., Chachisvilis, M., Zewail, A. H. J. Phys. Chem. A 1998, 102, 1657. 57 Garca-Ochoa, I., Diez Lpez, M. A., Vias, M. H., Santos, L., Martnez-Ataz, E., Amat-Guerri, F., Douhal, A. Chem. Eur. J. 1999, 5, 897. 58 Zhong, D. P., Douhal, A., Zewail, A. H. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 14052.
59 Douhal, A. in Femtochemistry, De Schry-
60 61 62
63 64 65 66 67 68 69
70
71
72
73
74
75
76 77 78
ver, F. C., De Feyter, S., Schweitzer, G. (Eds.), Wiley-VCH, Weinheim 2001, Ch. 15, p.267. Li, G., McGown, L. B. Science 1994, 264, 249. Pistolis, G., Malliaris, A. J. Phys. Chem. 1996, 100, 155623. Gibson, H. W., Bheda, M. C., Engen, P. T. Progr. Polym. Sci. 1994, 19, 843. Harada, A., Li, J., Kamachi, M. Nature 1992, 356, 325. Harada, A., Li, J., Kamachi, M. Nature 1993, 364, 516. Born, M., Ritter, H. Angew. Chem., Int. Ed. Engl. 1995, 34, 309. Harada, A. Supramol. Sci. 1996, 3, 19. Pistolis, G., Malliaris, A. J. Phys. Chem. B, 1998, 102, 1095. Raymo, F. M., Stoddart, F. J. Chem. Rev. 1999, 99, 1643. Eskin, B. A., Grotkowski, C. E., Connolly, C. P., Ghent, W. R. Biol. Trace Element Res. 1995, 49, 9. Fujimoto, T., Nakamura, A., Inoue, Y., Sakata, Y., Kneda, T. Tetrahedron Lett. 2001, 42, 7987. Julien, L., Canceill, J., Valeur, B., Bardez, E. , Lefvre, J.-P. , Lehn, J.-M., Mrachi-Artner, V., Pansu, R. J. Am. Chem. Soc. 1996, 118, 5432. Berberan-Santos, M. N., Choppinet, P., Fedorov, A., Jullien, L., Valeur, B. J. Am. Chem. Soc. 2000, 122, 11876. Cacialli, F., Wilson, J. S., Michels, J. J., Daniel, C., Silva, C., Friend, R. H., Severin, N., Samori, P., Rabe, J. P., O’connell, J. M., Taylor, P. N., Anderson, H. L. Nature Mater. 2002, 1, 160. Kabashin, A. V., Meunier, M., Kingston, C., Luong, J. H. T. J. Phys. Chem. B, 2003, 107, 4527. Balabai, N., Linton, B., Napper, A., Priyadarsky, S., Sukharevsky, A. P., Waldeck, D. H. J. Phys. Chem. B 1998, 102, 9617. Douhal, A., Lahmani, F.; ZehnackerRentien, A. Chem. Phys. 1993, 178, 493. Douhal, A.; Lahmani, F., Zewail, A. H. Chem. Phys. 1996, 207, 477. Lu, C., Hsieh, R.-M- R., Lee, I-R., Cheng, P-Y. Chem. Phys. Lett. 1999, 310, 103.
References 79 Lochbrunner, S., Schultz, T.,
Shaffer, J. P., Zgierski, M. Z., Stolow, A. J. Chem. Phys. 2001, 114, 2519. 80 Tobita, S., Yamamoto, M., Kurahayashi, N., Tsukagoshi, R., Nakamura, Y., Shizuka, H. J. Phys. Chem. A. 1998, 102, 5206. 81 Lochbrunner, S., Stock, K., De Waele, V., Riedle, E. in Femtochemistry and Femtobiology: Ultrafast Dynamics in Molecular Science, Douhal, A., Santamaria, J. (Eds.), World Scientific, Singapore 2002, p. 202. 82 Organero, J. A., Santos, L., Douhal, A. in Femtochemistry and Femtobiology: Ultrafast Dynamics in Molecular Science, Douhal, A., Santamaria, J. (Eds.), World Scientific, Singapore, 2002, p. 225. 83 Organero, J. A., Tormo, L., Douhal, A. Chem. Phys. Lett. 2002, 363, 409. 84 Organero, J. A., Douhal, A. Chem. Phys. Lett. 2003, 373, 426. 85 Organero, J. A., Garca-Ochoa, I., Moreno, M., Lluch, J. M., Santos L., Douhal, A. Chem. Phys. Lett. 2000, 328, 83. 86 Organero, J. A., Moreno, M., Santos, L., Lluch J. M., Douhal, A. J. Phys. Chem. A, 2000, 104, 8424. 87 Hu, C., Zwanzing, R, J. Chem. Phys. 1974, 60, 4354. 88 Smith, K. K., Kaufmann, J. Phys. Chem. 1981, 85, 2895. 89 Syage, J. A. Faraday Discuss. Chem. Soc. 1994, 97, 401. 90 Douhal, A., Lahmani, F., Zewail, A. H. Chem. Phys. 1996, 207, 477. 91 Limbach H., Manz J. (Eds.), Hydrogen Transfer: Experiment and Theory, Ber. Bunsengens. Phys. Chem. 1998, 102, Special Issue. 92 Genosar, L., Cohen, B., Huppert, D. J. Phys. Chem. A 2000, 104, 6689. 93 Cohen, B., Huppert, D. J. Phys. Chem. A 2002, 106, 1946. 94 Cohen, B., Huppert, D., Solnstev, K. M., Tsfadia, Y., Nachliel, E., Gutman, M. J. Am. Chem. Soc. 2002, 1124, 7539. 95 Tolbert, L. M., Solnstev, K. M. Acc. Chem. Res. 2002, 35, 19. 96 Mandal, D., Pal, S. K., Bhattacharyya, K. J. Phys. Chem. B. 1998, 102, 9710. 97 Abgaria, R. A., Uzan, B., Gill, D. J. Phys. Chem. 1989, 93, 3855. 98 Hansen, J. E., Pines, E., Fleming, G. R. J. Phys. Chem. 1992, 96, 6904.
99 Sukul, D., Pal, S. K., Mandal, D., Sen, S.,
100
101 102 103 104 105 106 107
108
109 110
111 112 113 114 115 116
117 118 119 120 121
122
Bhattacharyya, K. J. Phys. Chem. B. 2000, 104, 6128. Dutta, P., Halder, A.; Mukherjee, P., Sen, S., Bhattacharyya, K. Langmuir 2000, 18, 7867. Balasubramanian, S., Pal, S., Bagchi, B. Phys. Rev. Lett. 2002, 89, 115505. Senapati, S., Chandra, A. J. Phys. Chem. B 2001, 105, 5106. Simon, J. D. Acc. Chem. Res. 1988, 21, 21. Bagchi, B. Chandra, A. Adv. Chem. Phys. 1991, 1, 80. Ladanyi, B., Skaf, M. S. Annu. Rev. Phys. Chem. 1993, 335, 44. Suppan, P. J. Chem. Soc., Faraday Trans. 1 1987, 83, 495. Ferreira, J. A. B., Coutinho, P. J. G., Costa, S. M. B., Martinho, J. M. G. J. Chem. Phys. 2000, 262, 453. Cichos, F., Brown, R., Rempel, U., Von Borczyskowski, C. J. Phys. Chem. A 1999, 103, 2506. Shirota, H., Castner, E. W. J. Chem. Phys. 2000, 112, 2367. Frolicki, R., Jarzeba, W., Mostafavi, M., Lampre, I. J. Phys. Chem. A 2002, 106, 1708. Molotsky, T., Huppert, D. Phys. Chem. A, 2002, 106, 8525. Christie, R. M. Rev. Prog. Color. 1993, 23, 1. Hoult, J. R. S., Paya, M. Gen. Pharmac. 1996, 27, 713. Pitchumani, K., Velusamy, P., Srinivasan, C. Tetrahedron 1994, 45, 12979. Yamaguchi, H., Higashi, M. J. Inclusion Phenom. Mol. Recognit. Chem. 1990, 9, 51. Bergmark, W. R., Davis, A., York, C., Macintosh, A., Jones, G. J. Phys. Chem. 1990, 94, 5020. Asimov, M. M., Rubinov, A. N. J. Appl. Spectrosc. 1995, 62, 353. Ishiwata, S., Kamiya, M. Chemosphere 1998, 37, 479. Karnik, N. A., Prankerd, R. J., Perrin, J. H. Chirality 1991, 3, 124. Nag, A., Chakrabarty, T., Bahattacharyya, K. J. Phys. Chem. 1990, 94, 4203. Bergmark, W. R., Davies, A., York, C., Jones, G., II. J. Phys. Chem. 1990, 94, 5020. Vajda, S., Jimenez, R., Rosenthal, S. J., Fidler, V., Fleming, G. R., Castner, E. W.,
243
244
7 Intra- and Intermolecular Proton Transfer and Related Processes
123 124 125 126 127 128
129
130 131 132 133 134
135 136 137 138 139 140
141
142
143
Jr. J. Chem. Soc., Faraday Trans. 1995, 91, 867. Maroncelli, M., Fleming, G. R. J. Chem. Phys. 1988, 88, 5044. Richmond, G. L. Chem. Rev. 2002, 102, 2693. Ohmine, I., Saito, S. Acc. Chem. Res. 1999, 32, 741. Zabel, V., Saenger, W., Manson, S. A. J. Am. Chem. Soc. 1986, 108, 3664. Steiner, T., Saenger, W., Lechner, R. E. Mol. Phys. 1991, 72, 1211. Braesicke, K., Steiner, T., Saenger, W., Knapp, W. W. J. Mol. Graphics Mod. 2000, 118, 143. Garca-Ochoa, I., Diez Lopez, M.-A., Vias, M. H., Santos, L., Martnez Ataz, E.; S nchez, F., Douhal, A. Chem. Phys. Lett. 1998, 296, 335. Senapti, S., Chandra, A. J. Phys. Chem. B 2002, 105, 5106. Luisi, P. L., Straub, B. E., (Eds.), Reverse Micelles, Plenum Press, New York 1984. Backer, C. A., Whitten, D. G. J. Phys. Chem. 1987, 91, 865. Keh, E., Valeur, B. J. Colloid Interface Sci. 1981, 79, 465. Belletete, M., Lachapelle, M., Durocher, G. J. Phys. Chem. 1990, 94, 5337. Guha Ray, J., Sengupta, P. K. Chem. Phys. Lett. 1994, 230, 75. Zhu, D.-M., Wu, X., Schelly, Z. A. J. Phys. Chem. 1992, 96, 7121. Mashimo, S., Kuwabara, S., Yagihara, S., Higasi, K. J. Phys. Chem. 1987, 91, 6337. Quist, P. O., Halle, B. J. Chem. Soc. Faraday Trans. 1 1988, 84, 1033. Brown, D., Clarke, J. H. R. J. Phys. Chem. 1988, 92, 2881. Fukazaki, M., Miura, N., Shinyashiki, N., Kurita, D., Shioya, S., Haida, M., Mashimo, S. J. Phys. Chem. 1995, 99, 431. Cho, C. H., Chung, M., Lee, J., Nguyen, T., Singh, S., Vedamuthu, M., Yao, S., Zhu, J.-B., Robinson, G. W. J. Phys. Chem. 1995, 99, 7806. Riter, R. E., Willard, D. M., Levinger, N. E. J. Phys. Chem. B 1998, 102, 2705. Das, S., Datta, A., Bhattacharyya, K. J. Phys. Chem. A 1997, 101, 3299.
144 Belch, A. C., Berkowitz, M. Chem. Phys.
Lett. 1985, 113, 278. 145 Sanson, M. S. P., Kerr, I. D., Breed, J.,
Sankararamakrishnan, R. Biophys. J. 1996, 70, 693. 146 Zhang, L., Davis, H. T., Kroll, D. M., White, H. S. J. Phys. Chem. 1995, 99, 2878. 147 Lynden-Bell, R. M., Rasaiah, J. C. J. Chem. Phys. 1996, 105, 9266. 148 Linse, P. J. Chem. Phys. 1989, 90, 4992. 149 Faeder, J., Ladanyi, B. M. J. Chem. Phys. 2000, 104, 1033. 150 Chiu, S. W., Jakobsson, E., Subramanian, S., McCammon, J. A. Biophys. J. 1991, 60, 273. 151 Thompson, W. H. J. Chem. Phys. 2002, 117, 6618. 152 Senapati, S., Berkowitz, M. L. J. Chem. Phys. 2003, 118, 1937. 153 Venables, D. S., Huang, K., Schmuttenmaer, C. A. J. Phys. Chem. B 2001, 105, 9132. 154 Pal, S.K., Sukul, D., Mandal, D., Sen, S., Bhattacharyya, K. J. Phys. Chem. B. 2002, 104, 2613. 155 Baumann, R., Ferante, C., Deeg, F. W., Brauchle, C. J. Chem. Phys. 2001, 114, 5781. 156 Datta, A., Das, S., Mandal, D., Pal, S., Bhattacharyya, K. Langmuir, 1997, 13, 6922. 157 Gellman, S. H. (Ed.), Chem. Rev. 1997, 97, 1231. 158 Berde, C. B., Hudson, B. S., Simon, R. D., Sklar, L. A. J. Biol. Chem. 1979, 254, 391. 159 Rosenoer, V. M., Oratz, M., Rothschild, M. A. Albumin Structure, Function, and Uses, Pergamon Press, Oxford 1977. 160 Guallar, V., Moreno, M., Lluch, J. M., Amat-Guerri, F., Douhal, A. J. Phys. Chem. 1996, 100, 19789. 161 He, X. M., Carter, D. C. Nature (London) 1992, 358, 209. 162 Yui, H., Takei, M., Hirose, Y., Sawada, T. Rev. Sci. Instrum. 2003, 74, 907. 163 Suzuki, M., Yasaki, Y. Chem. Pharm. Bull. 1979, 27, 1343. 164 Suzuki, M., Yasaki, Y. Chem. Pharm. Bull. 1984, 32, 832.
245
8 Tautomerization in Porphycenes Jacek Waluk
8.1 Introduction
Porphyrins and metalloporphyrins are objects of intense studies in both basic and applied sciences. Owing to their crucial role in biological processes, such as photosynthesis, oxygen transport and activation, porphyrins have been labeled “Pigments of Life” [1]. The accuracy of this characterization is additionally confirmed by the use of porphyrins in medicine as phototherapeutic agents [2–6]. The potential of porphyrins as building blocks is enormous and includes, for example, artificial light-harvesting and photosynthetic systems [7–9], molecular memories [10, 11], photovoltaic devices [12], and many other advanced materials [13–18]. The prospect of applications stimulated a rapid development of synthetic procedures that resulted in obtaining new classes of compounds, such as expanded, contracted, or inverted porphyrins [19, 20]. Of particular interest in this area are constitutional isomers of porphyrin (also dubbed “reshuffled” porphyrins) [20], tetrapyrrole macrocycles which differ from the parent molecule in the way of linking the pyrrole rings by methine groups (Fig. 8.1). The research in this field started with the synthesis of porphycene in 1986 [21]. Since then, three more “nitrogen-in” isomers have been obtained: corrphycene [22], hemiporphycene [23, 24], and isoporphycene [25, 26]. Closely related to this class is an “inverted” (“N-confused”) porphyrin [27, 28]. All these molecules have been shown to be planar and aromatic. They also exhibit electronic spectra characteristic for porphyrins, with the lower intensity Q transitions in the red part of the visible region followed by stronger Soret bands in the near-UV (Fig. 8.2). However, the relative intensities of the Q and Soret transitions differ significantly among the series. The lowest intensity of Q bands is observed in porphyrin and corrphycene. Hemiporphycene reveals stronger Q bands, and porphycene even stronger ones. This behavior can be rationalized upon inspecting the energies of the frontier p orbitals. The analysis of HOMO and LUMO splitting based on the perimeter model [29] has led to correct predictions not only for relative absorption intensities, but also for signs and patterns in magnetic circular dichroism. These predictions were experimentally confirmed for porphycene [30], corrphycene [31], and hemiporphycene [32]. Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
246
8 Tautomerization in Porphycenes
N H
N H
N
N
Porphyrin
N H N
N H
N H N
H
N
Porphycene
N N
Corrphycene N
N H N
N H N
Hemiporphycene
N
N
N H
N
Isoporphycene
N
N NH
N H
HN
NH
H N
N
Inverted porphyrin
N HN
N
N H
NH N
H N
Figure 8.1 Constitutional isomers of porphyrin. The names are given for the compounds which have been synthesized to date.
Of all the porphyrin isomers, porphycene and its derivatives have been studied most thoroughly. DFT calculations predict [33] that porphycene 1 as a free base is the most stable of all isomers, including porphyrin 2. The reason for this exceptional stability of 1 is a very strong intramolecular double NH_N hydrogen bond (HB), due to, first, the rectangular shape of the inner cavity that leads to a nearly linear arrangement of the three atoms, and, second, a small N–N distance (2.63 in 1 [21] as compared to 2.90 in 2 [34]). In metal complexes, the relative stabilities of porphycene and porphyrin are reversed, since the larger, square-shaped cavity in the latter is much better suited to the accommodation of a metal ion. As will be demonstrated below, these differences in the cavity shape and distances have a huge impact on both the thermodynamics and kinetics of tautomerization. Moreover, it has been shown that the porphycene cavity dimensions are very sensitive to peripheral substituents, even such “mild” ones as alkyl groups. For variously alkylated porphycenes, the N–N distances can be varied from an extremely small value of 2.53 , resembling that in proton sponges [35] to 2.80 , close to the value for porphyrin. This provides a unique opportunity to study distance dependences in a class of very similar molecules. The material presented in this chapter will often be based on such comparisons and on the relationship with
8.2 Tautomerization in the Ground Electronic State
N
N
H N
Absorbance (arbitrary units)
N H
N H N
N H N
R
R R
R N H
R=C2H5
N
N H
N R
R R
R
R
R R
R N H
R=C2H5
N
N H N
R R
15
20
25
R R
30×103cm-1
Figure 8.2 Room temperature electronic absorption spectra. From top to bottom: porphyrin, porphycene, 2,3,6,7,11,12,17,18-octaethylcorrphycene, and 2,3,6,7,11,12,16,17-octaethylhemiporphycene.
porphyrin. The tautomerization characteristics will be discussed separately for the ground state and for the lowest excited singlet and triplet states.
8.2 Tautomerization in the Ground Electronic State 8.2.1 Structural Data
Different tautomeric forms can be envisaged for both 1 and 2. In the trans configuration, the protons are located on the opposite nitrogen atoms, whereas in the cis structure they are positioned on the adjacent ones (Fig. 8.3). Of the two cis forms of 1, the vicinal arrangement of two protons on the same bipyrrole unit (cis-1) is energetically much more favorable than that of the other possible species
247
8 Tautomerization in Porphycenes
N
N H
N H
H N
N
N
N H N
N H H N
cis-1
trans
N N
cis-2
Figure 8.3 Possible tautomeric forms of 1.
(cis-2). In principle, the structure with both protons shared equally by two nitrogen atoms is also possible, but the calculations place it at higher energies [33]. The crystal structure of free base porphyrin [34, 36, 37] clearly reveals the trans configuration. Interestingly, two inner protons maintain the same distance from both unprotonated nitrogen atoms, which results in D2h symmetry. This type of symmetry has been independently confirmed by linear dichroism experiments on 2 photooriented in low-temperature rare gas matrices [38, 39]. Thus, each proton participates in two intramolecular hydrogen bonds. Due to unfavorable geometry (N–N separation of 2.89 and the NHN angle of only 116 [40]) these bonds are rather weak. The IR active NH stretching frequency is observed in rare gas matrices at around 3320 cm–1 [38]. In porphycene, the situation is completely different. In the X-ray structure, the protons are equally delocalized over all four nitrogen atoms. The distance between hydrogen-bonded nitrogen atoms is 2.63 [21]. Interestingly, this value lies in between those calculated for the trans and cis forms of 1 (Table 8.1), suggesting the presence of both species in the crystal. The two intramolecular hydrogen bonds are strong not only because of the small N–N separation, but also due to a nearly linear arrangement, with an NHN angle of only 152 [40]. Comparison between the cavity geometries in 1 and 2 is presented in Fig. 8.4. Strong hydrogen bonds in 1 should result in the NH vibrations being shifted to low frequencies. Actually, the NH stretching vibration has not yet been identified in the IR spectrum of 1, even though the calculations predict that it should correspond to the most intense band [41, 42]. The IR and Raman experiments could (a)
N
H N
2.89 Å
N
N
152 0
1.03 Å
H
2.89 Å
N
N
1.10 Å
2.63 Å
(b)
116 0
248
H H
N 2.83 Å
N
Figure 8.4 The inner cavity and hydrogen bond parameters in 1 (a) and 2 (b) determined from solid state 15N NMR studies [40].
2.2 (1.6) 1.4 (0.7) 8.3 (8.1)
B3LYP/6-31G(d,p)
B3LYP/6-31G(d,p)
B3LYP/TZ2P[ f ]
MP2/6-31G(d)// B3LYP/6-31G(d)[ f ]
1
1a
2
2 17.0 (13.9)
16.2 (13.1)
2.4 (–0.5)
a Energies including zpve correction in parentheses; b first entry, the distance between hydrogen-bonded, second entry, between non-bonded nitrogen atoms (vertical and horizontal N–N distances in Fig. 8.3, respectively); c third entry, the distance between the nitrogen atoms on which the protons are located (upper horizontal N–N distance in Fig. 8.3); d Ref. [41]; e Ref. [33]; f Ref. [92].
8.9 (8.7)
2.0
BLYP/6-31G(d,p)[e]
1 4.1 (1.0)
5.7 (2.4)
5.1 (4.6)
MP2/6-31G(d)// B3LYP/6-31G(d)[d]
1
E(TS) [a]
4.9 (1.6)
DE(trans–cis) [a]
2.4 (1.9)
B3LYP/TZ2P [d]
1
Compound Method of calculation
24.8 (18.7)
24.4 (18.3)
3.6 (-1.7)
6.1 (0.6)
7.6 (1.6)
7.6 (1.6)
E(SS) [a]
trans–trans second-order saddle points (SS), and the inner cavity dimensions []. The results for the higher energy cis tautomer of 1 (cis-2) are not shown.
2.93
2.58/2.91
2.66/2.84
2.66/2.87
2.68/2.83
2.67/2.82
dNNtrans [b]
Tab. 8.1 Calculated relative energies (kcal mol–1) of ground state trans and cis forms, trans–cis transition states (TS),
2.55/2.91/2.95
2.61/2.84/2.89
2.62/2.86/2.92
2.64/2.83/2.89
2.63/2.82/2.88
dNNcis [c]
8.2 Tautomerization in the Ground Electronic State 249
250
8 Tautomerization in Porphycenes
not definitely establish the structure of the ground state tautomer. On the one hand, the mutual exclusion principle seems to be obeyed, which would indicate the trans form as the dominant species. However, calculations for the cis structure show that the intensities of the vibrational transitions that become IR-active due to lack of an inversion center should be very weak [42]. The in-plane rigidity of the porphycene skeleton is probably not very high, since the cavity dimensions are significantly influenced by alkyl substituents. The substitution at the ethylene bridge carbon atoms shortens the N–N distance to an extremely small value of 2.53 in both 9,10,19,20-tetramethyl porphycene 1a and the tetra-n-propyl derivative 1b. Substitution by four alkyl groups in positions 2, 7, 12, 17 does not strongly influence the cavity dimensions, as illustrated by the npropyl (1c) and tetra-tert-butyl (1d) derivatives. On the other hand, 2,3,6,712,13,16,17-octaethylporphycene 1e reveals the largest separation of the hydrogenbonded nitrogen atoms and the reversal of the long and short rectangle sides as compared to all other porphycenes. The cavity dimensions for several porphycenes are presented in Table 8.2.
N H
N
N H
H N
N
N
N H
H N
N
N
1b
1a
N H
N H N
N
1d
N H N
1c
N H N
N H N
1e
The differences in HB strength in 1 and 2 are nicely reflected in the values of the NMR chemical shifts of the inner protons (Table 8.2). The values for porphycene are shifted downfield from those of porphyrin, and correlate clearly with the N–N separation. The chemical shifts of the peripheral protons are very similar in both isomers.
8.2 Tautomerization in the Ground Electronic State Tab. 8.2 1H NMR chemical shifts D and the distances between
hydrogen-bonded nitrogen atoms (d) in several porphycenes and in 2. 1
1a
1b
1c
1e
2
D [ppm]
3.15
6.67
6.82
3.04
0.65
–3.76
d []
2.63
2.53
2.53
2.62
2.80
2.90
8.2.2 NMR Studies of Tautomerism
Numerous NMR experiments have been reported for variously substituted porphyrins, both in solution [43–66] and in the solid phase [58, 61, 63, 67, 68]. At elevated temperature, the trans–trans interconversion is fast on the NMR time scale. For example, for 15N-enriched porphyrin in toluene-d8 the rate constant at 298 K is more than 2 104 s–1; at 254 K, kHH = 1300 s–1 [63]. Further lowering of the temperature results in a complete localization of protons. Below about 230 K, the two trans tautomers do not interconvert in the dark. They can still be transformed into each other, however, upon photoirradiation, even at cryogenic temperatures [38, 39]. Initial NMR studies of porphyrin suggested a concerted double hydrogen transfer pathway. However, careful and elegant analysis of hydrogen/deuterium/tritium isotope effects on tautomerization rates measured at different temperatures [61, 63, 65] has led to the conclusion that the ground state reaction in porphyrin involves a stepwise mechanism. The experimental data were interpreted using a slightly modified one-dimensional tunneling model of Bell [69]. The transfer of the first hydrogen atom, creating the cis form, occurs via tunneling from a level that has to be thermally activated. The required minimum energy needed for the tunneling to occur, Em = 24.0 kJ mol–1 [63] consists of two contributions: (i) the difference between the cis and trans forms; (ii) the reorganization energy of the molecular skeleton. The value of Em is much smaller than that of the classical barrier, estimated as about 57 kJ mol–1 [70]. From the cis structure, the system may either go back to the substrate or, by the transfer of the second hydrogen atom, achieve the other trans tautomeric form. One should note that the cis structure of porphyrin has never been experimentally detected. This is most probably due to its short lifetime, for which the estimates range from less than 10 ps [70] to 10–8 s [63]. In porphycene, the rates, barriers and the overall tautomerization mechanism seem to be completely different. Comparison of the reaction for 1 and 2 in the crystalline state was performed using 15N CPMAS NMR (Fig. 8.5) [40, 68]. At elevated temperatures both molecules reveal only one peak, characteristic of a rapid inner hydrogen exchange. For porphyrin, lowering of the temperature from 356 to 192 K leads to line broadening and, finally, to the separation of =N– and NH
251
252
8 Tautomerization in Porphycenes
(b)
(a)
Figure 8.5 Solid state 15N NMR spectra of 1 (a) and 2 (b). Reprinted with permission from Ref. [68].
peaks, showing that the process becomes frozen. On the contrary, porphycene does not reveal any broadening. Below 213 K, four narrow peaks are observed, assigned to two nonequivalent asymmetric proton transfer systems. The tautomerization in each of them is extremely rapid, even at temperatures as low as 107 K. Two possibilities were considered: (i) two nonequivalent porphycene molecules in the crystal, each containing two proton transfer systems; (ii) each molecule in the crystal exhibiting four different tautomeric forms. The former case would involve only trans–trans equilibria, whereas for the latter, both trans and cis structures should be present. The degeneracy in both trans and cis forms is removed by intermolecular interactions in the crystal. Below 50 K, only the trans forms are observed [40]. Case (ii) seems more probable, since the room temperature X-ray structure of 1 shows only one type of molecule in the crystal, and also because the experimentally determined N–N distance lies in between the values calculated for the trans and cis forms. Three alkyl derivatives of porphycene, 1b, 1c, and 1e have also been studied using 15N CPMAS NMR [71]. As in the case of parent 1, the tautomerization was found to be so rapid that the rate constants could not be determined from the line shape analysis. It was thus not possible to establish a correlation between the cavity parameters and tautomerization dynamics. 1b and 1c revealed narrow doublets, whereas 1e showed one line that did not broaden, even at 173 K. 1e has the largest N– N distance among porphycenes and should therefore exhibit the weak-
8.2 Tautomerization in the Ground Electronic State
est hydrogen bonding. Even for this molecule, ground state tautomerization is very rapid on the NMR time scale. The 15N CPMAS NMR work on crystalline porphycene [40], coupled with the analysis of the 15N T1 relaxation times, resulted in the determination of the rate constants of the hydrogen transfer process. They varied from 3.66 108 s–1 at 355 K to 4.24 106 s–1 at 228 K. Strong coupling between the two hydrogen bonds was found and interpreted as indication that the tautomerization in porphycene occurs as a correlated process. The temperature dependence of the rate indicated the major role of tunneling, with an effective barrier of 31.8 kJ mol–1 and the value of Em = 5.9 kJ mol–1, much smaller than that in porphyrin. The evidence for tunneling agrees with the results obtained for 1 using a completely different experimental technique – optical excitation of a molecule isolated in a supersonic jet [72]. 8.2.3 Supersonic Jet Studies
H,H
H,H
H,D
A
A
D,D
Fluorescence intensity
The fluorescence excitation spectrum of parent porphycene isolated in an ultracold supersonic jet consists of doublets, separated by 4.4 cm–1 (Fig. 8.6). This behavior contrasts with that of porphyrin, which exhibits “normal” behavior, with single peaks corresponding to particular vibronic transitions [73]. Upon replacing one or two inner protons with deuterons, the splitting disappears (which, given the experimental resolution, means that it becomes less than 0.1 cm–1). Adding
B B
*
16200
16300
16400
16500 -1
Wavenumber [cm ] Figure 8.6 Fluorescence excitation spectra of 1 isolated in a supersonic jet. Inset, the 0–0 transitions observed for undeuterated, singly, and doubly deuterated 1. The peak marked with an asterisk corresponds to the complex of 1 with water.
253
254
8 Tautomerization in Porphycenes
water or alcohol to the sample results in the detection of complexes that do not reveal the doublet structure. Therefore, the splitting has been attributed to the ground state tunneling of two inner hydrogen atoms. The fluorescence excitation spectrum in singly and doubly deuterated 1 is shifted to the red, by approximately the same amount per each substituted proton. This indicates that the stabilization of the deuterated species is larger in S1 than in S0, which implies that the hydrogen bond is weaker in the excited state. Most probably, the molecule expands upon excitation, and the cavity becomes larger (or, at least, the shorter side of the rectangle increases). This finding, along with the observation that all the vibronic peaks reveal the same separation of the doublet components, suggests that the observed value of 4.4 cm–1 can be assigned to ground state tunneling splitting (Fig. 8.7). One can estimate the barrier to double hydrogen tunneling using a simple one-dimensional model [69, 74] that leads to the formula relating the observed splitting, DE, to the effective mass, m, barrier width, d, and barrier height, V: hv rd pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DE ¼ exp (8.1) 2mðV E0 Þ p " r is the shape parameter, close to unity and equal to p/4 for parabolic barriers. The values of m and d can be estimated within reasonable limits. The vibrational frequency, m, is more difficult to assess, because of the lack of experimental assignment for the NH stretching vibration. One can use the formula obtained for tunneling in symmetrical double-minimum potentials via a harmonic oscillator approximation [75]:
N N H H N N
N H N
S1
~ 0 cm-1
O++
S0
N H N
OO+
-
O-
O++
-
O-
4.4 cm -1
Figure 8.7 The ground and lowest excited singlet state potential energy profiles along the tautomerization coordinate in 1.
8.2 Tautomerization in the Ground Electronic State
DE ¼
ha3=2 d expðad2 Þ 2m 5=2
(8.2)
where a ¼ 2 mm=". Varying m between 1 and 2 and d between 0.55 and 0.65 , yields values of m ranging between 185 and 673 cm–1. These values, in turn, result in the estimated barrier heights of 217–1360 cm–1 (2.6–16.0 kJ mol–1). The barrier is evidently much lower than in porphyrin. The evaluation of the barrier for 1 using 15N NMR yielded the value of 25.9 kJ mol–1 [40]. It has to be remembered, however, that these measurements were done in the crystalline phase and are explicitly based on a slightly unsymmetrical double-minimum potential. For alkyl-substituted porphycenes 1a and 1b, with smaller N–N separation and thus stronger hydrogen bonds, one would expect a larger tunneling splitting. The experiments in the supersonic jets reveal a quite complicated pattern, different from that of parent porphycene [76]. Two peaks, separated by 12.5 cm–1 are observed in the 0–0 region of the fluorescence excitation spectrum (Fig. 8.8). This doublet structure does not disappear for singly and doubly deuterated compounds. Each of the peaks consists of doublets in undeuterated species and is associated with a different vibronic structure. Two low frequency modes (32 and 15500
15550
15600
15650
15600
15650
10 cm-1
H,H
8.5 cm-1
15450
H,D
Fluorescence intensity (arb. units)
(b)
D,D
15400
12.5 cm -1
(a)
15400
15450
15500
15550
Wavenumber [cm -1] Figure 8.8 Fluorescence excitation spectra of 1a in a supersonic jet. (a) Undeuterated species; (b) features assigned to the compound with one (H,D) or two (D,D) inner protons replaced by deuterons.
255
8 Tautomerization in Porphycenes
38 cm–1) are associated with the upper peak, whereas only one vibration (38 cm–1) related to the lower component is detected. Hole-burning experiments in the jets were performed to secure these assignments. These results can be interpreted as evidence for two different ground state structures, trans and cis tautomers. The calculations suggest that the two forms should have very similar energies (Table 8.1). The presence of two species in 1a and 1b has also been detected, via biexponential fluorescence decay, in solutions, glasses, polymers and rare gas matrices [77]. The values of tunneling splitting were obtained for ground and excited state cis and trans forms of undeuterated 1a. The splittings, similar for cis and trans species, indicate a larger barrier to tautomerization in S1 than in S0. 8.2.4 The Nonsymmetric Case: 2,7,12,17-Tetra-n-propyl-9-acetoxyporphycene
In asymmetrically-substituted porphycenes, the two trans (or cis) forms should no longer be degenerate. Indeed, the studies of 2,7,12,17-tetra-n-propyl-9-acetoxyporphycene 1f [78] reveal a splitting of the peak that corresponds to the S0–S1 transition in molecule 1c, which lacks the acetoxy substituent (Fig. 8.9). A doublet appears, with the intensity of each component about half that in 1c. This strongly suggests that the two peaks correspond to two trans tautomeric forms of 1f, 1f ¢ and 1f †. This assignment was corroborated by fluorescence polarization studies that monitored the anisotropy of 1f † emission while exciting both forms to their S1 and S2 states.
1f’’ 1f’ Absorbance (arb.un.)
Fluorescence intensity (arb.un.)
256
exc. 17600 exc. 26800
14000
16000
18000
Figure 8.9 Electronic absorption and fluorescence spectra of 1f measured at 20 K in poly(vinyl butyral) film. The two emission curves correspond to excitation of different fractions of the ground state tautomeric forms.
20000
8.2 Tautomerization in the Ground Electronic State
N
N H
N H
OAc
H
N
N
N H N
N
1f’
OAc
1f’’
Measurements of the temperature dependence of the absorption in solution, in glasses and in polymer films showed that practically no change in the intensity ratio of the peaks corresponding to the different tautomeric forms occurs in the low temperature region (20–100 K). Analysis of the absorption and fluorescence reveals that both forms should have very similar energies in the ground state, whereas in S1 they differ by about 1 kcal mol–1. In contrast to the absorption, fluorescence occurs practically only from one form, assigned to 1f †. This is true for both high and low temperatures (at 293 K, a weak shoulder assigned to 1f¢ can
N H N N H N
N
N H
OAc
N
OAc
H N
S
S0 Figure 8.10 Scheme of ground and lowest excited singlet state potential energy profiles along the tautomerization coordinate in 1f.
257
258
8 Tautomerization in Porphycenes
also be detected). The picture that emerges is that of a nearly symmetric doubleminimum ground state potential, and an asymmetric shape in S1 (Fig. 8.10). Most importantly, the constant ratio of the two forms in the low temperature range suggests tunneling as the mechanism of interconversion between the two nonequivalent trans tautomers. 8.2.5 Calculations
Table 8.1 shows the results of energy calculations of ground state trans and cis forms, as well as the energies of the transition states for single and double hydrogen transfer. For comparison, some results for porphyrin 2 have also been included. For both 1 and 2, inclusion of electron correlation is necessary to obtain a proper symmetry. The computational results confirm the large differences between 1 and 2 observed experimentally. Although the trans forms are always predicted as the most stable species, the cis tautomers are much closer in energy in porphycenes. Actually, for 1a both forms are predicted to be practically isoenergetic, which agrees nicely with the experimentally observed presence of two forms in this molecule. The differences in barrier heights are even more dramatic. This is best exemplified by calculations on porphycenes 1 and 1a: the inclusion of zero point energy results in the transition state energy being lower than that of the cis form in 1 and of both forms in 1a. These results show that the harmonic approximation is not appropriate for the vibrations involved in the hydrogen transfer path in porphycenes (NH stretch, in particular) and that the barriers to tautomerization must be very low. In summary, both experiment and calculations demonstrate low barriers for tautomerization in porphycene as compared to porphyrin. This may explain the tunneling effects readily observed for 1 and its derivatives, as well as the change in the reaction mechanism, from stepwise in 2 towards synchronous in 1. Moreover, the cis structures, postulated, but never observed for porphyrin, may be present in porphycenes, their population increasing with the strength of the intramolecular hydrogen bond, i.e., with the decrease in the distance between hydrogenbonded nitrogen atoms.
8.3 Tautomerization in the Lowest Excited Singlet State
Fluorescence of porphycene embedded in rigid media was found to be depolarized, both at room temperature in the poly(vinyl butyral) matrix [79] and at low temperatures in glasses [30, 80] (Fig. 8.11). In a rigid environment, where the reorientation of an excited chromophore is not possible, the direction of the S0–S1 transition moment should be the same in absorption and emission, leading, for excitation into S1, to the anisotropy value of 0.4. Instead, the observed values
8.3 Tautomerization in the Lowest Excited Singlet State A (b) 0.4 N H
0.2
N
Anisotropy
Anisotropy
0.4
N H N
0.0 -0.2
B (b)
0.2
N H N
0.0
N H N
-0.2 14
16
18
20
S1
14
16
14
S2
18
20
Wavenumber [103cm-1]
16
S1
Emission int.
(a)
Emission int.
(a)
14
18
20
18
20
S2
16
Wavenumber [103cm-1]
Figure 8.11 (a) Fluorescence (dotted line) and fluorescence excitation spectra; (b) anisotropy of fluorescence excitation of 1 (A) and 1e (B). Both samples were measured at 113 K in 1-propanol glass. In the excitation spectra, the emission was monitored at 15900 cm–1 (1) and at 14900 cm–1 (1e).
barely exceed 0.1. The depolarization is also observed upon excitation to S2. According to calculations, for this state the transition moment should be nearly orthogonal to that of the emitting S1 state, and the anisotropy should be close to – 0.2. The observed value, however, is close to zero. The depolarization of fluorescence has been observed at temperatures around 100 K not only for 1, but also for the two derivatives, 1b and 1c. in contrast, the measurements performed under the same conditions for 1e revealed no sign of depolarization. The “textbook” values of the anisotropy were obtained, i.e. 0.4 and about –0.2 for excitation into S1 and S2, respectively (Fig. 8.11). The octaethyl derivative 1e is the porphycene with the largest separation (2.80 ) between the hydrogen-bonded nitrogen atoms and should therefore exhibit the slowest tautomerization kinetics. It was thus concluded that the reduced anisotropy values observed in three different porphycenes are caused by excited state tautomerization [30, 80]. As shown in Fig. 8.12, the interconversion between the two trans tautomers changes the direction of the transition moment. Therefore, only a part of the excited state population emits fluorescence polarized parallel to that of the transition moment in S0–S1 absorption (this fraction should approach 0.5 if the tautomerization is fast compared to the excited state lifetime). For the remaining frac-
N H
N
259
N
H N
N H N
N H N
Figure 8.12 S0–S1 transition moment direction changes as a result of trans–trans conversion in 1.
260
8 Tautomerization in Porphycenes
tion of excited molecules, the angle between absorbing and emitting transition moments is large, which leads to decreased anisotropy values. In 1e, the excited state reaction is too slow to occur during the S1 lifetime, about 10 ns. The analysis of fluorescence anisotropy turned out to be a very powerful tool. First, depolarization provides a direct proof of excited state tautomerization that occurs on the timescale of the S1 lifetime (or faster), which is, at 293 K, of the order of 10 ns for 1 and 1c and ps in the case of 1a and 1b. It should be noted that the cis–cis tautomerization would not change the transition moment direction and thus cannot lead to depolarization. Cis–trans conversion, in turn, would result in much smaller changes in the anisotropy. The observed anisotropy values thus prove that the rapid excited state tautomerization in porphycene involves mostly trans–trans interconversion. A small fraction of cis structures may also be present, but it cannot be dominant. The same is true for the ground state, as revealed by simulations of expected anisotropy values assuming various fractions of cis tautomers in the ground and lowest excited singlet states [30, 82]. This is a very important result, given that previous structural assignments were mostly based on calculations, since they were impossible to obtain from X-ray data, or, in the case of NMR [40, 68], IR and Raman measurements [42], not unequivocal. Second, careful analysis of anisotropy data is useful not only with respect to investigation of structural and kinetic aspects of tautomerization, but also as a means to obtain detailed spectroscopic information about transition moment directions. Both procedures will be described below in more detail. 8.3.1 Tautomerization as a Tool to Determine Transition Moment Directions in Low Symmetry Molecules
The directions of transition moments in every chromophore are dictated by molecular symmetry. For the cis tautomers of porphycene (C2v point group), only three mutually orthogonal transition moment directions are allowed. On the other hand, the trans form is of C2h symmetry and, therefore, any direction in the molecular plane is possible, as well as the direction perpendicular to the plane. The determination of transition moment directions in such low symmetry molecules is not an easy task. However, in the case of “narcissistic” type of reactions exemplified by trans–trans conversion in 1, one can take advantage of an additional symmetry element introduced by the tautomerization process. Double hydrogen transfer converts the molecule into its image, with the horizontal and vertical mirror symmetry planes perpendicular to the molecular plane (Fig. 8.13). Thus, tautomerization results in the rotation of each in-plane transition moment direction. The angle of rotation is twice the value of the angle formed by a particular transition moment with the horizontal (or vertical) in-plane axis. It can be shown [80] that, for a fast excited state process, which results in equal population of both trans tautomers, the measured fluorescence anisotropy r will be expressed by the formula:
8.3 Tautomerization in the Lowest Excited Singlet State
rða; bÞ ¼ f 3½ cos 2 ðb a=2Þ þ cos 2 ðb þ a=2Þ 2 g=10
(8.3)
where b and a/2 are the angles between the molecular horizontal axis and the transition moment in absorption and emission, respectively. Measuring anisotropy upon excitation into S1 leads to the determination of b1 = a1/2, from the expression: rða; a=2Þ ¼ ½3 cos 2 ðaÞ þ 1=10
(8.4)
Knowledge of a enables one to obtain the directions of the moments of transitions to higher excited states. In order to determine the absolute values of the angles, the sign of at least one of them has to be known or assumed. Here, even approximate calculations are usually sufficient. This procedure can be extended to a general model that takes into account the possible presence of both trans and cis forms, each of them differently populated in S0 and S1. The resulting formulas are: rða; b; c; dÞ ¼ ð1 eÞrða; bÞ þ grðd cÞ þ ðe gÞrðb cÞ; g < e
(8.5)
rða; b; c; dÞ ¼ ð1 gÞrða; bÞ þ erðd cÞ þ ðg eÞrða; dÞ; g > e
(8.6)
where g is the fraction of ground state cis tautomers being excited, while e indicates the fraction of the cis form in the excited state; d and c denote the angles between the horizontal axis and the transition moments in absorption and emission, respectively, in the cis form. Due to symmetry, these angles can only assume values of 0 or 90. Application of this model to 1 resulted in the determination of the transition moments for the four lowest pp* transitions, responsible for the Q and Soret bands. It was found that for the lowest excited singlet state the transition moment is approximately parallel to the line connecting the protonated nitrogen atoms, whereas the S0–S2 transition moment is nearly orthogonal to this direction. This is similar to the case of free base porphyrin, where the molecular symmetry (D2h)
Sn - S0 S1 - S0 α/2
N H N
β
N
N
H N
α/2 H N
N β H N
S1 - S0 Sn - S0 Figure 8.13 General scheme of tautomerism in 1 and the angles relevant for the anisotropy values.
261
262
8 Tautomerization in Porphycenes
(b)
(a)
S1 S1 S3
S3 N H
N H N
N
S2
N H
S4
N H N
N S2 S4
Figure 8.14 Transition moment directions for the lowest singlet excited states of 1. (a) Experimental values, (b) the results of TD-DFT(B3LYP/6-31G(d,p)) calculations. S1 and S2 correspond to Q bands, S3 and S4 to Soret transitions (cf. also Fig. 8.2).
dictates that only these two in-plane transition moment directions are allowed. Interestingly, the anisotropy data for another low-symmetry (Cs) porphyrin isomer, 2,3,6,7,11,12,17,18-octaethylcorrphycene reproduce the same pattern [81]. The moments of the transitions corresponding to the two Soret bands in 1 lie approximately along the lines bisecting the two angles formed by the moments of transitions to S1 and S2 (Fig. 8.14). An independent verification of this procedure was possible for 1b [82]. The four n-propyl substituents ensure that this molecule can be oriented to a high degree in stretched polymer sheets. Linear dichroism (LD) measurements on the aligned samples resulted in the determination of transition moment directions. A pattern similar to that of parent 1 was obtained. Both LD and emission anisotropy procedures yielded similar values, which, additionally, confirmed that the assignment of fluorescence depolarization to excited state tautomerization was correct. 8.3.2 Determination of Tautomerization Rates from Anisotropy Measurements
Fluorescence anisotropy measurements can also be used to obtain the rates of the excited state tautomerization. Two variants can be applied. The first is based on the analysis of time-resolved anisotropy curves. These are constructed from measurements of the fluorescence decay recorded with different positions of the polarizers in the excitation and emission channels. The anisotropy decay reflects the movement of the transition moment and thus, the hydrogen exchange. For molecules with a long-lived S1 state, the anisotropy decay can also be caused by rotational diffusion. In order to avoid depolarization effects due to molecular rotation, the experiments should be carried out in rigid media, such as polymers or glasses. When the S1 lifetime is short compared to that of rotational diffusion, tautomerization rates can be determined even in solution. This is the case for 1b, for which time-resolved anisotropy measurements have been performed at 293 K, using a
8.3 Tautomerization in the Lowest Excited Singlet State
fluorescence setup with single picosecond resolution [77]. Fluorescence was found to be depolarized from the very onset of the signal, which puts the lower limit of the tautomerization rate at values larger than 1011 s–1. This extremely high rate agrees with expectations based on the very strong hydrogen bond in this molecule. For both 1a and 1b, biexponential fluorescence decays provide evidence for the presence of two forms, even at low temperatures. At the same time, fluorescence remains depolarized. It implies that the rate of excited trans–trans conversion may be faster than that of the cis–trans reaction. In other words, simultaneous transfer of two hydrogen atoms is favored over a single hydrogen transfer process. The above method requires quite long measurement times and a proper matching of decay curve amplitudes. Moreover, the noise increases rapidly at longer delay times. Another procedure, experimentally less demanding, based on the steady state anisotropy values also allows determination of the trans–trans interconversion rates. Figure 8.15 shows the anisotropy of fluorescence excitation curves obtained for 1 in polyvinyl butyral films in the temperature range 20– 293 K. Three temperature regions can be distinguished: (i) a high-temperature, fast-reaction regime, when the tautomerization proceeds on a time scale much shorter than the S1 decay; (ii) an intermediate region, where the rates of the reaction and of S1 deactivation are comparable; (iii) a low-temperature range, when the tautomerization is frozen, at least on the time scale of the S1 lifetime. The obEmission int. (arb. Un.)
(b)
S1 S2
16000
Anisotropy
0,4
16400
16800
17200 (a)
7.5 K
0,2
293 K 293 K
0,0 7.5 K -0,2 16000
16400
16800
17200 Wavenumber
Figure 8.15 (a) Steady state anisotropy of fluorescence excitation of 1 recorded in poly(vinyl butyral) film as a function of temperature. The spectra were taken at 293, 250, 215, 165, 125, 85, 65, 45, and 7.5 K. (b) The excitation spectrum at 85 K monitored at 15900 cm–1.
263
8 Tautomerization in Porphycenes
served fluorescence anisotropy r and the reaction rate kPT are related by the formula: 1 rð0Þ r (8.7) kPT ¼ s 2r rðaÞ rð0Þ where r(0) and r(a) are the anisotropies of the initially excited and tautomeric species, respectively, which can be obtained from measurements performed in the low and high-temperature regimes; s is the value of the fluorescence decay time. The same rates are assumed for forward and backward reaction. Thus, the only quantity required, other than the anisotropy values, is the fluorescence lifetime, which can usually be measured with high accuracy. Figure 8.16 illustrates the application of this procedure in the study of the temperature dependence of tautomerization in porphycene dissolved in poly(vinyl butyral) film in the temperature range 7.5–293 K. Arrhenius type behavior is observed. The apparent activation energy for tautomerization is about 0.55–0.05 kcal mol–1 (192–20 cm–1), a very small value compared to the barrier of several kcal mol–1, estimated on the basis of tunneling splitting [72] and molecular geometry. A tentative interpretation is to postulate that the hydrogen exchange occurs as a thermally activated synchronous tunneling process, and the activation corresponds to exciting a vibration that lowers the barrier for the process. Indeed, the calculations for 1 predict an ag vibration around 180 cm–1 [41, 42] of which the experimental counterpart is observed both in the ground and S1 states [42, 83]. The form of this mode corresponds exactly to what can be expected to facilitate the concerted transfer of two hydrogen atoms: the distance between the two pairs of hydrogen-bonded nitrogen atoms is simultaneously decreased, with both NH_N bonds becoming more linear (Fig. 8.17). An alternative, but less probable explanation would be to assume a mechanism analogous to that of porphyrin – thermally activated tunneling of a single hydrogen atom. However, to account for the fact that no significant fraction of cis tauto-
18.5
ln (kPT)
264
17.5
16.5
15.5 0.006
0.010
0.014
1/T Figure 8.16 Arrhenius plot for tautomerization rates obtained for 1 in polyvinyl butyral (see also Fig. 8.15).
8.4 Tautomerization in the Lowest Excited Triplet State
Figure 8.17 The form of the normal mode responsible for lowering of tautomerization barrier for simultaneous double hydrogen transfer (calculated using B3LYP/6-31G(d,p)).
mers could be observed in 1, it is necessary that the tunneling of the first hydrogen atom is followed by a rapid transfer of the second hydrogen. In the limit of the latter process being much faster than the transfer of the first hydrogen atom, the synchronous mechanism is recovered.
8.4 Tautomerization in the Lowest Excited Triplet State
The tautomerism of 1 in the triplet state has been studied by time-resolved electron paramagnetic resonance (TR EPR) and electron spin echo spectroscopy in glassy matrices in the temperature range 4–100 K [84, 85]. Remarkable temperature variations have been observed. Two different triplet state species were detected at higher temperatures, but only one in the low temperature region. This was interpreted as evidence for two tautomeric species, assigned to the trans and cis forms. Since both are observed at 100 K, it was concluded that the energy difference is about 0.8 kJ mol–1. This value is slightly higher than the value obtained by NMR for the ground state of crystalline 1. In the latter case, only trans forms were detected below 50 K [40]. The exchange of hydrogens between the two tautomers was found to be slow on the EPR time scale at 100 K. The upper limit of the reaction rate was estimated at this temperature as 7 108 s–1.
265
266
8 Tautomerization in Porphycenes
It may be instructive to compare the excited state behavior of 1 with that of 2. It is well known that photoexcitation of free base porphyrins leads to trans–trans conversion [86]. This process occurs even at liquid helium temperatures, with the efficiency estimated as about 1% [87]. The mechanism is still under debate. Most probably, photoinduced tautomerization does not occur in S1; it has been suggested that the reactions can proceed in T1 [88] or even via higher excited triplet states [87]. It was also postulated that the cis structure in T1 can be involved [89]. However, no such structure has yet been detected. The differences in tautomerization in the lowest excited singlet and triplet states of 1 and 2 reflect the pattern observed for the ground state. In contrast to porphyrin, both trans and cis structures are detected in porphycenes, separated by a very small energy gap. The tautomerization barriers are also much lower in 1. Finally, at least in the case of the lowest excited singlet state, synchronous transfer of two hydrogen atoms seems to be preferred over a stepwise mechanism, even when both forms are present (1a and 1b).
8.5 Tautomerization in Single Molecules of Porphycene
Numerous variants of single molecule spectroscopy [90] are based on fluorescence detection. In particular, analysis of the spatial patterns of the emission from a single molecule makes it possible to determine its orientation in three dimensions. In this procedure, molecules are treated as dipoles emitting electromagnetic radiation. During the experiment, which lasts for seconds to minutes, photons are collected from a single chromophore immobilized in a rigid environment. For porphycene, it is obvious that, due to tautomerization, the molecule cannot be considered as a single dipole. In the simplest case of trans–trans interconversion, the fluorescence can be envisaged as occurring from two nearly orthogonal dipoles (Fig. 8.12). If a fraction of cis forms is also present, a third dipole should be added, its direction bisecting the angle formed by the moments of the transitions in the two trans species. It is to be expected that the spatial pattern of the emission should in such cases be different from that due to a single dipole. This was confirmed in the experiment that resulted in the detection of fluorescence from well above 60 single porphycene molecules [91]. The so-called azimuthal polarization mode of the exciting light was used. Various spatial patterns of the emission were observed (Fig. 8.18). In many cases they consisted of nearly perfect rings. It is not possible to obtain such a pattern in the case of a single dipole. The simulations of intensity patterns led to the picture of two dipoles forming an angle of about 70, in perfect agreement with the results obtained from fluorescence anisotropy studies of bulk porphycene in glassy matrices [80]. Some molecules revealed double lobe emission intensity patterns. This could be interpreted in two ways. The first assumes a single dipole and thus, no tautomerization. The other, more probable, explanation is that these patterns are due to molecules that are oriented perpendicularly to the sample surface: for such orien-
8.6 Summary
(a)
(b)
Figure 8.18 Spatial patterns of fluorescence of single porphycene molecules A and B immobilized in poly(methyl methacrylate) at 293 K. (a) Experiment, (b) simulation [91].
tation, it is not possible to distinguish between the single and the multiple inplane transition dipole case. Thus, the molecular symmetry of free base porphycene that dictates a rotation of transition moment directions upon tautomerization has enabled the observation of a basic chemical reaction on a single molecule level. The procedure can be extended to studies of more complicated porphyrinoids, such as sapphyrin, a pentapyrrolic macrocycle in which three inner hydrogen atoms can migrate within the cavity formed by five nitrogen atoms.
8.6 Summary
Even though the studies of tautomerism in porphycenes have not yet reached the stage of definitive answers and final conclusions, the accumulated material is rich, diverse and fascinating. Many of the observed effects deserve to be characterized in more detail. These include tunneling splitting due to double hydrogen transfer, coexistence of trans and cis forms, the exact mechanism of trans–trans, cis–trans, and, possibly, also cis–cis conversions, energy differences and barriers between trans and cis structures, location of NH vibrations, etc. The available data demonstrate that it should be possible to investigate all these problems for three
267
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8 Tautomerization in Porphycenes
different electronic states, S0, S1, and T1. Proper characterization of structure and dynamics, including tunneling, for the excited states in particular, is also a challenge for computational methods. An important property of porphycenes is their ability to undergo significant changes in the dimensions of the inner cavity under the influence of such “delicate” substituents as alkyl groups. This provides a rare opportunity for systematic studies of the rate vs. distance (in general, rate–geometry) relationship. The observations gathered so far for the lowest excited singlet state behavior of several porphycenes show that a change of 0.25 in the N–N separation may lead to orders of magnitude variations in the tautomerization rates, which clearly points to the crucial role of tunneling. Such studies may also contribute to the understanding of the correlation between the inner protons, or even provide a model for their quantum entanglement. The data presented in this work demonstrate large differences between the tautomerization characteristics in porphycene and its parent isomer, free base porphyrin. The origin for these dissimilarities may be due to different electronic structure or to distinct geometries. It seems at present that the latter are mainly responsible for the different patterns of tautomerism in 1 and 2. In particular, strong, nearly linear hydrogen bonds in porphycenes lead to low barriers and rapid tautomerization rates. The electronic structure seems to play a less important role, as may be speculated on the basis of similar values of NMR chemical shifts of peripheral hydrogen atoms, or by considering analogies in the pattern of the electronic spectra. In order to elucidate in more detail the role of electronic structure in tautomerism, we are now studying porphyrins in which peripheral substitution leads to inner cavity parameters similar to those of porphycenes.
Acknowledgments
The author expresses his gratitude to Emanuel Vogel and Josef Michl, who exposed him to the beauty of porphycenes. Special thanks go to many coworkers that have contributed to the results presented in this work: Michał Gil, Alexander Starukhin, Alexander Kyrychenko, Natalia Urban´ska, Oksana Pietraszkiewicz, Marek Pietraszkiewicz, Yuriy Stepanenko, Jerzy Sepioł, Hubert Piwon´ski, Andrzej Mordzin´ski, Alexander Vdovin, Alfred Meixner, Clemens Stupperich, Achim Hartschuh, Kristine Birklund-Andersen, Alexander Gorski, Jacek Dobkowski, Paweł Borowicz and Graz˙yna Orzanowska. Financial support from the Polish Committee for Scientific Research (grant 3T09A 113 26) is appreciated.
References
References 1 A. R. Battersby, C. J. R. Fookes,
G. W. J. Matcham, E. McDonald, Nature 1980, 285, 17–21. 2 R. Bonnett, Chem. Soc. Rev. 1995, 24, 19–33. 3 T. J. Dougherty, C. J. Gomer, B. W. Henderson, G. Jori, D. Kessel, M. Korbelik, J. Moan, Q. Peng, J. Natl. Cancer Inst. 1998, 90, 889–905. 4 S. B. Brown, E. A. Brown, I. Walker, Lancet Oncol. 2004, 5, 497–508. 5 M. R. Detty, S. L. Gibson, S. J. Wagner, J. Med. Chem. 2004, 47, 3897–3915. 6 T. Maisch, R. M. Szeimies, G. Jori, C. Abels, Photochem. Photobiol. Sci. 2004, 3, 907–917. 7 S. L. Gould, G. Kodis, R. E. Palacios, L. de la Garza, A. Brune, D. Gust, T. A. Moore, A. L. Moore, J. Phys. Chem. B 2004, 108, 10566–10580. 8 D. Gust, T. A. Moore, A. L. Moore, Acc. Chem. Res. 2001, 34, 40–48. 9 W. M. Campbell, A. K. Burrell, D. L. Officer, K. W. Jolley, Coord. Chem. Rev. 2004, 248, 1363–1379. 10 A. Renn, U. P. Wild, A. Rebane, J. Phys. Chem. A 2002, 106, 3045–3060. 11 C. M. Carcel, J. K. Laha, R. S. Loewe, P. Thamyongkit, K. H. Schweikart, V. Misra, D. F. Bocian, J. S. Lindsey, J. Org. Chem. 2004, 69, 6739–6750. 12 T. Hasobe, P. V. Kamat, M. A. Absalom, Y. Kashiwagi, J. Sly, M. J. Crossley, K. Hosomizu, H. Imahori, S. Fukuzumi, J. Phys. Chem. B 2004, 108, 12865– 12872. 13 Y. Kobuke, K. Ogawa, Bull. Chem. Soc. Jpn. 2003, 76, 689–708. 14 C. M. Drain, J. D. Batteas, G. W. Flynn, T. Milic, N. Chi, D. G. Yablon, H. Sommers, Proc. Natl. Acad. Sci. U. S. A. 2002, 99, 6498–6502. 15 I. Washington, C. Brooks, N. J. Turro, K. Nakanishi, J. Am. Chem. Soc. 2004, 126, 9892–9893. 16 J. L. Sessler, S. Camiolo, P. A. Gale, Coord. Chem. Rev. 2003, 240, 17–55. 17 I. Okura, J. Porphyr. Phthalocy. 2002, 6, 268–270. 18 J. P. Collman, J. T. McDevitt, G. T. Yee, C. R. Leidner, L. G. McCullough,
W. A. Little, J. B. Torrance, Proc. Natl. Acad. Sci. U. S. A. 1986, 83, 4581–4585. 19 J. L. Sessler, S. J. Weghorn, Expanded, Contracted and Isomeric Porphyrins, Elsevier Science, Oxford, 1997. 20 The Porphyrin Handbook, K. M. Kadish, K. M. Smith, R. Guilard, (Eds.), Vol. 2, Academic Press, New York, 2000. 21 E. Vogel, M. Kcher, H. Schmickler, J. Lex, Angew. Chem. Int. Ed. Engl. 1986, 25, 257–259. 22 J. L. Sessler, E. A. Brucker, S. J. Weghorn, M. Kisters, M. Schafer, J. Lex, E. Vogel, Angew. Chem. Int. Ed. Engl. 1994, 33, 2308–2312. 23 H. J. Callot, A. Rohrer, T. Tschamber, B. Metz, New J. Chem. 1995, 19, 155– 159. 24 E. Vogel, M. Broring, S. J. Weghorn, P. Scholz, R. Deponte, J. Lex, H. Schmickler, K. Schaffner, S. E. Braslavsky, M. Muller, S. Porting, C. J. Fowler, J. L. Sessler, Angew. Chem. Int. Ed. Engl. 1997, 36, 1651–1654. 25 E. Vogel, M. Broring, C. Erben, R. Demuth, J. Lex, M. Nendel, K. N. Houk, Angew. Chem. Int. Ed. Engl. 1997, 36, 353–357. 26 E. Vogel, P. Scholz, R. Demuth, C. Erben, M. Broring, H. Schmickler, J. Lex, G. Hohlneicher, D. Bremm, Y. D. Wu, Angew. Chem. Int. Ed. Engl. 1999, 38, 2919–2923. ´ ski, 27 P. Chmielewski, L. Latos-Grazyn K. Rachlewicz, T. Głowiak, Angew. Chem. Int. Ed. Engl. 1994, 33, 779–781. 28 H. Furuta, T. Asano, T. Ogawa, J. Am. Chem. Soc. 1994, 116, 767–768. 29 J. Michl, Tetrahedron 1984, 40, 3845– 3934. 30 J. Waluk, M. Mller, P. Swiderek, M. Kcher, E. Vogel, G. Hohlneicher, J. Michl, J. Am. Chem. Soc. 1991, 113, 5511–5527. 31 A. Gorski, E. Vogel, J. L. Sessler, J. Waluk, J. Phys. Chem. A 2002, 106, 8139–8145. 32 A. Gorski, E. Vogel, J. L. Sessler, J. Waluk, Chem. Phys. 2002, 282, 37–49.
269
270
8 Tautomerization in Porphycenes 33 Y. D. Wu, K. W. K. Chan, C. P. Yip,
34 35
36 37 38 39 40
41
42 43 44 45 46
47 48 49 50 51 52 53
54 55 56
E. Vogel, D. A. Plattner, K. N. Houk, J. Org. Chem. 1997, 62, 9240–9250. L. E. Webb, E. B. Fleischer, J. Chem. Phys. 1965, 43, 3100–3111. E. Bartoszak, M. Jasklski, T. Gustaffson, I. Olovsson, E. Grech, Acta Crystallogr., Sect. B 1994, 50, 358–353. B. M. L. Chen, A. Tulinsky, J. Am. Chem. Soc. 1972, 94, 4144–4157. A. Tulinsky, Ann. N.Y. Acad. Sci. 1973, 206, 47–69. J. G. Radziszewski, J. Waluk, J. Michl, Chem. Phys. 1989, 136, 165. J. Radziszewski, J. Waluk, J. Michl, J. Mol. Spectrosc. 1990, 140, 373. U. Langer, C. Hoelger, B. Wehrle, L. Latanowicz, E. Vogel, H. H. Limbach, J. Phys. Org. Chem. 2000, 13, 23–34. P. M. Kozlowski, M. Z. Zgierski, J. Baker, J. Chem. Phys. 1998, 109, 5905– 5913. K. Malsch, G. Hohlneicher, J. Phys. Chem. A 1997, 101, 8409. E. D. Becker, R. B. Bradley, C. J. Watson, J. Am. Chem. Soc. 1961, 83, 3743–3748. C. B. Storm, Y. Teklu, 1972, 94, 1745– 1747. C. B. Storm, Y. Teklu, E. A. Sokoloski, Ann. N.Y. Acad. Sci. 1973, 206, 631–640. R. J. Abraham, G. E. Hawkes, K. C. Smith, Tetrahedron Lett. 1974, 16, 1483–1486. S. S. Eaton, G. R. Eaton, J. Am. Chem. Soc. 1977, 99, 1601–1604. C. S. Irving, A. Lapidot, J. Chem .Soc., Chem. Comm. 1977, 184–186. H. J. C. Yeh, J. Magn. Reson. 1977, 28, 365. J. Hennig, H. H. Limbach, J. Chem.Soc., Faraday Trans. 2 1979, 752–766. P. Stilbs, M. E. Moseley, J. Chem.Soc., Faraday Trans. 2 1980, 76, 729–731. J. Hennig, H. H. Limbach, J. Magn. Reson. 1982, 49, 322–328. H. H. Limbach, J. Hennig, D. Gerritzen, H. Rumpel, Faraday Discuss., Chem. Soc 1982, 74, 229–243. J. Hennig, H. H. Limbach, J. Am. Chem. Soc. 1984, 106, 292–298. P. Stilbs, J. Magn. Reson. 1984, 58, 152. M. Schlabach, B. Wehrle, H. H. Limbach, E. Bunnenberg, A. Knierzinger,
57
58
59
60
61
62
63
64
65
66
67
68
69 70
71 72
73
A. Y. L. Shu, B.-R. Tolf, C. Djerassi, J. Am. Chem. Soc. 1986, 108, 3856–3858. M. J. Crossley, L. D. Field, M. M. Harding, S. Sternhell, J. Am. Chem. Soc. 1987, 109. L. Frydman, A. Olivieri, L. E. Diaz, B. Frydman, F. G. Morin, C. Mayne, D. M. Grant, A. D. Adler, J. Am. Chem. Soc. 1988, 110, 336–342. M. Schlabach, H. Rumpel, H. H. Limbach, Angew. Chem. Int. Ed. Engl. 1989, 28, 76–79. M. Schlabach, G. Scherer, H. H. Limbach, J. Am. Chem. Soc. 1991, 113, 3550–3558. M. Schlabach, B. Wehrle, H. Rumpel, J. Braun, G. Scherer, H. H. Limbach, Ber. Bunsenges. Phys. Chem. 1992, 96, 821–833. M. Schlabach, H. H. Limbach, E. Bunnenberg, A. Y. L. Shu, B.-R. Tolf, C. Djerassi, J. Am. Chem. Soc. 1993, 115, 4554–4565. J. Braun, M. Schlabach, B. Wehrle, M. Kcher, E. Vogel, H. H. Limbach, J. Am. Chem. Soc. 1994, 116, 6593–6604. J. Braun, C. Hasenfratz, R. Schwesinger, H. H. Limbach, Angew. Chem. Int. Ed. Engl. 1994, 33, 2215–2217. J. Braun, H. H. Limbach, P. G. Williams, H. Morimoto, D. E. Wemmer, J. Am. Chem. Soc. 1996, 118, 7231–7232. J. Braun, R. Schwesinger, P. G. Williams, H. Morimoto, D. E. Wemmer, H. H. Limbach, J. Am. Chem. Soc. 1996, 118, 11101–11110. H. H. Limbach, J. Hennig, R. Kendrick, C. S. Yannoni, J. Am. Chem. Soc. 1984, 106, 4059–4060. B. Wehrle, H. H. Limbach, M. Kocher, O. Ermer, E. Vogel, Angew. Chem. Int. Ed. Engl. 1987, 26, 934–936. R. P. Bell, The Tunnel Effect in Chemistry, Chapman and Hall, London, 1980. Z. Smedarchina, M. Z. Zgierski, W. Siebrand, P. M. Kozlowski, J. Chem. Phys. 1998, 109, 1014–1024. B. Frydman, C. O. Fernandez, E. Vogel, J. Org. Chem. 1998, 63, 9385–9391. J. Sepioł, Y. Stepanenko, A. Vdovin, A. Mordzin´ski, E. Vogel, J. Waluk, Chem. Phys. Lett. 1998, 296, 549–556. U. Even, J. Jortner, J. Chem. Phys. 1982, 77, 4391–4399.
References 74 H. P. Trommsdorff, Adv. Photochem. 75 76
77
78 79
80 81 82
1998, 24, 147–204. M. D. Harmony, Chem. Phys. Lett. 1971, 10, 337–340. A. Vdovin, J. Sepioł, N. Urban´ska, M. Pietraszkiewicz, A. Mordzin´ski, J. Waluk, J. Am. Chem. Soc. 2006, 128, 2577–2586. M. Gil, P. Borowicz, D. Marks, H. Zhang, M. Glasbeek, J. Waluk, in preparation. M. Gil, J. Jasny, E. Vogel, J. Waluk, Chem. Phys. Lett. 2000, 323, 534–541. A. Kyrychenko, J. Herbich, M. Izydorzak, M. Gil, J. Dobkowski, F. Y. Wu, R. P. Thummel, J. Waluk, Isr. J. Chem. 1999, 39, 309–318. J. Waluk, E. Vogel, J. Phys. Chem. 1994, 98, 4530–4535. A. Gorski, E. Vogel, J. Waluk, in preparation. K. Birklund-Andersen, E. Vogel, J. Waluk, Chem. Phys. Lett. 1997, 271, 341.
83 A. Starukhin, E. Vogel, J. Waluk, J. Phys.
Chem. A 1998, 102, 9999–10006. 84 C. W. M. Kay, K. Mbius, Mol. Phys.
1998, 95, 1013–1019. 85 C. W. M. Kay, G. Elger, K. Mbius, Phys.
Chem. Chem. Phys. 1999, 1, 3999–4002. 86 O. N. Korotaev, R. I. Personov, Opt. Spec-
trosc. (Engl. Transl.) 1972, 32, 479–480. 87 S. Vlker, J. H. van der Waals, Mol.
Phys. 1976, 32, 1703–1718. 88 V. A. Kuz’mitskii, Chem. Phys. Rep.
1996, 15, 1783–1797. 89 S. S. Dvornikov, V. A. Kuz’mitskii,
V. N. Knyukshto, K. N. Solov’ev, Dokl. Akad. Nauk SSSR 1985, 282, 362–366. 90 R. Rigler, M. Orrit, T. Basche, Single Molecule Spectroscopy, Springer, Berlin, 2002. ´ ski, C. Stupperich, 91 H. Piwon A. Hartschuh, J. Sepioł, A. Meixner, J. Waluk, J. Am. Chem. Soc. 2005, 127, 5302–5303. 92 J. Baker, P. M. Kozlowski, A. A. Jarzecki, P. Pulay, Theor. Chem. Acc. 1997, 97, 59– 66.
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9 Proton Dynamics in Hydrogen-bonded Crystals Mikhail V. Vener
9.1 Introduction
In this chapter we will consider molecular crystals with normal hydrogen bonds in which the donor A:H interacts with an acceptor :B. The so-called “bifurcated” and “trifurcated” H-bonds [1] as well as the new multiform unconventional Hbonds [2] are beyond the scope of the present chapter. We will focus on the proton dynamics in molecular crystals with strong and moderate H-bonds [3] in the ground electronic state. Attention will be focused on the interpretation of the structural and spectroscopic manifestations of the dynamics of the bridging proton as established in X-ray, neutron diffraction, infrared, and inelastic neutron scattering (INS) studies of H-bonded crystals. Various theoretical approaches have been developed for the description of the structure, spectral properties, and proton tunneling in H-bonded systems [4–7]. Computations for particular H-bonded species in the gas phase have been performed [8]. Due to strong environmental effects the applicability of gas-phase calculations to the proton dynamics in H-bonded crystals is questionable. Many theoretical approaches are based on oversimplified models (harmonic potentials and one-dimensional treatment of proton tunneling) and they usually contain parameters obtained from the experiment to be interpreted. This is why a consistent view on hydrogen bonding phenomenon in molecular crystals is still far from being achieved. The aims of this article are: 1. To show that a uniform and noncontradictory description of the specific properties of molecular crystals with quasi-linear H-bonds can be obtained in terms of a two-dimensional (2D) treatment assuming strong coupling between the protontransfer coordinate and a low-frequency vibration. 2. To interpret experimental structural and spectroscopic regularities of crystals with a quasi-symmetric A_H_A fragment using a model 2D potential energy surface (PES).
Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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9 Proton Dynamics in Hydrogen-bonded Crystals
3. To describe quantitatively the effects of a crystalline environment on the structure, PES, and vibrational spectra of strong H-bonds in terms of density functional theory (DFT) calculations with periodic boundary conditions.
9.2 Tentative Study of Proton Dynamics in Crystals with Quasi-linear H-bonds
A qualitative description of the structural and spectroscopic properties of Hbonded crystals requires the use of a simple two-mode linear model (9.1). B__._H–A fi| s |‹ |‹ R fi|
(9.1)
Here A and B are “heavy” molecular fragments and their internal structure is not specified in detail now. The centers of gravity of the B, A and H particles lie on the same straight line. The proton coordinate (s) is measured from the center of gravity (.) of the whole system (9.1). The distance between the terminal atoms (rather than between the centers of gravity of fragments B and A) is usually taken as the coordinate R. Typical values of the reduced masses (m and M) and characteristic frequencies (mas and ms) corresponding to the s and R coordinates are: m ~ 1 and M > 10 a.u.; mas > 1000 and ms < 200 cm–1. Figure 9.1 presents a 2D PES U(s,R) for a symmetrical system B = A. A specific feature of this PES is a strong coupling between the two coordinates. Due to the
Rc
Rb Ra
Figure 9.1 Model 2D PES U(s,R) of the symmetrical A_H_A fragment. Closed loops (1–4) are isoenergy contour lines in arbitrary units.
9.2 Tentative Study of Proton Dynamics in Crystals with Quasi-linear H-bonds
Energy, cm-1 (a) R = Ra
-0.2
0.0
0.2 s, Å
(b) R = Rb
-0.3
0.0
(c) R = Rc
0.3 s, Å
-0.4
0.0
0.4 s, Å
Figure 9.2 Slices through the model 2D PES U(s,R) for three fixed R values: (a) R = Ra, (b) R = Rb, (c) R = Rc. For the sake of comparison the W(R) function, see Eq. (9.6), is set equal to zero. The four lowest proton adiabatic levels are shown but the lower pair is not resolved in (c).
coupling the shape of the profile along the proton coordinate parametrically depends on R. At R = Ra there is a one-well profile (Fig. 9.2(a)). At R = Rb there appears a small barrier (Fig. 9.2(b)), and at R = Rc a double-well profile with a relatively high barrier exists (Fig. 9.2(c)). The point is that the difference between Rc and Ra for the considered H-bonded crystals is around 0.2 , that is of the order of the amplitude of zero-point vibration along the coordinate R. The R coordinate is a typical example of a so-called promoting mode [7]. It does not change (B = A) or very slightly changes (B „ A) when the bridging proton shifts from A to B. However, it appreciably changes in the transition state and thus modifies the height of the potential barrier. 9.2.1 A Model 2D Hamiltonian
The 2D model of the linear B_H–A fragment, assuming a strong coupling between the proton (AH stretch) and low-frequency (B_A stretch) coordinates, was introduced by Stepanov [9, 10]. It seems to be the simplest model enabling one to interpret the different specific features of H-bonded systems [11–16]. In terms of this model, the vibrational wave function of the H-bonded system is written as U(s,R,q1, … ,qN–8) » W(s,R)f(q1) … f(qN–8)
(9.2)
Here N is the number of degrees of freedom; f(qi) is a harmonic wave function, and W(s,R) is the eigenfunction of the following 2D Hamiltonian: H=
"2 ¶2 "2 ¶2 + U(s,R) 2 2m ¶s 2M ¶R2
Kinematic coupling is supposed to be nil and reduced masses are written as:
(9.3)
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9 Proton Dynamics in Hydrogen-bonded Crystals
m¼
M H ðM A þ M B Þ » MH ; MH þ MA þ MB
M¼
MA MB >> m MA þ MB
(9.4)
Here MH, MA and MB stand for the mass of the corresponding particle. In the case of intramolecular H-bonds A and B may be treated as the terminal atoms, in the case of intermolecular H-bonds A and B may be considered as the “heavy” fragments. The 2D PES U(s,R) of the B_H–A fragment in a crystal can be obtained using DFT calculations with periodic boundary conditions (Section 9.3.2) or extracted from experimental data (Section 9.2.2). In the case of the model 2D PESs the equilibrium value of the B_A distance is usually defined by structural data. The barrier height along the proton coordinate V0 is the main control parameter whose variation allows one to reproduce the spectroscopic data. There are two possible approaches to solution of the Schrdinger equation with the model Hamiltonian (9.3). The first is based on direct solution using grid [17] and basis [18] methods or the so-called multiconfiguration time-dependent Hartree method [19]. (The latter method is a combination of grid and basis set methods in the sense that the time-dependent basis functions are represented on a suitable grid). The second approach uses a Born–Oppenheimer type separation between the motions of the light and heavy nuclei (the method of adiabatic separation between vibrational variables) [20]. In the second approach the wave function W(s,R) is written as: W(s,R) » Wvn(s,R) = uv ðs; RÞvvn ðRÞ
(9.5)
Here uv ðs; RÞ is the wave function of the “fast” subsystem (proton or deuteron, with quantum number v) depending on R as a parameter. vvn ðRÞ is the wave function of the “slow” subsystem (with quantum number n). The 2D PES can be written as: U(s,R) = V(s,R) + W(R)
(9.6)
Here V(s,R) is the proton (deuteron) potential energy, and W(R) is the B_A interaction energy. The wave equation for the motion of the “fast” subsystem is given by " # "2 ¶2 þ V ðs; RÞ uv ðs; RÞ ¼ ev ðRÞuv ðs; RÞ (9.7) 2m ¶s2 where the adiabatic proton (deuteron) terms ev(R) depend on R as a parameter. The shape of ev(R) depends on v and is different for H and D. The wave equation for the B_A stretch is " # "2 ¶2 þ ev ðRÞ þ W ðRÞ vvn ðRÞ ¼ Evn vvn ðRÞ (9.8) 2M ¶R2
9.2 Tentative Study of Proton Dynamics in Crystals with Quasi-linear H-bonds
The “effective” potential for the B..A stretch is different for H and D and depends on the value of v. Various methods of numerical solution of the 1D vibrational Schrdinger equation have been suggested in the literature, for example see Refs. [21, 22]. Attractive features of the adiabatic separation of vibrational variables are its relative simplicity and its provision for a clear picture in terms of modes (see the next section). As a result of solving the Schrdinger equation for the model Hamiltonian (9.3) one gets anharmonic frequencies and relative IR intensities (if the dipole moment function is available) in the particular region of the IR spectrum [23–25]. It should be noted, however, that in many theoretical studies only the energy spectrum of the model 2D Hamiltonian was considered [26, 27]. 9.2.2 Specific Features of H-bonded Crystals with a Quasi-symmetric O_H_O Fragment
In many crystals with strong or moderate H-bonds and a quasi-symmetric A_H_A fragment the proton is known to have two equilibrium positions separated by a potential barrier. The most convincing evidence for this can be provided by neutron diffraction methods. For crystals containing O_H_O fragments with an O_O equilibrium distance (Re) in the range 2.40–2.70 , neutron diffraction studies reveal the existence of two protonic density maxima separated by 0.1– 0.8 , see Table 1 in Ref. [28]. (Following results presented in Refs. [29, 30] it was assumed that the lower limit of the length of the O_O hydrogen bond is 2.40 ). Molecular crystals with strong or moderate H-bonds demonstrate several structural and spectroscopic regularities. (i) The O_O equilibrium distance changes upon deuteration to give the so-called Ubbelohde effect. DR = Re(D) – Re(H) is negative for Re ~ 2.40 . With increasing Re the DR value becomes positive to reach a maximum at Re ~ 2.55 , after which it decreases [31]. (ii) The proton stretching vibrational frequency (asymmetric vibration of the O_H_O fragment, or the OH stretch) mH is remarkably decreased when Re decreases from ~ 2.70 to 2.40 . The decrease is ~ 2700 cm–1 that is from ~ 3200 to ~ 500 cm–1 [32, 33]. (For the sake of simplicity, the subscript “as” is omitted in this Section). (iii) The dependence of the isotopic frequency ratio, c = mH/mD, on mH is non-monotonic. Upon frequency lowering (that is shortening of the O_O distance) c decreases to unity (and below) and then sharply increases. Novak [32] obtained this result for crystals with the O_H_O fragment, and Grech et al. [34] observed it for compounds with the N_H_N fragment. To interpret these regularities the model 2D PES U(s,R) was suggested [28, 33, 35] for crystals with a quasi-symmetric O_H_O fragment. It was assumed that strong coupling between the s and R coordinates is manifested in a special dependence of the barrier height V0 on R. With V0 taken as zero at R = 2.40 , it rises exponentially in the region 2.40 < R < 2.60 . At larger R the increase is much slower. Representative profiles along the proton coordinate at three “crucial” values of R are given in Fig. 9.2, with details provided by specific examples in the remainder of this section.
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R ~ 2.40 (Fig. 9.2(a), H5O2+ in crystals, see Section 9.3.2) The PES profile has the shape of a single symmetric well with the bridging proton (deuteron) localized at the center symmetry. The proton (deuteron) stretching frequencies are described as |0æ fi |1æ transitions with mH ~ 1100 cm–1 and mD ~ 800 cm–1 leading to the usual value of c (~ 1.35). When R is larger than 2.40 but the barrier remains small (with the |0æ level still above the barrier) the proton vibrational amplitude increases and the proton kinetic energy accordingly drops in every quantum state. This results in lowering of the proton |mæ levels, more for higher m values. Figures 9.2(a) and (b) (and extrapolation of Fig. 9.2(c) to higher levels) show the strong decrease for levels above the barrier maximum. R ~ 2.47 (Fig. 9.2(b), sodium hydrogen bis(4-nitrophenoxide)dihydrate [36]) The lowest proton level is slightly below the central barrier. The |0æ and |1æ levels draw together and the |0æ fi |1æ transition is around 600 cm–1, in accord with the experimental data [36]. The separation of the corresponding levels for the deuteron decreases faster with R growth than does the proton levels. This is why the c value is very high (~ 2). R ~ 2.56 (Fig. 9.2(c), chromous acid [33]) The barrier grows very fast in this region and the |0æ fi |1æ transition frequency is very low for the H and D species. At the temperature of the experiment the |1æ level is sufficiently populated that the |1æ fi |2æ transitions appear in the IR spectra. There may be strong scattering of the experimental stretching frequencies because of the two different frequencies arising from the asymmetric stretch of the O_H_O fragment. In principle, there exists one more IR active transition in the considered R region. This is |0æ fi |3æ, which has a frequency that may differ strongly from the frequency of the |1æ fi |2æ transition. The |0æ fi |3æ transition seems to be realized only for systems with the O_D_O fragment [33]. As a result, the c values are ~ 1.3 for the case of mH(|1æ fi |2æ)/mD(|1æ fi |2æ) and ~ 1.0 for the case of mH(|1æ fi |2æ)/mD(|0æ fi |3æ). R > 2.60 (Benzoic acid dimer, see Section 9.2.3.1) The barrier along the proton coordinate at the equilibrium O_O distance is very high (> 7000 cm–1 [37]) and the energy gap between levels |2æ and |3æ is very small (several wavenumbers). The wells become isolated and the hydrogen bond becomes identical with the asymmetric OH_O H-bonds of moderate strength, mH > 2700 cm–1 and c ~ 1.34 [11]. To interpret the Ubbelohde effect, the W(R) is assumed to be harmonic. According to Eqs. (9.6) and (9.7), the total energy of the O_H_O system at v = 0, E0(R), is given by E0(R) = e0(R) + (1/2) krr( R – R0)2
(9.9)
For simplicity, krr is a constant and R0 is some parameter. Using the equilibrium condition dE0/dR = 0 and Eq. (9.9), we obtain for the isotopic change in the O_O distance DR ( Re(D) – Re(H) » (1/krr) [(de0H(R)/dR)0 – (de0D(R)/dR)0]
(9.10)
9.2 Tentative Study of Proton Dynamics in Crystals with Quasi-linear H-bonds
Energy, cm-1
1200
800
400 2,40
2,45
2,50
2,55
2,60
R, Å Figure 9.3 The ground proton (solid line) and deuteron (dashed line) energy level e0(R), see Eq. (9.7), as function of R.
here the subscript “0” after the parenthesis refers to R0. Hence, knowing e0H(R) and e0D(R) and computing derivatives at various points R0, DR can be found for any Re. According to Fig. 9.3, the proton and deuteron adiabatic levels e0H and e0D show a different dependence on R. As a result, DR is negative for Re ~ 2.40 , with increasing Re it becomes positive, reaches a maximum at some Re, and then decreases. 9.2.3 Proton Transfer Assisted by a Low-frequency Mode Excitation
Due to the relatively small mass of the proton it is assumed that tunneling effects play a crucial role in many proton and hydrogen atom reactions, and that they determine many specific properties of H-bonded systems in the gas and condensed phases [38]. It should be noted, however, that proton tunneling has been proved experimentally for only a relatively small number of H-bonded systems in the gas phase and in crystals. In systems with equivalent initial and final states proton tunneling may be manifested as observable splitting of some vibrational states. Tunneling splittings of the ground and several excited vibrational states have been measured for systems with intramolecular [39–42] and intermolecular [43, 44] H-bonds in the gas phase. For some substances (9-hydroxyphenalenone derivatives) the tunneling splitting of the ground vibrational state was measured in the molecular crystals [45, 46]. For other systems (malonaldehyde) tunneling does not occur in the molecular crystals due to the crystal field effect, which produces asymmetry of the PES along the proton-transfer coordinate [47].
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In many molecular crystals that are formally symmetric according to their crystal structure, the double-minimum PESs are asymmetric [48–50]. As a rule, the asymmetry is of the order of 50–100 cm–1 and its lifetime is much longer than the duration of X-ray diffraction or spectroscopic experiments. This fact is of fundamental importance for the proton transfer phenomenon because it implies that the transfer of a charged (proton or deuteron) particle must be associated with a considerable energy of medium repolarization. The asymmetry makes it impossible to use the model by which proton tunneling occurs at the occasional moments when vibrational levels in two asymmetric wells become nearly degenerate under the action of environmental fluctuations (for example see Refs. [51, 52]). An alternative model for the proton transfer mechanism was used in Refs. [14, 35, 53, 54]. According to this model the proton transfer between two wells, being asymmetric, occurs by quantum jumps between vibrational levels under the action of random forces from the environment. It was applied to crystalline benzoic acid to describe the temperature dependence of the nuclear spin–lattice relaxation time, which was measured in the neutral dimer [48, 55] and in its deuterated analog. In solids there are many low-frequency modes which can influence the proton movement and thus affect its magnetic relaxation. Only the stretching and rocking intracomplex vibration modes seem to be sufficiently strongly coupled with the proton coordinate to account for relaxation. The O_O stretching vibration was used in Refs. [35, 56] as the low-frequency (promoting) mode.
9.2.3.1 Crystals with Moderate H-bonds Crystals with the quasi-symmetric O_H_O fragment and moderate H-bonds are characterized by the following parameter values: 2.60 < Re < 2.75 and 2500 < mH < 3400 cm–1 [1, 11, 32]. A typical example is the molecular crystal of benzoic acid dimer. At the equilibrium O_O distance (Re = 2.64 ) the barrier along the s coordinate is very high (the second doublet of the OH stretch lies under the peak). Because of the above-mentioned asymmetry in the crystal the energy difference between the two lowest energy levels DE can be written as [57]: DE =
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi J 2 þ A2
(9.11)
Here A is the energy asymmetry of the potential energy minima and J is the tunneling splitting of the ground vibrational state (in the considered doublewell potential when A equals zero). In benzoic acid crystals A ~ DE, because J ~ 0.2 cm–1 [58] and DE ~ 65 [48]. Asymmetry was introduced to the model 2D PES, see Eq. (9.6), by adding a new term A(s), describing the energy difference between the depths of the two wells. The solution of the 2D Schrdinger equation was found by the method of adiabatic separation, see Section 9.2.1. In so doing, only the symmetric coordinate s of a two-proton system was taken into account s = (1/2)(s1 – s2)
(9.12a)
9.2 Tentative Study of Proton Dynamics in Crystals with Quasi-linear H-bonds
Here si is the coordinate of the ith (i = 1, 2) proton, measured from the midpoint of the hydrogen bond bridge. The antisymmetric coordinate a was set to be zero: (9.12b)
a = (1/2)(s1 + s2)
Hence, the double-proton transfer was assumed to proceed via a concerted mechanism, with the one-dimensional kinetic-energy matrix appropriate to one particle of twice the proton mass. A similar model is widely used to analyze the vibrations of cyclic hydrogen-bonded dimers (for example, see Ref. [59]). The O_O coordinate in this case symbolizes the intermolecular stretching of a doubly H-bonded system. The problem of the double-proton transfer for the benzoic acid dimer is thereby reduced to a problem conceptually similar to that for a single O_H_O entity except for the denoted light atom mass and consequences of the asymmetric 2D PES. Calculations show that only the two lowest proton states, with v = 0 and v = 1 and the energy separation DE ~ 65 cm–1, have to be taken into account. The vibrational level of the second excited proton state v = 2 is too high (> 2700 cm–1) to be populated. Due to the PES asymmetry the proton in the ground state (v = 0) is located in the left well (an initial state), and in the first excited state (v = 1) the proton is located in the right well (a final state). In other words, the effective potential e0(R) + W(R), see Eq. (9.8), describes O_O levels in the left well (quantum number m), while the e1(R) + W(R) potential describes O_O levels in the right well (quantum number n). (W(R) was assumed to be an anharmonic function in Ref. [35]). Quantum transitions between different vibrational levels are induced by random forces acting from the surroundings. One can distinguish between two kinds of transition: 1. The O_O thermal excitation and de-excitation (intrawell transitions) |v,m> « |v,m¢>, (v = 0, left well, m „ m¢)
(9.13a)
|v,n> « |v,n¢>, (v = 1, right well, n „ n¢)
(9.13b)
2. The tunneling (interwell) transitions: |v,m> « |v¢,n>, (v „ v¢; v,v¢ = 0,1)
(9.14)
Calculations show that the proton transfer assisted by low-frequency vibration excitation predominates over the “pure tunneling” transition |0,0> « |1,0>. The probability of this particular transition is nearly 103 times smaller than the probability for the transition driven by the O_O vibrations (e.g., |0,2> « |1,3>). To interpret this result one has to consider values of the <0m|R|0m> matrix elements for different m. <0m|R|0m> =
RR
u0 ðs; RÞv0m ðRÞRu0 ðs; RÞv0m ðRÞdsdR =
R
v0m ðRÞRv0m ðRÞdR
(9.15)
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In terms of the model used, see Eq. (9.13a), it gives the effective value of R at different O_O levels when the tunneling particle is located in the left well (the initial state). One can see (Table 9.1) that excitation of the O_O vibrations on two quanta leads to the decrease in the effective value of R from 2.64 (the equilibrium O_O distance) to 2.61 .
Tab. 9.1 Values of the matrix element <0m|R|0m> computed as a function of m for two Re
distances. Matrix element
Moderate H-bonded crystal Re = 2.64 , V0(Re) > 7000 cm–1
Strong H-bonded crystal Re = 2.52 , V0(Re) ~ 2500 cm–1
<00|R|00>
2.64
2.520
<01|R|01>
2.618
2.580
<02|R|02>
2.610
2.589
<03|R|03>
2.638
2.602
It has already been mentioned (see Section 9.2.2) that the main characteristic feature of the model 2D PES [28, 33, 35, 56] is the special dependence of the barrier height V0 on R. V0 rises exponentially in the region 2.40 < R < 2.60 and at larger R values it increases much more slowly. This is why a relatively small decrease in the effective value of R leads to a strong decrease in the effective value of the barrier. As a result, the tunneling probability from the second excited O_O level |02> is much larger than that from the |00> level. The temperature dependence of the proton and deuteron spin relaxation times were calculated in Ref. [35]. It was assumed that (i) intrawell transitions, see Eqs. (9.13a) and (9.13b), proceed much more rapidly than those between wells, see Eq. (9.14); and (ii) that a factor characterizing the coupling of the proton to modes of the surrounding medium (excluding the O_O mode) is a function of the temperature only. Theoretical curves, see Figs. 5 and 6 in Ref. [35], are in reasonable agreement with experiment. The apparent activation energy of proton transfer is ~ 800 cm–1, while the potential barrier height in the proton coordinate is much larger (> 7000 cm–1). The discrepancy between these values is caused by the fact that the probability of the interwell transition depends non-monotonically on m (Figs. 2 and 3 in Ref. [35]). The probability reaches its maximum at the second excited O_O stretch level and then decreases for m > 3. This is why the temperature dependence of the total probability for interwell transitions increases at low temperatures, but levels off near room temperature. The described model resembles that used in Refs. [14, 55] to evaluate the temperature dependence of the nuclear spin–lattice relaxation time in the benzoic
9.2 Tentative Study of Proton Dynamics in Crystals with Quasi-linear H-bonds
acid dimer and its deuterated analog. The rocking mode was used as the low-frequency mode in Refs. [14, 55] and the potential barrier in the proton coordinate was set to be ~ 1800 cm–1. As a result, the energy gap between the two lowest proton levels (pair of levels) calculated with this PES (~ 1100 cm–1) is much lower than the experimental OH stretching frequency observed for carboxylic acid dimers (> 2700 cm–1) [32]. The quantum dynamics of proton transfer in the H-bonds of carboxylic acid dimers was also investigated using magnetic field-cycling NMR and optical spectroscopy in the low temperature region, and quasi-elastic neutron scattering at higher temperatures [60, 61]. The interpretation of these results has been done in terms of theoretical methods based on a perturbative instanton approach [61]. According to Refs. [35, 56] the mechanism of proton tunneling assisted by the excitation of low-frequency modes in molecular crystals with moderate H-bonds differs strongly from that in the gas phase [62]. In the isolated formic acid dimer the tunneling splitting increases monotonically with the O_O excitation, while in crystals the dependence of the probability of proton tunneling on the excitation low-frequency modes is non-monotonic.
9.2.3.2 Crystals with Strong H-bonds Crystals with a quasi-symmetric O_H_O fragment and strong H-bonds are characterized by the following parameter values: 2.40 < Re < 2.60 and mH < 2500 cm–1 [1, 32, 33]. The barrier along the proton coordinate varies from 0 to ~ 5000 cm–1. We will consider a model system with Re = 2.52 . In terms of the model 2D PES [35, 56] the second pair of the adiabatic proton levels |2æ and |3æ locate in the vicinity of the potential barrier maximum at this Re distance. At Re = 2.52 V0 ~ 2500 cm–1 the tunneling splitting is J » 85 cm–1, i.e. of the same order of magnitude as the energy asymmetry of potential, A ~ 30 cm–1 [49, 50, 63]. At this Re value only 60% of the proton density is localized in the left well in the ground state |00>. Hence, the transition |0,0 > « |1,0>, see Eq. (9.14), is not a complete proton tunneling but only a redistribution of the proton density over two wells. This effect can be observed in principle in some physical experiments (NMR [64], dielectric relaxation [65] etc.). Proton transfer at Re = 2.52 can be treated using the approach developed in the previous section, see Eqs. (9.13) and (9.14). According to Refs. [35, 56] for a model H-bonded system with Re ~ 2.52 no vibrational assistance of the proton tunneling occurs. This effect can be explained using the <0m|R|0m> matrix element for different m, see Eq. (9.15). The excitation of the low-frequency vibrations leads to an increase in the effective O_O distance (Table 9.1), i.e. to an increase in the effective barrier along the proton coordinate. To summarize, in molecular crystals with strong H-bonds the proton transfer is not assisted by low-frequency mode excitation. In other words, proton dynamics is apparently not coupled to the low-frequency vibrations, in agreement with the results of INS studies of different crystals with strong H-bonds [49, 50, 63].
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According to these papers “ … the proton transfer is totally decoupled from the heavy atom dynamics … ”.
9.2.3.3 Limitations of the Model 2D Treatment The 2D model [28, 33, 35, 56] enables one to get a qualitative agreement with the available structural and spectroscopic regularities established for molecular crystals with a quasi-symmetric O_H_O fragment. However, a strong dispersion of the experimental points implies that the considered properties do not depend on one variable (Re), but on several other characteristics; there are first bending of the O_H_O fragment, the chemical composition of the compound, and the crystal structure. To get a semi-quantitative, and in some cases quantitative, agreement with experiment, one has to increase the dimensionality of the PES, for example see [66–68], and to take into account effects of the crystalline environment, see Section 9.3. In some H-bonded systems, for example the hydrogen maleate ion [69], vibrations of the O_H_O fragment are mixed strongly with the other vibrations. This implies that Eq. (9.2) is not applicable to such systems and the W function depends on other vibrational coordinates, in particular, the CO stretch mode. In the case of synchronous proton transfer in cyclic H-bonded clusters consisting of a single type of monomer the s and R coordinates can be treated as “totally symmetric” OH and O_H_O stretches [70]. In order to compute anharmonic frequencies of the IR active asymmetric OH stretch the asymmetric coordinate a, see Eq. (9.12b), is to be taken into consideration, for example see Refs. [62, 71]. It was mentioned in Section 9.2.3.1 that two different model 2D PESs were used to evaluate the temperature dependence of the nuclear spin–lattice relaxation time in benzoic acid dimer. The problem arising in this connection is how to choose values for the fitting parameters entering the model PESs. In most investigations they are defined from the experiment to be interpreted. Unfortunately the potentials determined this way are as a rule unable to properly describe other experimental regularities and data (spectroscopic, structural) known for the same compounds. Moreover the agreement between theory and experiment disappears if the fitting parameter values are taken, for example, from spectroscopic data [72]. In Sections 9.2.3.2 and 9.2.3.3 it was assumed that the dynamic asymmetry caused by the environment has a long lifetime and that this asymmetry can be considered as static. In some cases a reorganization of the surroundings has to be included explicitly in the model Hamiltonian via the introduction of a so-called “reorganization” mode [7]. The energy gap between two wells, corresponding to the initial and final states, is a typical example of a reorganization coordinate [73]. Calculation procedures including the use of this variable for the description of proton transfer in condensed phase (polar solvents) are well developed (compare numerical modeling by molecular dynamics simulations [74] with the use of continuum approximation [75]).
9.2 Tentative Study of Proton Dynamics in Crystals with Quasi-linear H-bonds
9.2.4 Vibrational Spectra of H-bonded Crystals: IR versus INS
Vibrational spectroscopy is widely used in experimental studies of molecular crystals with H-bonds. In some cases low-temperature INS experiments are not in complete agreement with IR absorption spectra and potential functions determined with IR (or Raman) spectroscopy are quite different from those derived from INS measurements [76]. The inconsistencies may be arranged into two groups. (i) Low-temperature INS experiments on CrOOH are not in complete agreement with IR absorption spectra in the 1500–2500 cm–1 region [77]. (ii) In the IR spectra of sodium bifluoride (NaFHF) the mas(FHF) band starts at 1300 and extends up to 2000 cm–1 with some structure in the region due to combination bands of the type mas(FHF) + nms(F_F), n = 0,1, … [78]. In contrast, the INS spectrum of NaFHF shows a much narrower band due to mas(FHF) (full width halfheight ~ 159 cm–1) and no combinations [79]. Careful considerations of problems (i) and (ii) enable one to account for these apparently conflicting phenomena. (i) Spectroscopic studies of molecular crystals with strong and moderate H-bonds have been carried out under widely varying temperature conditions. The INS spectra are usually obtained at low temperatures (< 30 K) in the 0–2000 cm–1 region, while the IR or Raman absorption spectra of the same crystals at low temperatures are often not available and, moreover, the IR absorption is very weak in the low frequency region (< 300 cm–1). In the considered crystals the energy difference between the two lowest proton levels DE, see Eq. (9.11), is ~ 100 cm–1 and the thermal population of the first excited proton level is negligible at T < 30 K. This is why in the INS spectra practically all of the bands are due to transitions from the ground vibrational state. In the IR spectrum at T = 100–300 K the asymmetric stretch of the O_H_O fragment may be due to the transitions from the first excited proton level |1æ fi |2æ (Section 9.2.2). The other possible transition, namely |0æ fi |3æ is located above 2000 cm–1 (Fig. 9.2(b) and (c)). INS spectra are characterized by a relatively poor resolution in this high frequency region. Due to relatively small changes in the dipole moment associated with O_H_O bendings, these fundamentals often have relatively small intensities in the IR spectra. However, these bands correspond to large vibrational displacements of the proton, and they are usually clearly seen in the INS spectrum [30, 49]. Summarizing, the number of bands corresponding to the fundamental vibrations of the O_H_O fragment, and their frequencies in the considered crystals, may be different in the IR and INS spectra. (ii) Electric anharmonicity is one of the most important factors shaping absorption profiles in the IR spectra of systems with
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strong and moderate H-bonds, see for example Refs. [23, 66]. As a result, a large number of a relatively intensive nonfundamental transitions may appear in the IR spectra. In particular, the broad IR band associated with the asymmetric stretch of the O_H_O fragment is due to combinations with the O_O stretch. The change in the dipole moment function plays no role in the INS spectra and this is why the mas(OHO) bands in INS spectra are usually narrow and contain no combinations. Special attention should be paid to the spectroscopic manifestations of a crystalline environment on proton transfer and on vibrations of the O_H_O fragment. Direct evidence for these effects may come from comparison of the INS spectrum of the considered H-bonded system in the gas phase and in crystals. While this is not possible due to technical problems, the comparisons may be done theoretically using DFT calculations with periodic boundary conditions (Section 9.3). Comparison of the computed INS spectrum of the isolated H5O2+ ion with the computed spectrum of the ion in H5O2+ClO4– crystals (Fig. 9.7, later) shows that these spectra differ in the 1200–1600 cm–1 frequency region. This result implies that environmental effects may strongly affect the INS spectrum in the region of the asymmetric stretching and bending vibrations of the O_H_O fragment. A possible way to detect strong coupling between the asymmetric and symmetric stretches of the O_H_O fragment is to compare the low-temperature INS spectrum of the crystal with that obtained at relatively high temperature, that is when the first excited state of the O_O stretch is sufficiently populated. To our knowledge, such a comparison has not been done yet. Effective 1D potentials along the proton coordinate are often used to interpret the structure of spectroscopic regularities of H-bonded crystals. In this case the coupling with other vibrational modes is manifested through differences between the effective H and D potentials [80]. For example, effective 1D potentials were derived from band shape analysis of the OH (OD) IR and Raman stretching modes of KHCO3 (KDCO3) [81] and subsequently used for the interpretation of the INS spectrum of KHCO3 crystals [50]. The difference between the effective H and D potentials (see Fig. 3 in Ref. [50]) is due to coupling with some low-frequency modes.
9.3 DFT Calculations with Periodic Boundary Conditions
At present three different codes are widely used for calculations of the structural and spectroscopic properties of H-bonded crystals, for example see Refs. [82–85]. The Car–Parrinello molecular dynamics (CPMD) program [86] and the Vienna ab initio simulation program (VASP) [87, 88] use a plane wave basis set, while an atom centered set is used with periodic boundary conditions in the CRYSTAL
9.3 DFT Calculations with Periodic Boundary Conditions
package [89]. Different exchange-correlation functionals are implemented in these codes. In the first step the positions of all atoms in the cell are optimized. Cell parameters are usually borrowed from experiment. In some cases they are optimized [84] and in some cases not [85]. Harmonic frequency calculations verify that the computed structure corresponds to the global PES minimum. In the second step the anharmonic OH stretching [83, 84] frequency is estimated using 1D potential curves calculated as a function of the displacement for the hydrogen atom. In the third step classical molecular dynamics (MD) simulations are performed. The IR [85] or vibrational spectrum [82, 83] of the crystal is computed from the Fourier transform of the corresponding time correlation function (see Section 9.3.1). To compare the structural and spectroscopic properties of the H-bonded system in the crystal with those in the gas phase, one has to calculate a quasi-isolated system in a simulation box (CPMD and VASP), and to compute the system in the gas phase (CRYSTAL) with the same functional and basis set. 9.3.1 Evaluation of the Vibrational Spectra Using Classical MD Simulations
The IR spectrum is obtained as the Fourier transform of the autocorrelation function of the classical dipole moment M [90], calculated at every point of the MD trajectory: Z¥ 4 hx tanh Re eixt hM ðtÞMð0Þidt I ðxÞ ¼ x (9.16) e0 chn 4 kB T 0
where I(x) is the relative IR absorption at frequency x , T is the temperature, kB is the Boltzmann constant, c is the speed of light in vacuum, e0 is the dielectric constant of the vacuum, and n is the refractive index (which was treated as constant). The INS spectrum is calculated from the Fourier transform velocity autocorrelation functions of the atoms (Eq. (9.16) with velocities instead of the dipole moment), weighted by their inelastic neutron scattering cross-sections [91]. Since the value of the INS cross-section of the H atom is at least one order of magnitude larger than that of the other atoms, only the H atom velocities are usually taken into account. As a result, the I(x) values in the computed INS spectrum are related to the mean-square-displacements of the hydrogen atoms. However, the observed INS spectrum has its intensity given by the “scattering law”, S(Q,x), which depends on the momentum transfer Q, for example, see Eq. (1) in Ref. [30]. Our approach has avoided the impact of the momentum transfer. The difference between the simple simulation using displacements only and one including momentum transfer were considered in Ref. [92]. Comparison of Fig. 6 and 4b in that paper shows that the intensities are damped for larger wavenumbers (this would fit the present case) and the features broaden a lot. However, the peaks are at about the same position. Therefore, we hope that this will also be the case for the present study.
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9 Proton Dynamics in Hydrogen-bonded Crystals
The observed intensities also depend on the refractive index, which in general is frequency dependent [93]. This dependence is unknown in most cases and has not been considered. We note, however, that for liquid water the refractive index is virtually constant between 300 and 3500 cm–1 [94]. The dipole autocorrelation function is calculated classically and quantum corrections [95, 96] are introduced through the factor 2/[1+exp(–hx/2pkBT)]. Eq. (9.16) for the absorption spectrum has previously been applied in calculations of the far- and mid-IR spectra of liquid water [90, 97] and crystals [85]. The quantum correction damps the intensities of the low frequency motions and more sophisticated schemes [98] may lead to more severe damping of the low frequencies – as found for liquid water [99]. 9.3.2 Effects of Crystalline Environment on Strong H-bonds: the H5O2+ Ion
H5O2+ is a prototype for strongly H-bonded systems which plays an important role in condensed phase [7, 100, 101] and enzymatic reactions [102]. The H5O2+ structure in crystalline H5O2+ClO4– was determined by X-ray diffraction [103]. IR, Raman, and INS spectra are also available for this system [104, 105]. The point is that the different experimental studies were performed at the same temperature (T ~ 84 K). The IR spectrum of gas phase H5O2+ in the 800–2500 cm–1 region has only recently been measured [106, 107]. We use CPMD to simulate the structure, the PES of the O_H_O fragment, and the INS and IR spectra of H5O2+ in the H5O2+ClO4– crystal for comparison with results for the H5O2+ gas-phase species [108, 109]. The discussion addresses the following issues: 1. Environmental effects on the structure, the PES of the O_H_O fragment, and the vibrational spectrum of H5O2+. 2. The relation between the IR and INS spectra: specifically the broad IR bands compared to the relatively narrow INS bands for the O_H_O vibrations [110]. The CPMD calculations use the BLYP functional [111] with Trouillier–Martins [112] pseudo-potentials for core electrons. The kinetic energy cutoff for the plane wave basis set is 80 Ry. This value yields structures and harmonic frequencies of the isolated H5O2+ and ClO4– ions that are comparable to BLYP results obtained with large Gaussian basis sets (aug-cc-pVTZ [113]). The isolated H5O2+ ion was computed using the TURBOMOLE package [114–116] in BLYP/aug-cc-pVTZ approximation. The details of the computations may be found in Ref. [108].
9.3.2.1 The Structure and Harmonic Frequencies Dimensions of the unit cell (which contains four formula units of HClO4.2H2O) and positions of the heavy atoms were taken from Ref. [103]. Optimization of all atomic positions yields a structure with four equivalent H5O2+ClO4– units. In accord with the experimental data, the CPMD results suggest a structure in which the proton of the perchloric acid has been transferred to water and is shared by
9.3 DFT Calculations with Periodic Boundary Conditions
two water molecules, forming the H5O2+ ions. These H5O2+ ions are hydrogen bonded to the ClO4– ions. There are no hydrogen bonds between different H5O2+ ions. The theoretical crystal structure is orthorhombic, space group P212121. This was verified by a vibrational analysis which does not show imaginary frequencies. It should be noted that the X-ray study [103] considered the non-centrosymmetric Pn21a structure as a possible choice, but the centrosymmetric space group Pnma was accepted as most suitable. We find that the latter corresponds to a transition structure with one imaginary frequency (~ 78i cm–1). The transition P212121 fi Pnma fi P212121
(9.17)
corresponds to a simultaneous shift of the four bridging protons along the O_O line. The O_H distances in the O_H_O fragment of H5O2+ are equal in the transition structure, but differ in the minimum energy structure. The corresponding Cl–O distances in the two structures differ by less than 0.001 , while the O_O distances differ by up to 0.03 . The energy difference between the two structures is less than kBT at the experimental temperature. The large-amplitude vibration of the bridging H, see Eq. (9.17), complicates the determination of the crystal space group. The computed distances of different H-bonds in the crystal agree fairly well with the experimental values. The O_O distance in H5O2+ is 2.426 (2.424 ) and H-bonds between the H5O2+ and ClO4– ions vary from 2.72 to 2.78 (2.784, 2.788 ). Experimental values [103] are given in parenthesis. In the crystal and gas phase the H5O2+ ion can be considered as a nonrigid molecule because the bridging H undergoes large-amplitude vibrations. The symmetry point group of H5O2+ in the crystal is C2h 1). Approximate C2h symmetry of the H5O2+ ion has also been found in X-ray studies of crystalline hydrates of different acids [117]. The computed equilibrium O_O distances are 2.431 in the isolated H5O2+ ion and 2.426 in the crystal, i.e. they are virtually the same. The O_H_O fragment is slightly nonlinear in the gas phase (172) and becomes linear in the crystal. Due to the strength of the O_H_O bond, the crystalline environment changes the O_O distance only slightly, however, it changes the mutual orientation of the water molecules in H5O2+ as compared to the isolated species, see Fig. 9.4. As a result, in the crystal the bending potential along Y increases much faster than along X, and the frequencies of the two bending vibrations of the O_H_O fragment differ strongly in the crystal. In contrast, in the gas phase the bending potentials in the X- and Y-directions are more similar and the two bending modes are virtually degenerate, see Table 9.2. The harmonic frequencies of the isolated H5O2+ ion and the H5O2+ ion in the H5O2+ClO4– crystal are given for the region above 1000 cm–1 in Table 9.2. (The four fundamentals of the ClO4– anion and their multiple components are located 1) The symmetry of the H5O2+ ion in the Pnma
structure depends on the accuracy of the symmetrization procedure, e. For e = 10–5 a.u. one gets Ci; for e = 5 10–2
a.u. – C2h. The latter value is of the same order of magnitude as the bond distances correction used in the X-ray study [103], < 5.2 10–2 a.u.
289
290
9 Proton Dynamics in Hydrogen-bonded Crystals
(a)
C2 Y
Y Z
X
X
Z
(b)
C2h
Figure 9.4 Structure of H5O2+ in the gas phase (a) and in the crystal (b). The coordinate origin is at the midpoint between the oxygen atoms on the O_O line, Y is the C2 axis and Z is the O_O line. Tab. 9.2 Selected harmonic frequencies of the isolated H5O2+ ion computed using TURBOMOLE,
and those obtained for the crystal using CPMD. Units are cm–1. (IR relative intensities are given in parentheses). Assignment
Isolated H5O2+
H5O2+ in H5O2+ClO4– crystal
C2
TURBOMOLE[a]
CPMD[b]
O_H+_O asymm. stretch
B
1019 (1.0)
1023, 1130, 1180, 1237
O_H+_O bending
B
1411 (0.1)
1037, 1183, 1190, 1198
O_H+_O bending
A
1500 (0.03)
1710, 1713, 1716, 1727
H2O symm. bending
A
1652 (0.0)
1622, 1625, 1633, 1643
H2O asymm. bending
B
1707 (0.33)
1671, 1683, 1634, 1703
O–H stretch
B
3594 (0.03)
3214, 3221, 3229, 3234
O–H stretch
A
3609 (0.04)
3301, 3305, 3311, 3313
O–H stretch
B
3680 (0.08)
3357, 3358, 3358, 3366
O–H stretch
A
3681 (0.10)
3377, 3385, 3389, 3428
a BLYP/aug-cc-pVTZ, force constants calculated numerically from analytic gradients (step size 0.02 a.u.). b BLYP/plane-wave (80 Ry), force constants calculated numerically, the step length for the finite difference calculations was 0.01 a.u. in both directions.
9.3 DFT Calculations with Periodic Boundary Conditions
below 1000 cm–1 [104]). For the H5O2+ ion in the H5O2+ClO4– crystal the stretching and bending vibrations of the lateral water molecules are in the ranges 3214– 3428 cm–1 and 1671–1703 cm–1, respectively. The corresponding bands in the experimental IR spectrum (Fig. 3a in Ref. [104]) have maxima at 3200/3300 cm–1 and at 1700 cm–1, respectively. Harmonic frequencies of the asymmetric stretch of the O_H_O fragment vary from 1023 to 1237 cm–1 in the crystal. This may be explained by strong electrostatic interactions between neighbouring O_H_O fragments. (The distance between the nearest bridging protons is around 5.3 ). Frequencies for the lower of the two bending vibrations are between 1037 and 1198 cm–1 in a range overlapping with the range of the asymmetric stretches of the O_H_O fragment. Frequencies for the higher bending vibrations are in the narrow range of 1727–1740 cm–1 – very close to the bending vibrations of the terminal water molecules. Our calculations do not support a previous tentative assignment of the bands [104] observed around 1080 cm–1, and in the 1700– 1900 cm–1 range, to the bending and asymmetric stretching vibrations of the O_H_O fragment, respectively. According to the present calculations the bands between 1000 and 1400 cm–1 are due to the asymmetric stretch and bending vibrations of the O_H_O fragment, while the bands between 1600 and 1700 cm–1 are due to asymmetric bending vibrations of the terminal water molecules and to bending vibrations of the O_H_O fragment. For other crystals with strong Hbonds, K3H(SO4)2 and Rb3H(SO4)2, two intense INS bands near 1140 and 1550 cm–1 are assigned to the out-of-plane and in-plane bending modes of the O_H_O fragment [49].
9.3.2.2 The PES of the O_H_O Fragment Profiles of the PES of the O_H_O fragment along the Z coordinate (Fig. 9.4) for the isolated ion, and for the ion in the crystal, were evaluated at two O_O distances: the equilibrium Re value, and Re + 0.1 . In the CPMD calculations the positions of atoms in the considered O_H_O fragment were fixed, while positions of all other atoms in the cell were optimized. Calculations of the profiles in the isolated ion were performed in accord with the prescriptions of Ref. [118]. The potential along the Z coordinate is extremely flat in the vicinity of the global minimum, see Fig. 9.5, and for the larger O_O distance it turns into a double minimum function. In the crystal the potential is even flatter than in the isolated ion, and the barrier along the Z coordinate grows more rapidly than that in the gas phase ion. A possible explanation is as follows: When the bridging H shifts from the midpoint between the oxygen atoms the dipole moment increases rapidly. Due to electrostatic interactions with the crystalline environment, the nonsymmetric position of the H appears to be more stable than the symmetric location. This effect, evidently, is absent in the gas phase. The barrier height was calculated as a function of the O_O distance for the isolated ion, and for the ion in the H5O2+ClO4– crystal, see Fig. 9.6. In gas-phase Hbonded systems with a symmetric A_H_A fragment, where A = O or N, the potential barrier height is a function of R2 [119]. According to Fig. 9.6, the barrier
291
292
9 Proton Dynamics in Hydrogen-bonded Crystals
Energy, cm-1
1500
H5O2
+ +
Re + 0.1 Å
500
0
-
H5O2 ClO4
1000
Re -0,2
0,0
0,2
z, Å
Figure 9.5 Profiles of the PES of the O_H_O fragment along the Z coordinate (Fig. 9.4) in the isolated ion (dashed line) and the ion in the crystal (solid line) computed for two O_O distances: the equilibrium Re value and Re + 0.1 . Re = 2.426 (the ion in the crystal), Re = 2.431 (the isolated ion).
Energy, cm-1
1500
+
H5O2
+
1000
H5O2 ClO4
-
500
0 0,0
0,1
∆R, Å
0,2
0,3
Figure 9.6 The barrier height computed as a function of the O_O distance for the isolated ion (dashed line) and for the ion in the crystal (solid line).
in the crystal increases with increasing R much faster than for the gas phase system. This result supports a key assumption of the model 2D PES (Section 9.2). This is, namely, that in crystals with a quasi-symmetric O_H_O fragment the barrier rises exponentially in the region 2.40 < Re < 2.60 .
9.3 DFT Calculations with Periodic Boundary Conditions
9.3.2.3 Anharmonic INS and IR Spectra CPMD simulations were performed at constant volume and T = 84 K, which is the average temperature of different experimental studies of crystalline H5O2+ClO4– [103–105]. In dynamic runs a fictitious electron mass of 600 au and a time step of 0.12 fs were employed. The BLYP equilibrium geometry was used as a starting point. The trajectory length was 4.5 ps. Born–Oppenheimer molecular dynamics simulations with BLYP forces [120] of the isolated H5O2+ ion were made using the TURBOMOLE package. The simulations were performed at constant energy with T ~ 100 K, defined as the average of the kinetic energy. The equilibrium structure was used as a starting point. Inertial momenta were distributed randomly according to the desired kinetic temperature. The time step was 0.5 fs and the trajectory length was 3 ps. Theoretical spectra were calculated by averaging over two trajectories, obtained with opposite signs of the starting velocities. The computed INS spectrum of the H5O2+ClO4– crystal agrees well with the experimental one, see panels D and E in Fig. 9.7. In accord with experiment [105], there are two groups of bands below 850 cm–1 and two bands in the region between 1000 and 2000 cm–1. Because the scattering cross section of the proton exceeds that of other atoms by one order of magnitude, INS selectively probes modes in which H atoms are involved. Separate calculation of the velocity autocorrelation function of the bridging H only (Fig. 9.7 C) allows the identification of bands that are due to the O_H_O fragment. Comparison of spectra D and C shows that these are the two bands around 1150 and 1600 cm–1. Further information for the assignment comes from the harmonic frequencies and normal modes of H5O2+ in the H5O2+ClO4– crystals (Table 9.2). The intense band around 1150 cm–1 is caused by vibrations of the bridging proton (O_H_O asymmetric stretch and O_H_O bending), while the group of intense bands around 1600 cm–1 is caused by both bending vibrations of the O_H_O fragment and bending vibrations of the terminal water molecules. Comparison of spectra D and C (Fig. 9.7) shows that the bending vibrations of the terminal water molecules are at the low wavenumber side of the band around 1600 cm–1. Comparison of the computed INS spectrum of the isolated ion (panel B) with the spectrum of the ion in the crystal (panel D) shows that these spectra differ in the 1200–1600 cm–1 frequency region. Separate calculation of the velocity autocorrelation function of the bridging H only (Fig. 9.7A) indicates that the bands in this region correspond to vibrations of the bridging H. It implies that environmental effects change the INS spectrum strongly in the region of the asymmetric stretching and bending vibrations of the O_H_O fragment. Figure 9.8B shows the IR spectrum of the crystal obtained as the Fourier-transform of the dipole autocorrelation function, Eq. (9.16), in the 800–2000 cm–1 frequency region. Following assignment of the INS spectra (Figure 9.7) and the harmonic normal mode calculations (Table 9.2), the bands in the region between 1600 and 1700 cm–1 are due to asymmetric bending vibrations of the water molecules and the bending vibrations of the O_H_O fragment. The bands in the region between 1000 and 1300 cm–1 are assigned to the asymmetric stretch and
293
294
9 Proton Dynamics in Hydrogen-bonded Crystals 1
wavenumber, cm800
1200
1600
2000
(A)
(B)
(C)
(D)
5
(E)
4 3 2
50
100
(403)
(806)
150 200 Energy Transfer (MEV) (1209) (1612)
Figure 9.7 Experimental (E, Ref. [105]) and computed (D) INS spectrum of crystalline H5O2+ClO4–. Panel C shows the INS spectrum of crystalline H5O2+ClO4– computed from the velocity autocorrelation function of the brid-
250 (2015)
200 (2418) (cm–1)
ging H only. Panels B and A show the computed INS spectra of the isolated H5O2+ ion and the bridging H, respectively. Intensities are in arbitrary units.
9.3 DFT Calculations with Periodic Boundary Conditions
bending vibrations of the O_H_O fragment (Table 9.2). A very broad and flat absorption is observed for the H5O2+ClO4– crystal [103] in this region (upper panel in Fig. 9.8A). This is also true for the dihydrates of hydrogen chloride and hydrogen bromide [121] as well as for the dihydrates of halogenometallates of dioxonium [122]. According to experiment [104] shown at the top of Fig. 9.8 the IR intensities of the ClO4– fundamentals (< 1000 cm–1) are lower than those of the asymmetric stretches of the O_H_O fragment, while the present calculations using the “Dipole Dynamics” procedure [86] predict the largest IR intensities occur for the low frequency ClO4– vibrations. The reasons were discussed in Section 9.3.1. For the sake of comparison, computed and experimental IR spectra of the isolated H5O2+ ion are given in Fig. 9.8C and D, respectively. In contrast to the INS spectrum the effects of the crystalline environment are practically not seen in the 1200–1600 cm–1 region of the IR spectrum.
(A)
(B)
(C)
(D)
1000
1400
1800 -1
wavenumber, cm
Figure 9.8 Computed IR (B) spectra of crystalline H5O2+ClO4– compared to the experimental IR spectrum (A, Ref. [104]). The dotted line corresponds to the IR spectrum in the liquid phase at room temperature [104]. The
experimental (D, [106]) and computed (C) gas phase spectra in the region between 800 and 2000 cm–1 are also shown. Intensities are in arbitrary units.
295
296
9 Proton Dynamics in Hydrogen-bonded Crystals
Comparison of the theoretical INS and IR spectra of the H5O2+ClO4– crystal shows that the O_H_O band around 1150 cm–1 is much broader in the IR spectrum than in the INS one. Band broadening in the IR spectrum is caused by electric anharmonicities [23, 66] in addition to mechanical ones. Electric anharmonicities are absent in the INS spectrum and this explains the narrower bands. Summarizing, the assignment of bands in the INS and IR spectra of the H5O2+ ion in the H5O2+ClO4– crystal may be done in harmonic approximation.
9.4 Conclusions
A qualitative description of proton dynamics in H-bonded crystals requires a twodimensional treatment assuming strong coupling between the proton-transfer coordinate and a low-frequency vibration. Due to environmental effects, this coupling is much stronger in crystals than in isolated H-bonded species. DFT calculations with periodic boundary conditions show the barrier along the proton transfer coordinate increases with increase in the O_O distance much faster in crystals than in the gas phase system. Strong coupling between the two coordinates accounts for major structural and spectroscopic regularities experimentally obtained for molecular crystals with strong H-bonds and quasi-linear A_H_A fragment: (i) Large values for the Ubbelohde effect (the change in the O_O equilibrium distance upon deuteration); (ii) low frequencies (< 1000 cm–1) for the asymmetric stretch of the O_H_O fragment, mH; (iii) large variations (from 1 to 2) for the isotopic frequency ratio, c = mH/mD. The mechanism of proton tunneling assisted by low-frequency mode excitation in molecular crystals is clarified. (i) In crystals with moderate H-bonds it differs strongly from the mechanism of proton tunneling in the gas phase entity. In isolated H-bonded species the tunneling splitting increases monotonically with the O_O excitation, while in crystals the dependence of the probability of proton tunneling on a low-frequency mode excitation is non-monotonic. (ii) In molecular crystals with strong H-bonds proton transfer is not assisted by low-frequency mode excitation. In other words, proton dynamics is apparently not coupled to the low-frequency vibrations in strong H-bonded crystals.
Acknowledgment
The author thanks the Russian Federal Agency for Education (Program “Development of the Highest-School Scientific Potential: 2006–2008” Project 2.1.1.5051) and Alexander von Humboldt Foundation for financial support.
References
References 1 T. Steiner, Angew. Chem. Int. Ed. 2002,
41, 48. 2 L. M. Epstein, E. S. Shubina, Coord. Chem. Rev. 2002, 231, 165. 3 G. A. Jeffrey, An introduction to Hydrogen Bonding, Oxford University Press, Oxford, 1997. 4 The Hydrogen Bond. Recent Developments in Theory and Experiment, Vol. 1, P. Schuster, G. Zundel, C Sandorfy (Eds.), North-Holland, Amsterdam, 1976. 5 Chem. Phys. 1995, 170(3), Special Issue: Tunneling in Chemical Reactions, V. A. Benderskii, V. I. Goldanskii, J. Jortner (Eds.). 6 Theoretical Treatments of Hydrogen Bonding, D. Hadzi (Ed.), Willey, Chichester, 1997. 7 M. V. Basilevsky, M. V. Vener, Usp. Khim. 2003, 72, 3 (in Russian); M. V. Basilevsky, M. V. Vener, Russ. Chem. Rev. 2003, 72, 1 (Engl. Transl.). 8 S. Scheiner, Hydrogen Bonding. A Theoretical Perspective, Oxford University Press, Oxford, 1997. 9 B. I. Stepanov, Zh. Fiz. Khim. 1946, 20, 907 (in Russian). 10 B. I. Stepanov, Nature 1946, 157, 808. 11 N. D. Sokolov, V.A. Savel’ev, Chem. Phys. 1977, 22, 383. 12 T. Carrington, W. H. Miller, J. Chem. Phys. 1986, 84, 4364. 13 N. Sato, S. Iwata, J. Chem. Phys. 1988, 89, 2932. 14 R. Meyer, R. R. Ernst, J. Chem. Phys. 1990, 93, 5518. 15 H. Sekiya, Y. Nagashima, Y. Nishimura, J. Chem. Phys. 1990, 92, 5761. 16 J. L. Herek, S. Pedersen, L. Banares, A. H. Zewail, J. Chem. Phys. 1992, 97, 9046. 17 Z. Bazˇic, J. C. Light, Annu. Rev. Phys. Chem. 1989, 40, 469. 18 J. M. Bowman, B. Gazdy, J. Chem. Phys. 1991, 94, 454. 19 M. H. Beck, A. Jckle, G. A. Worth, H.-D. Meyer, Phys. Rep. 2000, 324, 1. 20 M. V. Vener, N. D. Sokolov, Chem. Phys. Lett. 1997, 264, 429. 21 B. W. Shore, J. Chem. Phys. 1973, 59, 6450.
22 B. R. Johnson, J. Chem. Phys. 1977, 67,
4086. 23 Y. Bouteiler, Chem. Phys. Lett. 1992, 198,
491. 24 L. Ojamae, I. Shavitt, S. J. Singer, Int.
25 26 27 28
29
30
31 32 33
34 35 36
37
38 39
40
J. Quantum Chem., Quantum Chem. Symp. 1995, 29, 657. J. Stare, J. Mavri, Comput. Phys. Commun. 2002, 143, 222. M. V. Vener, S. Scheiner, J. Phys. Chem. 1995, 99, 642. J. E. Del Bene, M. J. T. Jordan, J. Mol. Struct. Theochem. 2001, 573, 11. N. D. Sokolov, M. V. Vener, and V. A. Savel’ev, J. Mol. Struct. 1988, 177, 93. I. Olovson, P. G. Jonsson, in The Hydrogen Bond. Recent Developments in Theory and Experiment, P. Schuster, G. Zundel, C Sandorfy (Eds.), North-Holland, Amsterdam, 1976, Vol. 2, p. 426. J. Howard, J. Tomkinson, J. Eckert, J. A. Goldstone, A. D. Taylor, J. Chem. Phys. 1983, 78, 3150. M. Ichikawa, Acta Crystallogr. Sect. B. 1978, 34, 2074. A. Novak, Struct. Bond. 1974, 18, 177. N. D. Sokolov, M. V. Vener, V. A. Savel’ev, J. Mol. Struct. 1990, 222, 365 and references therein. E. Grech, Z. Malarski, L. Sobczyk, Chem. Phys. Lett. 1986, 128, 255. V. P. Sakun, M. V. Vener, N. D. Sokolov, J. Chem. Phys. 1996, 105, 379. M. M. Kreevoy, S. Marimanikkuppam, V. G. Young, J. Baran, M. Szafran, A. J. Schultz, F. Trouw, Ber. Bunsenges. Phys. Chem. 1998, 102, 370. Z. Smedarchina, A. Fernndez-Ramos, W. Siebrand, J. Chem. Phys. 2005, 122, 134309. R. P. Bell, The Tunnel Effect in Chemistry, Chapman & Hall, London, 1980. S. L. Baughcum, R. W. Duerst, W. F. Rowe, Z. Smith, E. B. Wilson, J. Am. Chem. Soc. 1981, 103, 6296. V. E. Bondybey, R. C. Haddon, J. H. English, J. Chem. Phys. 1984, 80, 5432.
297
298
9 Proton Dynamics in Hydrogen-bonded Crystals 41 K. Tanaka, H. Honjo, T. Tanaka,
H. Kohguchi, Y. Ososhima, Y. Endo, J. Chem. Phys. 1999, 110, 1969. 42 R. L. Redington, R. L. Sams, J. Phys. Chem. A. 2002, 106, 7494. 43 C. C. Costain, G. P. Srivastava, J. Chem. Phys. 1964, 41, 1620. 44 F. Madeja, M. Havenith, J. Chem. Phys. 2002, 117, 7162. 45 T. Matsuo, K. Kohno, M. Ohama, T. Mochida, A. Isuoka, T. Sugewara, Europhys. Lett. 1999, 47, 36. 46 T. Matsuo, S. Baluja, Y. Koike, M. Ohama, T. Mochide, T. Sugewara, Chem. Phys. Lett. 2001, 342, 22. 47 D. F. Firth, P. F. Barbara, H. P. Trommsdorff, Chem. Phys. 1989, 136, 349. 48 T. Agaki, F. Imashiro, T. Terao, N. Hirota, S. Hayashi, Chem. Phys. Lett. 1987, 139, 331. 49 F. Fillaux, A. Lauti, J. Tomkinson., G. J. Kearley, Chem. Phys. 1991, 154, 135. 50 F. Fillaux, B. Nicolai, M.H. Baron, A. Lautie, J. Tomkinson, G. J. Kerley, Ber. Bunsenges. Phys. Chem. 1998, 102, 384. 51 J. Ulstrup, Charge Transfer Processes in Polar Media, Springer-Verlag, Berlin, 1979. 52 R. I. Cukier, M. Morillo, J. Chem. Phys. 1990, 93, 2364. 53 P. E. Parris, R. Silbey, J. Chem. Phys. 1985, 83, 5619. 54 P. Bonacky, Chem. Phys. 1986, 109, 307. 55 A. Stockli, B. H. Meier, R. Kreis, R. Meyer, R. R. Ernst, J. Chem. Phys. 1990, 93, 1502. 56 N. D. Sokolov, M. V. Vener, Chem. Phys. 1992, 168, 29. 57 J. L. Skinner, H. P. Trommsdorff, J. Chem. Phys. 1988, 89, 897. 58 A. Oppenlnder, C. Rambaut, H. P. Trommsdorff, J.-C. Vial, Phys. Rev. Lett. 1989, 63, 1432. 59 S. Kushida, K. Nakamoto, J. Chem. Phys. 1964, 41, 1558. 60 A. J. Horsewill, D. F. Brougham, R. I. Jenkinson, C. J. McGloin, H. P. Trommsdorff, M. R. Johnson, Ber. Bunsenges. Phys. Chem. 1998, 102, 317. 61 M. A. Neumann, S. Craciun, A. Corval, M. R. Johnson, J. A. Horsewill,
V. A. Benderskii, H. P. Trommsdorff, Ber. Bunsenges. Phys. Chem. 1998, 102, 325. 62 N. Shida, P.F. Barbara, J. Almlf, J. Chem. Phys. 1991, 94, 3633. 63 F. Fillaux, J. Tomkinson, Chem. Phys. 1991, 158, 113. 64 P. M. Tolstoy, S. N. Smirnov, I. G. Shenderovich, N. S. Golubev, G. S. Denisov, H.-H. Limbach, J. Mol. Struct. 2004, 700, 19. 65 M. Polomska, T. Pawlowski, L. Szcsesniak, B. Hilczer, L. Kirpichnikova, Ferroelectrics 2002, 272, 81. 66 M. V. Vener, O. K hn, J. Sauer, J. Chem. Phys. 2001, 114, 240. 67 C. Emmeluth, M. A. Suhm, D. Luckhaus, J. Chem. Phys. 2003, 118, 2242. 68 N. DoÐlic, O. K hn, Z. Phys. Chem. 2003, 217, 1507. 69 F. Avbeij, M. HodoÐcek, D. Hadzˇi, Spectrochim. Acta Part A 1985, 41, 89. 70 M. V. Vener, J. Sauer, J. Chem. Phys. 2001, 114, 2623. 71 M. V. Vener, O. K hn, J. M. Bowman, Chem. Phys. Lett. 2001, 349, 562. 72 W. Siebrand, T. A. Widman, M. Z. Zgierski, Chem. Phys. Lett. 1983, 98, 108. 73 A.Warshel, J. K. Hwang, J. Chem. Phys. 1986, 84, 4938. 74 A. Staib, D. Borgis, J. T. Hynes, J. Chem. Phys. 1995, 102, 2487. 75 M. V. Basilevsky, A. V. Soudackov, M. V. Vener, Chem. Phys. 1995, 200, 87. 76 F. Fillaux, Int. Rev. Phys. Chem. 2000, 19, 553. 77 M. C. Lawrence, G. N. Robertson, J. Chem. Phys. 1987, 87, 3375. 78 E. Spinner, Aust. J. Chem. 1980, 33, 933. 79 T. C. Waddington, J. Howard, K. P. Brierly, J. Tomkinson, Chem. Phys. 1982, 64, 193. 80 R. G. Delaplane, J. A. Ibers, J. R. Ferraro, J. J. Rush, J. Chem. Phys. 1969, 50, 1920. 81 F. Fillaux, Chem. Phys. 1983, 74, 405. 82 C. A. Morrison, M. M. Siddick, P. J. Camp, C. C. Wilson, J. Am. Chem. Soc. 2005, 127, 4042. 83 F. Fontaine-Vive, M. R. Johnson, G. J. Kearly, J. A. K. Howard, S. F. Parker, J. Chem. Phys. 2006, 124, 234503.
References 84 M. Merawa, B. Civalleri, P. Ugliengo,
85 86
87 88
89
90 91 92 93
94
95 96 97 98 99 100
101
Y. Noel, A. Lichanot, J. Chem.Phys. 2003, 119, 1045. S. V. Churakov, B. Wunder, Phys. Chem. Miner. 2004, 31, 131. J. Hutter, M. Parrinello, A. Alavi, D. Marx, M. Tuckerman, W. Andreoni, A. Curioni, E. Fois, U. Rthlisberger, P. Giannozzi, T. Deutsch, D. Sebastiani, A. Laio, J. VandeVondele, A. Seitsonen, S. Billeter, CPMD, 3.5.2, IBM Research Laboratory and MPI f r Festkrperforschung, Stuttgart, 1995–2001. G. Kresse, J. Hafner, Phys. Rev. B. 1993, 47, 558; Phys. Rev. B. 1994, 49, 14251. G. Kresse, J. Futhm ller, Comput. Math. Sci. 1996, 6, 15; Phys. Rev. B. 1996, 54, 11169. V. R. Saunders, R. Dovesi, C. Roetti, M. Causa, N. M. Harrison, R. Orlando, C. M. Zicovich-Wilson, CRYSTAL 98 User’s Manual, Universita di Torino, Torino, 1998. W. B. Bosma, L. E. Fried, S. Mukamel, J. Chem. Phys. 1993, 98, 4413. B. Hudson, A. Warshel, G. R. Gordon, J. Chem. Phys. 1974, 61, 2929. H. Jobek, A. Tuel, M. Krossner, J. Sauer, J. Phys. Chem. 1996, 100, 19545. D. A. McQuarrie, Statistical Mechanics, Harper Collins, NewYork, 1973, Section 21-1. V. M. Zolotarev, B. A. Mikhailov, L. I. Alperovich, S. I. Popov, Opt. Spectrosc. 1969, 27, 430 (in Russian). M.-P. Gaigeot, M. Sprik, J. Phys. Chem. B. 2003, 107, 10344. R. Ramirez, T. Lopez-Ciudad, P. Kumar, D. Marx, J. Chem. Phys. 2004, 121, 3973. B. Guillot, J. Chem. Phys. 1991, 95, 1543. J. Borysow, M. Moraldi, L. Frommhold, Mol. Phys. 1985, 56, 913. H. Ahlborn, B. Space, P. B. Moore, J. Chem. Phys. 2000, 112, 8083. G. V. Yukhnevich, E. G. Tarakanova, V. D. Mayorov, N. B. Librovich, Usp. Khim. 1995, 64, 963 (in Russian); G. V. Yukhnevich, E. G. Tarakanova, V. D. Mayorov, N. B. Librovich, Russ. Chem. Rev. 1995, 64, 901 (Engl. Transl.). G. Zundel, Adv. Chem. Phys. 2000, 111, 1.
102 C. L. Perrin, J. B. Nielson, Annu. Rev.
Phys. Chem. 1997, 48, 511. 103 I. Olovsson, J. Chem. Phys. 1968, 49,
1063 and references therein. 104 A. C. Pavia, P. A. Gigu re, J. Chem.
Phys. 1970, 52, 3551. 105 D. J. Jones, J. Roziere, J. Penfold,
J. Tomkinson, J. Mol. Struct. 1989, 195, 283. 106 K. R. Asmis, N. L. Pivonka, G. Santambrogio, M. Br mmer, C. Kaposta, D. M. Neumark, L. Wste, Science. 2003, 299, 1375. 107 T. D. Fridgen, T. B. McMahon, L. MacAleese, J. Lemaire, P. Maitre, J. Phys. Chem. A 2004, 108, 9008. 108 M. V. Vener, J. Sauer, Phys. Chem. Chem. Phys. 2005, 7, 258. 109 M. V. Vener, J. Sauer, Khim. Fiz. 2005, 24, No. 6, 39 (in Russian). 110 G. J. Kearley, F. Fillaux, M. H. Baron, S. Bennington, J. Tomkinson, Science. 1994, 264, 1285. 111 A. D. Becke, Phys. Rev. A. 1988, 38, 3098; C. Lee, W. Yang, R. G. Parr, Phys. Rev. B 1988, 37, 785. 112 N. Troullier, J. L. Martins, Phys. Rev. B 1991, 43, 1993. 113 R. A. Kendall, T. H. Dunning Jr., R. J. Harrison, J. Chem. Phys. 1992, 96, 6796. 114 R. Ahlrichs, M. Br, M. Hser, H. Horn, C. Klmel, Chem. Phys. Lett. 1989, 162, 6796. 115 O. Treutler, R. Ahlrichs, J. Chem. Phys. 1995, 102, 346. 116 M. von Arnim, R. Ahlrichs, J. Comput. Chem. 1998, 19, 1746. 117 R. Minkwitz, S. Schneider, A. Kornath, Inorg. Chem. 1998, 37, 4662; and references therein. 118 M. V. Vener, J. Sauer, Chem. Phys. Lett. 1999, 312, 591. 119 S. Scheiner, J. Am. Chem. Soc. 1981, 103, 315. 120 S. D. Elliott, R. Ahlrichs, O. Kampe, M. M. Kappes, Phys. Chem. Chem. Phys. 2000, 2, 3415. 121 A. S. Gilbert, N. Sheppard, Chem. Commun. 1971, 7, 337. 122 G. Picotin, J. Roziere, J. Potier, A. Potier, Adv. Mol. Relax. Proc. 1975, 7, 177.
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Part III Hydrogen Transfer in Polar Environments
This section turns to reactions involving the transfer of a proton in (primarily) polar environments, opening with a theoretical presentation and finishing with three experimental chapters all exploiting the greatly enhanced acidity of aromatic photoacids (compared to ground electronic state acids) in probing the details of proton transfer. Kiefer and Hynes start off in Ch. 10 with a recounting of the theoretical description of the microscopic mechanisms and rate constants of such processes, here focused on acid-base type reactions, developed over the years in the latter’s group. The crucial quantum mechanical character of the proton’s nuclear motion even when there is no tunneling is emphasized, as are the rate-governing roles of the rearrangement of the polar environment and the vibrational motion of the atoms or groups between which the proton transfer occurs, such that the proton is not the reaction coordinate. Instead the proton follows these slower motions. Since this perspective differs strongly from many traditional views, special attention is given to experimental measures supporting this description, including free energy relations and kinetic isotope effects. Electronic rearrangements involved in the proton transfer are also discussed, for both the ground and excited electronic states; these also differ from many traditional views. Next, Ch. 11 by Lochbrunner, Schriever and Riedle deals with excited electronic state intramolecular tautomerization proton transfers in nonpolar, rather than polar, solvents. But there is a connection to the previous chapter: the ultrafast optical experiments discussed here emphasize evidence that the proton is not the reaction coordinate. The proton transfer is controlled by low vibrational modes of the photo-acids, rather than by the proton motion itself, an interpretation supported by separate vibrational spectroscopic studies and theoretical calculations The key role of modes reducing the donor-acceptor distance for proton transfer is highlighted, and for the featured molecule of this chapter, the proton adiabatically follows the low frequency modes, and no tunneling or barrier for the proton occurs. (See also Ch. 15 by Elsaesser for direct ultrafast vibrational studies on these issues). In Ch. 12, Pines and Pines return to proton transfer in polar solvents and investigate the factors affecting the photoacidity of weak organic acids such as phenols Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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by examining the use of the Frster cycle connecting the pKas of the excited and ground state acids. Their detailed analyses, which also involve free energy relations, demonstrate the usefulness of these thermodynamic tools in identifying the reasons for the enhancement of the photoacidity over that of the ground electronic state acid (typically six orders of magnitude in the rate constant). One emphasis is on the importance of the product side of the reaction, an aspect whose prediction is discussed at the conclusion of Ch. 10. The authors’ procedure is shown to be general, remarkably also being applicable for quantifying photoacidity even for systems which remain unreactive during the finite excited state lifetime. Tolbert and Solntsev conclude this Section as well as Volume 1 with a continuation of the theme of photoacidity and proton transfer, focusing special attention on the various factors crucial for producing very strong, or super’ photoacids. These authors consider the functioning of these photoacids not only in polar environments such as water, alcohols, and water-alcohol mixtures—whose differences are revealing for understanding the proton transfer details—but also some biological environments such as the green fluorescent protein.
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10 Theoretical Aspects of Proton Transfer Reactions in a Polar Environment Philip M. Kiefer and James T. Hynes
Overview
This chapter reviews some nontraditional theoretical views developed in this group on acid–base proton transfer reactions. Key ingredients in this picture are a completely quantum character for the proton motion, the identification of a solvent coordinate as the reaction coordinate, and attention to the hydrogen (H-) bond vibrational mode in the acid–base complex. Attention is also given to the electronic structure rearrangements associated with proton transfer. A general overview is presented for the rate constants, including the activation free energy, as well as for the associated primary kinetic isotope effects, for both the proton adiabatic (quantum but nontunneling) and nonadiabatic (tunneling) regimes. While the focus is on ground electronic state proton transfers, some aspects of excited state proton transfers are also discussed.
10.1 Introduction
In this chapter, we give an overview of some of the theoretical developments for proton transfer (PT) reactions, focusing on the efforts in the Hynes group [1–7]. PT is of obvious importance in both chemistry and biology [8], and consequently there has been extensive study of PT in solution [8–10] and other polar environments, e.g. enzymes [9c, 11]. Of particular importance in characterizing and comprehending PT reactions is understanding which properties of the reaction partners and surrounding environment affect the PT rate constant and related experimental observables. Among these observables, the most frequently employed by experimentalists are the reaction free energy (DG‡) and its relation to the reaction free energy (DGRXN) [8–10], and kinetic isotope effects (KIEs) [8–12]. In the description of PT provided in this chapter, these important aspects are given special focus and are analyzed with a picture that significantly differs from widely employed standard’ pictures for PT. We will begin this Introduction with a brief synopsis of these standard pictures and then highlight some of the key features of Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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10 Theoretical Aspects of Proton Transfer Reactions in a Polar Environment
the nontraditional perspective. Here and throughout this chapter we make no pretence of being complete in our discussion or referencing, and refer the interested reader to the cited articles from the group for more extensive discussion and references. Standard descriptions for PT have both classical over the barrier’ (nontunneling) and tunneling components, with the latter regarded as a correction to the former [8, 12–17]. The standard nontunneling view for KIEs traces back to Westheimer and Melander (W-M) [14]. Actually, most of the W-M discussion was developed for, and is more properly applied to, hydrogen atom transfers rather than to PT. Since however the W-M perspective has remained the cornerstone for most PT discussions, we present it here, making some changes to make it more appropriate for PT. In its simplest version, the W-M picture uses a collinear 3-center molecular system for PT, illustrated here for an acid–base reaction within a hydrogenbonded (H-bonded) complex, e.g. AH···B A–···HB+
(10.1)
While the basic formalism we present is more general, we will typically refer to the PT reaction Eq. (10.1) in a polar solvent throughout this chapter to illustrate the importance of the reactant and product charge distributions and the polarity of the environment. The reaction potential surface is a function of two coordinates, the A–H proton distance and the distance between the two heavy moieties, A···B. Along the minimum energy path, the reaction begins at a large heavy atom separation with the A–H proton distance constant, proceeds through a transition state (TS) A··H··B, and goes on to products with a large A–B separation and constant H–B distance to produce A–··HB+. In the limiting symmetric reaction case, the reaction coordinate at the TS is the unstable asymmetric stretch motion, which for heavy A and B moieties, is essentially the proton coordinate. Passage through the TS region is thus classical motion of the proton over the barrier in the proton coordinate. For asymmetric reactions, the TS location will shift (see below), but the proton’s motion across the TS always remains classical in the W-M description. Further aspects of the standard W-M approach are most usefully discussed via its treatment of KIEs for the rate constant resulting from isotopic substitution – most often replacement of H with D – which is widely used in assessing the character of the TS and the proton’s role therein. With the use of TS theory, the KIE arises from the exponentiated activation energies [8, 12–14]. For H versus D transfer, the KIE is given by kH =kD » exp½ðDG{H DG{D Þ=RT; DG{H DG{D » ZPE{H ZPERH ZPE{D þ ZPERD
(10.2)
10.1 Introduction
As is of course well-known, the KIEs originate, in this framework, from isotopic zero point energy (ZPE) differences between the reactant and the TS [8, 12–14, 18]. The relevant reactant region ZPE is just that of the A–H vibration in the reactant A–H···B complex, the motion transverse to the reaction coordinate in this R > ZPE R , due to the region. The reactant ZPE is larger for H than for D, ZPEH D lower reactant AH stretch vibration frequency for the more massive D. For a thermodynamically symmetric reaction (DGRXN = 0, a very important reference situation), the reaction path through the TS consists solely of the proton’s classical motion over the barrier (as noted above), so that there is no proton ZPE associated with this motion at the TS. Rather, the TS ZPE is associated with the transverse motion at the TS (just as for the reactant), which in the collinear model is a symmetric stretch, the heavy particle A–B vibration. Hence, at the TS, ZPE‡H = ZPE‡D for such a symmetric reaction. The net result is the complete “loss” of the ZPE for the proton stretching mode on going from reactant to TS for a symmetric reaccm–1) and a simple tion. Typical reactant proton stretch frequencies (xCH p~3000 ffiffiffi mass correlation between ZPEs (i.e. ZPED » ZPEH = 2) give an H vs. D KIE of about 7 at room temperature [8, 12–14]. For an asymmetric reaction, the reaction coordinate at the TS in the traditional view includes both proton and heavy particle classical motions: consistent with the Hammond postulate [15], the TS becomes more geometrically similar to the product as the reaction becomes more endothermic, and more similar to the reactant as it becomes more exothermic. Thus the transverse vibration at the TS – whose ZPE is relevant for the rate – more and more involves the proton motion, and in either limit approaches the bound proton stretch vibration of the product BH or the reactant AH. This effect decreases the KIE, resulting in a kH/kD vs. DGRXN trend which is maximal at DGRXN=0 and drops off as the reaction becomes more endo- or exo-thermic. A description of this behavior in terms of the wellknown Marcus relation for the activation free energy [19] will be discussed in Sections 10.2.1–10.2.3. (With apologies, we do not use the proper terms exergonic’ and endergonic’ in connection with the sign of the reaction free energy). The standard picture for classical proton motion over the barrier at the TS just described is sometimes supplemented with a quantum contribution via a tunneling correction [13, 16, 17, 20, 21]. Addition of tunneling corrections to the standard PT rate will obviously affect the KIE, including its reaction asymmetry dependence [13, 17]. Indeed, it has been argued that variation of the tunneling contribution versus reaction asymmetry is primarily responsible for the broad range in magnitude of observed KIE versus reaction asymmetry plots, instead of the variation of ZPE at the TS described above [17]. Various departures from experimental observations, such as non-Arrhenius rate behavior or KIEs much in excess of 10, typically are taken as indicating tunneling [8, 11–13, 17, 24]. We also remark that it is typical in such assessments of tunneling that it is regarded as a partial contribution to the rate, with the other contribution being classical over the barrier motion.
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Despite the success of the standard picture just described, it can be argued that a different picture would be more plausible. First, the standard description has a certain logical inconsistency in the TS description. In the symmetric case, proton motion is viewed as completely classical over the proton barrier. For any finite reaction asymmetry, however, the proton motion’s quantum character as a bound quantum vibration becomes extremely important, since it is that character that influences the frequency, and thus the ZPE, of the transverse TS motion. It seems difficult to maintain that proton motion within an H-bond can be both classical and quantum. Second, the standard picture presented above makes no reference to the solvent (while we focus here on the case of a solvent environment, very similar ideas will apply to more general polar environments such as enzyme active sites). To the degree that the solvent is included in standard descriptions, it is imagined to alter the rate via a differential equilibrium solvation of the TS and the reactant, again all within the standard framework recounted above [21, 25]. But the equilibrium solvation assumption – which requires the solvent motion to be fast compared to the relevant motion of the reacting solutes in the TS region – is completely implausible for the high frequency quantum proton motion; indeed, the opposite situation is more appropriate: the solvent is generally slow compared to the proton motion [1, 2, 26–28]. In the alternate, nontraditional picture of PT reactions [1–7, 26–28] employed herein, the reaction is driven by configurational changes in the surrounding polar environment, a feature of much modern work on PT reactions [1–7, 26–28], and the reaction activation free energy is largely determined by the environmental reorganization. In this picture, the rapidly vibrating proton follows the environment’s slower rearrangement, thereby producing a perspective in terms of the instantaneous proton potential for different environmental arrangements. (We will expand upon this statement in the two different regimes of PT described in succeeding sections). In order to clarify the essential features of the nontraditional picture, Fig. 10.1 displays the key features for a model overall symmetric PT reaction in a linear H-bonded complex. Three proton potential curves versus the proton coordinate are displayed, for solvent configurations appropriate to that of the reactant pair, the TS, and the product pair. These different states of solvation – or more simply the solvent’s nuclear electrical polarization state – distort the potential from being initially asymmetric favoring the proton residing on the acid, through an intermediate situation where a proton symmetric double well is established, and on to an asymmetric potential now favoring the proton residing on the base. The solvent motion is critical, due to the strong coupling of the reacting pair’s evolving charge distribution to the polar solvent polarization field. Furthermore, the high frequency quantum proton vibration adiabatically adjusts to the reorganizing solvent in the reactant and product regions; the reaction coordinate is a solvent coordinate, rather than the proton coordinate, and there is a free energy change up to the TS activation free energy as the solvent rearranges. For each of the three proton potentials in Fig. 10.1, the quantized ground proton vibrational energy, i.e. the ZPE, is indicated. For the TS solvent configuration,
10.1 Introduction
TS
R
P
G
A-H
A-H
Figure 10.1 Free energy curves versus proton position at the reactant R, transition state TS, and product P solvent configurations for a symmetric reaction. For both R and P, the ground state proton vibrational energy level (solid line) is indicated. For the transition
A-H state, the ground state proton vibrational energy level is indicated for a small (solid line) and a large (dotted line) H-bond separation, which correspond to adiabatic and nonadiabatic PT, respectively.
there are two possible cases for the zero point level: if it is above the proton barrier, the system is in what we term the quantum adiabatic PT limit, while if instead the level is below the barrier top, the reaction would involve proton tunneling [29], which we term the quantum nonadiabatic limit. In either case, the proton motion is a bound quantum vibration; there is no classical barrier crossing of the proton, in contrast to a conventional TS theory for the standard description. The distinction between the two regimes, whether the ground proton vibrational level is below or above the barrier in the proton coordinate, is critically determined by another important coordinate, the acid–base H-bond A–B separation Q. For weak H-bonds with large equilibrium A–B separations, the barrier in the proton coordinate will be large, requiring the proton to tunnel through the barrier, while for stronger H-bonds and smaller equilibrium A–B separations, the barrier is reduced such that nontunneling adiabatic PT occurs. Furthermore, the A–B vibrational frequency will also determine the thermal accessibility of smaller A–B separations where either tunneling is decreased with reduced barriers or, for nontunneling PT, the quantum vibrational proton mode adiabatically passes from R to P. Before proceeding, we should discuss some electronic structure aspects of PT. In much of the modeling discussed within for Eq. (10.1), we have employed a 2 valence bond (VB) state description, with the VB states corresponding to the limiting reactant (R) and product (P) forms of Eq. (10.1) for any geometry, i.e. the electronic wavefunction is jW el i ¼ cR jW R i þ cP jW P i
(10.3)
The two VB wavefunctions depend on the solute reacting pair coordinates; the coefficients also depends on these coordinates but in addition depend on a solvent coordinate characterizing the electric polarization state of the solvent, as further discussed in Section 10.2. In this description, the solute’s electronic wavefunction is polarized over the VB states by the polar environment [6, 30–32].
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The wavefunction description Eq. (10.3) corresponds closely to the Mulliken charge transfer picture of PT [33] shown in Fig. 10.2, in which a non-bonding (nB) electron of the base is transferred into an antibonding (r*AH) orbital of the acid. A naive interpretation of this would be that the transfer into the antibonding orbital of the acid weakens the AH bond and assists in allowing the transfer of the H species to the base; since the base is now positively charged, this would be transfer of an hydrogen atom H, not a proton H+. Such a view ignores the fact that the electronic coupling between the two VB states is very strong, ~1 eV [6, 28, 34–36] and the charge transfer is electronically adiabatic. (We stress that this is true for both the proton adiabatic and nonadiabatic regimes as we have defined them.) A more correct picture then is that electron transfer and H atom transfer are concerted and the charge carried by the hydrogen moiety in the PT would be something close to +0.5. The validity of the Mulliken picture has been tested in molecular orbital calculations, making no reference to the two VB state approximation, for the first PT of the acid dissociation of hydrofluoric acid HF in water [2c]. It was found that indeed during the PT there is electronic charge transfer out of the H2O base nonbonding orbital into the antibonding orbital of the HF acid, and that the charge on the hydrogenic species is approximately +0.5. This appears to be the first demonstration of the validity of the Mulliken charge transfer picture for PT. (There are further electronic structure issues for excited electronic state reactions, addressed in Section 10.4). σ*AH
nB
σAH A H
B
A- H B+
Figure 10.2 Qualitative orbital energy diagram of the Mulliken charge transfer picture for the two VB states of the H-bond PT complex AH···B.
Since both involve charge transfer, PT reactions share with (outer sphere) electron transfer (ET) reactions a key role for the polar environment. There are, however, a number of essential differences between PT and ET reactions. The feature just discussed, that the electronic coupling is large – as is typical for bond breaking and making reactions (See e.g. Ref. [31]) – is in strong contrast to the weak to very weak electronic coupling which applies for ET [37]. Another key difference is a strong dependence for PT on the H-bond A–B separation Q which must be accounted for in the dynamics. This is especially important for nonadiabatic tunneling PT reactions where the tunneling probability is exponentially sensitive to Q; the corresponding dependence for tunneling ET is much weaker, a feature arising from the more extreme quantum character of the electron compared to the proton [1]. As a consequence of these differences, one cannot directly take over equations valid for ET and apply them to PT, as is sometimes done. In succeeding sections, we recount the essential features of the adiabatic and nonadiabatic PT regimes. Section 10.2 describes the adiabatic PT picture as well as the resulting rate constant, activation free energy and KIEs, while Section 10.3 presents the nonadiabatic PT picture rate constant and KIEs. We focus throughout
10.2 Adiabatic Proton Transfer
on acid–base PT reactions in the ground electronic state, e.g. Eq. (10.1). Some aspects of excited electronic state PT reactions are referred to at various locations in the chapter. Concluding remarks are offered in Section 10.4.
10.2 Adiabatic Proton Transfer 10.2.1 General Picture
In the adiabatic PT limit, proton motion is quantum but is not tunneling, the reaction coordinate is the solvent, and the internal H-bond coordinate plays several important roles, to be described presently. These features have been examined in the Hynes group in a number of detailed realistic combined electronic structure/dynamics simulations of specific systems such as hydrochloric and hydrofluoric acids in water [2a–c]. While we will occasionally refer to results of these studies, for present purposes it is most useful to couch most of the discussion in terms of analytic studies by the present authors [3, 4] of the primary acid–base PT reaction event in a H-bonded complex, cf. Eq. (10.1), in a polar solvent, with the acid and base modeled to represent typical oxygen and nitrogen acid–base systems. The solvent is treated as a nonequilibrium dielectric continuum and the electronic structure aspects necessary to account for the bond breaking and making features of the PT are treated in terms of a two valence bond (VB) state description Eq. (10.3) involving VB wavefunctions corresponding to the limiting reactant and product forms, at every geometry, of Eq. (10.1) [6], as was mentioned in the Introduction in connection with the Mulliken charge transfer picture of PT. Details can be found in Ref. [3]. Finally, for the adiabatic PT regime, the A–B H-bond strength is to be sufficiently strong that the equilibrium reactant pair A–B separation is sufficiently small that, when the solvent rearrangement gives a symmetric double well in the proton coordinate, the proton potential barrier is sufficiently low such that the ZPE level of the proton lies above this barrier. Figure 10.3 displays the key features for a model overall symmetric PT reaction; for the moment, we consider first the simplified case where the A–B H-bond length Q is held fixed. Figure 10.3(a) shows the proton potential curve versus the proton coordinate and its ground vibrational wavefunctions and level, for solvent configurations appropriate to that of the reactant pair R, the transition state TS, and the product pair P. The proton vibrational level in the symmetric proton potential situation is indeed above the barrier, as required in the adiabatic PT limit. Inspection of the displayed proton wavefunction for the TS solvent configuration shows that the quantum delocalization of the proton is so extensive that any classical description is completely inappropriate. Thus the proton extends over a significant portion of the double well; in a classical, conventional TST description, one would consider instead the classical motion of the always localized proton over the top of this proton potential, taking the proton coordinate as
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the reaction coordinate, with an imaginary frequency in the limited region of the top of the proton potential. In the correct quantum description, the reaction coordinate is instead the solvent. Examples illustrating the above points involving a microscopic description of the solvent and a more detailed electronic structure description are available [2, 7] (see also Ref. [36]); Fig. 10.4 illustrates the proton level pattern for the first PT step in the acid dissociation of HCl in water [2b]. The physical picture of the adiabatic limit is that as the solvent reorganizes, the high frequency quantum proton vibration adiabatically adjusts. Indeed, this is one source of the terminology adiabatic PT’. Thus, the reaction coordinate is a solvent coordinate, rather than the proton coordinate, and there is a free energy change up to the TS activation free energy as the solvent rearranges, as shown in Fig. 10.3(b). The total free energy versus the solvent coordinate can be usefully decomposed into two basic contributions, shown in Fig. 10.3(b). These are, respectively, a ’bare’ free energy, Gmin, which is that corresponding to the situation where the
R
(a)
TS
P
G
A-H
A-H
A-H
(b) TS
G
R
ZPE
P Gmin
Solvent Reaction Coordinate
Figure 10.3 (a) Proton potential energy curves versus the proton coordinate at the reactant R, transition state TS, and product state P solvent configurations for a symmetric reaction. (The ordinate is labeled as a free energy G, since the potential energy curves at each solvent configuration point shown have a constant free energy contribution related to the solvent interaction). In each case, the ground state proton vibrational energy level (solid line) and wavefunction (dotted line) are
indicated. (b) Free energy curve for the symmetric PT system displayed in (a) with the proton quantized in its vibrational ground state versus solvent reaction coordinate (solid line). The solvent coordinate critical points corresponding to the proton potentials in the upper panel are indicated. The free energy at the minimum of the proton potential along the solvent coordinate Gmin (dotted line) is also shown. The difference between Gmin and G is the zero point energy.
Ene rg y ( kc a l/ m o l)
10.2 Adiabatic Proton Transfer R
qCl-H ( )
TS
the forward and reverse barri
is
0.01 kcal/mol).
qCl H ( )
P
qCl-H ( )
Figure 10.4 Proton transfer potentials characteristic of the reactant (left panel), TS (middle panel, and product (right panel) regions for the acid ionization PT of HCl in water [2b]. The Cl–O distance is 2.91 . The ground and first excited proton vibrational levels are indicated.
proton is located at its classical minimum free energy position for any given solvent coordinate, and the proton’s vibrational ZPE, measured from the latter potential minimum energy. The ZPE decreases as the TS in the solvent is approached, since the proton potential becomes more symmetric and the proton is delocalized in a larger potential region. Finally, as a technical point, the solvent coordinate in this figure is an alter ego of the solvent polarization, related to a certain energy gap DE defined such that for a thermodynamically symmetric PT reaction, it equals zero at the solvent TS where the proton potential is symmetric [2, 3, 7]. In order to extend the above description to include the H-bond coordinate Q, we display a contour plot in Fig. 10.5 of the free energy of the PT system with the proton motion already quantized in its ground vibrational, zero point level, as a function of Q and the solvent coordinate DE. Reactant and product wells are
Figure 10.5 Contour plot of the PT system free energy versus the solvent coordinate, DE, and the H-bond coordinate separation Q for a symmetric reaction. Contour spacings are 1 kcal mol–1.
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clearly evident, with the passage between them involving an H-bond coordinate compression, i.e., a stronger H-bond. Thus, the H-bond frequency will increase near the saddle point. For this model system, the Q frequencies are ~290 cm–1 near the reactant and product configurations and 550 cm–1 near the saddle point [3b]. Thus, the Q motion should also be quantized, and this was done in the approximation that the H-bond vibration is fast compared to the solvent motion. Figure 10.6 shows the resulting free energy curves versus the solvent coordinate for the first several H-bond vibrational states. While the excited vibrational state curves can be examined to deduce the impact of H-bond excitation on the rate [2d, 3b], under ordinary room temperature conditions, the rate will be dominated by the ground state l = 0 level curve, and we restrict further discussion to that case. Note that now there is a further contribution to the ZPE to G at the solvent TS and reactant (R) configuration arising from the quantized H-bond vibration. For the model symmetric reaction, the total change DZPE‡ from R to TS is –2.1 kcal mol–1, of which –2.5 kcal mol–1 arises from the quantized proton motion, which is more delocalized at TS than in R (see Fig. 10.1(a)), while +0.4 kcal mol–1 arises from the H-bond vibration, reflecting the (stronger) H-bond higher frequency at TS compared to R (cf. Fig. 10.5). Since the ZPE change enters the activation free energy, the H-bond ZPE exerts a non-negligible effect on the rate constant. Transition state theory (TST) can be applied in the solvent coordinate for the l = 0 curve in Fig. 10.6 and for the corresponding curves for different thermodynamic reaction asymmetry DGRXN [2d, 3b], and the rate constant for the adiabatic PT reaction is then given by [2–4, 6, 7] kTST ¼ ðxS =2pÞexp½DG{ =RT
(10.4)
in which the prefactor involves a solvent frequency related to the free energysolvent coordinate curvature of the solvent reactant well shown in Fig. 10.6 (l = 0), and DG‡ is the activation free energy evident in that same figure. There are several important points to make here. First, while the quantum proton motion is accounted for, this is a classical TST result; the TST assumption of no barrier recrossing has been applied to the classical solvent reaction coordinate. Second,
Figure 10.6 Free energy curves versus the solvent coordinate DE for a symmetric PT reaction with the quantized proton in its ground vibrational state and the quantized H-bond vibrational mode in the ground (l = 0), first excited (l = 1), and second excited (l = 2) energy states.
10.2 Adiabatic Proton Transfer
there can be barrier re-crossing effects that reduce the rate constant compared to the TST value. Since TS passage means changing the solvent polarization, there is a time dependent friction related to such polarization changes, leading to barrier recrossing. Such a correction has been calculated for a model adiabatic PT between phenol and trimethylamine in a molecular level solvent and found [2d, 38] to be in good agreement with Grote–Hynes theory [39], but in that case and in most cases such corrections should be minor; indeed Grote–Hynes theory shows why TST is generally an excellent approximation to the rate constant. Third, and most important, while a symmetric reaction has been discussed here, we have analytically derived [3] expressions for the individual components of a DG‡ vs. DGRXN quadratic free energy relation (FER) 1 1 DG{ ¼ DG{o þ DGRXN þ a ¢o DG2RXN 2 2
(10.5)
¢o , is (The over-bar notation for the Brønsted coefficient and its derivative, e.g. a introduced to distinguish it from the inverse coupling length aL used in Section 10.3) This result is closely related to, but more fundamentally based than the wellknown and widely employed (cf. Refs. [9c, 12]) Marcus relation [19] 1 ðDGRXN Þ2 DG{ ¼ DG{o þ DGRXN þ 2 16DG{o
(10.6)
Actually Eq. (10.6) was never derived for PT reactions and thus has to be regarded as empirical for them. It was instead derived [19, 37] for two separate cases: (i) for outer sphere electron transfer reactions, where there is strong coupling to the solvent but there is no bond breaking and forming, and thus no strong electronic coupling between the R and P VB states, and (ii) (more approximately) for gas phase atom transfer reactions, where there is strong electronic coupling but no strong electrostatic coupling to a polar environment. As we have emphasized earlier in this chapter, PT reactions are characterized simultaneously by strong electrostatic coupling to the environment and strong electronic coupling. While we refer the reader to Ref. [3] for a more detailed discussion, our Eq. (10.5) can be regarded as the appropriate FER for proton adiabatic PT reactions; the coefficient of its quadratic term differs in principle from that of Eq. (10.6) (although the numerical magnitude of the coefficients can sometimes be similar [3]). We make a few further remarks on this in Sections 10.2.2 and 10.2.3. Another FER exists that is based on an underlying electronic diabatic perspective (although aspects of the electronic coupling are included); the FER in the electronically adiabatic ET limit for a curve-crossing picture is [40] DG{ »
R 2 b ðk þ DGRXN Þ2 b{ þ 4k ðk þ DGRXN Þ
(10.7)
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10 Theoretical Aspects of Proton Transfer Reactions in a Polar Environment
Here, k is an electronically diabatic reorganization energy, now including both solvent and nuclear rearrangements, and the last two terms in Eq. (10.7) are leading order corrections to the barrier height with finite electronic resonance coupling at TS (b‡) and R (bR). This equation has only been tested under conditions such that a linear FER predominates [40]. It differs considerably from our Eq. (10.5). A first issue for Eq. (10.7) is that the proton is not quantized, a crucial feature in our perspective; even when some quantum corrections are incorporated [22 b–d], there is no proton ZPE contribution at the TS for a symmetric reaction, in contrast to the adiabatic PT result. Other issues concern the Brønsted coefficient variation and the associated Hammond postulate, e.g. Eq. (10.7) does not give a Brønsted coefficient of 0.5, which it should. The reader is referred to Ref. [3b] for a more detailed discussion of Eq. (10.7). We have emphasized above that the free energy contains a proton ZPE contribution, as seen in Fig. 10.3(b) and implicit in Fig. 10.5, which also contains an H-bond ZPE contribution. For the activation free energy DG‡, this will contribute the difference of the H and D ZPEs at the solvent TS and for the reactant. This leads [4] to quite a different picture for kinetic isotope effects (KIEs) than the standard one [8, 12–17], sketched in Section 10.1 and to be further discussed in Section 10.2.3. In the above description, the solvent coordinate DE has not been given a molecular visualization, other than our initial characterization in terms of the degree of the solvent electrical polarization. An explicit characterization in terms of solvent molecular motion can be given, although this requires simulation analysis. For example, Fig. 10.7(a) shows the key motions of the water molecules in the PT reaction of an excess proton in aqueous solution [2a, b]. Briefly, the coordination number of the proton–accepting water molecule is 4, while that of the hydronium ion H3O+ is 3 [2, 41] – and all these coordinations involve H-bonds. Thus, passage of the solvent coordinate through its TS involves the reduction of this coordination number, effected via a rearrangement of the water initially H-bonded to the proton-accepting water oxygen of the H2O to break that initially existing H-bond, while a similar but opposite rearrangement occurs to form an H-bond with the proton-donating H3O+ appropriate to the coordination that this H2O will become. This explicitly identified reaction coordinate motion involving H-bond rearrangement [2a, b], is closely related to the original suggestion of Newton [41], and has subsequently become widely accepted and discussed [42, 43]. Figure 10.7(b) shows a related picture of an acid ionization in aqueous solution HCl···H2O fi Cl–···H3O+ [2a, b], and similar results have been found of the ionization of HF in water [2c, d]). Again the key requirement of 3 H-bond coordination for H3O+ and 4 H-bond coordination for H2O is involved: an H-bond must be broken for the proton-accepting H2O to be appropriate to the coordination of the H3O+ that this H2O will become.
10.2 Adiabatic Proton Transfer
(a) + +
(b)
+ Cl
Cl
-
Figure 10.7 Schematic illustration of the reaction-promoting solvent motions for (a) the first PT from H3O+ to H2O and (b) the first PT step in the acid ionization proton transfer reaction of HCl in aqueous solution.
10.2.2 Adiabatic Proton Transfer Free Energy Relationship (FER)
We now turn to a detailed discussion of the activation free energy DG‡ which determines the adiabatic PT TST rate constant Eq. (10.4). In particular, we discuss the derived activation free energy–reaction free energy relation Eq. (10.5) and its components, in a molecular description. We focus on transfer of a proton, but include some aspects for deuteron transfer in preparation for a discussion of KIEs in Section 10.2.3. We begin with an overview of the total free energy of the reacting system versus the solvent reaction coordinate, which can be usefully decomposed into two basic contributions [3, 7], as shown in Fig. 10.3(b), G ¼ G min þ ZPE
(10.8)
These are respectively, a bare’ free energy, Gmin, corresponding to the situation where the proton and H-bond Q coordinate are located at their respective classical minimum position for any given solvent coordinate value, and the vibrational ZPE contributions of the proton and the H-bond mode, measured from the latter potential energy minimum. Figure 10.8 displays the H and D free energy curves for a symmetric and an asymmetric reaction for a model OH···O system [3, 4], explicitly showing the decomposition of the total free energy G according to Eq. (10.8). The ZPE contributions for both H and D from Fig. 10.8(a) and (b) are dis-
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316
10 Theoretical Aspects of Proton Transfer Reactions in a Polar Environment Figure 10.8 Ground state free energy curves for adiabatic PT (solid lines H and dotted lines D) with both the proton/deuteron and H-bond vibrations quantized: (a) symmetric reaction and (b) exothermic reaction. Dashed lines show the free energy curves Gmin excluding the ZPE. (c) The ZPE for the proton (solid line) and deuteron (dashed line), including H-bond vibration, vs. DE. The dashed curves in (a) and (b) plus the ZPE in (c) give the full free energy G, the solid curves in (a) and (b). DER, DEP, and DE‡ denote the reactant, product, and TS solvent coordinate values, respectively.
played as Fig. 10.8(c), and contain both the ZPE of the H or D vibration and that of the H-bond mode. The ZPE decreases as the TS in the solvent coordinate is approached, mainly due to the proton/deuteron potential becoming more symmetric and the proton/deuteron is delocalized in a larger region. The reaction barrier increases starting from an exothermic case (Fig. 10.8(b)) to an endothermic case (the reverse of Fig. 10.8(b)). From Fig. 10.8(a) and (b), it is seen that both the reactant well frequency xs and barrier height DG‡ are isotope-dependent. However, the contribution of xs to KIEs is minimal since it is largely governed by the solvent [4]; accordingly we regard xs as isotope-independent in all that follows. Figures 10.8(a) and (b) also indicate that the TS position DE‡ along the solvent coordinate shifts with reaction asymmetry. This is due to the fact that the addition of the ZPE to an asymmetric Gmin (cf. Fig. 10.8(b)) shifts the maximum of G away from the maximum of Gmin at DE = 0, in the direction consistent with the Hammond postulate [15], e.g. later for endothermic reactions DGRXN>0. This indicates that the ZPE contribution at DE‡ to the free energy barrier DG‡ in the solvent coordinate will increase with increasing reaction asymmetry, a crucial qualitative characteristic [3] to which we will return. Also visible in Fig. 10.8(b) is the isotope dependence of the shift DE‡ and the associated increase in ZPE at DE‡ with increasing reaction asymmetry; the latter leads to a KIE reduction, since the ZPE contribution at DE‡ will become more and more similar to that of the reactant. Here one can see that the variation in ZPE along the reaction coordinate and its isotopic difference plays a significant role in the reaction free energy barrier variation, and hence the KIE as well. We now turn to the individual components of the FER in Eq. (10.5). These are DG‡o, the intrinsic’ reaction barrier DG‡o = DG‡(DGRXN = 0) for the thermody-
10.2 Adiabatic Proton Transfer
namically symmetric reaction, a term linear in DGRXN whose coefficient is the Brønsted coefficient a ¼
¶DG{ ¶DGRXN
(10.9)
evaluated for the symmetric reaction, ao ¼ 1=2, and a quadratic term in DGRXN with a coefficient a ¢o , which is the Brønsted coefficient slope evaluated at DGRXN = 0 [44]. The intrinsic free energy barrier DG‡o, which provides a reference barrier height, can be analytically expressed as [3] DG{o ¼ DG{m;o þ ZPE{o ZPERo
(10.10)
which has a contribution from a certain solvent reorganization free energy, here called DG‡m,o, to go from solvent arrangements appropriate to the reactant complex to those TS solvent arrangements appropriate for a symmetric double well proton potential, and from the change Z‡o – ZRo =DZPE‡o of the ZPE in the proton and H-bond coordinates on going from the reactant to the TS for the symmetric reaction. Note that in the adiabatic PT picture, Z‡o refers to a proton vibration at the symmetric reaction TS; the proton coordinate is a transverse, nonreactive coordinate. The Brønsted coefficient Eq. (10.9) has played an important role in the FER. To discuss it, we need to specify the underlying electronic structure description we have employed for the PT reaction Eq. (10.1). This is a two state valence bond model [3, 6] in which the electronic wavefunction is given in terms of the limiting reactant and product electronic configurations for Eq. (10.1), i.e. Eq. (10.2) which we repeat here for convenience jW el i ¼ cR jW R i þ cP jW P i
(10.11)
The validity of this description was discussed in the Introduction. The Bronsted coefficient can be quantitatively described in the adiabatic PT picture by any of three differences between the TS and the reactant: of the separation in the solvent coordinate, of the electronic structure, and of the quantum-averaged nuclear structure [3, 4] 2 { 2 R cP cP DE { DE R hq Q=2i{ hq Q=2iR ¼ ¼ (10.12) a ¼ P R DE P DE R hq Q=2iP hq Q=2iR cP2 cP2 Here DE‡ – DER is the solvent reaction coordinate distance between the TS and reactant, and DEP – DER is the corresponding distance between the product and reactant. cP2 is the quantum average over the proton and H-bond vibrations of cP2, the limiting product contribution to the electronic structure. The electronic structure for each critical point (c = R, P, and ‡) is evaluated at the respective critical point position DEc (DEc = DER, DEP, or DE‡) along the reaction coordinate. The structural element is the quantum-averaged proton distance (over both
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10 Theoretical Aspects of Proton Transfer Reactions in a Polar Environment
proton and H-bond coordinates) from the H-bond’s center. As noted above, the TS structure (and the TS position along the reaction coordinate) for a symmetric reaction is halfway between that of the reactant and product, so that ao = 1/2, independent of isotope. We pause to remark that the Brønsted coefficient a has often been used to describe TS structure via the Hammond postulate [15] or the Evans–Polanyi relation [45], where a is viewed as a measure of the relative TS structure along the reaction coordinate, usually a bond order or bond length. The important point is that, although adiabatic PT has a quite different, environmental, coordinate as the reaction coordinate, Eq. (10.12) is consistent with that general picture, with a proper recognition that quantum averages are involved. The TS structure’s variation with reaction asymmetry is described by the Brønsted coefficient slope a ¢o , the derivative of Eq. (10.12) with respect to DGRXN evaluated for the symmetric reaction. In this manner, afor the FER in Eq. (10.12) is linearly related to the reaction asymmetry a ¼
1 þ a ¢o DGRXN 2
(10.13)
Expressions for a ¢o have been explicitly derived in Ref. [3]. A convenient expression is in terms of the free energy’s force constants along the reaction coordinate, kR and k‡, at the reactant and TS positions, and the reaction coordinate distance between the reactant and product DDE =DEP – DER (cf. Eq. (1.5) of Ref. [3b]) a ¢o ¼
1 1 1 þ DDE 2 k{ kR
(10.14)
Figure 10.9 displays a FER for a model system [3, 4], as well as our FER Eq. (10.5) using Eq. (10.14) for ao, and it shows that the analytical description for the FER gives a good account of the activation free energy–reaction free energy relation for the rate constant.
Figure 10.9 Free energy relationship DG‡ versus DGRXN for proton transfer for a model O···O system (o). Dotted line is Eq. (10.5) using Eq. (10.14) to evaluate a ¢o (DG‡oH = 3.27 kcal mol–1 and a ¢oH = 0.03 mol kcal–1).
10.2 Adiabatic Proton Transfer
As seen from Fig. 10.8, a key component of the TS structure variation is reflected in the variation of the ZPE along the reaction coordinate. This feature is incorporated in Eq. (10.14) since the force constant is the sum (via Eq. (10.6)) of the ZPE and Gmin variation [3, 4]. (We pause to note that Eq. (10.4) shows that the coefficients in the FERs Eqs. (10.5) and (10.6) are not the same [3, 4].) Further, since a is also directly related to the relative difference in structure between R and TS, i.e. the last expression in Eq. (10.12), the variation of ZPE versus DE directly correlates with structural variation along a reaction path’. A comparison between a reaction path’ described with quantum averages via the adiabatic PT picture and those with a classical description is presented in Section 10.2.3.5. We now turn to the isotope dependence of the FER, which will be important for the discussion of KIEs in Section 10.2.3. This dependence arises from the components DG‡o and ao of the FER. The isotope dependence of the intrinsic free energy barrier DG‡o given by Eq. (10.4) is, as is apparent in Fig. 10.8(a), due solely to the difference in the H and D ZPEs { R Z { þ Z R ¼ DZPE{ DZPE{ DG{oD DG{oH ¼ ZoD ZoD oH oH oD oH
(10.15)
Recall that the ZPE contains both that of isotope L and that of the H-bond vibrational mode. The latter’s contribution is, however, smaller in magnitude than the negative ZPE difference associated with the proton vibrational mode (–2.5 kcal mol–1 in Fig. 10.8). Thus, DZPE‡o is overall negative (e.g –2.1 kcal mol–1 from Fig. 10.8). Furthermore, this ZPE difference decreases as the mass of the pffiffiffiffiffiffi transferring particle L increases, as one would expect from a ZPE 1= mL mass dependence. This ZPE mass dependence is the key ingredient for adiabatic PT KIEs. The isotope dependence of the Brønsted slope a ¢o is most conveniently discussed in terms of the derivative of the expression involving force constants Eq. (10.14). These force constants certainly depend on the variation of the ZPE along the solvent reaction coordinate via Eq. (10.8). Accordingly, a ¢o can be cast in terms of these slopes plus the variation in the ZPE value at the reactant and TS positions with reaction asymmetry [4]. Since the ZPE variation is largest in the TS region, the first term in Eq. (10.14) is the most significant, and thus, the essential point is that the isotope difference a ¢oH a ¢oD is approximately proportional to the difference in the rate of increase of ZPE‡ with increasing reaction asymmetry between H and D. Further analysis of the isotope dependence of the intrinsic barrier DG‡o is useful for the KIE discussion. The intrinsic barrier’s isotope dependence in Eq. (10.15), arising only from the difference in ZPEs, illustrates a key common point of connection between the present and standard perspectives: in both cases, the difference in intrinsic barrier heights is related to the difference in a ZPE between the reactant and TS between both isotopes, resulting in a KIE which is maximal for DGRXN = 0 and falls off with increasing asymmetry. In standard treatments, the isotope mass scaling for the L contribution is pffiffiffiffiffiffi ZPEL 1= mL , which assumes harmonic potentials [12–14]. The proton potentials
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10 Theoretical Aspects of Proton Transfer Reactions in a Polar Environment
in Fig. 10.3 are not harmonic, especially at the TS, where there is a double well, and thus it is not obvious that the simple ZPE mass scaling holds. However, the following relation based on Eq. (10.15) and assuming that all ZPEs scale accordpffiffiffiffiffiffi ing to ZPEL 1= mL DG{oL2
DG{oL1
¼
DZPE{oL2
sffiffiffiffiffiffiffiffi! rffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffi! mL2 mH mH { ¼ DZPEoH 1 mL1 mL2 mL1
(10.16)
was shown to hold quite well numerically [4], to within 10%. (All differences in l DG‡o have been scaled to the ZPE difference DZPE0 for H in the last member). The significance of the numerical validity of Eq. (10.16) is that the adiabatic PT picture also generates the mass scaling of standard KIE theory.
10.2.3 Adiabatic Proton Transfer Kinetic Isotope Effects
The KIE for adiabatic PT is the ratio of individual rate constants, where each of these is of the form in Eq. (10.4), e.g. H versus D transfer . kH » exp ðDG{H DG{D Þ RT kD
(10.17)
Here, the reactant reaction coordinate frequencies xSH,D in Eq. (10.4) have been assumed equal [4]. From the FER analysis of Eq. (10.5), the explicit form for the KIE dependence on DGRXN is kH ¼ exp ðDG{oH DG{oD Þ=RT exp ð a ¢oH a ¢oD ÞDG2RXN =2RT kD
(10.18)
Further, an equivalent form re-expresses the first part of this in terms of the KIE for the symmetric reaction: kH kHo ¼ exp ða ¢oH a ¢oD ÞDG2RXN =2RT kD kDo
(10.19)
involving the isotopic difference of the symmetric reaction Bronsted slope Eq. (10.14). Before proceeding with the KIE analysis for adiabatic PT, it is worth stressing, for comparison with the standard picture, that there are four common experimental observations which are consistent with the standard picture for nontunneling PT KIEs, and which are thus viewed as supporting that picture: (i) the Arrhenius temperature dependence of the KIE (as well as of the individual isotope rate constants); (ii) the KIE – DGRXN behavior described in Section 10.1 (i.e. maximal for the symmetric case); (iii) the KIE range is ~2–10; and (iv) the wide applicability of the Swain–Schaad relationship [13, 46] connecting KIE ratios (e.g. kH =kT ¼ ðkD =kT Þ3:3 ). These observations have done much to maintain the stan-
10.2 Adiabatic Proton Transfer
dard picture as a widespread perspective for KIEs. It is therefore important that, as now discussed, these also follow from the present adiabatic PT picture [3, 4].
10.2.3.1 KIE Arrhenius Behavior The Arrhenius form for the adiabatic PT KIE in Eqs. (10.17)–(10.19) is consistent with the first set of experimental results (i), and the general form for the KIE is identical to that of the standard picture (i.e. the adiabatic PT Eq. (10.17) is similar to the standard Eq. (10.2)), despite significant differences in ingredients between the two pictures. The adiabatic PT rate constant’s Arrhenius temperature dependence follows from a temperature-independent DG‡. Additional temperature dependence is in principle present in both DG‡ (and the prefactor) in the above KIE expressions, but these effects are, with some exceptions, negligible for highly polar solvents [47]. The temperature dependence of DG‡ will be discussed further in Section 10. 2.4.
10.2.3.2 KIE Magnitude and Variation with Reaction Asymmetry The KIE behavior versus reaction asymmetry for adiabatic PT follows directly [4] from insertion of the isotopic difference between the FER curves described in Eqs. (10.18) and (10.19). The general feature that the KIE is maximal for DGRXN = 0 follows from a Brønsted coefficient for a symmetric reaction that is isotope-independent, ao = 1/2, which reflects the symmetric nature of the electronic structure of the reacting pair at the TS (cf. Eq. (10.12)) [48]. The decrease from the maximum, characterized by a gaussian fall-off with increasing reaction asymmetry, is due to the isotope dependence a ¢oH > a ¢oD . As discussed in Section 10.2.2, this isotope dependence is primarily due to the differential rate of change of ZPE‡ versus reaction asymmetry between H and D. Figure 10.10(a), which displays the H versus D KIE (T = 300 K) for the Fig. 10.8 PT system, makes these points concrete. The calculated KIE is maximum at DGRXN = 0 and drops off symmetrically as the reaction asymmetry is increased. The maximum KIE for the symmetric reaction and the KIE magnitude throughout the whole range are both consistent with experimental observations, (ii) and (iii), respectively. The origin of this last aspect is as follows. The intrinsic KIE magnitude in the adiabatic PT view is directly related to the isotopic difference TS–R ZPE difference DZPE‡o = Z‡o – ZRo (see Eqs. (10.15) and (10.17)), whose special feature is the presence of the ZPE for the bound proton vibration at the solvent coordinate TS. Together with the DZPE‡o mass dependence following from the ZPE mass-scaling discussed in Section 10.2.2, the maximum KIE magnitude will automatically fall in the same general range as in the standard view. Further, the KIE will fall off due to the increase in TS ZPE with increasing reaction asymmetry, also similar to the standard view.
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322
10 Theoretical Aspects of Proton Transfer Reactions in a Polar Environment Figure 10.10 (a) KIE kH/kD versus DGRXN (T = 300 K) for an adiabatic PT system (see the text for details). (b) Swain–Schaad slope ln(kH/kT)/ln(kD/kT) versus reaction asymmetry calculated for the PT system in (a).
The reaction free energy dependence on the KIE has often been modeled with an expression based on the empirical Marcus FER for PT Eq. (10.6) [9c, 19]. ! " # DG2RXN k kH= ¼ kHo= exp ln Ho=k kD kDo Do 16DG{oH DG{oD " # !2 DGRXN ln kHo=k » kHo=k exp { Do Do 4DGoH
(10.20)
Equation (10.20) is similar in form as well as numerically to Eqs. (10.18) and (10.19), but it relates the rate of fall-off of the KIE to the magnitude of the intrinsic reaction free energy barrier DG‡o, and not with the change of TS structure (i.e. variation in a) described above, a feature that is common between the present picture and the W-M picture described in Section 10.1. To further elucidate this point, consider DG‡, for the standard picture which is a function of a classical activation energy for the MEP DV‡ and a difference in ZPE between R and TS (analogous to Eq. (10.10))[4] DG{ ¼ DV { þ ZPE{ ZPER
(10.21)
The isotopic difference a ¢oH a ¢oD is thus a ¢oH a ¢oD »
¶2 ZPE{H ¶2 ZPE{D ¶DG2RXN ¶DG2RXN
(10.22)
where we have used the fact that the second derivative of DV‡ is isotope independent. The variation of reactant ZPE is much less than that in the TS, so that the latter dominates Eq. (10.22). With Eq. (10.22), one can clearly see the connection
10.2 Adiabatic Proton Transfer
between ZPE variation and the fall-off of the KIE with increased reaction asymmetry for the W-M picture. This is not the case for Eq. (10.20), however, where a ¢oH a ¢oD depends only on the magnitude of DG‡o and the ZPEs, and does not depend on any variation in ZPE. A detailed discussion and comparison with the Marcus relation is given in Ref. [3, 4].
10.2.3.3 Swain–Schaad Relationship The Swain–Schaad relationship has been an important experimental probe for PT reaction KIEs [11, 24, 46]. We have used [4] one of its forms for illustration lnðkH =kT Þ ¼ 3:3 lnðkD =kT Þ
(10.23)
pffiffiffiffi which assumes the ZPE mass correlation ZPE 1= m, discussed in Section 10.2.2, to relate the H, D, and T ZPEs in Eq. (10.2). Figure 10.10(b) displays the calculated adiabatic PT ln(kH/kT)/ln(kD/kT) versus reaction asymmetry for the same PT systems as in Fig. 10.10(a), and shows little variation from Eq. (10.23). Thus, conventional Swain–Schaad behavior also follows from the adiabatic PT picture. We now recount the reasons for this [4]. From the DGRXN-dependent form in Eq. (10.18) for the KIE, the ratio of natural logarithms needed for the Swain–Schaad relation in Eq. (10.23) can be written as ln
kH kT
ln
kD kT
¼
DZPE{oT DZPE{oH DG2RXN ð a ¢oH a ¢oT Þ=2 DZPE{oT DZPE{oD DG2RXN ð a ¢oD a ¢oT Þ=2
(10.24)
A first significant point is that the adiabatic PT form in Eq. (10.24) has the same important feature as the standard picture, via Eq. (10.2): the Swain–Schaad relation is independent of temperature. We first examine the symmetric case DGRXN = 0, for which the adiabatic PT expression via Eq. (10.15) shows that the magnitude is related solely to the reactant and TS ZPE difference. These ZPE differences were shown to obey the same mass scaling used to derive the Swain– Schaad relations, cf. Eq. (10.16); hence the Fig. 10.10(b) plot maximum is close to the traditionally expected value. While Fig. 10.10(b) also shows that there is a small variation with reaction asymmetry, in the adiabatic PT perspective, of the Swain–Schaad slope. This has a minimal net effect, however, as discussed in Ref. [4].
10.2.3.4 Further Discussion of Nontunneling Kinetic Isotope Effects We have already repeatedly emphasized several important fundamental distinctions between the adiabatic PT and the standard view. Despite these distinct differences in physical perspective between adiabatic PT and the standard WestheimerMelander (W-M) picture, we have emphasized [4] that a remarkable general similarity exists between the two perspectives. For adiabatic PT, the symmetric reac-
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10 Theoretical Aspects of Proton Transfer Reactions in a Polar Environment
tion KIE depends on the difference in magnitude of the TS–reactant difference DZPE‡o, and the KIE variation with reaction asymmetry is due to the variation of TS ZPE (and structure). These two points, in fact, are shared with the W-M picture (cf. Eq. (10.2)). We now enumerate the numerical and physical differences between the two perspectives [4]. The adiabatic PT maximum KIE in Fig. 10.10(a) is in the range of KIEs commonly expected in the standard W-M picture, item (iii), but it is somewhat smaller than the higher KIEs 5–10 that one would expect with the standard view. (The argument for this latter range is given in Refs. [12–14]. ) From Eqs. (10.16) and (10.17), the maximum H/D KIE is that of the symmetric reaction h . i kHo ¼ exp DG{oH DG{oD RT kDo " rffiffiffi!, # 1 { RT ¼ exp DZPEoH 1 2
(10.25)
with the second line following from the mass scaling of the ZPEs. Equation (10.25) is also used [8, 12, 13] as an estimate for the KIE in the standard W-M picture (cf. Eq. (10.2)). The different symmetric reaction KIE limits for the adiabatic PT and W-M pictures is entirely due to their different views of the TS reaction and transverse coordinates: for a symmetric reaction, there is always a finite proton TS ZPE contribution for adiabatic PT (~1 kcal mol–1 for H and ~ 0.7 kcal mol–1 for D { ¼ 0) in the W-M description. The [4]), whereas the proton TS ZPE is zero (ZoH maximum KIE is thus always smaller in the adiabatic PT view; using xR ~3200 cm–1 as the maximum reactant frequency, the maximum KIE without tunneling is ~6 at 300 K. A reduced xR reduces the minimum value to less than 3 (cf. Fig. 10.10(a)).
10.2.3.5 Transition State Geometric Structure in the Adiabatic PT Picture We have emphasized, throughout, the quite different perspectives of the standard PT and the adiabatic PT pictures, for the reaction coordinate and the relevant barriers, as well as for the rate constant and KIEs. While we have argued for the validity of the adiabatic PT picture, it is useful to pause here and add an important remark. One of the most widespread and important uses of KIEs is in making inferences, via the standard PT picture, about the geometrical structure of the TS of the PT reaction [14, 15, 45]. Indeed, images of the entire reaction path are generated in this fashion. This obviously involves a classical perception of the coordinates, and it is important to ask whether such assessments can legitimately be made when the coordinates of the acid–base PT system are treated classically. We have addressed this issue in Ref. [3b], where, for a model PT system in solution treated in the adiabatic PT fashion, we have generated a certain reaction path in the following fashion. At each value of the solvent coordinate DE, we have calculated the quantum averaged values and of the proton and H-bond coor-
10.2 Adiabatic Proton Transfer Figure 10.11 Calculated quantum averages vs. for an O···O system (solid line) [3b] and the BEBO curve (dotted line).
dinates, respectively. The relation between and is displayed in Fig. 10.11[3b] and is compared with a reaction path generated from a bond energy– bond order (BEBO) model [49], which is often used in the standard picture of PT and which completely ignores the solvent. It is seen that the two curves are quite close despite distinct differences between the two methods, most notably that in one case the proton and H-bond coordinates are treated fully quantum, while in the other case they are treated completely classically. This comparison demonstrates that one, in a certain sense, can retain the picture of a path in terms of quantum averaged coordinates and the connection between transition state structure’ and reaction asymmetry [3, 4]. We pause to note that we have determined that a recently proposed empirical quantum correction [50] improves the agreement with the quantum averaged solid line in Fig. 10.11, especially in the TS region. This correction was based on solid state NMR studies of H/D isotope effects on the geometries of strong NHN and OHN hydrogen bonded solids. The success of the model implies that the effects of different solvent configurations on H-bond geometries are similar to those produced by a combination of molecular acidity, basicity and local crystal fields. 10.2.4 Temperature Solvent Polarity Effects
The above discussion has assumed a polar environment in which the polarity does not significantly change upon temperature (T) variation. However, over a sufficiently large temperature range (larger than those we have considered), the static dielectric constants eo of liquids are known to change significantly with T, the solvent polarity decreasing with increasing T[51, 52]. For example, eo for water is ~88 at 273 K and decreases to ~55 at 373 K[51]. This type of solvent polarity change will drastically affect H-bonding and PT for systems such as acid ionization PT reactions Eq. (10.1) where the charge character of the reactant differs significantly from that of the product. For the reaction class in Eq. (10.1), the magnitude of the product solvation free energy will increase relative to the reactant with increasing solvent polarity, and thus the reaction asymmetry changes with eo variation, as dis-
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Figure 10.12 Reaction free energy curves for solvent dielectric eo values = 20, 30, 50, and 80. See Ref. [47] for details of calculation.
played in Fig. 10.12 [47]. This effect has been demonstrated experimentally [52] and theoretically [6]. One can also see in Fig. 10.12 that the PT reaction free energy barrier also changes, increasing with increasing T. The resulting PT rate constant k has a reduced effective activation energy in an Arrhenius plot due to the T-dependent solvent polarity effect [47]. It should be noted though that the Arrhenius behavior for the KIE is largely unchanged by solvent polarity variation via a cancellation of effects between isotopes [47].
10.3 Nonadiabatic Tunneling’ Proton Transfer
We now turn to the proton nonadiabatic, or tunneling, regime. We first briefly review the PT tunneling rate constant formalism [1], including the role of the H-bond mode, and then summarize the resulting KIE behaviors, focusing on adherence (or not) with the same KIE trends (i–iv) discussed in Section 10.2.3 for nontunneling PT. We here restrict the temperature to be close to room temperature and above where the H-bond mode with frequency "xQ is significantly populated, i.e. "xQ~RT and "xQ<
10.3 Nonadiabatic Tunneling’ Proton Transfer
with quantum features subsequently added. In our view, these suffer from some difficulties (for discussion, see Refs. [3–5]). The Russian school [26, 53, 54] pioneered in the late ’60s a perspective where the solvent played a key role in tunneling PT. While the approach of Refs. [26, 53, 54] shares some features with our perspective [1], there are several importance differences. First, the H-bond vibration is always treated classically, rather than by the general quantum mechanical treatment of Ref. 1. Most importantly, it is assumed in the Russian school approach that PT is electronically diabatic, in very strong contrast to the present assumption of electronic adiabaticity, a difference which leads to significant differences in experimental predictions [5b]. Our view is that most tunneling regime PT reactions are electronically adiabatic, with a rather strong electronic coupling – an aspect related to the fact that chemical bonds are broken and made – and that an electronically diabatic description is inappropriate [5b]. Finally, we should note that so-called proton -coupled electron transfer is a quite different reaction class, involving transfer of an electron over larger distances, where different considerations apply [34, 35]. 10.3.1 General Nonadiabatic Proton Transfer Perspective and Rate Constant
Figure 10.13 displays the physical picture for nonadiabatic PT, with a fixed H-bond separation, a constraint later relaxed. The system free energy as a function of the proton coordinate – involving the electronically adiabatic proton potential – is displayed with the reactant and product diabatic proton vibrational states indicated, for three values of the solvent coordinate characterizing different environmental configurations: reactant state R (Fig. 10.13(a)), transition state TS (Fig. 10.13(b)), and product state P (Fig. 10.13(c)). The R and P proton diabatic levels are found by solving the nuclear Schrdinger equation for the proton in each of the reactant and product wells, respectively. (Proton adiabatic levels are found by solving the Schrdinger equation for the entire proton potential.) The evolving diabatic ground proton vibrational states define free energies as a function of the environment rearrangement, shown in Fig. 10.13(d). At the thermally activated TS position, the proton reactant diabatic vibrational state is in resonance with the corresponding ground proton product state, and the proton can thus tunnel. The rate constant expressions quoted in this section were originally derived [1b,1c] from a dynamic perspective, i.e. from the time integral of the time correlation function (tcf) of the probability flux associated with the tunneling PT, and subsequently via other approaches [1a, d, e] including a curve crossing perspective [1a]. Beyond the rate constant results themselves, the dynamic tcf approach is revealing in connection with the passage from coherent tunneling – which leads to spectroscopic tunneling splitting but no kinetics – to the incoherent, kinetic limit where a tunneling PT rate constant exists; interestingly only a very small coupling of the PT system to the environment is required for this transition [1b, c].
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Figure 10.13 Free energy curves versus the proton position at (a) the reactant R, (b) transition state TS, and (c) product state P solvent configurations for nonadiabatic PT. In each case, the ground diabatic proton vibrational energy levels are indicated for both the reactant and product proton wells. (d) Free energy curves versus the solvent reaction coordinate for both diabatic proton levels displayed in (a–c).
The rate constant for nonadiabatic PT between reactant and product proton ground vibrational states with the H-bond separation Q fixed is [1, 26] k¼
C2 "
rffiffiffiffiffiffiffiffiffiffiffiffi p DG{ exp RT ES RT
(10.26)
where the free energy barrier DG‡ is DG{ ¼
ðDGRXN þ ES Þ2 4ES
(10.27)
and ES is the solvent reorganization (free) energy [55]. The tunneling probability is governed by the square of the proton coupling C, defined as one-half the resonance proton vibrational splitting [55], cf. Fig. 10.13(d). C increases as the H-bond separation decreases due to the increased tunneling probability for a smaller proton barrier; its Q dependence is predominantly linear exponential [1] CL ðQÞ ¼ CeqL exp½aL ðQ Qeq Þ ; CeqL = CL (Qeq)
(10.28)
where Qeq is the equilibrium H-bond separation in the reactant state and aL is the exponent characterizing the exponential dependence(L=H, D, and T). The mass Inffiffiffi particular, aL is dependence in Eq. (10.28) is contained within pffiffiffiaL and CeqL. p pffiffiffiffiffiffi expected to be of the form aL mL (e.g. aD » 2aH , and aT » 3aH ), with typical
10.3 Nonadiabatic Tunneling’ Proton Transfer
values aG~25–35 –1 [1]. We limit our discussion to the single most important mode modulating the proton barrier – the H-bond mode; but other modes that regulate the barrier through which the proton must tunnel, e.g. H-bond bending modes [4, 28, 56], can be treated in a similar fashion. For simplicity, a harmonic H-bond vibration UQ ðQÞ ¼ UQ;eq þ 12 mQ x2Q ðQ Qeq Þ2 has been assumed, with an effective mass mQ and vibrational frequency xQ, and for the moment, we retain the restriction to PT between ground proton vibrational levels in the reactant and product. For extremely low temperatures "xQ>>RT, the Q vibrational mode resides primarily in its ground state, and the PT rate expression is [1] " # ffi 2 rffiffiffiffiffiffiffiffiffiffiffi C00 p ðDGRXN þ ES Þ2 exp kL ¼ (10.29) ES RT " RT4ES which is similar to Eq. (10.26) except that the proton coupling C is replaced by its ground Q-vibrational state quantum average " # ðEaL EQ Þ 2 2 2 C00 ¼ jh0jCðQÞj0ij ¼ CeqL exp aL DQ þ (10.30) "xQ Here DQ ¼ QP;eq QR;eq is the difference in the P and R equilibrium Q positions, and EQ ¼ 12 mQ x2Q DQ 2 is the associated reorganization energy. EaL is a quantum energy associated with the tunneling probability’s variation with the Q vibration EaL ¼ "2 a2L =2mQ
(10.31)
Even with DQ = 0 (EQ = 0), C is increased from its fixed value C(Qeq) by exp(EaL/"xQ): there is a finite probability of smaller H-bond separations even at low T due to Q’s the zero point motion. The ratio EaL/"xQ identifies EaL as a quantum energy scale for the localization of the Q wavefunction [1, 5]. When EaL/"xQ << 1, the coupling C is essentially that for fixed Q=Qeq. As EaL/"xQ increases, C increases, corresponding to increased quantum accessibility of smaller Q values. As T is increased, contributions from excited Q vibrational states become more significant. For moderate to high temperatures "xQ~RT and "xQ<
ðDGRXN þ ES þ EaL Þ2 ~aL Þ 4ðES þ E
(10.33)
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~aL ¼ EaL 1 b"xQ cothð1 b"xQ Þ E 2 2
(10.34)
The square proton coupling factor in Eq. (10.32) is the thermal average over the Q vibrational states [1] E (10.35) hC2 i ¼ CL2 ðQeq Þexp 2 aL cothð12 b"xQ Þ "xQ The inverse length scale of the coupling, aL , contributes significantly (via EaL, Eq. (10.31)) to this average square coupling. In particular, the sensitivity of the coupling of C to Q dynamics is characterized by the ratio EaL/"xQ so that hC 2 i increases as this ratio increases. The energy factor EaL also appears in the reaction barrier in Eq. (10.33), as an energetic contribution to that barrier due to thermal activation of the H-bond mode. The isotopic dependence EaL mL in the barrier plays a key role in isotope and temperature effects, but before recounting these effects, we describe the inclusion of excited proton vibrational levels [1, 5]. In the discussion above, PT has been assumed to occur from the reactant ground proton diabatic vibrational state to the corresponding state in the product. However, for very exothermic or endothermic reactions (|DGRXN| ‡ ES + "xQ), excited proton vibrational states can become important: the proton can be transferred into an excited proton product vibrational state for an exothermic case and from a thermally excited reactant proton vibration for an endothermic case. Accordingly, free energy curves corresponding to excited diabatic proton vibrational states are added to the ground diabatic proton vibrational states in Fig. 10.13(d), displayed as Fig. 10.14. Each free energy curve corresponds to a diabatic proton vibrational level. There are now several transitions possible, with a specific tunneling resonance situation associated with each TS or intersection of the proton diabatic free energy curves. We now discuss a number of such transitions. Figure 10.15 displays the TS proton potentials for the four transitions in Fig. 10.14 [57]. Figure 10.15(b) shows the symmetric proton potential for the groundstate to ground-state (0–0) transition and the corresponding first excited state transition (1–1). The 1–1 transition will have a higher transition probability (larger C) because the excited proton level is closer to the proton barrier top. But this
Figure 10.14 Proton diabatic free energy curves versus the solvent reaction coordinate for individual reactant (nR) and product (nP) proton vibrational states. Several transitions are qualitatively indicated.
10.3 Nonadiabatic Tunneling’ Proton Transfer Figure 10.15 Proton potentials for the solvent coordinate TS for four proton vibrational transitions (nR–nP): (a) 0–1, (b) 0–0 and 1–1, and (c) 1–0. The lines indicate diabatic proton vibrational levels.
increased 1–1 transition tunneling probability comes at a cost of 1 quantum of proton vibration excitation, which is added to the activation energy. Figures 10.15(a) and (c) display the proton potentials with 0–1 and 1–0 transitions, respectively. Both will have an increased tunneling probability compared with the 0–0 transition due to a smaller proton barrier through which to tunnel. Reactant proton vibrational mode thermal excitation leads to the 1–0 transition, assisting endothermic reactions, while extra solvent activation leads to the 0–1 transition, assisting exothermic reactions. The interplay between the cost of thermal excitation and the gain from increased tunneling probability, and their isotope dependence, plays a significant role in KIEs. In a general formulation, excited proton vibrational states are included in the PT rate as a sum over all state-to-state PT rates knR finP from a proton reactant state nR to a product state nP kL ¼
PP nR nP
PnR knR finP
(10.36)
where each state-to-state rate is weighted by the reactant state thermal occupation P PnR ¼ expðbEnR Þ= expðbEnR Þ, and EnR ¼ "xR ðnR þ 1=2Þ. knR finP is a modified nR
version of Eq. (10.32). D
knR finP
E " # ffi Cn2R ;nP rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p DG{nR ;nP ¼ exp ~aL ÞRT " RT ðES þ E
where the reaction free energy barrier DG‡nR,nP is transition-dependent
(10.37)
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DG{nR ;nP ¼
ðDGRXN þ nP "xP nR "xR þ ES þ EaL Þ2 ~aL Þ 4ðES þ E
(10.38)
The proton coupling CeqL(nR>nP) is also transition-dependent, and increases as the quantum numbers nR and nP increase (more properly, the difference) because the proton coordinate barrier’s width and height are smaller as the proton level sits higher in either well [5]. The Q dependence of the coupling can still be approximated by the same form in Eq. (10.28) [5] CnR ;nP ðQÞ ¼ CnR ;nP ðQeq Þ exp½aL ðQ Qeq Þ
such that the thermal average of C2 for Eq. (10.37) is accordingly D E E Cn2R ;nP ¼ Cn2R ;nP ðQeq Þ exp 2 aL cothð12 b"xQ Þ "xQ
(10.39)
(10.40)
Figure 10.16 displays the logarithm of the rate constant versus DGRXN behavior using Eqs. (10.36) and (10.37) for an example PT reaction (T = 300 K; "xQ = 300 cm–1, V‡ = 25 kcal mol–1, ES = 8 kcal mol–1, mQ = 20 amu, "xH = 3200 cm–1, "xH‡ = 2700 cm–1, and aH = 28 –1). Contributions from individual transitions (nR – nP) are also indicated. In particular, Fig. 10.16 describes the dominance of the 0–0 transitions near DGRXN = 0 and the increased contributions from the 0–1 transition for exothermic reactions and from the 1–0 transition for endothermic reactions, as discussed above. Indeed, the rate constants for excited proton vibrational transitions will dominate for more asymmetric reactions. These aspects have an important influence on activation free energy behavior: the full rate constant continuously increases going from endo- to exothermic reactions due to the increased contributions of 0–nP transitions as the reaction becomes more exothermic, while, the drop in rate constant with increased reaction endothermicity is decreased with contributions from nR–0 transitions. In the next subsection, we will discuss an analytic FER for nonadiabatic PT, mainly for use in discussing KIEs. Figure 10.17 shows an application to the PT rate constants themselves and indicates that such a description captures the rate
Figure 10.16 Log k versus DGRXN (T = 300 K) for H including excited proton vibrational states (solid lines). Dotted lines indicate individual contributions from 0–0, 0–1, 1–0, and 0–2 transitions. Rate constants were calculated with Eqs. (10.36) and (10.37). (T = 300 K; "xQ = 300 cm–1, V‡ = 25 kcal mol–1, ES = 8 kcal mol–1, mQ = 20 amu, "xH = 3200 cm–1, "xH‡ = 2700 cm–1, and aH = 28 –1).
10.3 Nonadiabatic Tunneling’ Proton Transfer Figure 10.17 ln kH and ln kD versus DGRXN (bold lines) for the same system in Fig. 10.16 (parameters for D are appropriately mass scaled). Dotted lines are Eq. (10.36) using Eq. (10.37) to evaluate a ¢oL .
constant behavior with reaction asymmetry as long as the asymmetry is not too large; we return to this issue below. 10.3.2 Nonadiabatic Proton Transfer Kinetic Isotope Effects
We now review the KIE behaviors that follow from this nonadiabatic PT formalism, focusing on the four KIE observables (i)–(iv) analyzed in Section 10.2.3 [5]. The KIE magnitude and its variation with reaction asymmetry are first summarized, which serves to demonstrate the importance of excited proton and H-bond vibrational states, and the temperature dependence is then reviewed. We conclude with discussion of the Swain–Schaad relations. As will be seen, the present perspective gives several KIE results which are similar to that of traditional perspectives not including tunneling; there are however important exceptions to this statement which we will discuss. We pause to emphasize that the same basic nonadiabatic PT formalism can be applied to H atom transfers (for which there will generally be only weak coupling to the environment). For H atom transfers, the predicted KIEs can be very large ~104 [1e] and non-Arrhenius T dependence is marked – as opposed to the modest KIE values and Arhennius T behavior discussed here for PT; in such cases, the signatures of tunneling are obvious, in marked contrast to the situation for PT.
10.3.2.1 Kinetic Isotope Effect Magnitude and Variation with Reaction Asymmetry Traditional treatments of KIEs, mentioned at the beginning of Section 10.3, including those invoking tunneling along a minimum energy path, predict that the KIE is maximal for a symmetric reaction DGRXN = 0 [17]. As now recounted, a similar behavior results in the present perspective. We will also pay attention to the tunneling PT KIE magnitude (focusing on tunneling PT systems that give smaller KIE magnitudes which might be confused with nontunneling PT).
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Before presenting the KIE variation with reaction asymmetry for nonadiabatic PT, it will prove useful to first discuss the individual isotope PT rate constant Eq. (10.36)’s variation with reaction asymmetry, which must include tunneling prefactor terms as well as the activation free energy. This behavior was analyzed up through quadratic terms in DGRXN [5] to find lnkL ¼ lnkoL
aoL DGRXN a ¢oL DG2RXN RT 2RT
(10.41)
where koL is the symmetric reaction DGRXN = 0 rate constant and aoL and a ¢oL are respectively the familiar Brønsted coefficient [13–16] and its derivative evaluated for the symmetric reaction
¶ lnkL
¶2 lnkL
aoL ¼ RT ; a ¢oL ¼ RT (10.42)
¶DG ¶DG2 RXN o
RXN o
This analysis anticipates that the 0–0 rate kL00 will have a significant contribution near DGRXN = 0, and thus the rate expression in Eq. (10.36) can be written kL ¼ kL00 rL ;
rL ¼
PP nR nP
FnR ;nP
(10.43)
in terms of kL00 kL00 ¼
D E 2 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C0;0 p "
"
DG{L0;0 exp ~aL ÞRT RT ðES þ E
# (10.44)
and the rate enhancement qL due to excited proton vibrational states. The coefficient of each transition FnR,nP is [5] FnR ;nP
" # DDG{nR ;np pð"xR nR þ "xP nP Þ exp ¼ PnR exp "x{ RT
(10.45)
DDG{nR ;np is the difference between the general reaction barrier DG{nR ;np Eq. (10.38) and that, DG{L0;0 , for the 0–0 case DDG{nR ;nP ¼ DG{nR ;nP DG{L0;0 ¼
ðnP "xP nR "xR Þð2ðDGRXN þ ES þ EaL Þ þ nP "xP nR "xR Þ ~aL Þ 4ðES þ E (10.46)
Here, properties from the TS proton potential (cf. Fig. 10.1) are included, i.e. the curvatures in the wells, xR and xP, and at the top of the barrier x‡, as a means to relate CnR,nP to C0,0 [5].
10.3 Nonadiabatic Tunneling’ Proton Transfer
The Brønsted coefficient aoL and its derivative a ¢oL in Eq. (10.41) can thus be written as a sum of the 0–0 case plus a correction due to the contribution of excited proton vibrational transitions: aoL
a ¢oL
1 E þ EaL ¼ S þ ~aL 2 ES þ E
* + ¶DDG{nR ;nP ¶DGRXN
(10.47)
F
2* +2 3 !2 + * { { 1 ¶DDG ¶DDG n n ;n ;n R P R P 5 ¼ 4 ~aL ¶DGRXN ¶DGRXN F 2 ES þ E F
(10.48)
where <…>F denotes a certain average over the vibrationally excited proton states for the symmetric reaction (cf. Eqs. (10.42)–(10.44)) [5]; Eqs. (10.47) and (10.48) reduce to their respective quantities from the FER in Eq. (10.33) if these excitations are not taken into account. (As discussed in Ref. [5], the symmetric reaction Brønsted coefficient aoL deviates slightly from the value of 1/2, an effect which vanishes almost entirely in a more refined treatment.) One can explicitly relate aoL and a ¢oL to the proton excitations by considering the quantum number dependence in Eq. (10.46) yielding aoL ¼
1 ES þ EaL þ hnP "xP nR "xR iF ~aL 2 ES þ E
1 a ¢oL ¼ ~aL 2 ES þ E ( ·
1
1
~aL 2RT ES þ E
D
ðnP "xP nR "xR Þ
(10.49)
2
E F
) hðnP "xP
nR "xR Þi2F (10.50)
Finally, from development of the isotopic rate constant up through quadratic order in DGRXN Eq. (10.41), the logarithmic KIE is [5] lnðkH =kD Þ ¼ lnðkoH =koD Þ
ða ¢oH a ¢oD ÞDG2RXN 2RT
(10.51)
where the position of the maximum in a KIE versus reaction asymmetry plot (H vs. D) occurs for a symmetric reaction DGRXN = 0, a direct result of the isotope independence of aoL » 1=2. The asymmetry variation is governed by the isotopic difference a ¢oH a ¢oD in the Brønsted slope derivative Eq. (10.48), which is positive so that the KIE diminishes with increasing reaction asymmetry. We will illustrate the usefulness of this analytic result in a moment.
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The maximal KIE behavior for tunneling PT is illustrated numerically in Fig. 10.18, which employs the full rate constant expression (10.36), with Eq. (10.37), for the H and D isotopes, evaluated for the same PT system used to generate Fig. 10.16, (D parameters are appropriately mass scaled) [5]. Also displayed in Fig. 10.16 is the analytical behavior Eq. (10.49), utilizing Eq. (10.48) for a ¢oL (dotted lines). The agreement between Eq. (10.51) and the actual behavior is quite close, although a breakdown (|DGRXN| > 10 kcal mol–1) is apparent (see also Fig. 10.17). The KIE is maximal for DGRXN = 0 and falls off with increasing reaction asymmetry. This maximal KIE behavior is due to increased excitation in both the proton and H-bond modes, excitations that become more facile with increased reaction asymmetry [5]. H-bond excitation benefits D more than H because the D tunneling probability is more sensitive to changes in Q: see the EaL/"xQ ratio in Eq. (10.40) with EaH < EaD. The contribution from the excited states (cf. the second term in Eq. (10.48)) contributes about 20% to the coefficient difference for the model reactions examined. aoL is larger for D than for H, since excited states are more easily accessed due to the smaller quanta "xD < "xH[5]. The KIE magnitude in Fig. 10.18 is actually fairly small compared to expectations for a PT tunneling reaction. In fact, the KIE magnitude for fairly mildly asymmetric reactions might be considered consistent with nontunneling PT. To emphasize this important point, the KIE with a slightly lower H-bond vibrational frequency "xQ=275 cm–1 is also included, where the KIE magnitude decreases by a factor of 3, emphasizing the sensitivity of the KIE to the donor–acceptor frequency. Even for the symmetric reaction, the KIE is far smaller than traditionally expected for a tunneling reaction. Indeed, the KIE behavior versus DGRXN for this case cannot be distinguished from that for nontunneling PT.
Figure 10.18 kH/kD for a nonadiabatic PT system with "xQ = 300 cm–1 and "xQ = 275 cm–1 (solid lines). Dotted lines use the analytical form for the KIE versus DGRXN behavior in Eq. (10.51), using Eq. (10.48) to evaluate aoL .
10.3 Nonadiabatic Tunneling’ Proton Transfer
10.3.2.2 Temperature Behavior We now turn to the T dependence of the rate in Eq. (10.36) [5], which in general is certainly not Arrhenius. However, one must bear in mind that most experiments are conducted over a reasonably restricted temperature range where the behavior can appear to be Arrhenius, even though the PT is completely tunneling in character. We first consider the individual transition rates Eq. (10.37) which are weighted to give the overall rate constant Eq. (10.36). There are two contributions to the T dependence of these individual transition rates which dominate in Eq. (10.37). The first is contained within the exponential containing the reaction free energy barrier, which gives Arrhenius behavior if the components of the reaction barrier, ~aL (see Eq. (10.34)) and ES [5, 47], have only a minor T dependence. An impori.e. E tant point in this connection is that the impact of any such T dependence is suppressed if the reorganization energy is significant (ES > EaL), as it often will be for PT in a polar environment. The second contribution comes from the thermally averaged square proton coupling Eq. (10.40), and in principle is not Arrhenius. In addition to these T dependences for the individual transition rate constants, the thermal sum over excited proton transitions for the full rate in Eq. (10.36) is clearly also not in principle Arrhenius. Altogether, these contributions give rise to a nonlinear T dependence in an Arrhenius plot, as expected for tunneling PT [8, 11, 13, 14, 58]. (We immediately stress that this is not a non-Arrhenius behavior associated with a transition from high temperature, classical “over the barrier” PT to tunneling PT at lower temperatures; the entire description here is in the tunneling regime.) Nonetheless, the T dependence of the tunneling rate constant Eq. (10.36) was shown [5] to be effectively linear in an Arrhenius plot for a limited but non-negligible temperature range [59]. This is now discussed. In the analysis [5], the PT rate in proximity to a specific temperature To is written in an Arrhenius form kL ¼ kL ðTo Þexp½ðb b o ÞEAL
(10.52)
where the Arrhenius intercept is just the extrapolation from the rate at T = To to infinite temperature: AL ¼ kL ðTo Þexp½bo EAL , and EAL is determined by the slope in an Arrhenius plot. For illustrative purposes, the same system as in Fig. 10.16 was taken, and T was varied (T = 300–350 K), while keeping the reaction asymmetry constant, DGRXN = 0. The apparent Arrhenius rate and KIE behavior obtained in this limited T range are displayed in Fig. 10.19. The apparent activation energies for H and D differ considerably, with EAD almost twice EAH: EAH = 5.7 kcal mol–1 and EAD = 10.6 kcal mol–1; this results in a significant effective activation energy for the KIE EAD – EAH = 5.0 kcal mol–1, displayed in Fig. 10.19(b). These slopes can be quantitatively analyzed [5] to determine the contributions from the H-bond and proton vibration excitations. For this determination, the expansion in Eq. (10.43) of the rate constant in terms of the 0–0 transition and the contribution from excited proton vibrational
337
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10 Theoretical Aspects of Proton Transfer Reactions in a Polar Environment Figure 10.19 (a) lnkH (+) and lnkD (o) versus 1/RT (T = 300–350 K) for the PT system in Fig. 10.16 with DGRXN = 0. (b) ln(kH/kD) (+) for rate constants in (a). The lines are linear fits to the points. The slopes of the lines give the activation energies (a) EAH = 5.7 kcal mol–1; EAD = 10.6 kcal mol–1 and (b) KIE EA = 5.0 kcal mol–1.
states is also used. Here, the 0–0 rate kL00 and the excited state factor qL are evaluated at the mid-range temperature To koL = kL00(To) (e.g. To = 325 K in Fig. 10.19), such that kL(To) = qLkoL. The parameters in the resulting Arrhenius form Eq. (10.52) for the rate constant in this limited T region have the following forms [5] AL ¼ koL rL ðTo Þ exp ðbo EAL Þ ; D E EAL ¼ EaL ½coth2 ðb o "xQ =2Þ 1 þ DG{L0;0 þ DDG{nR ;nP
(10.53) D E Here DG‡L0,0 is the 0–0 reaction free energy barrier Eq. (10.33) and DDG{nR ;nP L is the activation free energy barrier contribution from excited proton states D
DDG{nR ;np
E L
PP ¼
nR nP
FoR;P ð"xR nR þDDG{n ;n Þ R p PP FoR;P
L
(10.54)
nR nP
where the symmetric reaction transition coefficient is FoR,P = FnR,nP(T = To) (cf. Eq. (10.45)). When compared to the numerical results in Fig. 10.19, Eq. (10.53) gives reasonable estimates for EAH and EAD, EAH = 6.1 kcal mol–1 and EAD = 11.2 kcal mol–1, which differ by less than 10% from the obtained numerical values. The decomposition of these apparent activation energies via Eq. (10.46) is useful [5] in determining which contributions are most important and how these contributions change with T, "xQ, reaction asymmetry, and solvent reorganization energy ES, as now reviewed. The first term in Eq. (10.53) is the activation energy contribution from the thermally averaged square coupling hC2 i Eq. (10.40), and as such is extremely sensitive to parameters affecting the H-bond mode-tunneling coupling, namely T, "xQ, and EaL. For the present system, this term dominates the activation energy for both H (60%) and D (66%). Furthermore, since EaL mL is mass sensitive, the
10.3 Nonadiabatic Tunneling’ Proton Transfer
predominant contribution to the activation energy difference determining the Arrhenius activitation energy factor for the KIE will be dominated by this first term. The coefficient {coth2(bo"xQ /2) – 1} in this term is very sensitive to To and "xQ, increasing drastically as To is increased or "xQ decreases, and the ratio "xQ /RTo determines the relative contribution for this first term. The second term in Eq. (10.53), the activation free energy barrier DG‡L0,0, is for the present system also significant for both H (39%) and D (25%). Of course, the magnitude of this term changes with reaction asymmetry, decreasing as the reaction goes from endo to exo-thermic (cf. Eq. (10.33)). Finally, the last term in Eq. (10.53) for EAL is the least important for the present example system, <1% for H and 9% for D. Its lack of importance correlates with the significance of the 0–0 transition in the overall rate, described here by qL~1, qH = 1.004 and qD = 1.25. More generally, however, qL will obviously change as the reaction becomes more asymmetric as well as with increasing T. With the above individual isotope Arrhenius parameter results in Eq. (10.53), the Arrhenius parameters for the KIE can be examined. The KIE Arrhenius slope is thus determined by the isotopic difference of the apparent activation energies EAL h i EAD EAH ¼ EaH ½coth2 ðb"xQ =2Þ 1 þ DG{Do DG{Ho þ
h i DDGnR ;nP D DDGnR ;nP H
(10.55)
For the chosen example, the first term arising from thermal H-bond excitation effects on the average squared coupling contributes, as predicted above, the most, 72%, the final term is next in significance at 20%, and the middle term contributes only 8%. The minimal significance of the (middle term) difference in 0–0 reaction barriers reflects the disparity ES > EaL that we have noted above should be expected for PT in a sufficiently polar environment. The increased contribution (third term) of the excited proton state contribution is due to the differential contribution of the 0–0 transition to the total rate, qH< qD [60]. The Arrhenius intercept AL in Eq. (10.53) is the extrapolation from the rate at T = To kL(To) = koLqL to infinite T, and thus the ratio of intercepts (H vs. D) is the extrapolation of the H vs. D KIE at To to infinite temperature AH= ¼ kH= AD kD o exp½b o ðEAD EAH Þ
(10.56)
where
kH= kD
¼ koH rH=k r oD D o
(10.57)
The significant isotopic difference of Arrhenius intercepts, i.e. AH „ AD, is a signature for a tunneling process [11]. For the Fig. 10.19(a) system, AH < AD, which is the case where the right-hand side of Eq. (10.56) is less than 1. If, however,
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10 Theoretical Aspects of Proton Transfer Reactions in a Polar Environment
EAD – EAH were ~1 for the system (and not ~5 kcal mol–1 as in Fig. 10.19), then one would instead have AH > AD; thus, tunneling itself imposes no relative size for the Arrhenius prefactor ratio. Clearly, the interplay between the (kH/kD)o magnitude and the difference EAD – EAH in Eq. (10.56) determines whether AH > AD or vice versa. This suggests that an alternate yet equivalent isotope analysis of Arrhenius plots would be to analyze (kH/kD)o and EAD – EAH rather than AH/AD and ED – EH [5]. The advantage is that there is a direct connection between the KIE magnitude and Arrhenius slope and the H-mode characteristics. Specifically, such an analysis [5] clearly demonstrates that larger KIE magnitudes result from longer (large acid–base separations) and more rigidly H-bonded complexes (large "xQ /RT), and small Arrhenius slopes arise with less probability of H-bond and proton mode excitation (i.e. low T and especially higher "xQ /RT ratios).
10.3.2.3 Swain–Schaad Relationship This final category of KIE behavior concerns the relative KIEs between the three isotopes H, D, and T via the Swain–Schaad relationship, cf. Eq. (10.23). Deviation from this relationship is regarded as a clear indication of tunneling [11, 61]. We noted in Section 10.2.3.3 that for the adiabatic PT regime, close adherence to the Swain–Schaad relations results from the fact that the isotope dependence arises from ZPE differences in the reaction free energy barrier, cf. Eq. (10.15). Further, these ZPE differences obey the same mass scaling used to derive the Swain– Schaad relations, cf. Eq. (10.16). In the nonadiabatic PT regime, the significant isotope dependencies lie in the tunneling prefactor (e.g hC2 i in Eq. (10.32)), not in ZPEs, and thus lead to deviations from Swain–Schaad behavior as a clear signature of tunneling. However, in the remaining discussion, we show that the situation need not be so straightforward. Traditionally, the Swain–Schaad relationship has been experimentally assessed by varying system parameters and plotting ln(kH/kT) versus ln(kD/kT) and determining whether this produces a line which goes through the origin and has a slope ~3.3 [8, 13, 14, 46]. However, Eq. (10.23) has also been assessed by plotting the ratio ln(kH/kT)/ln(kD/kT) versus a system parameter, such as temperature [11]. If the ratio deviates significantly from the value of ~3.3, the PT system is said to be tunneling. Here we recount our examination [5] of whether or not a nonadiabatic tunneling PT system can exhibit the Swain–Schaad behavior in Eq. (10.23) and simultaneously have a KIE magnitude that is normally consistent with adiabatic nontunneling PT, i.e. kH/kD £ 6 at T = 300 K [4, 8, 13, 14]. Figure 10.20(a) displays the ratio ln(kH/kT)/ln(kD/kT) for the same system in Fig. 10.16 except that the H-mode frequency has been increased to "xQ = 375 cm–1 (T = 300 K) [5]. The Swain–Schaad ratio is at the expected traditional value, but the H versus D KIE in Fig. 10.20(b) is clearly large enough to indicate tunneling PT. Beyond this, the T-variation of the Swain–Schaad ratio for this system shown in Fig. 10.20(c) displays a distinct deviation from Eq. (10.23) for part of the temperature range, and thus also allows confirmation of tunneling PT [62]. The lesson of this example is that while the traditionally appropriate Swain–Schaad ratio can be
10.4 Concluding Remarks Figure 10.20 (a) Swain–Schaad ratio ln(kH/kT)/ ln(kD/kT) versus reaction asymmetry for a nonadiabatic PT system with "xQ = 375 cm–1. (b) kH/kD for system in (a). (c) ln(kH/kT)/ln(kD/kT) versus 1/RT (T = 250–350 K) for the symmetric reaction in (a).
obtained – implying no tunneling – even for a tunneling PT system, it is difficult to find a tunneling PT reaction with both the Swain–Schaad ratio and KIE magnitude of the traditionally appropriate, i.e. nontunneling, values. This analysis indicates that the Schwain–Schaad ratio can be a clear indicator of tunneling [11], but examination over a parameter (e.g. T) range and simultaneous examination of the KIE magnitude can be necessary to establish this.
10.4 Concluding Remarks
In concluding this brief review, we content ourselves with a few remarks concerning perspectives for, and some limitations and extensions of, the theoretical treatments described. As we have discussed within, many of the experimental measures thought to support traditional descriptions of proton transfer (PT) also follow from the nontraditional perspective that we have presented. It is therefore important to ask which experimental signatures can be employed to distinguish between the different perspectives. We have noted several of these throughout the chapter. For example, in the proton adiabatic regime, the KIE magnitude for a symmetric reac-
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tion for the standard picture is larger (‡5) than that for the nontraditional view (£6); this point is discussed in Section 10.2.3.4 and in more detail elsewhere [4]. Indeed, experimental observations of PT KIEs exist [9c, 9e, 63, 64] which are consistent with the adiabatic PT predictions, but not with the standard picture. But we focus here instead on what we will call smoking guns’, by which we mean qualitative experimental signatures which would follow from the nontraditional perspective but which would definitely not be predicted from traditional points of view. A possible smoking gun would be infrared (IR)-induced PT, e.g. the driving of the acid–base PT reaction AH + B fi A– + HB+ , Eq. (10.1), by the IR excitation of the AH proton vibration. In a traditional perspective, the only role of the solvent would be to thwart the IR-induced reaction by vibrational de-excitation of the AH vibration. In the nontraditional perspective however, the nonequilibrium solvent can assist the IR-induced reaction [65]. This is currently under study via detailed simulations. In the nonadiabatic, tunneling PT regime, large KIE magnitudes and strong deviation from Swain–Schaad behavior for kinetic isotope effects are clear signatures of tunneling, as discussed in Section 10.3.2. However, these can follow not only from the nonadiabatic PT perspective critically involving nonequilibrium solvation reviewed here, but also from e.g. treatments where equilibrium solvation is assumed and some type of tunneling prefactor for the PT rate is included. A possible smoking gun for the nontraditional tunneling perspective where nonequilibrium solvation is central would be the observation of an inverted regime for PT. In analogy to electron transfer reactions [37], inverted regime behavior would be the eventual decrease of the rate constant with increasingly negative reaction free energy DGRXN. Such behavior has been reported experimentally [66, 67]; indeed agreement has been achieved [66] between the experimental findings and certain of the tunneling rate constant equations given in Sec. 10.3, for both the transfer of a proton and a deuteron. This is quite encouraging, but the situation is not so straightforward. It is likely that special characteristics of the experimental system studied in Ref [66] are involved in allowing inverted regime behavior to be observed. Indeed, Fig. 10.16 illustrates that in the two internal solute coordinate description used throughout, inverted regime behavior is observed only if the 0–0 transition between ground proton vibrational states in the reactant and product is accounted for. However, Fig. 10.16 also shows that this behavior disappears if excited proton vibrational state contributions to the rate are included. In brief, before the 0–0 rate constant has significantly declined, the 0–1 rate contribution has increased to avoid the decline of the overall rate constant, and so on for the various 0–nP transition contributions to higher product proton excited states. The special characteristics of the experimental system of Ref. [66] permitting inverted regime behavior – most likely related to the curvilinear character of the PT – and are still under study. There are assorted limitations to the theoretical descriptions we have described within. We refer the interested reader to the original papers for discussion of these and here concern ourselves solely with electronic structure issues. In the analyti-
10.4 Concluding Remarks
cal treatments described in this chapter, the electronic structure aspects were described in terms of a two valence bond (VB) basis, whose support was recounted in the Introduction. However, this kind of description is unlikely to apply to certain proton transfers, notably those involving carbon acids (cf. Ref. 42 in Ref. [3b]), where a third VB state will be necessary. Further electronic structure considerations are also necessary when treating excited electronic state proton transfer (ESPT) [68–71]. Among these is the origin of the well-known enhancement of the acidity in the excited state, i.e. a pKa reduction of ~ 6 units, for aromatic acids ArOH. Traditionally this has been explained in terms of a charge transfer (CT), upon electronic excitation, from the oxygen (O) of the acidic OH moiety into the aromatic portion of the acid; this would create a partial positive charge on O, thereby repelling the proton. However, it has been shown [70, 71] that there is very little such CT produced in the electronic excitation of the ground state acid; instead the acidity enhancement arises from a strong CT on the product side of the excited state reaction, i.e. from the O of the conjugate base of the acid into the aromatic ring system. Beyond this key aspect of ESPT, a number of issues concerning the proper description of the electronic state during ESPT [68–71] remain to be clarified in the future, an important task given that much current experimental investigation of PT is via ultrafast spectroscopy of excited state systems[43b–d, 72].
Acknowledgments
This work was supported in part by NSF grants CHE-9700419, CHE-0108314, and CHE-0417570. The work of PK at ENS was supported by a grant from the French ANR.
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References 1 (a) Borgis, D.; Hynes, J. T. J. Phys.
Chem. 1996, 100, 1118–1128; (b) Borgis, D.; Hynes, J. T. Chem. Phys. 1993, 170, 315–346; (c) Borgis, D.; Lee, S.; Hynes, J. T. Chem. Phys. Lett. 1989, 162, 19–26; (d) Borgis, D.; Hynes, J. T. J. Chem. Phys. 1991, 94, 3619–3628; (e) Lee, S.; Hynes, J. T. J. Chim. Phys. 1996, 99, 7557–7567. 2 (a) Ando K.; Hynes, J. T. J. Mol. Liq. 1995, 64, 25–34; (b) Ando, K.; Hynes, J. T. J. Phys. Chem. B 1997, 101, 10464– 10478; (c) Ando, K.; Hynes, J. T. J Phys Chem A 1999, 103, 10398–10408; (d) Staib, A.; Borgis, D.; Hynes, J. T. J. Chem. Phys. 1995, 102, 2487–2505; (e) Ando, K.; Hynes, J. T. Faraday Discuss. 1995, 102, 435–441; (f) Ando, K.; Hynes, J. T. Adv. Chem. Phys. 1999, 110, 381–430. 3 (a) Kiefer, P. M.; Hynes, J. T. J. Phys. Chem. A 2002, 106,1834–1849; (b) Kiefer, P. M.; Hynes, J. T. J. Phys. Chem. A 2002, 106, 1850–1861. 4 Kiefer, P. M.; Hynes, J. T. J. Phys. Chem. A 2003, 107, 9022–9039. 5 (a) Kiefer, P. M.; Hynes, J. T. J. Phys. Chem. A, 2004, 108, 11793–11808; (b) Kiefer, P. M.; Hynes, J. T. J. Phys. Chem. A 2004, 108, 11809–11818. 6 Timoneda, J. J.; Hynes J. T. J. Phys. Chem. 1991, 95, 10431–10442. 7 Gertner, B. J.; Hynes, J. T. Faraday Discuss. 1998, 110, 301–322. 8 (a) Bell, R. P. The Proton in Chemistry. 2nd edn. Cornell University Press, Ithaca, NY 1973; (b) Caldin, E.; Gold, V., Proton Transfer Reactions, Chapman and Hall, London 1975; (c) Kresge, A. J. Acc. Chem. Res. 1975, 8, 354–360; (d) Hibbert, F. Adv. Phys. Org. Chem. 1986, 22, 113–212; (e) Hibbert F. Adv. Phys. Org. Chem. 1990, 26, 255–379. 9 (a) Kreevoy, M. M.; Konasewich, D. E. Adv. Chem. Phys. 1972, 21, 243–252; (b) Kreevoy, M. M.; Oh, S-w. J. Am. Chem. Soc. 1973, 95, 4805–4810; (c) Kresge, A. J.; Silverman, D. N. Meth. Enz. 1999, 308, 276–297; (d) Kresge, A.J.; Chen, H. J.; Chiang, Y. J. Am. Chem. Soc. 1977, 99, 802–805; (e) Kresge, A.J.; Sagatys, D.
10
11
12
13
14
15
16
17
18
S.; Chen, H. L. J. Am. Chem. Soc. 1977, 99, 7228–7233; (f) McLennan, D. J.; Wong, R. J. Aust. J. Chem. 1976, 29, 787–798; (g) Lee, I.-S.; Jeoung, E.H.; Kreevoy, M. M. J. Am. Chem. Soc. 2001, 123, 7492–7496. (a) Bell, R. P., Goodall, D. M. Proc. R. Soc. London Ser. A 1966, 294, 273–297; (b) Dixon, J. E.; Bruice, T. C. J. Am. Chem. Soc. 1970, 92, 905 –909; (c) Pryor, W. A.; Kneipp, K. G. J. Am. Chem. Soc. 1971, 93 5584 –5586; (d) Bell, R. P.; Cox, B. G. J. Chem. Soc. B 1971, 783–785; (e) Bordwell, F. G.; Boyle, W. J. J. Am. Chem. Soc. 1975, 97, 3447–3452. (a) Cha, Y.; Murray, C. J.; Klinman, J. P. Science 1989, 243, 1325–1330; (b) Kohen, A.; Klinman, J. P. Acc. Chem. Res. 1998, 31, 397–404; (c) Kohen, A.; Klinman, J. P. Chem. Biol. 1999, 6, R191–R198; (d) Kohen, A.; Cannio, R.; Bartolucci, S.; Klinman, J. P. Nature 1999, 399, 496–499. Kresge, A. J., in Isotope Effects on Enzyme-Catalyzed Reactions, Cleland, W. W.; O’Leary, M. H.; Northrop, D. B. (Eds.), University Park Press, Baltimore, MD 1977, pp. 37–63. Melander, L.; Saunders, W. H. Reaction Rates of Isotopic Molecules, Wiley, New York 1980. (a) Westheimer, F. H. Chem. Rev. 1961, 61, 265–273; (b) Melander, L. Isotope Effects on Reaction Rates, The Ronald Press Co., New York 1960. (a) Hammond, G. S. J. Am. Chem. Soc. 1955, 77, 33–338; (b) Lowry, T. H.; Richardson, K. S. Mechanism and Theory in Organic Chemistry. 3rd edn. Harper Collins, New York 1987. More O’Ferral, R. A. in Proton Transfer Reactions, Caldin, E.; Gold, V. (Eds.), Chapman and Hall, London 1975, pp. 201–261. (a) Bell, R. P., The Tunnel Effect in Chemistry, Chapman and Hall, NewYork 1980; (b) Bell, R. P.; Sachs, W.H.; Tranter, R. L. Trans. Faraday Soc. 1971, 67, 1995–2003. A KIE expression of the form in Eq. (10.2) neglects any mass dependence in
References
19
20
21
22
the prefactor, the contribution of which is usually negligible, except in the case of tunneling [8, 11, 17], as well as assumes that the proton primarily resides in it ground (stretching and bending)vibrational state. (a) Marcus, R. A. J. Phys. Chem. 1968, 72, 891–899; (b) Cohen, A. O.; Marcus, R. A. J. Phys. Chem. 1968, 72, 4249– 4255; (c) Marcus, R.A. J. Am. Chem. Soc. 1969, 91, 7224–7225; (d) Marcus, R. A. Faraday Symp. Chem. Soc. 1975, 10, 60– 68. (a) Babamov, V. K.; Marcus, R. A. J. Chem. Phys. 1981, 74, 1790–1798; (b) Hiller, C.; Manz, J.; Miller, W. H.; Rmelt, J. J. Chem. Phys. 1983, 78, 3850–3856; (c) Miller, W. H. J. Am. Chem. Soc. 1979, 101, 6810–6814; (d) Skodje, R. T.; Truhlar, D. G.; Garrett, B. C. J. Chem. Phys. 1982, 77, 5955– 5976; (e) Marcus, R. A.; Coltrin M. E. J. Chem. Phys. 1977, 67, 2609–2613; (f) Garrett, B. C.; Truhlar, D. G. J. Chem. Phys. 1983, 79, 4931–4938; (g) Kim, Y.; Kreevoy, M. M. J. Am. Chem. Soc. 1992, 114, 7116–7123. Calculations of KIEs derived from a classical reaction path (e.g. the MEP) in the presence of a solvent or polar environment typically add quantum corrections to that path [22]. Such a reaction path, however, includes classical motion of the proton, especially near the TS, and thus this technique exhibits no difference in quantum corrections between H and D at the TS for a symmetric reaction (DGRXN=0) [22b], in contrast to the present picture. In variational TS theory for gas phase H atom transfer, the TS significantly deviates from the MEP TS and is isotope-dependent [23]. This feature has been calculated for PT in an enzyme, where the KIE has been diminished because the TS position significantly differs between H and D even in a symmetric case [22e]. For numerical calculations consistent with the standard view, see (a) Alhambra, C.; Corchado, J. C.; Snchez, M. L.; Gao, J.; Truhlar, D. G. J. Am. Chem. Soc. 2000, 122, 8197–8203; (b) Hwang, J.-K.; Warshel A. J. Phys Chem. 1993, 97, 10053–10058; (c) Hwang, J.-K.; Chu, Z.
T.; Yadav, A.; Warshel, A. J. Phys. Chem. 1991, 95, 8445–8448; (d) Hwang, J.-K.; Warshel, A. J. Am. Chem. Soc. 1996, 118, 11745–11751; (e) Alhambra, C.; Gao J.; Corchado, J. C.; Villa, J.; Truhlar, D. G. J. Am. Chem. Soc. 1999, 121, 2253–2258; (f) Cui, Q.; Karplus, M. J. Am. Chem. Soc. 2002, 124, 3093–3124. 23 Garrett, B.C.; Truhlar, D. G. J. Am. Chem. Soc. 1979, 101, 4534–4547. 24 Saunders, W. H. J. Am. Chem. Soc. 1985, 107, 164–169. 25 For examples of the equilibrium solvation picture for PT in a complex system, see (a) Bash, P. A.; Field, M. J.; Davenport, R. C.; Petsko, G. A.; Ringe, D.; Karplus, M. Biochemistry 1991, 30, 5826– 5832; (b) Cui, Q.; Karplus, M. J. Am. Chem. Soc. 2001, 123, 2284–2290; (c) Alhambra, C.; Corchado, J.; Snchez, M. L.; Garcia-Viloca, M.; Gao, J.; Truhlar, D.G. J. Phys. Chem. B 2001, 105, 11326–11340; (d) Cui, Q.; Elstner, M.; Karplus M. J. Phys. Chem. B 2002, 106, 2721–2740. 26 (a) Dogonadze, R. R.; Kuznetzov, A. M.; Levich, V. G. Electrochim. Acta 1968, 13, 1025–1044; (b) German, E. D.; Kuznetzov, A. M.; Dogonadze, R. R. J. Chem. Soc., Faraday Trans. II 1980, 76,1128– 1146; (c) Kuznetzov, A. M. Charge Transfer in Physics, Chemistry and Biology: Physical Mechanisms of Elementary Processes and an Introduction to the Theory. Gordon and Breach, Amsterdam 1995; (d) Kuznetzov, A.M.; Ulstrup, J. Can. J. Chem. 1999, 77, 1085–1096; (e) Shnel, J.; Gustav, K. Chem. Phys. 1984, 87, 179– 187. 27 (a) Basilevsky, M. V.; Soudackov, A.; Vener, M. V. Chem. Phys. 1995, 200, 87– 106; (b) Basilevsky, M. V.; Vener, M. V.; Davidovich, G. V., Soudackov, A. Chem. Phys. 1996, 208, 267–282; (c) Vener, M.V.; Rostov, I. V.; Soudackov, A.; Basilevsky, M. V. Chem. Phys. 2000, 254, 249–265. 28 (a) Agarwal, P. K.; Billeter, S. R.; Hammes-Schiffer S. J. Phys. Chem. B 2002, 106, 3283–3293; (b) Agarwal, P. K.; Billeter, S. R.; Rajagopalan, P. T.; Benkovic, S. J.; Hammes-Schiffer, S. P. N. A S. 2002, 99, 2794–2799; (c) Hammes-Schiffer, S. Chem Phys Chem
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10 Theoretical Aspects of Proton Transfer Reactions in a Polar Environment 2002, 3, 33–42; (d) Hammes-Schiffer, S.; Billeter, S. R.; Int. Rev. Phys. Chem. 2001, 20, 591–616; (e) Billeter, S. R.; Webb, S. P.; Agarwal, P. K.; Iordanov T, Hammes-Schiffer S. J. Am. Chem. Soc. 2001, 123, 11262–11272; (f) Billeter, S. R.; Webb, S. P.; Iordanov, T.; Agarwal, P. K.; Hammes-Schiffer, S. J. Chem. Phys. 2001, 114, 6925–6936. 29 While these two regimes are distinctly separated, there may exist real systems where different isotopes will be in different regimes. For example, the proton potential barrier at the solvent TS configuration may be small enough such that the proton ground vibration state may be above the barrier, but still large enough such that the deuteron ground vibration state, with a smaller ZPE, may be below the barrier. The present discussion assumes that all isotopes transfer in the same regime. 30 Kim, H. J.; Hynes, J. T. J. Chem. Phys. 1992, 96, 5088–5110 . 31 (a) Kim, H. J.; Hynes, J. T. J. Am. Chem. Soc. 1992, 114, 10508–10528; (b) Kim, H. J.; Hynes, J. T. J. Amer. Chem. Soc. 1992, 114, 10528–10537 . 32 Fonseca, T.; Kim, H. J.; Hynes, J. T. J. Photochem. Photobiol. A: Chem. 1994, 82, 67–79. 33 (a) Mulliken, R. S. J. Phys. Chem. 1952, 56, 801–822; (b) Mulliken, R. S. J. Chim. Phys. 1964, 61, 20–38; (c) Mulliken, R. S.; Person, W. B. Molecular Complexes , Wiley, New York, 1969. 34 (a) Cukier, R. I. J. Phys. Chem. 1996, 100, 15428–15443; (b) Cukier, R. I.; Nocera, D. Annu. Rev. Phys. Chem. 1998, 49, 337–369. 35 (a) Soudackov, A.; Hammes-Schiffer, S. J. Chem. Phys. 2000, 113, 2385–2396; (b) Iordanova, N.; Decornez, H.; HammesSchiffer, S. J. Am. Chem. Soc. 2001, 123, 3723–3733; (c) Iordanova, N.; HammesSchiffer, S. J. Am. Chem. Soc. 2002, 124, 4848–4856; (d) Hammes-Schiffer, S. Acc. Chem. Res. 2001, 34, 273–281. 36 Thompson, W. H.; Hynes J. T. J. Phys. Chem. A 2001, 105, 2582–2590. 37 (a) Marcus, R. A. J. Chem. Phys. 1956, 24, 966–978; (b) Marcus, R. A. J. Chem. Phys. 1956, 24, 979–988; (c) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta
1985, 811, 265–322; (d) Sutin, N. Prog. Inorg. Chem. 1983, 30, 441–498. 38 The recrossing correction was calculated for both ground and excited H-bond vibrational states at the transition state in Ref. [2d]. The reaction is in the adiabatic PT limit, as opposed to an earlier, more approximate treatment (Azzouz, H.; Borgis, D. J. Chem. Phys. 1993, 98, 7361–7374; Azzouz, H.; Borgis, D. J. Mol. Liq. 1994, 61, 17–36), an important feature to emphasize here since this earlier treatment of the reaction has been subsequently widely used as a reference model for various calculation methods. 39 Grote, R. F.; Hynes, J.T. J. Chem. Phys. 1980, 73, 2715–2732. 40 (a) Warshel, A. Computer Modeling of Chemical Reactions in Enzymes and Solutions, John Wiley & Sons, New York, 1991; (b) Kong, Y. S.; Warshel, A. J. Am. Chem. Soc. 1995, 117, 6234–6242; (c) Warshel, A.; Schweins, T.; Fothergil, M. J. Am. Chem. Soc. 1994, 116, 8437–8442; (d) Schweins, T.; Warshel, A. Biochemistry 1996, 35, 14232–14243; (e) qvist, J.; Warshel, A. Chem. Rev. 1993, 93, 2523– 2544; (f) Hwang, J.-K.; King, G.; Creighton, S.; Warshel, A. J. Am. Chem. Soc. 1988, 110, 5297–5311; (g) Warshel, A.; Hwang, J.-K. Faraday Discuss. 1992, 93, 225–238. 41 (a) Newton, M.D.; Ehrenson, S. J. Am. Chem. Soc. 1971, 93, 4971–4990; (b) Newton, M.D. J. Chem. Phys. 1977, 67, 5535–5546. 42 (a) Agmon, N. Chem. Phys. Lett. 1995, 244, 456–462; (b) Marx, D.; Tuckerman, M. E.; Hutter, J.; Parrinello, M. Nature 1999, 397, 601–604; (c) Geissler, P. L.; Dellago, C.; Chandler, D.; Hutter, J.; Parrinello, M. Science 2001, 291, 2121–2124; (d) Schmitt, U.W.; Voth, G. A. J. Phys. Chem. B 1998, 102, 5547– 5551; (e) Schmitt, U.W.; Voth, G. A. J. Chem. Phys. 1999, 111, 9361–9381; (f) Vuilleumier, R.; Borgis, D. J. Phys. Chem. B 1998, 102, 4261–4264; (g) Vuilleumier, R.; Borgis, D. J. Chem. Phys. 1999, 111, 4251–4266. 43 (a) For a perspective on this, we refer the reader to (b). In this connection, see also (c) and (d) concerning the issue of a
References
44
45
46
47 48
49 50
hydronium ion in the neighborhood of anion produced by PT. (b) Pines, E.; Pines D. in Ultrafast Hydrogen Bonding Dynamics and Proton Transfer Processes in the Condensed Phase, Elsaesser, T.; Bakker, H.J. (Eds.), Kluwer Academic, Amsterdam, 2002, 155–184; (c) Rini, M.; Magnes, B.-Z.; Pines, E.; Nibbering, E. T. J. Science 2003, 301, 349–352; (d) Mohammed, O. F.; Pines, D.; Dreyer, J.; Pines, E.; Nibbering, E. T. J. Science 2005, 310, 83–86. DGRXN is defined throughout as the free energy difference between reactant and product H-bond complexes, a free energy difference that is rarely experimentally determined. The full connection to experimentally determined quantities is discussed in Ref. 43 of Ref. [4]. (a) Evans, M. G.; Polanyi, M. Trans. Faraday Soc. 1936, 32, 1333–1360; (b) Evans, M. G.; Polanyi, M. Trans. Faraday Soc. 1938, 34, 11–24. The Evans–Polanyi relations were developed mainly for gas phase reactions but are also useful in solution in the context of the standard picture. Swain, G. G., Stivers, E. C.; Reuwer, J. F.; Schaad, L. J. J. Am. Chem. Soc. 1958, 80, 5885–5893. Kiefer, P. M.; Hynes J. T. Israel J. Chem. 2004, 44, 171–183. For real systems, ao is not expected to be exactly 0.5 due to ’intrinsic’ asymmetry, but the deviation from 0.5 for either H or D is not expected to be significant. For further discussion, see Ref. 45 of Ref. [4]. Pauling, L. J. Am. Chem. Soc. 1947, 69, 542–553. (a) Limbach,H.-H.; Pietrzak, M.; Benedict, H.; Tolstoy, P. M.; Golubev, N. S.; Denisov, G. S. J. Mol. Structure 2004, 706, 115–119; (b) Limbach, H.-H.; Pietrzak, M.; Sharif, S.; Tolstoy, P. M.; Shenderovich, I. G.; Smirnov, S. N.; Golubev, N. S.; Denisov, G. S. Chem. Eur. J. 2004 10, 5195–5204; (c) Limbach, H.-H.; Denisov, G. S.; Golubev, N. S. in Isotope Effects In Chemistry and Biology, Kohen, A.; Limbach,H.-H. (Eds.), Taylor & Francis, Boca Raton FL, 2005, Ch. 7, pp. 193–230.
51 (a) Eisenberg, D.; Kauzman, W. The
Structure and Properties of Water, Oxford University Press, New York, 1969; (b) Riddick, J. A.; Bunger, W. B. Organic Solvents: Physical Properties and Methods of Purification, 3rd edn., Wiley-Interscience, New York, 1970, pp. 67–88. 52 Shenderovich, I. G.; Burtsev, A. P.; Denisov, G. S.; Golubev, N. S.; Limbach, H. H. Magn. Reson. Chem. 2001, 39, S91–S99. 53 (a) Siebrand, W.; Wildman, T. A; Zgierski, M. Z. J. Am. Chem. Soc. 1984, 106, 4083–4089; (b) Siebrand, W.; Wildman, T. A; Zgierski, M. Z. J. Am. Chem. Soc. 1984, 106, 4089–4096. 54 (a) Cukier, R. I. J. Phys. Chem. B 2002, 106, 1746–1757; (b) Cukier, R. I.; Zhu, J. J Phys. Chem. B 1997, 101, 7180–7190. 55 The expression in Eqs. (10.26) and (10.27) is similar in form to that for weakly electronically coupled (electronically nonadiabatic) electron transfer [37], in that the proton coupling C is analogous to the electronic resonance coupling and the reorganization energy ES is analogous to the electronic diabatic solvent reorganization energy. Even though the reorganization energies and couplings are analogous, the physical picture behind the two reaction types is quite different. The reorganization energy for proton tunneling is the free energy difference associated with a Franck– Condon-like excitation (all nuclear and solvent modes other than the proton mode are held fixed) of the ground diabatic proton vibrational state at the equilibrium reactant solvent position to the ground product diabatic proton vibrational state, followed by relaxation along the solvent coordinate to the equilibrium solvent product position (See Fig. 10.13(d)). 56 Discussion of the influence of bending on these results can be found in Refs. [4] and [5a]. 57 The H-bond vibrational mode is assumed to remain significantly unchanged while the reaction coordinate fluctuates from the 0–0 TS to either the 0–1 or 1–0 TS.
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10 Theoretical Aspects of Proton Transfer Reactions in a Polar Environment 58 This is particularly true for H atom
transfer reactions because they are weakly coupled to a polar environment, i.e. small reorganization energies (cf. H atom transfer reaction in Ref. [1e]). 59 We note in passing that even for data over a broad temperature range where nonlinear behavior is observed, the analysis is useful to analyze different subregions in the nonlinear plot where the behavior is effectively linear, i.e. rate and KIE expressions for a given To and the local slope in an Arrhenius plot at To are obtained. 60 Excited state contributions described by qL have a key characteristic in that they increase with increased reaction asymmetry DGRXN and decreased reorganization energy ES [5]. Furthermore, the isotopic disparity qH< qD also increases with these trends, resulting in an increase in significance of the third difference in Eq. (10.55) with increased DGRXN and decreased ES [5]. 61 (a) Antoniou, D.; Schwartz, S. D. P. N. A. S. 1997, 94, 12360–12365; (b) Antoniou, D.; Schwartz, S. D. J. Chem. Phys. 1999, 110, 465–472; (c) Karmacharya, R.; Schwartz, S. D. J Chem. Phys. 1999, 110, 7376–7381. 62 Further remarks on the T dependence of the Swain–Schaad ratio can be found in Section 3c of Ref. [5]. 63 E. Pines, in Isotope Effects in Chemistry and Biology, Kohen, A.; Limbach, H.H. (Eds.), Marcel Decker, Inc., New York, 2005, Ch.16, pp. 451–464. 64 The observed KIEs [9c, 9e, 63] were measured by changing the solvent from
H2O to D2O, and while this change in solvent introduces other possible solvent isotope effects (i.e. viscosity), the rate limiting step in each case has been shown to be a PT step (or a series of PT steps), and thus the measured KIE corresponds to P. 65 Kim, H. J.; Staib, A.; Hynes, J. T. in Ultrafast Reaction Dynamics at AtomicScale Resolution Femtochemistry and Femtobiology, Nobel Symposium 101, Villy Sundstrom (Ed.), Imperial College Press, London, 1998, pp. 510–527. 66 (a) Peters, K. S; Cashin, A.; Timbers, P. J. Am. Chem. Soc. 2000, 122, 107–113; (b) Peters, K. S; Cashin, A. J. Phys. Chem. A 2000, 104, 4833–4838; (c) Peters, K. S.; Kim, G. J. Phys. Chem. A 2001, 105, 4177–4181. 67 Andrieux, C. P.; Gamby, J.; Hapiot, P.; Saveant, J.-M. J. Am. Chem. Soc. 2003, 125, 10119–10124. 68 Tran-Thi, T.-H; Gustavsson, T.; Prayer, C.; Pommeret, S.; Hynes, J. T. Chem. Phys. Lett. 2000, 329, 421–430 . 69 Tran-Thi, T.-H; Prayer, C.; Millie, P.; Uznanski, P.; Hynes, J. T. J. Phys. Chem. A 2002, 106, 2244–2255. 70 Hynes, J. T.; Tran-Thi, T.-H; Granucci, G. J. Photochem. Photobiol.; A. Photochemistry 2002, 154, 3–11. 71 Granucci, G.; Hynes, J. T.; Millie, P.; Tran-Thi, T.-H. J. Am. Chem. Soc. 2000, 122, 12235–12245. 72 Elsaesser, T. in Ultrafast Hydrogen Bonding Dynamics and Proton Transfer Processes in the Condensed Phase, Elsaesser, T.; Bakker, H.J. (Eds.), Kluwer Academic, Amsterdam, 2002, pp. 119–153.
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11 Direct Observation of Nuclear Motion during Ultrafast Intramolecular Proton Transfer Stefan Lochbrunner, Christian Schriever, and Eberhard Riedle
11.1 Introduction
Hydrogen dynamics is a fundamental issue in chemistry and molecular biology as the contributions in this handbook show. All organic compounds contain a large fraction of hydrogen atoms and the phenomenon of acidity as well as the sensitivity of many reactions on the pH-value mirror the ability of molecules to exchange protons [1, 2]. Hydrogen bridges are, in particular, important for the structure and function of proteins and their interaction with the environment [3]. Proton pumps for example are an important class of natural micromachines responsible for the energy management in halobacteria [4]. To understand hydrogen dynamics is therefore of fundamental importance [5]. In this chapter we describe the progress in understanding hydrogen dynamics via ultrafast spectroscopy of excited state intramolecular proton transfer (ESIPT). Femtosecond pump–probe spectroscopy provides a time resolution of the order of periods of high frequency vibrations and allows one to observe in real time the molecular motions during rearrangements and chemical reactions [6]. This results in a detailed picture of the reaction course and of the relevant mechanisms. ESIPT is particularly well suited to apply this technique to hydrogen dynamics. Contrary to ground state proton transfer, the process can be initiated by ultrashort light pulses, and the starting geometry is very well defined due to the intramolecular character. As we will see, ESIPT is associated with a wavepacket motion which allows one to reconstruct the reaction path in the multidimensional space of the relevant molecular coordinates. The chapter focuses on the ultrafast ESIPT found in molecules containing an H-chelate ring (see Fig. 11.1). We will discuss the spectral features associated with the ESIPT which are observed in experiments with a time resolution down to 30 fs. They are interpreted in terms of a wavepacket motion on an adiabatic potential energy surface connecting the Franck–Condon region of the enol-form with the minimum of the electronically excited keto configuration. The reaction coordinate is reconstructed from the coherently excited vibrational product modes observed in the experiment. Strong evidence is provided that skeletal modes deterHydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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11 Direct Observation of Nuclear Motion during Ultrafast Intramolecular Proton Transfer
Figure 11.1 Four ESIPT compounds considered in this study: 2-(2¢-hydroxyphenyl)benzothiazole (HBT), 1-hydroxy-2-acetonaphtone (HAN), 2-(2¢-hydroxyphenyl)benzoxazole (HBO), and ortho-hydroxybenzaldehyde (OHBA).
mine the dynamics whereas the proton itself plays a passive role and tunneling does not contribute significantly. The chapter is organized as follows. In the remainder of the introduction the investigated molecular systems are introduced. The experimental section describes a typical pump–probe setup for experiments with a very high time resolution. Then the transient absorption and the contributing processes are discussed. In the fourth section a model of the reaction mechanism is developed from the experimental findings. Then we discuss briefly the situation of parallel reaction channels, and finally the results and conclusion are summarized. The H-chelate ring is the common motif of many molecules exhibiting ESIPT (see Fig. 11.2). In the electronic ground state the enol-form with the hydrogen atom bound to the donor oxygen of the H-chelate ring is the stable tautomer. If the molecule is promoted to its first electronically excited state the hydrogen atom of the hydroxy group is transferred to a proton acceptor at the opposite site of the ring. The acceptor is typically a nitrogen or a second oxygen atom. Associated with the transfer is a shift of double bonds in the ring and a variation of the aro-
Figure 11.2 ESIPT scheme and steady state absorption and fluorescence spectra of HBT in cyclohexane (solid lines) and in ethanol (dashed lines) and of OHBA in cyclohexane (solid lines) and in methanol (dashed lines).
11.1 Introduction
maticity of the neighboring groups [7]. The ESIPT leads to a strong and characteristic Stokes shift between the UV absorption of the original enol-form and the visible fluorescence (see Fig. 11.2). Already in the seminal work of Weller the fluorescence is attributed to the reaction product, the keto-form [8]. The breaking of the OH-bond and the formation of a keto bond were unequivocally proven for the ESIPT of 2-(2¢-hydroxyphenyl)benzothiazole (HBT) by time-resolved infrared spectroscopy [9, 10]. It was found that the absorption band of the OH stretching vibration disappears upon UV excitation of HBT, and the C=O stretching band arises due to the ESIPT. After the ESIPT the molecules return by radiative decay or internal conversion (IC) to the electronic ground state of the keto-form (see Fig. 11.2). A very fast ground state proton transfer brings the molecule back to its enol-form [11]. In aprotic solvents, there is an intramolecular hydrogen bond between the hydroxy group of the H-chelate ring and the proton acceptor in the electronic ground state [12]. As long as this hydrogen bond exists, efficient proton transfer is found independent of the solvent. In polar solvents the hydrogen bond is broken for a high percentage of ESIPT molecules. The hydroxy group then forms an intermolecular hydrogen bond to solvent molecules and in many cases a cis–trans isomerisation takes place in the electronic ground state [13, 14]. In these molecules no ESIPT is possible and the fluorescence of the enol-form is observed, like e.g. for HBT in ethanol (see Fig. 11.2). In the case of ortho-hydroxybenzaldehyde (OHBA) dissolved in methanol the fluorescence exhibits two bands, one due to molecules which can undergo ESIPT and one at shorter wavelengths due to those which cannot. However, if ESIPT occurs, very similar time scales are observed for the process in gas phase and in different solvents. This indicates that the solvent has only a minor impact on the transfer dynamics itself [15]. Currently, investigations in our laboratory are in progress to clarify this point. In the following we assume that the influence of the solvent on the ESIPT can be neglected due to the intramolecular character of the reaction. In early investigations, transfer times of about 100 fs or less were observed for HBT in tetrachloroethylene [16], 2-(2¢-hydroxyphenyl)benzoxazole (HBO) in cyclohexane [17], and for methyl salicylate (MS) [18] and OHBA [19] in gas phase. For a number of ESIPT molecules very fast transfer times were found, even at cryogenic temperatures [20]. To resolve the evolution of the transfer and to learn about the mechanism the experimental time resolution had to be improved to better than 50 fs. Such experiments were only possible with the advent of Ti:sapphire laser systems and novel nonlinear sources for ultrashort tunable light pulses. Within the last ten years several experiments with extremely high time resolution have been performed. They revealed rich spectroscopic dynamics and resulted in a detailed picture of the ESIPT and the underlying mechanisms. Their comparative discussion is the central issue of this article.
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11.2 Time-resolved Absorption Measurements
The transient absorption setup used in our experiments is a versatile tool providing both the necessary time resolution and the tunability to investigate different compounds. The pump–probe spectrometer is based on two noncollinearly phase matched optical parametric amplifiers (NOPAs) (see Fig. 11.3) [21, 22]. The NOPAs are pumped by a regenerative Ti:sapphire laser amplifier delivering approximately 100 fs NIR pulses at around 800 nm with a repetition rate of 1 kHz. The NOPAs provide pulses tunable throughout the visible spectral region that are compressed by a fused silica prism sequence to below 20 fs. The output of NOPA 1 is frequency doubled to provide pump pulses which are suitable to excite the UV absorbing enol-form of the ESIPT molecules. The frequency doubling is typically done with a 100 lm thick BBO crystal cut for type I phase matching, and the dispersion of the resulting UV pulses is compensated with a second fused silica prism sequence. After passing a motorized delay stage the UV pulses are focused onto the sample to a spot size of 120 lm. A chopper blocks every second pump pulse to measure the pump-induced absorption changes with two consecutive probe pulses. As probe beam the output of NOPA 2 is used. It is focused to a size of 80 lm at the sample and crosses the pump beam with a small angle of 3. The sample transmission is measured by detecting the energy of the probe pulses with a photodiode behind the sample. To account for intensity fluctuations of the probe beam, a reference beam is split off before the sample and measured with a second photodiode. On a time scale of a few picoseconds orientational relaxation has no influence on the signal. For measurements covering longer delay times the polarizations of pump and probe beam can be set to the magic angle (54.7) relative to each other with a half wave plate in the pump beam path in order to avoid the influence of orientational relaxation. The sample is a 70 lm thick, free flowing liquid jet or a flow cell with a channel thickness of 120 lm. In both cases the excited volume of the sample solution is replaced by a fresh one between successive laser shots. The ESIPT molecules are dissolved in cyclohexane or other UV
Figure 11.3 Pump–probe absorption setup based on two NOPAs.
11.3 Spectral Signatures of Ultrafast ESIPT
compatible solvents with a concentration of 10–2–10–3 M resulting in an absorption of about 50% of the pump light. The detailed analysis of the time dependent absorption changes given below is only possible because the transmitted energy of the probe pulses is integrally detected and measurements at various spectral positions are performed by tuning the NOPA: In principle almost the complete visible region can be covered by the spectrum of a sub-5 fs pulse. If such pulses are applied they are dispersed before detection in order to obtain spectral selectivity [23, 24]. However, this results in strong coherent artifacts around time zero due to cross phase modulation with the pump pulses [25]. In such experiments the early time window of the experimental data, of the order of 100 fs, is usually excluded from the analysis of the molecular dynamics. Since the cross phase modulation does not change the energy of the probe pulses the integral detection is not sensitive to these artifacts and allows one to observe the molecular dynamics also in the direct vicinity of time zero.
11.3 Spectral Signatures of Ultrafast ESIPT
In the following we discuss the spectral signatures observed by ultrafast absorption spectroscopy of ESIPT molecules with a time resolution sufficient to temporally resolve the nuclear motions during the transfer. Pioneering work was performed on 2-(2¢-hydroxy-5¢-methylphenyl)benzotriazole (TINUVIN P), and for the first time oscillatory signal contributions associated with the ESIPT were observed [26]. Unfortunately, the extremely short lifetime of the electronically excited state of 150 fs [11] makes the analyses particular challenging. In order to uncover the characteristic features of the ESIPT dynamics and to develop a universal model we investigated a series of molecules with a longer S1 lifetime [27–29]. Two of them, HBT and HBO have a nitrogen atom as proton acceptor while in the other two, OHBA and 1-hydroxy-2-acetonaphtone (HAN) the proton switches between two oxygen atoms (see Fig. 11.1). The IC of these molecules varies markedly, but is much slower than in the case of TINUVIN P and does not mask the ESIPT dynamics. In the following the emphasis is put on HBT due to the extensive analyses available for this molecule. Meanwhile, however, similar dynamics have also been observed in 1,8-dihydroxyanthraquinone (DHAQ) [30], 2,5-bis(2¢-benzaoxazolyl)-hydroquinone (BBXHQ) [31], and 10-hydroxybenzo[h]quinoline (10-HBQ) [32]. The general features of ESIPT will be elaborated by comparison between HBT and the other compounds.
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11.3.1 Characteristic Features of the Transient Absorption
To initiate the proton transfer, ESIPT molecules are promoted to the S1 state by exciting them with an ultrashort UV pulse at their first absorption band, e.g. at 347 nm for HBT. Figure 11.4 gives an overview of the transient transmission after excitation of HBT, HBO, and HAN in cyclohexane, measured with a white light continuum in magic angle configuration. The spectra are dominated by excited state absorption (ESA), i.e. the absorption from the first electronically excited state to higher electronic states. Only in the UV and at about 500 to 600 nm are positive signals observed. In the UV, the transmission increase results from the bleaching of the electronic ground state. In the visible it is due to stimulated emission (SE). Comparing its spectral position and shape with the steady state fluorescence indicates that the stimulated emission stems from the electronically excited keto-form (compare with Fig. 11.2). This shows that the ESIPT and the emergence of the keto-form occurs well below the picosecond time scale. The changes observed on the picosecond time scale can be attributed to vibrational redistribution processes and internal conversion (see below).
Figure 11.4 Transient spectra after optical excitation of HBT, HBO, and HAN in cyclohexane measured with a white light continuum.
To characterize the proton transfer and the subsequent dynamics with 30 fs time resolution, the setup described in Section 11.2 is used. The transmission change, and thereby the appearance and evolution of the keto emission, is measured at various probe wavelengths covering the entire fluorescence band. The pump and probe polarization are set parallel since the transition dipole moment of the stimulated emission is parallel to the ground state absorption. The transmission change in dependence on the probe wavelength and the time delay between the pump and the probe pulses is shown in Fig. 11.5 for HBT [33]. Traces measured at probe wavelengths of 505 nm and 597 nm are depicted in Fig. 11.6(a). Figure 11.6(b) shows the time-dependent transmission change at 500 nm and 560 nm due to excitation of HBO at 340 nm in cyclohexane. The initial transmission decrease is caused by excited state absorption (ESA) which appears as soon as the molecule is promoted to the S1 state. The subse-
11.3 Spectral Signatures of Ultrafast ESIPT
Figure 11.5 Time-dependent transmission change for HBT dissolved in cyclohexane induced by optical excitation at 347 nm. The spectral evolution is reconstructed from time scans taken at various probe wavelengths.
Figure 11.6 (a) Time-dependent transmission change due to excitation of HBT at 347 nm probed at 505 nm and 597 nm. (b) Time-dependent transmission change in case of HBO excited at 340 nm and probed at 500 nm and 560 nm. The open circles are the data and the solid lines the fitted model functions. The insets show the Fourier transforms of the oscillatory signal components.
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quent positive transmission change is due to stimulated emission from the electronically excited keto-form, i.e. the product of the proton transfer [27]. In principle it can also result from the bleaching of ground state molecules. However, this possibility can be ruled out since ESIPT molecules in the electronic ground state absorb only in the UV and the positive transmission change is observed in the visible. The same holds for the oscillatory signal contributions which have to originate from the dynamics in the electronically excited state and are not due to ground state wavepackets. If the excitation and probe wavelengths are similar, ground state wavepackets prepared by impulsive stimulated Raman scattering contribute to the signal and usually mask oscillatory excited state contributions [34, 23]. In the case of ESIPT we can be sure that only dynamics in the electronically excited state contribute to the observed transmission changes, and this unambiguous assignment greatly simplifies the interpretation of the experiments. We obtained very similar experimental results for HBO [29], OHBA [35], and HAN [36] (see Fig. 11.6 and 11.7). They all exhibit a delayed transmission increase and pronounced oscillatory signal contributions with a couple of frequencies in the range up to 700 cm–1, as can be seen from the Fourier transforms of the oscillatory contributions depicted in Fig. 11.6 and 11.7 as insets. This observation was also made for a number of other ESIPT compounds [30–32].
Figure 11.7 (a) Transmission change at 500 nm and 560 nm in the case of HAN excited at 340 nm. (b) Transmission change measured at 500 nm and 630 nm in the case of OHBA excited at 340 nm.
11.3.2 Analysis
The analysis of the experimental results is performed by fitting a model function S(t) to the time traces of all applied probe wavelengths [33]. The function consists of a transmission decrease SESA ðtÞ at time zero due to ESA and a transmission increase SSE ðtÞ which rises step-like with a small delay and reflects the onset of
11.3 Spectral Signatures of Ultrafast ESIPT
the product emission. The total transient signal is convoluted with the Gaussian cross correlation CC(t). ( SðtÞ ¼ CCðtÞ
¼ CCðtÞ
SESA ðtÞ þ SSE ðtÞ þ 8 > < > :
X
AESA e
i
9 3 ttSE ðttSE Þ > = Afast e sfast þ Aslow e sslow SE SE 6 7 ðttSE Þ 5H ðt t HðtÞ þ 4 P Þ SE > þ Ai cosð2pmi t þ ui Þe si ; 2
s t slow
) SiOSC ðtÞ
i
The excited state absorption SESA ðtÞ sets in with a step at time zero modeled by the heavyside function HðtÞ and a negative valued amplitude AESA . The non-oscillating part of the stimulated emission SSE ðtÞ is delayed by tSE. It consists of a fast exponential component with amplitude Afast SE and a decay time sfast of about 250 fs and a slow component with amplitude Aslow SE and a decay time sslow . The fast contribution accounts for a red shift of the emission spectrum due to intramolecular vibrational redistribution and the slow one corresponds to the emission from the equilibrated keto-form in the electronically excited state [33]. The decay of the emission is due to the limited S1 lifetime, and therefore, the decay of the ESA is modeled with the same time constant sslow . The convolution with the cross correlation CC(t) can be expressed as a product with an appropriate error function. The oscillating signal contributions are modeled by damped cosine functions with frequencies mi , amplitudes Ai , phases ui and damping times si . Their emergence is delayed by the same amount tSE as the emission since they are attributed to the ESIPT product. With appropriately fitted parameters the model function can accurately reproduce the experimental data. This is illustrated by the fits shown in Fig. 11.6 and 11.7 as solid lines. The consistency of the parameters found is checked by their dependence on the probe wavelength [33]. In the following we concentrate on the delay of the emission rise and the oscillatory contributions. For HBT we find a delay of 33 fs in the blue wing and of 55 fs in the red wing of the emission spectrum [33]. In the case of HBO, OHBA and HAN the delay is determined to be 80 fs, 45 fs and 30 fs. The fitted frequencies of the oscillatory contributions match the Fourier transformations depicted in Fig. 11.6 and 11.7. Comprehensive listings of the fit results are given in Refs. [33, 35, 36]. 11.3.3 Ballistic Wavepacket Motion
As discussed above, a similar delay of the emission rise of about 50 fs is found for all investigated molecules. The wavelength dependence of the emission amplitude follows the cw emission spectrum [33] which is attributed to the keto-form, the product of the ESIPT. The transmission increase is therefore identified as the delayed rise of the emission from the keto-form. This assignment is also in agreement with recent fluorescent up-conversion experiments which measure the time
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evolution of the fluorescence [37]. The delay is the time passed until the molecule adopts the keto-form and represents the duration of the ESIPT. The observed delays are in agreement with the timescales determined in experiments on BBXHQ and MS even though these experiments assumed rate behavior for the ESIPT process [18, 31]. A second important observation is that the temporal shape of the emission rise follows a step function. This is demonstrated in Fig. 11.8. It shows the results of fitting an exponential increase convoluted with the crosscorrelation (a), a delayed step like rise convoluted with the crosscorrelation (b) and the complete model function (c) to an experimental trace of HBT at a probe wavelength of 564 nm where the oscillatory contributions are quite weak. The exponential increase and the delayed step function give almost the same ESIPT time [33]. However, the exponential increase deviates significantly from the data at short delay times whereas the step function matches quite accurately the essential shape of the trace. An exponential signal dependence is expected if the dynamics can be described as a rate governed population transfer between two states. This seems to be an inadequate model for the ESIPT. The step function on the other hand points to an almost classical ballistic motion along the potential energy surface (PES) [27]. The wavepacket prepared by the optical excitation moves completely to the product state without pronounced spreading or splitting. According to Ehrenfest’s theorem the center of gravity of the wavepacket then follows a classical trajectory along the PES. The population appears delayed but within a very short time interval in the product state. Such a ballistic wavepacket motion implies that the wavepacket stays confined during the process, in agreement with the observation of a coherent excitation of specific vibrations due to the ESIPT (see below). A ballistic wavepacket motion was experimentally demonstrated for the direct photoinduced dissociation of ICN [38] and iodobenzene [39]. Only recently, indications for a ballis-
Figure 11.8 Fits of different model functions to the time resolved transmission change of HBT at 564 nm. (a) Exponential rise, (b) delayed step, and (c) complete model function. All functions are convoluted with the cross correlation.
11.3 Spectral Signatures of Ultrafast ESIPT
tic behavior in a more complex situation were found in the case of the ring opening of 1,3-cyclohexadiene [40]. A ballistic wavepacket motion is incompatible with a tunneling process of the proton from the enol to the keto site. The transition probability of a single attempt is much smaller than 1 and many tunnel events are necessary for an efficient population transfer leading to a gradual population rise in the product state. However, if the proton itself would move from the enol to the keto site via a barrierless path, the ESIPT would take less than 10 fs because of the small proton mass [18]. This is a first indication that slower motions of the molecular skeleton are the speed determining factors and that the proton mode is not the relevant reaction coordinate [27]. 11.3.4 Coherently Excited Vibrations in Product Modes
The oscillatory signal contributions are due to vibrational wavepacket motions in the electronically excited product state and allow one to identify the participating modes. A vibrational wavepacket can be described as a phase coherent superposition of vibronic eigenstates belonging to the same electronic state. As long as wavepacket motion is observed the vibrational phase is still quite well defined. The electronic phase, i.e. the phase of the electronic wavefunction relative to other electronic states, is scrambled in solution within some 10 fs due to the interaction with the solvent [41], but this does not affect the wavepacket motion on a single PES. The vibrational wavepacket motion leads to a periodic variation of the optical transition energy and to an oscillatory spectral shift of the S1 emission and the transient Sn–S1 absorption spectra as depicted in Fig. 11.9. It causes the characteristic oscillation of the HBT emission spectrum shown in Fig. 11.5. The amplitude of the oscillatory signal contributions has a dependence on the probe wavelength which reflects directly the slope of the emission spectrum [31, 33]. The Fourier transforms as well as the fitting procedure reveal, depending on the molecule, two to four relevant frequencies below 700 cm–1 in the oscillatory signal contributions (see Fig. 11.6 and Fig. 11.7). The oscillations extend to some picoseconds. Obviously the vibrational dephasing occurs on a picosecond time scale
Figure 11.9 An oscillating wavepacket leads to periodic variation in the mean transition energy between two electronic states (a) and thereby to an oscillatory shift of the spectrum (b). The amplitude of the oscillating signal is proportional to the slope of the spectrum.
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although the wavepacket propagates on a reactive PES and the ESIPT molecule interacts with solvent molecules. Only modes with very low frequencies are damped within shorter times [33]. A faster damping for the coherently excited mode with the lowest frequency was also observed for 10-HBQ [32]. It was argued that this mode has a particularly large projection onto the reaction coordinate and exhibits therefore a larger anharmonicity, resulting in a faster spreading of the wavepacket along this coordinate. Preliminary experiments in our laboratory indicate that, contrary to intuition, the influence of the solvent on the damping time is very minor and the vibrational dephasing is an intrinsic property of the molecular PES. As argued above the observed frequencies are those of the vibrational eigenmodes of the electronically excited keto-form. To identify the coherently excited modes the frequencies are compared to steady state vibrational and Raman spectra as well as to results of ab initio calculations. The calculations are particularly helpful for the interpretation because they reveal not only the frequencies but also the nuclear movements and deformations of the molecule associated with a vibrational normal mode. Ab initio calculations of electronically excited states in molecules exhibiting reactive dynamics are very challenging. High level PESs for the complete ESIPT pathway from the Franck–Condon point to the keto minimum are up to now only available for HBT [7] and very few other compounds [42, 43]. It turns out that the frequencies of the skeletal modes vary only little from the electronically excited to the ground state. Therefore, we usually calculate the vibrational eigenmodes in the electronic ground state [35, 36] by means of density functional theory, as implemented in the Gaussian98 program package [44]. Figure 11.10 shows the calculated vibrational modes of HBT which appear in the transient absorption measurements [33]. The coherent excitation of the 113 cm–1 mode was also observed by time resolved vibrational spectroscopy [10]. In the frequency range up to 700 cm–1 several other eigenmodes exist but their
Figure 11.10 Coherently excited vibrational modes of HBT. mDFT are the frequencies calculated by density functional theory [7] and mPP the frequencies observed in pump–probe experiments [33].
11.3 Spectral Signatures of Ultrafast ESIPT
frequencies are not found in the experimental data and they obviously do not take part in the observed dynamics. The vibrational modes contributing to the wavepacket motion are in-plane deformations of the H-chelate ring [33]. They change strongly the distance between the proton donor and acceptor, in the case of HBT the oxygen and nitrogen atom. In addition, bond angles and lengths within the chelate ring are varied whereas moieties adjacent to the chelate ring are moved as a whole and are barely deformed. For the other molecules investigated we encounter a very similar situation [29, 35]. As a second example the coherently excited modes of HAN are shown in Fig. 11.11. The specific mechanisms responsible for the coherent excitation of vibrational modes can be determined from the phase of the signal oscillations. At the time a vibration starts, the molecule is at a turning point of its harmonic motion and the argument in the corresponding cosine function can be set to zero. According to this consideration the starting time of an oscillation can be calculated modulo half of a vibrational period from the fitting result of the phase. This analysis was performed in the case of HBT and is discussed in [33]. The three vibrations of higher frequency start at about 30 fs to 50 fs after the optical excitation when the product emission is observed for the first time. It can be concluded that these vibrational motions are excited by the electronic configuration change associated with the change from the enol to the keto-form. For the vibration with the lowest frequency (113 cm–1) the phase corresponds to a starting time shifted by a quarter of a vibrational period relative to the configuration change. Apparently, the molecule is initially accelerated along this coordinate. The mode is a bending motion of the entire molecule which reduces primarily the proton donor–acceptor distance and introduces only slight changes in other parameters (see Fig. 11.10). A coherent excitation of very similar vibrational modes was found in all ESIPT molecules we investigated and also in DHAQ [30], BBXHQ [31], and 10-HBQ [32]. In HBT and HBO this mode also modulates the
Figure 11.11 Coherently excited vibrational modes of HAN. The frequencies determined by ab initio calculations (mDFT) and found in resonance Raman spectra (mRaman) are compared to pump–probe measurements (mPP) [36].
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shape of the absorption spectrum which supports the conclusion that the initial motion after optical excitation has a large component along the in-plane bending coordinate of the entire molecular skeleton [17, 45]. For HBT and 10-HBQ it was found that the coherent oscillations in this mode show a faster damping than in higher frequency modes [32, 33]. It was argued that this is an indication for a pronounced anharmonicity reflecting again the intimate connection between this mode and the reaction coordinate [32].
11.4 Reaction Mechanism 11.4.1 Reduction of Donor–Acceptor Distance by Skeletal Motions
The observed proton transfer times of the order of 50 fs have already been discussed in earlier work with respect to the importance of skeletal vibrations [16–18, 46]. It was proposed that a reduction in the distance between the proton donor and the acceptor results in a decrease in the energetic barrier between the enoland the keto-form. At times when the barrier is suppressed the proton can tunnel or jump from its enol position to the keto site. In the case of HBO it was suggested that, in particular, the in-plane bending vibration modulates the donor– acceptor distance and thereby enables the proton movement [17]. This model was then applied to MS and to 2-(2¢-hydroxyphenyl)-5-phenyloxazole [18, 46]. However, due to insufficient time resolution of these experiments it was not possible to give experimental evidence for this model. Only when TINUVIN P was investigated with 25 fs laser pulses were oscillatory signal contributions detected [26]. They were attributed to coherently excited vibrations in two low frequency modes at 250 cm–1 and 470 cm–1. One is a translational motion of the triazole and the phenyl moieties against each other and the other a geared in-plane rotation of the two subunits. The authors interpreted the results in the framework of the model presented above, but attributed the modulation of the proton transfer barrier to a geared in-plane rotation. We and others found in many ESIPT molecules a strong coherent excitation of a skeletal in-plane bending mode and concluded that predominantly this motion results in the reduction of the donor–acceptor distance as it is discussed in Section 11.3.4. For TINUVIN P no direct evidence for the coherent excitation of the inplane bending mode was found [26]. However, in this case the short S1 lifetime of 150 fs does not allow the observation of oscillations with a period of about 300 fs which would result from the coherent excitation of the bending mode. Therefore it can be assumed that also in this case the in-plane bending motion of the molecular skeleton provides the primary contribution to the reduction of the donor– acceptor distance. In HBT, HBO, and TINUVIN P the skeletal stretch vibration is very strongly coherently excited [26, 27, 29] and contributes probably also quite strongly to the initial motion.
11.4 Reaction Mechanism
11.4.2 Multidimensional ESIPT Model
The irreversibility and efficiency of the ESIPT cannot be understood by a model consisting of only one low frequency mode and one high frequency proton mode. During every period of the low frequency vibration the ON-separation adopts a suitable distance where the energy barrier is suppressed and a back transfer of the proton should be possible. As discussed in Section 11.4.3 this inconsistency can be resolved by assuming that several low frequency modes are directly involved in the ESIPT. Our investigations lead to a multidimensional model of the ESIPT which can provide a comprehensive understanding of the experimental findings presented above [28, 29, 33]. The proposed evolution of the reaction is sketched in Fig. 11.12. The ballistic wavepacket motion demonstrates that no tunneling is involved and no significant energy barrier is encountered along the reaction path [27]. After optical excitation the molecule accelerates out of the Franck–Condon region, predominantly along the vibrational coordinate which causes an in-plane bending of the entire molecular skeleton and reduces the proton donor–acceptor distance. When it is shortened by a sufficient amount an electronic configuration change from the enol to the keto configuration takes place. The configuration change manifests itself in an occupation redistribution of the molecular orbitals and results in the breakage of the OH bond and the formation of the hydrogen acceptor bond and also in the shift of the double bonds in the chelate ring. Due to the small mass of the electrons, the configuration change itself can be regarded as instantaneous on the time scale of nuclear motions. In HBT it happens 30 to 50 fs after the excitation into the S1 state [27, 33]. Time-resolved IR experiments found the emergence of the C=O stretching vibration exactly on this time scale [10]
Figure 11.12 ESIPT model: directly after the optical excitation the H-chelate ring contracts and the donor–acceptor distance is reduced. Then an electronic configuration change (electronic switching) occurs and the keto bonds are formed. Subsequently, the molecule is accelerated towards the keto minimum and starts to oscillate around the equilibrium geometry in coherently excited modes.
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strongly supporting this interpretation. The new bonds are associated with a changed equilibrium geometry corresponding to the product minimum of the PES. At this moment the skeleton of the molecule has not yet adopted the new equilibrium geometry and is displaced from the product minimum (see righthand panel of Fig. 11.12). It accelerates towards this minimum and vibrational modes are coherently excited which reflect these changes in geometry. The phases of the coherently excited vibrations indicate that in this stage of the process the higher frequency skeletal modes are more involved than in the initial motion [33]. In previous models the proton position was treated as the key parameter. However, we find that the role of the proton is a very passive one [29, 33]. During the initial motion the proton is shifted by the movement of the oxygen towards the acceptor atom. Then the electronic configuration change breaks the bond between the proton and the donor and forms a new bond to the acceptor. During the subsequent wavepacket motion and the associated geometrical changes the proton is already fixed to the acceptor atom. At any time the proton is at its local potential minimum and is shifted in an adiabatic fashion from the enol to the keto site [27]. Several findings support this point of view: If the ESIPT is mainly the direct motion of the proton from the donor site to the acceptor site then it should be much faster because of the small proton mass [18] or must be hindered by a barrier. Tunnelling through the barrier as well as thermally activated crossing over the barrier should not lead to a ballistic wavepacket motion of the whole system as is observed (see Section 11.3.3). Furthermore, if the proton does not stay in its local minimum an excitation of its local vibrational mode should occur. However, high frequency vibrational modes associated with the N–H and C=O bond of the keto-form are not excited, as was experimentally demonstrated for HBT by timeresolved IR experiments [47]. This is in agreement with the following energy considerations [33]: Overall, the proton transfer releases only an energy of about 2500 cm–1. However, a couple of coherently excited skeletal modes is observed. Since all these modes must contain a few vibrational quanta after the transfer there is not enough energy left to significantly excite a high frequency mode. Recent picosecond time-resolved resonance Raman experiments were able to verify this consideration in the case of HBO [48]. After the ESIPT, anti-Stokes signals were found for several vibrational modes below 1000 cm–1 whereas high-frequency modes did not show indications for a vibrational excitation. It should be possible to prove the passive role of the proton with experiments on deuterated compounds. As soon as the motion or tunneling of the proton governs the transfer time a drastic increase in this time due to deuteration is expected. However, no variation of the ESIPT dynamics with deuteration has been observed so far [18, 19, 49, 50] although the precision of those experiments might not have been sufficient for a final decision. The passive role of the proton is further supported by resonance Raman experiments on HAN and 2-hydroxy-acetophenone in which no resonance enhancement for the OH stretching vibration was found [36, 51, 52]. In ab initio calculations a transition state for the proton transfer was found which is indeed characterized by a reduced donor–acceptor distance [53] and it was concluded that a strong coupling to the skeletal in-plane bending mode exists
11.4 Reaction Mechanism
[54, 55]. Recently, the S1-PES of HBT was characterized by extensive ab initio calculations [7]. The complete minimum energy path from the Franck–Condon point to the keto S1 minimum was calculated. It was found that first the oxygen nitrogen distance is reduced, then an electronic configuration change takes place, and subsequently the molecular skeleton relaxes to the equilibrium geometry of the keto-form. The analysis of the path in terms of normal modes reproduced the coherent excitation of exactly those modes which have been found in the experiment. Whether there is an energy barrier along the reaction path or not is difficult to decide on the basis of ab initio calculations. With increasing quality of the applied method almost vanishing barriers were calculated for HBT and OHBA [43]. The reason for the sensitivity to the method is that two electronic configurations determine the shape of the PES and electronic correlation effects have to be handled very accurately [42, 56]. In the case of HBT and HBO the proton acceptor is a nitrogen atom whereas in the case of OHBA and HAN it is a second oxygen atom. For the latter two the chelate ring is fairly symmetric. The degree of symmetry is much less for HBT and HBO. Nevertheless very similar evolutions of the ESIPT are found [28, 29, 36]. Thus the degree of symmetry seems not to be important for the mechanism. Likewise, the ESIPT is insensitive to subtleties of the energetics and the electronic wavefunction. The dynamics of the process is rather determined by motions of the nuclei along in-plane skeletal coordinates. Due to the insensitivity of the ESIPT to details of the reaction center we conclude that the proposed mechanism should be quite general for compounds exhibiting an ultrafast ESIPT within a H-chelate ring. And indeed, the experimental results on DHAQ [30], BBXHQ [31], and 10-HBQ [32] are in agreement with the model. 11.4.3 Micro-irreversibility
The multidimensional character of the process, i.e. the significant participation of several nuclear coordinates is also responsible for its irreversibility [28, 29]. For a reversal of the reaction a full recurrence in all coordinates would be necessary (see Fig. 11.13).
Figure 11.13 (a) In a one-dimensional system the proton transfer would be fully reversible as long as dissipation can be neglected. (b) In a multidimensional situation the wavepacket can not directly return to its origin because a simultaneous recurrence in all involved coordinates is necessary.
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This would need much longer than the period of a representative vibration. On this strongly extended time scale the energy flow into other degrees of freedom becomes significant and inhibits the back reaction. This leads to irreversibility, even though the coherence and the energy are lost within a duration many times longer than the actual ESIPT. Out-of-plane twisting vibrations might play a role as energy accepting modes. The coherent excitation of the twisting mode with the lowest frequency (about 60 cm–1) was recently observed in HBT [10] and in o-hydroxyacetophenone [57] and points to such vibrational redistribution processes. The example of ESIPT shows that vibrational coherences can exist for picoseconds, even in the situation of reactive dynamics. Therefore we think that the multidimensional character of ultrafast reactions is a prerequisite for their irreversibility. 11.4.4 Topology of the PES and Turns in the Reaction Path
After the electronic configuration change the donor–acceptor distance increases again to adopt the equilibrium geometry of the keto-form resulting in a turn in the reaction path. This is indicated in Fig. 11.14 as an ellipse on top of the reaction path at the transition from the enol to the keto dominated region of the S1 PES. The path thereby evades an energy barrier which separates the Franck–Condon region from the keto minimum, and which inhibits the direct transfer or jump of the proton to the keto site. This topology of the PES is in good agreement with previous suggestions for the case of TINUVIN P [26, 58] and was also found by the ab initio calculations of the ESIPT in HBT [7].
Figure 11.14 Sketch of the S1 PES and the proton transfer path. The reaction path from the Franck–Condon point (FC-point) to the keto-minimum exhibits two turns (ellipses). The slope at the Franck–Condon point is directed towards the equilibrium geometry of the enol configuration (enol-equilib.).
11.4 Reaction Mechanism
At the Franck–Condon point, the separation between the donor and acceptor is large, preventing a mixing between the enol and the keto configuration. The PES in this region is of almost pure enol character, resulting in the barrier for the OHstretch motion. Accordingly, Raman experiments did not find a resonance amplification for the OH-stretch vibration [36, 51, 52]. However, resonance Raman spectra of ESIPT compounds indicate that an additional bend in the reaction path exists directly after the Franck–Condon region. The resonance Raman cross section is large for coordinates with a strong slope of the potential energy at the Franck–Condon point and reveals the initial acceleration of a wavepacket launched by the optical excitation [59]. The intensity distributions in the resonance Raman spectra of HBT [60, 61] are different from the relative vibrational amplitudes in the time traces [33]. The slope at the Franck–Condon point does not reflect the excitation of the modes found after the proton transfer, and the major contributions to their excitation seems to occur after the wavepacket has left the Franck–Condon region. To clarify this point we investigated HAN with resonance Raman and transient absorption spectroscopy [36]. After the proton transfer a strong coherent excitation was found for the bending mode at 312 cm–1 and weaker excitation of the modes at 280 cm–1 and 368 cm–1 (see Fig. 11.7(a)). However, in the low frequency range of the resonance Raman spectrum a mode at 603 cm–1 gives the strongest signal which is completely absent in the timeresolved absorption data. Figure 11.11 shows that modes at 312 cm–1 and 368 cm–1 are dominated by in-plane deformations of the H-chelate ring, while the mode at 603 cm–1 is associated with a strong deformation of the naphthalene chromophore. The resonance Raman spectrum of HAN also exhibits strong lines in the spectral region of CC-stretch vibrations which indicates that the optical transition changes the electron density along the system of conjugated bonds [52]. Because of the limited amount of energy released by the proton transfer it can be excluded that these modes are significantly excited by the transfer. For HBO, time-resolved Raman experiments found that high frequency modes are indeed not excited after the ESIPT [48]. These observations show that the slope of the PES at the Franck– Condon point has projections on several coordinates which contribute negligibly to the transfer path. The slope points from the Franck–Condon point to the equilibrium geometry of the electronically excited enol-form (see Fig. 11.14). This direction reflects the geometric relaxation of the electronically excited chromophore and of the p-bonds. However, as soon as the launched wavepacket leaves the Franck–Condon region, the interaction with the keto configuration gains importance and the direction of the slope changes towards the reduction of the donor–acceptor distance. In conclusion, the resonance Raman spectrum provides evidence that the reaction path makes a first bend shortly after the Franck–Condon point. These considerations show also that the vibrations are dominantly excited by the reactive dynamics itself and the optical transition contributes only little. This is in agreement with the analysis of the vibrational phases. There it was found that in some of the modes the molecule starts to oscillate with a significant delay, which is not expected for a pure optical excitation [33].
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11.4.5 Comparison with Ground State Hydrogen Transfer Dynamics
Proton transfer in the electronic ground state is responsible for various phenomena in chemistry like e.g. the acidity of substances. The relative concentrations of involved molecules are given by the free enthalpies if a stationary equilibrium is established. However, dynamic aspects and reaction rates depend on the actual evolution of the transfer. Since proton transfer in the electronically excited state takes place on an adiabatic PES some of the conclusions can be transferred to ground state reactions. They also proceed on an adiabatic surface, the ground state PES, to which several electronic configurations associated with the different molecular arrangements and bond configurations contribute. Our results on ESIPT show that the transfer itself is governed by skeletal vibrational motions and the exchange of the proton represents an electronic configuration change occurring at specific deformations of the involved molecules. Therefore, the transfer rates in the electronic ground state should also be strongly affected by skeletal vibrations of the participating molecules. Consequently, recent theoretical work treating the proton dynamics focuses on the influence of skeletal vibrational coordinates and on solvent configurations [62–64]. The same holds for photoinduced intermolecular proton transfer between donor molecules and surrounding solvent molecules where several studies include low frequency coordinates in the description of the intermolecular transfer process [65, 66]. There are even deeper parallels. A comparison of hydrogen bonded systems with differing bond strength revealed the following correlation [67, 68]. With increasing hydrogen bond strength, the separation between the hydrogen atom and the donor atom increases. This increase is strictly related to a shortening of the donor–acceptor distance. The systems with the shortest donor–acceptor distances are always those in which the hydrogen atom is just in the middle between the donor and the acceptor atom. Shifting the hydrogen atom even more towards the acceptor just exchanges the role of donor and acceptor and their separation increases again. For hydrogen bonded systems, the dependence of the separation between hydrogen and donor atom on the donor–acceptor distance is sampled by different compounds. In the case of ESIPT a very similar correlation is fulfilled during the course of the reaction. The ESIPT path in the space spanned by the donor–acceptor distance and the hydrogen position resembles the correlation diagrams found in hydrogen bonded systems for these two quantities. 11.4.6 Internal Conversion
Most compounds exhibiting ESIPT experience subsequently a rather fast IC (see Section 11.1), which brings the molecule back to the electronic ground state. As discussed above, the ESIPT proceeds in all these molecules in a very similar manner. On the contrary, the time-resolved absorption measurements reveal that the lifetime of the first electronically excited state depends strongly on the molecule.
11.4 Reaction Mechanism
In solution it varies by three orders of magnitude from 300 ps in the case of HBT [16] down to 150 fs for TINUVIN P [11]. For OHBA we found that the S1 lifetime after excitation at 340 nm is 55 ps when the molecule is dissolved in cyclohexane, while in the gas phase the lifetime is 13 times shorter [19, 35]. The S1 lifetime exhibits a strong dependence on the excess energy which obeys an Arrhenius law with an energy barrier of about 200 meV. This points to a statistical behavior and one can apply the concept of an internal molecular temperature [35, 69]. The IC of OHBA is not sensitive on deuteration, indicating that the proton plays no important role in the IC process [19]. After the ESIPT, the dominant portion of the excess energy is stored in the vibrational modes, reflecting the geometry change between the enol and the keto-form (see above). If the IC were sensitive to the amount of vibrational energy in these modes it would be quite fast in the first few picoseconds and then it would slow down when vibrational redistribution leads to an energy flow into other modes. Since the IC does not show any indications of such behavior, we conclude that the significant coordinates for both processes are orthogonal to each other [35]. In this case the IC cannot directly profit from the energy content in the modes participating in the ESIPT and a vibrational redistribution is necessary, leading to a statistical energy distribution and behavior. A realistic model for the IC process must be able to explain the energy barrier, the statistical behavior, the efficiency and the variation with the molecule. Ab initio calculations on malonaldehyde indicate that a pr* state interacts with the S1 state, which has pp* character, resulting in an avoided crossing and an energy barrier [70]. With increasing deformation along the promoting coordinate, the pr* state also crosses the electronic ground state. A conical intersection is formed by the two PESs allowing a very fast and efficient transition to the ground state. A particularly attractive aspect of this model is that the barrier results from an avoided crossing between two electronically excited states. The barrier height depends sensitively on the relative energetic location of the two states, and slight variations in the energetics enter via the barrier height exponentially in the S1 lifetime. This would nicely explain why the lifetime varies that strongly with the molecule [28]. However, the suggested promoting coordinate is associated with a hydrogen detachment from the H-chelate ring [70]. In this case the process should be sensitive to deuteration, in contradiction to the experimental findings. Therefore we think that skeletal vibrations are responsible for the coupling between the electronic states [28]. By means of calculations it is also discussed that a torsion around the central carbon bond might be responsible for the IC. In the case of 2-(2¢-hydroxyphenyl)triazole a conical intersection between the electronically excited state and the ground state was calculated for a twist angle of nearly 90 [71]. However, the S1 lifetime of 10-HBQ, which cannot perform twisting motions due to its rigid geometry, is 260 ps [32] indicating that other modes are involved in the IC. At the moment, what are the important coordinates for the IC and whether a common mechanism for all ESIPT molecules exists are completely open questions.
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11.5 Reaction Path Specific Wavepacket Dynamics in Double Proton Transfer Molecules
For systems with parallel and branching reaction channels the question arises if, even in this situation, coherent wavepacket dynamics can be observed and, if so, can it be used to characterize the different channels and get an improved understanding of the mechanisms. A promising system to answer these questions is [2,2¢-bipyridyl]-3,3¢-diol (BP(OH)2) which contains two H-chelate rings (see Fig. 11.15). In aprotic solvents it exhibits both single and concerted double intramolecular proton transfer after it is promoted to the electronically excited state. Glasbeek and coworkers found that the single proton transfer occurs within less than 100 fs and leads to an intermediate mono-keto isomer which subsequently transforms with a time constant of 10 ps to the final di-keto-form [72, 73]. In addition, a second reaction channel exists which leads to the final di-keto product within less than 100 fs by a simultaneous transfer of both protons. The branching ratio between both channels varies strongly with the excess energy [72, 73]. We performed time-resolved absorption studies on BP(OH)2 solvated in cyclohexane applying various excitation and probe wavelengths. The time resolution of 30 fs allows one to observe both transfer processes and the associated coherent wavepacket dynamics in real time [50]. Figure 11.15 shows the time-resolved transmission change of BP(OH)2 in cyclohexane excited at 350 nm and probed at 480 nm. It exhibits pronounced oscillatory signal contributions typical for the ESIPT process. The two most dominant contributions at 196 cm–1 and 295 cm–1 (see inset of Fig. 11.15) are identified by comparison with ab initio calculations. The mode at 196 cm–1 is an antisymmetric in-plane bending vibration and is attributed to the single proton transfer. The mode at 295 cm–1 is a symmetric stretch vibration and participates in the double proton transfer. If BP(OH)2 is excited at 375 nm the oscillatory contributions at 196 cm–1 are strongly suppressed and much weaker than those at 295 cm–1. Since the mono-keto yield at 350 nm is 30% and only 16% at 375 nm [73] this observation confirms our assignment of the two modes to the two different reaction channels. The coherent excitation of the vibra-
Figure 11.15 Transmission change after optical excitation of BP(OH)2 at 350 nm probed at 480 nm. The Fourier transformation (inset) shows that two modes are dominating the oscillatory signal contributions.
11.5 Reaction Path Specific Wavepacket Dynamics in Double Proton Transfer Molecules
Figure 11.16 Reaction scheme and coherently excited vibrations in BP(OH)2. For the concerted double proton transfer both donor–acceptor distances have to be reduced simultaneously, leading to a symmetric contraction of the molecule and to the coherent excitation of the symmetric stretch vibration. For the single proton transfer the donor–acceptor distance in only one of the two H-chelate rings is compressed by an antisymmetric bending motion.
tional modes can be understood in the following way (see Fig. 11.16) [50]: In the case of the concerted double proton transfer the donor–acceptor distances in both H-chelate rings have to be reduced simultaneously by a symmetric contraction of the molecule. This results in the coherent excitation of the symmetric stretch vibration. For the single proton transfer the donor–acceptor distance in only one of the two H-chelate rings has to be compressed. This is most efficiently accomplished by an antisymmetric bending motion. The example demonstrates that different reaction channels result in different coherent wavepacket dynamics and these wavepacket motions can be distinguished from each other by measurements with different excitation wavelengths. Thereby the mechanisms responsible for both reaction channels can be uncovered. BP(OH)2 exhibits inversion symmetry. Because of the selection rules for electronic dipole transitions, the symmetric vibrational modes show up in the Raman spectrum and the antisymmetric modes in the infrared absorption spectrum [74]. The wavepacket motion in the antisymmetric bending vibration observed in the time-resolved experiments cannot be directly excited by the optical excitation. Therefore it has to be excited by the symmetry breaking single proton transfer itself. This shows unambiguously that the coherent wavepacket motion results from the ultrafast ESIPT and the associated electronic configuration change and does not reflect the direct optical excitation of the contributing vibronic levels. It answers positively the long-standing question whether a coherent wavepacket motion can be induced by an ultrafast reaction.
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11 Direct Observation of Nuclear Motion during Ultrafast Intramolecular Proton Transfer
11.6 Conclusions
Transient absorption experiments with a time resolution sufficient to resolve the motion of nuclei showed that the ultrafast ESIPT proceeds as a ballistic nuclear wavepacket motion. The wavepacket stays confined during the whole process and moves from the Franck–Condon region to the product minimum within about 50 fs. This time is given by the inertia of the involved nuclei. The subsequent ringing of the molecule in specific modes reflects the structural changes during the reaction. These signatures have been observed for a large number of ESIPT compounds and provide strong evidence for a common mechanism. In the Franck–Condon region the initial slope of the PES corresponds to a relaxation of the chromophore. However, the further evolution is dominated by an in-plane bending motion of the molecular skeleton, resulting in a reduction in the donor–acceptor distance. An electronic configuration change occurs when this distance is sufficiently shortened. Thereby the bonds are altered from the enol to the keto configuration. Then the donor–acceptor distance increases again and the molecular geometry relaxes along several skeletal modes towards the keto minimum of the S1 state. The proton itself stays at its local potential minimum and is passively shifted from the enol to the keto site by the skeletal motions during the transfer. This model accounts for the observation of a ballistic wavepacket motion, the coherent excitation of skeletal in-plane vibrations and the lack of excitation in high frequency modes. The topology of the S1 PES can be understood in terms of an enol / keto configuration mixing which is extremely sensitive to the donor– acceptor distance resulting in a high barrier for the OH stretch motion at the ground state equilibrium distance. Besides the electronic degrees of freedom several vibrational modes contribute and the essential features of the dynamics can only be understood by a multidimensional model. The multidimensional character causes an irreversible course of the ESIPT even though the transfer itself takes only 50 fs and vibrational dephasing occurs on a picosecond time scale. Nevertheless, most of the energetically accessible vibrations do not play a significant role and a realistic description of the ESIPT has to consider only a restricted number of vibrational degrees of freedom. As discussed in Ref. [22] we think that these are general features for many ultrafast molecular processes. The observation of vibrational wavepacket dynamics in a number of systems [6, 75, 76], which exhibit other ultrafast processes, supports this conclusion. A comparison between ESIPT and ground state hydrogen dynamics can be drawn in two ways. It can be concluded that the kinetics of ground state reactions are determined by skeletal modes and intermolecular motions which modulate the proton transfer barrier in such a way that at certain configurations it almost disappears. Second, the correlation found between the strength of a hydrogen bond and the donor–acceptor distance exhibits a very similar topology to the S1 PESs of ESIPT compounds and reflects the importance of configuration mixing.
References
In the case of intramolecular double proton transfer a wavepacket motion is found which depends, via the excess energy, on the branching ratio between concerted double and single proton transfer. It demonstrates that the coherent wavepacket dynamics in ESIPT molecules is driven by the ESIPT itself and is specific for the reaction path.
Acknowledgement
We thank Regina de Vivie-Riedle, Kai Stock, and Alexander Wurzer for most valuable contributions and acknowledge gratefully the financial support of the German Science Foundation. References 1 H.-H. Limbach, J. Manz (Eds.), special
issue on Hydrogen Transfer: Experiment and Theory, Ber. Bunsen-Ges. Phys. Chem., 1998, 102, 289–592. 2 A. J. Barnes, H.-H. Limbach (Eds.), special issue Horizons in Hydrogen Bond Research 2003, J. Mol. Struct. 2004, 700, 1–254. 3 T. Bountis (Ed.), Proton Transfer in Hydrogen-Bonded Systems, Plenum Press, New York, 1992. 4 U. Haupts, J. Tittor, D. Oesterhelt, Annu. Rev. Biophys. Biomol. Struct. 1999, 28, 367–399. 5 P. F. Barbara, H. P. Trommsdorff (Eds.), special issue on Spectroscopy and Dynamics of Elementary Proton Transfer in Polyatomic Systems, Chem. Phys. 1989, 136, 153–360. 6 A. H. Zewail, J. Phys. Chem. A 2000, 104, 5660–5694. 7 R. de Vivie-Riedle, V. De Waele, L. Kurtz, E. Riedle, J. Phys. Chem. A 2003, 107, 10591–10599. 8 A. Weller, Z. Elecktrochem. 1956, 60, 1144–1147. 9 T. Elsaesser, W. Kaiser, Chem. Phys. Lett. 1986, 128, 231–237. 10 M. Rini, A. Kummrow, J. Dreyer, E. T. J. Nibbering, T. Elsaesser, Faraday Discuss. 2002, 122, 27–40. 11 C. Chudoba, S. Lutgen, T. Jentzsch, E. Riedle, M. Woerner, T. Elsaesser, Chem. Phys. Lett. 1995, 240, 35–41.
12 A. L. Huston, G. W. Scott, A. Gupta,
J. Chem. Phys. 1982, 76, 4978–4985. 13 M. Mosquera, J. C. Penedo, M. C. Ros
Rodrguez, F. Rodrguez-Prieto, J. Phys. Chem. 1996, 100, 5398–5407. 14 J. A. Organero, I. Garca-Ochoa, M. Moreno, J. M. Lluch, L. Santos, A. Douhal, Chem. Phys. Lett. 328 (2000) 83–89. 15 O. K. Abou-Zied, R. Jimenez, E. H. Z. Thompson, D. P. Millar, F. E. Romesberg, J. Phys. Chem. A 2002, 106, 3665–3672 16 F. Laermer, T. Elsaesser, W. Kaiser, Chem. Phys. Lett. 1988, 148, 119–124. 17 T. Arthen-Engeland, T. Bultmann, N. P. Ernsting, M. A. Rodriguez, W. Thiel, Chem. Phys. 1992, 163, 43–53. 18 J. L. Herek, S. Pedersen, L. Baares, A. H. Zewail, J. Chem. Phys. 1992, 97, 9046–9061. 19 S. Lochbrunner, T. Schultz, M. Schmitt, J. P. Shaffer, M. Z. Zgierski, A. Stolow, J. Chem. Phys. 2001, 114, 2519–2522 20 P. F. Barbara, P. K. Walsh, L. E. Brus, J. Phys. Chem. 1989, 93, 29–34. 21 E. Riedle, M. Beutter, S. Lochbrunner, J. Piel, S. Schenkl, S. Sprlein, W. Zinth, Appl. Phys. B 71 (2000) 457–465. 22 A. J. Wurzer, S. Lochbrunner, E. Riedle, Appl. Phys. B 2000, 71, 405–409. 23 G. Cerullo, G. Lanzani, M. Muccini, C. Taliani, S. De Silvestri, Phys. Rev. Lett. 1999, 83, 231–234.
373
374
11 Direct Observation of Nuclear Motion during Ultrafast Intramolecular Proton Transfer 24 S. Adachi, V. M. Kobryanskii,
47 M. Rini, A. Kummrow, J. Dreyer,
T. Kobayashi, Phys. Rev. Lett. 2002, 89, 027401. 25 M. Lorenc, M. Ziolek, R. Naskrecki, J. Karolczak, J. Kubicki, A. Maciejewski, Appl. Phys. B 2002, 4, 19–27. 26 C. Chudoba, E. Riedle, M. Pfeiffer, T. Elsaesser, Chem. Phys. Lett. 1996, 263, 622–628. 27 S. Lochbrunner, A. J. Wurzer, E. Riedle, J. Chem. Phys. 2000, 112, 10699–10702. 28 S. Lochbrunner, E. Riedle, Recent Res. Devel. Chem. Phys. 2003, 4, 31–61. 29 S. Lochbrunner, K. Stock, E. Riedle, J. Mol. Struct. 2004, 700, 13–18. 30 J. Jethwa, D. Ouw, K. Winkler, N. Hartmann, P. Vhringer, Z. Phys. Chem. 2000, 214, 1367–1381. 31 N. P. Ernsting, S. A. Kovalenko, T. Senyushkina, J. Saam, V. Farztdinov, J. Phys. Chem. A 2001, 105, 3443–3453. 32 S. Takeuchi, T. Tahara, J. Phys. Chem. A 2005, 109, 10199–10207. 33 S. Lochbrunner, A. J. Wurzer, E. Riedle, J. Phys. Chem. A 2003, 107, 10580– 10590. 34 S. L. Dexheimer, Q. Wang, L. A. Peteanu, W. T. Pollard, R. A. Mathies, C. V. Shank, Chem. Phys. Lett. 1992, 188, 61–66. 35 K. Stock, T. Bizjak, S. Lochbrunner, Chem. Phys. Lett. 2002, 354, 409–416. 36 S. Lochbrunner, A. Szeghalmi, K. Stock, M. Schmitt, J. Chem. Phys. 2005, 122, Art. No. 244315-1–244315-9. 37 M. Sanz, A. Douhal, Chem. Phys. Lett. 2005, 401, 435–439. 38 M. J. Rosker, M. Dantus, A. H. Zewail, Science 1988, 241, 1200–1202. 39 P. Y. Cheng, D. Zhong, A. H. Zewail, Chem. Phys. Lett. 1995, 237, 399–405. 40 W. Fuß, W. E. Schmid, S. A. Trushin, J. Chem. Phys. 2000, 112, 8347–8362. 41 C. J. Bardeen, C. V. Shank, Chem. Phys. Lett. 1994, 226, 310–316. 42 A. L. Sobolewski, W. Domcke, Phys. Chem. Chem. Phys. 1999, 1, 3065–3072. 43 A. J. A. Aquino, H. Lischka, C. Httig, J. Phys. Chem. A 2005, 109, 3201–3208 44 M. J. Frisch et al., Gaussian 98, Revision A.7. 45 M. Wiechmann, H. Port, J. Lumin. 1991, 48 & 49, 217–223 46 A. Douhal, F. Lahmani, A. H. Zewail, Chem. Phys. 1996, 207, 477–498
E. T. J. Nibbering, T. Elsaesser, Chem. Phys. Lett. 2003, 374, 13–19 48 V. Kozich, J. Dreyer, A. Vodchits, W. Werncke, Chem. Phys. Lett. 2005, 415, 121–125. 49 W. Frey, F. Laermer, T. Elsaesser, J. Phys. Chem. 1991, 95, 10391–10395. 50 S. Lochbrunner, K. Stock, C. Schriever, E. Riedle, in Ultrafast Phenomena XIV, T. Kobayashi, T. Okada, T. Kobayashi, K. Nelson, S. De Silvestri (Eds.,) Springer-Verlag, Berlin, 2005, pp. 491– 495. 51 L. A. Peteanu, R. A. Mathies, J. Phys. Chem. 1992, 96, 6910–6916. 52 A. V. Szeghalmi, V. Engel, M. Z. Zgierski, J. Popp, M. Schmitt, J. Raman Spectrosc. 2006, 37, 148–160. 53 M. A. Rios, M. C. Rios, J. Phys. Chem. 1995, 99, 12456–12460. 54 M. A. Rios, M. C. Rios, J. Phys. Chem. A 1998, 102, 1560–1567. 55 V. Gualler, V. S. Batista, W. H. Miller, J. Chem. Phys. 2000, 113, 9510–9522. 56 S. Scheiner, J. Phys. Chem. A 2000, 104, 5898–5909. 57 C. Su, J.-Y. Lin, R.-M. R. Hsieh, P.Y. Cheng, J. Phys. Chem. A 2002, 106, 11997-12001. 58 M. Pfeiffer, A. Lau, K. Lenz, T. Elsaesser, Chem. Phys. Lett. 1997, 268, 258-264. 59 E. J. Heller, R. L. Sundberg, D. Tannor, J. Phys. Chem. 1982, 86, 1822-1833. 60 M. Pfeiffer, K. Lenz, A. Lau, T. Elsaesser, J. Raman Spectrosc. 1995, 26, 607–615. 61 M. Pfeiffer, K. Lenz, A. Lau, T. Elsaesser, T. Steinke, J. Raman Spectrosc. 1997, 28, 61–72. 62 K. Ando, J. T. Hynes, J. Phys. Chem. B 1997, 101, 10464–10478. 63 O. Khn, J. Phys. Chem. A 2002, 106, 7671–7679. 64 P. M. Kiefer, J. T. Hynes, J. Phys. Chem. A 2003, 107, 9022–9039. 65 D. Borgis, J. T. Hynes, J. Phys. Chem. 1996, 100, 1118–1128. 66 R. I. Cukier, J. J. Zhu, J. Chem. Phys. 1999, 110, 9587–9597. 67 H. Benedict, H.-H. Limbach, M. Wehlan, W.-P. Fehlhammer, N. S. Golubev, R. Janoschek, J. Am. Chem. Soc. 1998, 129, 2949–2950.
References 68 P. M. Tolstoy, S. N. Smirnov,
69
70 71
72
I. G. Shenderovich, N. S. Golubev, G. S. Denisov, H.-H. Limbach, J. Mol. Struct. 2004, 700, 19–27 F. Emmerling, M. Lettenberger, A. Laubereau, J. Phys. Chem. 1996, 100, 19251–19256. A. L. Sobolewski, W. Domcke, J. Phys. Chem. A 1999, 103, 4494–4504 M. J. Paterson, M. A. Robb, L. Blancafort, A. D. DeBellis, J. Am Chem. Soc. 2004, 126, 2012–2922. H. Zhang, P. van der Meulen, M. Glasbeek, Chem. Phys. Lett. 1996, 253, 97–102.
73 D. Marks, P. Prosposito, H. Zhang,
M. Glasbeek, Chem. Phys. Lett. 1998, 289, 535–540. 74 P. Borowicz, O. Faurskov-Nielsen, D. H. Christensen, L. Adamowicz, A. Les, J. Waluk, Spectrochim. Acta A 1998, 54, 1291–1305. 75 A. J. Wurzer, T. Wilhelm, J. Piel, E. Riedle, Chem. Phys. Lett. 1999, 299, 296–302. 76 V. De Waele, M. Beutter, U. Schmidhammer, E. Riedle, J. Daub, Chem. Phys. Lett. 2004, 390, 328–334.
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12 Solvent Assisted Photoacidity Dina Pines and Ehud Pines
12.1 Introduction
Proton transfer [1–33] and electron transfer [33–38] are among the most common classes of chemical reactions in nature. Similar to electron transfer, the main outcome of a proton transfer reaction is the net transfer of a charge. However, unlike electron transfer, proton transfer reactions involving large organic molecules are usually localized between two donor and acceptor atoms. Proton transfer reactions are inherently reversible in the ground electronic state of the proton donor and proton acceptor molecules. The inherent reversibility of the proton transfer reaction is usually maintained in the electronic excited-state of photoacids and photobases in aqueous solutions. Most proton transfer reactions involve relatively small changes in the backbone structure of the proton donor and proton acceptor molecules. These ensuing changes fully reverse upon back-transfer of a proton, either by the back-recombination of the dissociated (geminate) proton or following recombination with a proton coming from the bulk solution [39–62]. Proton transfer is very sensitive to the environment, which usually affects both the yield and the rate of the proton transfer reaction. Aqueous solutions are the most common environment accommodating proton transfer reactions due to the high dielectric constant and extensive hydrogen-bond interactions of the aqueous medium which act both to stabilize charged products and to establish the reaction coordinate along which the proton is transferred. Following the pioneering work of Brønsted and Lowry it has been customary to define proton donors as Brønsted acids and proton acceptors as Brønsted bases [1, 2]: AH (acid) + B (base) . A– (conjugated base) + BH+ (conjugated acid)
(12.1)
where the acid and base molecules prior to proton transfer may either be charged or neutral species. The pKa and pKb scales in aqueous solutions (B=H2O, BH+”H+ in Eq. (1)) serve to define the extent of acidity and basicity of the proton donor and the proton acceptor, respectively, Eqs. (12.2) and (12.3). Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
378
12 Solvent Assisted Photoacidity
Ka = [A–][H+]/[AH]
(12.2)
Kb = [AH][OH–]/[A–]
(12.3)
with KaKb = Kw, Kw = [H+][OH–] = 10–14 at room temperature. The self-concentration of water [H2O] = 55.3 M at room temperature is usually included in the respective equilibrium constants.
12.2 Photoacids, Photoacidity and Frster Cycle 12.2.1 Photoacids and Photobases
Photoacids [5, 9, 17–20, 24–28] and photobases are organic dyes which become stronger acids or stronger bases in the electronic excited-state (Figs. 12.1–12.3). They have been used extensively in the past 50 years to study the kinetics and mechanism of proton-transfer reactions in aqueous solutions [3–28, 39–81] and as very efficient means of creating rapid change in the pH of a solution, the so called pH-jump [82–86]. Unlike excited-state electron transfer reactions, proton transfer reactions are usually reversible on the potential surface of the excited-state of the photoacid and the photobase [39–62]. For that reason excited-state proton transfer reactions are very useful for modeling ordinary ground state acid–base reactions. Research into photoacids and photobases mainly originated with the seminal studies of Frster [3–6] and Weller [7–11]. Frster correctly assigned the large Stokes shift in the fluorescence emission of several hydroxy- and amine-substituted dyes to very fast excited-state proton transfer reaction to the solvent [3]. The unit charge change upon proton transfer results in the fluorescence emission originating from a new fluorescing chromophore, the conjugated photobase. It was Frster who suggested that the acidity of photoacids in the excited state may be estimated by using a thermodynamic cycle, the so-called “Frster cycle” [5]. Frster’s assumption was that electronic excitation of a photoacid acts to shift its ground state equilibrium constant Ka to a new value K*a, where K*a > Ka and may be defined thermodynamically similarly to Ka, K*a = [(A–)*][H+]/[A*H]
(12.4)
Where an asterisk on a concentration symbol indicates that the species is in the electronic excited state. In Eq. (10.4) A*H is the excited photoacid and (A–)* is the excited (conjugated) photobase.
12.2 Photoacids, Photoacidity and Frster Cycle
12.2.2 Use of the Frster Cycle to Estimate the Photoacidity of Photoacids
The K*a of a photoacid may be estimated by combining the Frster cycle (Fig. 12.4) [5] with the equilibrium constant of the photoacid in the ground state, which should be independently known to facilitate the calculation. Arguably, of even greater importance than the ability to estimate the absolute photoacidity when the ground state acidity is accurately known, the Frster cycle provides a general thermodynamic cycle for estimating the relative change in the acidity of a chromophore upon electronic excitation, DpK*a = pKa – pK*a, independent of prior knowledge of the ground state pKa. One may, thus, distinguish between the Frster photoacidity, DpK*a, and the absolute photoacidity of a molecule when in the excited state as defined by its K*a (or pK*a) value. Furthermore, it is often correct to assume that, while the absolute photoacidity depends on intramolecular properties of the photoacid as well as on solvent properties, Frster photoacidity depends mainly on intramolecular rearrangements in the electron density of the photoacid and its conjugated photobase upon electronic excitation. The Frster acidity, DpK*a, may be found with the aid of the Frster cycle (Fig. 12.4) and is given by Eq. (12.5) DpK*a = pKa – pK*a = N (DGFEG – DG¢FEG) / (RT ln 10)
(12.5)
where N is the Avogadro constant and DGFEG and DG¢FEG are the two Frster energy gaps which are the free-energy gaps separating the ground state and the stable (thermodynamic) energy levels of the photoacid and photobase while in their electronic excited states, respectively. Clearly, Frster cycle bears a sound physical meaning when excited-state proton transfer is inherently reversible so the two thermodynamically stable energy levels of the photoacid and the photobase in the excited state could have equilibrated, providing that they lived long enough in the excited state. Assuming inherent reversibility of the proton transfer reaction in the excited state, one may proceed and define the equilibrium constant of such an excited-state process independent of the system actually reaching equilibrium populations during the finite (ns-short) lifetime of the excited state. In the following discussion we refer to the thermodynamically stable states of the photoacid and photobase while in the electronically excited state as the “Frster levels” and the free energy gap that separates them from their respective ground-state (thermodynamic) energy levels as the Frster energy gap (FEG, DGFEG, DG¢FEG, respectively). It is worth pointing out that the Frster cycle does not constitute by itself proof for its physical validity. It rather defines a general thermodynamic cycle for estimating the change in the equilibrium constant, DpK*a, of a photoacid upon electronic excitation, assuming the acid– base equilibrium is shifted from the ground electronic state to the excited electronic state of the photoacid.
379
380
12 Solvent Assisted Photoacidity
(a) OH
OH
OH SO3
SO3
1N2S
1N
1N3S
OH
OH
OH
O 3S SO3
SO3
SO3
1N3, 6d iS
1N5S
1N4S
OH OH
OH
H3C Cl
CH3
CN CH3
1N4Cl
1N5CN
Figure 12.1 (a) Molecular structure of 1-naphthol (1N), 1-naphthol-2-sulfonate (1N2S), 1-naphthol-3-sulfonate (1N3S ), 1-naphthol-4-sulfonate (1N4S), 1-naphthol-5-sulfonate (1N5S ), 1-naphthol-3,6-disulfonate (1N3,6diS), 1-naphthol-4-chlorate (1N4Cl), 1-naphthol-5-cyano (1N5CN), and 1-naphthol-5-tetrabutyl (1N5tBu).
1N5tBu
12.2 Photoacids, Photoacidity and Frster Cycle
(b) CN OH
OH
OH
CN
2N
2N5CN
2N8CN
CN OH
OH
H3C CN
2N5,8diCN
2N6Me
SO3 OH
OH
O3S
O3 S
2N6,8diS
SO3
2N3,6diS
Figure 12.1 (b) Molecular structure of 2-naphthol (2N), 2-naphthol-5-cyano- (2N5CN), 2-naphthol-8-cyano (2N8CN), 2-naphthol-6,8-disulfonate (2N6,8diS) 2-naphthol-6-methyl- (2N6Me), 2-naphthol-5,8-dicyano (2N5,8diCN ) and 2-naphthol-3,6-disulfonate (2N3,6diS).
381
382
12 Solvent Assisted Photoacidity O Me2N OH
S
OH
O3S
OH
O3S
SO3
O
O
O S
S Me2N
1HP
O
O
NMe2
HPTS
HPTA
Figure 12.2 Molecular structure of 1-hydroxypyrene (1HP), 8-hydroxypyrene-1,3,6-dimethylsulfamide (HPTA) and 8-hydroxypyrene 1,3,6-trisulfonate (HPTS). NH3
NH2Me
AP
MAP
NHMe2
DMAP
O3S
NH3
O3S
SO3
APTS
Figure 12.3 Molecular structure of protonated amine photoacids: 1-aminopyrene (1AP), N-methyl-1-aminopyrene (MAP), N,N-dimethyl-1-aminopyrene (DMAP), 8-aminopyrene-1,3,6trisulfonate (APTS).
12.2 Photoacids, Photoacidity and Frster Cycle
(A )*+ H+ –
S1> g>
(AH)* ∆GFEG
∆G'FEG
A + H+ –
AH
Figure 12.4 Frster cycle of photoacids in the gas phase. Energy levels are for a general photoacid A*H and its conjugated base (A–)*. S1> is the first singlet excited state and |g> is the ground-state. DGFEG and DG¢FEG (the Frster energy gap) are the free energy gaps separating the vibronically relaxed ground state and the vibronically relaxed excited state energy levels of the photoacid and photobase, respectively.
The situation is not straightforward when the acid–base equilibria take place in solution. Unlike the schematic gas-phase situation (Fig. 12.4) vertical electronic transitions of large molecules in solution are followed by various intramolecular relaxation processes and by solvent relaxation around the excited photoacid and photobase. As a result, the location of the Frster levels with respect to their corresponding ground state levels may only be estimated from the corresponding vertical transition energies. There are several methods for determining the respective FEG energies of a photoacid and a photobase which have been reviewed by Grabowski and Grabowska [71]. The method which is usually recommended is to average the transition energies from and to the ground electronic state of the photoacid and the conjugated photobase [9, 19, 27, 71–76]. The transition energies are usually taken from the location of the peak absorption and peak fluorescence spectra of the photoacid and conjugated photobase, hmAb and hmEm and hm¢Ab and hm¢Em for the photoacid and the photobase, respectively. The averages of the optical transition energies thus found are considered the FEG energies of the Frster cycle. Thus, the transition energies in the photoacid and conjugated photobase sides are calculated independently of each other, from their respective absorption and emission spectra. The procedure of averaging between the energies of the absorption transition, hmAb, and the fluorescence transition, hmEm, is mainly aimed at minimizing the effect of solvent relaxation on determining the final (relaxed) location of the energy level of the acid (and base). The difference in free energy between the directly accessed electronic level and the thermodynamically relaxed Frster level generally depends on both intramolecular and intermolecular relaxation processes. For the electronic excited state one may denote the total free energy of relaxation following the absorption of a photon by DGs and DG¢s for the photoacid and photobase, respectively. Similarly, DGg and DG¢g denote the excess free energy of the vertically accessed level in the ground state of the photoacid and photobase, respectively, following the emission of a photon from the corresponding Frster levels of the photoacid and the photobase. The energy levels and averaging procedure appropriate for solutions of photoacids are depicted in Fig. 12.5.
383
384
12 Solvent Assisted Photoacidity
∆Gs
A*H hvEm
hvAb
S1>
∆G's (A¯)*
S1’>
∆GFEG
hv’Em
hv’Ab
∆G’FEG
'
AH
∆Gg
g>
Figure 12.5 Frster cycle of photoacids in solution. Energy levels are for a general photoacid A*H and its conjugated base (A–)*. |S1> is the excited-state of the acid and |S¢1> of the base, |g> is the ground-state of the acid and |g¢> of the anion, respectively. hmAb and hm¢Ab are the energy of the absorption transition. hmEm and hm¢Ab are the energy of the fluorescence transition of the acid and base, respectively. DGFEG and DG¢FEG (the Frster
g’>
∆G g
A¯
energy gaps) are the free energy gaps separating the thermodynamically relaxed ground state and the thermodynamically relaxed excited state energy levels of the photoacid and photobase, respectively. DGg and DGS are the relaxation free energies of the acid immediately following the electronic transition in the ground and excited state respectively and DG¢g and DG¢S are the corresponding free relaxation of the base.
Using the symbols of Fig. 12.5 one has for the average of the absorption and emission transitions of the photoacid (AH): (hmAb + hmEm)/2 = (DGFEG+DGs +DGFEG–DGg)/2 = DGFEG + (DGs–DGg)/2
(12.6)
Similarly, averaging the energies of the optical transitions of the photobase (A–) yields: (hm¢ Ab + hm¢ Em)/2 = (DG¢FEG +DG¢s +DG¢FEG–DG¢g)/2 = DG¢FEG +(DG¢s–DG¢g)/2
(12.7)
In Eqs. (12.6) and (12.7) DGFEG and DG¢FEG are the Frster energy gaps (FEG) in the photoacid and photobase side, respectively. DGs and DGg are the total free energy of relaxation in the target electronic state following absorption and emission of a photon, respectively. It follows that averaging between the absorption and emission energies results in cancellation of errors, which usually results in better estimation of the FEG energies as compared to either using the absorption or emission energies alone. Furthermore, the total error in determining, DGFEG and DG¢FEG is only half that of the difference in the relaxation energies in the ground and the excited state, thus reducing the residual error by half, Eqs. (12.6) and (12.7). The total error in carrying out the Frster cycle with the averaged transition energies of the photoacid and photobase rather than with the thermodynamic DGFEG and DG¢FEG values may be estimated by the following simple algebraic consideration, Eq. (12.8).
12.2 Photoacids, Photoacidity and Frster Cycle
DGFEG–DG¢FEG = (hmAb+hmEm)/2 – (hm¢Ab +hm¢ Em)/2 + (DGs–DGg –DG¢s+DG¢g)/2
(12.8)
The difference between the ground-state and excited-state equilibrium constants of the photoacid as defined thermodynamically by the Frster cycle, DpK*a (therm), is given by: DpK*a(therm) = (DGFEG–DG¢FEG )/(RT ln 10) = ((hmAb–DGs)–(hm¢A– DG¢s))/(RT ln 10)
(12.9)
So relaxations in the excited photoacid side to below the vertically accessed level act to decrease photoacidity while corresponding relaxations in the excited photobase side act to increase it. The difference between the calculated value DpK*a (cal) when using averaged transition frequencies and the thermodynamic value, DpK*a (therm) may be found by the following procedure: DpK*a (cal) = [(hmAb+hmEm)/2 – (hm¢Ab+ hm¢Em)/2]/ (RT ln 10)
(12.10)
The error in DpK*a when applying Eq. (12.10) rather then Eq. (12.9) is given by: DpK*a (therm) – DpK*a (cal) = [N (DGg – DGs + DG¢s – DG¢g)/2 ] / (RT ln 10) (12.11)
It is not immediately clear which of the relaxation free energy terms appearing in Eq. (12.11) are more important than the others. In conditions where there is little electronic rearrangement in the excited states of the photoacid and photobase DGs and DG¢g are likely to be larger than DG¢s and DGg. The former transitions involve solvent relaxation following vertical electronic transitions to the electronically excited photoacid which is the more polar form of the photoacid and transition to the ground-state photobase which is more charge localized than the excited-state photobase and hence undergoes stronger interactions with the solvent. This is the situation for electronic transitions which only involve modest changes in the electronic structure both in the photoacid and photobase sides. Photoacids where excitation to the relatively nonpolar 1Lb state (see below) takes place may conform to this scenario. One such example is the So–S1 transition of 2-naphthol. A useful classification of the electronic levels of aromatic molecules was given by Platt. The two lowest electronic levels common to all cata-condensed hydrocarbons are, according to Platt’s notation [7, 88] the 1La and 1Lb levels. In Platt’s notation the subscripts a and b refer to the direction of the electronic polarization. In general, a refers to an electronic state whose eigenfunction nodes pass through the carbon atoms forming the aromatic ring, and b refers to a state whose eigenfunction nodes pass through the carbon–carbon bonds. For the naphthalene ring system the a band is polarized along the short axis of the molecule in a transverse polarization and the b band is polarized along the long axis.
385
12 Solvent Assisted Photoacidity
(a) 1.0
Absorption (normalized)
386
1 2 3 4 5
2N
0.8 0.6
1
La
0.4 0.2 0.0 260
1
280
300
Lb
320
340
λ, nm
(b)
1
La
1
Lb
Figure 12.6 (a)Absorption spectra of 2-naphthol in several solvents of different polarity: 1- c-hexane, 2- ethanol, 3- formamide, 4-DMSO, 5-water. (b) La/Lb scheme for naphthalene. Adapted from Ref. [95].
The two lowest-energy electronic absorption bands of 2-naphthol in various solvents are shown in Fig. 12.6. These are assigned to transitions to the 1Lb state (S1) and to the 1La state (S2). In cases where the vertically accessed excited state level of the photoacid and the relaxed excited state level of the photoacid are both the relatively nonpolar 1Lb state the difference between the calculated value and the thermodynamic value of pK*a is expected to be small. It has indeed been found that Frster cycle with average transition frequencies is a very good approximation for calculating DpK*a values of photoacids in the 1Lb electronic excited state [75]. The situation is more complex when two different singlet states are involved in the photon-absorption and photon-emission processes of the photoacid [76, 89– 96]. Following Baba and Suzuki [89–91], we have suggested that the blue-side in the absorption band of 1-naphthol belongs to the 1La transition and the red-side of the absorption band of 1-naphthol belongs to the 1Lb transition [92, 93] (see Fig. 12.7). The level structure of such a photoacid is congested and is portrayed in Fig. 12.8. Here the full Eq. (12.11) should be considered with potentially much larger deviations from the energies of the true Frster cycle transitions.
12.2 Photoacids, Photoacidity and Frster Cycle
Absorption (normalized)
1
1.0
1N
La 1
0.8 0.6
1 2 3 4 5
0.4 0.2 0.0 260
Lb
280
300
320
340
λ, nm Figure 12.7 Absorption spectra of 1-naphthol in several solvents of different polarity: 1 – c-hexane, 2 – ethanol, 3 – formamide, 4 – DMSO, 5 – water. The spectral range is identical to that of Fig. 12.6. Adapted from Ref. [95].
∆Gs
A*H hvEm AH
hvAb
1 La 1 L b 1 Lb 1 La
∆GFEG
∆G'La
hv’Em
(A-)* hv’Ab ∆G’g
∆G’FEG
A-
∆G g
Figure 12.8 Frster cycle of photoacids in solution when two different singlet states are involved in the photon absorption and photon emission processes of the photoacid i.e., the 1Lb and the 1La states. The four possible
excitation-emission cycle scenarios involving the ground state and the two excited state levels are: 1La : 1Lb, 1La : 1La, 1Lb : 1Lb, 1Lb : 1La (see text). All symbols are as defined in Fig. 12.5.
12.2.3 Direct Methods for Determining the Photoacidity of Photoacids
In certain cases of well-behaved photoacids, typically having pK*a values in the range of 0–3, Frster cycle predictions may be tested against pK*a values found by two direct experimental methods. The first is titration of the excited photoacid with a stronger mineral acid until an “end–point” is reached [9]. The titration of the excited photoacid is monitored by following the change in the relative quantum yield of the photoacid or the photobase as a function of the solution pH. Taking the steady-state fluorescence spectra of the photoacid at each titration point is
387
388
12 Solvent Assisted Photoacidity
sufficient for this purpose [7–11]. The value of K*a is found by analyzing the inflection point of the titration curve. This method is reliable when the acid–base equilibrium is not affected by proton quenching and when the photoacidity of the photoacid is not very large or not too small for the excited state dissociation to be appreciable. The second independent method for finding K*a is by direct time-resolved measurements of the proton-dissociation and proton-recombination reaction rates of the excited photoacid. These measurements have traditionally utilized timeresolved fluorescence and absorption spectroscopy. They were originally developed by Weller [7–11] and Frster [3–6] and have been widely in use in photoacid research [17,18, 27]. Assuming homogenous proton recombination and unidirectional dissociation reaction one has, for the excited-state equilibrium constant: pK* a = – log(k*d/k*r)
(12.12)
where k*r and k*d are the bimolecular (homogeneous) proton recombination and the unimolecular proton dissociation rate constants of the excited photoacid, respectively. Recently, the usefulness of fs-resolved mid-IR measurements of some vibrational markers of the photoacid and the photobase was demonstrated by Nibbering et al. [97–100]. Direct mid-IR absorption spectroscopy has thus proved to be an additional tool for directly monitoring the proton-transfer kinetics of photoacids while in the excited state. The main disadvantage of the direct methods for the determination of K*a values is that these methods are usually cumbersome and are only feasible for a limited range of photoacidities of well behaved photoacids. This is due to limitations imposed by the short lifetime of the excited state and/or competing excited-state reactions and also due to either a very large or a very small K*a value of the photoacid. These complicating conditions are very common and put limits on the usefulness of the time resolved measurements of any observable that depends on monitoring the actual progress of the proton dissociation and proton recombination reactions of the photoacid. When the limitations on the time-resolved measurements are considerable, Frster cycle calculations do not usually agree well with the directly estimated pK*a value of the photoacid. Such discrepancies have been attributed many times to limitations inherent to the Frster cycle and have even have led to questioning of its general validity. In comparison, it has been much less often suggested that the source of the discrepancy lies in difficulties associated with the time resolved measurements. Below we review in detail the evidence for the general validity of the Frster cycle concept and the various experimental limitations imposed on its practical use.
12.3 Evidence for the General Validity of the Frster Cycle and the K*a Scale
12.3 Evidence for the General Validity of the Frster Cycle and the K*a Scale
Because of its general applicability, relative ease of the steady-state measurements, and the simplicity of the thermodynamic cycle, the Frster cycle has become the main tool for the initial determination of the extent of photoacidity [9, 27, 71–78]. However, this has not been done without considerable debate about the validity of a thermodynamic approach to short-lived excited-state species. Additional concern has been with the correct identification of the thermodynamically stable excitedstate energy levels using conventional steady-state optical spectroscopy in solution [16, 71, 75, 76]. Chief among the arguments against the routine use of Frster cycle has been the short ns-lifetime of the singlet state of most photoacids which many times does not allow even a partial establishment of a chemical equilibrium in the straightforward thermodynamic sense. In particular, the situation becomes unclear when either one of the two excited-state proton transfer reactions (proton dissociation and proton recombination) is much slower than the fluorescence lifetime of the excited photoacid. In the extreme situation, the photoacid may appear to be completely nonreactive within the lifetime of the excited state. Such situations prevent the observation of the excited-state proton transfer process and render impossible the determination of the excited-state K*a by any of the direct methods of measurement. The general validity of the Frster cycle approach is undoubtedly linked first of all with the reality of the assumed microscopic reversibility of excited-state proton transfer reactions. Secondly, the reliability of the K*a scale should be checked, when possible, against directly determined K*a values of well behaved photoacids. Furthermore, for the general validity of the K*a scale to hold as defined by the Frster cycle its validity should not depend on the photoacid actually reaching equilibrium conditions or even on observing at all an excited-state proton transfer reaction within the finite lifetime of the excited state. These assertions should be carefully tested and checked before establishing the general applicability of the Frster cycle. 12.3.1 Evidence for the General Validity of the Frster Cycle Based on Time-resolved and Steady State Measurements of Excited-state Proton Transfer of Photoacids
Arguably, the first evidence for the general validity of the pK*a scale came from steady-state fluorescence titrations of well behaved photoacids such as 2-naphthol [27]. As already indicated, this method was largely developed by Weller [9] and resulted in K*a values which were in general agreement with the Frster cycle predictions (see below). More direct evidence for the inherent microscopic reversibility of an excitedstate proton transfer reaction was found in ps-time-resolved measurements of a strongly reactive photoacid, namely HPTS (Fig. 12.2). With its conjugated-base, fourfold charged, the observation of the back (geminate) recombination of the pro-
389
390
12 Solvent Assisted Photoacidity
ton following the photoacid dissociation has become feasible. Pines and Huppert were first to report on the geminate recombination reaction of an excited photoacid [39–42]. They found that, following the dissociation of excited HPTS (also commercially known as pyranine), proton recombination occurred reversibly so that the ultimate fate of the so-formed excited photoacid was to dissociate again. Over relatively long times of observation, the repeated cycles of dissociation– recombination were found to occur in the excited state without quenching and to cause the populations of the reacting species to converge into a pseudo-equilibrium situation while being in the excited state. The equilibrating system was found to be continuously perturbed by the diffusion of the two geminate reactants away from each other. This gradual separation of the ion pair by diffusion away has been found to monotonically decrease the average concentration of the dissociated proton with respect to its geminate photobase anion. Following the initial series of observations and their correct physical modeling by Pines and Huppert [39–43] Pines, Huppert and Agmon [43–48] arrived at an analytic expression describing the decaying amplitude of the photoacid at long times: [A*H]t K* a (4pDt)–3/2
(12.13)
where t is the time elapsed from the moment of the initial dissociation of the photoacid and D is the mutual diffusion coefficient between the proton and the conjugated photobase. Equation (5.12) was verified over relatively long observation times in conditions where only diminishing small concentrations of the photoacid remained in the excited state, down to about 10–4 of the initial population. (Fig. 12.9). The experimental verification of Eq. (12.13) was carried out after normalizing the decaying photoacid population with the observed fluorescence lifetime of the conjugated photobase, s¢0, Eq. (12.14): [A*H]t exp(t/s0¢) K* a (4pDt)–3/2
(12.14)
Equation (12.14) was found to be exact by Gopich and Agmon when the nonreactive lifetime of the photoacid equals that of the photobase. Reviews of the extensive kinetic analysis done over the past 20 years in order to refine the basic geminate-recombination model have been recently published by Pines and Pines [25] and by Agmon [48]. A further step to establish the validity of the K*a has been undertaken by Pines and Fleming [49] and was extended by Pines et al. [50, 51] and by Solntsev et al. [52, 53]. These authors have shown that the concept of an excited-state equilibrium constant holds in the more kinetically demanding (and more general) situation of proton quenching in parallel to reversible geminate rocombination. 1-Naphthol exemplifies such a situation when, in addition to undergoing reversible proton dissociation, the population of the excited photoacid has been shown to be self-quenched by the dissociated geminate proton as well as by bulk protons. In such cases irreversible recombination (quenching) of the proton competes with
12.3 Evidence for the General Validity of the Frster Cycle and the K*a Scale
10
0
-1
10
-2
*
[A H]t
10
-3
10
-4
10
-5
10
-6
10
0
5
10
15
20
25
30
35
Time (ns) Figure 12.9 Semi-logarithmic plot of normalized fluorescence decay of HPTS. Points are experimental data (kex = 375 nm, kem = 420 nm) after lifetime correction. Data taken in water at pH = 6.10 after background subtraction. The solid line is a numerical solution of the
Debye–Smoluchovski equation (Ref. [44]) convoluted with the instrument response function. Parameters are a = 6.30 , kd = 125 ps–1, kr = 7.90 ns–1, RD = 28.3 , D = 930 2 ns–1 (K*a = 26.5). The asymptotic slope is –1.50. Adapted from Ref. [60].
Scheme 1
reversible recombination of the proton at the original site of the dissociation, Scheme 12.1. To account for the additional proton quenching reaction, the long time decay of the photoacid population, Eq. (12.14), should be corrected and take the form of Eq. (12.15) [50–52]. [A*H]t exp(t/s¢) K* a [A –*]¥ 2 (4p Dt) –3/2
(12.15)
where [A–*]¥ is the surviving fraction of the unquenched geminate pairs from the initial excited-state population. The normalized fraction of the surviving pairs is equal to the ultimate escape probability of the pair, while avoiding self-neutralization, X¥. In the case of infinite lifetimes X¥ = 1 for reversible recombination reac-
391
392
12 Solvent Assisted Photoacidity
tions without quenching and is less than unity when a parallel quenching reaction takes place. Gopich and Agmon [54–57] have extended the above analysis even further to include conditions when the excited-state lifetimes of the photoacid differ from that of the conjugated photobase. The effect of unequal excited-state lifetimes of the photoacid and the photobase was originally considered by Weller in order to correct for pK*a values found by direct fluorescence-titration of the photoacid while in the excited state. He showed that the relative kinetic effectiveness of the proton dissociation reaction from the photoacid and the back-protonation reaction of the photobase depends on the ratio of their respective excited-state lifetimes [7, 9], Eq. (12.16). f= 1 ðk*r Þs¢0 f0 ¼ þ ðc– Þ2 ½Hþ f¢= kd s0 k*d s0 f¢0
(12.16)
where f=f0 and f¢=f¢0 are the relative fluorescence quantum yields of the photoacid and photobase, respectively, which change upon titration and serve to monitor its progress as a function of the concentration of the mineral acids. s0 and s¢0 are the fluorescence lifetime of the photoacid and photobase, respectively, in the absence of proton transfer. c– is the mean activity coefficient of the strong mineral acid used to titrate the photoacid. Equations (12.12) and (12.16) serve to demonstrate the macroscopic reversibility of the proton transfer reaction in the excited state while Eqs. (12.13)–(12.15) describe the microscopic reversibility of the same reaction. The observation that over long times the time dependence of the population of the photoacid followed Eq. (12.13) (or Eq. (12.15)) in the case of selfquenching [49–53, 58]) have demonstrated the general microscopic validity of K*a, even in a most demanding situation where the excited state is rapidly quenched back to the ground state. The final stage of this yet unfinished saga has been to directly demonstrate the establishment of an actual excited-state (acid–base) equilibrium by performing time-resolved titration of the photoacid while in the excited-state (Fig. 12.10). This was done in conditions where proton dissociation was initiated by short laser pulse excitation in the presence of strong mineral acids [59–61]. Following the initial dissociation of the excited photoacid the population of the photoacid relaxed to its equilibrium concentration with the photobase. The relaxation-to-equilibrium process was carried out with the excited photobase reversibly reacting with both the dissociated proton and the large excess of bulk protons introduced by the mineral acid. At long times the reaction was predicted to follow Eq. (12.17) [62], [A*H]t – [A*H]¥ K*a (4pDt)–3/2 / (1+cKeq)3
(12.17)
Equation (12.17) was verified by Pines and Pines [60] who were able to demonstrate the predicted analytic dependence of the relaxation kinetics on the bulk concentration of the mineral acid (HClO4) used to titrate the excited photoacid.
12.3 Evidence for the General Validity of the Frster Cycle and the K*a Scale 0
10
a -1
b c d
*
[A H]t
10
-2
e
-3
f
10
10
-4
10
0
5
10
15
20
25
30
Time, ns Figure 12.10 Semi-logarithmic plots of the normalized fluorescence decay of 2N6,8diS in the presence of a strong acid. Points are experimental data after lifetime correction; (a–e) in water acidified by HClO4. (pH = 2.0, 2.52, 2.83, 3.11, 3.72, respectively), (f) in water at pH = 6.10, ([HClO4] = 0). Adapted from Ref. [60].
The advantage of Eqs. (12.13)–(12.15) and (12.17) was that they allowed the direct determination of the excited-state equilibrium constant by a single kinetic measurement. The proton dissociation rate constant and hence also the proton recombination rate constant may also be found from the same measurement. Although this method has been applied successfully in only a few cases [60, 61], the K*a values thus found have been in very good agreement with K*a values independently estimated from the Frster cycle or by steady-state titrations. 12.3.2 Evidence Based on Free Energy Correlations
More subtle methods for verifying the validity of the Frster cycle for estimating the K*a of weak photoacids have been successfully used, even in cases of very weak photoacids where no apparent dissociation of the photoacid has been observed. These methods rely on measuring the reactivity of photoacids toward stronger bases than water. It was demonstrated that the reactivity of excited photoacids follows general structure–reactivity laws, photoacids having similar structural features but different excited-state acidities can be grouped and correlated [101–103] (Fig. 12.8). Once the reactivity of a photoacid has been correlated within a family of similar photoacids according to its K*a (either the Frster cycle value or a directly measured one), its reactivity toward strong bases could be estimated and then verified experimentally (Fig. 12.11). Such procedures using for example
393
394
12 Solvent Assisted Photoacidity
Eq. (12.18) for the correlation between the proton transfer rate, kp, and K*a (the dependence on K*a enters through the free energy of activation term DGa , see below) usually result in very good agreement between the observed reactivity of the photoacid and its Frster cycle K*a value. kp k*oexp(–DG*a/kT)
(12.18)
where (k*o)–1 is the frequency factor of the specific family of reactions, DG*a is the effective activation energy of the proton transfer reaction in the excited state which may be estimated using the Marcus BEBO equation [104], Eq. (12.19) DGa = DGo/2 + DGo# + DG o# cosh[DGoln2/( 2DG o#)] /ln2
(12.19)
or alternatively assuming the reaction takes place in the “normal” region of the celebrated Marcus charge-transfer theory (MCT) (as opposed to “inverted” reaction conditions when the activation energy increases although the reaction becomes increasingly favored thermodynamically) where the activation energy decreases when the reaction is more favorable thermodynamically. The MCT theory was originally developed for the activation free energy of electron transfer reactions in solution [34–36], Eq. (12.20) DGa = (1+DGo/4 DGo# )2 DG o#
(12.20)
DGo# is the solvent-dependent activation energy of the charge-exchange reaction when the total free energy change (DGo = RT log pK*a ) in the proton transfer is equal to zero. Eqs. (12.19) and (12.20) are practically equivalent in the photoacidity range that has been studied so far which seems to display only “normal” reaction behavior where the proton transfer rate increases monotonically as a function of the increase in the relative strength of the base compared to the acid (see Fig. 12.12). A very convincing support for the existence of solvent controlled proton dissociation reactions in aqueous solutions has risen from the theoretical studies of Ando and Hynes [105–108] who have studied the proton dissociation of simple mineral acids HCl and HF in aqueous solutions. The two acids seem to follow a solvent-controlled proton transfer mechanism with a Marcus-like dependence of the activation energy on the acid strength. Recently, a free energy relationship for proton transfer reactions in a polar environment in which the proton is treated quantum mechanically was found by Kiefer and Hynes [109, 110]. Despite the quite different conceptual basis of the treatment the findings bear similarity to those resulting from the Marcus equation Eq. (12.19) which has been used to correlate the proton transfer rates of photoacids with their pK*a [ 101, 102 ] . The case of 1-hydroxypyrene is illuminating in this respect. Being one of the first photoacids studied by Weller [9], its pK*a = –log (K*a) was estimated by Weller using the Frster cycle, pK*a = 3.7, but the photoacid was not observed to dissociate in water [111]. Several explanations were offered for this apparent lack of con-
12.3 Evidence for the General Validity of the Frster Cycle and the K*a Scale 12
Marcus CT BEBO
10 8
HP
4
-1
log(kp(s ))
6
2
20 15
∆Ga
0
10
-2
5
-4
0 -10 -5
-6 -8
0
5
∆ pKa
-10 -8 -6 -4 -2
0
10 15
2
4
6
8
10 12 14 16
*
pKa
Figure 12.11 The free energy correlation found in photoacid dissociation reactions taken at room temperature. Solid line is the fit using Marcus BEBO equation (Eq. (12.19)) and dashed line the fit using Marcus CT equation (Eq. (12.20)). The free energy barrier for
a symmetric proton transfer is 2.4 kcal mol–1 (BEBO equation) and 2.2 kcal mol–1 (Marcus CT equation), respectively. The dependence of the activation free energy on the pKa* of the photoacid as calculated using the BEBO equation (Eq. (12.19)) is shown as the inset.
12.0 11.5 11.0 10.5
HP-KAc
-1
log(kp(sec ))
10.0 9.5 9.0 8.5
HP-KForm
8.0 7.5 7.0 6.5 6.0 5.5 -12
-10
-8
-6
-4
-2
0
2
4
6
pK*a-pKbase Figure 12.12 The free energy correlation found in photoacid dissociation to water and in the direct proton transfer reactions between photoacids and carboxylic bases (potassium acetate (KAc and potassium formate (KForm)) taken at room temperature.
The free energy barrier, 2.9 kcal mol–1, found for the total set of proton transfer reactions is 0.5 kcal higher than that found for the sub-set of the proton-dissociation-to-water reactions (Fig. 12.11).
395
396
12 Solvent Assisted Photoacidity
sistency of the Frster cycle. These invoked the inadequacy of the Frster cycle for describing the photoacidity of very weak photoacids and the idea that weak photoacids may differ kinetically from strong photoacids by not dissociating so readily in the excited state. The reason given for the latter behavior invoked the electronic structure of weak photoacids which has been suggested to be inherently less polar and less reactive than that of strong photoacids [132–134]. The first singlet state of weak photoacids has been suggested to be the 1Lb state while strong photoacids like HPTS have been thought to undergo solvent-influenced level crossing to a more polar 1La state [135–137]. However, several reports have shown that 1-hydroxypyrene behaves as a proper photoacid in so far as the strengthening of its hydrogen-bonding interactions in the excited state and its ability to transfer a proton to stronger-than-water bases both in aqueous and nonaqueous solutions [9]. Using the correlation shown in Fig. 12.12 Pines et al. were able to show that in fact the reactivity of excited 1-hydroxypyrene toward acetate bases is consistent with a pK*a value of about 4.1, which agrees very well with the Frster cycle estimation of its pK*a, (Fig. 12.13). Finally, it has been demonstrated recently (Fig. 12.14) [112–114] that about 1% of the population of 1-hydroxypyrene does dissociate at room temperature (k*p = 5 106 s–1) which is in good agreement with predictions based on correlating the pK*a (Frster cycle) value by the BEBO model of Marcus (Fig. 12.11). It thus seems that the Frster cycle calculation does provide a reliable way of estimating K*a even when the proton transfer reaction is two orders of magnitude slower than the excited-state decay rate. One may also conclude from Fig. 12.12, which correlates both 1Lb and 1La, acids that the proton transfer rate within a family of photoacids is uniquely determined by the K*a value of the photoacid, regardless of whether it is in the 1Lb or 1La state. This means that internal changes in the electronic structure of excited photoacids leading to changes in the fluorescing level of the photoacid may not constitute a significant kinetic control for the rate of the proton transfer from weak photoacids. However, these electronic anion
acid 6.3 4.6
water ∆pK
HP HPTS
Figure 12.13 Frster cycle of HP and HPTS photoacids in water. Energy levels are for the photoacids A*H and their conjugated base (A–)*. The energy levels of both photoacids are normalized to the energy of the ground state level of the photoacids. The Frster cycle is plotted to scale in the units of pK, pK = DG / log RT. HP: pKa = 8.7, DpK*a = 5.1, pK*a = 3.6. HPTS pKa = 8.0, DpK*a = 6.1, pK*a = 1.9.
12.4 Factors Affecting Photoacidity
140
(a)
Intensity, normalized
120 100
Intensity, a.u.
1.0
pH 6 pH 3 pH 12
80 60
(b)
0.5
40 20
0.0 0 400
450
500
550
600
Wavelength, nm Figure 12.14 (a) Fluorescence spectra of 1-hydroxypyrene at 80 C measured under the excitation of the photoacid at pH 6 (circles) and at pH 3 where negligible photoacid dissociation occurs due to much faster proton recombination process with bulk protons (dashes), and under direct excitation of the photobase at pH 12 (solid line). (b) Dashed
400
450
500
550
600
Wavelength, nm line is the photobase fluorescence obtained by subtraction of fluorescence spectra of HP at pH 6 and pH 3 measured in H2O at 20 C. The photobase fluorescence obtained under direct excitation of the photobase at pH 12 is also plotted for comparison (solid line). Adapted from Ref. [114].
changes should result in a change in the K*a value of the photoacid, which in turn would affect the proton dissociation rate by means of Eqs. (12.18)–(12.20), see also the discussion in Section 12.5 below.
12.4 Factors Affecting Photoacidity 12.4.1 General Considerations
What are the important intramolecular and intermolecular factors affecting photoacidity? Clearly, photoacidity by itself is the result of some intramolecular changes in the electronic structure of the excited photoacid and its photobase enhancing its Brønsted acidity as compared to the situation existing in the electronic ground state. By the same token, acidity and basicity largely depend on the chemical and physical properties of the solvent in which the acid–base reactions take place. Judging by the available literature it seems that Frster cycle calculations are very useful in predicting the relative change in the Ka, i.e. DpK*a of most photoacids upon
397
398
12 Solvent Assisted Photoacidity
electronic excitation, independent of the photoacid being a strong or a weak acid in the ground state. However, the absolute value of K*a, which determines the actual strength of the photoacid depends on the corresponding ground-state equilibrium constant which in turn is a solvent-dependent property. It follows that it is possible that the absolute acidity of an excited photoacid may be very low, depending on the solvent, while still exhibiting considerable Frster photoacidity. 12.4.2 Comparing the Solvent Effect on the Photoacidities of Neutral and Cationic Photoacids
Similar to the situation prevailing for uncharged ground-state acids, uncharged photoacids which exhibit strong acidity are most commonly found in water which is, arguably, the best overall solvent-medium for solvating free ions produced by the photoacid dissociation. This situation dramatically changes upon moving to less polar solvents where neutral photoacids become much weaker acids. This is essentially due to a decrease in their ground-state acidity and not because of a large decrease in their photoacidity. Some relevant data on the pK*a’s is collected in Tables 12.1 and 12.2 where the Frster cycle photoacidity of 1-naphthol and 2-naphthol is listed in several solvents where the ground-state acidity of the photoacid is known. In comparison with the considerable decrease in the ground-state acidity on moving from aqueous solutions to the less polar solvents, the Frster acidities, as judged by the DpK*a values in the same solvents, DpK*a = pKa – pK*a, do not change by much and even seem to increase with decreasing solvent polarity. The extent of the marked decrease in the ground state acidity of neutral photoacids on moving from water to less polar solvents has been so overwhelming as to identify photoacidity with actually observing excited-state proton transfer which occurs almost exclusively in an aqueous environment. The term “enhanced photoacids” has been introduced by Tolbert [22–24] to describe neutral photoacids being strong enough to still appreciably dissociate in nonaqueous (albeit still polar) solvents. However, the situation becomes much more blurred when cationic photoacids (Fig. 12.3), which undergo an acid–base equilibrium of the form AH+ . A + H+, are considered. In such cases proton dissociation does not cause the formation of an ion pair so the proton-dissociation reaction is isoelectric. Here the polarity of the solvent does not play a dominant role as with neutral-acid dissociation, while other factors such as solvent basicity toward the proton may become more important. Not surprisingly, cationic photoacids may even increase their acidity and their photoacidity in less polar but more basic solvents than pure water. An example is the proton dissociation reaction of protonated aminopyrenes RN*H3+ (Fig. 12.3) [19, 25, 101, 115, 116]. The K*a values of this family of cationic photoacids are very large with some pK*a values approaching the acidity of strong mineral acids (Fig. 12.15). The proton transfer rate of these photoacids (and their pKa values) increases in mixtures of water/organic solvent solutions until it reaches a maximum rate at water compositions of about 50–70% (M/M) [101]. Further decrease in the water content causes the proton transfer rate to decrease
12.4 Factors Affecting Photoacidity
again until it reaches its value in the pure organic solvent. (Fig. 12.16). For tertiary amine photoacids, RN(CH3)2H+ the maximum rate of proton transfer may be more than an order of magnitude greater than the corresponding rate in pure water. Such a complex dependence on solvent composition reveals the complex role that the solvent has in proton transfer reactions. Not only does the solvent need to stabilize the dissociating proton and its conjugated base, it also provides the hydrogen-bonding network necessary for the proton to transfer efficiently by the Grotthuss mechanism, i.e. along hydrogen-bonding networks of water [117– 124]. The complex dependence of the proton transfer rate on the solvent composition is once more not a unique property of the excited photoacid–solvent system. It is rather similar in both ground-state and excited-state proton transfer reactions of cationic acids.
Tab. 12.1 pKa, pKa* and DpK*a values of 1-naphthol in water, methanol and DMSO.
Solvent
pKa
DpK*a 1L /1L a b
pK*a 1L /1L [a] a b
water
9.3
10.3/6.9
–1.0/2.4
methanol
13.9
11.1/8.4
2.8/5.5
DMSO
17.1[b]
12.3/9.7
4.8/7.4
a pK*a values when calculated by the Frster cycle using either the S0fiS2 (1La) absorption energy or the S0fiS1 (1Lb) absorption energy. b Ref. 139.
Tab. 12.2 pKa, DpK*a and pK*a values of 2-naphthol in water,
methanol and DMSO from Frster cycle calculations. Solvent
pK0a
DpK*a
pK*a
water
9.6
6.3
3.3
methanol
14.2
6.6
7.6
DMSO
16.2
10.0
6.2
pK(meth) – pK(water)
4.6
0.3
4.3
399
12 Solvent Assisted Photoacidity
1.4
acid
Acetonitrile base
1.0
1.2
base 0.8
1.0
Intensity
Intensity (a.u.)
1.2
70%HClO4
0.8 0.6
0.6
0.4
0.4 0.2
acid
0.2 350
400
450
500
550
600
0.0 400
Wavelength (mm)
450
500
550
600
Wavelength (mm)
Figure 12.15 Dissociation of protonated APTS in acetonitrile and in 70% HClO4. About 50% of the photoacid (fluorescence maximum at 395 nm) dissociates to form the conjugated photobase (fluorescence maximum at 530 nm) in HClO4 and about 20% in acetonitrile within the excited-state lifetime of the photoacid. Adapted from Ref. [116]. Methanol DMSO THF Acetonitrile
100
τ (ns)
400
10
0.0
0.2
0.4
0.6
0.8
1.0
% mol organic solvent
Figure 12.16 Proton dissociation lifetimes time of protonated 2-AP photoacid as a function of the molar fraction of organic co-solvent in water solutions. Ref. [116].
12.4.3 The Effect of Substituents on the Photoacidity of Aromatic Alcohols
The situation considered so far has been of the solvent affecting ground-state acidity while intramolecular changes in the charge density of the chromophore upon electronic excitation determine the extent of the photoacidity of the photoacid relative to its corresponding ground state acidity. The relative contribution of the
12.4 Factors Affecting Photoacidity
Frster photoacidity to the total (absolute) acidity of photoacids in their electronic excited state may be estimated directly from the corresponding pKa and pK*a values. Additional questions are the extent to which photoacidity may be tuned by suitable substituents which also affect the ground state acidity of the photoacid and, alternatively, by the choice of the solvent. Table 12.3 compares the effect of several substituents on the ground- and excited-state acidities of several photoacids. The first conclusion that may be drawn from this table is that ring substituents cause the Ka and K*a of aromatic photoacids to change in the same direction. It follows that one may discuss the effect of various types of substituents on photoacidity using arguments and terminology that have been traditionally used for ground state acids. In particular, Hammett [127, 128] and Taft [129, 131] have contributed much to the discussion of the substituent effect on equilibrium and reactivity of aromatic acids in the ground electronic state. Their arguments seem to be valid also for the excited state of aromatic acids but with different scaling factors (i.e., different values in the Hammett Equation) [24].
Tab. 12.3 pKa and pKa* values of some common photoacids in water.
Photoacid
pKa
Ref.
pKa*
Ref.
1-naphthol
9.4
125
–0.2
49
1-naphthol 3,6-disulfonate
8.56
126
1.1
79
5-cyano-1-naphthol
8.5
103
–2.8
103
1-naphthol-4-sulfonate
8.27
74
–0.1
74
2-naphthol
9.6
125
–2.8
23
5,8-dicyano-2-naphthol
7.8
23
–4.5
23
5-cyano-2-naphthol
8.75
23
–0.3
23
8-cyano-2-naphthol
8.35
23
–0.4
23
2-naphthol-6,8-disulfonate
8.99
126
0.7
78
1-hydroxypyrene
8.7
27
3.6
27
HPTS
8.0
45
1.4
45
HPTA
5.6
116
–0.8
116
Finally, the observed net effect of substituents on either increasing or decreasing photoacidity is less than 3 pK*a units, even in the most extreme cases studied so far [24, 69]. This only constitutes about one third of the total acidity change upon electronic excitation. Apparently, in most cases, one may treat the substituent effect as a perturbation to the electronic structure of the unsubstituted chromophore even when the aromatic acid is in the electronic excited state [69].
401
402
12 Solvent Assisted Photoacidity
Figure 12.13 compares the photoacidities of 1-hydroxypyrene and HPTS. The considerable effect of the 3 sulfonate groups that are located on the 3, 6, 8 positions of the pyrene system of HPTS is evident. The difference in the ground state acidity of the two photoacids is about 0.9 pK*a units, HPTS being the stronger ground-state acid. In the excited state the difference in acidity increases to about 2.3 pK*a units, again HPTS being the stronger photoacid. It follows that the Frster photoacidity of HPTS is larger than the Frster photoacidity of 1-hydroxypyrene by about 1.4 pK*a units. As the position of the OH group is the same for the two photoacids most of the change in photoacidity is likely to originate from the combined inductive effect of the 3-sulfonate groups. Apparently, the inductive effect is about three times larger in the excited state of HPTS than in the ground (a)
anion
acid
5.2
La
6.3
La
methanol
∆pK
(b)
acid
1N5tBu 1N5S
anion 5.2
Lb Lb
∆pK
4.7
methanol
1N5tBu 1N5S
Figure 12.17 Frster cycle of 1N5tBu [150] and 1N5S photoacids in methanol. The energy levels are normalized to the energy of the ground state level of photoacids. (a) 1L cycle: 1N5S: pK = 12.9 (estimated from a a pKa in water), DpK*a = 8.5 and pK*a = 4.4.
1N5tBu: pKa = 14.4 (estimated from pKa in water), DpK*a =11.1 and pK*a = 3.3. (b) 1Lb cycle: 1N5S: pKa = 12.9 (estimated from pKa in water), DpK*a = 7.4 and pK*a = 5.5. 1N5tBu: pKa= 14.4 (estimated from pKa in water), DpK*a = 8.4 and pK*a = 6.0.
12.4 Factors Affecting Photoacidity
state. Plotting the Frster cycle levels of the two photoacids on a normalized energy scale shows the increased photoacidity of HPTS to be the result of greater photobase stabilization, presumably because of the greater charge transfer away from the negatively charged oxygen atom to the substituted pyrene system. The enhanced charge transfer process from the OH group to the aromatic system of HPTS makes the photoacid considerably more acidic and its photobase a much weaker base as compared to the situation prevailing in the acid–base equilibrium of 1-hydroxypyrene. The net result of the two effects is to increase the acidity of HPTS over that of 1-hydroxypyrene, indicating larger sensitivity to the electronic excitation of the photobase side [69, 136, 137]. The effect of the three substituents in stabilizing the Frster level of the photoacid is nevertheless considerable. This may indicate a change in the nature of the Frster level of the photoacid, from 1Lb in 1-hydroxypyrene to more polar S1 level in HPTS which has some charge-transfer character [100]. As a final example we compare the photoacidities of 1-naphthol-5-sulfonate and 1-naphthol 5-tetrabutyl. The Frster cycle of the two photoacids was measured in methanol. The 5-position of the 1-naphthol system is considered the most sensitive to substituents (Table 12.4). As discussed in the HPTS case the sulfonate Tab. 12.4 DpK*a values of some common hydroxyarene
photoacids from Frster cycle calculations in methanol. Photoacid
DpK*a 1L /1L [a] a b
1-naphthol
11.1/8.4
1-naphthol-2-sulfonate
11.0/7.4
1-naphthol-3-sulfonate
11.3/8.0
1-naphthol-4-sulfonate
8.2/6.5
1-naphthol-5-sulfonate
8.5/7.4
1-naphthol-4-chlorate
9.4[b]
1-naphthol-5-tetrabutyl
11.1/8.4
1-naphthol 3,6-disulfonate
12.6/9.5
2-naphthol
6.6 [b]
2-naphthol-6,8-disulfonate
7.3 [b]
HPTS
6.9 [b]
HPTA
7.1 [b]
a DpK*a values when calculated the Frster cycle using either the S0fiS2 (1La) absorption energy or the S0fiS1 (1Lb) absorption energy. b Calculated with the S0 « S1 transition.
403
404
12 Solvent Assisted Photoacidity
group enhances charge transfer from the oxygen atom to the aromatic system (Hammett rp value = 0.09). The situation is reversed with the tetrabutyl group which is an electron-withdrawing group (rp = – 0.197) [128]. Figure 12.17 is very illuminating in showing the large difference in the effect of the two types of substituents on the location of the Frster levels of the photoacids. Interestingly, in this case the photoacid side and the photobase side are almost equally affected by the change in substituents so the photoacidity of the two photoacids in methanol is almost equal. It follows that 5-sulfonate-1-naphthol is a much stronger photoacid, mainly because it is already a much stronger acid in the ground state having pKa = 8.4 compared to the pKa = 9.8 of 1-naphthol-5-tetrabutyl. Also shown in Fig. 12.17 is the substituent effect on the energy of the S0–S2 transition. Clearly, the more charge-transfer promoting substituent lowers the energy of the vertically accessed S2 level more than the corresponding relative stabilization of the S0–S1 transition, presumably because the S0–S2 transition of 1-naphthol derivatives is to the polar 1La state.
12.5 Solvent Assisted Photoacidity: The 1La, 1Lb Paradigm
A more complex situation may arise when polar interactions with the solvent not only stabilize the Frster levels of the photoacid and photobase but also select it. In such cases Frster acidity may depend to a large extent on the solvent. In particular, the possibility of the solvent determining the nature of the first singlet state of the photoacid has been of considerable interest and a matter of debate in recent years [132–137]. It was suggested that in polar solvents 1La-type singlet states comprise the photoacidity states, while in less polar solvents less-polar 1L -type singlet states make up the photoacidity states. This so-called “level inverb sion” in polar solvents has been suggested to be an additional, and sometimes the dominant mechanism which is responsible for neutral photoacids being so much less reactive in solvents other than water [132–137]. It has been argued that in water proton dissociation occurs from polar 1La-type states which exhibit a negligible barrier for proton dissociation, while in less polar solvents proton dissociation occurs from relatively nonpolar 1Lb-type states by an activated process which may involve a slow (solvent activated) internal conversion to the more reactive 1La state. The difference in reactivity between the two close-lying singlet states of 1-naphthol was suggested to be so large that level crossing from the 1Lb to the more polar 1La state was considered the rate determining step for proton dissociation [132–134]. A support for this reactivity model was found in molecular dynamics simulations of the proton dissociation reaction of excited 1-naphthol in solvent clusters [131– 134]. However, this model finds limited support in measurements of photoacids in liquid solutions. More recently, a modified 1Lb–1La scenario was suggested to be a dominant factor in the photoacidity of HPTS in the liquid phase [135–138]. Based on sub-ps measurements of HPTS, proton dissociation was argued to consist of two acti-
12.5 Solvent Assisted Photoacidity: The 1La, 1Lb Paradigm
vated processes. In the first stage, the local excited state of the photoacid converts to a charge transfer state from which proton dissociation occurs. However, the experimental evidence was not conclusive and this reactive model of HPTS remains under debate. A recent time-resolved absorption study of HPTS carried out in the mid-IR range with sub-150 fs measurement did not find support for relatively slow internal conversion to a charge transferred state in the time range studied. It was observed, rather, that the patterns of the ring vibrations of excited HPTS change with the change in solvent but with no apparent time-resolved dynamics, thus suggesting solvent-influenced modification of the first singlet state of HPTS which occurs faster than the time resolution of the experiment (150 fs) [100]. As mentioned above, the extent by which the solvent influences the Frster photoacidity may be checked using the Frster cycle with the transition energies of the photoacid and the conjugated photobase measured independently in the solvent in question. However, the estimation of K*a values by Frster cycle in solvents where no proton transfer was observed has been a questionable practice over the more than 50 years of photoacid research. In such cases Frster cycle calculations may be carried out when it is possible to generate the conjugated photobase by deprotonating the photoacid in the ground state. This is usually done by introducing a strong proton-base to the photoacid solution. The gap between the ground-state and excited-state energy levels of the conjugated photobase may then be found by direct excitation of the ground-state photobase. Such measurements are independent of whether the photoacid dissociates appreciably in the excitedstate to form the photobase. The energy gap between the two pairs of energy levels needed to complete the Frster cycle may thus be found and the value of DpK*a compiled. Below we carry out a survey of the Frster cycle photoacidity of several well known photoacids in order to examine the 1Lb –1La paradigm. Arguably, the best examples are 1-naphthol which is considered to be a 1La photoacid, 2–naphthol (1Lb acid), 1-hydroxypyrene (1Lb) and HPTS ( S1). Tables 12.1 and 12.2 compare the DpK*a values for 1 and 2-naphthols in water, methanol and DMSO solvents. It is clear that the Frster acidities of the photoacids do not diminish on moving from water to the less polar solvent but, rather, tend to increase in the less polar solvents. The observation that Frster cycle photoacidity increases on moving from water to less polar solvents was first made by a research group headed by Hynes [138]. The increase in the photoacidity in these solvents is more than compensated by the decrease in the ground-state acidity of the photoacid. Estimation of the ground state pKa’s in the same solvents show the considerable decrease in the overall acidity of the photoacids in nonaqueous solutions to be a ground-state effect (i.e., originating from a process also occurring in the ground state of the photoacid, so it cannot be uniquely associated with the excited electronic level of the photoacid). In addition, one may try to analyze the photoacidity behavior according to the nature of the first singlet state of the photoacid, being either 1Lb or, presumably, the more polar 1La state. Important conclusions may be drawn simply by comparing between photoacids having
405
406
12 Solvent Assisted Photoacidity anion
acid La Lb
1.8 0.9
water
∆pK
1Na 2Na
Figure 12.18 Frster cycle of 1N and 2N photoacids in water. The energy levels of both photoacids are normalized to the energy of the ground state level.1N: pKa = 9.3, DpK*a = 10.3 (1La) and 6.9 (1Lb), pK*a = –1.0 (1La) and 2.4 (1Lb). 2N: pKa = 9.6, DpK*a = 6.3 and pK*a = 3.3. anion
acid 1.4
La 3.1 Lb
∆pK
methanol
1N 2N
Figure 12.19 Frster cycle of 1N and 2N photoacids in methanol. The energy levels of both photoacids are normalized to the energy of the ground state level. 1N: pKa = 13.9 (estimated from pKa in water), DpK*a = 11.1 (1La) and 8.4 (1Lb) pK*a = 2.8 (1La) and 5.5 (1Lb). 2N: pKa = 14.2 (estimated from pKa in water), DpK*a = 6.6 and pK*a = 7.6
known excited-state level structure. Figures 12.13 and 12.17–12.21 portray the Frster cycle levels of several photoacids in different solvents as found by the spectra-averaging procedure discussed in this chapter. The figures are drawn to scale with the Frster energies of the different states shown with respect to the Frster energy of the photoacid in the ground state, which is considered the reference energy level. The energy separating between the ground state and the various excited state levels of the photoacid and the photobase is given in pKa (pK*a) units. The first general observation drawn from Tables 12.1 and 12.2 and Figs. 12.17– 12.21 is that photoacids in 1La-like levels are generally stronger than photoacids in 1L -like levels by several pK* units. a b
12.5 Solvent Assisted Photoacidity: The 1La, 1Lb Paradigm acid
anion
La
1.3
Lb
∆pK
1N 2N
DMSO
Figure 12.20 Frster cycle of 1N and 2N photoacids in DMSO. The energy levels of both photoacids are normalized to the energy of the ground state level. 1N: pKa =17.1 (estimated from pKa in water), DpK*a =12.3 (1La) and 9.7 (1Lb), pK*a = 4.8 (1La) and 7.4 (1Lb). 2N: pKa= 16.2 (estimated from pKa in water), DpK*a =10.0, pK*a = 6.2. acid
1-Na
La
anion 5.2
Lb
∆pK
DMSO water
Figure 12.21 Frster cycle of 1N photoacid in DMSO and water. The energy levels of the photoacid in DMSO and water are normalized to the energy of the ground state level. DMSO: pKa = 17.1 (estimated from pKa in water), DpK*a = 12.3 (1La) and 9.7 (1Lb), pK*a = 4.8 (1La) and 7.4 (1Lb). Water: pKa = 9.3, DpK*a = 10.3 (1La) and 6.9 (1Lb), pK*a= –1.0 (1La) and 2.4 (1Lb).
Figure 12.18 compares the locations of the Frster levels of the two isomers of naphthol, the 1-naphthol and 2-naphthol photoacids in water. The level structure of 1-naphthol is more congested than that of 2-naphthol which results in some uncertainty about the nature of the electronic level accessed from the ground state and the nature of the excited Frster level. Comparing the level structure of the two isomers reveals that the increased acidity of the 1-isomer over the 2-isomer is due to better stabilization of 1-naphtholate as compared to 2-naphtholate. This indicates a larger charge transfer process in the 1-isomer of the photobase than in the 2-naphtholate case.
407
408
12 Solvent Assisted Photoacidity
When assuming the excitation to be directly to the 1La state the calculated Frster photoacidity increases by 3.4 pKa units. The observation that the S0 to 1Lb transition of 1-naphthol results in calculated Frster acidities considerably smaller than the experimental ones, while the S0 to 1La transition of the same molecule results in calculated Frster acidities being only slightly larger than the experimental photoacidity was made by Schulman [77] and discussed by Harris and Selinger [76]. This observation was put forward as an argument in favor of calculating the Frster cycle in cases of suspected 1Lb to 1La level crossing with the S0–S2 transition energy instead of the S0–S1 transition. However, level crossing in the acid side of 1-naphthol is unlikely to be the main reason for the Frster cycle failing to predict the extent of the photoacidity of the molecule so the better fit with experiment using the S0–S2 transition should be considered accidental. The improved correspondence between the Frster cycle and the experimental value of K*a is likely to be the result of cancellation of errors (Eq. (12.11)). The relative failure of the Frster cycle in the case of 1-naphthol is probably due to abnormally large reorganization energy in the excited photobase side of 1-naphthol and due to a large horizontal shift between S1 and S0 potential wells. This results in a vertical down-transition from the Frster level to high vibronic levels in the ground state. The resulting two large reorganization-energy terms apparently do not cancel out by the two other reorganization terms appearing in Eq. (12.11). The situation is different with 2-naphthol. In this case there is only a small Stokes shift between the absorption wavelength and the fluorescence wavelength in the photoacid side, pointing to an S1 level resembling more the ground-state level than in the case of the 1-naphthol isomer. Moving to less polar solvents usually increases the photoacidity of 1La photoacids. This implies the destabilization of the Frster level of the photoacid with respect to the Frster level of the conjugated photobase on-going from aqueous to nonaqueous solutions, (Figs. 12.18–12.21). 1-Naphthol and 2-naphthol are again of particular interest. The two photoacid isomers differ by the position of the OH substituent and by the character of their first singlet state. Which of the two is more important in determining the extent of photoacidity? Comparison between the pKa of 1-naphthol and 2-naphthol in water reveals that 1-naphthol is already the stronger acid in the ground state by about 0.3 pKa units. In the excited state the difference in the acidity of the two naphthols isomers increases by about 150-fold, to about 2.5 pKa units. The increased acidity of 1-naphthol over 2-naphthol has been attributed to the first singlet state of 1-naphthol being in the more polar 1La state. However, the effect of a photoacid crossing to the 1La state ultimately being below a 1Lb state is to stabilize the Frster level of the exited photoacid and so to decrease its photoacidity and not to increase it (Figs. 12.18–12.20). If level crossing in the acid side were the only process to occur then the photoacidity of 1-naphthol should have been less that that of 2-naphthol. To explain the overall increased photoacidity of 1-naphthol one has to invoke the anion side (base) of the photoacid, i.e. to assume much larger stabilization of the 1-naphtholate anion than that of the 2-naphtholate anion, which more than compensates for the changes occurring on the photo-
12.5 Solvent Assisted Photoacidity: The 1La, 1Lb Paradigm
acid side. A conclusion may be drawn that the increased photoacidity of 1-naphthol over that of 2-naphthol must be due to much larger rearrangements in the electronic structure in the photobase side of 1-naphthol. It is still a matter for further research to decide which process is dominant in making the basicity of the excited 1-naphtholate anion considerably smaller than the basicity of the 2-naphtholate anion. Is it because the a-position in the naphthalene ring is more susceptible to charge transfer than the b-position or is it because 1-naphtholate is in an altogether different (more polar) electronic state akin to the 1L state of the photoacid side? Whatever the answer, it is clear that 1-naphthol is a a stronger photoacid than 2-naphthol because of much greater intramolecular stabilization of the anionic charge of 1-naphtholate. These assertions are verified when the Frster cycle of the two isomers is compared. Figures 12.18–12.20 show the level structure of the two naphthol isomers both normalized to the energy of the ground state of the 2-naphthol molecule. Clearly evident is the effect of greater stabilization of the excited 1-naphtholate as compared to excited 2-naphtholate. The difference in the stabilities of the two anions increases in methanol, Fig. 12.19. The effect of assuming direct absorption to S2 in the case of 1-naphthol is to bring the Frster level of 1-naphthol above that of 2-naphthol, which contradicts the starting point of this discussion, namely that the 1La level may become the Frster level only in cases where solvent relaxation brings it down to below the 1Lb level. Making the same assumption of direct excitation to 1La in the less polar solvents DMSO and methanol only makes this inconsistency worse, Figs. 12.19 and 12.20). Figure 12.21 compares the Frster cycle of 1-naphthol in water and in DMSO. DMSO is a polar aprotic solvent which is unable to stabilize the naphtholate anion by hydrogen-bonding interactions. This results in very large destabilization of the naphtholate anion in the ground state and a very large decrease in the groundstate acidity in DMSO, pKa = 17.1, compared to 9.3 in water [139]. The situation is reversed in the excited state, where the photoacidity of 1-naphthol is much larger in DMSO than in water, DpK*a (Frster cycle) = 9.7 and 6.9 assuming 1Lb transition, for DMSO and water, respectively. It is evident from Fig. 12.21 that the increased photoacidity in DMSO is due to a decrease in the destabilization of the excited naphtholate anion as compared to the situation in the ground state. The observation, that being in the excited state levels out the effect of the strong (specific) hydrogen-bonding interaction existing in the ground state of 1-naphtholate is important. It shows that 1-naphthol is a much weaker base in the excited state than in the ground state so it becomes insensitive in the excited state to whether the solvent is a strong hydrogen-bond donating one (water) or a very weak one (DMSO). A similar conclusion may be drawn by performing the Kamlet–Taft analysis [140–142] on the spectral shifts of 1-naphtholate in different solvents [143]. Indeed, such an analysis has shown that 1-naphtholate does not form hydrogen bonds in the excited state. Similar analysis on 2-naphtholate derivatives yielded the same conclusions [144]. As a final note we point out that proton transfer may involve a more complex mechanism than that implied by the Brønsted model for proton transfer between
409
410
12 Solvent Assisted Photoacidity
acid and base. One such model was recently discussed in connection with photoacidity in the gas phase. In this reaction model excited state hydrogen transfer (ESHT) occurs [145–149]. This model has been recently described by Sobolewski and Domcke [145, 146] and used in excited state dynamics studies of gas phase phenol clustered with ammonia or water molecules of the Jouvet group [147]. In this model it is argued that a level crossing between the initially excited 1pp* state and a 1pr* state facilitates the migration of an electron from the photoacid to the solvent. The electron transfer reaction is followed by proton transfer with a net transfer of a hydrogen atom. Modeling photoacidity as ESHT has also been used as in an experiment where donor and acceptor groups are connected through a wire of ammonia molecules [148]. A conical intersection of the 1pr* state with the S0 state leads to an efficient internal conversion pathway for phenol–ammonia clusters. Net proton transfer on the other hand should involve at least one more step with an electron back transfer to the photoacid, producing the photobase and solvated proton as separate species. Conical intersections connecting the locally excited 1pp* state and the ground state with a 1pp* charge transfer state strongly stabilized by the transfer of a proton is the mechanism of the enhanced excitedstate decay of hydrogen-bonded aromatic dimers in the experiments of Hertel group [149]. However, Brønsted photoacidity as described by the Frster cycle has been found to be the major mechanism of proton transfer from photoacids in aqueous solutions. However, parallel reactive routes which involve electron transfer apparently do exist in aqueous solutions of photoacids where proton and electrons are both detected following photoexcitation with extra energy over the S1 excitation energies.
12.6 Summary
Photoacids have been consistently proven to be important research tools in solution chemistry over the past 50 years. Understanding photoacidity is a basic requirement for this field to develop further and to expand behind its traditional boundaries of acid–base research in aqueous solutions. Photoacidity is affected by intramolecular charge rearrangement which is initiated by optical excitation and also by intermolecular interactions with the solvent. The Frster cycle is the primary tool for estimating the photoacidity of an aromatic dye. Important insight has been gained on the factors affecting photoacidity using direct time-resolved measurements and Frster cycle considerations: 1. Photoacidity may be defined regardless of proton dissociation occurring or not during the finite lifetime of the photoacid in the excited state. Photoacidity may also be defined in nonpolar solvents using the Frster cycle. 2. Generally speaking, photoacids behave similarly to groundstate acids as far as the solvent effect and the substituent effect on acidity and photoacidity is concerned.
References
3. Marked photoacidity is mainly the result of large rearrangements in the anion (photobase) side of the photoacid equilibrium. 4. Structural factors of an intramolecular process increasing the stability of only the photoacid side will decrease photoacidity. It follows that the reasons for the increased photoacidity of 1La photoacids which undergo internal conversion from the locally excited, less polar 1Lb state to the polar 1La state should be found in the photobase side of the photoacid–photobase equilibrium rather than in the photoacid side. 5. Partial charge transfer to the aromatic ring may be important both in the photoacid and the photobase side. In the acid side this process is usually of a smaller magnitude than in the photobase side and will make the acidic proton more positively charged and more susceptible to hydrogen bonding. In the photobase side charge transfer to the aromatic ring is considerable and acts to increase the total photoacidity of the photoacid.
Acknowledgments
We cordially acknowledge the important contributions by our former group members Ben-Zion Magnes and Tamar Barak. We are also grateful for the financial support of the German-Israeli Foundation for Scientific Research and Development (Project GIF 722/01), the Israel Science Foundation (Project ISF 562/04) and The James Franck German-Israeli Binational Program on Laser-Matter Interaction.
References 1 Brønsted, J. N., Rev. Trav. Chim. 42 2 3 4 5 6 7 8
(1923), 718. Brønsted, J. N., Chem. Rev. 5 (1928), 231. Frster, Th., Natur. 36 (1949), 186. Frster, Th., Z. Electrochem. Angew. Phys. Chem. 42 (1952), 531. Frster, Th., Elektrochem. 54 (1950), 42. Frster, Th., Pure Appl. Chem. 4 (1970), 43. Weller, A., Z. Electrochem. 58 (1954), 849. Weller, A., Z., Phys. Chem. N. F. 17 (1958), 224.
9 Weller, A., Prog. React. Kinet. 1 (1961),
187. 10 Urban, W., Weller, A., Ber. Bunsen-Ges.
Phys. Chem. 67 (1958), 787. 11 Weller, A. H., Discuss. Faraday Soc. 27
(1959), 28. 12 Eigen, M., Kruse, W., De Maeyer, L.,
Prog. React. Kinet. 2 (1964), 285. 13 Eigen, M., Angew. Chem., Int. Ed. Engl. 3
(1964), 1. 14 Wei, Y., Wang, W., Yeh, J. M., Wang, B.,
Yang, D. C., Murray, J. K., Adv. Mater. 6 (1994), 372.
411
412
12 Solvent Assisted Photoacidity 15 Martinov, I. Y., Demyashkevich, A. B.,
Uzhinov B. M., Kuzmin, M. G., Russ. Chem. Phys. 46 (1977), 3. 16 Politi, M. J., Brand, O., Fendler, J. H., J. Phys. Chem. 89 (1985), 2345. 17 Vander Donckt, E., Prog. React. Kinet. 5 (1970), 273. 18 Schulman, S. G., in Modern Fluorescence Spectroscopy, Wehry, E. L. (Ed.), Plenum Press, New York, 1976, Vol. 2, p. 239. 19 Shisuka, H., Acc. Chem. Res. 18 (1985), 41. 20 Arnaut, L. G., Formosinho, S. J., J. Photochem. Photobiol. A 75 (1993), 21. 21 Van, P., Shukla, D., Chem. Rev. 93 (1993), 571. 22 Tolbert, L. M., Haubrich, J. E., J. Am. Chem. Soc. 112 (1990), 863. 23 Tolbert, L. M., Haubrich, J. E., J. Am. Chem. Soc. 116 (1994), 10593. 24 Tolbert, L. M., Solntsev, K. M., Acc. Chem. Res. 35 (2002), 19. 25 Pines, E., Pines, D., in Ultrafast Hydrogen Bonding Dynamics and Proton Transfer Processes in the Condensed Phase, Elsaesser, T., Bakker, H. J. (Eds.), Kluwer Academic Publishers, Dordrecht, 2002, pp. 155–184. 26 Pines, E., in Chemistry of Phenols, Rappoport Z. (Ed.), Wiley, New York, 2003, pp. 491–529. 27 Ireland, J. F., Wyatt, P. A. H., Adv. Phys. Org. Chem. 12 (1976), 131. 28 Agmon, N., J. Phys. Chem. A 109 (2005), 13. 29 Luecke, H., Richter, H.T., Lanyi J. K., Science 280 (1998), 1934. 30 Khlbrandt, W., Nature 406 (2000), 569. 31 DeCoursey, T. E., Physiol. Rev. 83 (2003), 475. 32 Zimmer, M., Chem. Rev. 102 (2002), 759. 33 Kosower, E. M., Huppert, D., Annu. Rev. Phys. Chem. 37 (1986), 127. 34 Marcus, R. A., J. Annu. Rev. Phys. Chem. 15 (1964), 155. 35 Marcus, R. A., J. Am. Chem. Soc. 91 (1969), 7244. 36 Marcus, R. A., Faraday Discuss. Chem. Soc. 74 (1982), 7. 37 Kuznetov, M., Ustrup, J., Electron Transfer in Chemistry and Biology, Wiley- Interscience, Chichester, 1999.
38 Electron Transfer in Chemistry, Balzani, V.
(Ed), Wiley-VCH, Weinheim, 2001. 39 Pines, E., Geminate Recombination in
Excited State Proton Transfer, Ph.D. Thesis, Tel-Aviv University, 1989. 40 Pines, E., Huppert, D., Chem. Phys. Lett. 126 (1986), 88. 41 Huppert, D., Pines, E., Intermolecular proton transfer, in Advances in Chemical Reaction Dynamics, NATO ASI Series Vol. 184 D, Riedel Publishing Company, 1986, pp. 171–178. 42 Pines, E,. Huppert, D., J. Phys. Chem. 84 (1986), 3576. 43 Pines, E., Huppert, D., Agmon, N., J. Chem. Phys. 88 (1988), 5620. 44 Agmon, N, Pines, E., Huppert, D., J. Chem. Phys. 88 (1988), 5631. 45 Pines, E., Huppert, D., J. Am. Chem. Soc. 111 (1989), 4096. 46 Huppert, D., Pines, E., Agmon, N., J. Opt. Soc. Am. B 7 (1990), 1545. 47 Pines, E., and Huppert, D., Agmon, N., J. Phys. Chem. 95 (1991), 666. 48 Agmon, N., J. Phys. Chem. A 109 (2005), 13. 49 Pines, E., Fleming, G. R., Chem. Phys. 183 (1994), 393. 50 Pines, E., Tepper, D., Magnes, B.-Z., Pines, Barak, T., Ber. Bunsen-Ges. Phys. Chem. 102 (1998), 504. 51 Pines, E., Magnes, B-Z., Barak, T., J. Phys. Chem. A 105 (2001), 9674. 52 Gopich, I.V., Solntsev, K. M., Agmon, N., J. Chem. Phys. 110 (1999), 2164. 53 Solntsev, K. M., Abouou Al-Ainain, S., Il’ichev Y. V., Kuzmin M. G., Photochem. Photobiol. A 175 (2005) 178. 54 Agmon, N., Gopich I. V., Chem. Phys. Lett. 302 (1999), 399. 55 Gopich, I. V., Agmon, N., J. Chem. Phys. 110 (1999), 10433. 56 Gopich, I. V., Agmon, N., Phys. Rev. Lett. 84 (2000), 2730. 57 Agmon, N., Gopich, I. V., J. Chem. Phys. 112 (2000), 2863. 58 Solntsev, K. M., Huppert, D., Agmon, N., Phys. Rev. Lett. 15 (2001), 3427. 59 Huppert, D., Goldberg, S., Masad, Y., Agmon, N., Phys. Rev. Lett. 68 (1992), 3932. 60 Pines, D., Pines, E., J. Chem. Phys. 115 (2001), 951.
References 61 Solntsev, K. M., Huppert, D., Agmon,
N., J. Phys. Chem. A 105 (2001), 5868. 62 Gopich, I. V., Ovchinnikov, A. A., Szabo, A., Phys. Rev. Lett. 86 (2001), 922. 63 Tolbert, L. M., Nesselroth, S. M., J. Phys. Chem. 95 (1991), 1031. 64 Carmeli, I., Huppert, D., Tolbert, L. M., Haubrich, J. E., Chem. Phys.,Lett. 260 (1996) 109. 65 Huppert, D., Tolbert, L., M., LinaresSamaniego, S. L., J. Chem. Phys. A 101 (1997), 4602. 66 Solntsev, K. M., Huppert, D., Agmon, N., Tolbert, L. M., J. Am. Chem. Soc. 120 (1998), 7981. 67 Solntsev, K. M., Huppert, D., Agmon, N., Tolbert, L. M., J. Phys. Chem. A 104 (2000), 4658. 68 Clower, C., Solntsev, K.M., Kowalik, J., Tolbert, L. M., Huppert, D., J. Phys. Chem. A 106 (2002), 3114. 69 Agmon, N., Rettig, W., Groth, C., J. Am. Chem. Soc., 124 (2002), 1089. 70 Htun, M., Th., Suwaiyan, A., Klein, U. K. A., Chem. Phys. Lett., 243 (1995), 506. 71 Grabowski, Z. R., Grabowska, A., Z. Phys. Chem., 101 (1976), 197. 72 Mulder, W. H., J. Photochem. Photobiol. A 161 (2003), 21. 73 Wehry, E. L., Rogers, L. B., J. Am. Chem. Soc. 87 (1965), 4234. 74 Henson, M. C., Wyatt, A. H., J. Chem. Soc., Faraday Trans. 2 71 (1974), 669. 75 Harris, C. M., Selinger, B. K., J. Phys. Chem. 84 (1980), 891. 76 Harris, C. M., Selinger, B. K., J. Phys. Chem. 84 (1980), 1366. 77 Schulman, S. G., Spectrosc. Lett. 6 (1973), 197. 78 Schulman, S. G. Rosenberg, L. S.,Vincent, W. R. Jr., Underberg, W. J. M., J. Am. Chem. Soc. 102 (1979),142. 79 Lee, J., Robinson, G. W., Webb, S. P., Philips, L.A., Clark, J. H., J. Am. Chem. Soc. 108 (1986), 6538. 80 Rived, F., Roses, M., Bosch, E., Anal. Chim. Acta 374 (1998), 309. 81 Roses, M., Rived, F., Bosch, E., J. Chromatogr. A 867 (2000), 45. 82 Gutman, M., Huppert, D., Pines, E., J. Am. Chem. Soc. 103 (1981), 3709. 83 Pines, E., Huppert, D., J. Phys. Chem. 87 (1983), 4471.
84 Gutman, M., Nachliel, E., Gershon, E.,
Giniger, R., Pines, E., J. Am. Chem. Soc. 105 (1983), 2210. 85 Gutman, M., Methods Biochem. Anal. 30 (1984), 1. 86 Gutman, M., Nachliel, E., Annu. Rev. Phys. Chem. 48 (1997), 3. 87 Platt, J. R., J. Chem. Phys. 1949, 17, 484. 88 Platt, J. R., Systematics of the Electronic Spectra of Conjugated Molecules: A Source Book, John Wiley & Sons, Chicago, 1964. 89 Baba, H., Suzuki S., J. Chem. Phys. 35 (1118), 1961. 90 Suzuki, S., Baba, H., Bull. Chem. Soc. Jpn. 40 (2199), 1967. 91 Suzuki, S., Fujii T., Sata, K., Bull. Chem. Soc. Jpn. 45 (1937), 1972. 92 Sano, H., Tachiya, M., J. Chem. Phys. 71 (1276), 1979. 93 Kasha, M., Discuss. Faraday Soc. 9 (14), 1950. 94 Tramer, A., Zaborovska, M., Acta Phys. Pol. 24 (1968), 821. 95 Magnes, B-Z., Strashnikova, N., Pines, E., Isr. J. Chem. 39 (1999), 361. 96 Magnes, B.-Z., Pines, D., Strashnikova, N., Pines, E., Solid State Ionics 168 (2004), 225. 97 Rini, M., Magnes, B.-Z., Pines, E., Nibbering, E. T., Science 301 (2003), 349. 98 Rini, M., Mohammed, O. F., Magnes, B.-Z., Pines, E., Nibbering, E. T. J, Bimodal intermolecular proton transfer in water: photoacid-base pairs studied with ultrafast infrared spectroscopy, in “Ultrafast Molecular Events in Chemistry and Biology”, J. T. Hynes, M. Martin (Eds.), Elsevier, Amsterdam, 2004, pp. 189–192. 99 Rini, M., Magnes, B.-Z., Pines, D., Pines, E., Nibbering, E. T. J., J. Chem. Phys. 121 (2004), 959. 100 Mohammed, O. F., J. Dreyer, Magnes, B.-Z., Pines E., Nibbering, E.T. J., ChemPhysChem 6 (2005), 625. 101 Pines, E., Fleming, G. R., J. Phys. Chem. 95 (1991), 10448. 102 Pines, E., Magnes, B. Z., Lang, M. J., Fleming, G. R., Chem. Phys. Lett. 281 (1997), 413. 103 Pines, E. Pines,D., Barak, T., Magnes, B.-Z., Tolbert, L. M., Haubrich, J. E.,
413
414
12 Solvent Assisted Photoacidity Ber. Bunsen-Ges. Phys. Chem. 102 (1998), 511. 104 Cohen, A. O., Marcus, R. A., J. Phys. Chem. 72 (1968), 4249. 105 Ando, K., Hynes, J.T., in Structure and Reactivity in Aqueous Solution: Characterization of Chemical and Biological Systems, Cramer, C. J., Truhlar, D. G. (Eds.), American Chemical Society, Washington DC, 1994. 106 Ando, K., Hynes, J.T., J. Mol. Liq. 64 (1995), 25. 107 Ando, K., Hynes, J. T., J. Phys. Chem. B 101 (1997), 1046. 108 Ando, K., Hynes, J. T., J. Phys. Chem. A 103 (1999), 10398. 109 Kiefer, P. M., Hynes, J. T., J. Phys. Chem. A 106 (2002), 1834. 110 Kiefer, P. M., Hynes, J. T., J. Phys. Chem. A 106 (2002), 1850. 111 Thomas, J. K., Milosavljevic, B. H., Photochem. Photobiol. Sci., 1 (2002), 1. 112 Pines, D. Barak, T. Magnes, B.-Z., Pines, E., The Photoacidity of 1-Hydroxypyrene from Frster Cycle to Marcus Theory, Summer School, Molecular Basis of Fast and Ultrafast Processes, Algarve (Portugal), June 12th-15th 2003. 113 Kombarova, S. V., Il’ichev, Y. V., Langmuir 20 (2004), 6158. 114 Magnes, B. Z., Barak, T., Pines, D., Pines, E., The Photoacidity of 1-Hydroxypyrene from Frster Cycle to Marcus Theory, in preparation. 115 Shiobara, S., Tajima, S., Tobita, S., Chem. Phys. Lett. 380 (2003), 673. 116 Barak, T., Dynamic and Thermodynamics Aspects of Proton Transfer from Cationic and Neutral Photoacids in Solutions, Ph.D. Thesis, Ben-Gurion University, 2005. 117 de Grotthuss, C. J. T., Ann. Chim. Phys. LVIII (1806), 54. 118 Danneel, Z. Elektrochem. Angew. Phys. Chem. 11 (1905), 249. 119 Agmon, N., Chem. Phys. Lett. 244 (1995), 456. 120 Hynes, J. T., Nature 397 (1999), 565. 121 Marx, D., Tuckerman M. E., Hutter, J., Parrinello, M., Nature 397 (1999), 601. 122 Vuilleumier, R., Borgis, D., J. Chem. Phys. 111 (1999), 4251.
123 Schmitt U. W., Voth, G. A., J. Chem.
Phys. 111 (1999), 9361. 124 Lapid, H., Agmon, N., Petersen, M. K.,
Voth, G. A., J. Chem. Phys. 122 (2005) in press. 125 Bryson, A., Matthews, R. W., Aust. J. Chem. 16 (1963), 401. 126 Dictionary of Organic Compounds, 5th edn., Chapman and Hall, New York, 1982. 127 Hammett, L. P., Trans. Faraday Soc., 34 (1938), 156. 128 Hammett, L. P., Physical Organic Chemistry, McGraw-Hill Book Co., New York, 1940, p. 186. 129 Taft, R. W., J. Am. Chem. Soc. 74 (1952), 3120. 130 Taft, R. W., J. Am. Chem. Soc. 86 (1964), 5189. 131 Taft, R. W., Lewis, I. C., J. Am. Chem. Soc. 80 (1958), 2441. 132 Knochenmuss, R., Muino, P. L., Wickleder, C., J. Phys. Chem. 100 (1996), 11218. 133 Knochenmuss, R., Leutwyler, S., J. Chem. Phys. 91 (1989), 1268. 134 Knochenmuss, R., Fischer, I., Int. J. Mass Spectrom.12137 (2002), 1. 135 Tran-Thi, T.-H., Gustavsson, T., Prayer, C., Pommeret, S., Hynes, J. T., Chem. Phys. Lett. 329 (2000), 421. 136 Hynes, J. T., Tran-Thi, T.-H., Gustavsson, T., J. Photochem. Photobiol. A 154 (2002), 3. 137 Tran-Thi, T.-H., Prayer C., Millie P., Uznansky, P., Hynes, J. T., J. Phys. Chem. A 106 (2002), 2244. 138 Hynes, J. T., personal communication. 139 Bordwell, F. G., Acc. Chem. Res. 21 (1988), 456. 140 Taft, R. W., Abboud, J.-L., Kamlet, M. J., J. Org. Chem. 49 (1984), 2001. 141 Abraham, M. H., Buist, G., J., Grellier, P. L., Mcill, R. A., Ptior, D. V., Oliver, S., Turner, E., Morris, J. J., Taylor P.J., Nicolet, P., Maria, P.-C., Gal, J-F., Bboud, J.L. M., Doherty, R. M., Kamlet, M. J., Shuely, W. J., Taft, R. W., J. Phys. Org., Chem., 2 (1989), 540. 142 Reichardt, C., Solvents and Solvent Effects in Organic Chemistry, 2nd edn., VCH, Weinheim, 1990. 143 Magnes, B. Z., Photophysics and Solute–Solvent Interactions in the Excited
References Electronic State of Photoacids. Ph.D. Thesis, Ben-Gurion University (2004). 144 Solntsev, K. M., Huppert, D., Agmon, N., J. Phys. Chem. A 102 (1998), 9599. 145 Sobolewski, A. L., Domcke, W., Dedonder-Lardeux, C., Jouvet, C., Phys. Chem. Chem. Phys. 4 (2002), 1093. 146 Domcke, W., Sobolewski, A. L., Science 302 (2003), 1693. 147 David, O., Dedonder-Lardeux, C., Jouvet, C., Int. Rev. Phys. Chem. 21 (2002), 499.
148 Tanner, C., Manca, C., Leutwyler, S.,
Science 302 (2003), 1736. 149 Schultz, Th., Samoylova, E., Radloff, W.,
Hertel, I. V., Sobolewski, A. L., Domcke, W., Science 306 (2004), 1765. 150 Synthesized by Prof. L. M. Tolbert’s group, School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, GA 30332-0400.
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13 Design and Implementation of “Super” Photoacids Laren M. Tolbert and Kyril M. Solntsev
13.1 Introduction
Electron and proton transfer (see Eqs. (13.1) and (13.2), involve obvious similarities. When the starting materials are neutral, both result in the formation of charge and in the necessity for separation of charge to stabilize the product states. In principle, both can occur in the ground state, but transfer that is exoergic only in the excited state allows the use of time-resolved spectroscopic techniques to determine the details of solvation and structural reorganization. For electron transfer, the development of such techniques and the accompanying theoretical rationale, most especially the Marcus theory, has been one of the triumphs of modern mechanistic chemistry. D + A fi D+ + A–.
(13.1)
AH + B fi A– + BH+
(13.2)
The relationship between driving force and proton transfer has been much more elusive despite considerable evidence that the vast photosynthetic electron transfer machinery mainly exists to set up a charge gradient to drive proton transfer. This is due to a combination of two factors. First, there is a vast reservoir of readily available materials with which to examine electron transfer. Second, the relationship between rates and driving force for electron transfer, based upon the excitation energies and the relevant redox potentials (the Rehm–Weller equation [1]) is reasonably straightforward. In contrast, the relationship between rates and driving force for excited-state pKa * ¼ pKa DEo;o =2:3RT
(13.3)
proton transfer (based upon relative pKas and calculated through the Frster equation, Eq. (13.3) [2]) is less straightforward. For instance, the existence of a so-called “inverted” region for proton transfer has been the subject of much controversy Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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13 Design and Implementation of “Super” Photoacids
(see Chapter 10 by J. T. Hynes). This is due to a number of factors, of which the most important is the presence of at least one additional reaction coordinate, that of the proton transfer event itself. There are also a number of additional coordinates. For instance, because of the large solvent proton affinities, the proton is invariably accompanied by solvent (“chaperoned”) on its trajectory from conjugate acid to base. Moreover, for hydroxylic molecules, there may be intervening solvent molecules between acid and base (defined by the Grotthus mechanism) [3] which may involve discrete protonated intermediates (stepwise mechanism) or a concerted mechanism with a single transition state (see Fig. 13.1). Finally, the solvation or protonation of the incipient conjugate base may contribute to the reaction mechanism. The kinetic method of pKa* determination is much more reliable, though not so widely used (see below). R
R R
O
H O
R
-
O
H
concerted
O
H
A H O R
O
H O
H
H O
A
R
O R
R
O
H
O
H
H H
O
O
R
ste
O
R
R R
H
pw
ise
R R AO R
O
H O
H
O+ R
H R
O
H
-
O
H O
R
H
Figure 13.1 Stepwise or concerted proton transfer.
Since the vast photosynthetic and photoresponsive electron-transfer machinery exists largely to create a proton gradient, proton transfer is arguably a more important reaction. But because most redox systems, both natural and synthetic, can be optically pumped, electron transfer has been more extensively studied, leading to one of the triumphs of modern mechanistic chemistry, the Marcus theory. Progress on proton transfer has been more sluggish, due both to a paucity of natural and synthetic candidates for optically-pumped proton transfer and to the need for more sophisticated models for this complicated process. Moreover, since proton transfer in nature involves heterogeneous systems, understanding the structural and energetic requirements for proton transfer, including the initial solvation, nuclear motion within the transition structure, charge separation, and diffusional recombination becomes paramount. On a broader level, this will facilitate prog-
13.1 Introduction
ress in a myriad of areas in which proton transfer is required, including “green” solvents such as supercritical fluids and “solventless” systems. This requires the development of systems which couple photoacids to biochemical reaction mechanisms. The microscopic details of proton transfer are shown in Fig. 13.1. These include the initial hydrogen bonding step, solvation of the transferring proton, the Grotthus “relay” mechanism, and the nature of the proton acceptor. For the last several years, we and others have sought to elucidate details of each of these factors, ultimately weaving these into a comprehensive picture of proton transfer. Since many of the kinetic steps are extremely fast, this effort has required the synthesis of previously unavailable strong photoacids which result in ultrafast proton transfer upon photoexcitation, preparation of model compounds which incorporate “solvent” molecules, and rigorous photophysical analysis of the rates of proton transfer resulting from photoexcitation. A number of molecules have been predicted to be strong photoacids [4, 5] An examination of the simple thermodynamic cycle represented by Eq. (13.3) for a proton-containing molecule and its conjugate base yields the simple yet deceptive prediction that in its excited state the molecule is a stronger acid than in the ground state if the absorption or emission spectrum of the conjugate base is characterized by a bathochromic shift relative to that of the conjugate acid. Thus molecules that undergo significant colorization upon deprotonation, e.g., triarylmethane dyes, should be powerful proton donors. Unlike the relatively simple Marcus theory for electron transfer, proton transfer rates cannot be correlated well with driving force. For instance, 9-phenylfluorene has a predicted pKa* of –13, yet it is photochemically inert, even in the presence of bases. Such thermodynamic acidity has not been evinced in prototropic behavior for photoexcited hydrocarbons to yield observed excited-state carbanions during our studies of carbanion photochemistry [6], although Wan has developed several possibilities for their intermediacy [7]. In contrast, hydroxyarenes have a long and rich history of use in excited-state proton transfer studies. The occurrence of proton transfer has been shown to be strongly correlated with the degree of ground-state hydrogen bonding, which provides a preorganization step for the proton transfer [8]. Thus oxygen-centered hydroxyarenes, which exhibit this phenomenon, have formed the basis for most such studies. However, their relatively high pKa has limited most such studies to aqueous solvent systems. A limited number of commercially available hydroxyarenes, including hydroxypyrenetrisulfonate (“pyranine”, HPTS), have somewhat higher photoacidities than naphthols and have been used as photoacids for experiments requiring instant changes in acidity, e.g., “pH jump.” Again, HPTS is limited to aqueous solvents. In order to improve photoacidity, therefore, strategic substitution by an electronwithdrawing group should result in proton transfer competitive with excited-state decay. The generic system is shown in Fig. 13.2. The hydroxyarenes have conjugate bases that are odd-alternant ions and thus yield to straightforward theoretical treatments. Moreover, odd-alternant ions have nonbonding molecular orbitals that are oxygen centered, while the excited states invariably produce charge distribu-
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13 Design and Implementation of “Super” Photoacids
hν EWG
π-System
− OH
+.
-.
.
O + H+
-CN -SO 3 CF3 -NO -COR
Figure 13.2 Generic photoacid.
tion at sites distal from oxygen, reducing the basicity of the excited-state anion and, by analogy, increasing the acidity of the conjugate base. This is equivalent to Weller’s “intramolecular charge transfer” rationalization of the acidity in photoexcited hydroxyarenes [9]. Further compelling and instructive examples are provided by Lewis’ studies of 3-hydroxy and 4-hydroxystilbene [10]. 3-Hydroxystilbene, for which the conjugate base does not allow ground-state delocalization into the distal aromatic ring, shows considerable excited-state basicity through population of a more delocalized excited state.
13.2 Excited-state Proton Transfer (ESPT) 13.2.1 1-Naphthol vs. 2-Naphthol
Naphthalene possesses nearly degenerate excited states, La and Lb, which are characterized by their polarization along the long axis (“through bond” or Lb) or along the short axis (“through atom” or La). The differences in symmetries can be understood by an appeal to the topologies of the HOMO and the two close lying LUMOs (see Fig. 13.3). Substitution by the hydroxy group apparently produces a reversal
hν
+ Lb
Figure 13.3 Relevant MOs for 2-naphtholate.
La
13.2 Excited-state Proton Transfer (ESPT)
in the position of the lowest excited state, depending upon the site of substitution. For 1-naphthol the lowest energy state is La and for 2-naphthol Lb. The photophysics of 1-naphthol is complicated by a pronounced proton quenching, which is manifested by the near absence of neutral fluorescence at all pHs and by a pKa* of 0.5 [11]. Years ago, we postulated that forward proton transfer to give 1-naphtholate was accompanied by reprotonation in the distal ring. The LUMO represented in Fig. 13.3 suggested that reprotonation should occur at C-5 or C-8. Indeed, we observed that 1-naphthol undergoes efficient H/D exchange at C-5 and C-8, with significant preference for the C-5 position [12]. In contrast, 2-naphthol exhibits little or no proton quenching and a “normal” pKa* of 2.8, a fact which has been attributed to the diffuse nature of the latter and a more localized La for the former. We propose that adiabatic protonation yields a highly delocalized tetraenone (see Fig. 13.4), which undergoes rapid internal conversion. In contrast, adiabatic protonation of 2-naphtholate is endothermic, yielding a higherenergy cross-conjugated enone. In support of this mechanism, we have synthesized 5-tert-butyl-1-naphthol. Indeed, this molecule undergoes an apparent excited-state (ipso) protonation at C-5 to regenerate 1-naphthol through a process analogous to the quenching of 1-naphthol itself (see Fig. 13.4). O -*
O -R
D+
R
OH
R
D
+
D
R = H, t-butyl Figure 13.4 Exchange at C-5 in 1-naphthol.
Although simple hydroxyarenes such as 1- and 2-naphthol exhibit only modest gains in acidity upon photoexcitation, the quenching behavior of 1-naphthol, together with the theoretical underpinning, suggests that increases in acidity should occur by placement of electron-withdrawing groups at sites of large electron density in the excited state. Thus 5-cyano-, 8-cyano-, and 5,8-dicyano-2-naphthols show greatly increased photoacidity, and Frster acidities down to pKa* of –4.5 and lower have been obtained. These investigations have allowed the extension of proton transfer dynamics from aqueous to nonaqueous solvents and even to the gas phase, allowing a change of solvent from water (R = H in Fig. 13.1) to alcohol (R=alkyl). Interestingly, Agmon et al. predicted that 3,5,8-tricyano-2-naphthol might be the ultimate superphotoacid from this family [13].
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13 Design and Implementation of “Super” Photoacids
13.2.2 “Super” Photoacids
The high acidity of 1-naphthol, coupled with the enhanced basicity at C-5 and C-8, suggested that the introduction of electron-withdrawing groups at these positions should lower the energy of the conjugate base and produce even higher acidities. Although the nitro group should be the most electron-withdrawing, nitroarenes are notoriously photoactive. Therefore, we concentrated our initial efforts on the more stable cyano and methanesulfonyl groups. Initially, 5-cyano-1-naphthol (5CN1) and 5,8-dicyano-1-naphthol (DCN1) were prepared but were discovered to undergo rapid quenching, a phenomenon we associate with a protonation (presumably on nitrogen) similar to the result observed in 1-naphthol. Also synthesized and studied were 5-, 6-, 7-, and 8-cyano-2-naphthols (5CN2, 6CN2, 7CN2, and 8CN2) and 5-methanesulfonyl-2-naphthol (5MSN2). With a Hammett r-value for the methanesulfonyl group nearly identical to that for cyano, we did not see differences in photophysics between 5CN2 and 5MSN2 and abandoned further work with methanesulfonyl groups, although 5-methanesulfonyl-1-naphthol provided a first experimental verification of a theoretical prediction of a kinetic transition in reversible binding reactions, driven by the difference in effective lifetimes of the bound and unbound states [14] (see below). In contrast, 5,8-dicyano-2naphthol (DCN2) [15], with a calculated Frster pKa* of –4.5, has become the workhorse for our studies in nonaqueous solvents. For 2-naphthol, substitution in the 5 and 8 positions apparently adds additional vibronic modes that promote switching of the La and Lb states. This supposition has been confirmed by gas phase measurements [16]. The “true” acidity of a photoacid is a difficult-to-obtain quantity. Formally, since pKa* = –log(kpt/k-pt), where kpt and k–pt are overall rates for forward and back proton transfer, respectively, the pKa* obtained from the Frster calculation must be considered approximate. k
DSE
þ þ dis ! ! R*OH ½R*O *:::H ðr¼aÞ R*O þ H k
(13.4)
rec
Another approach is fluorescence titration, in which the emission from the conjugate base is examined as a function of pH. Again, the presence of competing processes may lead to erroneous results. In the scheme represented by Eq. (13.4), because of the electrostatic field generated by the counterion upon dissociation, an adiabatic recombination occurs to regenerate the excited acid (R*OH), which again dissociates and causing apparent nonexponential behavior for the excited state decay. In order to treat this problem, Huppert and Agmon used the Debye– Smoluchowski equation (DSE) to obtain the pKa*s [17] This approach allows pKa* determination from a single kinetic measurement at a neutral pH: pKa * ¼ log
kdis expðRD =aÞ krec
(13.5)
13.2 Excited-state Proton Transfer (ESPT)
In Eqs. (13.4) and (13.5) kdis and krec are dissociation and recombination rate constants within a contact ion pair of a radius a, RD is the Debye radius. For the systems with pronounced geminate recombination it is possible to fit nonlinear R*OH decay to a numerical solution of a system of DSE equations [18]. Equation (13.5) is a vivid example of the difference between excited-state electron and proton transfer studies. In the latter case both kinetic and thermodynamic parameters of the process could be determined directly from the same experiment, while for electron transfer DG of the reaction is usually estimated from electrochemical or other data. In collaboration with Huppert, we were able to determine the pKa*s by laser spectroscopy (Table 13.1). What emerges from this analysis is that (i) the measured pKa*s are higher than the calculated ones, and (ii) substituents at C-5 and C-8 are more effective at lowering pKa* for either 1- or 2-naphthol.
Table 13.1 Excited-state equilibrium constants for cyano-substituted 2-naphthols.
Compound
pKa* (DSE)
DCN2
pKa* (Frster)
pKa*(fluor.)
–4.5
5CN2
–0.75
–1.2
1.7
6CN2
–0.37
0.2
0.5
7CN2
–0.21
–1.3
2.0
8CN2
–0.76
–0.4
0.7
N2
2.8
In principle, 6-hydroxyquinoline (6HQ), which has a nitrogen atom at the position corresponding to C-5 in 2-naphthol, should exhibit enhanced acidity, especially if the nitrogen is converted into an electron-withdrawing group. This is also true for 7-hydroxyquinoline, by analogy with C-8 of 2-naphthol. Indeed, this is what Bardez and, more recently, Leutwyler report – an effect that involves a “hydrogen-bonding wire” [19]. In this case, the increased basicity at nitrogen leads to rapid nitrogen protonation (Fig. 13.5) [20]. Thus the photophysics of this species are characterized by weak emission from the tautomers rather than from the conjugate base, although one can estimate a pKa* for the excited-state quinolinium species as approaching –13. N-Methyl hydroxyquinolinium species, which are isoelectronic to the protonated form of hydroxyquinolines, have similar properties. These compounds demonstrate remarkable increased photoacidity – protolytic photodissociation in water
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13 Design and Implementation of “Super” Photoacids
O
T*
NH (O)
-O
<5 ps ONLY FOR HQs
46 ps
10 ps NH (O)+
HO
Excited state
NH (O)+
R
R
HO
25 ps
HO
N (O)
R
R
R
-O
HO NH (O) +
-O
<5 ps N (O)
Ground state
decays at 0.9 ns
R
N (O)
R
N (O)
R
Figure 13.5 Tautomerization vs. proton transfer in hydroxy-quinolines and their N-Oxides.
occurs at 2 ps [21]. This rate for intermolecular ESPT to water is among the fastest reported to date. An ultrafast ESPT from this compound was also observed in the series of alcohols [22]. Several flavilium ions and anthocyanins [23], all carrying positive charge on the aromatic ring next to the phenolic one, are also reported to be superphotoacids with ultrafast ESPT to water. An alternative approach, which avoids creating an organic salt, is to modify the acidity of 6HQ by converting the latter into 6-hydroxyquinoline-N-oxide (6HQNO), preserving the electronegativity of the molecule. 2-Methyl-6-hydroxyquinoline-N-oxide (MeHQNO) was also prepared. Our studies with these molecules indicate a significant increase in acidity over the corresponding 5CN2 and the resulting photoproduct is an anion, not tautomer (Fig. 13.6) [24]. This happens due to oxidation of the nitrogen atom that diminishes its strong photobasicity, so in contrast to 6HQ no excited-state protonation is observed in neutral and basic media (Fig. 13.5). A complication of this chemistry is the slow but significant photodeoxygenation to yield 6HQ, as well as the known rearrangement to yield a quinolinone. Although the latter process can be inhibited by substitution at C-2 with methyl, the deoxygenation still proceeds slowly. Aromatic N-oxides, including a few hydroxyaromatic compounds [25], have a wide application in life sciences studies, so the combination of enhanced ESPT reactivity and efficient photodeoxygenation in combination with bright fluorescence makes hydroxyaromatic N-oxides possible candidates for the modulation of biological activity with simultaneous monitoring by fluorescence spectroscopy/microscopy methods.
13.2 Excited-state Proton Transfer (ESPT)
N*
(a)
C* A*
T*
HO
Normalized emission
N
(b)
350
400
450
500
550
600
CH3
in methanol neutral 650 + HClO4 + NaOH HO N
C H3
O
350
400
450
500
nm
550
600
650
Figure 13.6 Emission from (a) MeHQ and (b) MeHQNO. N*, C*, A*, and T* correspond to neutral, cation, anion, and tautomer.
Notwithstanding the remarkable acidity of cyanated naphthols and hydroxyquinolines N-oxides, which allows them to transfer protons at rates competitive with excited-state decay to a number of organic acceptors, including sulfoxides and alcohols, the rates are still too sluggish to initiate bimolecular reactions (see below). We have synthesized the even more acidic perfluoroalkanesulfonylnaphthols, including 6-perfluorohexanesulfonyl-2-naphthol (6pFSN2) and 6-trifluoromethanesulfonyl-2-naphthol [26]. However, aggregation with these molecules has become a significant problem and has, up to now, defeated their use in proton transfer studies.
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13 Design and Implementation of “Super” Photoacids
13.2.3 Fluorinated Phenols
Other phenols with electron-withdrawing groups have been reported to have behavior reminiscent of “super” photoacids. However, a complication has proved to be photohydrolysis of the carbon – fluorine bond, leading to carboxylic acid product. Thus trifluoromethylnaphthols undergo photohydrolysis to yield naphthalene carboxylic acids [27]. Boule has reported that fluorophenols undergo photodehalogenation to products of rearrangement and hydrolysis [28]. A recent report has appeared on the use of a fluorinated phenol [29] as a reversible photocatalyst for cationic polymerization of phenyl glycidyl ether. However, this report must be viewed with a great deal of skepticism, given the tendency for photohydrolysis of phenols. Thus irreversible formation of traces of acid which induce polymerization through a chemically amplified mechanism cannot be ruled out. Similarly, the polymerization of formaldehyde by low-temperature irradiation of a nitrophenol [30] may have similar mechanistic origins. Nevertheless, the latter reactions provide tantalizing support for the use of “super” photoacids in carrying out proton-initiated reaction.
13.3 Nature of the Solvent 13.3.1 Hydrogen Bonding and Solvatochromism in Super Photoacids
Proton transfer in both ground and excited states includes formation and breaking of hydrogen bonds. The degree of prior formation of hydrogen-bonded complexes and redistribution of the hydrogen bonds after excitation can be estimated using solvatochromic analysis of the absorption/excitation and the emission spectra. A Kamlet–Taft approach [31] allows separation of general (polar) and specific (H-bonding) solvation responsible for ground- and excited-state stabilization of super photoacids that have large excited-state dipole moments in the excited state. Using this method, we [8, 32] and others [33] have determined several types of hydrogen bonds of super photoacids with solvents (HS) and estimated their relative strengths. In amphoteric solvents, such as water and alcohols, two types of hydrogen bonds exist for neutral super photoacids (Fig. 13.7). Type 2 is much higher is energy than type 1 and makes a major contribution to the solvatochromism of ground- and excited-state species. The type 1 bond is totally cleaved in the excited state which supports the mechanism of intramolecular charge transfer after excitation. Stabilization of the excited state anion via a type 3 hydrogen bond is probably one of the major factors determining the relative reactivity of super photoacids. The time scale of type 2 bond strengthening in 8-hydroxypyrene-1,3,6tris(dimethylsulfonamide), or, in other words, selective solvation due to H-bonding, is amazingly fast, about 55 fs [33].
13.3 Nature of the Solvent
HS
HS
1 O H
3 2
SH
-
O
ESPT
+ HSH+
C
C
N
N
Figure 13.7 Hydrogen bonds in 5CN2.
13.3.2 Dynamics in Water and Mixed Solvents
As was mentioned before, in bulk water the pKa* of super photoacids is negative, so protolytic photodissociation is exergonic and should not depend on the acid nature. Indeed, similar to electron-transfer reactions [1] a Bronsted-type plot kpt (or kdis) vs. pKa* reaches a constant limiting value in the region of exergonic proton transfer. Several known characteristic ESPT dissociation times of super photoacids in water approach minimal values of a few picoseconds [21, 23, 34, 35]. These values are close to the longitudinal relaxation time around single-water-molecule charge in water that is probably the rate-limiting step of intermolecular ESPT in solution. One of the earliest and most persistent questions concerning ESPT has been the anomalous solvent effect. The simple naphthols exhibit efficient proton transfer in water but not in alcohols. This observation is surprising, given the fact that the proton affinity of the simple alcohols is higher than that for water [36]. At intermediate water concentrations, the relationship between the rate of proton transfer and water concentration in methanol or ethanol solution is roughly fourth-order. The nonlinear response to water concentration has led to a series of papers on the structure of water (and other solvents) during proton transfer. Robinson [37] postulates that the proton transfer in aqueous solvent systems is the result of formation of a water cluster of order 4–1, that is, the generation of a tetrahedral coordination sphere for the proton that consists only of water molecules. Thus the underlying kinetics reflect the rate-limiting formation of a water cluster at the rate determining step. Huppert and Agmon have challenged Robinson’s conclusions and the intervention of solvent clustering [38]. Rather, they postulate that the kinetics simply reflect the number of hydrogen bonds, both made and broken, required to facilitate the proton transfer at the transition state. The fact that water provides two hydrogen bonds, while methanol only one, is critical in that methanol alone must “give up” a hydrogen bond in order to form a new one, making the rate noncompetitive with excited-state decay. This distinction is subtle, but has important consequences for the kinetics. We have synthesized molecules in which an intramolecular solvating group, a hydroxyalkane, serves to substitute for one molecule of solvent, thus reducing the molecularity of the pro-
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13 Design and Implementation of “Super” Photoacids
ton transfer. The resulting increase in proton transfer rate serves to demonstrate the importance of entropy in controlling the proton transfer transition state [39]. Recently, Hynes has used high-level calculations to make predictions about the trajectory of proton transfer and the role of solvent reorganization in the evolution of the reaction coordinate [40]. From these calculations emerges a picture that is consistent with the Huppert–Agmon model. To study solvent effects in aqueous mixtures we have used the non-hydrogenbond-donating solvent tetrahydrofuran. With 5CN2, the molecularity with respect to water is lowered to 3, while that for DCN2 is lowered to 2 (Fig. 13.8). Clearly there is a relationship between molecularity and driving force. It is also interesting that the molecularity, or order, with respect to water, is entirely contained in the hydrogen bonds donated by water, not alcohol, since there is no methanol present.
14
CN OH
12 10
Φo/Φf
428
CN
OH
8 CN
6 OH
4 2 0
0
1
2
3
4
5
6
[H2O], M Figure 13.8 Effect of water on proton transfer from N2, 5CN2, and DCN2.
In methanol–water mixtures where ESPT is observed already in the absence of water, we separated the methanol- and water-dependent components of the protolytic dissociation rate constant for several photoacids [41]. As in THF–water mixtures, the water-dependent component has a power-law dependence on water concentration. The magnitude of the exponent decreased with the increase in photoacid strength. 13.3.3 Dynamics in Nonaqueous Solvents
A problem with 1- and 2-naphthol as substrates is that proton transfer is slower than solvent reorganization and, in any event, not observed in nonaqueous abasic
13.3 Nature of the Solvent
solvents. In contrast, super photoacids exhibit anion fluorescence in a wide array of anhydrous solvents, including alcohols, as shown in the steady-state emission shown in Fig. 13.9. With superphotoacids, proton transfer still occurs efficiently, even at low temperatures in alcohols. The Arrhenius plot of proton transfer exhibits a two-stage process: (i) a nearly barrierless solvent-dependent process near room temperature and above and (ii) a ca. 3 kcal mol–1 barrier at low temperatures which is solvent independent (Fig. 13.10) [42]. The preexponential term at room temperature represents the proton transfer coordinate. At low temperature, solvent reorganization is rate-limiting. Thus we have for the first time observed proton transfer which is rate-limited by solvent relaxation, which supports the Hynes model in methanol [14]. Most curious is the presence of nearly identical kinetic deuterium isotope effects for both steps, an observation that is consistent with the hydrogen bonded network being involved both in solvent reorganization and in the proton transfer event itself. Similar effects were observed by Peon et al. in the symmetrical system, i.e. abstraction of proton from alcohols by super photobases (carbenes) was also rate limited by solvent relaxation [43].
Figure 13.9 Steady-state emission of DCN2 in simple alcohols.
Nonlinear behavior is also observed in the wide-range (0.1–2.5 GPa) pressure dependence of the ESPT rate of DCN2 in alcohols [44]. At low pressure, the protolytic photodissociation rate slightly increases, reaching the maximum value. With further pressure increase this rate decreases below the initial value at atmospheric pressure (Fig. 13.11). To explain the unique nonexponential dependence of ESPT rate constants on pressure, as well as temperature, Huppert et al. have developed an approximate stepwise two coordinate proton-transfer model that bridges the high-temperature nonadiabatic proton tunneling limit with the rate constant kNA dis
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13 Design and Implementation of “Super” Photoacids
MeOH EtOH PrOH
10.0 9.6
Figure 13.10 Arrhenius plot for photoinduced proton transfer from DCN2 to alcohols. Dashed line represents 25 C.
9.2
log kdis
430
8.8 8.4 8.0 7.6 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5
1000/T
Figure 13.11 Fit to the stepwise two-coordinate model according to Eq. (13.6) as a function of pressure (solid line) along with the experimental data for DCN2 NA and kAD are shown as dashed and dotted lines, respectively. in ethanol. kdis dis Reproduced from Ref. [44a] by permission of the American Chemical Society.
13.3 Nature of the Solvent
and the low-temperature adiabatic solvent controlled limit with rate constant kAD dis (Eq. (13.6)). kdis ðT; PÞ ¼
AD kNA dis ðT; PÞkdis ðT; PÞ NA kdis ðT; PÞ þ kAD dis ðT; PÞ
(13.6)
A decrease in the protolytic photodissociation rate of DCN2 with increasing pressure is also observed in supercritical CO2/methanol mixtures with constant methanol molarity and molality [45]. This effect is currently under investigation. Another interesting aspect of the excited-state proton transfer kinetics is the nonexponential long-time asymptotic behavior of R*OH and R*O– fluorescence. This effect was initially observed for R*OH decay of pyranine in water and was quantitatively described by the diffusion-influenced geminate recombination [17]. Super photoacids capable of ESPT in a wide array of nonaqueous solvents expanded the range of tunable kinetic regimes. Agmon and coworkers predicted theoretically [46] and one demonstrated experimentally [14] that, depending on the ratio of the proton dissociation rate constant and fluorescence lifetimes of R*OH and R*O–, several asymptotic regimes are possible for photoacids. For instance, not only the most common power-law t–3/2 decay, but also 1/t and even exponential growth are seen for R*OH asymptotic behavior! Therefore, excitedstate proton transfer serves as unique tool for verifying interesting aspects of modern theoretical chemical kinetics. 13.3.4 ESPT in the Gas Phase
Gas-phase spectroscopic investigations of photoacids and their clusters with various solvent molecules are extremely important because they offer several opportunities unavailable in the liquid phase [16, 19c, 47] Our studies of gas phase spectroscopy and ESPT kinetics of super photoacids expanded the range of molecular systems systematically investigated using commercially available 1- and 2-naphthols. In the gas phase excitation and emission spectra of isolated molecules are so structured that the fine features of the rotation isomers can be clearly identified. We have found extensive spectroscopic indications of vibronic coupling between La and Lb states that, by analogy with 1-naphthol, is probably one of the main factors responsible for the ESPT triggering. Such coupling adds more polar La character to the initially excited low polar Lb state [16a]. Another important advantage of the molecular beams is the possibility of selective generation and investigation of the photoacid–solvent clusters of the controlled molecular composition. Clusters of 5CN2 with various numbers of water, ammonia, methanol and DMSO molecules, generated in a molecular beam, have been investigated by resonant two-photon ionization and fluorescence spectroscopies (Fig. 13.12) [16a]. We have observed an interesting correlation between the strength of the photoacid and the ESPT size threshold. In 5CN2–ammonia clusters the threshold for ESPT is either 3 or 4 ammonia molecules, while for
431
432
(a)
13 Design and Implementation of “Super” Photoacids
(b) Figure 13.12 Fluorescence spectra of some (a) 5CN2–(NH3)n and (b) 5CN2–(H2O)n cluster distributions. The mass spectra corresponding to the fluorescence spectra are inset on the left. Red-shifted ESPT emission appears for n (a) > 3 or 4, and (b) > 8–10. Excitation was at 29100 cm–1 for spectra C–H, and ionization was at 36350 cm–1. The largest, rightmost peak in each spectrum is
predominantly scattered laser excitation light. The free molecule was excited at the transrotamer origin, as was the n = 1 cluster. The dashed line(s) in (a) indicates the blue shift of the ESPT emission with increasing cluster size, and in (b) helps to compare the position and shape of the molecular emission. Reproduced from Ref . [16a] by permission of the American Chemical Society.
1-naphthol-ammonia complexes it is 4. A more pronounced effect of increased photoacidity is observed in 5CN2–(H2O)n clusters. For this strong photoacid ESPT appears at n » 10, as compared to 25–30 in 1-naphthol. The relatively slow fluorescence rise time of the excited 5CN2 anion in both cases and several other factors may indicate the nonadiabatic model of the ESPT in which dynamic solvent relaxation after photoexcitation is a key aspect of the EPST process [16c]. In contrast to room-temperature solutions and the above two cases no ESPT is observed in 5CN2 clusters with methanol, methanol–water and DMSO. At the same time the steady-state emission of R*OH demonstrated significant bathochromic shift with increasing cluster size. We explain the absence of ESPT by a simple thermodynamic factor. In bulk methanol and DMSO the protolytic photodissociation is endergonic. So, the difference in ESPT reactivity between bulk and clusters could be attributed to significant cooling of the latter, leading to enthalpic effects being dominant. We expect that the strongest photoacid DCN2 will extend the range of gas-phase clusters where intermolecular ESPT is observed.
13.4 ESPT in Biological Systems
13.3.5 Stereochemistry
One of our long-range goals is to provide experiments that allow us to construct models for proton transfer in biological media. Certainly one of the most dramatic aspects of biological systems involving proton transfer is their high stereoselectivity. Thus we wondered if we could find stereospecificity in proton transfer in chiral solvents. The nub of the question is represented in Fig. 13.13, in which we see that, if proton transfer involves interaction between solvent molecules, a transition state involving homochiral solvent molecules will have a different geometry than one involving heterochiral molecules. Thus the proton transfer rates should be different in racemic and nonracemic solvents. This is exactly what we found, with a preference for the homochiral transition state of almost 3:1 [48]. We can see that an enzyme, with its highly structured transition state, should lead to high stereoselectivity for proton transfer. Currently we are investigating chiral photoacids to see if there is a rate dependence of the proton transfer on the chirality of the acceptor. Altogether, we mention that the chirality preservation in the transition state is a prerequisite for stereoselectivity in the photoinduced proton transfer. CN
CN O
H
H
O
O
H
H CN S
H
H O H
O
CN H
S
H
O H
CN O
H
H O H
CN S
H
O H
Figure 13.13 Proton transfer in a chiral solvent.
13.4 ESPT in Biological Systems
Despite the paucity of examples of excited-state proton transfer in biology, we believe that ESPT has great potential for the development of tools to examine in vitro and in vivo proton transfer. Almost by definition, biological media represent nonhomogeneous reaction media which serve to test theories of proton transfer and present opportunities to develop methods for examining the dynamics of proteins. Several examples of biological photoacids have begun to emerge:
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13 Design and Implementation of “Super” Photoacids
Our attention was initially drawn to a medically significant group of hydroxyquinolines, the camptothecin family of topoisomerase I inhibitors [49]. 10-Hydroxycamptothecin (10HCT) and its Mannich derivative topotecan exhibit fluorescence behavior that is, on the basis of our previous studies, entirely rationalizable, if previously unrecognized, as involving prototropic behavior [50]. Whether such behavior also mirrors differences in bioavailability is still a matter of conjecture. The search for new pharmaceuticals and biological mechanisms is beyond the scope of this chapter. Nevertheless, we were intrigued by the prospect that 10-hydroxycamptochecin and topotecan could exhibit excited-state proton transfer in biological media and thus provide insight into the action of proton transfer probes in biology. Indeed, the emission of 10HCT is different from that of the parent 6HQ, and very similar to 6HQNO showing ESPT in pure methanol, isoemissive fluorescence spectra in methanol–water mixtures, and exhibiting no excited-state protonation at nitrogen (Fig. 13.14). Clearly, the additional electron-withdrawing pyridone group acts to diminish the excited-state basicity of the quinoline nitrogen [51], and acid–base photochemistry of 10HCT resembles that of 6HQNO (Fig. 13.5). In water-rich solutions the protolytic photodissociation rate was more than 85 1 ns–1, clearly placing 10HCT among other super photoacids. Despite the presence of several acid–basic groups, the excited-state proton transfer behavior is “normal”, exhibiting the typical nanosecond power-law asymptotic dependence common for such systems. In the shorter time domain, an intermediate with the lifetime of 3 ps was detected in a time-resolved pump–probe signal of R*OH form. We may associate it with the recently suggested “loose” hydrogenbonded complex, therefore making ESPTa three-step process [52].
1.0
R*OH
HO
O
pure MeOH
N N
Fluorescence intensity, a.u.
434
0.8
O 10HCT HO
30 mol % H2O
0.6 -
R*O
0.4
0.2
0.0
400
450
500
550
Wavelength, nm Figure 13.14 Emission from 10HCT.
600
650
O
13.4 ESPT in Biological Systems
13.4.1 The Green Fluorescent Protein (GFP) or “ESPT in a Box”
The green fluorescent protein (GFP) of the jellyfish Aequorea Victoria has attracted great interest as a biological fluorescence marker and as one of the few demonstrated examples of excited-state proton transfer in nature [53]. The wild-type chromophore p-hydroxybenzylidenediazolone is formed without co-factors via posttranslational cyclization followed by an autoxidation of a tripeptide unit of the 238 amino acid polypeptide sequence (Fig. 13.15) [54]. Single-crystal X-ray diffraction reveals that the chromophore is threaded through the center of an 11-stranded b-barrel forming a coaxial helix which stabilizes the chromophore from the surrounding medium, including water [55, 56]. Additional noncovalent coupling of the chromophore to the protein backbone is facilitated via an extended hydrogenbonded network [57]. Q183
R96 H N R 168 N R H148 H R N
R
+
H
R
N
H N
H
O
O
O
H
O
R O
H
N
Q69
H
w22
O
R
N
O
H
S205
Q94
H
O
O 146 R
H
O
N H
N
O
H
62 203 R
N
R
H
N
O
-
E222
H
O H
H
O
w19 H
H O O w12 w27 H H NH
R
R 68
Figure 13.15 GFP active-site structure. Adapted from Ref. [57]. Hydrogens added for emphasis.
At room temperature, wtGFP (wild-type GFP) exhibits two main absorption peaks with maxima at 398 nm (band A) and 478 nm (band B). Several groups have studied the excited state dynamics of wtGFP [58–63]. These led to the conclusion that the two visible absorption bands of the wtGFP correspond to protonated and deprotonated ground-state conformations, while upon photoexcitation the acid form A rapidly deprotonates to form the B form. In addition, ultrafast kinetics suggests the presence of a third intermediate I which involves a proton transfer without conformational relaxation to the B form [64].
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13 Design and Implementation of “Super” Photoacids
Although the vast majority of users of GFP and its derivatives can use these probes without resort to the mechanistic details, the unique barrel structure of the chromophore “box” makes this an ideal system to study proton transfer in a geometrically rigorously well-defined environment. While previous time-resolved studies of GFP have focused on emission decay at short times up to 150 ps [58–63] Huppert et al have focused on fluorescence at longer times (up to 10 ns). Using the TCSPC technique with a dynamic range of about 4 decades and extending the monitoring range of the emission to much longer times, they find that the fluorescence decay of R*OH is nonexponential up to 10 ns. Using a reversible geminate recombination model to fit the fluorescence data of wtGFP samples, they have concluded that the proton is transferred to the proton accepting moieties (hydroxy groups and waters) that are close to the chromophore. As the proton hops from one proton acceptor site to another, its motion can be approximated by a random walk in three dimensions, and hence a diffusion constant can be assigned to such motion. The proton can also recombine to its original site, the hydroxy group of the wtGFP chromophore, and thus repopulate the protonated form, ROH*, giving rise to the asymptotic power law [65]. Since the excited-state pKa* of the GFP chromophore is less than zero already in the protein, then this chromophore, by analogy with the hydroxycamptothecin outlined above, also falls into the category of biological “super” photoacids. Isolated synthetic GFP and its derivatives do not fluoresce outside the b-barrel at room temperature due to very effective internal conversion related to isomerization along the double bond [59–63]. Deep understanding of the photophysics of these dyes as well as synthesis of their fluorescence derivatives capable of ESPT are our immediate goals. We anticipate further studies in biological proton transfer will be facilitated by these powerful new photophysical tools.
13.5 Conclusions
The studies performed to date suggest that “super” photoacids have an important role to play in unraveling the surprisingly complex dynamics of proton transfer, particularly in organized media for which diffusion is less straightforward. Such studies would be facilitated by photoacids with even stronger acidities but without side reactions. Particularly tantalizing is the possibility of time-resolved proton transfer studies of relevance to proton-catalyzed biological reactions, which demands coupling of high-photoacidity with well-characterized protein environments. Such studies are necessarily still in their infancy.
Acknowledgements
Support of this research by the U.S. National Science Foundation, under Grant CHE-0456892, is gratefully acknowledged.
References
References 1 Rehm, D.; Weller, A. Isr. J. Chem. 1970,
8, 259–271. 2 (a) Frster, T. Z. Elektrochem. 1950, 54, 42; (b) Weller, A. Z. Elektrochem. 1952, 56, 662–668. 3 Agmon, N. Chem. Phys. Lett. 1995, 244, 456–462. 4 Tolbert, L. M., Solntsev, K. M. Acc. Chem. Res. 2002, 35, 19–27. 5 For reviews, see (a) Ireland, J. F.; Wyatt, P. A. H. Adv. Phys. Org. Chem. 1976, 12, 131–221; (b) Schulman, S. G. Fluorescence and Phosphorescence Spectroscopy, Pergamon Press, Elmsford, NY, 1977; (c) Huppert, D.; Gutman, M.; Kaufman, K. J. in Laser Studies of Proton Transfer, Advances in Chemical Physics, Jortner, J.; Levine, R.D., Rice, S.A., Eds.; Wiley, New York, 1981, Vol. 47; (d) Shizuka, H. Acc. Chem. Res. 1985, 18, 141–147; (e) Arnaut, L. G.; Formosinho, S. J. J. Photochem. Photobiol. A 1993, 75, 1–20; (f) Agmon, N. J. Phys. Chem. A 2005, 109, 13–35. 6 Tolbert, L. M. Acc. Chem. Res. 1986, 19, 268–273. 7 (a) Flegel, M.; Lukeman, M.; Huck, L.; Wan, P. J. Am. Chem. Soc. 2004, 126, 7890–7897; (b) Lukeman, M.; Veale, D.; Wan, P.; Munasinghe, V. R. N.; Corrie, J. E. T. Can. J. Chem. 2004, 82, 240–253; (c) Shukla, D.; Lukeman, M.; Shi, Y.; Wan, P. J. Photochem Photobiol. A 2002, 154, 93–105; (d) Budac, D.; Wan, P. Can. J. Chem. 1996, 74, 1447–1464; (e) Wan, P.; Shukla, D. Chem. Rev. 1993, 93, 571–584; (f) Budac, D.; Wan, P. J. Org. Chem. 1992, 57, 887–894. 8 Solntsev, K. M.; Huppert, D.; Tolbert, L. M.; Agmon, N. J. Am. Chem. Soc. 1998, 120, 7981–7982. 9 Weller, A. Prog. React. Kinet. 1961, 1, 189–214. 10 Lewis, F. D.; Crompton, E. M. J. Am. Chem. Soc. 2003, 125, 4044–4045. 11 (a) Pines, E.; Tepper, D.; Magnes, B.-Z.; Pines, D.; Barak, T. Ber. Bunsen-Ges. Phys. Chem. 1998, 102, 504–510; (b) Pines, E.; Fleming, G. R. Chem. Phys. 1994, 183, 393–402.
12 Webb, S. P.; Philips, L. A.; Yeh, S. W.;
Tolbert, L. M.; Clark, J. H. J. Phys. Chem. 1986, 90, 5154–5164. 13 Agmon, N.; Rettig, W.; Groth, C. J. Am. Chem. Soc. 2002, 124, 1089–1096. 14 Solntsev, K. M.; Huppert, D., Agmon, N. Phys. Rev. Lett. 2001, 86, 3427–3430. 15 (a) Tolbert, L. M.; Haubrich, J. E. J. Am. Chem. Soc. 1994, 116, 10593–10600; (b) Tolbert, L. M.; Haubrich, J. E. J. Am. Chem. Soc. 1990, 112, 8163–8165. 16 (a) Knochenmuss, R.; Solntsev, K. M.; Tolbert, L. M. J. Phys. Chem. A 2001, 105, 6393–6401; (b) Knochenmuss, R.; Fischer, I.; Luhrs, D.; Lin, Q. Isr. J. Chem. 1999, 39, 221–230. 17 (a) Pines, E.; Huppert, D.; Agmon, N. J. Chem. Phys. 1988, 88, 5620–5630; (b) Agmon, N.; Pines, E.; Huppert, D. J. Chem. Phys. 1988, 88, 5631–5638. 18 Krissinel, E. B.; Agmon, N. J. Comput. Sci. 1996, 17, 1085–1098. 19 (a) Bardez, E. Isr. J. Chem. 1999, 39, 319–332; (b) Bardez, E.; Fedorov, A.; Berberan-Santos, M. N.; Martinho, J. M. G. J. Phys. Chem. A 1999, 103, 4131–4136; (c) Tanner, C.; Manca, C.; Leutwyler, S. Science 2003, 302, 1736–1739. 20 Poizat, O.; Bardez, E.; Buntinx, G.; Alain, V. J. Phys. Chem. A 2004, 108, 1873–1880. 21 Kim, T. G.; Topp, M. R. J .Phys. Chem. A 2004, 108, 10060–10065. 22 Prez Lustres, J. L. personal communication. 23 Moreira, P. F., Jr.; Giestas, L.; Yihwa, C.; Vautier-Giongo, C.; Quina, F. H.; Maanita, A. L.; Lima, J. C. J. Phys. Chem. A 2003, 107, 4203–4210. 24 Solntsev, K. M.; Clower, C. E.; Tolbert, L. M.; Huppert, D. J. Am. Chem. Soc. 2005, 127, 8534–8544. 25 (a) Maklashina, E.; Cecchini, G. Arch. Biochem. Biophys. 1999, 369, 223–232; (b) Rothery, R. A.; Blasco, F.; Weiner, J. H. Biochemistry, 2001, 40, 5260–5268; (c) McMillian, M. K.; Li, L.; Parker, J. B.; Patel, L.; Zhong, Z.; Gunnett, J. W.; Powers, W. J.; Johnson, M. D. Cell Biol. Toxicol. 2002, 18, 157–173; (d) Sim-
437
438
13 Design and Implementation of “Super” Photoacids kovic, M.; Frerman, F. E. Biochem. J. 2004, 378, 633–640; (e) Reyes, R.; Martinez, J. C.; Delgado, N. M.; Merchant-Larios, H. Arch. Androl. 2002, 48, 209–219; (f) Handbook of Fluorescent Probes and Research Products, 9th Edn., Haughland, R. P.; Ed., Molecular Probes, Eugene, OR, 2003, Ch. 15.2. 26 (a) Kowalik, J.; VanDerveer, D.; Clower, C.; Tolbert, L. M. Chem. Commun. 1999, 2007–2008; (b) Clower, C.; Solntsev, K. M.; Kowalik, J.; Tolbert, L. M.; Huppert, D. J. Phys. Chem. A 2002, 106, 3114–3122. 27 Seiler, P.; Wirz, J. Tetrahedron Lett. 1971, 1683–1686. 28 Boule, P.; Richard, C.; David-Oudjehani, K.; Grabner, G. Proc. Indian Acad. Sci., Chem. Sci. 1997, 109, 509–519. 29 Hino, T.; Endo, T. Macromolecules 2004, 37, 1671–1673. 30 Mansueto, E. S.; Wight, C. A. J. Am. Chem. Soc. 1989, 111, 1900–1901. 31 Kamlet, M. J.; Abboud, J.-L. M.; Abraham, M. H.; Taft, R. W. J. Org. Chem. 1983, 48, 2877–2887. 32 Solntsev, K. M.; Huppert, D.; Agmon, N. J. Phys. Chem. A 1999, 103, 6984–6997. 33 Pines, E.; Pines, D.; Ma, I.-Z.; Fleming, G. R. ChemPhysChem 2004, 5, 1315–1327. 34 Pines, E.; Pines, D.; Barak, T.; Magnes, B.-Z.; Tolbert, L. M.; Haubrich, J. Ber. Bunsen.-Ges. Phys. Chem. 1998, 102, 511–517. 35 Lewis, F. D.; Sinks, L. E.; Weigel, W.; Sajimon, M. C.; Crompton, E. M. J. Phys. Chem. A 2005, 109, 2443–2451. 36 Meot-Ner, M. J. Am. Chem. Soc. 1992, 114, 3312–3322. 37 (a) Lee, J.; Robinson, G. W.; Webb, S. P.; Philips, L. A.; Clark, J. H. J. Am. Chem. Soc. 1986, 108, 6538–6542; (b) Yao, S. H.; Lee, J.; Robinson, G. W. J. Am. Chem. Soc. 1990, 112, 5698–5700; (c) Krishnan, R.; Lee, J.; Robinson, G. W. J. Phys. Chem. 1990, 94, 6365–6367. 38 Agmon, N.; Huppert, D.; Masad, A.; Pines, E. J. Phys. Chem. 1991, 95, 10407–10413. 39 Tolbert, L. M.; Harvey, L.C.; Lum, R. C. J. Phys. Chem. 1993, 97, 13335–13340.
40 (a) Gertner, B. J.; Peslherbe, G. H.;
Hynes, J. T. Isr. J. Chem. 1999, 39, 273–281; (b) Ando, K.; Hynes, J. T. J. Mol. Liq. 1995, 64, 25–37; (c) Ando, K.; Hynes, J. T.; in Structure, Energetics and Reactivity on Aqueous Solutions, Cramer, C. J.; Truhlar, D. G., Eds.; ACS Books, Washington DC, 1994. 41 Solntsev, K. M.; Huppert, D.; Agmon, N.; Tolbert, L. M. J. Phys. Chem. A 2000, 104, 4658–4669 42 (a) Carmeli, I.; Huppert, D.; Tolbert, L. M.; Haubrich, J. E. Chem. Phys. Lett. 1996, 260, 109–114; (b) Cohen, B.; Huppert, D. J. Phys. Chem. A 2000, 104, 2663–2667. 43 Peon, J.; Polshakov, D.; Kohler, B. J. Am. Chem. Soc. 2002, 124, 6428–6438. 44 (a) Koifman, N.; Cohen, B.; Huppert, D. J. Phys. Chem. A 2002, 106, 4336–4344; (b) Genosar, L.; Leiderman, P.; Koifman, N.; Huppert, D. J. Phys. Chem. A. 2004, 108, 309–319. 45 Nunes, R.; Arnaut, L. G.; Solntsev, K. M.; Tolbert, L. M.; Formosinho, S. J. Am. Chem. Soc. 2005, 127, 11890–11891. 46 Gopich, I. V.; Solntsev, K. M.; Agmon, N. J. Chem. Phys. 1999, 110, 2164–2174. 47 Knochenmuss, R.; Fisher, I. Int. J. Mass. Spectrom. 2002, 220, 343–257. 48 Solntsev, K. M.; Tolbert, L. M.; Cohen, B.; Huppert, D.; Hayashi, Y.; Feldman, Y. J. Am. Chem. Soc. 2002, 124, 9046–9047. 49 (a) Mi, Z.; Burke, T. G. Biochemistry 1994, 33, 12540–12545; (b) Mi, Z.; Burke, T. G. Biochemistry 1994, 33, 10325–10336; (c) Burke, T. G.; Malak, H.; Gryczynski, I.; Mi, Z.; Lakowicz, J. R. Anal. Biochem. 1996, 242, 266–270. 50 Tolbert, L. M.; Nesselroth, S. M. J. Phys. Chem. 1991, 95, 10331–10336. 51 (a) Ashkenazi, S.; Leiderman, P.; Huppert, D.; Solntsev, K. M.; Tolbert, L. M. in Femtochemistry and Photobiology, Martin and Hynes, J. T., Eds., Elsevier, Amsterdam 2004, pp. 201–206; (b) Solntsev, K. M.; Sullivan, E. N.; Tolbert, L. M.; Ashkenazi, S.; Leiderman, P.; Huppert, D. J. Am. Chem. Soc. 2004, 126, 12701–12708. 52 Rini, M.; Pines, D.; Magnes, B.-Z.; Pines, E.; Nibbering, E. T. J. J. Chem. Phys. 2004, 121, 9593–9610.
References 53 Zimmer, M. Chem. Rev. 2002, 102, 54
55
56
57
58
59
759–781. (a) Tsien, R. Y. Annu. Rev. Biochem. 1998, 67 509–544, (b) Cubitt, A. B.; Heim, R.; Adams, S. R.; Boyd, A. E.; Gross, L. A.; Tsien, R. Y. Trends Biochem. Sci. 1995, 20, 448–455. Orm, M.; Cubitt, A. B.; Kallio, K.; Gross, L. A.; Tsien, R. Y.; Remington, S. J. Science 1996, 273, 1392–1395. (a) Yang, F.; Moss, L. G.; Phillips, G. N. J. Nature Biotech. 1996, 14, 1246; (b) Suhling, K.; Siegel, J.; Phillips, D.; French, P. M. W.; Leveque-Fort, S.; Webb, S. E. D.; Davis, D. M. Biophys. J. 2002, 83, 3589–3595. Brejc, K.; Sixma, T. K.; Kitts, P. A.; Kain, S. R.; Tsien, R. Y.; Orm, M.; Remington, S. J. Proc. Natl. Acad. Sci. USA 1997, 94, 2306–2311. Chattoraj, M.; King, B. A.; Bublitz, G. U.; Boxer, S. G. Proc. Natl. Acad. Sci. USA 1996, 93, 8362–8367. (a) Voityuk, A. A.; Kummer, A. D.; Michel-Beyerle, M.-E.; Rosch, N. Chem. Phys. 2001, 269, 83–91; (b) Kummer, A. D.; Wiehler, J.; Rehaber, H.; Kompa, C.; Steipe, B.; Michel-Beyerle, M. E. J. Phys. Chem. B 2000, 104, 4791–4798; (c) Voityuk, A. A.; Michel-Beyerle, M. E.; Rosch, N. Chem. Phys. Lett. 1998, 296,
269–276; (d) Youvan, D. C.; MichelBeyerle, M. E. Nature Biotech. 1996, 14, 1219–1220; (e) Kummer, A. D.; Kompa, C.; Lossau, H.; Pollinger-Dammer, F.; Michel-Beyerle, M. E.; Silva, C. M.; Bylina, E. J.; Coleman, W. J.; Yang, M. M.; Youvan, D. C. Chem. Phys. 1998, 237, 183–193. 60 Striker, G.; Subramanian, V.; Seidel, C. A. M.; Volkmer, A. J. Phys. Chem. B 1999, 103, 8612–8617. 61 Winkler, K.; Lindner, J. R.; Subramanian, V.; Jovin, T. M.; Vohringer, P. Phys. Chem. Chem. Phys. 2002, 4, 1072–1081. 62 Litvinenko, K. L.; Webber, N. M.; Meech, S. R. Bull. Chem. Soc. Jpn. 2002, 75, 1065–1070. 63 Cotlet, M.; Hofkens, J.; Maus, M.; Gensch, T.; Van der Auweraer, M.; Michiels, J.; Dirix, G. Van Guyse, M.; Vanderleyden, J.; Visser, A. J. W. G.; De Schryver, F. C. J. Phys. Chem. B 2001, 105, 4999–5006. 64 Wiehler, J.; Jung, G.; Seebacher, C.; Zumbusch, A.; Steipe, B. ChemBioChem 2003, 4, 1164–1171. 65 Leiderman, P.; Ben-Ziv, M.; Genosar, L.; Huppert, D.; Solntsev; K. M.; Tolbert, L. M. J. Phys. Chem. B 2004, 108, 8043–8053.
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Part IV Hydrogen Transfer in Protic Systems
This Section addresses, in two sets of two chapters, two recent developments in proton transfer: the ultrafast vibrational spectroscopic probing of the microscopic details of proton transfer in water and elsewhere, and the emergence of protoncoupled electron transfer reactions as a major reaction class. Nibbering and Pines open in Ch. 14 with ultrafast acid-base reaction dynamics in aqueous solutions, using femtosecond (fs) resolved infrared (IR) spectroscopy to monitor an electronically excited aromatic photoacid, an acetate ion base, and the solvated proton. These optical pump-IR probe experiments thus involve “vibrational markers” to follow the dynamics. At high acetate levels, a bimodal proton transfer emerges between acid and base pairs in close proximity: a sub150fs proton transfer between directly bonded pairs, and a sequential stepwise proton transfer on a picosecond (ps) time scale for acid-base pairs separated by a water bridge. These studies bear on the well-known Eigen mechanism for acidbase chemistry, as well as the Grotthus mechanism of proton transport, here involved in a chemical reaction context. In Ch. 15, Elsaesser continues the theme of ultrafast vibrational spectroscopy as a powerful tool to elucidate hydrogen dynamics. The focus here is on, first, hydrogen bond dynamics in the ground electronic state of complexes, some of which exhibit proton transfer in the excited electronic state, and, second, the direct observation of low frequency vibrations coupled to intramolecular proton transfer in the excited electronic state. Inert rather than protic solvents are used to clearly expose the detailed key vibrational features, unobscured by the broad spectral features of protic solvents. Among the central observations (for a particular enol-keto tautomerization) are, first, that the ground state intramolecular hydrogen bond in this molecule is strongly modulated by a weakly damped low frequency mode, and, second, that the excited state ultrafast proton transfer requires motion among the low frequency vibrational modes, which in fact determines the time scale of the transfer. Hammes-Schiffer expounds in Ch. 16 her group’s theoretical formulation for proton-coupled electron transfer (PCET) mechanism and rates, pointing out the similarities with the separate special limits of electron transfer and (tunneling) proton transfer, and emphasizing the new features of PCET. The latter include the Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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simultaneous importance of two solvent (or environmental) coordinates associated with the electron and proton aspects of the rate process. The resulting rate expressions feature the simultaneous appearance of reorganization energy contributions and of low frequency vibrational contributions, the two naturally following from the involvement of both proton and electron transfer. The power of this approach is illustrated by a number of applications for rate constants and kinetic isotope effects, including an enzyme-catalyzed PCET. Hodgkiss, Rosenthal and Nocera pursue the PCET theme in Ch. 17 in a detailed exposition, illustrated with examples from many areas of chemistry and biochemistry, many involving transition metals. The authors emphasize the connection with hydrogen atom transfer, in its “pure” limit a synchronous, strongly adiabatic coupled transfer of the electron and the proton, without the development of charge separation, i.e. the standard image of hydrogen atom transfer. Away from this limit, the various signatures of the assorted types of PCET are classified, discussed and illustrated, with a particular stress on the simultaneous consideration of mechanism and geometry.
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14 Bimolecular Proton Transfer in Solution Erik T. J. Nibbering and Ehud Pines
14.1 Intermolecular Proton Transfer in the Liquid Phase
Proton transfer between Brønsted acids and bases in aqueous solution is a key chemical process [1–4]. Proton transfer occurs between water molecules at close range e.g. in the autoionization of water [5], in the proton conductivity in water (von Grotthuss mechanism) [6–13], and in acid dissociation in water [14–18]. Neutralization reactions between acid and bases often occur in aqueous solutions and are mediated by water [19]. Water actively takes part in the channelling of protons through membrane proteins [20–22] or in the dynamics of photosensor proteins [23]. It is thus of great importance to investigate the dynamics of proton transfer and the role that the solvent water plays. The ultimate goal is to grasp the microscopic mechanisms determining the time scales and efficiencies of proton transfer. Since the days of “flash spectroscopy” much effort has been dedicated to the elucidation of the dynamics of proton transfer induced by an optical trigger pulse, allowing a well-defined time zero in time-resolved studies [2, 24]. Here, a pump pulse tuned in the ultraviolet or visible (UV/vis) region of the electromagnetic spectrum promotes a molecule to an electronically excited state with a significantly altered electronic charge distribution, causing a prompt hydrogen or proton shift away from the donor side to accepting groups. An early limitation on deciphering the inherent ultrafast dynamics of proton transfer has been the time resolution of time-resolved spectroscopy. The development of picosecond UV/vis spectroscopy in the early 80s marks the beginning of the era of time-resolved proton transfer studies. In the following decade femtosecond spectroscopy became a common tool. In these studies the proton transfer dynamics have been followed typically by monitoring electronic transitions through emission (time correlated single photon counting and up-conversion techniques) or absorbance changes using pump–probe methods with UV/vis probe pulses. Ultrafast UV/vis spectroscopy has until now been used extensively in the case of excited state intramolecular hydrogen or proton transfer (ESIHT/ESIPT) [25–27], where donor and acceptor groups, linked by the hydrogen or proton, are part of the same molecule [28, 29]. The dynamics and microscopic mechanisms of Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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14 Bimolecular Proton Transfer in Solution
ESIHT or ESIPT have been studied in fine detail, see also Chapters 9, 14 and 20, without interference from any additional processes where translation or reorientation of donor and acceptor groups are required to facilitate the hydrogen or proton transfer reaction. This is unlike the situation of intermolecular proton transfer where mutual diffusion of the donor (acid) and acceptor (base) makes up part of the overall reaction dynamics. Since the seminal works of Weller and Eigen, intermolecular proton transfer in solution is understood to be assisted by mutual diffusion of the acid and base molecules towards forming an encounter pair [2–4], after which the proton is exchanged by an “on-contact” reaction rate kr (Fig. 14.1) Only rough estimations of kr have been made due to lack of direct observation methods. Often values in the range of (10 ps)–1–(0.1 ps)–1 have been suggested when acid and base are at a reaction contact radius a of 6 to 8 (see Fig. 14.1). Direct access to the actual proton transfer, however, has remained problematic due to the slower diffusion process, limiting the overall dynamics to the diffusion assisted reaction rate kD. Only when the “on-contact” transfer rate becomes much slower does a transition from diffusion-limited to activation-controlled reaction dynamics occur. As a result, the nature of the contact reaction pair in aqueous solutions has remained an unsolved problem. This is also caused by the many different roles water plays in facilitating bimolecular proton transfer reactions in aqueous solutions. Proton transfer may occur when a proton donor (acid) and a proton acceptor (base) are directly connected by a hydrogen bond, forming the proton transfer reaction coordinate. Alternatively, proton transfer may be achieved through bridging water molecules, either in a concerted fashion or by a sequential, von Grotthuss-type of hopping mechanism. Encounter Stage = Reaction Stage
Diffusion Stage
B-B
B-B
kD
+ +
BB
Diffusion Stage
B -B
+ +
a
reactants
+
BB
3RO-H ROH
k-D
B-B
B-B
+
33-RO-H ROH
kr
+ +
BB-
+
a
reactive complex
+ +
BB
44--
4 4-RO-H RO RO
RO RO-H RO
BB--
+
k’D
HB HB
k-r
+ +
a
k’-D
proton-transfered complex
Figure 14.1 Eigen–Weller model for proton transfer reactions between acids and bases, that react when at contact distance a. (Adapted from Ref. [136].)
+
HB HB
+
a
products
14.2 Photoacids as Ultrafast Optical Triggers for Proton Transfer
14.2 Photoacids as Ultrafast Optical Triggers for Proton Transfer
Photoacids, first investigated by Frster and Weller [2, 30–32], are a class of molecules that exhibit a strong change in acidity upon electronic excitation [33–36]. Examples of photoacid compounds are naphthols, pyrenols and aminopyrenes [34, 37]. Typically, the pKa value of ground state photoacids and the pK*a value of electronically excited photoacids in their first singlet states differ by 5–10 pKa units [38]. A stronger, “super”, photoacidic behavior can be accomplished with electronegative sidegroups enhancing the photoacidity of the functional acidic group of the aromatic molecular system [39–41], see also Chapter 19. As a result photoacids are an ideal means for optically triggering proton transfer reactions [42], where the acids may be excited with optical light pulses as short as a few femtoseconds. Photoacids have been used in geminate recombination and acid–base neutralization studies [2–4] (see following sections), where elementary stages in bimolecular proton transfer can be investigated [37 , 43], and may be even used in pH-jump studies affecting biomolecular systems [44–46]. Upon electronic excitation a photoacid releases its proton to the solvent or a scavenging acceptor, while converting to its conjugate photobase. The origin of photoacidity has until now been a subject of intense debate. The nature of the photoacid electronically excited state charge distribution must be considered in conjunction with the proton accepting solvent, that typically is water. Correlations between rate, equilibrium constant and free energy of proton transfer can be made [47]. Solvatochromic shifts in absorbance and emission can be analysed with the Kamlet–Taft approach [48], providing insight into the dipole moment interactions and the hydrogen bond donating and accepting capabilities of the photoacid states [38, 49–53]. Traditionally the nature of the acidity of the photoacid S1-state has been ascribed to intramolecular charge transfer (CT) from the nonbonding orbital of the hydroxyl oxygen to the aromatic ring p*-orbital [33, 36, 54, 55]. The enhanced acidity in the S1-state is ascribed to the Coulombic repulsion between the partial positive charge on the OH group and in particular on the H-atom as a result of partial CT to the aromatic backbone. In this picture the excited state proton transfer dynamics resemble the conventional dynamics of proton transfer in the ground state. It is described by an activated transition in a two-state reaction model (Fig. 14.2(a)), where an optically excited photoacid state converts into the excited conjugated photobase upon proton transfer. A second model invokes the occurrence of and the internal conversion between nearby lying electronically excited levels of the photoacid (Fig. 14.2(b)). Typically two energetically nearby spectroscopically accessible states can be reached for aromatic molecules upon electronic excitation, with light polarized either along the through-bond axis (1Lb-state) or along the through-atom axis (1La-state). The 1Lb state is the lowest singlet level in the gas phase, while the more polar 1La state is thought to be the more stable singlet state in polar solvents. Thus, a singlet–singlet level crossing may occur in polar solvents like water when the vertical excita-
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446
14 Bimolecular Proton Transfer in Solution (a) Two-state reaction model CT ArOH
(b) Three-state LE-CT reaction model
h hν
PT ArO− hν
S0 ArOH
S0 ArOH
(c) Three-state hydrogen transfer model 1πσ* ArOH
1ππ*
ArOH
1 ππ*
(d) Three-state strong coupling reaction model S2 ArOH
S1 ArOH
PT ArO−
ArO−
hν
hν S0 ArOH
CT ArOH
LE ArOH
PT ArO−
S0 ArOH
Figure 14.2 Different models to explain excited state photoacidity: the two state model (a), the three state model with nonadiabatic level crossing between LE (1Lb) and CT (1La) states, the excited state hydrogen transfer model (c), and the three state model with strongly coupled 1Lb and 1La states (d). (Adapted from Ref. [76].)
tion is to the 1Lb state and the ensuing solvent relaxation process is capable of shifting the excited-state population of the photoacid to the 1La state. For 1-naphthol the 1Lb fi 1La transition has been considered to be the proton transfer rate determining step [56–58]. In contrast, in a recent combined experimental/theoretical study of pyranine (8-hydroxy-1,3,6-trisulfonate-pyrene; HPTS) [59–61] it has been concluded that the rate determining step in the excited state proton dissociation reaction is not the conversion from the optically accessible locally excited (LE) state (resembling the properties of the 1Lb-state of naphthalene) to the electronically excited CT state (resembling the 1La-state character of naphthalene), but the transition of the photoacid CT to photobase CT states. A third model, where excited state hydrogen transfer (ESHT) rather than proton transfer is supposed to occur [62, 63] (Fig. 14.2(c)), has recently emerged from excited state dynamics studies of gas phase phenol clustered with ammonia or water molecules [64]. In this model a level crossing between the initially excited 1pp* state and a 1pr*-state leads to a concerted migration of an electron and a proton from the photoacid to the solvent, with a net transfer of a hydrogen atom as a result. This model has been invoked in an experiment on 7-hydroxyquinoline where donor and acceptor groups are connected through a wire of ammonia molecules [65–67]. A conical intersection of the 1pr*-state with the S0 state leads to an efficient internal conversion pathway for phenol-ammonia clusters [64], and in 2-amino-pyridine clusters [68]. Net proton transfer on the other hand should
14.2 Photoacids as Ultrafast Optical Triggers for Proton Transfer
Absorbance Change(mOD)
involve at least one more step with an electron back-transfer to the photoacid, producing the photobase and solvated proton as separate species. Typically the proton transfer reaction has been followed by probing electronic transitions of the photoacid S1-state and of the photobase S1-state, using UV/vis pump–probe or time-resolved fluorescence. Electronic transitions are strongly sensitive to solvent reorganization (solvation dynamics) [69–71]. For time-dependent changes of electronic bands it remains however problematic to disentangle the contributions of solvent reorganization from those of level crossings, including the proton transfer event. Vibrational transitions are typically less affected by solvent reorganization, with the hydroxyl stretching oscillator in a hydrogen bond as the exception to the rule [72–74]. As a result vibrational spectroscopy may enable a clear distinction between the time scales of electronic state transitions and of solvent reorganization at early pulse delays [75]. Recently, the excited state characteristics of HPTS have been probed with midinfrared pulses providing insight into state-specific vibrational modes [76]. In Fig. 14.3 the absorbance changes in the fingerprint region of HPTS are shown to be solvent dependent. The fact that these vibrational band patterns appear within the time resolution of 150 fs, without any additional changes up to several tens of picoseconds, indicates that previous observations of a 2.5 ps time component in UV/vis pump–probe experiments [59, 60] previously assigned to a 1Lb fi 1La level crossing in HPTS are more likely be due to solvation dynamics. In addition, the time-dependent frequency position and magnitude of the hydroxyl stretching band of HPTS indicate the significant impact of solvent reorganization on the solute–solvent interactions of the hydroxyl group of the photoacid compounds [53]. Comparison with results obtained on the methoxy derivative of HPTS reveals that these absorbance changes are strongly affected by a solvent dependent electronic
6 4 2 0 -2
HPTS in
D2O MeOD DMSO-d6
-4
1600
1500 1400 1300 -1 Wavenumber (cm )
Figure 14.3 Solvent dependent fingerprint spectra of HPTS in the excited state as indicated by the positive absorbance changes after excitation at 400 nm. Negative signals indicate bleach contributions due to vibrational transitions in the electronic ground state. (Adapted from Ref. [76].)
447
448
14 Bimolecular Proton Transfer in Solution
state configuration. A strong solvent dependent coupling between the energetically nearby lying 1Lb and 1La-states of HPTS (Fig. 14.2(d)), in similar fashion as in the description of gas phase 1-naphthol–ammonia clusters [56, 58], has been postulated as the underlying reason for these observations. Future developments in comparison of experimental vibrational mode patterns with quantum chemical calculations may reveal the molecular origins of photoacidity.
14.3 Proton Recombination and Acid–Base Neutralization
Acids are in equilibrium with their conjugate bases in protic solvents, where the relative concentrations depend on the pKa value. The observed dynamics of an electronically excited photoacid, typically interpreted as the proton transfer rate to the (protic) solvent [77, 78], is thus governed by the equilibration dynamics to the new configuration – as long as the photoacid and conjugate photobase remain in the electronically excited state – as dictated by the new excited state pKa* value. Depending on the pH of the solvent one can observe the reversible time-dependent geminate recombination of the photobase with the released proton [79–83], or even the reaction of the photobase with other protons present in solution. Proton transfer dynamics of photoacids to the solvent have thus, being reversible in nature, been modelled using the Debye–von Smoluchowski equation for diffusion-assisted reaction dynamics in a large body of experimental work on HPTS [84–87] and naphthols [88–92], with additional studies on the temperature dependence [93–98], and the pressure dependence [99–101], as well as the effects of special media such as reverse micelles [102] or chiral environments [103]. Moreover, results modelled with the Debye–von Smoluchowski approach have also been reported for proton acceptors triggered by optical excitation (photobases) [104, 105], and for molecular compounds with both photoacid and photobase functionalities, such as 10-hydroxycamptothecin [106] and coumarin 4 [107]. It can be expected that proton diffusion also plays a role in hydroxyquinoline compounds [108–112]. Finally, proton diffusion has been suggested in the long time dynamics of green fluorescent protein [113], where the chromophore functions as a photoacid [23, 114], with an initial proton release on a 3–20 ps time scale [115, 116]. The diffusive kinetics of geminate pairs have been predicted to show a t–3/2 time-dependent decaying behavior [117–122]. Early experiments showed, in contrast, a t–a decay, with a being dependent on the proton concentration [123]. Experiments on longer time ranges with improved sensitivity are prerequisites for an accurate determination of the asymptotic behavior [124]. In fact, recent measurements on HPTS have demonstrated the validity of the theoretically predicted t–3/2 decay law (see Fig. 14.4) [125]. For 5-(methanesulfonyl)-1-naphthol a kinetic transition from power law to exponential has been reported due to a short photobase lifetime [126]. Neutralization of the photoacids as a result of direct proton transfer to (scavenging) bases has also been explored in time-resolved studies. Whereas initial work
14.4 Reaction Dynamics Probing with Vibrational Marker Modes 0
10
-1
10
-2
10
-3
10
-4
10
-5
10
-6
pH 1.97 pH 2.38
pH 3.03 pH 2.77
*
[HPTS ]t
10
pH 6.10
0
5
10
15
20
25
30
35
Time (ns) Figure 14.4 Semi-logarithmic plot of normalized fluorescence decay of excited HPTS. Points are experimental data (kex = 375 nm, kem = 420 nm) in water acidified by HClO4 after lifetime correction. The geminate recombination data (pH = 6) is fitted by a numerical solution of the Debye–von Smoluchowski equation convoluted with the instrument response function after lifetime correction. (Adapted from Ref. [125].)
used a Stern–Volmer quenching analysis [127, 128], it has been realized in a timeresolved fluorescence study that when working with high base concentrations, the apparent “on-contact” reaction rate can be obtained, despite the typically much slower diffusion rates [129]. The apparent “on-contact” reaction rates of naphthol and pyrenol derivatives with acetate or formate bases were found to range from (6 ps)–1 for 5-cyano-1-naphthol and (500 ps)–1 for 1-pyrenol. Debye–von Smoluchowski dynamics [130] have been included in UV/vis pump–probe neutralization studies of HPTS with acetate [131] and 2-naphthol-6-sulfonate and acetate [132, 133]. A more extensive listing of “on-contact” reaction rates has recently been published [134].
14.4 Reaction Dynamics Probing with Vibrational Marker Modes
The bimolecular reaction dynamics of geminate recombination or acid–base neutralization have until recently been studied with time-resolved techniques probing electronic transitions. Time-resolved fluorescence using time-correlated single photon counting detection is limited to a time resolution of a few picoseconds. UV/vis pump–probe experiments, in principle, may have a time resolution of a few tens of femtoseconds, but may be hampered by overlapping contributions of
449
14 Bimolecular Proton Transfer in Solution
bleach (stimulated emission) and transient excited-state absorbance. A major disadvantage is that the reaction dynamics can only be inspected on the side of the photoacid/photobase with optical pulses. The experimental results thus only give information on the time scales when the proton dissociates from the photoacid. In particular, the arrival time when the proton arrives at a mineral base, such as acetate, cannot be determined in practice with optical pulses. Vibrational spectroscopy on the other hand can be used to follow the dynamics of both acid and base molecules [75]. Disadvantages include the lower cross sections for vibrational transitions and the frequent overlap with solvent bands. In particular water has a substantial steady-state absorbance throughout the mid-infrared, limiting the sample thicknesses to less than 100 lm. Recently, the potential of ultrafast mid-infrared spectroscopy has been demonstrated for the study of these aqueous proton transfer reactions [135, 136]. Here the reaction dynamics have been followed by inspection of vibrational marker modes of the photoacid HPTS, the conjugate photobase HPTS–, and the conjugate acid of the base acetate –OAc, i.e. acetic acid. When exciting HPTS dissolved at a fixed concentration of 20 mM in D2O, with varying amounts of the base acetate added (ranging from 0.25–4 M), the deuteron transfer reaction can be followed in real time by inspection of the decay of the 1486 cm–1 marker mode of the photoacid, the rise of signal at the 1503 cm–1 transition of the conjugated photobase, and the rise of the C=O stretching band of acetic acid at 1720 cm–1 (Fig. 14.5). At low base concentrations (0.25–0.5 M) deuteron transfer to the solvent, followed by deuteron pick-up by acetate, dominates the dynamics, as can be learned from a faster rise of the photobase signal than of the acetic acid band (Fig. 14.5). This feature cannot be observed in time-resolved fluorescence or UV/vis pump–probe measurements where it was Photobase or Acetic Acid Signal (norm.)
450
2 1 M KOAc
0.5 M KOAc
0.25 M KOAc
0
0
500
0 500 0 Pulse Delay (ps)
500
Figure 14.5 Comparison of the rise of the vibrational marker bands of the conjugate photobase of HPTS in the electronically excited state (dots) and of acetic acid (solid lines) at low base concentrations, indicating the initial deuteron release to the solvent and subsequent deuteron pick-up by the base.
1000
14.4 Reaction Dynamics Probing with Vibrational Marker Modes
indirectly studied by monitoring the proton-scavenging effect of a base on diminishing the geminate recombination reaction of the photoacid [129, 131]. At high base concentrations (> 1 M) practically identical rise times for photobase and acetic acid are observed, indicating a dominant direct deuteron transfer mechanism from the photoacid to the base. At these high concentrations the observed reaction dynamics are bimodal (Fig. 14.6). The two contributions to the signals can be ascribed to HPTS···–OAc complexes with a pre-formed hydrogen bond along the reaction coordinate, and initially uncomplexed HPTS that first has to form an encounter pair with –OAc before a reaction can proceed. The preformed complex shows deuteron transfer faster than 150 fs. In contrast, for the fraction of initially uncomplexed HPTS, where the reaction coordinate is estab4 M KOAc
Signal (arb. units)
4 M KOAc
2 M KOAc
2 M KOAc
1 M KOAc
0.5 M KOAc
(b)
(a) 0
20 40 60 80 100 120 0
20
40
60
80 100 120
Pulse Delay (ps) Figure 14.6 Rise of the carbonyl stretching marker mode of acetic acid for different concentrations of acetate (dots) in the reaction with HPTS. The solid lines denote calculated signals including contributions by “tight” complexes and diffusion assisted kinetics (a), or by “tight” complexes and “loose” complexes in addition to diffusion assisted kinetics (b). (Adapted from Ref. [136].)
lished by the diffusion of the reactants and by solvent fluctuations, a much slower bimolecular reaction rate on contact (a = 6.3 ) of (12 ps)–1 M–1 is found from data analysis using the theory of diffusion-controlled bimolecular reaction dynamics as given by von Smoluchowski with Szabo–Collins–Kimball (SCK) radiative boundary conditions [130], assuming fully screened potential at the high base concentrations used (Fig. 14.6(a)) [135]. A better fit is achieved when a static reaction component (with a time constant of 6 ps) is added to the SCK model (Fig. 14.6(b)), describing a fraction of reactive pairs already at close range (but not directly complexed) to each other at the time of initiation of the reaction, and thus not delayed by diffusion [136]. In addition, the correlation between the intrinsic (bimolecular) proton transfer constant of the SCK model (k0) and the intrinsic unimolecular proton recombination constant of the Eigen–Weller model (kr) was demonstrated for the first time to be in accordance with the analysis of Shoup and Szabo [137].
451
452
14 Bimolecular Proton Transfer in Solution
The fact that the deuteron transfer reaction in the pre-formed “tight” HPTS···–OAc complex is at least 2 orders of magnitude faster than the “loose” HPTS···(H2O)n···–OAc encounter complex leads to the important finding that the deuteron transfer mechanism as initially suggested by Eigen and Weller has to be refined. One explanation follows the line of argument that the acid and base in the encounter complex can only react after substantial rearrangement of water molecules in the solvation shells before acid and base reach direct contact (Fig. 14.7), and the slower reaction rate of the encounter complex is due to this bottleneck solvent rearrangement dynamics. An alternative explanation lies in the possibility of a von Grotthuss-type of hopping of the proton from the acid to the base via solvation shell water molecules (Fig. 14.8), in which case acid and base never reach direct contact and the overall proton transfer reaction is considerably slower than the hopping time of the proton along a single hydrogen-bond. Reaction Stage
Encounter Stage
B -B
B-B
+ +
BB
Encounter Stage
33-RO-H ROH
BB--
+ +
kr
+
BB
B-B
B -B
+
kPT
+ +
BB
3 3-BRO-H RO-H -B ROH
k’r
+
BB-
4 4--
44-RO RO-H RO
HB RO-H RO -HB RO
HB HB
k-r
+ +
k-PT
+ +
k’-r
a
reactants encounter “loose“ complex
+
directly bound reactive “tight“ complex
Figure 14.7 Refined model for proton transfer between acids and bases with a three-stage mechanism consisting of diffusion, encounter and reaction stages. In this model the Eigen– Weller “on-contact” reaction rate kr is to be
directly bound proton-transferred proton-transfe “tight“ complex
+ +
a
products encounter “loose“ complex
understood as a solvent reorganization rate. The “loose” complexes rearrange then into “tight” complexes, that promptly react with the proton transfer rate kPT. (Adapted from Ref. [136].)
Recent experimental results on the acid–base neutralization reaction between HPTS and the carboxylic bases mono-, di- and trichloracetate have revealed the underlying mechanisms of proton transfer of the “loose” complexes [138]. It turns out that a sequential, von Grotthuss-type of hopping occurs through a water molecule bridging the HPTS photoacid and the carboxylic base. Figure 14.9 shows the transient spectra obtained with a solution of 20 mM HPTS in D2O with 1 M of monochloroacetate –OAc-Cl added. At early pulse delays about 20% of HPTS has released its deuteron, as is indicated by the appearance of the HPTS– photobase marker band at 1435 cm–1 within the time resolution. A vibrational marker band at 1850 cm–1 indicates the transient existence of hydrated deuterons. Comparison with literature values for hydrated proton species with well-defined surroundings
14.4 Reaction Dynamics Probing with Vibrational Marker Modes Encounter Stage = Reaction Stage B B
B B
-
B B
-
-
+
+
+ +
B B
-
k1
33-
RO RO - H ROH
BB -
k2
44
-
+
+
BB -
44
RO - H RO
H2O
+ a
+ +
BB -
RO
-
k-1
a
reactants encounter “loose“ complex
RO - H RO
H3O+
B-
RO
HB
+
+
k-2
Absorbance Change (mOD)
(a)
+
+
a
products encounter “loose“ complex
intermediate “loose“ complex with hydronium
-100 ps 0.5 ps 5 ps 10 ps 80 ps 300 ps 1000 ps
(b)
-10 ps 0.5 ps 5 ps 50 ps 100 ps 300 ps
3
2
2
1
1
0
0 1700 1750 1800 1850 2500 2550 -1 Wavenumber (cm )
Figure 14.9 Transient spectra of the reaction of HPTS with 1 M –OAc-Cl in D2O, showing the response of the C=O stretching band of DOAc-Cl at 1720 cm–1 and the hydronium O–D stretching band at 1850 cm–1 (a). For comparison the transient response of the hydronium O–H stretching band at 2570 cm–1 measured with 1 M –OAc-Cl in H2O is shown in (b). (Adapted from Ref. [138].)
H2 O
+ +
Figure 14.8 Proton transfer mechanism of the “loose” complexes ROH···(H2O)n···B– with a sequential, von Grotthuss-type, hopping of protons through water bridges. For HPTS and monochloroacetate the first transfer to the water bridge forming the hydronium ion H3O+ is ultrafast, and the second transfer to the base is slower. (Adapted from Ref. [136].)
3
-
2600
2650
+
HB HB
453
454
14 Bimolecular Proton Transfer in Solution
[139–144] strongly suggests that the hydrated deuterons exists as hydronium ions, D3O+. A similar transient band is detected at 2570 cm–1 for measurements performed in H2O, in full accordance with an H/D isotope effect on the transition frequency of H3O+ vs. D3O+. Kinetic modelling shows that the initial transfer in the “loose” HPTS···(D2O)···–OAc-Cl complex occurs faster than the time resolution. The second transfer, generating HPTS–···(D2O)···DOAc-Cl, has a much slower rate of (25 ps)–1. The findings of the proton transfer reaction of HPTS with –OAc-Cl are reminiscent of the results of theoretical studies for acid dissociation of hydrogen halides in water [14–17] Here the proton transfers in a hopping fashion from the first to the secondary solvation shells, away from the dissociating hydrogen halide, with the rate determining step being the cleavage of a hydrogen bond in the protonaccepting water molecule, which must change its coordination number from 4 to 3. This mechanism for proton transfer appears to be a general one: the proton transmission through water, named after von Grotthuss as a dedication [7] to his landmark electrolysis measurements of aqueous ion solutions [6], also occurs by sequential hopping to neighboring water molecules and involves similar rearrangements of the hydrogen-bonding network, although the full details of the Grotthuss mechanism in water are yet to be fully deciphered. Perhaps the most fundamental aspect of proton solvation in pure water have come from ab initio molecular dynamics simulations [10, 12, 13] that have demonstrated a continuous exchange between the Eigen cation H3O+(H2O)3 (i.e. H9O4+) [3] and the Zundel cation H5O2+ (i.e. H2O···H+···OH2) [145] in liquid water. In the acid–base reaction between HPTS and –OAc-Cl the observed marker bands of D3O+ at 1850 cm–1 and of H3O+ at 2570 cm–1 indicate that in the encounter (reactive) complex between HPTS– and –OAc-Cl (that is water depleted to facilitate the acid–base reaction) the Eigen solvation core, the H3O+ cation, plays a key role. In particular the frequency position of the hydrated proton band observed for the ionic complex HPTS–···H3O+···–OAc-Cl is very similar to that observed for the Eigen cation H3O+(H2O)3, as recently measured in dedicated experiments of hydrated proton clusters [144], and calculated for the Eigen cation in the proton wire of bacteriorhodopsin [143]. This finding strongly suggests that in our experiments the hydrated proton is the Eigen solvation core with a symmetric hydrogen bonding configuration, i.e. (H3O+)L3 with L hydrogen accepting groups. Here the intermediate HPTS–···D3O+/H3O+···–OAc-Cl complex appears to contain only the hydronium ion, hydrogen bonded in an almost symmetric three-fold way and thus resembling the hydronium core of the Eigen cation. A role of the Zundel cation H5O2+ in the proton transfer dynamics is suggested less likely, since its vibrational transitions are located at other frequency positions [143, 144, 146]. The present results on the reaction dynamics between HPTS and the family of acetate bases demonstrate that a base-induced sequential proton transfer mechanism at close acid–base proximities is at the heart of aqueous acid–base proton transfer reactions. The experimentally found, relatively long lived, intermediate ionic complex consisting of photobase, hydrated proton and carboxylic base, indicates the special property of carboxylic bases, a finding with important implica-
References
tions not only for proton protein channels, where the dynamics of various intermediate stages are dictated by glutamic and aspartic amino acid functionalities [20–22] but also for wild type green fluorescent protein (GFP), in which the photoacid chromophore releases a proton through a water bridge to the carboxylic side group of Glu222 [23, 147]. Acknowledgment
We cordially acknowledge the important contributions by our present and former group members Matteo Rini, Omar F. Mohammed, Ben-Zion Magnes, Dina Pines. We also thank the German-Israeli Foundation for Scientific Research and Development, the Israel Science Foundation, and the Egyptian Government for financial support (Project GIF 722/01, Project ISF 562/04 for EP and a long term mission fellowship for OFM).
References 1 R. P. Bell, The Proton in Chemistry,
2 3 4
5
6 7 8 9 10
11 12 13
Chapman and Hall, London, 2nd edn., 1973. A. Weller, Prog. React. Kinet. 1961, 1, 187–213. M. Eigen, Angew. Chem. Int. Ed. 1964, 3, 1–19. M. Eigen, W. Kruse, G. Maass, L. DeMaeyer, Prog. React. Kinet. 1964, 2, 285. P. L. Geissler, C. Dellago, D. Chandler, J. Hutter, M. Parrinello, Science 2001, 291, 2121–2124. C. J. T. de Grotthuss, Ann. Chim. 1806, LVIII, 54–74. H. Danneel, Z. Elektrochem. Angew. Phys. Chem. 1905, 11, 249–252. N. Agmon, Chem. Phys. Lett. 1995, 244, 456–462. J. T. Hynes, Nature 1999, 397, 565. D. Marx, M. E. Tuckerman, J. Hutter, M. Parrinello, Nature 1999, 397, 601–604. R. Vuilleumier, D. Borgis, J. Chem. Phys. 1999, 111, 4251–4266. U. W. Schmitt, G. A. Voth, J. Chem. Phys. 1999, 111, 9361–9381. H. Lapid, N. Agmon, M. K. Petersen, G. A. Voth, J. Chem. Phys. 2005, 122, 014506.
14 K. Ando, J. T. Hynes, J. Phys. Chem. B
1997, 101, 10464–10478. 15 K. Ando, J. T. Hynes, Adv. Chem. Phys.
1999, 110, 381–430. 16 K. Ando, J. T. Hynes, J. Phys. Chem. A
1999, 103, 10398–10408. 17 A. Al-Halabi, R. Bianco, J. T. Hynes,
J. Phys. Chem. A 2002, 106, 7639–7645. 18 R. Bianco, J. T. Hynes, Theor. Chem. Acc.
2004, 111, 182–187. 19 F. Hibbert, Adv. Phys. Org. Chem. 1986,
22, 113–212. 20 H. Luecke, H. T. Richter, J. K. Lanyi,
Science 1998, 280, 1934–1937. 21 W. Khlbrandt, Nature 2000, 406,
569–570. 22 T. E. DeCoursey, Physiol. Rev. 2003, 83,
475–579. 23 M. Zimmer, Chem. Rev. 2002, 102,
759–781. 24 M. Eigen, in Nobel Lectures, Chemistry
1963–1970, Elsevier, Amsterdam, 1972, pp. 170–203. 25 T. Elsaesser, in Femtosecond Chemistry, Vol. 2 , J. Manz, L. Wste (Eds.), VCH, Weinheim, Germany, 1995, p. 563. 26 A. Douhal, F. Lahmani, A. H. Zewail, Chem. Phys. 1996, 207, 477–498. 27 T. Elsaesser, in Ultrafast Hydrogen Bonding Dynamics and Proton Transfer Processes in the Condensed Phase, Vol. 23,
455
456
14 Bimolecular Proton Transfer in Solution T. Elsaesser, H. J. Bakker (Eds.), Kluwer Academic Publishers, Dordrecht, 2002, pp. 119–153. 28 W. Klpffer, Adv. Photochem. 1977, 10, 311–358. 29 S. J. Formosinho, L. G. Arnaut, J. Photochem. Photobiol. A 1993, 75, 21–48. 30 T. Frster, Die Naturwissenschaften 1949, 36, 186–187. 31 T. Frster, Z. Elektrochem 1950, 54, 42–46. 32 T. Frster, Z. Elektrochem 1950, 54, 531–535. 33 E. Vander Donckt, Prog. React. Kinet. 1970, 5, 273–299. 34 J. F. Ireland, P. A. H. Wyatt, Adv. Phys. Org. Chem. 1976, 12, 131–221. 35 I. Y. Martynov, A. B. Demyashkevich, B. M. Uzhinov, M. G. Kuz’min, Russ. Chem. Rev. [Usp. Khim.] 1977, 46, 1–15 [13–31]. 36 L. G. Arnaut, S. J. Formosinho, J. Photochem. Photobiol. A 1993, 75, 1–20. 37 E. Pines, D. Pines, in Ref. [27], pp. 155–184. 38 E. Pines, in Chemistry of Phenols, Z. Rappoport (Ed.), Wiley, New York, 2003, pp. 491–529. 39 L. M. Tolbert, J. E. Haubrich, J. Am. Chem. Soc. 1990, 112, 8163–8165. 40 L. M. Tolbert, J. E. Haubrich, J. Am. Chem. Soc. 1994, 116, 10593–10600. 41 L. M. Tolbert, K. M. Solntsev, Acc. Chem. Res. 2002, 35, 19–27. 42 E. M. Kosower, D. Huppert, Annu. Rev. Phys. Chem. 1986, 37, 127–156. 43 N. Agmon, J. Phys. Chem. A 2005, 109, 13–35. 44 E. Pines, D. Huppert, J. Phys. Chem. 1983, 87, 4471–4478. 45 M. Gutman, Methods Biochem. Anal. 1984, 30, 1–103. 46 M. Gutman, E. Nachliel, Annu. Rev. Phys. Chem. 1997, 48, 329–356. 47 E. Pines, G. R. Fleming, J. Phys. Chem. 1991, 95, 10448–10457. 48 M. J. Kamlet, J. L. M. Abboud, M. H. Abraham, R. W. Taft, J. Org. Chem. 1983, 48, 2877–2887. 49 N. Barrash-Shiftan, B. B. Brauer, E. Pines, J. Phys. Org. Chem. 1998, 11, 743–750.
50 K. M. Solntsev, D. Huppert,
L. M. Tolbert, N. Agmon, J. Am. Chem. Soc. 1998, 120, 7981–7982. 51 K. M. Solntsev, D. Huppert, N. Agmon, J. Phys. Chem. A 1998, 102, 9599–9606. 52 B.-Z. Magnes, D. Pines, N. Strashnikova, E. Pines, Solid State Ionics 2004, 168, 225–233. 53 E. Pines, D. Pines, Y.-Z. Ma, G. R. Fleming, ChemPhysChem 2004, 5, 1315–1327. 54 M. Barroso, L. G. Arnaut, S. J. Formosinho, J. Photochem. Photobiol. A 2003, 160, 227–227. 55 N. Agmon, W. Rettig, C. Groth, J. Am. Chem. Soc. 2002, 124, 1089–1096. 56 R. Knochenmuss, I. Fischer, D. Lhrs, Q. Lin, Isr. J. Chem. 1999, 39, 221–230. 57 B.Z. Magnes, N. V. Strashnikova, E. Pines, Isr. J. Chem. 1999, 39, 361–373. 58 R. Knochenmuss, I. Fischer, Int. J. Mass Spectrom. 2002, 220, 343–357. 59 T. H. Tran-Thi, T. Gustavsson, C. Prayer, S. Pommeret, J. T. Hynes, Chem. Phys. Lett. 2000, 329, 421–430. 60 T.-H. Tran-Thi, C. Prayer, P. Milli, P. Uznanski, J. T. Hynes, J. Phys. Chem. A 2002, 106, 2244 –2255. 61 J. T. Hynes, T. H. Tran-Thi, G. Granucci, J. Photochem. Photobiol. A 2002, 154, 3–11. 62 A. L. Sobolewski, W. Domcke, C. Dedonder-Lardeux, C. Jouvet, Phys. Chem. Chem. Phys. 2002, 4, 1093–1100. 63 W. Domcke, A. L. Sobolewski, Science 2003, 302, 1693–1694. 64 O. David, C. Dedonder-Lardeux, C. Jouvet, Int. Rev. Phys. Chem. 2002, 21, 499–523. 65 C. Tanner, C. Manca, S. Leutwyler, Science 2003, 302, 1736–1739. 66 C. Manca, C. Tanner, S. Coussan, A. Bach, S. Leutwyler, J. Chem. Phys. 2004, 121, 2578–2590. 67 C. Tanner, C. Manca, S. Leutwyler, J. Chem. Phys. 2005, 122. 68 T. Schultz, E. Samoylova, W. Radloff, I. V. Hertel, A. L. Sobolewski, W. Domcke, Science 2004, 306, 1765–1768. 69 G. R. Fleming, M. Cho, Annu. Rev. Phys. Chem. 1996, 47, 109–134.
References 70 W. P. de Boeij, M. S. Pshenichnikov,
D. A. Wiersma, Annu. Rev. Phys. Chem. 1998, 49, 99–123. 71 M. Glasbeek, H. Zhang, Chem. Rev. 2004, 104, 1929–1954. 72 C. Chudoba, E. T. J. Nibbering, T. Elsaesser, Phys. Rev. Lett. 1998, 81, 3010–3013. 73 C. Chudoba, E. T. J. Nibbering, T. Elsaesser, J. Phys. Chem. A 1999, 103, 5625–5628. 74 E. T. J. Nibbering, C. Chudoba, T. Elsaesser, Isr. J. Chem. 1999, 39, 333–347. 75 E. T. J. Nibbering, H. Fidder, E. Pines, Annu. Rev. Phys. Chem. 2005, 56, 337–367. 76 O. F. Mohammed, J. Dreyer, B.-Z. Magnes, E. Pines, E. T. J. Nibbering, ChemPhysChem 2005, 6, 625–636. 77 S. P. Webb, L. A. Philips, S. W. Yeh, L. M. Tolbert, J. H. Clark, J. Phys. Chem. 1986, 90, 5154–5164. 78 R. Krishnan, J. Lee, G. W. Robinson, J. Phys. Chem. 1990, 94, 6365–6367. 79 E. Pines, D. Huppert, Chem. Phys. Lett. 1986, 126, 88–91. 80 E. Pines, D. Huppert, J. Chem. Phys. 1986, 84, 3576–3577. 81 E. Pines, D. Huppert, N. Agmon, J. Chem. Phys. 1988, 88, 5620–5630. 82 N. Agmon, E. Pines, D. Huppert, J. Chem. Phys. 1988, 88, 5631–5638. 83 N. Agmon, J. Chem. Phys. 1988, 88, 5639–5642. 84 D. Huppert, E. Pines, N. Agmon, J. Opt. Soc. Am. B 1990, 7, 1545–1550. 85 N. Agmon, D. Huppert, A. Masad, E. Pines, J. Phys. Chem. 1991, 95, 10407–10413. 86 A. Masad, D. Huppert, Chem. Phys. Lett. 1991, 180, 409–415. 87 S. Y. Goldberg, E. Pines, D. Huppert, Chem. Phys. Lett. 1992, 192, 77–81. 88 I. Carmeli, D. Huppert, L. M. Tolbert, J. E. Haubrich, Chem. Phys. Lett. 1996, 260, 109–114. 89 D. Huppert, L. M. Tolbert, S. LinaresSamaniego, J. Phys. Chem. A 1997, 101, 4602–4605. 90 K. M. Solntsev, D. Huppert, N. Agmon, J. Phys. Chem. A 1999, 103, 6984–6997.
91 K. M. Solntsev, D. Huppert, N. Agmon,
92
93 94
95 96 97 98 99 100
101
102
103
104 105
106
107 108 109 110 111
L. M. Tolbert, J. Phys. Chem. A 2000, 104, 4658–4669. C. Clower, K. M. Solntsev, J. Kowalik, L. M. Tolbert, D. Huppert, J. Phys. Chem. A 2002, 106, 3114–3122. B. Cohen, D. Huppert, J. Phys. Chem. A 2000, 104, 2663–2667. B. Cohen, P. Leiderman, D. Huppert, J. Phys. Chem. A 2002, 106, 11115–11122. B. Cohen, P. Leiderman, D. Huppert, J. Phys. Chem. A 2003, 107, 1433–1440. E. Pines, B.-Z. Magnes, T. Barak, J. Phys. Chem. A 2001, 105, 9674–9680. B. Cohen, D. Huppert, J. Phys. Chem. A 2001, 105, 2980–2988. B. Cohen, J. Segal, D. Huppert, J. Phys. Chem. A 2002, 106, 7462–7467. N. Koifman, B. Cohen, D. Huppert, J. Phys. Chem. A 2002, 106, 4336–4344. L. Genosar, P. Leiderman, N. Koifman, D. Huppert, J. Phys. Chem. A 2004, 108, 309–319. L. Genosar, P. Leiderman, N. Koifman, D. Huppert, J. Phys. Chem. A 2004, 108, 1779–1789. B. Cohen, D. Huppert, K. M. Solntsev, Y. Tsfadia, E. Nachliel, M. Gutman, J. Am. Chem. Soc. 2002, 124, 7539–7547. K. M. Solntsev, L. M. Tolbert, B. Cohen, D. Huppert, Y. Hayashi, Y. Feldman, J. Am. Chem. Soc. 2002, 124, 9046–9047. B. Cohen, D. Huppert, J. Phys. Chem. A 2002, 106, 1946–1955. S. R. Keiding, D. Madsen, J. Larsen, S. K. Jensen, J. Thøgersen, Chem. Phys. Lett. 2004, 390, 94–97. K. M. Solntsev, E. N. Sullivant, L. M. Tolbert, S. Ashkenazi, P. Leiderman, D. Huppert, J. Am. Chem. Soc. 2004, 126, 12701–12708. B. Cohen, D. Huppert, J. Phys. Chem. A 2001, 105, 7157–7164. E. Bardez, I. Devol, B. Larrey, B. Valeur, J. Phys. Chem. B 1997, 101, 7786–7793. E. Bardez, Isr. J. Chem. 1999, 39, 319–332. S. Kohtani, A. Tagami, R. Nakagaki, Chem. Phys. Lett. 2000, 316, 88–93. O. Poizat, E. Bardez, G. Buntinx, V. Alain, J. Phys. Chem. A 2004, 108, 1873–1880.
457
458
14 Bimolecular Proton Transfer in Solution 112 T. G. Kim, M. R. Topp, J. Phys. Chem. A 113
114
115
116
117 118 119 120 121 122
123
124 125 126 127
128 129
130
2004, 108, 10060–10065. P. Leiderman, M. Ben-Ziv, L. Genosar, D. Huppert, K. M. Solntsev, L. M. Tolbert, J. Phys. Chem. B 2004, 108, 8043–8053. K. Brejc, T. K. Sixma, P. A. Kitts, S. R. Kain, R. Y. Tsien, M. Ormo, S. J. Remington, Proc. Natl. Acad. Sci. USA 1997, 94, 2306–2311. M. Chattoraj, B. A. King, G. U. Bublitz, S. G. Boxer, Proc. Natl. Acad. Sci. USA 1996, 93, 8362–8367. K. Winkler, J. R. Lindner, V. Subramaniam, T. M. Jovin, P. Vhringer, Phys. Chem. Chem. Phys. 2002, 4, 1072–1081. A. Szabo, R. Zwanzig, J. Stat. Phys. 1991, 65, 1057–1083. A. Szabo, J. Chem. Phys. 1991, 95, 2481–2490. W. Naumann, N. V. Shokhirev, A. Szabo, Phys. Rev. Lett. 1997, 79, 3074–3077. I. V. Gopich, N. Agmon, Phys. Rev. Lett. 2000, 84, 2730–2733. N. Agmon, I. V. Gopich, J. Chem. Phys. 2000, 112, 2863–2869. I. V. Gopich, A. A. Ovchinnikov, A. Szabo, Phys. Rev. Lett. 2001, 86, 922–925. D. Huppert, S. Y. Goldberg, A. Masad, N. Agmon, Phys. Rev. Lett. 1992, 68, 3932–3935. K. M. Solntsev, D. Huppert, N. Agmon, J. Phys. Chem. A 2001, 105, 5868–5876. D. Pines, E. Pines, J. Chem. Phys. 2001, 115, 951–953. K. M. Solntsev, D. Huppert, N. Agmon, Phys. Rev. Lett. 2001, 86, 3427–3430. M. Lawrence, C. J. Marzzacco, C. Morton, C. Schwab, A. M. Halpern, J. Phys. Chem. 1991, 95, 10294–10299. L. M. Tolbert, S. M. Nesselroth, J. Phys. Chem. 1991, 95, 10331–10336. E. Pines, B. Z. Magnes, M. J. Lang, G. R. Fleming, Chem. Phys. Lett. 1997, 281, 413–420. A. Szabo, J. Phys. Chem. 1989, 93, 6929–6939.
131 L. Genosar, B. Cohen, D. Huppert,
J. Phys. Chem. A 2000, 104, 6689–6698. 132 B. Cohen, D. Huppert, N. Agmon,
J. Am. Chem. Soc. 2000, 122, 9838–9839. 133 B. Cohen, D. Huppert, N. Agmon,
J. Phys. Chem. A 2001, 105, 7165–7173. 134 M. Barroso, L. G. Arnaut,
135
136
137 138
139 140
141 142 143
144
145 146
147
S. J. Formosinho, J. Photochem. Photobiol. A 2002, 154, 13–21. M. Rini, B.-Z. Magnes, E. Pines, E. T. J. Nibbering, Science 2003, 301, 349–352. M. Rini, D. Pines, B.-Z. Magnes, E. Pines, E. T. J. Nibbering, J. Chem. Phys. 2004, 121, 9593–9610. D. Shoup, A. Szabo, Biophys. J. 1982, 40, 33–39. O. F. Mohammed, D. Pines, J. Dreyer, E. Pines, E. T. J. Nibbering, Science 2005, 310, 83–86. B. S. Ault, G. C. Pimentel, J. Phys. Chem. 1973, 77, 57–61. J. M. Williams, in The Hydrogen Bond: Recent developments in Theory and Experiments, Vol. II. Structure and Spectroscopy, P. Schuster, G. Zundel, C. Sandorfy, (Eds.), North Holland, Amsterdam, 1976, pp. 655–682. L. Delzeit, B. Rowland, J. P. Devlin, J. Phys. Chem. 1993, 97, 10312–10318. E. S. Stoyanov, C. A. Reed, J. Phys. Chem. A 2004, 108, 907–913. R. Rousseau, V. Kleinschmidt, U. W. Schmitt, D. Marx, Angew. Chem. Int. Ed. 2004, 43, 4804–4807. J. M. Headrick, E. G. Diken, R. S. Walters, N. I. Hammer, R. A. Christie, J. Cui, E. M. Myshakin, M. A. Duncan, M. A. Johnson, K. D. Jordan, Science 2005, 308, 1765–1769. G. Zundel, Adv. Chem. Phys. 2000, 111, 1–217. K. R. Asmis, N. L. Pivonka, G. Santambrogio, M. Brummer, C. Kaposta, D. M. Neumark, L. Wste, Science 2003, 299, 1375–1377. D. Stoner-Ma, A. A. Jaye, P. Matousek, M. Towrie, S. R. Meech, P. J. Tonge, J. Am. Chem. Soc. 2005, 127, 2864–2865.
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15 Coherent Low-frequency Motions in Condensed Phase Hydrogen Bonding and Transfer Thomas Elsaesser
15.1 Introduction
Hydrogen bonding represents a local interaction which determines the fluctuating structure of liquids forming extended molecular networks, e.g., water and alcohols, as well as macromolecular structure of biological relevance. Hydrogen bonds also play a key role in hydrogen and proton transfer processes in both electronic ground and excited states [1, 2]. The structural dynamics of hydrogen bonds and proton transfer processes are determined by motions along nuclear coordinates which are characterized by vibrational periods in the femtosecond time domain. For instance, the period of an O–H stretching vibration is of the order of 10 fs whereas low-frequency modes of hydrogen bonds display periods of up to several hundred femtoseconds. In general, vibrational modes of hydrogen bonds show pronounced coupling to each other, resulting in a highly complex dynamics of structural changes. The dynamics of hydrogen bonded systems cover a wide range in time, from about 50 fs up to tens of picoseconds [2]. Linear vibrational spectroscopy, a standard tool of hydrogen bond research, provides the steady-state, i.e., time-averaged infrared and Raman spectra, giving very limited insight into the processes underlying such dynamics. In most cases, there is no quantitative understanding of vibrational line shapes and the different broadening mechanisms, in spite of extensive theoretical work on molecular potential energy surfaces and vibrational couplings. Much more infomation is available from studies of the nonlinear vibrational response in which the macroscopic vibrational polarization and/or changes in vibrational absorption display a higher order dependence on the amplitude of the radiation fields interacting with the sample. Nonlinear vibrational spectroscopy in the femtosecond time domain allows one to observe ultrafast hydrogen bond dynamics in real-time and to separate different microscopic couplings in the nonlinear response [3, 4]. Quantum coherent vibrational dynamics of hydrogen bonds in liquids is a topic of substantial current interest [5] and both coherent nuclear motions, i.e., vibrational wavepackets, and processes of vibrational dephasing and relaxation have been studied recently by ultrafast pump–probe and Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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photon echo techniques. In photoinduced hydrogen transfer, measurements of transient vibrational spectra in electronically excited states provide direct information on the molecular structure of reaction products and on reaction pathways [6–8]. In this chapter, coherent low-frequency motions and their role in hydrogen bond dynamics and hydrogen transfer are discussed. In Section 15.2, the basic vibrational excitations and couplings in a hydrogen bond are introduced. Recent results on coherent low-frequency motions of intra- and intermolecular hydrogen bonds in the electronic ground state are presented in Section 15.3. The role of low-frequency motions in excited state intramolecular hydrogen transfer is addressed in Section 15.4, followed by some conclusions (Section 15.5).
15.2 Vibrational Excitations of Hydrogen Bonded Systems
The formation of hydrogen bonds results in pronounced changes of the vibrational spectra of the molecules involved [1, 9]. In an X–H···Y bonding geometry, the stretching mode of the X–H donor group displays the most prominent modifications, i.e., a red-shift and – in most cases – a substantial spectral broadening and reshaping. The red-shift reflects the reduced force constant of the oscillator and/or the enhanced anharmonicity of the vibrational potential along the X–H stretching coordinate, i.e., an enhanced diagonal anharmonicity. The red-shift has been used to characterize the strength of hydrogen bonds [10]. Spectral broadening can arise from a number of mechanisms, among them anharmonic coupling to low-frequency modes, Fermi resonances with overtone and combination tone levels of fingerprint modes, vibrational dephasing, and inhomogeneous broadening due to different hydrogen bonding geometries in the molecular ensemble [11–15]. In the weak attractive potential between hydrogen donor and acceptor groups, new modes occur which are connected with motions of the heavy atoms and affect the geometry of the hydrogen bond. The small force constants and the large reduced mass of such hydrogen bond modes result in low frequencies between 50 and 300 cm–1, corresponding to vibrational periods of 110 to 660 fs. Such periods are much longer than that of the X–H stretching mode and, thus, there is a clear separation of the time scales of hydrogen bond and X–H stretching motions. Third- and higher order terms of the vibrational potential containing mixed products of vibrational coordinates result in a coupling of different modes. Anharmonic coupling exists between the high-frequency X–H stretching mode and lowfrequency hydrogen bond modes and has been considered a potential broadening mechanism of the X–H, e.g., O–H stretching band [9, 11, 12]. The separation of time scales of the low- and high-frequency modes allows for a theoretical description in which the different states of the O–H stretching oscillator define adiabatic potential energy surfaces for the low-frequency modes [Fig. 15.1 (a)], similar to the separation of electronic and nuclear degrees of freedom in the Born–Oppen-
15.2 Vibrational Excitations of Hydrogen Bonded Systems
heimer picture of vibronic transitions. Vibrational transitions from different levels of the low-frequency oscillator in the vOH = 0 state to different low-frequency levels in the vOH = 1 state with a shifted origin of the potential result in a progression of lines which is centered at the pure X–H stretching transition and display a mutual line separation by one quantum "X of the low-frequency mode [Fig. 15.1 (b)]. The absorption strength is determined by the dipole moment of the vOH = 0 fi 1 transition of the O–H stretching mode and the Franck–Condon factors between the optically coupled levels of the low-frequency mode. With increasing difference in quantum number of the low-frequency mode in the vOH = 0 and 1 states, the Franck–Condon factors decrease and the progression lines become weaker for larger frequency separation from the progression center. For each low-frequency mode coupling to an O–H stretching oscillator, an independent progression of lines occurs. Such mechanisms can result in a strong broadening and/or spectral substructure of the overall O–H stretching band, even for a small number of absorption lines with large Franck–Condon factors. Thirdorder coupling strengths of the O–H stretching mode and hydrogen bond modes in acetic acid dimers of up to 100 cm–1 have been calculated recently [16].
Figure 15.1 Anharmonic coupling of the O–H stretching mode q and a low-frequency hydrogen bond (O...O) mode Q. (a) Potential energy diagram for the low-frequency mode in a single hydrogen bond. The potential energy surfaces as defined by the stretching mode and the quantum levels of the low-frequency mode are plotted for the vOH = 0 and 1 states as a function of the slow-mode coordinate Q.
(b) Progression of vibrational lines centered at the pure O–H stretching transition x0 with a line separation X, the frequency of the mode Q. (c) Potential energy diagram for two excitonically coupled O–H stretching oscillators. The two vOH = 1 potentials are separated by 2V0 (V0: excitonic coupling). (d) Progressions of vibrational lines resulting from the coupling scheme in (c).
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15 Coherent Low-frequency Motions in Condensed Phase Hydrogen Bonding and Transfer
In systems with several identical O–H groups and/or hydrogen bonds, excitonic coupling occurs between resonant oscillators. Such interaction which can be mediated by through-bond or through-space, e.g., dipole–dipole interactions, results in vibrational excitations delocalized over the different oscillators. Cyclic carboxylic acid dimers represent important model systems with coupled oscillators which have been analyzed theoretically by Marechal and Witkowski [12]. In their approach, the vOH = 0 states of the two O–H oscillators are considered degenerate and the coupling comes into play whenever one of the oscillators is excited. The excitonic coupling leads to a splitting of the vOH = 1 states [Fig. 15.1 (c)]. Considering both anharmonic and excitonic coupling, the coupled system has been described by taking into account the C2 symmetry of the pffiffifficyclic dimer and introducing symmetrized vibrational coordinates q = (1/ 2)(q1 – q2) and Qi,g,u = g,u pffiffiffi (1/ 2)(Qi,1 – Qi,2) (i = 1,2,..) for the stretching and the low-frequency modes i, respectively. Taking into account this symmetry and evaluating the dipole selection rules, one finds that transitions between |vu (qu)> states are infrared active whereas transitions between |vg (qg)> states contribute to the Raman band of the O–H stretching mode (vu,g: vibrational quantum numbers) [12, 14, 15]. The vu = 1 potential energy surface along the gerade Qi,g coordinate remains unaltered whereas the excitonic coupling V0 leads to a splitting of the vu = 1 potential energy surface along the ungerade Qi,u coordinate by 2V0. The resulting line shape consists of two different progressions between the vi,Q = 0 level of the Qi,u mode in the vu = 0 state and the vi;Q levels in the vu = 1 state as well as between the vi,Q = 1 level in the vu = 0 state and the vi;Qþ levels in the vu = 1 state [Fig. 15.1 (d)]. Simultaneously, the number of quanta in the Qi,g mode can be changed when exciting the system to the vOH = 1 state, introducing an additional degeneracy of the lines in the respective progression. An individual molecule displays only one progression, depending on whether the vi,Q = 0 or vi,Q = 1 level in the vu = 0 state is populated. In an ensemble of molecules at finite vibrational temperature, both levels are populated and both series of lines contribute to the overall vibrational band. The excitonic coupling strength of the O–H stretching oscillators in carboxylic acid dimers has remained uncertain. Early work [12] has suggested values of V0 = –85 cm–1 whereas a later analysis assumed much smaller values [13]. For the C=O stretching oscillators of acetic acid dimers, a coupling strength of approximately 50 cm–1 has been reported [17]. Fermi resonances between the vOH = 1 state of the stretching mode and overtones or combination bands of modes in the fingerprint range result in a splitting of the O–H stretching transition into different components with a separation determined by the respective coupling. For large couplings, Fermi resonances have a strong influence on the line shape of the O–H stretching band, leading to features like the so-called Evans window. Studies of the linear absorption band of the O–H stretching mode in carboxylic acid dimers have suggested Fermi resonances between the vOH = 1 level and the dOH = 2 bending level, as well as between vOH = 1 and combination tones of dOH with vC–O and vC=O stretching modes [13]. More recent theoretical work suggests an absolute value of the third order coupling for such modes of the order of 100 cm–1 and attributes the coarse shape of the O–H
15.3 Low-frequency Wavepacket Dynamics of Hydrogen Bonds in the Electronic Ground State
stretching band to Fermi resonances, without, however, allowing for a full quantitative understanding [18, 19]. Very recently, nonlinear two-dimensional (2D) infrared spectroscopy provided direct evidence for Fermi resonances through off-diagonal peaks in the 2D spectra [20]. A theoretical analysis of such experiments gave couplings of 40 to 150 cm–1 between the O–H stretching mode and combination and overtones of fingerprint vibrations. This has allowed for a quantitative modeling of the linear O–H stretching absorption spectrum [21]. In summary, the couplings discussed so far transform the hydrogen stretching oscillator into a vibrational multi-level system with a multitude of transition lines. The interaction with the fluctuating surrounding leads to an additional broadening of the individual lines by vibrational dephasing [22–25]. Nonlinear vibrational spectroscopy allows one to separate the different couplings in the nonlinear timeresolved response following femtosecond vibrational excitation. In particular, the coherent vibrational dynamics can be isolated from processes of population relaxation [26] and energy redistribution.
15.3 Low-frequency Wavepacket Dynamics of Hydrogen Bonds in the Electronic Ground State
The multi-level character of X–H stretching excitations in hydrogen bonds allows the preparation of quantum-coherent superpositions of states. Excitation of a set of transitions within the O–H stretching band by a broadband femtosecond pulse creates a wavepacket moving along the low-frequency vibrational coordinates contributing to this superposition. In many liquids, such motions are rapidly damped due to coupling with the fluctuating environment. In recent pump–probe experiments, however, underdamped, i.e., oscillatory motions along hydrogen bond modes have been observed for picoseconds after impulsive excitation by 100 fs pulses. In the following, we review such results. 15.3.1 Intramolecular Hydrogen Bonds
Low-frequency wavepacket dynamics were first observed in intramolecular hydrogen bonds with a well-defined geometry [27–31]. The enol tautomer of 2-(2¢-hydroxyphenyl)benzothiazole (HBT) represents such a system: in the electronic ground state, an O–H···N or – in the deuterated compound HBT-D (Fig. 15.2) – an O–D···N bond is formed with a strongly red-shifted and broadened hydrogen/ deuterium donor stretching band. In this enol ground state, the hydrogen bond dynamics have been studied in mid-infrared pump–probe experiments with a time resolution of 100 fs. The pump pulse created a vibrational excitation on the O–H or O–D stretching band and the resulting change of O–H/O–D stretching absorption was measured by weak probe pulses [31]. In Fig. 15.3, results of a pump–probe study of HBT-D dissolved in toluene are summarized. The spectrally
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15 Coherent Low-frequency Motions in Condensed Phase Hydrogen Bonding and Transfer D
0.2 Absorbance
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0.1
0.0
2400
2300
2200
2100
2000
Frequency (cm-1) Figure 15.2 Molecular structure of HBT-D together with the linear O–D stretching band (concentration of HBT in toluene c = 0.15 M).
resolved change of vibrational absorption [Fig. 15.3 (a)] exhibits a decrease in absorption (bleaching) with a maximum at 2210 cm–1 and an enhanced absorption at higher frequencies. The bleaching is due to the depletion of the vOD = 0 state and stimulated emission from the vOD = 1 state, whereas the blue-shifted absorption originates from a hot ground state formed by femtosecond relaxation of the v = 1 state of the O–D stretching oscillator. In the hot ground state, the vOD = 1 state has been depopulated and other anharmonically coupled vibrations have accepted the excess energy supplied by the pump pulse. On a time scale of several tens of picoseconds, the hot ground state cools by energy transfer to the surrounding solvent. In Fig. 15.3 (b), the change in vibrational absorption is plotted as a function of pump–probe delay for two different frequency positions in the probe spectrum. The signals at negative delay times and around delay zero are dominated by the perturbed free induction decay of the vibrational polarization and the coherent pump–probe coupling. At positive delay times, i.e., for a sequential interaction of the molecules with pump and probe pulses, the transients exhibit strong oscillations with a period of 280 fs. Oscillations with this period occur throughout the O–D stretching band. The corresponding Fourier transform [Fig. 15.3 (c), lower trace] peaks at 120 cm–1. The electric field envelope of the femtosecond pump pulse which is short compared to the period of the oscillations in Fig. 15.3 (b) covers a frequency range much broader than the energy spacing of individual levels of the low-frequency mode. In other words, the pump spectrum overlaps with several lines of the vibrational progression depicted in Fig. 15.1 (b). As a result, impulsive dipole excitation from the vOD = 0 to 1 state creates a nonstationary superposition of the wavefunctions of low-frequency levels in the vOD = 1 state with a well-defined mutual phase. This quantum-coherent wavepacket oscillates in the vOD = 1 state with the frequency X of the low-frequency mode and leads to a modulation of O–H stretching absorption which is measured by the probe pulses. In addition to the wavepacket in the vOD = 1 state, impulsive Raman excitation within the spectral envelope of
15.3 Low-frequency Wavepacket Dynamics of Hydrogen Bonds in the Electronic Ground State
Figure 15.3 (a) Transient O–D absorption spectra of HBT-D for delay times of 0.3 ps (points), 1 ps (circles), and 4 ps (squares). The change of absorbance DA = –log(T/T0) is plotted as a function of probe frequency (T,T0: transmission with and without excitation). (b) Time-resolved absorbance changes measured at probe frequencies of 2188 and
(a)
(c)
(b) (b)
(d)
2358 cm–1. Pronounced oscillatory signals are observed. (c) Fourier transform of the oscillatory absorbance changes of (b) (lower trace) and resonance Raman spectrum of HBT displaying a low-frequency band at 120 cm–1 (upper trace). (d) Microsopic elongations connected with a wavepacket motion along the 120 cm–1 in-plane mode.
the pump pulse creates a wavepacket in the vOD = 0 state, also undergoing oscillatory motion and modulating the O–H stretching absorption. The oscillatory absorbance change is observed over a period of 1 to 2 ps, pointing to a comparably slow vibrational dephasing, i.e., loss of mutual phase of the wavefunctions contributing to the underlying wavepacket. The wavepacket in the vOD = 1 state is damped effectively by population relaxation on a time scale of several hundreds of femtoseconds and, consequently, makes a minor contribution to the long-lived oscillations. In contrast, the wavepacket in the vOD = 0 state is exclusively damped by fluctuating forces exerted by the liquid environment and/or other intramolecular modes of HBT. Obviously, such damping is comparatively weak, resulting in an underdamped character of the low-frequency motions. The phase of the oscillatory pump–probe signal displays a change by approximately p at the maximum of the O–D stretching band, even for pump pulses centered in the wing of the linear absorption band [31]. This finding demonstrates a resonant enhancement of the Raman generation process by the O–D stretching transition moment, pointing again to a strong anharmonic coupling of the low- and high-frequency modes.
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15 Coherent Low-frequency Motions in Condensed Phase Hydrogen Bonding and Transfer
The frequency of the coherent motions agrees very well with the position of a low-frequency Raman band of HBT [Fig. 15.3 (c), upper trace]. Motion along this mode is connected with the microscopic elongations shown in Fig. 15.3 (d) which lead to a strong modulation of the geometry of the intramolecular hydrogen bond. Thus, our time-resolved data give a direct real-time image of hydrogen bond motions. The impulsive excitation scheme of low-frequency wavepackets applied here is not mode-specific. In principle, all modes displaying a finite anharmonic coupling to the O–H/O–D stretching mode and a vibrational frequency which is smaller than or comparable to the pump bandwidth are excited. This subset of modes can include vibrations not affecting the hydrogen bond geometry directly. In HBT, low-frequency wavepacket motion is dominated by a single mode modulating the length and strength of the hydrogen bond. In the next section, acetic acid dimers displaying coherent motions along several low-frequency modes will be discussed. 15.3.2 Hydrogen Bonded Dimers
Cyclic dimers of carboxylic acids represent important model systems forming two coupled intermolecular hydrogen bonds [Fig. 15.1 (d), inset of Fig. 15.4]. The linear vibrational spectra of carboxylic acid dimers have been studied in detail, both in the gas and the liquid phase, and a substantial theoretical effort has been undertaken to understand the line shape of their O–H and/or O–D stretching bands. In contrast, there have been only a few experiments on the nonlinear vibrational
Figure 15.4 (a) Linear O–H stretching band of cyclic acetic acid dimers. (b) Transient vibrational absorption spectra measured for different pump–probe delays. The change of vibrational absorbance DA|| for pump and probe pulses of parallel linear polarization is plotted as a function of the probe frequency.
15.3 Low-frequency Wavepacket Dynamics of Hydrogen Bonds in the Electronic Ground State
response. The coupling of the two carbonyl oscillators in acetic acid dimers has been investigated by femtosecond pump–probe and photon-echo measurements [17] and vibrational relaxation following O–H stretching excitation has been addressed in picosecond pump–probe studies [32]. In the following, recent extensive pump–probe studies of cyclic acetic acid dimers in the femtosecond time domain are presented [16, 33, 34]. Dimer structures containing two O–H···O (OH/OH dimer) or two O–D···O (OD/OD dimer) hydrogen bonds were dissolved in CCl4 at concentrations between 0.2 and 0.8 M. Two-color pump–probe experiments with independently tunable pump and probe pulses were performed with a 100 fs time resolution. Approximately 1% of the dimers present in the sample volume were excited by the 1 lJ pump pulse. After interaction with the sample, the probe pulses were spectrally dispersed to measure transient vibrational spectra with a spectral resolution of 6 cm–1. The steady state and the transient O–H stretching absorption spectra of OH/OH dimers are displayed in Fig. 15.4 (a) and (b), respectively. The transient spectra show a strong bleaching in the central part of the steady-state band and enhanced absorption on the red and blue wing. The bleaching which consists of a series of comparably narrow spectral dips, originates from the depopulation of the vOH = 0 state and stimulated emission from the vOH = 1 state. The enhanced absorption at small frequencies is due to the red-shifted vOH = 1 fi 2 transition and decays by depopulation of the vOH = 1 state with a lifetime of approximately 200 fs. The enhanced absorption on the blue side is caused by the vibrationally hot ground state formed by relaxation of the vOH = 1 state, similar to the behavior discussed for HBT-D. This transient absorption decays by vibrational cooling on a 10 to 50 ps time scale. Transient spectra have also been measured for the OD/OD and the mixed OH/OD dimers – both on the O–H and O–D stretching bands – and display very similar behavior. The time evolution of the nonlinear O–H stretching absorption shows pronounced oscillatory signals for all types of dimers studied. In Fig. 15.5, data for OD/OD dimers are presented which were recorded at 3 different spectral positions in the O–D stretching band. For positive delay times, one finds rate-like kinetics which is due to population and thermal relaxation of the excited dimers and, more importantly, superimposed by very strong oscillatory absorption changes. In contrast to the intramolecular hydrogen bonds discussed above, the time-dependent amplitude of the oscillations displays a slow modulation with an increase and a decrease on a time scale of several hundreds of femtoseconds. Such features of a beatnote demonstrate the presence of more than one oscillation frequency. In Fig. 15.6 (a), the Fourier transforms of the oscillatory signals are plotted for the 3 spectral positions. There are 3 prominent frequency components, a strong doublet with maxima at 145 and 170 cm–1 and a much weaker component around 50 cm–1. Comparative pump–probe studies of OH/OH dimers reveal a similar doublet at 145 and 170 cm–1 with slightly changed relative intensities of the two components. The 50 cm–1 component is practically absent in the OH/OH case.
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15 Coherent Low-frequency Motions in Condensed Phase Hydrogen Bonding and Transfer
Figure 15.5 (a) – (c) Time-resolved change of O–D stretching absorbance as a function of the pump–probe delay for 3 different probe frequencies (solid lines). Around delay zero, coherent pump–probe coupling leads to a strong signal. The absorbance changes for positive delay times consist of rate-like components due to population relaxation of the
O–D stretching oscillator and oscillatory contributions. Dash-dotted lines: Numerical fits of the rate-like signals. (d) – (f) Oscillatory signals after subtraction of the rate-like components. The oscillations are due to coherent wavepacket motions along several low-frequency modes.
Figure 15.6 (a) Fourier spectra of the oscillatory absorbance changes of Fig. 15.5 (d) – (f). The spectra are scaled relative to each other and display 3 low-frequency modes. (b) Low-frequency spontaneous Raman spectrum of acetic acid (taken from Ref. [35]).
15.3 Low-frequency Wavepacket Dynamics of Hydrogen Bonds in the Electronic Ground State
The two stretching oscillators in the OH/OH and OD/OD dimers should display an excitonic coupling resulting in a splitting of their v = 1 states, on top of the anharmonic coupling to low-frequency modes. In the linear absorption spectrum of the ensemble of dimers, this results in two separate low-frequency progressions originating from the vQ = 0 and vQ = 1 levels in the v = 0 state of the stretching vibrations [cf. Fig. 15.1 (d)]. In thermal equilibrium, a particular dimer populates only one of the vQ levels at a certain instant in time and, thus, only one of the progressions can be excited. Consequently, a quantum coherent nonstationary superposition of the split vOH = 1 states of the stretching mode cannot be excited in an individual dimer and quantum beats due to excitonic coupling are absent in the pump–probe signal. This behavior is also evident from the identical oscillatory response of OD/OD and OH/OD dimers, the latter displaying negligible excitonic coupling because of the large frequency mismatch between the O–H and the O–D stretching oscillator. A contribution of quantum beats between states split by Fermi resonances can also be ruled out. There are different Fermi resonances within the O–H and O–D stretching bands [13, 21]. Depending on the spectral positions of pump and probe, this should lead to a variation of the oscillation frequencies, in particular when comparing O–H and O–D stretching excitations. Such behavior is absent in the experiment demonstrating identical oscillation frequencies for O–H and O–D stretching excitation which remain unchanged throughout the respective stretching band. The oscillatory absorption changes are due to coherent wavepacket motions along several low-frequency modes which anharmonically couple to the stretching modes. Wavepackets in the v = 0 state of the O–H or O–D stretching oscillators which are generated through an impulsive resonantly enhanced Raman process, govern the oscillatory response whereas wavepackets in the v = 1 states are strongly damped by the fast depopulation processes. Low-frequency modes of acetic acid have been studied in a number of Raman experiments. The spectrum in Fig. 15.6 (b) was taken from Ref. [35] and displays three maxima around 50, 120 and 160 cm–1. The number of subbands in such strongly broadened spectra and their assignment have remained controversial [36]. Recently, the character of the different low-frequency modes and their anharmonic coupling to the O–H stretching mode have been studied in normal mode calculations based on density functional theory [16]. In Fig. 15.7 (a), the calculated Raman transitions (solid bars) and the respective cubic force constants for coupling to the hydrogen stretching mode (hatched bars) are shown for the OH/OH and OD/OD dimers. There are four vibrations, the methyl torsion at 44 cm–1 [Fig. 15.7 (b)], the out-of-plane wagging mode at 118 cm–1, the in-plane bending mode around 155 cm–1 [Fig. 15.7 (c)], and the dimer stretching mode at 174 cm–1 [Fig. 15.7 (d)]. In this group, the in-plane bending and the dimer stretching modes couple strongly to the hydrogen/deuterium stretching mode via a third-order term in the vibrational potential that dominates compared to higher order terms. The coupling of the methyl torsion is much weaker, that of the out-of-plane wagging mode even negligible. Such theoretical results are in good agreement with the experimental find-
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15 Coherent Low-frequency Motions in Condensed Phase Hydrogen Bonding and Transfer
(b)
(c)
(d)
Figure 15.7 (a) Calculated low-frequency Raman spectra (solid bars, left ordinate) and cubic force constants U describing the coupling to the O–H or O–D stretching modes (hatched bars, right ordinate scale). Plus and minus signs indicate the sign of the force constants. (b) – (d) Microscopic elongations of the methyl torsion at 50 cm–1, the dimer in-plane bending at 155 cm–1 and the dimer stretching at 170 cm–1.
15.4 Low-frequency Motions in Excited State Hydrogen Transfer
ings: the strong doublet in the Fourier spectra [Fig. 15.6 (a)] is assigned to the inplane dimer bending and the dimer stretching, the weak band around 50 cm–1 to the methyl torsion. The out-of-plane wagging is not observed at all. It should be noted that the spectra derived from the oscillatory pump–probe signals, i.e., time domain data, allow a much better separation of the low-frequency modes coupling than the steady-state spontaneous Raman spectra. The calculated anharmonic couplings U of the O–H/O–D stretching vibrations and the 3 low-frequency modes observed are of the same order of magnitude as the couplings calculated for Fermi resonances between the vOH = 1 state and combination and overtones of the O–H bending and other fingerprint modes [21]. In conclusion, the results presented here demonstrate how nonlinear pump– probe spectroscopy allows isolation of the anharmonic couplings of hydrogen bond modes and the O–H/O–D stretching mode. Such couplings underlie oscillatory wavepacket motions contributing to the pump–probe signals, whereas excitonic couplings and Fermi resonances play a minor role. The results for cyclic acetic acid dimers demonstrate coherent intermolecular motions for several picoseconds. This should allow the generation of tailored vibrational wavepackets by excitation with phase-shaped infrared pulses and may pave the way towards controlled infrared-induced hydrogen transfer in the electronic ground state.
15.4 Low-frequency Motions in Excited State Hydrogen Transfer
Transient vibrational spectra of electronically excited molecules give insight into local changes of molecular geometries due to photoinduced hydrogen transfer which occur in systems like HBT. An early picosecond infrared study of the photoinduced enol-keto transformation of HBT [Fig. 15.8 (a)] has revealed new vibrational bands at 1535 cm–1 and 2900 cm–1 [7]. The band at 1540 cm–1 was attributed to the stretching vibration of the carbonyl (C=O) group formed by hydrogen transfer and being part of a strong hydrogen bond with the newly formed N–H group of the keto tautomer. The comparatively low frequency of the new band is due to the fact that this mode involves, in addition to the carbonyl stretch, elongations of bonds in the phenyl ring. Correspondingly, the band around 2900 cm–1 was interpreted as an N–H stretching band. The new bands were formed within the time resolution of the experiment of 5 ps, pointing to a much faster hydrogen transfer process. A similar study with substantially improved time resolution has been reported recently [8, 37, 38]. In such experiments, HBT was excited to the enol-S1 state by a 40 fs pulse at 350 nm, i.e., nearly resonant to the S0–S1 transition. Transient vibrational spectra were measured with 100 fs mid-infrared probe pulses which were spectrally dispersed after interaction with the sample. Such spectra are displayed in Fig. 15.8 (b) for different delay times, together with the stationary vibrational spectrum in the enol ground state of HBT [Fig. 15.8 (c)]. In agreement with Ref. [7], the spectra display a prominent new band around 1530 cm–1 with a spectral
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15 Coherent Low-frequency Motions in Condensed Phase Hydrogen Bonding and Transfer
Figure 15.8 (a) Molecular structures of the enol (left) and keto (right) tautomer of HBT. (b) Transient vibrational spectra of HBT after femtosecond excitation of the enol tautomer at 335 nm. The change in vibrational absorbance in mOD is plotted as a function of probe frequency for different time delays after electronic excitation. The spectra show the build-up of the carbonyl stretching band of the keto tautomer at 1535 cm–1. The absorbance changes at lower frequencies are due to skeletal modes. (c) Ground state
vibrational spectrum of enol HBT. (d) Frequency position of the center of the carbonyl stretching band as a function of delay time. Data (points) and numerical rate equation fit of the blue shift with time constants of 0.5 and 5 ps (solid line). (e) Deviation of the center position from the rate-like blue-shift of (d) (points). The solid line represents a calculated oscillatory response with oscillation frequencies of 60 and 120 cm–1 and a damping time of 1 ps.
width of about 15 cm–1. The formation of this band occurs with a delay of 30 to 50 fs, representing a measure of the hydrogen transfer time. With increasing time delay, this band shows a continuous blue shift by about 5 cm–1 which is superimposed by weak oscillations of the line center position [Fig. 15.8 (d) and (e)]. The oscillations consist of a prominent 120 cm–1 frequency component and a weak 60 cm–1 contribution. The carbonyl stretching and other fingerprint bands of keto HBT show only minor changes of their spectral envelope and the spectrally integrated absorption as a function of time. In particular, contributions from the v = 1 fi 2 transition of the respective mode are absent. Thus, the carbonyl group of the keto tautomer is formed without excitation of its stretching motion and the fingerprint modes at frequencies between 1000 and 1500 cm–1 remain in their v = 0 states. On the other hand, the energy difference between the enol S1 and the keto S1 state of approxi-
15.4 Low-frequency Motions in Excited State Hydrogen Transfer
mately 3000 cm–1 is released as excess energy in the hydrogen transfer process. Such excess energy is mainly contained in low-frequency modes of the keto species, as has been discussed in detail in Ref. [8]. Resonance Raman studies of HBT with excitation in the range of the S0–S1 absorption band have demonstrated large Franck–Condon factors of the in-plane mode at 120 cm–1 as well as other low-frequency modes at 266, 293, 505, and 537 cm–1 [39]. Thus, the 120 cm–1 oscillator is elongated upon photoexcitation to the S1 state and undergoes an underdamped oscillatory wavepacket motion. The latter becomes visible through oscillations of the frequency position of the keto carbonyl stretching vibration to which the 120 cm–1 mode couples anharmonically. As the carbonyl stretching mode is a clear signature of the keto reaction product formed in the excited state, a potential contribution of coherent motions in the enol ground state (created through a pump-induced Raman process) is not visible. It is important to note that the low-frequency oscillations persist much longer than the hydrogen transfer time of 30 to 50 fs, showing that the transfer reaction does not result in a damping of such in-plane motion. In an indirect approach not providing structural information, femtosecond excited state hydrogen transfer has been studied via the transient electronic spectra of the initial and the product species [38, 40–43] . In most cases, the predominant ground state species was excited in the range of its S0¢–S1¢ absorption band and the onset of stimulated emission or fluorescence [44] on the S1–S0 transition of the product species was monitored. Some of such studies have been performed with sub-30 fs pump and probe pulses, i.e., a somewhat higher time resolution than the infrared experiment discussed above. Oscillatory signals superimposed on the rise of product emission have been observed for the first time with the benzotriazole compound TINUVIN P [41]. In TINUVIN P, oscillation frequencies of 250 and 470 cm–1 were found, reflecting quantum-coherent wavepacket motions along two low-frequency modes with large Franck–Condon factors. Due to the coupling of those modes to the electronic transition of the keto-type product species, the product emission exhibits oscillations. The two modes observed strongly modulate the intramolecular hydrogen bonding geometry. In HBT, systematic pump–probe studies show a femtosecond rise time of keto emission depending on the spectral position within the emission band, i.e., ranging from about 60 fs at 530 nm to 170 fs around 650 nm [40, 42, 43]. Such kinetics are superimposed by oscillatory wavepacket motions with frequencies of 118, 254, 289 and 529 cm–1 [42, 43]. The hydrogen transfer occurring on a 50 fs time scale points to an essentially barrierless excited state potential along the reaction pathway. The transfer appears, however, much slower than the period of the O–H stretching vibration of approximately 10 fs. This fact demonstrates that hydrogen transfer does not involve a simple stretching motion towards the acceptor atom but requires motion along vibrational modes at low frequencies. Taking into account both femtosecond pump–probe data and the results of resonance Raman studies, the following qualitative picture of excited state hydrogen transfer emerges:
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1. Excitation of the enol species to the S1 state induces a redistribution of electronic charge. For a strong electronic coupling between the initially excited vibronic states and the keto excited state, this charge redistribution occurs on a time scale much faster than 20 fs and establishes an excited state potential energy surface with a minimum for the keto-type configuration of the molecule. 2. The initial dynamics of hydrogen transfer on this potential energy surface are determined by the propagation of the vibrational wavepacket created upon electronic excitation. This wavepacket is made up of Raman active modes with high Franck–Condon factors which are excited within the spectral width of the electric field envelope of the pump pulse. In particular, low-frequency modes including the 120 cm–1 in-plane vibration contribute. In contrast, the O–H stretching mode with a negligible Franck-Condon factor is not part of the wavepacket. The low-frequency wavepacket oscillations persist for 1–2 ps, demonstrating that the vibrational potential of such modes is not changed significantly upon hydrogen transfer. 3. The non-instantaneous (30–60 fs) rise of both the carbonyl stretching absorption and the keto emission shows that the excited state reaction pathway involves propagation along low-frequency modes. In the initial Franck–Condon window where the wavepacket is created by electronic excitation, a barrier exists along the hydrogen coordinate preventing a direct hydrogen transfer along this coordinate. With increasing time, the motion of the wavepacket along individual or a combination of low-frequency modes brings the system into a range of the excited state potential where a barrierless channel exists for motion along a high-frequency coordinate. In this range, the hydrogen is transferred from the enol to the keto configuration. The overall time for hydrogen transfer is set by a fraction of the period of a low-frequency mode. The fact that the 120 cm–1 mode with a period of 280 fs strongly modulates the hydrogen bond geometry and displays a pronounced anharmonic coupling to both the O–H stretching mode of enol-HBT (cf. Section 15.3.1) and the carbonyl stretching of keto-HBT suggests a prominent role of this mode in hydrogen transfer. 4. Hydrogen transfer represents a non-reversible reaction with a quantum yield close to 100%, i.e., there is no return to the enol geometry after the fast formation of the keto product. Calculations of wavepacket propagation in the S1 state, assuming harmonic potentials for the modes contributing to
15.5 Conclusions
the initial wavepacket, demonstrate a substantial spreading of the wavepacket on the 30–50 fs time scale. In addition, intramolecular vibrational relaxation leads to a transfer of excitation into a multitude of other modes, corresponding to a multidimensional dephasing process. Both mechanisms stabilize the keto product, even though the directly excited low-frequency modes involved in the reaction continue to oscillate for periods much longer than the hydrogen transfer time. The weak 60 cm–1 frequency component present in the oscillations of Fig. 15.8 (e) is due to an underdamped mode which is not Raman active and, thus, not elongated upon electronic excitation. Instead, it is excited by vibrational redistribution on a time scale shorter than the vibrational period of 550 fs. At later times, transient populations of a larger manifold of modes also underlie the blue-shift of the fingerprint modes mediated via anharmonic couplings [8, 45].
15.5 Conclusions
The results discussed in this chapter demonstrate a prominent role of vibrational low-frequency quantum coherences for the structural and reactive dynamics of hydrogen bonds in the liquid phase. Underdamped oscillatory motions of modes directly affecting the hydrogen bonding geometry have been induced via vibrational excitation of the hydrogen donor stretching mode in the electronic ground state or via electronic excitation to the S1 state of molecules undergoing ultrafast intramolecular hydrogen transfer. In the electronic ground state, femtosecond excitation of the O–H or O–D stretching vibrations generates a nonstationary coherent superposition of several quantum states of a low-frequency mode that couples anharmonically to the fast stretching vibration. In the intramolecular hydrogen bonds investigated, coherent motions are dominated by a single mode, whereas motions along several underdamped modes have been found in hydrogen-bonded dimers of acetic acid. The coherent low-frequency response is dominated by wavepackets in the vOH = 0 state which are created through a Raman process resonantly enhanced by the O–H stretching transition dipole. The occurrence of wavepacket motions also confirms the much debated picture of vibrational lowfrequency progressions within the strongly broadened O–H stretching bands, as introduced in the early theoretical literature on linear vibrational spectra. The picosecond decay of low-frequency coherences allows generation and manipulation of vibrational motion with phase-shaped infrared pulses. This may be of particular interest for reactive systems in which processes of hydrogen transfer along hydrogen bonds occur and may become accessible for optical control. In excited state hydrogen transfer occurring on sub-100 fs time scales, Ramanactive low-frequency modes that couple strongly to the electronic S0–S1 transition,
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are part of the reaction coordinate. Quantum coherent propagation along such coordinates sets the time scale for the intramolecular transfer of the hydrogen, creating new molecular structure without significant excitation of high-frequency vibrational modes. The excess energy released in the reaction is contained in lowfrequency vibrations of the product species. Spreading of the vibronic wavepacket and vibrational relaxation are crucial for the stabilization of the reaction product. This qualitative picture describes hydrogen transfer along a pre-existing intramolecular hydrogen bond for a larger class of molecular systems. A quantitative description, however, requires a more detailed analysis of nuclear motions and anharmonic couplings in the electronically excited state.
Acknowledgements
I would like to acknowledge the important contributions of my present and former coworkers Jens Stenger, Dorte Madsen, Nils Huse, Karsten Heyne, Jens Dreyer, Peter Hamm, and Erik Nibbering to the work reviewed in this chapter. It is my pleasure to thank Casey Hynes for many interesting discussions. I also thank the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie for financial support.
References 1 P. Schuster, G. Zundel, C. Sandorfy
(Eds.), The Hydrogen Bond: Recent Developments in Theory and Experiment, Vol. I–III, North Holland, Amsterdam, 1976. 2 T. Elsaesser, H. J. Bakker (Eds.), Ultrafast Hydrogen Bonding Dynamics and Proton Transfer Processes in the Condensed Phase, Kluwer, Dordrecht, 2002. 3 S. Mukamel, Principles of Nonlinear Optical Spectroscopy, Oxford University Press, Oxford, 1995. 4 M. D. Fayer (Ed.), Ultrafast Infrared and Raman Spectroscopy, Marcel Dekker, New York, 2001. 5 E. T. J. Nibbering, T. Elsaesser, Chem. Rev. 2004, 104, 1887–1914. 6 T. Elsaesser, W. Kaiser, W. Lttke, J. Phys. Chem. 1986, 90, 2901–2905. 7 T. Elsaesser, W. Kaiser, Chem. Phys. Lett. 1986, 128, 231–237. 8 M. Rini, J. Dreyer, E.T.J. Nibbering, T. Elsaesser, Chem. Phys. Lett. 2003, 374, 13–19.
9 C. Sandorfy, Bull. Pol. Acad. Sci: Chem.
1995, 43, 7–24. 10 W. Mikenda, S. Steinbock, J. Mol. Struct.
1996, 384, 159–163. 11 B. I. Stepanov, Nature 1946, 157, 808–
810. 12 Y. Marchal, A. J. Witkowski, J. Chem.
Phys. 1968, 48, 3697–3705. 13 Y. Marchal, J. Chem. Phys. 1987, 87,
6344–6353. 14 O. Henri-Rousseau, P. Blaise,
15 16
17 18
D. Chamma, Adv. Chem. Phys. 2002, 121, 241–309. D. Chamma, O. Henri-Rousseau, Chem. Phys. 1999, 248, 53–70. K. Heyne, N. Huse, J. Dreyer, E. T. J. Nibbering, T. Elsaesser, S. Mukamel, J. Chem. Phys. 2004, 121, 902–913. M. Lim, R. M. Hochstrasser, J. Chem. Phys. 2001, 115, 7629–7643. G. M. Florio, T. S. Zwier, E. M. Myshakin, K. D. Jordan,
References E. L. Sibert III, J. Chem. Phys. 2003, 118, 1735–1746. 19 C. Emmeluth, M. A. Suhm, D. Luckhaus, J. Chem. Phys. 2003, 118, 2242–2255. 20 N. Huse, B. D. Bruner, M. L. Cowan, J. Dreyer, E. T. J. Nibbering, R. J. D. Miller, T. Elsaesser, Phys. Rev. Lett., submitted. 21 J. Dreyer, J. Chem. Phys., submitted. 22 D. W. Oxtoby, Adv. Chem. Phys. 1979, 40, 1–48. 23 N. Rsch, M. Ratner, J. Chem. Phys. 1974, 61, 3344–3351. 24 S. Bratos, J. Chem. Phys. 1975, 63, 3499– 3509. 25 G. N. Robertson, J. Yarwood, J. Chem. Phys. 1978, 32, 267–282. 26 R. Rey, K. B. Moller, J. T. Hynes, Chem. Rev. 2004, 104, 1915–1928. 27 J. Stenger, D. Madsen, J. Dreyer, E. T. J. Nibbering, P. Hamm, T. Elsaesser, J. Phys. Chem. A 2001, 105, 2929–2932. 28 D. Madsen, J. Stenger, J. Dreyer, P. Hamm, E. T. J. Nibbering, T. Elsaesser, Bull. Chem. Soc. Jpn. 2002, 75, 909–917. 29 H. Naundorf, G. A. Worth, H. D. Meyer, O. Khn, J. Phys. Chem. A 2002, 106, 719–724. 30 O. Khn O, H. Naundorf, Phys. Chem. Chem. Phys. 2003, 5, 79–86. 31 D. Madsen, J. Stenger, J. Dreyer, E. T. J. Nibbering, P. Hamm, T. Elsaesser, Chem. Phys. Lett. 2001, 341, 56–62.
32 G. Seifert, T. Patzlaff, H. Graener,
Chem. Phys. Lett. 2001, 333, 248–254. 33 K. Heyne, N. Huse, E. T. J. Nibbering,
T. Elsaesser, Chem. Phys. Lett. 2003, 369, 591–596. 34 K. Heyne, N. Huse, E. T. J. Nibbering, T. Elsaesser, J. Phys: Condens. Matter 2003, 15, S129–S136. 35 O. F. Nielsen, P. A. Lund, J. Chem. Phys. 1983, 78, 652–655. 36 T. Nakabayashi, K. Kosugi, N. Nishi, J. Phys. Chem. A 1999, 103, 8595–8603. 37 M. Rini, A. Kummrow, J. Dreyer, E. T. J. Nibbering, T. Elsaesser, Faraday Discuss. 2002, 122, 27–40. 38 T. Elsaesser, in: Ultrafast Hydrogen Bonding Dynamics and Proton Transfer Processes in the Condensed Phase, T. Elsaesser, H.J. Bakker (Eds.), Kluwer, Dordrecht, 2002, pp. 119–153. 39 M. Pfeiffer, K. Lenz, A. Lau, T. Elsaesser, T. Steinke, J. Raman Spectrosc. 1997, 28, 61–72. 40 F. Laermer, T. Elsaesser, W. Kaiser, Chem. Phys. Lett. 1988, 148, 119–124. 41 C. Chudoba, E. Riedle, M. Pfeiffer, T. Elsaesser, Chem. Phys. Lett. 1996, 263, 622–628. 42 S. Lochbrunner, A. J. Wurzer, E. Riedle, J. Chem. Phys. 2000, 112, 10699–10702. 43 S. Lochbrunner, A. J. Wurzer, E. Riedle, J. Phys. Chem. A 2003, 107, 10580– 10590. 44 D. Marks, H. Zhang, P. Borowicz, A. Grabowska, M. Glasbeek, Chem. Phys. Lett. 1999, 309, 19–25. 45 P. Hamm, S. M. Ohline, W. Zinth, J. Chem. Phys. 1997, 106, 519–529.
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16 Proton-Coupled Electron Transfer: Theoretical Formulation and Applications Sharon Hammes-Schiffer
16.1 Introduction
The coupling between proton and electron transfer plays an important role in a wide range of chemical and biological processes, including photosynthesis [1–7], respiration [8, 9], and numerous enzyme reactions [10]. The coupled transfer of protons and electrons is denoted proton-coupled electron transfer (PCET) [11–14]. In general, the electron and proton can transfer between different centers and can transfer either in the same direction or in different directions. A variety of model systems have been investigated experimentally to elucidate the general mechanisms of PCET reactions [15–20]. The theoretical description of these types of PCET reactions is challenging due to the quantum nature of the transferring electron and proton, the importance of nonadiabatic effects, and the wide range of timescales associated with the reaction. A number of theoretical approaches have been developed to address these challenges [21–36]. This chapter presents a general theoretical formulation for PCET and summarizes the applications of this theory to a wide range of experimentally relevant systems. Section 16.2 reviews the fundamental physical concepts of PCET reactions and discusses approaches for inclusion of the proton donor–acceptor motion, explicit molecular solvent and protein, and the corresponding dynamical effects. Section 16.3 provides an overview of theoretical studies of PCET reactions in solution and in proteins. General conclusions are given in Section 16.4.
Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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16.2 Theoretical Formulation for PCET 16.2.1 Fundamental Concepts
PCET systems involve a wide range of timescales associated with the active electrons (i.e., the transferring electron and the bonding electrons in the proton transfer interface), transferring proton(s), donor and acceptor groups, and solvent electrons and nuclei. In our theoretical formulation [26–28], the active electrons and transferring proton are treated quantum mechanically. The solvent is described with either a dielectric continuum or an explicit molecular representation. The Born–Oppenheimer approach [37], which assumes that the solvent electronic degrees of freedom are infinitely fast relative to all other degrees of freedom, is adopted. The electron donor and acceptor are assumed to be fixed in space, which is a reasonable approximation for systems in which the electron donor and acceptor consist of heavy groups such as metal complexes. The motion of the proton donor and acceptor has been included at a number of different levels [30]. The effects of additional intramolecular vibrations of the solute have also been included [27, 38–40]. In our theoretical formulation for PCET [26, 27], the electronic structure of the solute is described in the framework of a four-state valence bond (VB) model [41]. The most basic PCET reaction involving the transfer of one electron and one proton may be described in terms of the following four diabatic electronic basis states: þ ð1aÞ D e Dp H Ap Ae þ ð1bÞ D e Dp HAp Ae
ð2aÞ De Dp Hþ Ap A e
(16.1)
ð2bÞ De Dp þ HAp A e
where 1 and 2 denote the electron transfer (ET) state, and a and b denote the proton transfer (PT) state. Given these four VB states, PT processes can be described as 1afi1b and 2afi2b transitions, ET processes as 1afi2a and 1bfi2b transitions, and EPT processes as 1afi2b and 1bfi2a transitions. Here EPT processes refer to synchronous electron and proton transfer. The general formulation for PCET can be represented in terms of a dielectric continuum environment or an explicit molecular environment. In both representations, the free energy of the PCET system can be expressed in terms of the solute coordinates rp and R and two scalar solvent coordinates zp and ze corresponding to the PT and ET reactions, respectively [26, 42, 43]. In the dielectric continuum model for the environment, the solvent or protein is represented as a dielectric continuum characterized by the electronic (e¥ ) and inertial (e0 ) dielectric constants. The scalar solvent coordinates zp and ze represent the differences in elec-
16.2 Theoretical Formulation for PCET
trostatic interaction energies of the charge densities ri corresponding to the VB basis states involved in the PT and ET reactions, respectively, with the inertial polarization potential Uin ðrÞ of the solvent: Z zp ¼ ze ¼
Z
drðr1b r1a ÞUin ðrÞ (16.2) drðr2a r1a ÞUin ðrÞ
In general, these solvent coordinates depend on the solute coordinates rp and R, but this dependence is usually very weak and can be neglected. In the molecular description of the solvent, the scalar coordinates zp and ze are functions of the solvent coordinates nand can be defined in terms of the solute–solvent interaction potential Ws rp ; R; n as el el el zp ðnÞ ¼ wel 1b Ws w1b w1a Ws w1a el el el el ze ðnÞ ¼ w2a Ws w2a w1a Ws w1a
(16.3)
where the wel i are the wavefunctions corresponding to the VB states defined in Eq. (16.1). For many PCET systems, the single PT reaction is electronically adiabatic and the single ET reaction is electronically nonadiabatic. Here electronically adiabatic refers to reactions occurring in a single electronic state, and electronically nonadiabatic refers to reactions involving multiple electronic states. The electronically adiabatic (or nonadiabatic) limit corresponds to strong (or weak) electronic coupling between the charge transfer states. Even for cases in which the single ET reaction is electronically adiabatic, the overall PCET reaction is usually nonadiabatic, because the coupling between the reactant and product vibronic states is small due to averaging over the reactant and product proton vibrational wavefunctions (i.e., due to the small overlap factor, analogous to the Franck–Condon factor in theories for single ET [40, 44]). In this case, the ET diabatic free energy surfaces corresponding to ET states 1 and 2 are calculated as mixtures of the a and b PT states. The reactants (I) are mixtures of the 1a and 1b states, and the products (II) are mixtures of the 2a and 2b states. The proton vibrational states are calculated for both the reactant (I) and product (II) ET diabatic surfaces, resulting in two sets of two-dimensional vibronic free energy surfaces that may be approximated as paraboloids. In this theoretical formulation, the PCET reaction is described in terms of nonadiabatic transitions from the reactant (I) to the product (II) ET diabatic surfaces. Thus, the ET diabatic states I and II, respectively, may be viewed as the reactant and product PCET states. The unimolecular rate expression derived in Ref. [27] for a fixed proton donor– acceptor distance is
481
482
16 Proton-Coupled Electron Transfer: Theoretical Formulation and Applications fIg fIIg 1=2 2p X I X 2 DGylm k¼ Pl Vlm 4pklm kB T exp " l kB T m
! (16.4)
where the summations are over the reactant and product vibronic states, PlI is the Boltzmann probability for state Il, and DGylm is the free energy barrier defined as DGylm
¼
DGolm þ klm
2 (16.5)
4klm
In this expression the free energy of reaction is defined as eIl zIl DG0lm ¼ eII zIIm zIl zIIm m p ; e p ; e
(16.6)
IIm are the solvent coordinates for the minima of the and zIIm where zIl zIl ; z p ; e p e ET diabatic free energy surfaces eIl zp ; ze and eII z ; z m p e , respectively. Moreover, the outer-sphere reorganization energy is defined as eIl zIl ¼ eII eII zIl zIIm klm ¼ eIl zIIm zIIm zIl zIl zIIm p ; e p ; e m p ; e m p ; e
(16.7)
The free energy difference and outer-sphere reorganization energy are indicated in Fig. 16.1. The coupling Vlm in the PCET rate expression is defined as D E Vlm ¼ fIl V rp ; zyp fII m
p
(16.8)
where the subscript of the angular brackets integration over rp, zyp is the indicates value of zp in the intersection region, V rp ; zp is the electronic coupling between states I and II, and fIl and fII m are the proton vibrational wavefunctions for the reactant and product vibronic states, respectively. For many systems [45, 46], the coupling is approximately proportional to the overlap between the reactant and product proton vibrational wavefunctions: D E Vlm » V el fIl jfII m
p
(16.9)
where V el is a constant effective electronic coupling. The effects of inner-sphere solute modes have also been included in this theoretical formulation for several different regimes [27, 38–40]. In the high-temperature approximation for uncoupled solute modes, the inner-sphere reorganization energy is added to the outer-sphere reorganization energy in Eq. (16.7) [45, 47]. Despite the similarity in form, the rate expression given in Eq. (16.4) for PCET is fundamentally different than the conventional rate expression for single electron transfer with uncoupled intramolecular solute modes [40, 44]. The most fundamental difference is that the reorganization energies, equilibrium free energy
16.2 Theoretical Formulation for PCET
Figure 16.1 Two-dimensional vibronic free energy surfaces as functions of two collective solvent coordinates, zp and ze, for a PCET reaction. The lowest energy reactant and product free energy surfaces are shown. The minima for the reactant surfaces, respectively, are and product zIl and zIIm . The free energy difference DG0lm zIl zIIm p ; e p ; e and outer-sphere reorganization energy klm are indicated.
differences, and couplings in Eq. 4 are defined in terms of two-dimensional paraboloids instead of one-dimensional parabolas. Another important difference is that the reorganization energies in Eq. 4 are different for each pair of intersecting ET diabatic surfaces due to varying positions of the minima within the reactant and product states, whereas in conventional single electron transfer theory the reorganization energy is the same for all pairs of intersecting parabolas. The final difference is that the coupling in Eq. 4 cannot be expressed rigorously as the product of a constant coupling and an overlap of the reactant and product vibrational wavefunctions because the electronic coupling depends on the proton coordinate. As mentioned above, however, this separation of the coupling is a reasonable approximation for many PCET reactions. 16.2.2 Proton Donor–Acceptor Motion
The proton donor–acceptor motion plays an important role in PCET reactions. This motion modulates the proton tunneling distance and therefore the overlap between the reactant and product proton vibrational wavefunctions. Thus, the nonadiabatic coupling between the reactant and product vibronic states for PCET
483
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16 Proton-Coupled Electron Transfer: Theoretical Formulation and Applications
reactions depends strongly on the proton donor–acceptor distance. We have derived nonadiabatic rate expressions that include the effects of the proton donor– acceptor vibrational motion in a number of different regimes [30]. In the simplest case, the R mode is characterized by a low frequency and is not dynamically coupled to the fluctuations of the solvent. The system is assumed to maintain an equilibrium distribution along the R coordinate. In this case, we can exclude the R mode from the dynamical description and consider an equilibrium ensemble of PCET systems with fixed proton donor–acceptor distances. The electrons and transferring proton are assumed to be adiabatic with respect to the R coordinate and solvent coordinates within the reactant and product states. Thus, the reaction is described in terms of nonadiabatic transitions between two sets of corresponding to R; z ; z intersecting free energy surfaces eIl R; zp ; ze and eII p e m the reactant and product electron–proton vibronic states for fixed R. For each fixed value of R, we recover the nonadiabatic rate expression given in Eq. (16.4). In this regime, all of the quantities in the rate expression, including the Boltzmann factors, depend explicitly on the coordinate R. Since the PCET system is assumed to be in equilibrium along the coordinate R, the total rate constant can be calculated by integrating Eq. (16.4) with a renormalized distribution function over all R distances:
kaver ¼
1 "
Z¥ dR 0
fIg X l
fIIg 2 X „ PlI ðRÞ Vlm ðRÞ m
8 i2 9 sffiffiffiffiffiffiffiffiffiffiffiffiffi > h 0 > < = b DG ð R Þ þ k ð R Þ lm lm pb exp > klm ðRÞ > 4klm ðRÞ : ; (16.10)
The above rate expression does not follow rigorously from the Golden Rule general expression. Nevertheless, it provides a physically reasonable method for estimating the rate constant in cases for which the dynamical coupling of the slow R mode to the solvent fluctuations is negligible. In another limit, the R mode is characterized by a high frequency X and a relatively low reduced mass M. In this case, the motion along the R mode occurs on a much faster timescale than the timescale associated with the dominant solvent fluctuations, so the R mode fluctuations are dynamically uncoupled from the solvent fluctuations. In contrast to the previous case of the slow dynamically uncoupled R mode, however, the quantum character of this motion becomes important, especially at low temperatures where b"X>>1. To include these quantum effects, the R mode can be treated quantum mechanically on the same level as the electron and proton coordinates. The electrons, transferring proton, and R mode are assumed to be adiabatic with respect to the solvent coordinates within the reactant and product states. Thus, the reaction can be described in terms ofnonadiabatic transitions between two sets of intersecting free energy surfaces eIk zp ; ze and eII l zp ; ze corresponding to the reactant and product electron–pro-
16.2 Theoretical Formulation for PCET
ton–R-mode states. The resulting nonadiabatic rate expression in the high-temperature limit of a Debye solvent is quant
k
fIg fIIg 1 X I X „ 2 ¼ Pk Vkl " k l
sffiffiffiffiffiffi ( 2 ) b DG0kl þ kkl pb exp kkl 4kkl
(16.11)
This expression formally resembles the expression in Eq. (16.4) except that the quantities are calculated for pairs of mixed electron–proton–R-mode vibronic free energy surfaces. 16.2.3 Dynamical Effects
Recently, we derived rate expressions that include the dynamical effects of both the R mode and the solvent, as well as the quantum character of the R mode [30]. As mentioned above, one of the most important effects of the R coordinate motion in PCET systems is the modulation of the proton tunneling distance and thereby the nonadiabatic coupling between the reactant and product vibronic states. The fluctuations of the nonadiabatic coupling due to the R motion can be dynamically coupled to the fluctuations of the solvent degrees of freedom, which are responsible for bringing the system into the degenerate state required for nonadiabatic transitions. Here we consider the case in which the electron and transferring proton are adiabatic with respect to the R mode and solvent within the reactant and product states. The R mode is treated dynamically on the same level as the solvent modes in order to include the effects of the dynamical coupling between the R mode and the solvent. To facilitate the derivation of analytical rate expressions, the R dependence of the overall coupling Vlm is approximated by a single exponential:
ð0Þ Il Vlm » Vlm exp alm R R
(16.12)
Il is the equilibrium value of the R coordinate on the reactant surface Il, where R ð0Þ Il , and alm can be calculated from the R Vlm is the value of the coupling at R dependence of the coupling. The justification for this approximation is that the nonadiabatic coupling can be approximated as the product of a constant electronic coupling and a Franck–Condon overlap of the reactant and product proton vibrational wavefunctions, as given in Eq. (16.9). For PCET reactions, typically this overlap depends only weakly on the solvent coordinates but depends very strongly on the proton donor–acceptor separation R. For a simple model based on two ground state harmonic oscillator wavefunctions with centers separated by R, the overlap increases exponentially with decreasing R. The approximation in Eq. (16.12) has been shown to be reasonable for model PCET systems and was also used previously for nonadiabatic proton transfer systems [48–50].
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16 Proton-Coupled Electron Transfer: Theoretical Formulation and Applications
In this case, the nonadiabatic rate constant can be expressed as kdyn ¼
fIg X
PlI
fIIg X
l
kdyn lm
(16.13)
m
dyn
where the partial rate constant klm describes nonadiabatic transitions between the quantum states for the pair of electron–proton vibronic surfaces Il and IIm and can be written as an integral of the time-dependent probability flux correlation function jlm ðtÞ: kdyn lm ¼
1 "2
Z¥ jlm ðtÞdt
(16.14)
¥
We have used this formulation to derive rate expressions for both a dielectric continuum and a molecular representation of the environment.
16.2.3.1 Dielectric Continuum Representation of the Environment For a dielectric continuum environment, the probability flux correlation function is given by: i 0 ð0Þ 2 DG þ kz þ kR t jcont ðtÞ ¼ Vlm exp " · exp
1 2 "
8 <2Mk : "2
Zt
a
Zs1 ds1
0
pffiffiffiffiffiffiffiffiffiffi 4i ½CR ð0Þ þ CR ðtÞ 2 MX ka kR "
0
2MX2 kR ds2 CZ ðs1 s2 Þ "2
Zt CR ðsÞds
Zt
Zs1 ds2 CR ðs1 s2 Þ
ds1 0
ð16:15Þ
0
0
9 = ;
Although the indices l and m are omitted in Eq. (16.15) for simplicity, the quantities in this expression in terms of a pair of reactant and product free are defined energy surfaces eIl R; zp ; ze and eII m R; zp ; ze . The time correlation functions for the R mode and the solvent variables are given by CR ðtÞ ¼ hdRð0ÞdRðtÞi, where dRðtÞ ¼ RðtÞ hRi, and CZ ðtÞ ¼ hdZð0ÞdZðtÞi. In the continuum solvent representation, ~ e ze ðtÞ ~ p zp ðtÞ zIl þ K dZðtÞ ¼ K zIl p e
(16.16)
Il ~ p ¼ Kz z zIl zIIm þ Kz z zIl zIIm þ Kz R R R IIm K p p e e p p p e p
(16.17)
16.2 Theoretical Formulation for PCET
Il ~ e ¼ Kz z zIl zIIm þ Kz z zIl zIIm þ Kz R R R IIm K p p e e p e e e e ¶2 eIl R; zp ; ze Kxy ¼ ¶x¶y
; x; y ¼ R; zp ; ze
(16.18)
(16.19)
Il zIl zIl p ; e ;R
In Eq. 16.16, DG0 is the reaction free energy defined as the difference in the equilibrium free energies for the reactant and product surfaces: IIm zIIm Il ; zIl eIl R DG0lm ¼ eII zIIm zIl m R ; p ; e p ; e
(16.20)
The R mode reduced mass M and frequency X are related to the reactant surface eIl R; zp ; ze through the second derivative at the minimum: ¶2 eIl R; zp ; ze MX2 ¼ R Il ;zIlp ;zIle ¶R2
(16.21)
kz and kR are the solvent and R-mode reorganization energies, respectively, defined as Il ; zIIm ; zIIm eI R Il ; zIl ; zIl kz ¼ eIl R p e l p e 1 IIm ; zIl Il ; zIl kR ¼ eIl R eIl R » MX2 DR2 zIl zIl p ; e p ; e 2
(16.22)
(16.23)
IIm R Il is the difference between the equilibrium R coordinates where DR ¼ R on the reactant and product surfaces. Finally, the quantum coupling term ka is defined as ka ¼
"2 a2lm 2M
(16.24)
Previously, expressions similar to Eq. 16.15 were derived and analyzed by Borgis, Lee, and Hynes in the context of vibrationally nonadiabatic proton transfer reactions in solution [49, 51, 52]. Note that the time correlation function for the solvent variables is fundamentally different for PCET reactions because PCET reactions involve two correlated solvent coordinates zp and ze rather than a single solvent coordinate zp. Moreover, the physical meaning of the quantum coupling term ka is fundamentally different for PCET reactions because the coupling for PCET reactions involves ET nonadiabatic coupling as well as PT coupling. The most interesting features of the expression in Eq. (16.15) are the termspinffiffiffiffiffiffiffiffiffi theffi exponential that are proportional to the quantum coupling term ka and to ka kR .
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16 Proton-Coupled Electron Transfer: Theoretical Formulation and Applications
These terms reflect the dynamical correlations between the R mode and the nonadiabatic coupling fluctuations. The rate expression in Eq. (16.15) can be simplified significantly under a series of well-defined approximations. In the short-time high-temperature approximation for a Debye solvent, the solvent dynamics is negligible on the time scale of the probability flux correlation function, leading to the following simplification: 2 1 exp4 2 "
Zt
Zs1 ds1
0
0
3
kz t2 5 ds2 CZ ðs1 s2 Þ ¼ exp 2 b"
(16.25)
Moreover, when the probability flux correlation function decays on a time scale shorter than the time scale of the solvent effects on the R motion, the solvent effects on the R motion can be neglected. In this case, CR ðtÞ can be approximated by the standard analytical expression for the time correlation function of an undamped quantum mechanical harmonic oscillator [53]: CR ðtÞ ¼
" 1 coth b"X cos Xt þ i sin Xt 2MX 2
(16.26)
These approximations lead to the following closed analytical expression for the dyn nonadiabatic partial rate klm :
kdyn lm
ð0Þ 2 Vlm
Z¥ 2ka f 1 ¼ 2 exp dsexp vs2 þ pð cos s 1Þ þ iðq sin s þ hsÞ "X 2 " X
(16.27)
¥
where the dimensionless parameters are defined as
1 2k DG0 þ kz f ¼ coth b"X ; v ¼ 2 z 2 ; h ¼ 2 "X b" X pffiffiffiffiffiffiffiffiffiffi kR ka kR þ ka 2 p¼f ; "X "X
pffiffiffiffiffiffiffiffiffiffi kR ka kR þ ka 2f q¼ "X "X
(16.28)
Again the indices l and m are omitted for simplicity. Note that the imaginary part of the rate in Eq. (16.27) is identically zero. The PT analog of this expression is given in Refs. [49, 51, 52]. The real part of the integrand in Eq. (16.27) is a damped oscillating function of the frequency-scaled time s ¼ Xt. The strength of the damping factor exp½vs2 =2 depends on the temperature, the solvent reorganization energy kz, and the R mode quantum energy "X. Note that in the regime considered here, the solvent fluctuations are the key element responsible for damping the quantum coherent electron–proton tunneling. In the absence of the solvent reorganization (i.e., kz ¼ 0), the time integral in Eq. (16.27) is divergent and the reaction rate constant is not defined. Ref. [50] provides an alternative approach that avoids these diver-
16.2 Theoretical Formulation for PCET
gences by performing a transformation of a model Hamiltonian corresponding to proton transfer. Since the thermal average of the transformed perturbation is zero, the integral of the time correlation function is convergent for the entire range of system parameters. In certain limiting regimes, the time integral in Eq. (16.27) can be simplified to obtain closed analytical rate expressions. In the high temperature (low frequency) limit for the R mode (b"X << 1) the partial rate can be expressed as
khighT ¼ lm
ð0Þ 2 Vlm "
4ka exp b"2 X2
2 3 4 pffiffiffiffiffiffiffiffiffiffi 2 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0þk
k b DG k 6 u z a R pb k 7 b"X 7 u exp6 2 z 7 ·u 6 4 t 4ktot ktot 5 4ka kR ktot 1 2 ktot ð16:29Þ
where ktot ¼ kz þ kR þ ka . This expression closely resembles the analogous expression in Eq. (16.4) for fixed R with a few important distinctions. First, it has an additional temperature-dependent exponential prefactor exp 4ka b"2 X2 , which results in non-Arrhenius behavior of the rate constant at high.temperatures. Sec2 0 ond, the conventional Marcus activation barrier pffiffiffiffiffiffiffiffiffi ffi ðDG þ kz Þ ð4kz Þ is modified due to the presence of the cross term 4 ka kR ðb"XÞ, which is a quantum effect that is related to the dynamical correlation between the R mode and the nonadiabatic coupling fluctuations. Note that if ka ¼ kR ¼ 0 (i.e., the coupling is independent of R and the equilibrium value of R is the same for reactant and product free energy surfaces), this expression is identical to the previously derived rate expression for PCET reactions with fixed R, as evident by a comparison to Eq. (16.4). In the low temperature (high frequency) limit for the R mode in the strong solvation regime (i.e., jDG0 j < kz ), the partial rate can be expressed as:
lowT klm
¼
ð0Þ 2 Vlm "
# " pffiffiffiffiffi pffiffiffiffiffi2 #sffiffiffiffiffiffi " ka kR 2ka pb b ðDG0 þ kz Þ2 exp exp exp kz "X "X 4kz (16.30)
which is similar to the previously derived PCET rate expressions except for the additional exponential prefactors that modify the nonadiabatic coupling. In this quantum limit for the R mode, the rate expression corresponds qualitatively to the expression in Eq. (16.11) for the case of a fast quantized R mode. The square of the coupling in conjunction with the two additional exponential prefactors in Eq. (16.30) can be interpreted in terms of the square of the coupling between the reactant and product R mode vibrational ground states. Transitions involving R mode vibrationally excited states are not significant at low temperatures. Note that
489
490
16 Proton-Coupled Electron Transfer: Theoretical Formulation and Applications
typical PCET reactions are expected to be in the strong solvation regime, in which the solvent reorganization energy exceeds the absolute reaction free energy. The rate expression can also be derived for the weak solvation regime, following the procedure in Ref. [54]. Moreover, the rigorous derivation of the low-temperature rate expressions for proton transfer reactions given in Ref. [50] could also be applied to PCET reactions.
16.2.3.2 Molecular Representation of the Environment In the molecular representation of the environment, the solvent/protein coordinates n are treated explicitly. In this case, the probability flux correlation function is:
i ~ ð0Þ 2 exp þ D dR t jMD ð t Þ ¼ V exp 2a dR E lm l lm lm l lm lm " · exp
1 "2
8 < :
a2lm ½CR ð0Þ
Zt
Zs1 ds2 CE ðs1 s2 Þ
ds1 0
2ialm ~ lm D þ CR ðtÞ "
0
1 "2
Zt CR ðsÞds
(16.31)
0
Zt
Zs1 ds2 CD ðs1 s2 ÞCR ðs1 s2 Þ
ds1 0
0
9 = ;
where the time evolution on the reactant vibronic surface is described in terms of the energy gap Il Il Il ; nðtÞ ¼ eII R ; n eI R ;n E lm ðtÞ ¼ Delm R m l
(16.32)
the derivative of the energy gap ~ lm ðnðtÞÞ ¼ D
¶Delm ¶R R¼R Il
(16.33)
and the R mode. The time correlation function for the energy gap is defined as CE ðtÞ ¼ dE lm ð0ÞdE lm ðtÞ , where dE lm ðtÞ ¼ E lm ðtÞ E lm . The time correlation functions for the other variables are defined analogously. Note that the probability flux expression in Eq. (16.31) is analogous to the probability flux expression given in Ref. [55] for vibrationally nonadiabatic PT reactions occurring on a single adiabatic electronic state. In PCET reactions, however, the energy gap and coupling are defined for pairs of electron–proton vibronic surfaces corresponding to different electronic states. The above quantities can be evaluated with molecular dynamics simulations of the full solute–solvent system on the reactant vibronic surface eIl ðR; nÞ. Specifi 2 Il i can be calculated from cally, the quantities CR ðtÞ, hdR i, and dRl ¼ hRðtÞ R a molecular dynamics simulation with an unconstrained R coordinate, and the ~ lm , CE ðtÞ, and CD ðtÞ can be calculated from molecular quantities E lm , D
16.2 Theoretical Formulation for PCET
dynamics simulations of the full solute–solvent system with the R coordinate fixed Il . Alternatively, the time correlation function CR ðtÞ can be calculated to R ¼ R in terms of a frequency shift correlation function, which is obtained from a simu Il , and the calculation of lation of the system with the R coordinate fixed to R ¼ R the correlation function for an undamped quantum mechanical harmonic oscillator [55]. Typically the solvent effects on the R mode occur on a much longer time scale than the decay of the probability flux correlation function, and the solvent effects on the R mode can be neglected. In this case, the correlation functions involving the R coordinate can be calculated directly from the analytical expressions for an undamped quantum mechanical harmonic oscillator, as given in Eq. (16.26). The rate expression in Eq. (16.31) can be simplified under the following welldefined conditions: the coupling between the R coordinate and the solvent coordinates is neglected, the surfaces are approximated to be harmonic along the R coordinate, and the R mode frequency isassumed to be the same for both the reactant and product surfaces. In this case, dRl ¼ hdRi ¼ 0 and the energy gap derivative defined in Eq. (16.31) becomes ~ lm ” MX2 DRlm ~ lm ¼ K D
(16.34)
where the R mode frequency X is given by ¶2 eIl ðR; nÞ MX ¼ ¶R2 2
(16.35) Il R¼R
Under these conditions, the expression in Eq. (16.31) simplifies to: i ð0Þ 2 E lm t jMD;harm ðtÞ ¼ Vlm exp lm " 8 t < ~ lm Z 2ialm K 2 CR ðsÞds · exp alm ½CR ð0Þ þ CR ðtÞ : " 0
1 2 "
Zt
Zs1 ds2 CE ðs1 s2 Þ
ds1 0
0
~2 K lm "2
Zt
Zs1 ds2 CR ðs1 s2 Þ
ds1 0
0
9 = ;
(16.36) In Eq. (16.36), the quantities E lm and CE ðtÞ can be evaluated with molecular dynamics simulations of the full solute–solvent system on the constrained reac Il ; nÞ. Since the effects of the solvent on the R mode tant vibronic surface eIl ðR ¼ R are neglected in this limit, the quantities pertaining to the R coordinate can be calculated from analytical expressions for an undamped quantum mechanical harmonic oscillator with frequency X and reduced mass M, as given in Eq. (16.26). In this manner, the quantum character of the R coordinate is included in the rate
491
492
16 Proton-Coupled Electron Transfer: Theoretical Formulation and Applications
expression. Thus, all of the quantities required for the calculation of the nonadiabatic flux can be calculated from a single molecular dynamics simulation on the constrained reactant vibronic surface. Note that the form of Eq. (16.36) is the same as the form of Eq. (16.15), which was derived for a continuum representation of the environment. We have used this theoretical formulation to analyze the dynamical aspects of model PCET reactions in solution with molecular dynamics simulations [56, 57]. For these model systems, the time dependence of the probability flux correlation function is dominated by the solvent damping term, and only the short-time equilibrium fluctuations of the solvent impact the rate. The proton donor–acceptor motion does not impact the dynamical behavior of the reaction but does influence the magnitude of the rate. Although this dynamical treatment is analogous to the previous treatment of vibrationally nonadiabatic PT reactions [49, 51, 52], a number of important new issues arise for PCET reactions. In general, PCET reactions are described by at least a four-state model representing the four charge transfer states rather than the two-state model used for single PT reactions. As a result, general PCET reactions are described in terms of at least two scalar solvent coordinates corresponding to ET and PT rather than the single scalar solvent coordinate used for single PT reactions. The use of two scalar solvent coordinates leads to fundamentally different solvent terms in the rate expressions based on a dielectric continuum representation of the solvent. In addition, the previous work on vibrationally nonadiabatic PT reactions assumed that the reaction was electronically adiabatic (i.e., the reaction occurs on the electronic ground state). In contrast, typically PCET reactions are electronically nonadiabatic and occur on two different electronic surfaces corresponding to the two diabatic ET states. Thus, the coupling for PCET reactions involves ET nonadiabatic coupling as well as PT coupling.
16.3 Applications
We have applied this theoretical formulation [26–28] to a series of PCET reactions. The systems were chosen based on the availability of experimental data that had not yet been fully explained. The systems that will be discussed in this section are iron bi-imidazoline complexes, ruthenium polypyridyl complexes, amidinium-carboxylate interfaces, DNA–acrylamide complexes, tyrosine oxidation, and the enzyme lipoxygenase. In all cases, the solvent was treated as a dielectric continuum [58, 59]. 16.3.1 PCET in Solution
A comparative experimental study of single ET and PCET reactions in the iron biimidazoline complexes shown in Fig. 16.2 indicated that the rates of ET and PCET
16.3 Applications 2+
NH HN N
FeII
N N
HN NH
2+
NH
N
HN
N N
NH-----N
- N
N
NH
HN
N
FeIII
N N
N HN
NH
FeIII
-
N -----HN
N
HN
N
NH
N
HN
2+
NH HN
N
N N
N N
N
2+
NH HN
NH
FeII
N N
N
HN NH
Figure 16.2 PCET reaction between iron bi-imidazoline complexes [45]. For the corresponding single electron transfer reaction, all nitrogen atoms are protonated.
are similar [15]. Previously this result was explained in the context of adiabatic Marcus theory, and the PCET reaction was viewed as a hydrogen atom transfer involving negligible solute charge rearrangement, leading to zero solvent reorganization energy [15]. The similarity of the ET and PCET rates was thought to be due to the compensation of the larger solvent reorganization energy for ET by a larger solute reorganization energy for PCET. The kinetic isotope effect (KIE) for PCET was measured to be a moderate value of 2.3. Our calculations, which were based on nonadiabatic rate expressions for ET and PCET, provided an alternative explanation for the experimental results [45]. The fundamental PCET mechanism for this reaction is illustrated in Fig. 16.3. In our calculations, the inner-sphere reorganization involving the Fe–N bonds was assumed to be the same for both ET and PCET. The solvent reorganization energies klm for the dominant contributions to the PCET reaction were found to be substantial and were »1–3 kcal mol–1 lower than the solvent reorganization energy for single ET. The overall coupling for PCET was found to be smaller than the coupling for ET due to averaging over the reactant and product hydrogen vibrational wavefunctions (i.e., multiplying by the vibrational overlap factor in Eq. (16.9)). The calculations indicated that the similarity of the rates for ET and PCET is due mainly to the compensation of the larger solvent reorganization energy for ET by the smaller coupling for PCET. The moderate KIE was determined to arise from the relatively large overlap factor and the significant contributions from excited vibronic states. An experimental study [16,17] of PCET in the ruthenium polypyridyl complexes shown in Fig. 16.4 revealed that the CompB rate is nearly one order of magnitude larger than the CompA rate, and the CompA KIE of 16.1 is larger than the CompB KIE of 11.4. As shown in Fig. 16.5, our density functional theory calculations [46] illustrated that the steric crowding near the oxygen proton acceptor is significantly greater for CompA than for CompB. Consistent with this observation, our nonadiabatic rate calculations [46] implied that the proton donor–acceptor distance is larger for CompA than for CompB, leading to a larger overlap between the reactant and product hydrogen vibrational wavefunctions for CompB than for CompA, as shown in Fig. 16.6. The rate for CompB is larger than the rate for CompA because the rate increases as this overlap factor increases. The KIE for CompB is smaller than the KIE for CompA because the KIE decreases as this overlap factor increases. Both of these KIEs are larger than the KIE for the iron bi-imidazoline complexes described above because the vibrational overlap factor is smaller for the ruthenium systems.
493
16 Proton-Coupled Electron Transfer: Theoretical Formulation and Applications
(b)
(a)
A
20 20
I
II
10
B C
A
0 _
_
_
_
(zpI,z eI) (zpII,zeII) Solvent Coordinate (kcal/mol)
10
Free Energy (kcal/mol)
Free Energy (kcal/mol)
494
0 B
20 10 0
C
20 10 0 -0.3
0
0.3
rp (Å) Figure 16.3 Illustration of the fundamental mechanism for the PCET reaction depicted in Fig. 16.2. (a) Slice of the two-dimensional ET diabatic free energy surface along the line connecting the two minima. The lowest energy reactant (I) and product (II) free energy surfaces are shown in blue and red, respectively. Points A, B, and C represent the equilibrium reactant configuration, the intersection point, and the equilibrium
product configuration, respectively. (b) Proton potential energy curves and corresponding ground state proton vibrational wavefunctions as functions of the proton coordinate rp for the solvent coordinates associated with points A, B, and C indicated in (a). The proton potential energy curves and vibrational wavefunctions denote the reactant (or product) ET diabatic free energy surface. Reproduced from Ref. [45].
In addition, this theory has been applied to PCET through amidinium-carboxylate salt bridges, in which the ET reaction is coupled to the motion of two protons at the proton transfer interface [60]. In this case, the reaction is described in terms of eight valence bond states to include all possible charge transfer states, two hydrogen nuclei are treated quantum mechanically, and the free energy surfaces depend on three solvent coordinates corresponding to the electron and two proton transfer reactions. Experimental studies of photoinduced PCET in analogous systems revealed that the rate for the donor–(amidinium-carboxylate)–acceptor system is substantially slower than the rate for the switched interface donor–(carboxylate-amidinium)–acceptor system [18]. The calculations illustrated that this difference in rates is due mainly to the opposite dipole moments at the proton transfer interfaces for the two systems, leading to an endothermic reaction for the donor– (amidinium-carboxylate)–acceptor system and an exothermic reaction for the switched interface system.
16.3 Applications
CompA 2+
N
RuII
OH2 ----------- O N
N
2+
2+ N
N
N
N
RuIV
N
N
2+
N
RuIII
OH
HO
N
N
N
N
N
N
N
RuIII
N N
N
CompB 2+ N N
RuII
OH2 ----------- O N
N N
2+
2+ N
N N
Ru N
2+
N
IV N
N
RuIII
N
OH N
N N
HO
RuIII
N
N N
N
Figure 16.4 PCET comproportionation reactions in ruthenium polypyridyl complexes [46].
CompA
CompB
Figure 16.5 Structures optimized with density functional theory for the acceptor complexes in Fig. 16.4. Reproduced from Ref. [46].
495
496
16 Proton-Coupled Electron Transfer: Theoretical Formulation and Applications
Figure 16.6 Reactant (I) and product (II) vibrational wavefunctions for H (solid) and D (dashed) for the reactions shown in Fig. 16.4. The overlap is smaller for CompA than for CompB because the O–O distance is larger for CompA due to greater steric crowding near the acceptor oxygen. Reproduced from Ref. [46].
We have also applied this theory to biologically relevant systems, such as PCET in DNA–acrylamide complexes [61]. Experiments implied that PCET may occur in such complexes [62]. The influence of neighboring DNA base pairs was determined theoretically by studying both solvated thymine–acrylamide and solvated DNA– acrylamide models. The calculations indicated that the final product corresponds to single ET for the solvated thymine–acrylamide complex but to a net PCET reaction for the solvated DNA–acrylamide models. This difference is due to a decrease in solvent accessibility in the presence of DNA, which alters the relative free energies of the ET and PCET product states. Thus, the balance between ET and PCET in the DNA–acrylamide system is highly sensitive to the solvation properties of the system. Another recent application [63] of this theory was to the compound depicted in Fig. 16.7, which was designed to model tyrosine oxidation in Photosystem II [3–7]. Upon photoexcitation of the complex to produce Ru(III), an electron is transferred to the ruthenium from the tyrosine, which is concurrently deprotonated. The dependence of the rates on pH and temperature was measured experimentally [20]. The mechanism was determined to be PCET at pH<10 when the tyrosine is initially protonated and single ET for pH>10 when the tyrosine is initially deprotonated. As shown in Fig. 16.8, the PCET rate increases monotonically with pH, whereas the single ET rate is independent of pH and two orders of magnitude faster than the PCET rate. The calculations reproduced these experimentally observed trends. The pH dependence for the PCET reaction resulted from the decrease in the PT and PCET reaction free energies with pH. The calculations indicated that the larger rate for single ET arises from a combination of factors, including the greater exoergicity for ET, the smaller solvent reorganization energy
16.3 Applications 3+
COOEt
PT
H O
O HN
HO
H
ET
eN
N
RuIII
N
N
N
N
Figure 16.7 PCET reaction in a model for tyrosine oxidation in photosystem II. In the first step of the experiment, the rutheniumtris-bipyridine portion absorbs light, and the excited electron is transferred to an external methyl viologen acceptor. In the second step, which is shown here, the tyrosine portion transfers an electron to the ruthenium and is deprotonated. Reproduced from Ref. [63].
1.0E+08
Rate [1/s]
1.0E+07
1.0E+06
1.0E+05
1.0E+04
1.0E+03 5
6
7
8
9
10
11
12
13
pH Figure 16.8 Experimental and theoretical data for the pH dependence of the rates for single electron transfer and PCET in the tyrosine oxidation model shown in Fig. 16.7. The experimental values are denoted with open circles. The theoretical PCET rates are denoted with filled circles, and the theoretical ET rate is represented by a solid line because it is independent of pH. The ET and PT couplings were fit to the experimental ET rate at pH>10 and PCET rate at pH 7. Reproduced from Ref. [63].
for ET, and the averaging of the coupling for PCET over the reactant and product hydrogen vibrational wavefunctions (i.e., the vibrational overlap factor). The calculated temperature dependence of the rates and the deuterium kinetic isotope effects were also consistent with the experimental results.
497
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16 Proton-Coupled Electron Transfer: Theoretical Formulation and Applications
16.3.2 PCET in a Protein
Recently we applied this theory to the PCET reaction catalyzed by soybean lipoxygenase and investigated the role of the proton donor–acceptor motion for this enzyme reaction [47]. This investigation was motivated by experimental measurements of unusually large KIEs at room temperature in conjunction with a weak temperature dependence of the rates [64]. Lipoxygenases catalyze the oxidation of unsaturated fatty acids and have a wide range of biomedical applications [65, 66]. Kinetic studies have shown that the hydrogen transfer from the carbon atom C11 of the linoleic acid substrate to the Fe(III)–OH cofactor is rate limiting above 32 C for SLO [64]. The deuterium KIE on the catalytic rate has been measured experimentally to be as high as 81 at room temperature [64, 67–71]. The rates for hydrogen and deuterium transfer were found to depend only weakly on temperature [64]. Various theoretical models have been invoked to analyze the temperature dependence of the KIEs [36, 47, 64, 67, 68, 72, 73]. In our calculations [47], we treated the net hydrogen transfer reaction catalyzed by lipoxygenase as a PCET mechanism, as illustrated in Fig. 16.9. Quantum mechanical calculations indicate that the electron transfers from the p system of the linoleic acid to an orbital localized on the Fe(III) center, and the proton transfers
Figure 16.9 The PCET reaction catalyzed by soybean lipoxygenase. This reaction entails a net hydrogen atom transfer from the linoleic acid substrate to the Fe(III)–OH cofactor. This conformation was obtained from docking calculations that included the entire soybean lipoxygenase protein. Reproduced from Ref. [47].
16.3 Applications
from the donor carbon to the oxygen acceptor [74]. Moreover, analysis of the thermodynamic properties of the single PT and ET reactions, as well as the concerted PCET mechanism, indicates that the single PT and ET reactions are significantly endothermic, whereas the PCET reaction is exothermic [47, 64, 74]. These analyses imply that the mechanism is PCET, where the electron and proton transfer simultaneously between different sites. As shown in Fig. 16.10, the temperature dependence of the rates and KIEs predicted by the multistate continuum theory is in remarkable agreement with the experimental data [47]. The calculations indicate that the weak temperature dependence of the rates is due to the relatively small free energy barrier arising 1000
–1
Rate(s )
Hydrogen
100
10 Deuterium
KIE
120 100 80 60 3.1
3.3 3.5 –1 1000/T (K )
3.7
Figure 16.10 Temperature dependence of the rates and KIEs for the PCET reaction catalyzed by soybean lipoxygenase. The theoretical results are denoted with open triangles, and the experimental data are denoted with closed circles. The theoretical results were generated with the multistate continuum theory including the proton donor–acceptor vibrational motion. Reproduced from Ref. [47].
from a balance between the reorganization energy and the reaction free energy. The unusually high KIE of 81 arises from the small overlap of the reactant and product proton vibrational wavefunctions and the dominance of the lowest energy reactant and product vibronic states in the tunneling process. The proton donor– acceptor vibrational motion was included in our calculations. The dominant contribution to the overall rate was found to correspond to a proton donor–acceptor distance that is significantly smaller than the equilibrium donor–acceptor distance. This dominant distance is determined by a balance between the larger coupling and the smaller Boltzmann factor as the distance decreases. Thus, the proton donor–acceptor vibrational motion plays an important role in decreasing the dominant donor–acceptor distance relative to its equilibrium value to facilitate the PCET reaction. The quantum mechanical and nonequilibrium dynamical aspects of the proton donor–acceptor vibrational motion are not essential for the description of the experimentally observed temperature dependence of the rates and KIES within the framework of this model.
499
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16 Proton-Coupled Electron Transfer: Theoretical Formulation and Applications
16.4 Conclusions
This chapter describes a general theoretical formulation for PCET and summarizes the results of applications to a wide range of different types of PCET reactions in solution and enzymes. This theoretical formulation treats the active electrons and transferring proton(s) quantum mechanically and includes the interactions among the electrons, proton(s), and solvent or protein environment. Moreover, this formulation allows the inclusion of the proton donor–acceptor motion, explicit molecular solvent and protein, and dynamical effects. The theory described here is directly applicable to nonadiabatic PCET reactions accompanied by substantial solute charge redistribution and solvent reorganization. Within this framework, hydrogen atom transfer is considered as a special type of PCET in which the electron and proton are transferred between the same sites [31, 75]. Note that this definition of hydrogen atom transfer is not rigorous due to the delocalized nature of electrons and protons. Nevertheless, this terminology is used throughout the literature. An important characteristic of hydrogen atom transfer reactions is the lack of significant solute charge redistribution and solvent reorganization. As a result, hydrogen atom transfer reactions tend to be dominated by solute reorganization. Moreover, hydrogen atom transfer reactions are typically electronically adiabatic (i.e., occur on the electronic ground state), although they may be vibrationally nonadiabatic. Currently we are extending this theoretical formulation to study hydrogen atom transfer reactions. Theoretical calculations on model PCET systems have assisted in the interpretation of experimental data and have provided insight into the underlying fundamental principles of PCET reactions. The theoretical framework described in this chapter enables the prediction of experimentally testable trends in rates and kinetic isotope effects. The interplay between experiment and theory will be vital to further progress in the field.
Acknowledgments
This work was supported by NIH grant GM56207 and NSF grant CHE-0096357. I am grateful to Alexander Soudackov, Nedialka Iordanova, and Elizabeth Hatcher for useful discussions and generation of the figures.
References
References 1 Babcock, G. T.; Barry, B. A.; Debus,
R. J.; Hoganson, C. W.; Atamian, M.; McIntosh, L.; Sithole, I.; Yocum, C. F., Biochemistry, 1989, 28, 9557–9565. 2 Okamura, M. Y.; Feher, G., Annu. Rev. Biochem., 1992, 61, 861–896. 3 Tommos, C.; Tang, X.-S.; Warncke, K.; Hoganson, C. W.; Styring, S.; McCracken, J.; Diner, B. A.; Babcock, G. T., J. Am. Chem. Soc., 1995, 117, 10325–10335. 4 Hoganson, C. W.; Babcock, G. T., Science, 1997, 277, 1953–1956. 5 Hoganson, C. W.; Lydakis-Simantiris, N.; Tang, X.-S.; Tommos, C.; Warncke, K.; Babcock, G. T.; Diner, B. A.; McCracken, J.; Styring, S., Photosynth. Res., 1995, 47, 177–184. 6 Blomberg, M. R. A.; Siegbahn, P. E. M.; Styring, S.; Babcock, G. T.; Akermark, B.; Korall, P., J. Am. Chem. Soc., 1997, 119, 8285–8292. 7 Diner, B. A.; Babcock, G. T.; in Oxygenic Photosynthesis: The Light Reactions; Ort, D. R., Yocum, C. F., Eds., Kluwer: Dordrecht, 1996, pp. 213–247. 8 Babcock, G. T.; Wikstrom, M., Nature, 1992, 356, 301–309. 9 Malmstrom, B. G., Acc. Chem. Res., 1993, 26, 332–338. 10 Siegbahn, P. E. M.; Eriksson, L.; Himo, F.; Pavlov, M., J. Phys. Chem. B, 1998, 102, 10622–10629. 11 Chang, C. J.; Chang, M. C. Y.; Damrauer, N. H.; Nocera, D. G., Biochim. Biophys. Acta - Bioenergetics, 2004, 1655, 13–28. 12 Cukier, R. I., Biochim. Biophys. Acta-Bioenergetics, 2004, 1655, 37–44. 13 Hammes-Schiffer, S.; Iordanova, N., Biochim. Biophys. Acta-Bioenergetics, 2004, 1655, 29–36. 14 Mayer, J. M., Annu. Rev. Phys. Chem., 2004, 55, 363–390. 15 Roth, J. P.; Lovel, S.; Mayer, J. M., J. Am. Chem. Soc., 2000, 122, 5486–5498. 16 Binstead, R. A.; Meyer, T. J., J. Am. Chem. Soc., 1987, 109, 3287–3297. 17 Farrer, B. T.; Thorp, H. H., Inorg. Chem., 1999, 38, 2497–2502.
18 Kirby, J. P.; Roberts, J. A.; Nocera, D. G.,
J. Am. Chem. Soc., 1997, 119, 9230–9236. 19 Huynh, M. H. V.; Meyer, T. J., Angew. Chem. Int. Ed., 2002, 41, 1395–1398. 20 Sjodin, M.; Styring, S.; Akermark, B.; Sun, L.; Hammarstrom, L., J. Am. Chem. Soc., 2000, 122, 3932–3936. 21 Cukier, R. I., J. Phys. Chem., 1994, 98, 2377–2381. 22 Cukier, R. I., J. Phys. Chem., 1996, 100, 15428–15443. 23 Cukier, R. I.; Nocera, D. G., Annu. Rev. Phys. Chem., 1998, 49, 337–369. 24 Cukier, R. I., J. Phys. Chem. A, 1999, 103, 5989–5995. 25 Cukier, R. I., J. Phys. Chem. B, 2002, 106, 1746–1757. 26 Soudackov, A.; Hammes-Schiffer, S., J. Chem. Phys., 1999, 111, 4672–4687. 27 Soudackov, A.; Hammes-Schiffer, S., J. Chem. Phys., 2000, 113, 2385–2396. 28 Hammes-Schiffer, S., Acc. Chem. Res., 2001, 34, 273–281. 29 Hammes-Schiffer, S., in Electron Transfer in Chemistry Vol I. Principles, Theories, Methods, and Techniques, Balzani, V., Ed., Wiley-VCH, Weinheim, 2001, pp. 189–214. 30 Soudackov, A.; Hatcher, E.; Hammes-Schiffer, S., J. Chem. Phys., 2005, 122, 014505. 31 Mayer, J. M.; Hrovat, D. A.; Thomas, J. L.; Borden, W. T., J. Am. Chem. Soc., 2002, 124, 11142–11147. 32 Mincer, J. S.; Schwartz, S. D., J. Chem. Phys., 2004, 120, 7755–7760. 33 Georgievskii, Y.; Stuchebrukhov, A. A., J. Chem. Phys., 2000, 113, 10438–10450. 34 Moore, D. B.; Martinez, T. J., J. Phys. Chem. A, 2000, 104, 2367–2374. 35 Siegbahn, P. E. M.; Blomberg, M. R. A.; Crabtree, R. H., Theoret. Chem. Acc., 1997, 97, 289–300. 36 Siebrand, W.; Smedarchina, Z., J. Phys. Chem. B, 2004, 108, 4185–4195. 37 Kim, H. J.; Hynes, J. T., J. Chem. Phys., 1992, 96, 5088–5110. 38 Kestner, N. R.; Logan, J.; Jortner, J., J. Phys. Chem., 1974, 78, 2148.
501
502
16 Proton-Coupled Electron Transfer: Theoretical Formulation and Applications 39 Ulstrup, J.; Jortner, J., J. Chem. Phys.,
1975, 63, 4358. 40 Bixon, M.; Jortner, J., Adv. Chem. Phys., 1999, 106, 35–202. 41 Warshel, A. Computer Modeling of Chemical Reactions in Enzymes and Solutions; John Wiley & Sons, New York, 1991. 42 Basilevsky, M. V.; Chudinov, G. E.; Newton, M. D., Chem. Phys., 1994, 179, 263–278. 43 Basilevsky, M. V.; Vener, M. V., J. Mol. Struct.: THEOCHEM, 1997, 398, 81. 44 Barbara, P. F.; Meyer, T. J.; Ratner, M. A., J. Phys. Chem., 1996, 100, 13148–13168. 45 Iordanova, N.; Decornez, H.; Hammes-Schiffer, S., J. Am. Chem. Soc., 2001, 123, 3723–3733. 46 Iordanova, N.; Hammes-Schiffer, S., J. Am. Chem. Soc., 2002, 124, 4848–4856. 47 Hatcher, E.; Soudackov, A. V.; Hammes-Schiffer, S., J. Am. Chem. Soc., 2004, 126, 5763–5775. 48 Trakhtenberg, L. I.; Klochikhim, V. L.; Pshezhetsky, S. Y., Chem. Phys., 1982, 69, 121–134. 49 Borgis, D. C.; Lee, S. Y.; Hynes, J. T., Chem. Phys. Lett., 1989, 162, 19–26. 50 Suarez, A.; Silbey, R., J. Chem. Phys., 1991, 94, 4809–4816. 51 Borgis, D.; Hynes, J. T., Chem. Phys., 1993, 170, 315–346. 52 Borgis, D.; Hynes, J. T., J. Chem. Phys., 1991, 94, 3619–3628. 53 Chandler, D., in Classical and Quantum Dynamics in Condensed Phase Simulations; Berne, B. J., Ciccotti, G., Coker, D. F., Eds.; World Scientific, Singapore, 1998, pp. 3–23. 54 Borgis, D.; Hynes, J. T., Chem. Phys., 1993, 170, 315–346. 55 Borgis, D.; Hynes, J. T., J. Chem. Phys., 1991, 94, 3619–3628. 56 Hatcher, E.; Soudackov, A.; Hammes-Schiffer, S., Chem. Phys., 2005, 319, 93–100. 57 Hatcher, E.; Soudackov, A.; Hammes-Schiffer, S., J. Phys. Chem. B, 2005, 109, 18565–18574.
58 Basilevsky, M. V.; Rostov, I. V.; Newton,
M. D., Chem. Phys., 1998, 232, 189–199. 59 Newton, M. D.; Basilevsky, M. V.;
Rostov, I. V., Chem. Phys., 1998, 232, 201–210. 60 Rostov, I.; Hammes-Schiffer, S., J. Chem. Phys., 2001, 115, 285–296. 61 Carra, C.; Iordanova, N.; Hammes-Schiffer, S., J. Phys. Chem. B, 2002, 106, 8415–8421. 62 Taylor, J.; Eliezer, I.; Sevilla, M. D., J. Phys. Chem. B, 2001, 105, 1614–1617. 63 Carra, C.; Iordanova, N.; HammesSchiffer, S., J. Am. Chem. Soc., 2003, 125, 10429–10436. 64 Knapp, M. J.; Rickert, K. W.; Klinman, J. P., J. Am. Chem. Soc., 2002, 124, 3865–3874. 65 Samuelsson, B.; Dahlen, S.-E.; Lindgren, J.; Rouzer, C. A.; Serhan, C. N., Science, 1987, 237, 1171–1176. 66 Holman, T. R.; Zhou, J.; Solomon, E. L., J. Am. Chem. Soc., 1998, 120, 12564–12572. 67 Rickert, K. W.; Klinman, J. P., Biochemistry, 1999, 38, 12218–12228. 68 Jonsson, T.; Glickman, M. H.; Sun, S.; Klinman, J. P., J. Am. Chem. Soc., 1996, 118, 10319–10320. 69 Glickman, M. H.; Wiseman, J. S.; Klinman, J. P., J. Am. Chem. Soc., 1994, 116, 793–794. 70 Hwang, C.-C.; Grissom, C. B., J. Am. Chem. Soc., 1994, 116, 795–796. 71 Lewis, E. R.; Johansen, E.; Holman, T. R., J. Am. Chem. Soc., 1999, 121, 1395–1396. 72 Olsson, M. H. M.; Siegbahn, P. E. M.; Warshel, A., J. Biol. Inorg. Chem., 2004, 9, 96–99. 73 Olsson, M. H. M.; Siegbahn, P. E. M.; Warshel, A., J. Am. Chem. Soc., 2004, 126, 2820–2828. 74 Lehnert, N.; Solomon, E. L., J. Biol. Inorg. Chem., 2003, 8, 294–305. 75 Hammes-Schiffer, S., ChemPhysChem, 2002, 3, 33–42.
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17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer in Model Systems Justin M. Hodgkiss, Joel Rosenthal, and Daniel G. Nocera
17.1 Introduction
A hydrogen atom transfer (HAT) reaction encompasses a proton transfer (PT) and electron transfer (ET). To this end, the HAT reaction is a subclass of the more general reaction of proton-coupled electron transfer (PCET). In PCET, the thermodynamics for electron and proton transport mandate that they couple. This is most easily elucidated by the square scheme shown in Fig. 17.1 [1]. The four corners of the scheme comprise the thermodynamic limiting (and measurable) species for any PCET event that involves the transfer of a single electron and a single proton. The edges of the square represent the fundamental ET (horizontal lines) and PT steps (vertical lines) that connect the four potential PCET species. The diagonal line represents a HAT where the PCET event is concerted and synchronous with a single transition state (i.e., no detectable intermediates). The thermochemistry of the total PCET reaction is path-independent; therefore the free energy of the diagonal PCET reaction is equivalent to the sum of either ET/PT or PT/ET stepwise pathways around the edges of the square. It is important to realize that the two De
Dp
Ap
H
ET
Ae
De+
Dp
Ap
H
Ae–
Con
cert ed P CET or H AT
PT
De
Dp–
H
Ap+
Ae
ET
PT
De+
Dp–
H
Ap+
Figure 17.1 The generalized square-scheme describing the PCET reaction space. PCET reactions coordinate ET and PT at four distinct sites; De and Dp are the electron and proton donors respectively, while Ae and Ap are the corresponding acceptors. The thermodynamics associated with PCET or HAT is equivalent to the sum of the stepwise ET and PT steps around the edges. Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
Ae–
504
17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer
sets of ET and PT equilibria are both distinct from one another and contain different thermodynamic information. The two ET equilibria are defined by the reduction potentials of the reactants in each protonation state. The two PT equilibria are defined by the pKas of the protonated species in each oxidation state. With the limiting thermodynamics for a PCET event defined, one can often make inferences about the mechanism by which the coupled transfer takes place. In all cases, the driving force for concerted PCET is more favorable than for the competing initial ET or PT steps of the stepwise processes. If this were not true, these ET-only or PT-only states at the corners of Fig. 17.1 (versus the diagonal PCET state) would be the thermodynamic product [1]. In some cases, either or both of the intermediate states are so far uphill that their existence can be ruled out. The thermochemical properties (i.e. pKa or Ered) measured for the isolated species can be significantly perturbed when considering the interaction of species undergoing a PCET reaction. Since PCET reactions usually take place within an encounter or precursor complex with a preferred orientation, it may be necessary to account for hydrogen bonding or steric interactions that can favor or disfavor certain intermediates [2]. Many definitions and descriptions of HAT, prior to the emergence of PCET as a field of study, did not adequately take into account the complexity embodied by Fig. 17.1. HAT is traditionally defined as the transfer of an electron and a proton from one location to another along a spatially coincidental pathway. In this case, the electron and proton are donated from one atom and they are accepted by another atom. These transfers are well described mechanistically as the diagonal pathway of Fig. 17.1 and they have been treated formally by a number of investigators [3, 4]. However, many reactions treated within a formalism of HAT are more complex as ET and PT are site-differentiated either along uni- or bidirectional pathways. As will be discussed in this chapter, traditional descriptions of HAT do not address how the electron and proton transfer events are coordinated mechanistically in these more complicated reactions and more general treatments of PCET are warranted. 17.1.1 Formulation of HAT as a PCET Reaction
A PCET reaction is described by four separate transfer sites derived from a donor and an acceptor for both an electron and a proton [5]. This four state description of PCET gives rise to two important considerations. A geometric aspect to PCET arises when considering the different possible spatial configurations of the four transfer sites. A HAT reaction comprises just one possible arrangement – where the electron and proton transfer sites are coincidental – however this need not be the case for PCET in general. In addition, the two-dimensional reaction space spanned by the four PCET states shown in Fig. 17.1 encompasses infinite mechanistic possibilities (i.e., pathways) for the coordinated transfer of an electron and a proton. These two issues of geometry and mechanism must be taken into account
17.1 Introduction
in a description of a PCET reaction and consequently for the specific reaction subset of HAT. Stepwise PT and ET reactions occur along the edges of Fig. 17.1, while PCET includes the entire space within the square. The stepwise and PCET mechanisms (including HAT) are clearly distinct. The PCET mechanism is defined by a single transition state in which the proton and electron both transfer in one step, with no intermediate states populated along the reaction coordinate; PCET is thus concerted but the electron and proton events can be asynchronous as opposed to their synchronous transfer for a HAT reaction. In a stepwise mechanism, an intermediate is formed and there are two distinct rate constants for the forward reaction and two separate transition states. Stepwise ET/PT or PT/ET can, in principle, be broken down and treated experimentally and theoretically as separate ET and PT events. Like any series of reactions, the rate-limiting rule applies, kET/PT = kET–1 + kPT–1
(17.1)
The overall reaction is thus described by conventional treatments of ET [6–12] and PT [12–15]. The stepwise reaction mechanism is tangential to HAT but nevertheless is important to consider in a discussion of HAT. If the second step is fast, the intermediate state may not be observed and the stepwise mechanism may not be recognized. We will return to this point in Section 17.2. Concerted PCET provides a mechanistic framework for HAT [16, 17]. Cukier, Hammes-Schiffer and their coworkers have theoretically described the physics of negotiating this two-dimensional electron–proton tunneling space [18–28]. A detailed theoretical account of PCET as it pertains to HAT may be found elsewhere in this volume, but a few general comments are warranted. The description of the two-dimensional transfer event is dictated by coordinates describing the electron and proton, as shown in Fig. 17.2. Both are charged particles whose transfers occur within a medium and separate solvent coordinates ze and zp are required for the electron and the proton, respectively. These solvent coordinates are analogous to the single solvent coordinates employed in ET or PT reactions and as such they are parametric in the distance coordinates of the electron and proton. In this representation, a family of pathways may be used to describe PCET, depending on how closely the reaction approaches the limiting stepwise pathways on the edges. Regions of this space are designated as displaying more ET-like or more PT-like character in their transition-states and reaction kinetics. The degree of collective solvent motion required for the ET versus PT components for a given PCET geometry may dictate that the one solvent coordinate is much more likely to dominate the transition state. For this reason, the different pathways available may be of significant consequence to the overall rate of the reaction. For instance, in a nonpolar environment, a diagonal path that keeps charge separation minimized may be kinetically preferred in view of the large energetic cost associated with creating a dipole in a low dielectric environment. In this case, the reaction is driven by inner-sphere modes rather than solvent fluctuations. On the other hand, in a high dielectric environment, thermodynamic parameters such as pKas or reduction
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17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer
Figure 17.2 The four-state PCET reaction in a solvent coordinate system. The four states are abbreviated with labels according to the initial and final states of the electron (i and f, respectively), and the initial and final states of the proton (a and b, respectively). The coordinates ze and zp refer to the collective solvent coordinates that are coupled to ET and PT, respectively. A concerted PCET reaction can
have a trajectory anywhere within this space with a single transition state. The synchronicity of the reaction reflects the nature of this trajectory; the synchronous HAT reaction is defined by the strictly diagonal line, whereas deviation from this line reflects asynchronous PCET with varying degrees of ET or PT character dominating the transition state.
potentials may drive the charge to separate via a more PT-like or ET-like transition state as long as the medium can support the increased polarization. Within the context of Fig. 17.2, HAT is the special case of the diagonal path. The electron and proton can transfer more or less synchronously along the same physical coordinate (re and rp), in which case there is no development of polarization to couple to the solvent. The reaction then follows the diagonal path in Fig. 17.2, which is only available in the HAT geometry where ET and PT coordinates are coincidental. All other PCET geometries require some degree of charge-separation (and hence divergence of ze and zp) in order to connect their initial and final states. It is important to reiterate that all paths within the square of Fig. 17.2 will be described by a single transition state and may be thought of as concerted, despite the asynchronous nature of the electron and proton transfer. The height of the barrier and its position relative to reactants and products depend on the nature of the pathway. Notwithstanding, because all paths are described by a single transition state, it is difficult to use linear free energy relations to glean detailed mechanistic information as to the precise nature of the PCET event. Ingenious system design, broad substrate scope, temperature dependences of rate constants, kinetic isotope effects, and new time-resolved laser methods that correlate proton and electron are needed to pin down the precise nature of the HAT-PCET mechanism.
17.1 Introduction
17.1.2 Scope of Chapter
Several recent reviews have explored PCET [1, 5, 23, 24, 29, 30] and specifically HAT [1, 16, 17] from reaction chemistry and theoretical perspectives. This chapter will not exhaustively re-examine this material, but rather introduce a descriptive framework for the electron and proton that adequately depicts both the geometric and mechanistic complexities of PCET and its relation to HAT. Most examples will be restricted to systems in which kinetics have been measured and discussed within a PCET framework. Accordingly, more classical topics, such as radical organic photochemistry (e.g., Norrish Type I and II reactions) will not be considered. This chapter will specifically consider the cases schematically represented in Fig. 17.3.
Figure 17.3 General geometries of PCET reactions defined by the spatial configuration of the four transfer elements, De, Dp, Ae, and Ap. In the Type A reaction, ET and PT coordinates are unidirectional with little or no sitedifferentiation. The latter case is formally an HAT reaction. Type B also represents unidirectional PCET, but with significant differen-
tiation between the ET and PT sites. Type C represents a bidirectional PCET reaction where the electron is transferred to Ae and the proton is dissociated to the bulk. The opposite reaction can occur with ET from De and proton association from the bulk. Type D is the case of bidirectional PCET that employs specific Ae and Ap sites.
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17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer
17.1.2.1 Unidirectional PCET The electron and the proton transfer along collinear coordinates. The Type A case of Fig. 17.3 illustrates a limiting scenario for the electron and proton originating from the same group (i.e., as a hydrogen atom) and transferring along collinear coordinates to their respective acceptor sites. When the electron and proton acceptor sites are not differentiated, the traditional definition of HAT is realized. However, in the most general description of unidirectional PCET, the electron and proton can be site-differentiated on both the donor and acceptor sides of the reaction (Type B in Fig. 17.3). In the Type B configuration, the ET coordinate can be considerably longer than the PT coordinate, which remains confined to a hydrogen bonding length scale. Nevertheless, the thermodynamic relations for each limiting case are still defined by the square scheme of Fig. 17.1. Coupling between the electron and proton transfer sites ensures that Ered values for the ET sites depend on the position of the proton, while pKa values for the PT sites depend on the oxidation state of the redox sites. This is not meant to imply that the mechanisms for all cases of unidirectional PCET are indistinguishable. For the site-differentiated situation where the ET coordinate extends beyond the PT coordinate, considerable charge separation may accompany the reaction, and the ET reaction becomes nonadiabatically coupled through the PT interface. For true HAT, the reaction can proceed without charge separation and in a strongly coupled adiabatic manner.
17.1.2.2 Bidirectional PCET The theoretical treatments of PCET confirm that proton motion can affect electron transport even when the electron and proton do not move along a collinear path. All that is required for direct coupling is that the kinetics (and thermodynamics) of electron transport depend on the position of a specific proton or set of protons at any given time. The two cases highlighted in Fig. 17.3 describe a majority of experimental bidirectional PCET systems studied to date. In nonspecific 3-point PCET (Type C in Fig. 17.3), one molecule donates both an electron and a proton. The electron is transferred to an oxidant with no proton accepting ability, while the proton dissociates and is received by bulk solvent. Although the PT coordinate is less well defined than in other PCET reactions, there can still be tight and specific coupling between ET and PT. The microscopic reverse – where an electron is accepted from a reductant and a proton is taken from the bulk solvent – may also occur. In site-specified 3-point PCET (Type D in Fig. 17.3), a donor is again the nexus of ET and PT events, donating both an electron and a proton in a coordinated manner. Again, the electron is transferred to an oxidant with no proton accepting ability, but rather than being released to the solvent, the proton is transferred to a specific site of another component (usually via a pre-formed hydrogen bond). One can also imagine the microscopic reverse of this reaction, where a reductant and an acid group transfer an electron and a proton, respectively, to an electron/proton acceptor in a coordinated fashion. This chapter is organized about the four PCET geometries illustrated in Fig. 17.3. Section 17.2 will describe the experiments applied to gain mechanistic infor-
17.2 Methods of HAT and PCET Study
mation from PCET reactions, and how their interpretation can often have peculiarities specific to PCET. Sections 17.3 and 17.4 detail the characteristics found in each of the uni- and bidirectional PCET geometries, respectively, from an experimental point of view. We will see that relationships do exist between geometry and mechanism, however they do not necessarily exhibit a one-to-one correspondence and hence the need to discuss both geometry and mechanism. Section 17.5 will discuss biological examples of PCET reactions, and Section 17.6 will introduce emerging coherent laser methods to probe correlated structural and solvent dynamics.
17.2 Methods of HAT and PCET Study
The complexity of PCET and its relation to HAT suggests that rate constants for the process are best measured directly using time-resolved methods that are capable of detecting intermediates, if present. Due to the disparate timescales and the diverse molecular nature of the species involved, different methods of reaction initiation and spectroscopic detection are needed to probe the various PCET reactions of Fig. 17.3. Many PCET reactions occur from a pre-organized and well-defined precursor complex; such designs are simplifying inasmuch as the diffusional component of the PCET reaction is eliminated. These types of diffusion-free reactions invariably rely on fast to ultrafast laser methods to photoinitiate and monitor the PCET transformation directly. Slower PCET reactions are often kinetically resolved in solution without the need for excited states. However, inherent PCET kinetics can be masked by diffusion terms and the kinetics of attaining the PCET precursor geometry. In these cases, the transformation of a substrate is monitored with the implicit assumption that the PCET or HAT step is rate determining. For fast reactions, the simplest kinetics experiment is to resolve the disappearance of the reactants, for example, by transient emission if the reaction can be photoinitiated and a reactant is luminescent. If there are multiple reaction channels available for reactant decay, the kinetics are described by a mono-exponential decay according to the sum of these rates of which PCET is only one. A more powerful experiment is to observe the disappearance of PCET reactants and growth of PCET products directly. In photoinitiated optical experiments, this means probing by transient absorption (TA) spectroscopy rather than transient emission. If PCET proceeds in a concerted fashion then concomitant mono-exponential disappearance of reactant and growth of product will be observed. If a stepwise mechanism operates, the growth of the products will be delayed (and fit by a bi-exponential function), however, this observation does not reveal the sequence in which the electron and proton were transferred. Moreover, in the limit where one of the steps is significantly faster then the other, the bi-exponential character of the kinetics trace will not be discernible, and the reaction may appear as if it were concerted.
509
510
17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer
Direct observation of intermediates (or lack thereof) provides credence to any mechanistic assignment. Integrated rate expressions for the intermediates will generally be less convoluted than the products since they are further upstream in the kinetic cascade. However, it is often difficult to observe independent spectroscopic signatures for each of the four PCET states. This is partly a consequence of the inherent coupling between electronic states and protonic states in PCET systems. In addition, PCET systems have not incorporated design elements for independent spectroscopic signatures of the proton and the electron. If it is determined that PCET occurs in a concerted step, no further information can be obtained about the two-dimensional trajectory from kinetics alone. It is conceivable that a concerted PCET reaction could be dominated by either the proton or the electron solvent coordinate (thus approaching the edges of the fourstate diagram in what is termed asynchronous PCET); however if no intermediate states are transiently populated, ensemble kinetics measurements only reveal the time-dependent statistical populations of the initial and final states rather than the reaction coordinate itself. For example, consider a concerted PCET reaction where kPCET = 109 s–1. The reactant population is depleted on a nanosecond timescale, yet an individual electron/proton tunneling event could still occur on a subpicosecond timescale, where the remainder of the one nanosecond is spent in inconsequential fluctuations of the solvent coordinates. Even if there is a strong spectral signature to characterize the actual transfer event, it will contribute a mere blip’ in the time-course of the reaction whose ensemble kinetics are defined on a longer timescale. This blip will be lost in an ensemble measurement because molecules are not negotiating the reaction coordinate in unison. A deeper understanding of the two-dimensional trajectory can be gained by correlating the concerted PCET rate constant to the effect of the various other parameters that probe the nature of the transition state. 17.2.1 Free Energy Correlations
A general understanding as to how changes in reaction free energy affect kinetics has been developed for selected reaction types. In such reactions, a relative displacement of reactant and product surfaces (DDGo) is reflected in a proportional displacement of the barrier between them (DDG‡). This leads to linear correlations between reaction free energies and the activation energies (or natural log of rate constants) over a narrow range of reactants and energy differences, assuming factors like DS‡ and electronic coupling are constant. These principles are responsible for the success of Hammett free energy correlations, Brnsted plots for PT reactions, Marcus theory for ET reactions and Evans–Polanyi relations for HAT reactions involving organic radicals [31–34]. In concerted PCET reactions, insight as to the nature of the transition state may be garnered from free energy correlations. For example, an asynchronous transfer that is dominated by the ET coordinate will have a polarized transition state and exhibit a rate correlation with Ered (or ionization energy). Conversely, a genuinely synchronous HAT reaction will
17.2 Methods of HAT and PCET Study
have a neutral transition state and exhibit a rate correlation with BDE. This issue is discussed in depth in Section 17.3.1. 17.2.2 Solvent Dependence
The solvent dielectric constant is a measure of how effectively the solvent medium screens the force between separated charges [35]. All PCET geometries except HAT involve some degree of charge separation, therefore the surface that defines the free energies of the four states and the barriers between them is a function of the solvent dielectric constant. Indeed, fluctuations in the electron and proton solvent coordinates drive these PCET reactions [5, 23, 24]. The extent to which electron and proton solvent coordinates contribute to the character of the transition state(s) is subject to the geometric constraints of the system, namely the origin and destination of the proton relative to the electron. For example, if PT is confined to a relatively short distance within a long-distance ET coordinate, as in the collinear systems described in Section 17.3.2, the solvent dependence is more ETlike. 17.2.3 Deuterium Kinetic Isotope Effects
The deuterium kinetic isotope effect (KIE) for a PCET reaction is defined as the ratio of rate constants for the reactions involving a protonated species and the deuterated analogue (kH/kD) [36–38]. This ratio reflects the degree of proton motion required to reach the transition state, and is one of the most tangible kinetic benchmarks through which theoretical PCET rate expressions can connect with experimental observations [16, 23, 28]. Classically, a reaction whose ratedetermining step is breaking a bond to hydrogen will proceed faster than the deuterium case because the reaction coordinate must involve a hydrogen (deuterium) vibrational mode. The heavier deuterium atom has a lower zero-point energy in this mode, which is manifest in a higher activation energy to reach the transition state. Large KIEs can result when the proton quantum-mechanically tunnels, because tunneling rates scale according to the overlap between reactant and product wavefunctions. Vibrational wavefunctions involving the heavier deuterium atom are less diffuse than those of hydrogen, leading to less favorable tunneling overlap for deuteron transfer. This differentiation is amplified when the transfer distance is increased. Finally, it is important to note that the observation of KIE „ 1 does not necessarily prove formal PT in the rate-determining step. For example, proton vibrational motion or displacement that does not result in PT can still be important to the reaction transition state geometry thus inducing a small KIE [39–41]. KIEs are frequently measured to determine whether PCET reactions proceed via stepwise or concerted mechanisms. Small KIEs are frequently cited as evidence for an asynchronous PCET or stepwise ET/PT reaction whereas large KIEs often
511
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17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer
are attributed to HAT [42–48]. However, KIEs exhibit pronounced distance dependences that can compromise such generalities. A large KIE can result, even for asynchronous PCET, if the transfer of the proton occurs over a large distance [28]. Conversely, a HAT can have a modest KIE if the transfer is occurring over a very compressed length scale [16]. Inverse KIEs (< 1) are encountered under rare circumstances, for example, when there are more thermally accessible deuteron states contributing to PCET [49]. KIEs are often complemented with other kinetic correlations to resolve ambiguities arising from intermediate magnitudes of KIE. 17.2.4 Temperature Dependence
Reaction rate expressions can be partitioned into two general terms: (i) an exponential thermal activation energy term that typically dominates the temperature dependence of reactions; and (ii) a pre-exponential term representing the probability of crossing from the reactant to the product surface in the thermally activated complex. Measuring the temperature dependence of reaction rates and fitting to the appropriate rate equation allows these terms to be separated experimentally, which is particularly valuable for interpreting PCET kinetics. For example, temperature dependence measurements reveal the activation barrier of a concerted PCET reaction for comparison with those of ET or PT steps. Comparison of pre-exponential terms exposes the effect that a PT network has on mediating electronic coupling. Temperature dependent rate measurements can be used to complement deuterium KIE measurements and determine whether the isotope effect originates from differences in activation energies or coupling.
17.3 Unidirectional PCET 17.3.1 Type A: Hydrogen Abstraction
HAT between X and Y is described as follows, X–H + .Y fi X. + H–Y
(17.2)
The electron comes from the X–H bond (typically sigma), and transfers collinearly with the proton to become part of the new H–Y bond. Eq. (17.2) aptly describes the hydrogen abstraction reactions of organic radicals. Figure 17.4(a) shows the traditional arrow-pushing scheme for the reaction where a donor atom X provides both the electron and proton to atom Y, which accepts them both. The reaction is driven by hydrogen atom acceptors that exhibit a high affinity for an electron and a proton together. For example, .Cl is an exceptionally reactive HAT participant as opposed to its more inert periodic table relative, .I, because .Cl hydrogen abstrac-
17.3 Unidirectional PCET
Figure 17.4 Schematic representation of the differences between HAT involving radicals and PCET involving transition metal complexes.
tions are more exothermic by roughly 32 kcal mol–1 compared to that of .I. Similarly, radical reactions employing .Br are typically much more selective than the corresponding reactions involving .Cl, due to the fact that the reaction with .Br is 15 kcal mol–1 less exothermic [50]. Based on Eq. (17.2), early treatments of HAT emphasize the orbital contributions of the singly occupied HOMOs of the donor and acceptor and bond strengths. From the perspective of PCET models [16], the close-range linear orbital pathway makes it reasonable that the electron and proton transfer adiabatically in a synchronous manner along the diagonal of Fig. 17.2, avoiding a polarized transition state. Indeed, such reactions do contain signatures of synchronous transfer through a neutral transition state. For example, they exhibit a linear correlation of log k with BDE, lack of dependence on solvent dielectric constant, and KIEs indicative of bond breaking in the transition state. Equation (17.2) has been extended by substituting the organic oxidant .Y with a transition metal complex. The case for HAT begins with a discussion of the thermochemistry presented in Fig. 17.1. Mayer and coworkers have defined the thermochemistry of proton-coupled oxidation of dihydroanthracene (DHA) by a FeIII bis-imidazole complex (FeIIIHbim). This PCET reaction is shown in Table 17.1(a), with the deprotonated FeIIIHbim and DHA reacting to give the fully protonated and reduced FeIIH2bim and monohydroanthracenyl radical (HA.) [51]. The thermodynamics of the individual PCET, ET and PT steps have been measured for this system and are shown in Fig. 17.5 [51–54]. ET from DHA to FeIIIHbim is uphill by DGo = 55 kcal mol–1 and PT is uphill by DGo = 32 kcal mol–1. By comparison, the concerted PCET process is only uphill by ~2 kcal mol–1. It is therefore concluded that the oxidation of DHA by FeIIIHbim has a large thermochemical bias that favors the concerted PCET process over either stepwise pathway. Furthermore, the experimentally determined activation barrier (DG‡ = 22 kcal mol–1) is
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17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer
significantly smaller than the energy required to populate either of the potential intermediate states, ruling out both stepwise mechanisms.
Tab. 17.1 Various mechanistic studies of PCET involving transition metal complexes.
PCET mechanistic studies a
b c d
e
f
The evidence for authentic HAT reactions involving reactions in which .Y = metal complex is derived from the correlation of the log of the observed rate constant, log k, to the X–H bond strength. The treatment is effectively encompassed by an Evans–Polanyi relationship [31–34], which relates the driving force of a series of hydrogen atom abstraction reactions to the activation energy (Ea) [55–57]. The connection of Ea to enthalpic quantities such as bond strength is most robust when similar hydrogen atom donors and hydrogen atom acceptors are compared, based on the assumption that the transition state entropy and geometry are constant across the series [58]. The oxidation of typical hydrocarbons of varying hydrogen atom donor ability by permanganate [59] is exemplary of this approach. Table 17.1(b) illustrates that the rate constants and activation enthalpies of hydrogen atom abstraction correlate well with the change in enthalpy for the abstraction process. This change in enthalpy is a measure of the difference between the
17.3 Unidirectional PCET
Figure 17.5 Thermochemical scheme for reaction between FeIIIHbim and dihydroanthracene. Figure adapted from Ref. [51].
strengths of the substrate C–H bond which is broken and that of the O–H bond which is being formed. The successful application of Evans–Polanyi correlations of the type shown in Fig. 17.6 for transition metal oxidants has led to the generalization that these reactions proceed by a synchronous PCET process that is mechanistically identical to hydrogen abstraction by an organic radical oxidant [52, 54]. We note however that the reactivity summarized in Table 17.1 for transition metal acceptors fundamentally differs from their organic counterparts in one important aspect – the proton and electron accepting sites for the reactions in Table 17.1 are distinct. It has been well documented that transition metal complexes that are capable of abstracting hydrogen atoms from substrates do not need to have unpaired spin density at the abstracting atom [52]. With the unpaired spin residing mainly at the transition metal center, upon completion of a PCET event, the electron is transferred to the metal (M(n+1) fi Mn) while the proton comes to rest at the ligand. The same is true for a variety of hydrogen abstraction reactions accomplished by metal oxo complexes. Hydrogen is transferred to the oxo ligand with concomitant reduction of the metal. More generally, HAT is distinguished from the organic radical reactivity as illustrated in Fig. 17.4(b). Because the sites for electron and proton transfer are site-differentiated, the possibility for charge separation between the electron and proton is more likely and a PCET description of the overall kinetics, as opposed to a more classical HAT one, is more accurate. This has been theoretically described for the specific case of Table 17.1(a) [60]. The challenge of pinning down the exact nature of the reaction mechanism, whether it is a synchronous PCET or not, from BDEs is highlighted by the oxidation of hydrocarbons by the nonheme FeIV=O complex [61–64] shown in Table 17.1(c). Figure 17.7(a) plots the measured second order rate constants for the oxidation of hydrocarbons by [(N4Py)FeIV=O]2+ against the BDEs of the hydrocarbons
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17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer
Figure 17.6 (a) Log k versus DH for PCET between various hydrocarbons and Bu4NMnO4 (Table 3.1b); (b) relation between DH‡ and DH for PCET between various hydrocarbons and Bu4NMnO4 (Table 3.1b). Figure adapted from Ref. [59].
[64]. A good correlation holds between the substrate BDE and log k for oxidation. We note, however, that the reaction is performed in acetonitrile as a solvent. The BDE of acetonitrile (BDEC–H = 94.8 kcal mol–1) [65, 66] is less than that of cyclohexane (BDEC–H = 99.5 kcal mol–1), which is oxidized at an appreciable rate. The inertness of acetonitrile is all the more striking inasmuch as its concentration as a neat solvent is 10–102 times greater than the hydrocarbon substrate. The oxo complex does decompose slowly over time at a rate of 5.8 10–5 s–1. If one assumes that this decomposition rate is essentially equivalent to the rate of hydrogen atom abstraction of acetonitrile by the [(N4Py)FeIV=O]2+, then the Polanyi correlation for BDE is compromised (Fig. 17.7(a)). Conversely, acetonitrile as a substrate for oxi-
17.3 Unidirectional PCET
Figure 17.7 Thermo-kinetic relation for oxidation of various hydrocarbons by a FeIV=O complex (Table 3.1c). Figure adapted from Ref. [64].
dation is described by a plot of ln k2 (in M–1 s–1) vs. the ionization potential (IE) of the substrate. An equally strong correlation is observed for all the data, including acetonitrile (Fig. 17.7(b)) [67]. The IE correlation might suggest a PCET mechanism that is asynchronous, with an ET-like transition state in the upper right section of Fig. 17.2. Alternatively, the Evans–Polanyi relation may breakdown for acetonitrile owing to different entropic contributions to the transition state and thus the HAT correlation prevails for [(N4Py)FeIV=O]2+ reactivity. At the same time, the system exhibits high KIEs for substrate oxidation [64], ostensibly supporting a HAT mechanism. But it has been suggested that asynchronous PCET can lower the frequencies of transition state vibrations that contribute heavily to the KIEs [67–70]. In such cases, anomalously high kinetic isotope effects can be observed for an asynchronous PCET as well. The point here is that a simple BDE correlation becomes obscured in the light of the results of Fig. 17.7(b). Similar discrepancies between BDE and IE correlations appear in other oxidations carried out by transition metal oxo compounds. The reaction of [RuIV(bpy)2 (py)O]2+ with hydrocarbons of varying reducing ability (i.e., varying hydrogen atom donor ability) is shown in Table 17.1(d) [71, 72]. The organic substrates that were studied are listed in Table 17.2 along with the respective BDE, IE and hydrogen abstraction rate data in acetonitrile. Again, the inability to oxidize acetonitrile is surprising given that toluene reacts at k = 6.4 10–3 M–1 s–1; both acetonitrile (BDEC-H = 94.8 kcal mol–1) and toluene (BDEC-H = 90 kcal mol–1) [73] have similar enthalpies for hydrogen atom abstraction. In the absence of a reported self decay rate, it is reasonable to assume that the rate of hydrogen atom abstraction involving acetonitrile must be of the order of k £ 10–7 M–1 s–1. This estimate is based on the concentration difference of acetonitrile (~19 M) versus substrate (0.1 M) and an expected decay rate that would be ~10–2 slower than that recorded for the least reactive substrate studied k ~ 10–3 M–1 s–1. A plot of the data shown in Table 17.2 with the exclusion of acetonitrile and anthracene shows a very strong correlation between the log k for oxidation of aliphatic hydrocarbons with BDE (Fig. 17.8(a));
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17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer
the correlation is compromised when acetonitrile and anthracene are included on the plot. As shown in Fig. 17.8(b), if log k is plotted against substrate IE, a good correlation is observed. Although the correlation of Fig. 17.8(b) is somewhat inferior to that of Fig. 17.8(a) with respect to the typical hydrocarbons such as toluene and DHA, all the substrates are accommodated by the IE plot.
Tab. 17.2 Thermodynamic and kinetic data for substrate
oxidation by [(bpy)2(py)RuIV=O]2+, adapted from Ref. [71]. Substrate
k (M–1 s–1)
BDE (C–H) (kcal mol–1)
xanthene
5.77 102
75.5
DHA
1.25 102
78
IE (eV) 7.65 –
indene
10.8
78.9
8.14
fluorine
21.9
80
7.91
cyclohexene
0.92
81.6
8.95
cumene
0.033
84.8
8.73
ethylbenzene
0.022
87
8.77
toluene
6.4 10–3
90
8.83
anthracene
0.27
~111
7.44
Figure 17.8 Thermo-kinetic relation for oxidation of various hydrocarbons by a RuIV=O complex (Table 3.1d). Figure adapted from Ref. [71].
17.3 Unidirectional PCET
The ambiguity in the data presented in Figs. 17.7 and 17.8 arises from the relation between IE and BDE shown in Fig. 17.9. As illustrated by the figure, the BDEC-H and IE for most simple hydrocarbon substrates correlate with one another. This is especially true of the hydrocarbons used in the aforementioned thermo-kinetic correlations (shown within the small box in Fig. 17.9). Even methane, which is difficult to oxidize in a controlled fashion, fits the overall trend. Given the parallel between IE and BDE for most typical hydrocarbon substrates lacking polar functional groups, correlations between log k vs. BDE, and log k vs. IE produce very similar plots and cannot uniquely distinguish between synchronous (HAT) and asynchronous PCET. For this reason, outliers to the correlation in Fig. 17.9 are the most interesting from a mechanistic perspective. These substrates are either aromatic (i.e., benzene and anthracene) or contain either polar functional groups (acetonitrile, formaldehyde and ethanol) or double and triple bonds (i.e., acetylene and cyclohexadiene). The discrepancies highlighted by Figs. 17.7 and 17.8 may be due to a breakdown of the Evans–Polanyi relation for a HAT reaction or alternatively the contribution of asynchronous PCET induced by the site-differentiation inherent to the metal oxidations as presented in Fig. 17.4. Studies that comprehensively treat the IE vs. BDE issue are therefore valuable. A penetrating study [74, 75] by Fukuzumi, Itoh and coworkers has attempted to address this issue by undertaking a comparative study of the oxidation of a series of phenols by a metal complex vs. an organic radical.
Figure 17.9 Thermodynamic relationship between bond dissociation energy (BDE) and ionization energy (IE) for a variety of hydrocarbons. The small box contains data for hydrocarbon substrates that have been typically used for BDE correlations.
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17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer
Phenol oxidations by metal complexes employ the (l-g2:g2-peroxo)dicopper(II) and bis(l-oxo)-dicopper(III) complexes shown in Table 17.1(e) and (f), respectively as the oxidants [75]. In this study, the rate of phenol oxidation was correlated with phenol oxidation potential (Eoox). We note that the use of the oxidation potential is more appropriate than the IEs of Figs. 17.7 and 17.8, since the latter approximates a gas phase internal energy for oxidation whereas the oxidation potential is the free energy for the solution reaction. Reaction of the substrates shown in Table 17.3 with the complexes in Table 17.1(e) and (f) allowed the determination of a Marcus driving force dependence for the oxidation reaction. As performed in the original work, Figure 17.10 presents the rate constants for oxidation vs. the Eoox of the various phenols. In addition the figure includes a plot of the rate data vs. BDE values [66] of the substrate. Whereas there is no discernible correlation between the oxidation kinetics and substrate BDE, the correlation with Eoox is very strong. The possibility of a stepwise ET/PT or PT/ET is ruled out by the slope of the line. A process in which ET is rate determining is predicted to yield a Marcus slope of –0.5 [6]; alternatively, a rate-determining PT step is predicted to yield a slope of e
e
f
f
Figure 17.10 Thermo-kinetic relation for oxidation of various phenols of Table 17.3 by a set of dicopper-dioxygen complexes (e and f, see Table 17.1). Figure adapted from Ref. [75].
17.3 Unidirectional PCET Tab. 17.3 Thermodynamic and kinetic data for substrate oxidation by l-g2:g2-peroxo)dicopper(II)
(A) and bis(l-oxo)-dicopper(III) (B) complexes and cumylperoxide radical (C). E0ox / V (vs. SCE)
ArOH
OMe
1
k2 / M–1 s–1 A
B
C
1.43
16.6
–
70
1.46
3.84
–
28
1.49
1.51
41.4
8.6
1.52
0.36
15.1
8.3
1.52
0.22
13.1
9.0
1.54
0.17
7.5
11
1.58
0.015
0.47
61
1.61
0.0077
0.30
–
1.62
0.0040
0.18
17
1.63
0.0026
0.10
–
HO
But
t
Bu
2 HO OPh
3 HO Ph
4 HO t
Bu
5 HO CH3
6 HO
7
But
t
Bu
HO t
Bu F
8 HO
9
But HO t
Bu Cl
10 HO
521
522
17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer
–1.0 [76]. When, however, the rates of electron and proton transfer are comparable and coupled to each other, intermediate slopes are obtained (between –0.5 and –1.0) [76–78]. Accordingly, the measured Marcus slopes of –0.72 and –0.71 support the assignment of a concerted PCET process for the oxidation of the substituted phenols by the Cu metal complexes. Additionally, KIEs of 1.21 to 1.56 are also consistent with an asynchronous PCET process in which there is some proton motion but a large ET component in the transition state. Oxidation of the same set of substituted phenols listed in Table 17.3 was also undertaken employing the organic oxidant, cumylperoxyl radical (Cum.). Unlike the metal based oxidation, Fig. 17.11 shows that the phenol oxidation rate constants do not correlate well with the substrate Eoox anny better than with substrate BDE. This behavior implicates a more synchronous HAT mechanism for the organic radical oxidant. Cum •
Cum •
Figure 17.11 Thermo-kinetic relation for oxidation of various phenols of Table 17.3 by cumylperoxide radical (Cum.). Figure adapted from Ref. [75].
We emphasize that all of the hydrogen abstraction reactions described and listed in Table 17.1 are concerted because they are described by a single transition state within the square of Fig. 17.2, rather than proceeding stepwise around the edges of Fig. 17.1. The paramount mechanistic issue that we have highlighted in this section is whether the two-dimensional trajectories are best described by a true HAT (concerted and synchronous) reaction along the diagonal of Fig. 17.2, or a PCET (concerted and asynchronous) reaction with a nondiagonal trajectory. The energy of the transition state can vary remarkably between the two mechanisms depending on the charge separation in the transition state. The PCET reaction may be induced when the electron and proton acceptors are site-differentiated. Additionally, this mechanism may be favored when the hydrogen donor has polar groups (e.g., acetonitrile) that can stabilize a more polar transition state associated with an asynchronous trajectory. To resolve this issue, the relative energy barriers for concerted PCET reactions need to be assessed as a function of substrate. In
17.3 Unidirectional PCET
this regard, PCET/HAT studies taking advantage of broadened substrate scope, solvent effects, and temperature dependences in addition to studies of isotope effects may be able to deliver a unified mechanistic picture. 17.3.2 Type B: Site Differentiated PCET
PCET can occur when the electron and proton are site-differentiated on both the donor and acceptor sides of the reaction. The PT coordinate must still be constrained to a hydrogen bond length scale, however, it is feasible for the ET coordinate to span an extended distance [79–81]. Nevertheless, coupling between the electron and proton may be strong since the redox potentials depend on the protonation state and the pKas depend on the redox state. Consequently, the square scheme of Fig. 17.1 must be used to evaluate the attendant thermodynamics. From a geometric perspective, Type B PCET reactions begin to look less like HAT, and are more reminiscent of a nonadiabatic ET reaction through a hydrogenbonded bridge. The electrostatic energy terms are dominated by the longer ET coordinate. In this description, the proton occupies a position in the electron tunneling pathway so the electronic coupling term becomes parametric in the coordinate of the proton. This means that ET through the hydrogen bonding bridge can depend on proton fluctuations, regardless of whether or not the proton is formally transferred. Such reactions are especially important in biology since ET in many proteins and enzymes is supported along pathways exhibiting hydrogen bond contacts between amino acid residues and polypeptide chains [82–84]. In model systems used to study Type B PCET reactions, the PCET complex is provided by self-assembly, which entails the noncovalent interaction of two or more molecular subunits to form a complex structure whose properties are determined by the nature and positioning of the molecular components [85–91]. The strengths and geometries of hydrogen bonds through which ET occurs can profoundly affect the PCET kinetics [92, 93].
17.3.2.1 PCET across Symmetric Hydrogen Bonding Interfaces Type B PCET has been examined at a mechanistic level following the strategy outlined in Fig. 17.12. In this scheme, PCET is photoinduced between an electron donor (De) and acceptor (Ae) spanned by a hydrogen bonding interface ([H+]), which contains the Dp–Ap pair. The first De–[H+]–Ae construct to be studied was supramolecule 1, which is formed from the association of a ZnII porphyrin donor with a 3,4-dinitrobenzoic acid acceptor by a carboxylic acid dimer interface [94]. In nonpolar, nonhydrogen bonding solvents such as CH2Cl2, 1 assembles with an association constant of KA = 552 M–1, as determined by IR shifts upon titration of the two components. This result is in good agreement with the association constants measured by static fluorescence quenching (KA = 698 M–1). Static quenching of 1 was not observed when the carboxylic acid dimer was disrupted by the addition of polar hydrogen bonding solvents or upon esterification of the donor and acceptor pair.
523
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17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer h
e– De
[H+]
Ae
+
De
–
[H+]
Ae
e– Ru(II) polypyridyl or De = Zn(II) porphyrin [H+] Symmetric O O H
H O O
Ae = organic acceptor
[H+] Asymmetric H N H N H H
O O
Figure 17.12 General strategy for the study of photoinduced PCET in model DeDp–ApAe systems.
The charge transfer properties of 1 were monitored optically by following the formation and decay of ZnII porphyrin cation on picosecond time scales. The forward and reverse PCET rate constants of protonated 1 were kfwd = 5.0 1010 s–1 and kback = 1.0 1010 s–1. The deuterated analog of 1 gave a rate constant of kfwd = 3.0 1010 s–1 and kback = 6.2 109 s–1, yielding KIEs of 1.7 and 1.6 for the forward and reverse PCET reactions, respectively. As theoretically elaborated [20, 95], it is this observed deuterium isotope effect that reveals coupling between electron and proton. The results obtained for 1 provided the first direct experimental measurement of PCET in a model system. Comparison of the kinetics recorded for 1 with those of covalently linked model systems with similar donor–acceptor separation and driving force [96], reveals that the rates of ET for these systems are of a similar order of magnitude. These results confirmed that hydrogen-bonding pathways for ET can in fact compete with electronic tunneling through covalent bonds [82, 97] as predicted by tunneling models [98]. Attempts to probe the electronic coupling through hydrogen bonds more quantitatively were made using supramolecular dyad 2 [99]. This dyad is similar to 1, inasmuch as a ZnII porphyrin functions as De and a carboxylic acid dimer functions as the hydrogen bonding interface. The main distinction between 1 and 2 lies in the identity of the Ae. For 2, it is a FeIII chloride porphyrin as opposed to the dinitrobenzoate. Time-resolved fluorescence quenching of the ZnII porphyrin across the hydrogen bonding interface yields a quenching rate of k = 8.1 109 s–1,
17.3 Unidirectional PCET
which was attributed to ET. This result was compared to the rate of decay of the ZnII porphyrin singlet excited state of 3 and 4, which juxtapose the same two redox sites between covalent r (3) and p (4) bridges containing the same number of bonds as 2. The rates measured for 3 and 4 were k = 4.3 109 s–1 and k = 8.8 109 s–1, respectively [99]. The fact that the ET rate constant is nearly doubled when comparing the carboxylic acid bridged 2 with the system bridged by the saturated carbon bridge (3) was attributed to greater electronic coupling mediated by the hydrogen bonding scaffold. This result opposes ab initio analysis of 2–4 [83] that predicts a weaker electronic coupling through the hydrogen bond interface of 2. The discrepancy may be resolved once the driving forces of the systems are considered. In the experimental study, redox potentials were deduced from porphyrin precursors rather than the electron transfer reactants themselves. 2 may have a higher driving force for ET and hence the free energy, as opposed to the electronic coupling, is the reason for the faster observed rate of the hydrogen bonded complex. Furthermore, energy transfer, and not electron transfer, from the singlet excited state of the ZnII porphyrin to the FeIII porphyrin may be the primary contribution to the quenching reaction mechanism. Recent TA studies have established that energy transfer prevails between ZnII and FeIII porphyrins for five-coordinate high-spin heme centers [100], as is the case for 2–4. Only when the heme is coordinated by two strong-field ligands does the quenching mechanism switch from an energy transfer to an electron transfer. Type B PCET systems of Fig. 17.3 may also be assembled using the three-point hydrogen bond of Watson–Crick base pairs such as guanine (G) and cytosine (C). Sessler and coworkers provided the first example of this assembly with 5, for which only energy transfer is observed [101, 102]. A Type B PCET is realized when the cytosine of the GC base pair is appended with an Ae functional group. In 6, a ZnII porphyrin serves as De and p-benzoquinone as Ae [103]. Time resolved fluorescence quenching experiments reveal that the rate of ET across the GC interface
525
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17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer
is kET = 4.2 108 s–1. Control experiments carried out with porphyrin and benzoquinone subunits that lack the Watson–Crick base pair functionality show no fluorescence quenching at similar concentrations, clearly indicating that the proton interface mediates the charge transfer event. Although the distance from the porphyrin De of 6 to the benzoquinone Ae is on the order of ~20 , the complex as a whole is highly flexible with a myriad of possible conformations that can allow ET to occur through space. To address this concern, more rigid systems such as 7 have been developed [104]. The greater rigidity of 7 as compared to 6 may be evident from its higher association constant (KA = 1.6 104 M–1). Time-resolved emission experiments reveal that the rate of ET (kET ~ 8 108 s–1) for the rigid system was nearly double that for the flexible complex. This is a noteworthy result, considering that the driving force for ET in 7 (DGs ~ -43 kJ mol–1) is substantially less than that for 6 (DGs ~ -96 kJ mol–1). The complexities of photoinducing a PCET reaction become apparent when W-band
17.3 Unidirectional PCET
time-resolved EPR experiments are performed on 8 [105, 106]. EPR signals are observed that are consistent with intersystem crossing from the singlet to the triplet excited state prior to ET. Unlike covalent De–Ae ET systems, the PT interface of DeDp–ApAe assemblies can strongly modulate the ET to the extent that internal conversion processes can compete kinetically with the charge transfer event.
The dicarboxylic acid dimers and Watson–Crick base-paired hydrogen bonding interfaces described above are similar, in that the protonic networks are uncharged and very little charge redistribution occurs within the interface upon ET from donor to acceptor. For the former, proton displacement from one side of the interface is compensated by the concomitant displacement of a proton from the opposite side owing to the inability of a carboxylic acid to support two protons. The same is true for the Watson–Crick base pairs, which are not easily ionized [107]. Since charge redistribution within these types of interfaces is negligible, the only mechanism available to couple electron and proton arises from the dependence of electronic coupling on the position of the protons within the interface [19, 20, 95]. As a result, the effect of the proton on the ET kinetics for symmetric hydrogen bonding interfaces is small and derived mostly from the electronic coupling matrix element as opposed to Franck–Condon terms.
17.3.2.2 PCET across Polarized Hydrogen Bonding Interfaces A more pronounced role of the proton in the photoinduced PCET event can be imposed in model systems that contain a hydrogen bond interface composed of Dp and Ap pairs possessing pKas that can support the transfer of a proton. We have designed PCET networks assembled from asymmetric amidinium–carboxylate salt bridges. In the solid state, the amidinium–carboxylate interface is ionic in nature and combines the dipole of an electrostatic ion-pair interaction within a hydrogen bonding network [108, 109]. The amidinium–carboxylate salt bridge in-
527
528
17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer
teraction is similar to the arginine–asparatate (Arg–Asp) salt bridge, which is an important structural element in countless biological systems including dihyrofolate reductases [110], cyctochrome c oxidase [111–115] and nitric oxide synthase [116–118] but at the same time is more amenable to PCET studies. As shown in Fig. 17.13, whereas the guanidinium group of arginine has multiple carboxylate binding interactions, the amidinium group can adopt only one two-point binding mode for carboxylate, thereby simplifying the supramolecular chemistry for donor–acceptor association.
Figure 17.13 Two-point binding modes for guandinium– carboxylate and amidinium–carboxylate salt-bridges.
The installation of an amidinium moiety on the periphery of De units permits the formation of supramolecular De–[H+]–Ae systems for the study of PCET. Interaction of an amidinium group with a carboxylate yields a unidirectional and remarkably stable two-point hydrogen bond, making it an effective association motif for the formation of such supramolecular complexes [119–122]. The location of the proton within the [H+] interface and the nature of its potential energy surface is of primary importance when considering the proton’s effect on ET kinetics. One important factor to consider is the relative pKas of Dp and Ap. Until recently, the pKa of a donor amidinium in organic solutions had not been discerned owing to the absence of a simple experimental observable. To confront this issue, purpurin 9 was prepared, in which conjugation between amidinium functionality and chromophore permits the protonation state of Dp to be ascertained simply by monitoring shifts of the Soret and Q bands of the porphyrin framework [123]. Titration of 9 with bases of known pKa reveals that the amidinium purpurin (pKa
17.3 Unidirectional PCET
= 9.55 – 0.10 in CH3CN) is considerably more acidic than carboxylic acids such as benzoic acid and acetic acid in organic solvents (pKa values of 20.1 and 22.3 in CH3CN, respectively [124]). These relative pKa values imply the prevalence of the amidine–carboxylic acid tautomer (Fig. 17.14, left) in low dielectric environments as opposed the amidinium–carboxylate salt bridge (Fig. 17.14, right), which is expected on the basis of aqueous pKa values (amidinium salts, pKa ~ 11–12 and carboxylic acids, pKa ~ 5–6 [125]). The precise nature of the tautomeric form that dominates the PCET assembly in low dielectric solvents has been elucidated by examining the optical spectrum of 9 bound to various anionic conjugates. Figure 17.15 shows that the spectrum of 9:benzoate shifts relative to that of the purpurin amidinium 9. The observed shift matches the shift seen upon deprotonation of the amidinium to amidine with DMAP, suggesting that Dp within the 9:benzoate complex is more amidine-like than amidinium-like. As a comparison, the 9:phenylsulfonate complex was also assembled and the optical spectrum in this case (Fig. 17.15) shows the definite presence of amidinium, and not the amidine. The phenylsulfonate is much more acidic than benzoate in organic solvents, thus explaining the differences between the two associated pairs. Comparison of these spectra leads to the conclusion that the [H+] interface is on the razor’s edge of the two tautomeric forms of Fig. 17.14. That such a delicate balance exists between tautomers is not an obvious prediction based solely on DpKas. The ~10 pKa unit difference in 9:benzoate favors the amidine–carboxylic acid form by ~ 0.6 eV. However, a simple electrostatic calculation [123] for a positive and negative charge at a salt bridge distance of 3.8 translates into a stabilization energy of –0.50 eV in the solvent THF, which nearly offsets the stabilization of the amidine-carboxylic acid tautomer derived from the DpKa. Electron-rich carboxylates such as benzoate are sufficiently basic that the amidine–carboxylic acid hydrogen bond interaction prevails while the interface retains its ionic nature for more acidic carboxylic acids and various sulfonic acids. A case in point for the ionic tautomer comes from kinetics studies of supramolecules 10 and 11 (see Table 17.4). Both compounds juxtapose a modified [Ru(bpy)3]2+, De, and a 3,5-dinitrobenzene, Ae, between amidinium-carboxylate and carboxylate-amidinium hydrogen bonding interfaces [126, 127]. The geometry of each of the assemblies was constant, affording a pair of model compounds that directly probe the effect of interface directionality on PCET kinetics. Since PCET
Figure 17.14 The two possible tautomers for assembly of amidines with carboxylic acids. The neutral interface is favored for basic carboxylates in low dielectric solvents. The ionic interface is favored for electron-poor carboxylates and in polar solvents.
529
17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer
Absorbance
530
410
400
500
420
430 440 λ / nm
600 λ / nm
450
460
700
Figure 17.15 Absorption spectra of amidinium purpurin 9 (0.63 10–6 M) in protonated amidinium form (black, solid line), deprotonated amidine form (gray, solid line) and with a large excess of benzoate (8.5 10–2 M) (black, dotted) and a large excess of phenyl sulfonate (black, dashed) in CH2Cl2.
is photoinitiated from the long-lived triplet metal-to-ligand charge transfer (3MLCT) state of the RuII polypyridyl center, intermolecular ET reactions can compete with the desired intramolecular PCET reaction of the self-assembled complex. The intra- versus inter- charge transfer pathways can be deciphered from the concentration dependence of the observed rate constants. As is shown in Table 17.4, the directionality of the asymmetric hydrogen bonding interface has a pronounced effect on the rate of intramolecular ET from De to Ae. The rate constant for PCET in the De-[amidinium-carboxylate]-Ae system (10) is roughly 40 times slower than that for the De-[carboxylate-amidinium]-Ae complex (11). The large difference in PCET kinetics which is observed upon reversal of the asymmetric hydrogen bonding interface is due in part to the direction of ET relative to the orientation of the salt bridge. For 10, the direction of the salt-bridge dipole is in the direction of PCET, however, for complex 11 the salt-bridge dipole opposes the direction of charge transfer. The salt-bridge orientation difference also contributes favorably to
17.3 Unidirectional PCET
the ET driving force for 11 and unfavorably for 10. Additionally, differences in hydrogen bond strengths for 10 and 11 may also play a role in the disparate kinetics data since these bonds modulate the electronic coupling through the saltbridge. Together, these results strongly implicate an ionized amidinium-carboxylate salt bridge, as shown in Fig. 17.14 (right). The result is consistent with the increased acidity of an Ae owing to the presence of the electron-withdrawing groups on the aromatic ring.
Tab. 17.4 Rates for unimolecular and bimolecular electron transfer
for DeDp–ApAe complexes with amidinium–carboxylate interfaces. PCET model system
DGs/eV
kET (M–1 s–1)[a]
kPCET (s–1)[b]
10
–0.14
1.2 109
8.4 106
11
–0.23
3.3 109
3.1 108
a The bimolecular reaction of the respective consitituents (non-hydrogen bonded) as determined by Stern–Volmer quenching kinetics. b Unimolecular electron transfer of the associated DeDp–ApAe pair.
The direction of the PCET reaction may be switched by catenating the RuII polypyridyl photocenter to an electron donor in place of an electron acceptor. In 12 and 13, the photoexcited RuII center is reduced by dimethylaniline. In order to accomplish these studies, a redesign of the RuII polypyridyl complexes was undertaken, such that the excited state electron of the photooxidant could be removed from the charge transfer pathway upon excitation into the MLCT state. This was achieved by modifying the bpy ligands of the RuII complex with strongly electron withdrawing diethylcarboxyl groups [128]. The rate of intramolecular PCET was determined by time-resolved emission for 12 (kPCET = 1.7 109 s–1), whereas the switched-interface congener, 13, showed no evidence of PCET within the 3MLCT excited state lifetime. This comparison is consistent with the comparative kinetic studies of the switched interface systems described above (10 and 11) in that the directionality of the bridging interface has a profound effect on PCET kinetics. In both comparisons, charge transfer for De-[carboxylate-amidinium]-Ae assemblies
531
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17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer
can be very fast, while PCET is attenuated in De-[amidinium-carboxylate]-Ae complexes. As for 10 and 11, the dominant source of the kinetics disparity in the comparison of 12 and 13 is undoubtedly the amplified thermodynamic bias induced by the orientation of the salt-bridge, which retards PCET when the electron traverses an ionic salt bridge oriented such that the amidinium is on De.
The large changes in optical density for ET [129–132] and PT [133–138] products of porphyrins make them ideal candidates for the study of PCET by transient absorption spectroscopy. In the three cases listed in Table 17.5, the porphyrin– amidinium conjugates 14 [139] and 15 [140] employ 3,5-dinitrobenzoic acid as the acceptor. The flexibility allowed by the vinyl bridge of 14 is eliminated by fusing the amidinium functionality directly onto the porphyrin macrocycle at the b-position of the ring. Compound 15, which provided the first X-ray structural characterization of a De–[amidinium-carboxylate]–Ae assembly, reveals that the amidinium group and the macrocyclic ring can be in electronic structural communication. This conjugation may be slightly attenuated due to amidinium–porphyrin canting. The PCET rates listed in Table 17.5 show that the salt-bridge (as mentioned above, this tautomer should dominate for a 3,5-dinitrobenzoic acid as Ae) attenuates the charge transport rate by ~102 when compared to that of covalently linked ZnII porphyrin-[spacer]-quinone (spacer = rigid polycyclic bridge) systems of nearly equivalent driving forces [96]. The attenuated rate for the hydrogen bonding system is even more pronounced given the 3 shorter donor acceptor distance for 15 as compared to the covalent system. Indeed, the notable effect that the asymmetric hydrogen bonding interface has on the kinetics of PCET for 15
17.3 Unidirectional PCET Tab. 17.5 Rates for unimolecular and bimolecular electron
transfer for porphyrin-based DeDp–ApAe complexes with amidinium–carboxylate interfaces. PCET model system[a]
kPCET (s–1)
14-DNB
7.5 108
15-DNB
6.4 107
a DNB represents 3,5-dinitrobenzoate.
suggests that strong coupling of the protonic interface to the electron transfer pathway is enhanced by the direct attachment of the amidinium functionality to the porphyrin redox cofactor. An alternative approach for the study of PCET across amidinium–carboxylate interfaces relies on the formation of ternary complexes such as that shown for 16 [141]. A N-propylisonicotinamidine serves as a ditopic spacer between a ZnII tetraphenylporphyrin donor and 3,4-dinitrobenzoate acceptor. The PCET assembly is afforded by the axial coordination of the pyridyl group to the ZnII porphyrin (Ka = 1.9 108 M–2 in CH2Cl2). A benefit of this approach is a significantly reduced synthetic investment required for the incorporation of Dp/Ap into the assembly. Moreover, the system is highly modular and the De porphyrin can be
533
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17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer
changed with relative ease. Fluorescence quenching of the ZnII porphyrin in the presence of the ditopic isonicotinamidine spacer and dinitrobenzoate yields a k = 1.9 109 s–1, which is notably faster than that observed for 14 or 15. The disparate rate constants for the two types of systems may reflect significantly different electronic coupling for the differing topologies. In most cases, PCET is implicated without the direct detection of appropriate reaction products. The challenge to the direct kinetic measurement by TA spectroscopy for such systems arises as a direct consequence of the presence of the proton transfer network proximal to the electron transfer pathway. In tightly coupled networks such as those for 14–16, the hydrogen bonding interface significantly retards the ET rate such that charge transport is slow with respect to the dynamics of the photoexcited porphyrin donor. Large changes in optical intensities associated with S1 fi T1 interconversions often overwhelm the absorption signatures of the distinct PCET intermediates. Consequently, the measurement of charge transport in the strongly coupled PCET networks described above has been confined to monitoring the disappearance of the S1 excited state by time-resolved emission spectroscopy. As discussed previously, this approach can be problematic because the dynamics of fluorescence decay are not necessarily specific to charge transport. Furthermore, PCET can proceed from non-emitting states to which time resolved emission spectroscopy is blind [105, 141]. Accordingly, there is great benefit offered by systems that allow the PCET kinetics to be determined directly from observed charge transport intermediates. Amidinium porphyrins featuring an amidinium functionality directly attached to the porphyrin framework at the meso- and b-positions [142], 17 and 18, respectively, are systems that provide the desired optical signatures of PCET reactions. 1H NMR spectroscopy shows [143], that association of 18 to the naphthalenediimide (NI) carboxylate to form 19 in THF (Ka = (2.4 – 0.6) 104) occurs by a twopoint hydrogen bond and that p-stacking between the porphyrin macrocycle and diimide acceptor is not a prevalent association mechanism. Carboxylate binding experiments carried out with purpurin 9, as described above, indicate that the NI carboxylate is basic enough to deprotonate porphyrin amidiniums in organic solvent. Accordingly, it is believed that for dyad 19, an uncharged amidine–carboxylic acid interface is established by the relatively basic acceptor, as opposed to the ionic amidinium–carboxylate bridge that is observed for the more acidic dinitrobenzoic acid acceptor used in previous PCET studies. TA optical signatures of the PCET reaction products were expected in the 600–700 nm region, namely the one-electron reduced diimide (De ~ 5000 at 610 nm) and the porphyrin cation radical (De ~ 5000 at 660 nm). However, the growth of the PCET product could not be resolved at most wavelengths due to the dominance of spectral signatures asso-
17.3 Unidirectional PCET
ciated with S1 fi T1 intersystem crossing in both bound and unbound porphyrins. [143]. This issue was remedied by performing single-wavelength kinetics at the S1–T1 isosbestic point (kprobe = 650 nm) of unbound porphyrin 18. Figure 17.16 (top) shows a collection of transient spectra for 18 at 500 ps, 1 ns and 2 ns. The small circle indicates the existence of the S1–T1 isosbestic point. Monitoring the PCET reaction kinetics at the unique wavelength, at which the dynamics of the
(a)
(b)
Figure 17.16 (a) TA spectra for 18 recorded at 500 ps, 1 ns and 2 ns. Circle denotes the S1–T1 isosbestic point at 650 nm. (b) Pump probe kinetics for 18 (solid circles) and 19 (open circles) at 650 nm.
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17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer
excited states for unbound 18 are effectively nulled, allows the absorption features of the PCET products to be detected against a “flat” background. The transient absorption data recorded at the S1–T1 isosbestic point are shown in Fig. 17.16 (bottom). The solid circles show that the kinetics for 18 are invariant with time because the probe is at an isosbestic point. The same experiment for 19 results in a clear rise and decay that is associated with the formation of the porphyrin cation radical by PCET, followed by its subsequent decay. The kinetics were fit to yield forward and reverse PCET rates of kPCET = 9.3 108 s–1 and 1.4 109 s–1, respectively [143]. This work has allowed the reverse rate of a PCET reaction across an amidinium-carboxylate salt bridge to be measured for the first time. In the light of these measurements, it can be seen that the forward PCET rate for 19 is nearly two orders of magnitude slower than those measured for covalently linked ZnII porphyrin–naphthalenediimide dyads of comparable driving forces [144, 145]. The TA results obtained for 19 are noteworthy because this work outlines a method to detect PCET intermediates by transient optical spectroscopy. The propensity of PT networks to retard charge transfer rates has practical consequences for mechanistic studies of PCET reactions. Attenuated rates translate to low yields of PCET intermediates. For this reason, it is difficult to observe PCET intermediates directly by time-resolved methods. Assembly 19 shows, however, that PCET intermediates can be spectrally uncovered when the transient difference signal between S1 and T1 excited states is minimized. This procedure, which is similar to one previously exploited in studies of D–A dyads [146] and heme protein–protein complexes [147], opens the door to a host of future experiments designed to directly monitor rates of electron transfer that are strongly coupled to proton motion. Variable temperature time-resolved experiments and KIE measurements on 19 have provided the most rigorous kinetics information of any Type B PCET system studied to date [49]. The slope and y-intercept of the modified Arrhenius plots (Fig. 17.17) permit the separation of nuclear and electronic contributions to the PCET rate. Weak electronic coupling matrix elements of 2.4 and 1.9 cm–1, respectively, for the protonated and deuterated forms of 19 attest to a coupling bottleneck through the interface. As shown in Fig. 17.17, two different isotope effects are observed at high and low temperatures for 19 with a protonated and deuterated interface. A reverse isotope effect (i.e., kH/kD < 1) is observed as T approaches 120 K (kH/kD = 0.9, 120 K) whereas a normal isotope effect (i.e., kH/kD > 1) is recovered as the temperature is increased (kH/kD = 1.2, 300 K). The transition between these limits is smooth, with a crossover temperature of T ~ 160 K. This trend is interpreted in a model where fluctuations within the hydrogen bonding bridge dynamically modulate electronic coupling for ET, and consequently the rate of charge-separation becomes sensitive to the nature of proton modes within the bridge. Thermal population of vibrational states is the most likely cause of the reverse isotope effect in this system, where the low frequency mode is a localized vibration in the hydrogen bond. At low enough temperatures, the thermallyinduced shift in the deuteron probability density contributes more to the PCET rate than the 1H form of the interface (due to the difference in zero-point ener-
17.4 Bidirectional PCET
Figure 17.17 Temperature dependence of the rate of PCET in protonated 19 (solid circles) and deuterated 19 (open circles) in the solvent 2-MeTHF. Data are presented in a modified Arrhenius form with linear fits. Figure adapted from Ref. [49].
gies). The normal isotope effect is recovered with increasing temperature as the lowest lying excited states of the hydrogen bond vibration of interest begin contributing to the PCET rate. This microscopic insight into the role of mediating protons is very pertinent to collinear PCET in biology, where asymmetrical hydrogen bonding networks are frequently the bottlenecks for electron transport. However, this level of understanding can only be reached when the relevant dynamics are isolated in well-defined and spectroscopically-accessible model systems such as in 19.
17.4 Bidirectional PCET
The square scheme in Fig. 17.1 applies equally well to the Types C and D bidirectional PCET schemes of Fig. 17.3. While that statement may seem trivial, it has the profound implication that the thermodynamics associated with a PT reaction can exert control over the rate and even the direction of an ET reaction along a spatially distinct coordinate. However, the thermodynamic square scheme conceals the major caveat to PCET; the transfer of the proton, as the heavier particle, is fundamentally limited to short distances whereas the electron, as the lighter particle, may transfer over very long distances [79–81]. The orthogonalization of ET and PT coordinates resolves the predicament of their disparate length scales while maintaining direct coupling. The electron can tunnel over a long distance and be coupled to a specific short-distance PT event that involves an additional acid or base group positioned nearby. Type C systems are relatively easy to study since the PT coordinate is not controlled. The Type D system is more challenging because a specific structure is imposed on the PT coordinate. In either case, the bidirectional approach is valuable since ET (redox potential) and PT (pKa) parameters can be varied independently and correlated with resulting PCET rates.
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17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer
17.4.1 Type C: Non-Specific 3-Point PCET
In this PCET configuration, a donor (De/Dp) transfers an electron to an acceptor (Ae) and loses a proton to the bulk (Eq. (C) in Fig. 17.3). Though there is no specific proton acceptor, the PCET event may be tightly coordinated and correlated to bulk properties of the medium, particularly the pH. Hammarstrm and coworkers have conducted a thorough investigation of dissociative PCET from tyrosine (Y) using ruthenium-tyrosine model complexes. The work is motivated by the crucial role that tyrosine residues, play in chargeseparation reactions in biology, particularly in Photosystem II (PS II). The model systems do not contain a specific PT coordinate as in PSII [148–156], yet the simplicity of the system permits the balance of stepwise versus concerted PCET to be studied in a controlled fashion. In the initial model system ([Ru]–Y, 20) [157], the oxidant is RuIII tris(bipyridine) (designated [Ru]), which is generated from the starting RuII state by the flashquench method. The Y moiety is covalently linked to one of the bipyridine ligands via an amide bond. The rate of ET from Y to the metal center of [Ru] as a function of pH was measured in water. These results are reproduced in Fig. 17.18. The data falls into two distinct pH regions, separated by the pKa (~10) of Y. Above pH 10, the rate constant for charge transfer is ~100-fold greater, and independent of pH. Here, Y is initially deprotonated, and this region simply corresponds to ET from tyrosinate to RuIII. In the low-pH region, the rate constant increases monotonically with increasing pH. Y is initially protonated, and the authors invoke a concerted PCET mechanism to account for this slope. A stepwise ET/PT mechanism can be ruled out because it does not give rise to pH-dependence in the rate of ET from Y to [Ru]. A gated stepwise PT/ET mechanism could give rise to pH-dependence, but this mechanism is also ruled out because the pKa constrains the maximum rate via this mechanism to ~10 s–1, which is too slow to account for the observed rate constants of >104 s–1. The authors interpret their data for both pH regimes in the framework of Marcus’ theory for ET [6, 7], which employs three parameters; driving force (–DGo), reorganization energy (k), and electronic coupling (V). In the region above the pKa of Y, –DGo is greater (due to a lower oxidation potential of tyrosinate; EY– = 0.77 V vs. NHE) [157] and is independent of pH. Below this pH, –DGo increases with increasing pH, which is a consequence of the pH-dependent potential of the tyrosine/tyrosyl radical couple (EY = (EYo – [(RTln10/F) pH), where EYo = 1.34 V vs. NHE) [157]. The Marcus treatment indeed predicts a positive corre-
17.4 Bidirectional PCET
Figure 17.18 pH dependence of RuIII reduction in system 20. The slope below pH 10 is indicative of a concerted Type C PCET reaction. Figure adapted from Ref. [157].
lation between the rate constant and pH for concerted PCET, consistent with measurements in the low-pH region. The physical nature of the concerted PCET reaction was further explored by measuring the temperature dependences of the rate constants in both the low-pH and high-pH regimes to afford an estimate of the Marcus reorganization energy, k (after correction for the entropic contribution to DGo since the proton is dissociated to the bulk) [157, 158]. The reorganization energy associated with the concerted PCET reaction (pH = 6.5) was found to be 1.4 eV, compared with only 0.9 eV for the pure ET reaction at pH 12. The greater reorganization energy for the concerted PCET reaction was attributed to the contribution of O–H bond breaking to the reaction coordinate. The KIEs of 1.5–3 measured in the low-pH regime [158] also support the idea that an O–H stretching motion is implicated in the reaction coordinate. Hammes-Schiffer and coworkers offer an alternative description of the same data [159] using their multi-state continuum theory developed specifically for PCET reactions. They also find that the PCET reaction carries a greater reorganization energy than the ET reaction. However, it is in the form of an outer-sphere (solvent) reorganization energy rather than an inner-sphere reorganization energy (associated with O–H bond cleavage). The increased solvent reorganization energy is justified because in a bidirectional geometry, the PT event adds to the chargeseparation that the solvent must accommodate. The O–H bond cleavage is nevertheless an essential contribution to the attenuated PCET rate relative to ET in Hammes-Schiffer’s model. In this case, it is in the form of a hydrogen vibrational wavefunction overlap factor. In other words, the PCET reaction has an attenuated coupling relative to ET due to averaging over the reactant and product vibronic states. Prior to this work, Cukier had also formulated a theory for dissociative
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PCET, where the previous model is modified to include a repulsive surface for proton motion in the final state [21]. The PCET rates are found to be rather sensitive to the nature of the repulsive surface – which is coupled to the solvent. Hammarstrm and coworkers developed related model compounds to explore the balance between concerted and consecutive PCET reactions. One such compound ([Ru]–W, 21) retains the original RuIII tris(bipyridine) core, however, the Y of 20 is replaced with tryptophan (W), which is easier to oxidize (EWo = 1.13 V vs. NHE) but harder to deprotonate (pKa(W) ~17, pKa(W.+) ~4.7) [160]. A pH-independent rate is observed in the region 4.7 < pH < 9, beyond which the rate monotonically increases with increasing pH. The pH-independence is indicative of a stepwise ET/PT mechanism, an assignment that is also supported by resolving the ensuing PT step by TA spectroscopy. A third model compound (MeC(O)O–[Ru]–Y, 22) differs from [Ru]–Y by the ethylester substituents added to the bipyridine ligands [160]. This increases the potential of the RuII/RuIII couple by ~0.24 eV, while the oxidation potential and pKa of the remote Y residue remain unperturbed. Interestingly, at pH < 6, the rate constant becomes independent of pH, despite there being a pH-dependent driving force for PCET. This is a signature of switching to a consecutive ET/PT mechanism, analogous to the behavior observed for [Ru]–W at low-pH and in contrast to [Ru]–Y. The temperature-dependence of RuIII reduction in MeC(O)O–[Ru]–Y in the low-pH and high-pH regimes reveal that the reorganization energy for the concerted PCET process is twice that of the ET step in the consecutive mechanism (2.4 eV vs. 1.2 eV). When the measurements MeC(O)O–[Ru]–Y were performed in D2O, the ET rate remained slow and independent of pH over the entire range studied. This indicates that the concerted PCET mechanism cannot compete with consecutive ET/PT. This leads to the estimate of a deuterium KIE > 10 for the concerted PCET reaction in this system.
17.4 Bidirectional PCET
Hammarstrm and coworkers unify their data from the model compounds into the following picture. In a system that can undergo both concerted PCET and consecutive ET/PT to yield the same ultimate product, these two channels are in kinetic competition. The issue of which channel dominates depends largely on the balance of the driving force and the reorganization energy. The driving force is necessarily more favorable for a concerted PCET reaction (because it includes the thermodynamically favorable PT component), but on the other hand, concerted PCET carries the kinetic cost of a greater reorganization energy compared with consecutive ET/PT. Note that Hammes-Schiffer and coworkers’ model invokes a vibrational overlap factor rather than reorganization energy as the main basis of the rate attenuation associated with concerted PCET, nevertheless, a parallel argument can be made. The problem reduces to the relative thermodynamics of the ET and PT components in the square scheme in Fig. 17.1. When the driving force for ET is large relative to PT, the small gain in driving force for concerted PCET is outweighed by the kinetic cost in terms of the activation energy. In this situation, the consecutive ET/PT mechanism is expected to dominate. This theory also explains the pH-independent region in [Ru]–W; the proton affinity of W means that PT does not contribute enough additional driving force to offset the attenuation inherent to the concerted mechanism. MeC(O)O–[Ru]–Y also proceeds via the consecutive ET/PT mechanism in the low-pH region, despite there being an appreciable driving force for PT (as in [Ru]–Y). However, the enhanced driving force for the ET component in this system relative to [Ru]–Y means that the additional driving force from the PT component is simply not required. In dissociative PCET systems, the driving force for PT increases with pH, which accounts for the eventual switch to a concerted PCET mechanism for [Ru]–W and MeC(O)O–[Ru]– Y at higher pH. This insight points to concerted PCET as an important mechanism in biology, where thermodynamic driving force for ET is typically conservative. Type C PCET also describes several studies focused on the oxidation of guanine. Guanine (G) is the most easily oxidized of all nucleobases, and appears to be a trap for oxidative damage in DNA [161–167]. The pKa of G shifts from 9.5 to 3.9 upon oxidation [161], thereby committing the deprotonation of N1 to accompany G oxidation in this pH regime. In fact, the strong coupling between ET and PT in nucleobases has been the source of substantial uncertainty in the determination of their redox potentials, due to the involvement of PT. Seidel and coworkers carried out a series of electrochemical measurements on nucleobases in aqueous and aprotic solvents [168]. They found that driving forces for ET in aqueous solution can be more favorable by 0.5–0.8 eV, due to coupled PT and hydrophobic interactions. Thorp and coworkers examined the oxidation of G in duplex DNA using a series of metal-polypyridyl oxidants of varying driving force [78]. A Marcus plot yields a slope of ~ –0.8. As discussed in Section 17.3.1, a stepwise mechanism with a ratedetermining ET step produces a slope of –0.5 whereas a rate-determining PT step produces a slope of –1.0. The observations of an intermediate slope and attendant KIE of 2.1 signify that a PCET mechanism is operable. It is noted that in other
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studies, G has been oxidized directly to the radical cation, G.+, without concerted deprotonation [169–171]. Those systems employed much stronger oxidants, whereas ET-only reactions in Thorp’s system are either endothermic or weakly exothermic. Accordingly, it is only necessary to couple to PT in a concerted step when there is otherwise insufficient driving force, consistent with the conclusions from the aforementioned Y and W oxidation studies. Type C (associative) PCET in Fig. 17.3 describes the microscopic reverse of the nonspecific 3-point PCET in which a proton is lost to solvent. Instead, an acceptor is the recipient of an electron from a reductant and a proton from the solvent. This associative 3-point PCET has been found to occur in pyrimidine nucleobases, particularly cytosine (C), where N3 is protonated upon reduction. Geacintov and coworkers studied photoinduced ET in benzo[a]pyrenetetrol (BPT)–nucleoside complexes in aqueous solution and in the polar aprotic solvent DMSO [171]. Evaluation of the available driving forces for ET indicate that there is insufficient driving force for 1BPT* to reduce the pyrimidines C and thymine (T), unless reduction is coupled to the uptake of a proton. Accordingly, they find a lack of quenching by C and T in DMSO, however efficient quenching is observed in water. TA spectroscopy confirms the formation of BPT.+, and thermodynamics suggests that PT from water must accompany ET to the pyrimidine nucleobase. The authors find deuterium KIEs of 1.5–2.0 when the reactions are carried out in D2O, which supports the proposed PCET mechanism. Wagenknecht, Fiebig and their coworkers have used ultrafast spectroscopy to study reductive electron transport in pyrimidine nucleobases on the picosecond timescale. They developed a series of pyrene-modified nucleosides, in which the nucleosides are directly bound to pyrene, which acts as a photoreductant [172–174]. The first model compound (pyrene–dU) employed deoxyuridine (dU) as a model for the deoxythymidine nucleoside [172, 173]. The emission intensity from 1(pyrene)* was measured as a function of pH in water. The emission is completely quenched in the low-pH range, and the fluorescence intensity follows a typical sigmoidal curve, with an inflection point at pH » 5.5 reflecting the pKa of the protonated pyrene.+–dU(H). biradical. However, TA spectroscopy reveals that the ET product (pyrene.+–dU.–) is initially formed in both pH regimes, therefore concerted protonation is not requisite for ET in this system, and the pH dependence of the emission intensity cannot simply be interpreted as quenching by concerted PCET in the low-pH regime. Instead, it is believed that pyrene.+–dU.–, is rapidly formed in a pure ET process regardless of pH. It is nonemissive, but is in equilibrium with the locally-excited state, (pyrene)*–dU, meaning that emission can still be observed. However, at pH < 5, pyrene.+–dU.– is subsequently protonated, and efficient nonradiative decay prevents repopulation of the local-excited state, and thus emission is mitigated. In this system, there is sufficient driving force for ET without coupling to PT, and in the appropriate pH range, PT will ensue to complete a consecutive ET/PT mechanism. Similar behavior was observed when dU was replaced with deoxyadenosine (dA), and with dG, however in that case, the pH-dependent emission intensity curve was inverted because dG was oxidized (and deprotonated) [173]. When dC was used, fluorescence was effi-
17.4 Bidirectional PCET
ciently quenched across the entire pH range of 1.5–12.5. This suggests that the pKa of pyrene.+–dC(H). is greater than 13. Further investigations on the pyrene–dC system (23) were undertaken in the polar and aprotic solvent acetonitrile (MeCN) in order to distinguish between pure ET and PCET reaction channels [174]. Fluorescence quenching was not observed. Moreover TA measurements reveal no ET dynamics, indicating that the pure ET reaction is endothermic. Similar measurements were undertaken in water at pH 5 and pH 11, where the formation of pyrene.+ is observed and timeresolved, along with the disappearance of 1(pyrene)*. By comparison to the MeCN data, the authors contend that pyrene.+ must be formed by a concerted PCET mechanism (directly forming pyrene.+–dC(H.)), rather than via an energetically costly pyrene.+–dC.– intermediate. The kinetics fit to a model that indicates that PCET is 3-fold faster at pH 5 than at pH 11, supporting the concerted PCET mechanism. The trend in this case is the reverse of that discussed above for Y oxidation in [Ru]–Y due to the opposite sense of the reaction. The issue of concerted versus stepwise PCET in the reduction of pyrimidine nucleobases also parallels the findings in 20–22. The nucleobase dU has a greater electron affinity compared with dC [168], but a weaker proton affinity. This is the basis for the consecutive ET/PT mechanism observed in pyrene–dU as compared with the concerted mechanism in pyrene–dC (23).
17.4.2 Type D: Site-Specified 3-Point PCET
Many ETs to an oxidant (or from a reductant) are accompanied by PT to a specific base (or from a specific acid), usually via a preformed hydrogen bond. As discussed in Section 17.5, Type D PCET often describes the transfer of a net hydrogen atom in Nature. It is the specific coordinate for PT that distinguishes Type D PCET from its Type C counterpart of Section 17.4.1. Unlike proteins, which exert control over transfer distances by positioning amino acid residues according to the tertiary structure, most ternary PCET reactions studied in model systems to date are trimolecular reactions. This complicates kinetics measurements and analysis, and can mask the underlying physics. The PCET yield depends on both the association constant (Kassoc) to form the PCET precursor complex, and the subsequent pseudo-bimolecular PCET rate constant (kPCET). It is imperative to decouple the measurement of Kassoc and kPCET to
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allow rigorous comparisons among a carefully chosen series of reactants, since many variations in model compounds can affect both quantities. Linschitz and coworkers pioneered the study of Type D PCET in model systems with extensive studies on 24 and derivatives. Ae is the triplet excited state of fullerene (3C60), De/Dp is a substituted phenol, and Ap is typically a substituted pyridine (py) [175, 176]. The pseudo-first-order rate constant of 3C60 decay (kobs) was measured as a function of [phenol] and [py], with k0 representing the rate in the absence of phenol. Plots of (kobs– k0)/[phenol] vs. [py] were fit to yield both the association constant for the phenol:py complex (Kphenol:py), and the rate constant attributed to quenching from the bound complex. Independent measurements of the association constant using Mataga’s titration treatment [177, 178] agree with the values for Kphenol:py obtained from fitting to the kinetic model over a wide range of Kphenol:py. Their analysis reveals that the phenol:py complex dominates the quenching of 3C60. The authors establish that the reaction proceeds according to the Type D process of Fig. 17.3 by using TA spectroscopy to detect PCET products directly; C60.–, py–H+, and the neutral phenoxyl radical are all generated concomitantly with the loss of 3C60. As expected for a ternary PCET reaction that separates charge, the PCET quantum yield is found to increase as a function of solvent polarity. Furthermore, 3C60 quenching is two orders of magnitude faster when trimethylpyridine is the proton acceptor, as compared to DMSO, which has comparable hydrogen bonding ability but cannot accept a proton from the oxidized phenol. The KIEs measured reflect complete PT coupled to ET in the case of the trimethylpyridine acceptor (kH/kD = 1.65), and ET coupled to a hydrogen bonding interaction for DMSO (kH/kD = 1.06). Moreover, the temperature dependence of the deuterium KIE in the former reaction reveals that its origin lies in the activation energy rather than electronic coupling. These results establish that, with the appropriately chosen proton acceptor, the electron and proton are both transferred to their respective acceptor sites concurrently. The modularity of 24 permits PCET rates to be easily examined as a function of the pKa of Ap. For a wide range of substituted phenols, and in various solvents, the concerted PCET rates consistently track the increasing basicity of the substituted pyridine. Moreover, these measurements, when taken together with their temperature dependence, reveal that PCET becomes more kinetically competent owing to a lower activation barrier as the PT component becomes more exergonic. It is interesting to note, that this conclusion is also obtained in Section 17.4.1 for effectively the same De/Dp. The difference between 20 and 24 is that for the latter, the hydrogen bonded Ae, rather than the bulk pH, determines the PT driving force.
17.4 Bidirectional PCET
20 has been adapted to a Type D PCET model system (25) by the addition of two dipicolyamine ligands to Y [179]. The modification introduces an Ap site as an intramolecular hydrogen bond acceptor. The system was designed to mimic the interaction between YZ and H190 in PSII. Transient EPR measurements (coupled to a flash-quench experiment) in water revealed that .Y is formed, confirming a PCET process. Flash-quench kinetics measurements reveal that 25 undergoes PCET at a rate two orders of magnitude faster than 20. This acceleration in 25 is attributed to the intramolecular hydrogen bond, which decreases the oxidation potential of Y. Although the proton is ultimately lost to water, the dipicolyamine appears to acts as a primary proton acceptor (i.e., Ap) along a PT coordinate that is established by an intermolecular hydrogen bonding interaction. Similarly, Mayer and coworkers have studied the oxidation of a phenol that has a proton accepting amine group attached at the 2 position [180]. They carried out the reaction with a variety of oxidants to show that oxidation is coupled to concerted PT to the amine within an intramolecular hydrogen bond.
System 26 uses an extrinsic base to tune the reducing power of a-hydroxy radicals [181]. The photochemically generated diphenylketyl radical serves as De/Dp–H, Ae is 1,2,4,5-tetracyanobenzene (TCB), and Ap is a substituted pyridine (py). In the absence of the pyridine to facilitate PT, the ET reaction from the ketyl radical to TCB is endothermic by 0.4 eV. Consequently, the diphenylketyl radical decays slowly to reconstitute the starting reactants with no net reaction taking place. When coupled to PT by pre-associating the
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diphenylketyl radical with an Ap, the reaction can become thermodynamically favorable. For example, when lutidine is added as Ap, the driving force of the PT component increases by 0.8 eV, thus making the overall PCET reaction exergonic by 0.4 eV. TA spectroscopy confirms that addition of lutidine accelerates decay of the diphenylketyl radical, and a concomitant rise in the transient absorption of TCB.– is observed. Note that direct PT from the diphenylketyl radical to the lutidine without coupling to ET is thermodynamically unfavorable and products of this reaction were not observed. Since experimental observations and thermodynamic arguments rule out direct ET and direct PT (per Fig. 17.1), a concerted PCET mechanism is implied, whereby the diphenylketyl radical transfers an electron to TCB and a proton to the py in a single step. The PCET reaction rate for 26 has been slowed by using a less basic proton acceptor, thus reducing the driving force for the concerted PCET reaction. When lutidine is replaced with 2-Cl-py, the driving force diminishes from 0.4 eV to < 0.1 eV, and accordingly kPCET decreases by a factor of four. A KIE of 3.2 was measured when the deuterated diphenylketyl radical was used and Ap was 2-Cl-py. This magnitude certainly supports the mechanism of concerted PCET. Type D reactions can operate in reverse wherein an electron and proton converge at Ae/Ap. The development of 27 by Linschitz and coworkers [182] employs chloranil (CA) as Ae/Ap, 3C60 as De, and an alcohol or carboxylic acid (R–OH) as Dp. This study was conducted in essentially the same manner as phenol oxidation for 24, however the mechanisms were found to differ as a result of the proton’s role in the PCET reaction. In the absence of R–OH, CA can quench 3C60, albeit slowly. The instability of the charge-separated state results in a reverse ET reaction that rapidly depletes the radical yield. The rate of ET from 3C60 to CA increases sharply upon addition of R–OH that is a strong hydrogen bond donor such as hexafluoro-2-propanol (HFIPA). Weaker R–OH hydrogen-bonding substrates such as trifluoroethanol (TFE) have a negligible effect on ET rates. Formal PT need not be invoked to rationalize these data; strong hydrogen bonding accelerates ET by shifting the reduction of the quinone to less negative potentials. Electrochemical measurements support this explanation. Quinone reduction potentials are found to track the hydrogen bonding ability of R–OH groups in aprotic solvents [183]. PCET products are only observed when R–OH is a very strong proton donor (in addition to being a strong hydrogen bond donor), such as trifluoroacetic acid (TFA, pKa = 3.45 in DMSO). In such cases, the neutral semiquinone (CAH.), C60.+, and R–O– are the PCET products. The first two of these were identified by TA spectroscopy; their absorption features grow concomitantly with the decay of
17.4 Bidirectional PCET 3C . 60
These observations lead to the conclusions: (i) ET is accelerated by strong hydrogen-bonding between CA and R–OH; (ii) rapid PT within the hydrogenbonded complex ensues to generate the PCET products only when Dp is a sufficiently strong proton donor; and, (iii) if PT occurs, it prolongs the lifetime of C60.+. In other words, coupling PT to an ET reaction can enhance the utility of charge-separated states, regardless of whether the mechanism of PCET is concerted or consecutive. Moore, Moore, Gust and their coworkers have developed 3-point PCET systems that incorporate all the necessary ET and PT components within molecular dyads and triads [184]. In 28, De is the singlet excited state of a free-base porphyrin, Ae/ Ap is a naphthoquinone moiety that connects to the porphyrin via an amide linkage, and Dp is a carboxylic acid that is attached to the bridgehead of a norbornene system fused to the naphthoquinone. The carboxylic acid associates to the carbonyl group of the quinone by a hydrogen bond. The intramolecular hydrogen bonding interaction shifts the reduction potential of the quinones to more positive potential, thereby accelerating ET from the porphyrin to the quinone. The enhanced quenching rate is reflected by the three-fold shortening of the porphyrin fluorescence lifetime of 28 as compared with a control compound in which the norbornene and carboxylic acid are absent. Using TA spectroscopy, the fate of the charge-separated state was tracked by probing the TA signature of the porphyrin cation radical, P.+. An increase in the lifetime of P.+ from < 250 fs to ~4 ps for 28 (compared with the control compound) was ascribed to a fast PT (~1 ps), which followed ET. This is well justified considering that the quinone becomes more basic by >10 pKa units upon reduction within the pre-established hydrogen bond network. Analogous to Linschitz’ quinone system 27, a hydrogen bonding and proton-donating group appropriately positioned with respect to a quinone leads to accelerated charge-separation and prolonged lifetimes. Type D PCET clearly demonstrates the role of an extrinsic proton donor or acceptor in modulating the rate and direction of ET along a spatially separate coordinate, and in doing so stabilizes charged intermediates. In this way, the proton manages charge separation as long as the electronic states of Ae/Ap are tightly coupled to the protonic states of De/Dp. This idea is schematically depicted in Fig. 17.19. In the thermodynamic square scheme, this translates into large shifts in De/Ae redox potentials, depending on whether or not the proton is bound, and large shifts in Dp/Ap pKa, depending on the accompanying oxidation state. For example, phenols (or tyrosine residues in biology) are found to be very prevalent in bidirectional PCET reactions that proceed according to Eq. (D) of Fig. 17.3 since
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Figure 17.19 Schematic depiction of off-pathway PT as a means to assist long distance electron relaying. The coupled PT exerts control over the ET rate and direction by modulating the redox potential of the relay intermediate relative to De and Ae.
the pKa of phenol shifts from 10 to –2 upon one-electron oxidation [185, 186]. Likewise, quinones (or other ketones) are frequently involved in orthogonal PCET reactions in the reverse direction on account of their pronounced pKa-redox coupling. There are common features among these species (and others discussed such as guanine and cytosine) that give rise to the strong pKa-redox coupling. They are aromatic molecules that have energetically accessible frontier electronic orbitals, thus allowing facile ET with minimal structural distortion. They also integrate hetero-atoms (typically oxygen or nitrogen) that are basic and thus able to support PT. Importantly, they are typically part of a small framework – typically based on a six-membered ring, ensuring that significant amplitudes of the frontier electronic orbitals reside on the hetero-atoms to increase pKa-redox coupling. In other words, rather than extensively delocalizing charge, which is typically the paradigm for facile ET, focusing changes in charge onto acid–base functionalities amplifies pKa-redox coupling, which can then be used as a control-handle when incorporated into a bidirectional PCET configuration.
17.5 The Different Types of PCET in Biology
Nature provides striking examples of each of the types of PCET discussed in this chapter. Enzymes often rely on PCET to affect primary metabolic steps involving charge transport and catalysis. Amino acid radical generation and transport is synonymous with PCET [187], as is the activation of substrate bonds at enzyme active sites [29]. PCET is especially prevalent for metallo-cofactors that activate
17.5 The Different Types of PCET in Biology
substrates at carbon, oxygen, nitrogen, and sulfur atoms. In order to access these different types of reactivity, enzymes impart exquisite control over both ET and PT coordinates via the protein tertiary structure. Type A PCET reactions describe amino acid radical generation steps in many enzymes, since the electron and proton transfer from the same site as a hydrogen atom [188]. Similarly, substrate activation at C–H bonds typically occurs via a Type A configuration at oxidized cofactors such as those in lipoxygenase [47, 48] galactose oxidase [189–191] and ribonucleotide reductase (Y oxidation at the di-iron cofactor, vide infra) [192]. Here, the “HATs” are more akin to the transition metal mediated reactions of Section 17.3.1 since the final site of the electron and proton are on site differentiated at Ae (redox cofactor) and Ap (a ligand). Type B PCET represents a largely inevitable scenario in many proteins where electron transfer coordinates traverse the hydrogen bonding networks that are required to establish tertiary structure. In the case where the ET coordinate is long and no X–H bond is broken, the hydrogen bond modulates the kinetics for ET via the electronic coupling matrix element. Pathway models for ET in proteins have explicitly parametrized the effect of hydrogen bonding conduits in recognition of the ubiquity of Type B PCET in biology [82–84]. The coupling between the proton and electron is more pronounced and thermodynamically derived when X–H bond breaking is involved. Type D PCET is utilized in Nature to effect a variety of catalytic processes because it allows enzymes to manage the disparate electron and proton length scales. The PT network is established by the tertiary structure of the protein matrix about a redox center. Figure 17.20 depicts a generalized scheme of PCET at a M–OH center. PCET reactions can affect oxidation or reduction at the metal center when an appropriate PT site is positioned nearby. The reactions are coupled to changes in the M–O bond order. Many oxidases also derive function from PT networks orthogonalized to redox-active M–O–O–H centers. Examples include peroxidases, catalases, and cytochrome P450 mono-oxygenases [193–198]. The hemeoxo intermediates, Compound I (P.+FeIV=O, P = porphyrin) and Compound II (PFeIV=O), are generated upon protonation of ferric peroxy species at the unbound oxygen atom and loss of water in concert with oxidation at the metal redox center and increase in the M–O bond order. Proton-donating amino acid residues at well-defined distances from the porphyrin redox platform orchestrate
Figure 17.20 Schematic depiction of metal-centered bidirectional PCET. Oxidation (or reduction) at the M–OH center is coupled to loss (or gain) of a proton and an increase (or decrease) in the M–O bond order.
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these metal-centered PCET reactions. The structure of cytochrome P450 [193] (Fig. 17.21) establishes the presence of a hard-wired water channel to direct protons to and from the heme redox cofactor. Compounds I and II are also photogenerated in modified microperoxidases upon oxidation of a ferric hydroxy species (PFeIII–OH) coupled to deprotonation to reveal the terminal oxo [199, 200].
Figure 17.21 Crystal structure of cytochrome P450, displaying a water channel above the heme. Figure adapted from Ref. [193].
The so-called Hangman porphyrin’ models [201] were developed as a simplified construct of the bidirectional PCET networks of heme enzymes. Compound 29 suspends a pendant acid group from a xanthene spacer at a fixed distance from the porphyrin platform. The structurally characterized Hangman porphyrin xanthene (HPX) (Fig. 17.22) shows that a water molecule (with a binding energy of 5.8 kcal mol–1) [202] is suspended between the xanthene carboxylic acid hanging group and the hydroxide ligand [201]. This is the first synthetic redox-active site displaying an assembled water molecule as part of a structurally well-defined PT network. As in mono-oxygenases, PT from the acid–base hanging group in (HPX)MIII–O–O–H (HPX = Hangman porphyrin xanthene, M = Fe, Mn) peroxide complexes yields (HP.+X)MIV=O [203]. In the presence of olefins, epoxidation occurs at high turnover [202] (M = Mn). In the absence of substrate, the Com-
17.5 The Different Types of PCET in Biology
Figure 17.22 Crystal structure of the ferric hydroxide form of Hangman porphyrin 29 showing the water channel within the Hangman cleft. Figure adapted from Ref. [201].
pound I-type intermediate reacts with peroxide to generate oxygen and water in a catalase-like reaction, also at high turnover [204] (M = Fe). Mono-oxygenase and catalase activities are lost when the Hangman pillar is extended and the proton must transfer over long distance [202]. Activity is also severely reduced when the pKa of the hanging acid–base group is increased [204]. The studies on these Hangman porphyrins and other macrocyclic Hangman platforms [205] clearly demonstrate that exceptional catalysis may be achieved when redox and PT properties of a cofactor are controlled independently. A key requirement is that the PT distance is kept short, which may be accomplished by orthogonalizing ET and PT coordinates. The benefits of incorporating PT functionality into redox catalysis can only be realized when a suitable geometry is established. Moreover, the Hangman platforms show that a multifunctional activity of a single metalloporphyrin-based scaffold is achieved by the addition of proton control to a redox platform. This observation is evocative of natural heme-dependent proteins that employ a conserved protoporphyrin IX cofactor to affect a myriad of chemical reactivities. Other oxidases also derive function from bidirectional PCET pathways at the enzyme active site. The recent crystal structures of PSII [206, 207] support suggestions that as the oxygen evolving complex (OEC) steps through its various S-states [208, 209], substrate derived protons are shuttled to the lumen via a proton exit channel, the headwater of which appears to be the D61 residue hydrogen-bonded to Mn-bound water [210]. The protons are liberated with the proton-coupled oxidation of the Mn–OH2 site. As shown by the structure reproduced in Fig. 17.23, D61 is diametrically opposite to YZ, which has long been known [148, 151, 152] to be the electron relay between the PS II reaction center and OEC. Notwithstanding,
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17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer
ET PT PT
Figure 17.23 The 3.4 resolution structure of the oxygen evolving complex (OEC) and the immediate peptide environment. The directions of proposed PT and ET pathways are indicated with arrows. Figure adapted from Ref. [206].
YZ employs bidirectional PCET in its role as an electron relay. For the reasons described in Fig. 17.1, and consistent with the numerous related model systems described in Section 17.4, oxidation of YZ requires proton dissociation from the phenolic oxygen. Functional schemes of PSII prior to the crystal structure suggested that the proton was lost to a water channel via the primary acceptor H190 (i.e., a Type D PCET reaction) [155, 156] and hence YZ was the nexus for the requisite electron and proton transport to and from OEC. However, the more recently obtained crystal structure shows the YZ-H190 pair to be relatively isolated by ahelices. This potentially supports a rocking model’, where the phenolic proton rocks back and forth between YZ and H190 concomitantly with the cycling of the YZ oxidation state as it relays holes [211, 212]. This case serves as a perfect example of the manner in which orthogonal PCET is used to control charge-transport, as illustrated in Fig. 17.19. The coupled PT occurs to a base (H190) that is off-pathway from electron transport. Its function is to modulate reversibly the oxidation potential of an electron transport intermediate (YZ) that is on-pathway. It is crucial that H190 is positioned close enough to YZ to be effective in this role. As well as establishing the PT coordinate, the hydrogen bonding interaction presumably also relieves the activation energy associated with the PCET reaction. Bidirectional PCET is also featured on the reduction side of the photosynthetic apparatus. In the bacterial photosynthetic reaction center, two sequential photoinduced ET reactions from the P680* excited state to a quinone molecule (QB) are coupled to the uptake of two protons to form the hydroquinone [213–215]. This diffuses into the inter-membrane quinone pool and is re-oxidized at the Q0 binding site of the cytochrome bc1 and coupled to translocation of the protons across the membrane, thereby driving ATP production. These PCET reactions are best described by a Type D mechanism because the PCET of QB appears to involve specifically engineered PT coordinates among amino acid residues [215]. In this case PT ultimately takes place to and from the bulk solvent. Coupling remains tight in
17.5 The Different Types of PCET in Biology
the thermodynamic sense because the reduction potential of the quinone depends on the chemical potential of the coupled proton. In other words, ET is coupled to the local pH via a PT network and this coupling is manifest in the proton-pump that drives ATP production. Bidirectional PCET also manifests itself in reductases. Crystal structures of hydrogenases [216–218] indicate that the mechanism for hydrogen production occurs by transporting protons into the active site along pathways distinct from those traversed by the electron equivalents. Electrons are putatively injected into the active site via a chain of [FeS] clusters, while proton channels and acid–base residues at the active site manage the substrate inventory. Class I E. coli ribonucleotide reductase (RNR) exploits all the PCET variances of Fig. 17.3 in order to catalyze the reduction of nucleoside diphosphates to deoxynucleoside diphosphates. This reaction demands radical transport across two subunits and over a remarkable 35 distance [187, 188, 219]. The crystal structures of both R1 and R2 subunits have been solved independently [220–222] and a docking model has been proposed [220]. R2 harbors the diferric tyrosyl radical (.Y122) cofactor that initiates nucleotide reduction by generating a transient thiyl radical (.C439) in the enzyme active site located >35 away in R1 [223]. Substrate conversion is initiated by a hydrogen atom abstraction (Type A PCET) at the 3¢ position of the substrate by .C439 [192]. Figure 17.24 presents the current model for radical transport in RNR [30]. Beginning at the Y122 cofactor, a bidirectional PCET step (Type D) involving PT between Y122 and the di-iron oxo/hydroxo cofactor [223] is suggested to lead to .Y122 radical generation. Oxidation of Y356, the redox terminus of the R2 pathway, demands a PCET reaction takes place, but this too appears to be bidirectional
H+(out)
+
e– , H
long distance H+
e–
H+
Figure 17.24 Proposed model for radical transport in RNR. The model employs both uni- and bidirectional PCET steps. The mode of transport at the interface (between Y356 and 731) is undefined. Figure adapted from Ref. [30].
553
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17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer
with the PT occurring off pathway as determined from R2 mutants in which the pKa and redox potential of Y356 is systematically altered with non-natural amino acids [224–228]. The proton of the tyrosine at 356 appears to be lost to the bulk (i.e., a Type C reaction). By moving the protons at Y122 and Y356 off pathway, the radical transport in R2 involves a long distance ET coupled to short PT hops at the tyrosine endpoints. In setting up the radical transport pathway in this fashion, the very different PT and ET length scales are managed in RNR. Dipeptide W–Y studies suggest that the direction of ET along the pathway may be controlled by an off-pathway PT step between W48 and D236 [229]. PCET in R1 has been studied in detail using photo-generated .Y sources in place of Y356 [30, 230], hence circumventing the R2 subunit and paving the way for photochemical activity studies (and potentially time-resolved kinetics measurements). Additional studies have been undertaken with various mutants incorporating fluorinated Y residues that perturb the thermodynamic parameters (Ered and pKa) in a controlled fashion [30, 224, 227, 228]. Within R1, the combination of mutant activity studies suggests a unidirectional (Type A) PCET pathway through R1 in which both the electron and proton are transferred between Y731-Y730C439. The close proximity of these three residues lends credence to this proposition.
17.6 Application of Emerging Ultrafast Spectroscopy to PCET
Direct kinetics measurements of PCET and HAT reactions to date have primarily focused on detecting the ET component of the transformation by time-resolved optical measurements. But this is only half the story in a PCET and HAT reaction. Insight into PCET and HAT reaction mechanisms will be expanded considerably by experimental methods that directly probe the structural changes accompanying the PT component of the reaction. Optical changes associated with PT can be designed into Dp or Ap components of the system [123] but generally they are overwhelmed in ultraviolet and visible spectral regions by those associated with ET. A more promising line of inquiry for the purposes of directly detecting PT will likely involve transient spectroscopies that probe the IR spectral region. PT inherently involves motion of nuclei and changes in bonding. As a result, PT is accompanied by distinctive signatures in the IR region. At the very least, a proton shift or complete transfer from X–H to Y will cause the loss of X–H vibrations concomitantly with the gain of H–Y vibrations. Depending on the nature of the proton donor and acceptor groups, distinctive IR shifts may also propagate several bonds away. For example, the amidinium–carboxylate salt bridge was found to be a particularly effective interface for investigating collinear PCET reactions (see Section 17.3.2). Deprotonation of the amidinium on the Dp side of the interface to produce the corresponding amidine is reflected in a red-shift of the C–N stretching frequency by ~30 cm–1 [231]. This counter-intuitive shift is in line with observations for the protonation/deprotonation of other Schiff base complexes, and is
17.6 Application of Emerging Ultrafast Spectroscopy to PCET
explained by the mixing of anti-bonding character of the nitrogen lone-pair of the C–N bond [232]. It is emphasized here that the relevant amidine/amidinium vibration lies outside the fingerprint region of the porphyrins that are frequently employed as electron donors, enabling easy observation with IR ultrafast probe sources. Furthermore, PT can result in shifts of C–O stretching frequencies on the Ap side of the amidinium–carboxylate interface, in addition to changes in N–H and O–H stretches. The IR wavelengths required to probe the evolution of these signatures on an ultrafast timescale have recently become easily accessible using difference frequency generation methods [233]. HAT and PCET reactions of metal oxos also exhibit large changes in frequency owing to a formal change in bond order from two to one. Accordingly, we expect IR probe TA spectroscopy to become a routine tool for future investigations of PCET kinetics. With ET and PT kinetics in hand, a correlation of the rate constants to parameters such as solvent dielectric constant and reaction free energy can help to describe the nature of the transition state and the two-dimensional trajectory of a concerted PCET reaction. The coupling of the charge shift resulting from electron and proton motion to the polarization of the surrounding environment is a distinguishing characteristic of PCET reactions of Type B to D, as well as many of the Type A reactions as discussed in Section 17.3.1. Thus, new experimental tools that probe the solute and solvent modes of the PCET reaction coordinate will be valuable. Of these, multidimensional optical and IR spectroscopies hold the most promise as a powerful tool to study molecular structure and chemical dynamics [234–238]. A 2D IR spectrum is obtained via a sequence of pulses in the time domain, and it characterizes how transient excitation of molecular vibrations at one frequency effect vibrations at a different frequency. Such experiments reveal vibrational couplings as off-diagonal peaks, and correlate the motion of different molecular entities on femtosecond to picosecond time scales, providing a characterization of transient and timeevolving structure. This type of information will undoubtedly be valuable for PCET, where correlated nuclear motion gets to the heart of how a PCET reaction proceeds on the most detailed level. Application of 2D IR spectroscopy to PCET models of Section 17.3.2 is a logical starting point for this type of investigation. 2D methods can unravel the correlated nuclear motion in a PCET reaction and in principle decipher how vibrational coupling in the Dp/Ap interface couples to the ET event between the Ae/De sites. These data can identify the structural dynamics within the interface that promote PCET reactions in much the same way that local hydrogen bonding structure and dynamics mediate excited state PT reactions [239, 240]. In these experiments, the PCET reaction can be triggered by an ultrafast resonant visible laser pulse (as in a standard TA experiment) and a sequence of IR pulses may be employed to build a transient 2D IR spectrum. These experiments demand that systems be chosen so that the ET and PT events occur on an ultrafast timescale. Another novel ultrafast methodology that has rapidly matured and is poised for PCET applications is time-domain nonresonant third-order Raman (TOR) spectroscopy [241–243], which can directly detect the low-frequency response of liquids. Blank and coworkers have successfully applied this technique to probe the
555
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17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer
role of the solvent in excited state intramolecular PT reactions and ultrafast solvation dynamics [244–247]. Prior to this work, inferences regarding the solvent response were made by comparing the observed kinetics to known timescales of solvent response, and by interpreting solvent-induced spectral shifts in the solute (reporter) molecules [248–251]. The more direct experiments of Blank revealed a nonequilibrium solvent response in the excited state PT reaction [245, 246]. The solvent response lagged behind progress along the PT reaction coordinate, leading to the breakdown of linear response and inducing time-dependent evolution of the reaction free energy surface. PCET rate formalisms are cast primarily in terms of solvent coordinates for both the electron and proton, since both are charged particles that couple to the solvent polarization [5, 24]. In a concerted PCET reaction, the coupled transfer must occur via a common transition state and a common solvent configuration on both solvent coordinates. An ultrafast PCET reaction could be photoinitiated with resonant excitation, and a TOR probe would subsequently reveal the evolution of the two-dimensional reaction coordinate via the solvent response. Working in concert, these experiments would offer a powerful means to evaluate the coupling between the two coordinates in different types of PCET reactions and thus enable the PCET trajectories within the 2D space of Fig. 17.2 to be determined with much greater clarity.
Acknowledgment
J.R. thanks the Fannie and John Hertz Foundation for a pre-doctoral fellowship. The work on PCET and the activation of small molecules by PCET has been supported by grants from the NIH (GM47274) and the DOE DE-FG02-05ER15745.
References 1 J. M. Mayer, Annu. Rev. Phys. Chem. 2 3 4 5 6 7 8
2004, 55, 363. J. D. Soper, J. M. Mayer, J. Am. Chem. Soc. 2003, 125, 12217. J. S. Jaworski, Trends Phys. Chem. 2003, 9, 51. J. Robertson, P. Jayasheela, R. K. Lush, Chem. Soc. Rev., 2001, 30, 94. R. I. Cukier, D. G. Nocera, Annu. Rev. Phys. Chem. 1998, 49, 337. R. A. Marcus, N. Sutin, Biochim. Biophys. Acta 1985, 811, 265. R. A. Marcus, J. Chem. Phys. 1956, 24, 966. N. S. Hush, Trans. Faraday Soc. 1961, 57, 557.
9 G. L. Closs, J. R. Miller, Science 1988,
240, 440. 10 Electron Transfer in Chemistry, V. Balzani
11 12
13 14 15
(Ed.), Wiley-VCH, Weinheim, 2001–2002, Vol. 1–5. P. F. Barbara, T. J. Meyer, M. A. Ratner, J. Phys. Chem. 1996, 100, 13148. Electron and Proton Transfer In Chemistry and Biology, A. Muller (Ed.), Elsevier, Amsterdam, 1992. Proton-transfer Reactions, E. Caldin, V. Gold (Eds.), Wiley, New York, 1975. P. M. Kiefer, J. T. Hynes, Solid State Ionics, 2004, 168, 219. K. Ando, J. T. Hynes, Adv. Chem. Phys. 1999, 110, 381.
References 16 R. I. Cukier, J. Phys. Chem. B. 2002, 106,
1746. 17 S. Hammes-Schiffer, ChemPhysChem, 2002, 3, 33. 18 R. I. Cukier, J. Phys. Chem.1996, 100, 15428. 19 R. I. Cukier, J. Phys. Chem. 1994, 98, 2377. 20 X. G. Zhau, R. I. Cukier, J. Phys. Chem. 1995, 99, 945. 21 R. I. Cukier, J. Phys. Chem. A 1999, 103, 5989. 22 R. I. Cukier, Biochim. Biophys. Acta 2004, 1655, 37. 23 S. Hammes-Schiffer, in Electron Transfer in Chemistry; V. Balzani (Ed.), Wiley-VCH: Weinheim, 2001, Vol. 1.1.5, p. 189. 24 S. Hammes-Schiffer, Acc. Chem. Res. 2001, 34, 273. 25 S. Hammes-Schiffer, N. Iordanova, Biochim. Biophys. Acta 2004, 1655, 29. 26 A. Soudackov, S. Hammes-Schiffer, J. Chem. Phys. 1999, 111, 4672. 27 A. Soudackov, S. Hammes-Schiffer, J. Chem. Phys. 2000, 113, 2385. 28 H. Decornez, S. Hammes-Schiffer, J. Phys. Chem. A. 2000, 104, 9370. 29 C. J. Chang, M. C. Y. Chang, N. H. Damrauer, D. G. Nocera, Biochim. Biophys. Acta 2004, 1655, 13. 30 S. Y. Reece, J. M. Hodgkiss, J. Stubbe, D. G. Nocera, Philos. Trans. R. Soc. London, Ser. B 2006, 361, in press. 31 O. Exner, in Correlation Analysis in Chemistry, N. B. Chapman, J. Shorter (Eds.), Plenum, New York, 1978, p. 439. 32 R. H. Lowry, K. S. Richardson, Mechanism and Theory in Organic Chemistry, 3rd Edn. Harper & Row, New York, 1987. 33 F. A. Carroll, Perspectives on Structure and Mechanism in Organic Chemistry, 4th Edn. Brooks/Cole, Pacific Grove, CA, 1998. 34 B. Miller, Advanced Organic Chemistry, Pearson Education, New York, 1997. 35 Techniques of Chemistry Vol. II, Organic Solvents: Physical Properties and Methods of Purification, 3rd Edn., p. 57. 36 K. B. Wiberg, Chem. Rev. 1955, 55, 713. 37 F. H. Westheimer, Chem. Rev. 1961, 61, 265.
38 S. E. Scheppele, Chem. Rev. 1972, 72,
511. 39 E. Buhks, M. Bixon, J. Jortner, J. Phys.
Chem. 1981, 85, 3763. 40 N. Sutin, Acc. Chem. Res. 1982, 15, 275. 41 T. Guarr, E. Buhks, G. McLendon, J. Am.
Chem. Soc. 1983, 105, 3763. 42 R. A. Binstead, T. J. Meyer, J. Am. Chem.
Soc. 1987, 109, 3287. 43 R. A. Binstead, M. E. McGuire,
A. Dovletoglou, W. K. Seok, L. E. Roecker, T. J. Meyer, J. Am. Chem. Soc. 1992, 114, 173. 44 M.-H. V. Huynh, T. J. Meyer, P. S. White, J. Am. Chem. Soc. 1999, 121, 4530. 45 M.-H. V. Huynh, P. S. White, T. J. Meyer, Angew. Chem. Int. Ed. 2000, 39, 4101. 46 M.-H. V. Huynh, T. J. Meyer, Angew. Chem. Int. Ed. 2002, 41, 1395. 47 A. Kohen, J. P. Klinman, Acc. Chem. Res. 1998, 31, 397. 48 Z.-X. Liang, J. P. Klinman, Curr. Opin. Struct. Biol. 2004, 14, 648. 49 J. M. Hodgkiss, N. H. Damrauer, S. Press, J. Rosenthal, D. G. Nocera, J. Phys. Chem. B. 2006, in press. 50 J. M. Mayer, Thermodynamic Influences on C-H Bond Oxidation, in Biomimetic Oxidations Catalyzed by Transition Metal Complexes, Imperial College Press, London, 2000, p. 1. 51 J. P. Roth, J. M. Mayer, Inorg. Chem. 1999, 38, 2760. 52 J. M. Mayer, Acc. Chem. Res. 1998, 31, 441. 53 J. P. Roth, S. Lovell, J. M. Mayer, J. Am. Chem. Soc. 2000, 122, 5486. 54 J. M. Mayer, I. J. Rhile, Biochim. Biophys. Acta. 2004, 1655, 51. 55 J. K. Kochi, Free Radicals, Wiley, New York, 1973. 56 J. M. Tedder, Ang. Chem. Int. Ed. Engl. 1982, 21, 401. 57 K. R. Korzekwa, J. P. Jones, J. R. Gillette, J. Am. Chem. Soc. 1990, 112, 7042. 58 J. H. Knox, Oxidation of Organic Compounds; Vol. 2, F. R. Mayo (Ed.), Adv. Chem. Series, 1968, 76, 11. 59 K. A. Gardner, L. L. Kuehnert, J. M. Mayer, Inorg. Chem. 1997, 36, 2069.
557
558
17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer 60 N. Iordanova, H. Decornez, S. Hammes-
Schiffer, J. Am. Chem. Soc. 2001, 123, 3723. 61 J. U. Rohde, J. H. In, M. H. Lim, W. W. Brennessel, M. R. Bukowski, A. Stubna, E. Mnck, W. Nam, L. Que Jr., Science 2003, 299, 1037. 62 M. H. Lim, J. U. Rohde, A. Stubna, M. R. Bukowski, M. Costas, R. Y. N. Ho, E. Mnck, W. Nam, L. Que Jr., Proc. Natl. Acad. Sci.U.S.A 2003, 100, 3665. 63 A. Decker, J. U. Rhode, L. Que Jr., E. I. Solomon, J. Am. Chem. Soc. 2004, 126, 5378. 64 J. Kaizer, E. J. Klinker, N. Y. Oh, J. U. Rohde, W. J. Song, A. Stubna, J. Kim, E. Mnck, W. Nam, L. Que Jr., J. Am. Chem. Soc. 2004, 126, 472. 65 J. Berkowitz, G. B. Ellison, D. Gutman, J. Phys. Chem. 1994, 98, 2744. 66 R. Y. Luo, Handbook of Bond Dissociation Energies in Organic Compounds, CRC Press: Boca Raton, 2003. 67 O. L. Sydora, J. I. Goldsmith, T. P. Vaid, A. E. Miller, P. T. Wolczanski, H. D. Abrua, Polyhedron, 2004, 23, 2841. 68 B. K. Carpenter, J. Am. Chem. Soc. 1995,117, 6336. 69 B. J. Bahnson, J. P. Klinman, Methods Enzymol. 1995, 249, 373. 70 L. M. Slaughter, P. T. Wolczanski, T. R. Klinckman, T. R. Cundari, J. Am. Chem. Soc., 2000, 122, 7953. 71 J. R. Bryant, J. M. Mayer, J. Am. Chem. Soc. 2003, 125, 10351. 72 J. R. Bryant, T. Matsuo, J. M. Mayer, Inorg. Chem. 2004, 34, 1587. 73 V. Bierbaum, C. DePuy, G. Davico, B. Ellison, Int. J. Mass Spectrom. Ion Phys. 1996, 156, 109. 74 S. Itoh, H. Kumei, M. Taki, S. Nagatomo, T. Kitagawa, S. Fukuzumi, J. Am. Chem. Soc. 2001, 123, 6708. 75 T. Osako, K. Ohkubo, M. Taki, Y. Tachi, S. Fukuzumi, S. Itoh, J. Am. Chem. Soc. 2003, 125, 11027. 76 M. S. Ran, J. T. Hupp, J. Phys. Chem. 1990, 94, 2378. 77 Y. Goto, Y. Watanabe, S. Fukuzumi, J. P. Jones, J. P. Dinnocenzo, J. Am. Chem. Soc. 1998, 120, 10762. 78 S. C. Weatherly, I. V. Yang, H. H. Thorp, J. Am. Chem. Soc. 2001, 123, 1236.
79 C. C. Moser, J. M. Keske, K. Warncke,
80 81 82
83
84 85
86 87 88
89 90 91
92
93 94
95
96
97 98 99
R. S. Farid, P. L. Dutton, Nature, 1992, 355, 796. J. R. Winkler, H. B. Gray, Chem. Rev. 1992, 92, 369. H. B. Gray, J. R. Winkler, Annu. Rev. Biochem. 1996, 65, 537. D. N. Beratan, J. N. Onuchic, J. J. Hopfield, J. Chem. Phys. 1987, 86, 4488. D. N. Beratan, J. N. Onuchic, J. R. Winkler, H. B. Gray, Science, 1992, 258, 1740. J. Lin, I. A. Balabin, D. N. Beratan, Science 2005, 310, 1311. J.-M. Lehn, Supramolecular Chemistry: Concepts and Perspectives, VCH, Weinheim, 1995. F. Vgtle, Supramolecular Chemistry: An Introduction, Marutzen, Tokyo, 1995. D. Philp, J. F. Stoddart, Angew. Chem. Int. Ed. 1996, 35, 1154. J. R. Fredericks, A. D. Hamilton, In Comprehensive Supramolecular Chemistry, Y. Murakami (Ed.), Pergamon, Oxford, 1996, Vol. 3. G. M. Whitesides, J. P. Mathias, C. T. Seto, Science 1991, 254, 1312. M. M. Conn, J. Rebek, Jr., Chem. Rev. 1997, 97, 1647. J. W. Steed, J. L. Atwood, Supramolecular Chemistry, John Wiley & Sons, West Sussex, UK, 2000. G. A. Jeffrey, An Introduction to Hydrogen Bonding, Oxford University Press, New York, 1997. M. C. Etter, Acc. Chem. Res. 1990, 23, 120. C. Turr , C. K. Chang, G. E. Leroi, R. I. Cukier, D. G. Nocera, J. Am. Chem. Soc. 1992, 114, 4013. E. Cukier, S. Daniels, E. Vinson, R. J. Cave, J. Phys. Chem. A 2002, 106, 11240. M. R. Wasielewski, M. P. Niemszyk, W. A. Svec, E. B. Pewitt, J. Am. Chem. Soc. 1985, 107, 1080. J. N. Onuchic, D. N. Beratan, J. Chem. Phys. 1990, 92, 722. D. N. Beratan, J. N. Betts, J. N. Onuchic, Science 1991, 252, 1285. P. J. F. de Rege, S. A. Williams, M. J. Therien, Science, 1995, 269, 1409.
References 100 K. Pettersson, K. Kils , J. M rtensson,
116 B. R. Crane, A. S. Arvai, D. K. Ghosh,
B. Albinsson, J. Am. Chem. Soc. 2004, 126, 6710. 101 A. Harriman, D. J. Magda, J. L. Sessler, J. Chem. Soc.,Chem. Commun. 1991, 245. 102 A. Harriman, D. J. Magda, J. L. Sessler. J. Phys. Chem. 1991, 95, 1530. 103 A. Harriman, Y. Kubo, J. L. Sessler, J. Am. Chem. Soc. 1992, 114, 388. 104 J. L. Sessler, B. Wang, A. Harriman, J. Am. Chem. Soc. 1993, 115, 10418. 105 A. Berman, E. S. Israeli, H. Levanon, B. Wang, J. L. Sessler, J. Am. Chem. Soc. 1995, 117, 8252. 106 M. Asano-Someda, H. Levanon, J. L. Sessler, R. Wang, Mol. Phys. 1998, 95, 935. 107 J. L. Sessler, B. Wang, S. L. Springs, C. T. Brown, in Comprehensive Supramoleuclar Chemistry; Y. Murakami (Ed.), Pergamon, Oxford, 1997, Vol. 4, p. 311. 108 W. L. Jorgenson, J. Pranata, J. Am. Chem. Soc. 1990, 112, 2008. 109 J. Pranata, S. G. Wierschke, W. L. Jorgensen, J. Am. Chem. Soc. 1991, 113, 2810. 110 E. H. Howell, J. E. Villafranca, M. S. Warren, S. J. Oatley, J. Kraut, Science 1986, 231, 1123. 111 C. Ostermeier, A. Harrenga, U. Ermler, H. Michel, Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 10547. 112 S. Iwata, C. Ostermeier, B. Ludwig, H. Michel, Nature 1995, 376, 660. 113 S. Yoshikawa, K. Shinzawa-Itoh, R. Nakashima, R. Yaono, E. Yamashia, N. Inoue, M. Yao, M. J. Fei, C. P. Libeu, T. Mizushima, H. Yamaguchi, T. Tomizaki, T. Tsukihara, Science 1998, 280, 1723. 114 T. Tsukihara, H. Aoyama. E. Yamashia, T. Tomizaki, H. Yamaguchi, K. Shinzawa-Itoh, R. Nakashima, R. Yaono, S. Yoshikawa, Science 1996, 272, 1136. 115 T. Tsukihara, H. Aoyama. E. Yamashia, T. Tomizaki, H. Yamaguchi, K. Shinzawa-Itoh, R. Nakashima, R. Yaono, S. Yoshikawa, Science 1995, 269, 1069.
C. Wu, E. D. Getzoff, D. J. Stuehr, J. A. Tainer, Science, 1998, 279, 2121. 117 T. O. Fischmann, A. Hruza, X. Da Niu, J. D. Fosseta, C. A. Lunn, E. Dolphin, A. J. Prongay, P. Reichert, D. J. Lundell, S. K. Narula, P. C. Weber, Nat. Struct. Biol. 1999, 6, 233. 118 C. S. Raman, H. Li, P. Martasek, V. Kral, B. S. S. Masters, T. L. Poulos, Cell 1998, 95, 939. 119 D. Papoutsakis, J. P. Kirby, J. E. Jackson, D. G. Nocera, Chem. Eur. J. 1999, 5, 1474. 120 J. Otsuki, K. Iwasaki, Y. Nakano, M. Itou, Y. Araki, O. Ito, Chem. Eur. J. 2004, 10, 3461. 121 S. Camiolo, P. A. Gale, M. I. Ogden, B. W. Skelton, A. H. White, J. Chem. Soc., Perkin Trans. 2 2001, 1294. 122 A. Terfort, G. von Kiedrowski, Angew. Chem. Int. Ed. Engl. 1991, 5, 654. 123 J. Rosenthal, J. M. Hodgkiss, E. Young, D. G. Nocera, J. Am. Chem. Soc. 2006, in press. 124 K. Izutsu, Acid–Base Dissociation Constants in Dipolar Aprotic Solvents, Blackwell Scientific, Cambridge, USA, 1990. 125 M.B. Smith, J. March, March’s Advanced Organic Chemistry, 5th Edn., John Wiley and Sons, New York, 2001. 126 J. P. Kirby, J. A. Roberts, D. G. Nocera, J. Am. Chem. Soc. 1997, 119, 9230. 127 J. A. Roberts, J. P. Kirby, D. G. Nocera, J. Am. Chem. Soc. 1995, 117, 8051. 128 J. A. Roberts, J. P. Kirby, S. T. Wall, D. G. Nocera, Inorg. Chim. Acta 1997, 263, 395. 129 R. H. Felton, D. Dolphin, D. C. Borg, J. Fajer, J. Am. Chem. Soc. 1969, 91, 196. 130 J. H. Fuhrhop, P. Wasser, D. Riesner, D. Mauzerall, J. Am. Chem. Soc. 1974, 94, 7996. 131 W. A. Oertling, A. Salehi, Y. C. Chung, G. E. Leroi, C. K. Chang, G. T. Babcock, J. Phys. Chem. 1987, 91, 5887. 132 D. Daulton, R. H. Felton, Acc. Chem. Res. 1974, 7, 26. 133 R. I. Walter, J. Am. Chem. Soc, 1953, 75, 3860. 134 B. Ward, P. M. Callahan, R. Young, G. T. Babcock, C. K. Chang, J. Am. Chem. Soc. 1983, 105, 634.
559
560
17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer 135 J. D. Petke, G. M. Maggiora, J. Am. 136 137
138
139
140
141
142
143
144
145
146
147
148 149 150
151
Chem. Soc. 1984, 106, 3129. B. Ward, C. K. Chang, R. Young, J. Am. Chem. Soc. 1984, 106, 3943. L. K. Hanson, C. K. Chang, B. Ward, P. M. Callahan, G. T. Babcock, J. D. Head, J. Am. Chem. Soc. 1984, 106, 3950. E. C. A. Ojadi, H. Linschitz, M. Gouterman, R. I. Walter, J. S. Lindsey, R. W. Wagner, P. R. Droupadi, W. Wang, J. Phys. Chem. 1993, 97, 13192. J. P. Kirby, N. A. van Dantzig, C. K. Chang, D. G. Nocera, Tetrahedron Lett. 1995, 36, 3477. Y. Deng, J. A. Roberts, S.-M. Peng, C. K. Chang, D. G. Nocera, Angew. Chem. Int. Ed. 1997, 36, 2124. J. Otsuki, M. Takatsuki, M. Kaneko, H. Miwa, T. Takido, M. Seno, K. Okamoto, H. Imahori, M. Fujitsuka, Y. Araki, O. Ito, S. Fukuzumi, J. Phys. Chem. A 2003, 107, 379. C.-Y. Yeh, S. E. Miller, S. D. Carpenter, D. G. Nocera, Inorg. Chem. 2001, 40, 3643. N. H. Damrauer, J. M. Hodgkiss, J. Rosenthal, D. G. Nocera, J. Phys. Chem. B 2004, 108, 6315. A. Osuka, R. Yoneshima, H. Shiratori, S. Okada, S. Taniguchi, N. Mataga, J. Chem. Soc., Chem. Commun. 1998, 1567. J. L. Sessler, M. Sathiosatham, C. T. Brown, T. A. Rhodes, G. Wiederrecht, J. Am. Chem. Soc. 2001, 123, 3655. S. R. Greenfield, W. A. Svec, D. Gosztola, M. R. Wasielewski, J. Am. Chem. Soc. 1996, 118, 6767. N. Liang, A. G. Mauk, G. J. Pielak, J. A. Johnson, M. Smith, B. M. Hoffman, Science 1988, 240, 311. B. Barry, G. T. Babcock, Proc. Natl. Acad. Sci. U.S.A. 1987, 84, 7099. H.-A. Chu, A. P. Nguyen, R. J. Debus, Biochemistry 1995, 34, 5839. A.-M. A. Hays, I. R. Vassiliev, J. H. Golbeck, R. J. Debus, Biochemistry 1999, 38, 11851. R. J. Debus, B. A. Barry, G. T. Babcock, L. McIntosh, Proc. Natl. Acad. Sci. U.S.A. 1988, 85, 427.
152 R. J. Debus, B. A. Barry, I. Sithole,
153 154 155 156 157
158
159
160
161 162 163 164 165
166
167 168
169
170
171
G. T. Babcock, L. McIntosh, Biochemistry 1988, 27, 9071. B. A. Diner, Biochim. Biophys. Acta 2001, 1503, 147. R. J. Debus, Biochim. Biophys. Acta 2001, 1503, 164. C. Tommos, G. T. Babcock, Acc. Chem. Res. 1998 31, 18. C. Tommos, G. T. Babcock, Biochim. Biophys. Acta 2000, 1458, 199. M. Sjdin, S. Styring, B. kermark, L. Sun, L. Hammarstrm, J. Am. Chem. Soc. 2000, 122, 3932. M. Sjdin, R. Ghanem, T. Polivka, J. Pan, S. Styring, L. Sun, V. Sundstrm, L. Hammarstrm, Phys. Chem. Chem. Phys. 2004, 6, 4851. C. Carra, N. Iordanova, S. HammesSchiffer, J. Am. Chem. Soc. 2003, 125, 10429. M. Sjdin, S. Styring, H. Wolpher, Y. Xu, L. Sun, L. Hammarstrm, J. Am. Chem. Soc. 2005, 127, 3855. L. P. Candeias, S. Steenken, J. Am. Chem. Soc. 1989, 111, 1094. E. M. Boon, J. K. Barton, Curr. Opin. Struct. Biol. 2002, 12, 320. B. Giese, Annu. Rev. Biochem. 2002, 71, 51. B. Giese, Acc. Chem. Res. 2000, 33, 631. F. D. Lewis, in Electron Transfer in Chemistry, Balzani, V. (Ed.), Wiley-VCH, Weinheim, 2001, Vol. 3.1.5, p. 105. F. D. Lewis, R. L. Letsinger, M. R. Wasielewski, Acc. Chem. Res. 2001, 34, 159. G. B. Schuster, Acc. Chem. Res. 2000, 33, 253. C. A. M. Siedel, A. Schulz, M. H. M. Sauer, J. Phys. Chem. 1996, 100, 5541. F. D. Lewis, T. Wu, Y. Zhang, R. L. Letsinger, S. R. Greenfield, M. R. Wasielewski, Science 1997, 277, 673. F. D. Lewis, X. Liu, J. Liu, S. E. Miller, R. T. Hayes, M. R. Wasielewski, Nature 2000, 406, 51. V. Y. Shafirovich, S. H. Courtney, N. Ya, N. E. Geacintov, J. Am. Chem. Soc. 1995, 117, 4920.
References 172 N. Amann, E. Pandurski, T. Fiebig,
173 174
175 176 177
178 179
180 181 182 183 184
185 186 187
188 189 190 191
192
H.-A. Wagenknecht, Angew. Chem. Int. Ed. 2002, 41, 2978. R. Huber, T. Fiebig, H.-A. Wagenknecht, Chem. Commun. 2003, 1878. M. Ratchev, E. Mayer, N. Amann, H.-A. Wagenknecht, T. Fiebig, ChemPhysChem 2004, 5, 706. L. Bicz k, H. Linschitz, J. Phys. Chem. 1995, 99, 1843. L. Bicz k, N. Gupta, H. Linschitz, J. Am. Chem. Soc. 1997, 119, 12601. H. Miyasaka, A. Tabata, S. Ojima, N. Ikeda, N. Mataga, J. Phys. Chem. 1993, 97, 8222. N. Mataga, S. Tsuno, Bull. Chem. Soc. Jpn. 1957, 30, 368. L. Sun, M. Burkitt, M. Tamm, M. K. Raymond, M. Abrahamsson, D. LeGourrirec, Y. Frapart, A. Magnuson, P. H. Kenz, P. Brandt, A. Tran, L. Hammarstrm, S. Styring, B. kermark, J. Am. Chem. Soc. 1999, 121, 6834. I. J. Rhile, J. M. Mayer, J. Am. Chem. Soc., 2004, 126, 12718. D. Shukla, R. H. Young, S. Farid, J. Phys. Chem. A 2004, 108, 10386. L. Bicz k, H. Linschitz, J. Phys. Chem. A 2001, 105, 11051. N. Gupta, H. Linschitz, J. Am. Chem. Soc. 1997, 119, 6384. S.-C. Hung, A. N. MacPherson, S. Lin, P. A. Liddel, G. R. Seely, A. Moore, T. Moore, D. Gust, J. Am. Chem. Soc. 1995, 117, 1657. E. J. Land, G. Porter, E. Strachan, Trans. Faraday Soc. 1961, 57, 1885. W. T. Dixon, D. Murphy, J. Chem. Soc., Faraday Trans. II 1976, 72, 1221. J. Stubbe, D. G. Nocera, C. S. Yee, M. C. Y. Chang, Chem. Rev. 2003, 103, 2167. J. Stubbe, W. A. van der Donk, Chem. Rev. 1998, 98, 705. A. Maradufu, G. M. Cree, A. S. Perlin, Can. J. Chem. 1971, 49, 3429. J. W. Whittaker, Arch. Biochem. Biophys. 2005, 433, 227. N. Ito, S. E. V. Phillips, K. D. S. Yadav, P. F. Knowles, J. Mol. Biol. 1994, 238, 794. J. Stubbe, M. Ator, T. Krenitsky, J. Biol. Chem. 1983, 258, 1625.
193 T. L. Poulos, B. C. Finzel, A. J. Howard,
Biochemistry 1986, 25, 5314. 194 M. Vidakovic, S. G. Sligar, H. Li,
T. L. Poulos, Biochemistry 1998, 37, 9211. 195 A. E. Pond, A. P. Ledbetter, M. Sono,
D. B. Goodin, J. H. Dawson, in Electron Transfer in Chemistry, V. Balzani (Ed.), Wiley-VC, Weinheim, 2001, Vol. 3.1.4; p. 56. 196 B. Meunier, S. P. de Visser, S. Shaik, Chem. Rev. 2004, 104, 3947. 197 S. L. Newmyer, P. R. Ortiz de Montellano, J. Biol. Chem. 1995, 270, 19430. 198 M. Tanaka, K. Ishimori, M. Mukai, T. Kitagawa, I. Morishima, Biochemistry 1997, 36, 9889. 199 D. W. Low, J. R. Winkler, H. B. Gray, J. Am. Chem. Soc. 1996, 118, 117. 200 J. Berglund, T. Pascher, J. R. Winkler, H. B. Gray, J. Am. Chem. Soc. 1997, 119, 2464. 201 C.-Y. Yeh, C. J. Chang, D. G. Nocera, J. Am. Chem. Soc. 2001, 123, 1513. 202 C. J. Chang, L. L. Chng, D. G. Nocera, J. Am. Chem. Soc. 2003, 125, 1866. 203 J. L. Dempsey, A. J. Esswein, D. R. Manke, J. Rosenthal, J. D., Soper, D. G. Nocera, Inorg. Chem. 2005, 44, 6879. 204 L. L. Chng, C. J. Chang, D. G. Nocera, Org. Lett. 2003, 5, 2421. 205 S.-Y. Liu, D. G. Nocera, J. Am. Chem. Soc. 2005, 127, 5278. 206 K. N. Ferreira, T. M. Iverson, K. Maghlaoui, J. Barber, S. Iwata, Science 2004, 303, 1831. 207 B. Loll, J. Kern, W. Saenger, A. Zouni, J. Biesiadka, Nature 2005, 438, 1040. 208 C. W. Hoganson, C. Tommos, Biochim. Biophys. Acta 2004, 1655, 116. 209 J. S. Vrettos, G. W. Brudvig, Philos. Trans. R. Soc. London, Ser. B 2002, 357, 1395. 210 J. Barber, K. Ferreira, K. Maghlaoui, S. Iwata, Phys. Chem. Chem. Phys 2004, 6, 4737. 211 M. Haumann, W. Junge, Biochim. Biophys. Acta 1999, 1411, 86. 212 W. Junge, M. Haumann, R. Ahlbrink, A. Mulkidjanian, J. Clausen, Phil. Trans. R.l Soc. Lond. B 2002, 357, 1407.
561
562
17 The Relation between Hydrogen Atom Transfer and Proton-coupled Electron Transfer 213 W. A. Cramer, D. B. Knaff, Energy
Transduction in Biological Membranes, Springer-Verlag, New York, 1990. 214 J. Deisenhofer, J. R. Norris Jr., The Photosynthetic Reaction Center, Vol. I and II. Academic Press, San Diego, CA, 1993. 215 M. Y. Okamura, M. L. Paddock, M. S. Graige, G. Feher, Biochim. Biophys. Acta 2000, 1458, 148. 216 J. W. Peters, W. N. Lanzilotta, B. J. Lemon, L. C. Seefeldt, Science 1998 282, 1853. 217 Y. Nicolet, C. Piras, P. Legrand, C. E. Hatchikian, J. C. FontecillaCamps, Structure 1999, 7, 13. 218 A. Volbeda, J. C. Fontecilla-Camps, Coord. Chem. Rev. 2005, 249, 1609. 219 A. Jordan, P. Reichard, Annu. Rev. Biochem.1998, 67, 71. 220 U. Uhlin, H. Eklund, Nature 1994, 370, 533. 221 P. Nordlund, B.-M. Sjberg, H. Eklund, Nature 1990, 345, 593. 222 M. Hgbom, M. Galander, M. Andersson, M. Kolberg, W. Hofbauer, G. Lassmann, P. Nordlund, F. Lendzian, Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 3209. 223 J. Stubbe, P. Riggs-Gelasco, Trends Biochem. Sci. 1998, 23, 438. 224 C. S. Yee, M. C. Y. Chang, J. Ge, D. G. Nocera, J. Stubbe, J. Am. Chem. Soc. 2003, 125, 10506. 225 C. S. Yee, M. R. Seyedsayamdost, M. C. Y. Chang, D. G. Nocera, J. Stubbe, Biochemistry 2003, 42, 14541. 226 M. C. Y. Chang, C. S. Yee, D. G. Nocera, J. Stubbe, J. Am. Chem. Soc. 2004, 126, 16702. 227 M. R. Seyedsayamdost, S. Y. Reece, D. G. Nocera, J. Stubbe, J. Am. Chem. Soc. 2006, 128, 1569. 228 M. R. Seyedsayamdost, C. S. Yee, S. Y. Reece, D. G. Nocera, J. Stubbe, J. Am. Chem. Soc. 2006, 128, 1562. 229 S. Y. Reece, J. Stubbe, D. G. Nocera, Biochim. Biophys. Acta 2005, 1706, 232. 230 M. C. Y. Chang, C. S. Yee, J. Stubbe, D. G. Nocera, Proc. Nat. Acad. Sci. USA 2004, 101, 6882.
231 Y.-Q. Deng, D. G. Nocera, unpublished
results. 232 J. J. Lopez-Garriga, G. T. Babcock and
J. F. Harrison, J. Am. Chem. Soc. 1986, 108, 7241. 233 P. Hamm, R. A. Kaindl, J. Stenger, Opt. Lett. 2000, 25, 1798. 234 S. Mukamel, Annu. Rev. Phys. Chem. 2000, 51, 691. 235 M. Khalil, N. Demirdven, A. Tokmakoff, J. Phys. Chem. A 2003, 107, 5258. 236 M. T. Zanni, R. M. Hochstrasser, Curr. Opin. Struct. Biol. 2001, 11, 516. 237 J. C. Wright, Int. Rev. Phys. Chem. 2002, 21, 185. 238 S. Woutersen, P. Hamm, J. Phys. Condens. Matter 2002, 14, R1035. 239 R. I. Cukier, J. Zhu J. Chem. Phys. 1999,110, 9587. 240 O. Vendrell, M. Moreno, J. M. Lluch, S. Hammes-Schiffer, J. Phys. Chem. B 2004, 108, 6616. 241 J. D. Simon, Acc. Chem. Res. 1988, 21, 128. 242 M. Cho, M. Du, N. F. Scherer, G. R. Fleming, S. Mukamel, J. Chem. Phys. 1993, 99, 2410. 243 S. Ruhman, B. Kohler, A. G. Joly, K. A. Nelson, Chem. Phys. Lett. 1987, 141, 16. 244 D. F. Underwood, D. A. Blank, J. Phys. Chem. A 2003, 107, 956. 245 S. J. Schmidtke, D. F. Underwood, D. A. Blank, J. Am. Chem. Soc. 2004, 126, 8620. 246 S. J. Schmidtke, D. F. Underwood, D. A. Blank, J. Phys. Chem. A 2005, 109, 7033. 247 D. F. Underwood, D. A. Blank, J. Phys. Chem. A 2005, 109, 3295. 248 P. Barbara, G. Walker, T. Smith, Science, 1992, 256, 975. 249 T. Smith, K. Zaklika, K. Thakur, P. Barbara, J. Am. Chem. Soc. 1991, 113, 4035. 250 R. Jimenez, G. R. Fleming, P. V. Kumar, M. Maroncelli, Nature 1994, 369, 471. 251 M. L. Horng, J. A. Gardecki, A. Papazyan, M. Maroncelli, J. Phys. Chem. 1995, 99, 17311.
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Part V Hydrogen Transfer in Organic and Organometallic Reactions
Part V is devoted to the study of H transfers in organic and organometallic reactions and systems. In Ch. 18 Koch describes kinetic studies of proton abstraction from CH groups by methoxide anion, of the reverse proton transfer from methanol to hydrogen bonded carbanion intermediates, and of proton transfer associated with methoxide promoted dehydrohalogenation reactions. Substitutent effects, kinetic isotope effects and ab initio calculations are treated. Of great importance is the extent of charge delocalization in the carbanions formed which determine the “kinetic” and “thermodynamic” acidities. In Ch. 19 Williams describes theoretical simulations of free-energy-relationships in proton transfer processes. Both linear and non-linear relations are observed, usually described in terms of Brønsted coefficients or Marcus intrinsic barriers. Derived from empirical data, the phenomenological parameters of themselves do not lead to satisfying explanations at a fundamental molecular level. Theoretical simulations can fill in this gap. In 1983 Kubas et al. found that transition metals can contain hydrogen not only in atomic (hydride) but also in molecular (H2) form in side-on coordination. This field is reviewed in Ch. 20 by Kubas. The structure and dynamics of hydrogen containing transition metal complexes is studied mainly by neutron diffraction, neutron scattering, NMR, NMR relaxometry, IR and other spectroscopic. Naturally, quantum-mechanical treatments give rise to very detailed insights. Dihydrogen molecules bound to metals exhibit rotational tunnel splittings of the order of 1011 Hz observed by inelastic neutron scattering. When the rotational barriers are larger values of about 102 Hz are observed as “exchange couplings” by NMR. On top of the coherent rotational tunneling process incoherent exchange is observed as well. Proton donors can form hydrogen bonds to transition metal hydrides, forming complexes of the type M-H···H-A. The authors shows the implication of these unusual features for the elementary steps of homogeneous and heterogeneous catalysis. In Ch. 21 Buntkowsky and Limbach review recent NMR work on the dynamics of dihydrogen and dideuterium in the coordination sphere of transition metals. In addition to inelastic neutron scattering and liquid state NMR, the effects of coherent (exchange couplings) and incoherent rotational tunneling of D2 pairs in transiHydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
564
tion metal hydrogen complexes are described, providing information about the corresponding dynamic H/D isotope effects. It is shown that the size of the rotational tunnel splittings as compared to those of magnetic nuclear interaction is the main control parameter which governs the transition metal catalyzed magnetic ortho-para hydrogen spin conversion. Applications in chemistry and medicine are discussed.
565
18 Formation of Hydrogen-bonded Carbanions as Intermediates in Hydron Transfer between Carbon and Oxygen Heinz F. Koch
This chapter is divided into three sections: Proton transfer from carbon acids to methoxide ion; proton ttransfer from methanol to carbanion intermediates; proton transfer associated with methoxide promoted dehydrohalogenation reactions.
18.1 Proton Transfer from Carbon Acids to Methoxide Ion
Knowledge of equilibrium pKa values of carbon acids is important for an understanding of organic chemistry; however, they are not always reliable indicators of relative rates for proton transfer reactions. Ritchie [1] predicted in 1969 that carbon acids whose conjugate bases have localized charge will show “kinetic acidities” greater than their thermodynamic acidities. This is illustrated by the weaker acid pentafluorobenzene-t [PFB-t], pKa = 25.8 [2], with a methanolic sodium methoxide catalyzed protodetritiation rate, k = 2.57 · 10–2 M– 1 s–1 [3], that is 15 times faster at 25 C than that for 9-phenylfluorene-9-t [9-PhFl-9-t], pKa = 18.5 and k = 1.54 · 10–3 M–1 s–1 [4]. Primary kinetic isotope effects [PKIE] can be used to determine C–H bond breaking in the rate limiting steps of any reaction mechanism. Normal hydrogen isotope effects are largely due to zero-point energy differences of the stretching frequencies of C–H vs. C–D bonds. If only stretching frequencies are considered the value for kH/kD would be 6.2 for the C–iH bond. With allowance for bending vibrations this could result in a kH/kD = 10, kH/kT = 27 and kD/kT = 2.7 at 25 C [5]. Melander [6] and Westheimer [7] suggested that lower values of kH/kD could be due to residual zero-point energy in an asymmetric transition structure. For this reason the magnitude of kH/kD was often used to assign early or late transition structures for hydron-transfer reactions. Smaller values due to asymmetric transition structures should still obey the Swain–Schaad relationship [8], kH/kT = (kH/kD)1.442. The kD/kT = 1.0 associated with the exchange reactions of PFBiH suggest that the C–H bond is not broken in the rate limiting step and this differs significantly from the kD/kT of 2.54 measured from the reactions of 9-PhFl-9-iH.
Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
18 Formation of Hydrogen-bonded Carbanions as Intermediates in Hydron Transfer
In a 1975 Account, Kresge addressed “fast” vs. “slow” proton transfer [9]: “It is common experience that proton transfer between electronegative atoms such as oxygen and nitrogen is very fast whereas that involving carbon is usually quite slow. This would seem to be related to the fact that the electron pair which receives the proton onto an oxygen or nitrogen base is generally localized on a single atom, as in ammonia or amines. The corresponding pair of a carbon base, on the other hand, except in unusual circumstances, is strongly delocalized away from the atom to which the proton becomes attached; this is so, for example, in nitronate and enolate ions, the reprotonation of which are classic examples of slow proton transfer.” The study of proton transfer from C–H bonds to a base [“kinetic acidity”] in aqueous media was largely carried out on compounds that generated nitronate or enolate anions and owed their stability to p-delocalization of the negative charge. Since the sp orbital of phenylacetylide ion is orthogonal to the p-bonds, Kresge chose the aqueous base catalyzed hydron exchange of phenylacetylene to study hydron-transfer reactions of localized carbanions [10]. The near unity PKIE associated with these exchange reactions is similar to the results obtained for PFB, where the C6F5– anion [PFB–] is localized in an sp2 orbital that is orthogonal to the p-electrons of the benzene ring. On the other hand, the 9-phenylfluorenyl anion [9-PhFl –] is a highly p-delocalized aromatic anion. If a C–H bond is not broken in a rate-limiting step, it is not possible to know the rate of proton transfer. Cram first suggested that near unity isotope effects for hydron exchange reactions are due to an internal-return mechanism with hydron transfer occurring prior to the rate-limiting step in the reaction mechanism [11]. The seven-step process given below would be for an internal-return mechanism applied to deuterium exchange of a carbon acid using methanolic methoxide as the base. The process starts as one of the three methanols associated with the lone pair electrons of a methoxide ion joins the bulk solvent and is replaced by the carbon acid forming the encounter complex, EC-d.
HOMe
D
CH3
HOMe
_ D.... O .... ....
.... ....
C
_ MeOH.... O
C
HOMe
EC-d
CH3
(18.1)
HOMe
The system is now ready to have the deuterium transfer from the carbon to methoxide ion, kD 1 , and generate a hydrogen-bonded carbanion, HB-d. The internal return step, kD 1 , can compete with any forward reaction and would regenerate the encounter complex EC-d.
C
EC-d
CH3
HOMe
k1D kD_ 1
_ C....D
HOMe
.... ....
HOMe
_ D.... O .... ....
566
HB-d
O
CH3
HOMe
(18.2)
18.1 Proton Transfer from Carbon Acids to Methoxide Ion
The next forward step occurs when the hydrogen bond breaks, kD 2 , to form a free carbanion, FC-d, that is not stabilized by any direct contact with the DOCH3 that is still in the best position to interact with the lone pair of the carbanion, kD 2 .
O
HB-d
D
CH3
HOMe
k2
kD_ 2
C
_
HOMe
D
.... ....
HOMe
.... ....
_ C....D
O
CH3
(18.3)
HOMe
FC-d
The exchange, kexc, occurs when a CH3OH replaces the CH3OD in the most favorable position.
D
O
CH3
k exc
HOMe
FC-d
C
_
FC-h
DOMe
H
.... ....
HOMe
.... ....
C
_
O
CH3
(18.4)
HOMe
To complete the reaction there are three steps using CH3OH in place of CH3OD in steps 3, 2 and 1. When kexc is greater than kH 2 , the rate law for this mechanism is: kobs ¼
k1 k2 k1 þ k2
(18.5)
There are two extremes for this rate law: (i) when k–1 >> k2, then kobs = [ k1 / k–1 ] k2, and (ii) when k2 >> k–1, then kobs = k1. For case (i) second order kinetics and near unity experimental PKIE values are expected. On the other hand for case (ii) second order kinetics are measured with normal experimental values of the PKIE that obey the Swain–Schaad relationship. A major contribution to the analysis of isotope effects associated with cases where there is no single rate-limiting step was made by the Streitwieser group in 1971 [4, 12]. Using single temperature rate constants for all three hydrogen isotopes and the Swain–Schaad relationship, they calculate an internal-return parameter, a = k–1/k2, associated with the experimental rate constants for each of the isotopic exchange measurements. 1) The rate constant for the actual hydron transfer step can now be calculated: k1 = kobs (a + 1) 1) The original Swain–Schaad relationship8
(kH/kT) = (kH/kD)1.442 becomes (kH/kT) = (kD/kT)3.26. For hydron exchange reactions the later relationship is more useful. The
(18.6) Streitwieser treatment uses 3.344 instead of 3.26 as the exponent [12]. We use the 3.344 value for our calculations.
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18 Formation of Hydrogen-bonded Carbanions as Intermediates in Hydron Transfer
This analysis can be applied to the methoxide-catalyzed rates of the exchange reactions for 9-PhFl-9-iH that result in kD/kT = 2.53 and kH/kT = 15.9. 2) To satisfy Swain–Schaad, the value of kH/kT should be 20.6 or 22.3 depending on the value of the exponent used.1) The deviations from the Swain–Schaad relationship predict that a small amount of internal return is associated with the hydron exchange reactions of 9-PhFl-9-iH. The internal return is negligible for 9-PhFl-9-t (aT = 0.016) and 9-PhFl-9-d (aD = 0.050), but cannot be ignored for 9-PhFl (aH = 0.49). 3) Experimental isotope effects that are near unity in magnitude do not allow the calculation of any a values; however, the return step must be at least 50 times faster than the forward step. Therefore, after making a correction for internal return, the hydron exchange reaction from the weaker acid, PFB-t is at least 750 times faster than that from the stronger acid, 9-PhFl-9-t. Since fluorine-containing organic compounds are more acidic than the hydrocarbon analogs, we started to study benzylic compounds that have trifluoromethyl groups and chlorine atoms to increase their acidity. Two compounds with rates of protodetritiation similar to that for 9-PhFl-9-t were of interest: C6H5CH(CF3)2 1 and p-CF3C6H4CHClCF3 [p-CF3-2]. Measurement of the pKa values for 1 and p-CF3-2 are not possible in solution due to elimination of a b-fluoride. However, Mishima has been able to obtained their gas phase acidities, DG0acid = 335.3 kcal mol–1 for 1 and DG0acid = 337.4 kcal mol–1 for p-CF3-2, and these are close to that for 9-PhFl, DG0acid = 335.6 kcal mol–1 [13]. Although the protodetritiation and gas phase acidities are similar for these three compounds, the near unity experimental kD/kT values obtained from the reactions of 1 and p-CF3-2 differ significantly from that for 9-PhFl and are similar to the value for PFB. This suggests a significant amount of internal return associated with the hydron transfer reactions of 1 and p-CF3-2. The effects of substituents on the phenyl ring of 9-PhFl are also very different from those on the phenyl ring of 1, Table 18.1. The negative charge for the 9-PhFl– anion would not be p-delocalized into the phenyl ring, and a Hammett plot using the four 9-YPhFl compounds results in a rho of 2.1, which is similar to that obtained for the hydrolysis of methyl benzoates. A plot with the six Y-I compounds results in a rho value of 4.9, which is similar that obtained for the protodetritiation reactions of ring-substituted toluene-a-t’s with lithium cyclohexylamide in cyclohexylamine [14]. Although the gas phase acidity of C6H5CHClCF3 2, DG0acid = 348.7 kcal mol–1, is about the same as that for PFB, DG0acid = 349.2 kcal mol–1, the reaction of 2 is too slow in methanolic sodium methoxide and was carried out in ethanolic sodium ethoxide. Reactions in methanolic sodium methoxide are about 20 times slower than those in ethanol [see m-ClC6H4CTClCF3 and m-CF3C6H4CTClCF3 in Table 18.1]. When the ethoxide rate for the protodetritiation of 2-t is corrected for the change in base systems the reaction is 66,000 times slower at 25 C than that for 2) Reference [4] has values of kD / kT of
2.54–0.11 to 2.46–0.20 and kH / kT of 16.1–0.6 to 15.9–0.6. Our values are from our Arrhenius plots for all three isotopes of 9-PhFl-9-iH, see Table 18.1.
3) The equation for aT is given in Ref. 12
p. 5099. We thank Professor Andrew Streiwieser for supplying the equations to calculate aH and aD.
18.1 Proton Transfer from Carbon Acids to Methoxide Ion
569
Table 18.1. Rate constants and activation parameters for methanolic sodium
methoxide promoted hydron exchange reactions. Compound
DG0Acid
k, M–1s–1 (25 C)
DH‡, kcal / Tmol
DS‡,eu (25 C)
m-CF3C6H4CD(CF3)2
326.8
4.12 E-1
20.79 – 0.18
9.4 – 0.7
m-CF3C6H4CT(CF3)2
4.74 E-1
21.60 – 0.10
12.4 – 0.4
–19 to
m-CF3C6H4CT(CF3)2 [MeOD]
1.33
20.63 – 0.02
11.2 – 0.1
–29 to –10 [3]
m-CF3C6H4CH(CF3)2 [MeOD]
1.32
20.34 – 0.12
10.2 – 0.5
–25 to –5 [4]
Temp. range,C [no. of points] –20 to –5 [4] 0 [4]
m-FC6H4CD(CF3)2
331.5
8.50 E-2
21.55 – 0.08
8.8 – 0.3
–10 to 15 [4]
p-ClC6H4CD(CF3)2
331.4
3.45 E-2
23.10 – 0.16
12.2 – 0.6
0 to 20 [5]
C6H5CD(CF3)2
335.3
2.13 E-3[a]
24.42 – 0.12
11.2 + 0.4
0 to 50 [7]
C6H5CT(CF3)2
2.09 E-3
24.26 – 0.07
10.6 – 0.2
5 to 50 [7]
C6H5CT(CF3)2 [MeOD]
5.49 E-3
23.85 – 0.07
11.1 – 0.2
5 to 50 [9]
C6H5CH(CF3)2 [MeOD]
6.14 E-3
23.86 – 0.13
11.4 – 0.4
10 to 50 [5]
m-CH3C6H4CD(CF3)2
336.3
1.04 E-3
24.97 – 0.15
11.5 – 0.5
20 to 40 [5]
p-CH3C6H4CD(CF3)2
337.0
4.70 E-4
25.53 – 0.20
11.9 – 0.7
25 to 45 [5]
p-NO2C6H4CDClCF3
329.8
4.40
16.62 – 0.05
0.1 – 0.2
–50 to –30 [4]
4.04 E+1
16.23 – 0.19
3.2 – 0.8
–55 to –40 [3]
p-NO2C6H4CHClCF3 [MeOD] 3,5-(CF3)2C6H3CDClCF
332.4
7.51 E-2
22.48 – 0.07
11.7 – 0.3
–5 to 25 [6]
3,5-F2C6H3CDClCF3
340.5
1.82 E-3
25.36 – 0.10
14.0 – 0.4
10 to 30 [3]
p-CF3C6H4CDClCF3
337.4
8.58 E-4
25.90 – 0.08
14.3 – 0.3
20 to 45 [6]
p-CF3C6H4CTClCF3
7.91
E-4[c]
25.42 – 0.08
12.5 – 0.3
20 to 55 [8]
p-CF3C6H4CTClCF3 [MeOD]
2.06 E-3[c]
24.86 – 0.13
12.5 – 0.4
20 to 45 [6]
1.09 E-4
26.36 – 0.11
11.7 – 0.3
30 to 55 [7]
m-CF3C6H4CTClCF3
1.03 E-4
26.67 – 0.12
12.7 – 0.4
30 to 60 [5]
m-CF3C6H4CTClCF3 [MeOD]
2.77 E-4
25.81 – 0.33
11.8 – 1.1
30 to 50 [3]
[EtOH]
2.20 E-3
25.25 – 0.16
14.0 – 0.5
10 to 40 [7]
m-CF3C6H4CHClCF3 [MeOD]
3.03 E-4
25.51 – 0.14
10.9 – 0.5
30 to 50 [3]
4.16 E-5
26.96 – 0.08
11.8 – 0.3
35 to 59 [5]
7.74 E-4
25.31 – 0.16
12.1 – 0.5
25 to 50 [5]
2.36 E-5
27.85 – 0.06
13.7 – 0.2
40 to 65 [5]
m-CF3C6H4CDClCF3
m-ClC6H4CTClCF3
340.1
343.2
[EtOH] m-FC6H4CDClCF3
344.6
570
18 Formation of Hydrogen-bonded Carbanions as Intermediates in Hydron Transfer
Table 18.1 Continued.
Compound
DG0Acid
k, M–1s–1 (25 C)
DH‡, kcal / Tmol
C6H5CTClCF3 [EtOH]
348.7
9.03 E-6
26.54 – 0.01
2.08 E-5
26.41 – 0.14
8.6 – 0.4
40 to 80 [5]
[EtOD]
DS‡,eu (25 C) 7.4 – 0.1
Temp. range,C [no. of points] 50 to 80 [3]
9-(p-CF3C6H4)-fluorene-9-t
326.9
2.03 E-2
15.78 – 0.11
–13.4 – 0.4
–10 to 25 [4]
9-(m-CF3C6H4)-fluorene-9-t
327.4
1.58 E-2
17.07 – 0.06
–9.5 – 0.2
0 to 20 [3]
3.38 E-2
16.29 – 0.14
–10.6 – 0.5
–10 to 10 [3]
[MeOD] 9-m-FC6H4)-fluorene-9-t
331.3
8.24 E-3
17.84 – 0.05
–8.2 – 0.2
0 to 25 [4]
9-Phenylfluorene-9-d
335.6[b]
3.89 E-3
17.22 – 0.04
–11.8 – 0.1
5 to 35 [3]
9-Phenylfluorene-9-t
1.54 E-3
18.42 – 0.13
–9.6 – 0.4
25 to 45 [5]
9-Phenylfluorene-9-t [MeOD]
3.25 E- 3
18.13 – 0.07
–9.1 – 0.2
25 to 40 [3]
9-Phenylfluorene-9-h [MeOD]
5.16 E-2
15.18 – 0.07
–13.5 – 0.3
–25 to 5 [6]
CDCl2CF3
348.2
1.93 E-2[d]
21
5
0 to 20 [2]
C6F5D
349.2
3.07 E-2
19.52 – 0.19
0.0 – 0.7
0 to 21 [5]
C6F5T
2.96 E-2[e]
19.76 – 0.07
0.7 – 0.2
–15 to 15 [6]
C6F5T [MeOD]
5.93 E-2
19.45 – 0.05
1.1 – 0.2
–20 to 15 [4]
C6F5H [MeOD]
6.53 E-2
19.25 – 0.07
0.6 – 0.3
–15 to 10 [4]
a Reference [25] b Lias, S. G.; Bartmess, J. E.; Leibman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, G. W. J Phys. Chem., Ref. Data 1 1988, 17, Suppl. 1. c Ref. [37] d Ref. [20a] e Data in Ref. [3] gave the following: C6F5T, k = 2.57 E-2 (25 C), DH‡ = 19.92 – 0.05 kcal/mol–1,DS‡ = 1.0 – 0.2 eu.
PFB-t. The much stronger acid 3,5-(CF3)2C6H3CDClCF3, DG0acid = 332.4 kcal mol–1, has a rate of deuterium exchange that is only 2.5 times faster than that for PFB-d. Do all the reactions with near unity isotope effects have the same balance of steps in an internal return mechanism, and should these compounds be compared with each other? The activation entropies, DS‡, should be in the same range when reactions have a similar balance of steps that contribute to the value of kobs in the internal-return mechanism. The exchange reactions of 9-phenylfluorenes have experimental PKIE values that are normal in magnitude, but do not obey the Swain–Schaad relationship,
18.1 Proton Transfer from Carbon Acids to Methoxide Ion
suggesting that there is a small amount of internal return associated with these reactions. Reactions of methanolic sodium methoxide and the four 9-YPhFl-9-t in Table 18.1 result in experimental DS‡ with values between – 8 and –13 eu. Such values are consistent with the second order kinetics of a bimolecular reaction and suggest that an encounter complex, EC, could be the dominating step along the reaction path. The reactions of methanolic sodium methoxide with 15 YC6H4CH=CF2 have experimental DS‡ values that range from –12 to –20 eu [15]. The rate-limiting step for the reaction of CH3O– with CF2=CHC6H5 generates a carbanion intermediate, {CH3OCF2CHC6H5}–, and would result in bimolecular kinetics. This reaction will be discussed in Section 18.2. Reactions that have large amounts of internal return are ones with near unity experimental isotope effects, and these normally have activation entropies of around +10 eu. This is true for the hydron exchange reactions of the six YC6H4CiH(CF3)2 and four YC6H4CiHClCF3 listed in Table 18.1 that resulted in experimental DS‡ values from +12 to +14 eu. An exception to this is p-NO2C6H4CiHClCF3 where the DS‡ values are between 0 and +2 eu; however, this compound also differs from the others with kH/kD » 3 after correcting for a solvent isotope effect kOD/kOH of 2.6. This can be due to the more p-delocalized carbanion having much less internal return than the other ring substituted hydrogenbonded carbanion intermediates. Another exception to the higher activation entropy is PFB with DS‡ values of about +1 eu and a near unity PKIE. To get a better understanding of these reactions density functional calculations using B3LYP/6-31+G(d,p) were carried out on the energetics of some of the intermediates associated with the reactions of 9-PhFl, 1, 2 and PFB. Zuilhof first performed calculations to evaluate the stability of any possible intermediates for the reaction of C6H5CH(CF3)2 1, and CH3O– to {C6H5C(CF3)2}– and CH3OH. An encounter complex, EC, that is not in an energy minimum is 30.1 kcal mol–1 more stable than the two reactants, and proceeds by a barrierless process to form the hydrogen-bonded intermediate that is 13.1 kcal mol–1 more stable [16]. More recent calculations for C6H5CHClCF3 have an encounter complex at a definite energy minimum that is 19.1 kcal mol–1 more stable than reactants and a hydrogen-bonded carbanion that is 6.5 kcal mol–1 more stable than the encounter complex. It is not surprising that the process is highly exothermic since calculations are for gas phase species and the DG0acid of 375.5 kcal mol–1 for methanol [17] makes it a weaker acid than toluene. Since these calculations did not agree with the experimental observations, our current calculations start with three methanols solvating the methoxide ion, and follow the steps outlined in Eqs. (18.1)–(18.3). Calculations for the reaction of 1 and CH3O–(HOCH3)3 to {C6H5CH(CF3)2··· OCH3(HOCH3)2}– and CH3OH now requires + 4.7 kcal mol–1, see Fig. 18.1. The energy used in the calculation for the released CH3OH is one third of the energy of HOCH3(HOCH3)2. Proton transfer to form {C6H5C(CF3)2···HOCH3(HOCH3)2}–, requires another + 4.1 kcal mol–1 and then +1.1 kcal mol–1 is needed to generate {C6H5C(CF3)2}– and HOCH3(HOCH3)2. We have not yet calculated transition structures associated with these reactions; however, the energetics are
571
18 Formation of Hydrogen-bonded Carbanions as Intermediates in Hydron Transfer
reasonable for a mechanism that has the proton transfer with significant internal return dominating the rate of reaction. A big difference occurs when comparing the calculations for 1and 9-PhFl. The 9-PhFl requires +11.1 kcal mol–1 to form the corresponding encounter complex, and the formation of the hydrogen-bonded carbanion is then favorable by –3.7 kcal mol–1. The formation of the 9-PhFl– and HOCH3(HOCH3)2 requires +1.2 kcal mol–1. Therefore, the calculations for 9-PhFl can support the measurement of negative activation entropies that are attributed to a bimolecular reaction that forms an encounter complex as the major factor in the overall rate process [18]. When calculations are carried out to compare the reactions of 2with those of PFB, the formation of the two encounter complexes are similar to those calculated for 1, with values of +5.5 kcal mol–1 (2) and +5.1 kcal mol–1 (PFB). Differences between the reactions of 2 and PFB occur for proton transfer to generate the corresponding hydrogen-bonded carbanions with +7.8 kcal mol–1 for 2 compared to only +1.3 kcal mol–1 for the reactions of PFB. This difference is offset in the last Ph
HOMe .. . H O. CH3 .. HOMe
-
+ 1.2 kcal
F
Ph
F CF3
F
+ 1.1 kcal CH3
CH3 O (MeOH)2MeOH
-
Ph
H F
O H
Ph
CH3 H
O
F CF3
F
- 3.7 kcal
+ 4.1 kcal CH3 O
(MeOH)2MeO H
CH3
CH3 H
O
H
H
Ph
F
CH3OH
F
Ph
CF3 F
+ 11.1 kcal H
Ph
+ 4.7 kcal
HOMe . _ .. MeOH O. CH3 .. HOMe
H F
F
.. .
572
Ph
9-PhFl Figure 18.1 Energies from B3LYP/6-31 + G(d,p) calculations.
CF3 F
I
O
18.2 Proton Transfer from Methanol to Carbanion Intermediates
step to form {C6H5CClCF3}– and (HOCH3)3, +7.3 kcal mol–1, compared to the formation of PFB– and (HOCH3)3, +15.3 kcal mol–1. Since the exchange reactions of PFB are 66000 times faster than those for 2, it is apparently not necessary to form PFB–. The exchange must be able to occur from the hydrogen-bonded intermediate, and this is the same conclusion as from the DS‡ of +1 eu for the reactions of PFB compared to values of > +10 eu for the reactions of methanolic sodium methoxide with the Y-2 compounds. Calculations are still needed to assess the actual mechanism of the exchange process for PFB as well as to obtain the energetics for barriers associated with the exchange processes.
18.2 Proton Transfer from Methanol to Carbanion Intermediates
In 1948 Miller reported the reactivity of 1,1-difluoroalkenes toward nucleophiles by the rapid methoxide ion catalyzed addition of methanol to CF2=CCl2 to give a saturated ether, CH3OCF2CHCl2 [19]. Hine’s group carried out kinetic studies of the methoxide-promoted dehydrofluorination of CHCl2CF3 [55 C and 70 C] with CH3OCF2CHCl2 and CH3OCF=CCl2 as the isolated products [20]. The formation of the saturated ether is expected since the reaction of methanolic sodium methoxide and CF2=CCl2 has a half life of 40 min at 0 C. Since the elimination of CH3OCF2CHCl2 is twice as fast as that of CHCl2CF3, the formation of CH3OCF=CCl2 is a secondary reaction product. The rate of methoxide-catalyzed exchange of CH3OCF2CDCl2 is over 7000 times faster than the extrapolated rate of dehydrofluorination for CH3OCF2CHCl2 at 20 C, and it is not surprising that the carbanion, {CH3OCF2CCl2}–, generated from the reaction of methoxide and CF2=CCl2 adds a proton to form the saturated ether rather than eliminating a fluoride ion to generate a vinyl ether. The two types of reactions are an excellent method to generate the same carbanion intermediate by different approaches. Our first use of this method was the detailed study of the reactions of C6H5C(CF3)=CF2 with ethanolic sodium ethoxide. Much to our surprise, the carbanion intermediate, {C6H5C(CF3)CF2OC2H5}–, generated during the reaction at –78 C favors elimination of fluoride ion to give 85% of two vinyl ethers, C6H5C(CF3)=CFOC2H5, and only 15% of the saturated ether, C6H5CH(CF3)CF2OC2H5 [21]. When the reaction is carried out in C2H5OD the amount of saturated ether remains almost constant at 13% and suggests hydron transfer to the carbanion occurs with a near unity isotope effect. Elimination and exchange kinetics required higher temperatures. The ethoxide-promoted dehydrofluorination of C6H5CH(CF3)CF2OCH3 also occurs with a near unity value for kH/kD at 25 C. Reaction of C6H5CH(CF3)CF2OCH3 in C2H5OD results in 3–4% deuterium incorporation at 20% elimination that matches the partitioning of carbanions generated from the reaction of C6H5C(CF3)=CF2 in C2H5OD at 25 C. Since there is no loss of the methoxide group, the nucleophilic addition of alkoxide, kN, is not reversible. This suggests a mechanism similar to that for reactions occurring with internal return, Scheme 18.1 [22].
573
574
18 Formation of Hydrogen-bonded Carbanions as Intermediates in Hydron Transfer
CF 3 C6 H5 C C2H5 OCF2 k -1
CF3
CF 3
H. -. OC2 H5
C6 H5
k1
.. C6 H5 C HOC2 H5 C2 H5 OCF2
-
C CF F2
OC C2 H5
kN
-
k2 k -2
CF 3 C6 H5 C C2H5OC C F2
-
HOC 2 H5
k Elim CF3 C 6 H5
C
CFOC 2 H5 +
-
F-
Scheme 18.1
The encounter complex of the saturated ether can transfer the proton, k1, to form a hydrogen-bonded carbanion intermediate. Internal return, k–1, regenerates the encounter complex and can wash out the experimental PKIE. The free carbanion is generated by breaking the hydrogen bond, k2. The ejection of fluoride ion to form the vinyl ether requires formation of the free carbanion. The reaction of ethoxide with C6H5C(CF3)=CF2 directly forms the free carbanion, {C6H5C(CF3)CF2OC2H5}–, and it partitions between ejecting fluoride ion, kElim, and forming the hydrogen-bonded carbanion, k–2. Since k–1 >> k2, the rate-limiting step for making the saturated ether would be the formation of the hydrogen-bonded carbanion, k–2, and this does not involve a hydron transfer. Eaborn and coworkers reported PKIE values for the protonation of various benzylic anions by methanol [23]. Anions are generated in situ by the reaction of methanolic sodium methoxide with YC6H4CH2Si(CH3)3. CH3O- + (CH3)3SiCH2C6H4Y fi CH3OSi(CH3)3 + –CH2C6H4Y CH3OiH + –CH2C6H4Y fi CH3O– + iHCH2C6H4Y
(18.7)
Isotope effects were calculated from the known initial ratio of CH3OH:CH3OD and the measured H:D ratio in iHCH2C6H4Y. This resulted in kH/kD » 1.2 at 25 C for the protonation of a variety of –CH2C6H4Y. The value of kH/kD became 10 for pNO2C6H4CH2– and both fluorenyl and 9-methylfluorenyl anions. This suggested a study using benzylic anions generated by reactions of methanolic sodium methoxide with a series of YC6H4CH=CF2 compounds [15].
18.2 Proton Transfer from Methanol to Carbanion Intermediates
CH3O– + CF2=CHC6H4Y fi {CH3OCF2CHC6H4Y}– CH3OiH + {CH3OCF2CHC6H4Y}– fi CH3OCF2CHiHC6H4Y
(18.8)
Generating carbanions in situ by reaction of methoxide with either alkyltrimethylsilanes or b,b-difluorostyrenes has several advantages. Reactions occur at lower temperatures and the problem of internal return is eliminated. The methanol solvent molecules are excellent trapping reagents for carbanions and only an intramolecular trap appears to be more efficient. The carbanions generated from the b,b-difluorostyrenes have the added advantage of an intra-molecular trapping agent due to the elimination of a b-fluoride ion. CH3OiH +{CH3OCF2CHC6H4Y}– fi CH3OCF2CHiHC6H4Y + CH3OCF=CHC6H4Y
(18.9)
The product ratios and isotope effects associated with the reactions of p-NO2C6H4CH=CF2 can be compared to those of m-NO2C6H4CH=CF2, which has results similar to other YC6H4CH=CF2 compounds [24]. Isotope effects for hydron transfer to neutralize {m-NO2C6H4CHCF2OCH3}– increase slightly from kH/kD = 1.20 at –50 C to kH/kD = 1.39 at +50 C, and this trend is the same for the reactions of other YC6H4CH=CF2. The isotope effects differ significantly for the neutralization of {p-NO2C6H4CHCF2OCH3}– with larger values that decrease with increasing temperature in a normal fashion: kH/kD = 11.3 at –70 C and 6.44 at +25 C. Partitioning of the carbanions between hydron transfer and fluoride ion loss is also different. The {p-NO2C6H4CHCF2OCH3}– gives 94% p-NO2C6H4CH2CF2OCH3, and equal amounts of E- and Z-p-NO2C6H4CH=CFOCH3 at –70 C. Formation of the saturated ether decreases to 50% with equal amounts of the E- and Z-vinyl ethers at 25 C. This differs from the reactions of {m-NO2C6H4CHCF2OCH3}– where the amount of saturated ether increases slightly from 53% at –50 C to 59% at +50 C and the E:Z ratios decrease from 6:1 at –50 C to 3:1 at +50 C. The reactions of methanolic methoxide with CF2=CCl2 can be compared to those of CF2=CClC6H5 where a benzene ring replaces a chlorine atom. Although the rates of reaction are similar at 0 C, product distributions are different as CF2=CCl2 forms only CH3OCF2CHCl2, and the reactions of CF2=CClC6H5 result in 49% of the saturated ether, CH3OCF2CHClC6H5, and 51% of the vinyl ethers, E- and Z-CH3OCF=CClC6H5. There is a similarity between the rates of dehydrofluorinations for CHCl2CF3, k = 1.9 · 10–5 M– 1 s–1 at 70 C in methanol [20b], and those of C6H5CHClCF3 2, k = 3.7 · 10–4 M–1 s–1 at 75 C in ethanol (a correction is necessary to account for rate enhancement by ethoxide over methoxide). In both dehydrofluorinations the rates of exchange are faster than the elimination; however, the big difference is the ease of the exchange for CDCl2CF3, k = 1.93 · 10–2 M– 1 s–1 at 25 C in methanol, and that for C6H5CDClCF3, k = 6.73 · 10–3 M– 1 s–1 at 75 C in ethanol [25]. The replacement of a chlorine with a phenyl ring dramatically alters the transfer of a hydron from an alcohol to a carbanion. The gas phase acidities and rates of
575
576
18 Formation of Hydrogen-bonded Carbanions as Intermediates in Hydron Transfer
methoxide-catalyzed exchange of CDCl2CF3 and PFB-d are similar, Table 18.1. The difference between {C6H5CClCF3}–, 2–, and either the PFB– or (CCl2CF3}– anions is that 2– is a p-delocalized anion and both the PFB– and (CCl2CF3}– have their negative charge in localized sp2 or sp3 orbitals.
18.3 Proton Transfer Associated with Methoxide Promoted Dehydrohalogenation Reactions
The E2 mechanism for alkoxide-promoted dehydrohalogenations is generally thought to be concerted with the breaking of the C–H and C–X bonds and the formation of the O–H and p-bond occurring in the transition structure [26]:
X b C a C
d c
H OR
Obtaining both an isotope effect, kH/kD, and an element effect, kHBr/kHCl, are the experimental evidence that the C–H and C–X bonds are breaking in the transition structure. Since measurement of heavy atom isotope effects requires special instrumentation, the element effect has taken the place of heavy atom isotope effects in most investigations. The element effect was first proposed by Bunnett in a 1957 paper dealing with the nucleophilic substitution reactions of activated aromatic compounds [27], and later applied to dehydrohalogenation mechanisms by Bartsch and Bunnett [28]. The lack of any incorporation of deuterium prior to elimination has also been used as experimental evidence favoring the concerted mechanism [29]. The stereochemistry should be a trans-elimination. The consequences of hydrogen-bonded carbanions as the first intermediate for proton transfer from the carbon acid to methoxide have important mechanistic implications when considering dehydrohalogenation reactions. If a group on the beta carbon can leave from that hydrogen-bonded carbanion, HB-h, the experimental results would be similar to those expected for the concerted E2 mechanism. The hydrogen bond will inhibit exchange of that proton if the reaction is carried out in CH3OD and will retain any stereochemistry at the carbanion site. This is illustrated by the methoxide-promoted dehydrochlorination in Scheme 18.2 where kElim >> kH 2 . Hydrogen isotope effects for methoxide-promoted dehydrohalogenations of C6H5CiHClCF2Cl, kH/kD = 2.35, and C6H5CHBrCF2Br, kH/kD = 4.10, with a kHBr/kHCl of 66 at 0 C could suggest a concerted mechanism with asymmetric
18.3 Proton Transfer Associated with Methoxide Promoted Dehydrohalogenation Reactions
b
DOMe . _ .. O C H c .. CH3 . d DOMe EC-h
H
.. .
k1
a b DOMe .. Cl C _ . O H C c .. CH3 . d DOMe HB-h
kElim
a
C
b Cl
.. .
a
Cl C
k
H
1
H
k2
.. .
a b DOMe .. Cl C _ . O H C c .. CH3 . d DOMe HB-h
k
H
2
a b Cl C _ c C + d
c
C
_
d
DOMe .. . H O. CH3 .. DOMe
FC-h
Scheme 18.2
transition structures. Since the C–Cl bond is stronger than the C–Br bond the smaller PKIE associated with the dehydrochlorination could suggest a later transition structure. The problem is that there are anomalous Arrhenius parameters with EaD EaH = 0.0 and AH/AD = 2.4 for C6H5CiHClCF2Cl and EaD EaH = 0.1 and AH/AD = 3.9 for C6H5CiHBrCF2Br [30]. Isotope effects come from zero-point energy differences and Arrhenius parameters should be due to differences in the activation energies, EaD EaH ¼ RTlnðkH =kD Þwith AH/AD = 1. Therefore, these anomalous Arrhenius parameters rule out the concerted E2 mechanism. What Arrhenius parameters would be expected from a reaction that occurs by an internal-return mechanism? Dahlberg calculated the anticipated Arrhenius behavior for elimination reactions occurring by the mechanism shown in Scheme 18.2 [31]. Several surprising situations were obtained. Mid-range values of kH/kD could be modeled with normal Arrhenius behavior, AH/AD » 1. Also possible are normal values of kH/kD that have low values of AH/AD normally considered to come from reactions that feature quantum mechanical tunneling. Although there were situations that resulted in AH/AD > 1, no model explained the values of AH/AD and EaD EaH obtained in our dehydrohalogenations. However, the calculations are able to model a number of other systems. Shiner and Smith obtained Arrhenius parameters for ethanolic sodium ethoxide-promoted dehydrobromination reactions of C6H5CH(CH3)CH2Br over a 50 C range. The kH/kD of 7.51 at 25 C was normal, but the AH/AD of 0.4 was considered experimental evidence for reaction occurring with quantum mechanical tunneling [32]. Shiner and Martin later reported tritium rates and corrected the earlier data for small amounts of a substitution reaction that formed C6H5CH(CH3)CH2OC2H5 [33]. Corrected values at 25 C were kH/kD = 7.82 and kD/kT = 2.65. To satisfy the Swain–Schaad relationship the experimental (kH/kT)obs of 20.6 should be 17% to 26% greater with (kH/kT)obs of 23 or 26 [11]. Dahlberg was able to model their results with an internal-return mechanism [34].
577
578
18 Formation of Hydrogen-bonded Carbanions as Intermediates in Hydron Transfer
The methoxide-promoted elimination reactions of four YC6H4CiHXCH2X can be modeled by using all three hydrogen isotopes, Table 18.2. The results for m-ClC6H4CiHBrCH2Br have such a small internal return parameter, aH = 0.045 at 25 C, that a concerted mechanism cannot be ruled out; however, a DS‡ of –3 eu is in line with an elimination occurring from a hydrogen-bonded carbanion intermediate. The aH = 0.59 for m-ClC6H4CiHClCH2Cl and m-CF3C6H4CiHClCH2Cl as well as the DS‡ values of 0 to –2 eu definitely favor the two-step mechanism over a concerted pathway. That p-CF3C6H4CiHClCH2F, aH = 2.1, reactions have more internal return is not surprising since breaking a C–F bond requires more energy than for a C–Cl bond. The rates of p-CF3C6H4CiHClCH2Cl and p-CF3C6H4CiHClCH2F have an element effect of kHCl/kHF = 54. Can a two-step reaction with internal return have a large element effect associated with dehydrohalogenation?
Table 18.2. Internal return parameters associated with
methanolic sodium methoxide-promoted promoted dehydrohalogenation reactions at 25 C.[a] Compound
k, M–1 s–1
DH‡, kcal mol–1
DS‡, eu
kH/kD or kD/kT
aiH
m-ClC6H4CHClCH2Cl
1.60 10–3
21.1 – 0.1
–0.5 – 0.1
3.40
0.59
m-ClC6H4CDClCH2Cl
4.71 10–4
21.9 – 0.1
–0.4 – 0.5
1.83
0.14
m-ClC6H4CTClCH2Cl
2.58 10–4
22.3 – 0.2
–0.0 – 0.5
m-CF3C6H4CHClCH2Cl
3.34 10–3
20.3 – 0.1
–1.7 – 0.2
3.49
0.59
m-CF3C6H4CDClCH2Cl
9.58
10–4
21.1 – 0.1
–1.7 – 0.2
1.88
0.13
p-CF3C6H4CTClCH2Cl
5.10
10–4
21.5 – 0.1
–1.5 – 0.3
p-CF3C6H4CHClCH2Cl
8.03 10–3
20.1 – 0.1
–0.7 – 0.2
p-CF3C6H4CDClCH2Cl
2.14 10–3
20.7 – 0.1
–1.3 – 0.1
p-CF3C6H4CHClCH2F
1.49 10–4
23.4 – 0.1
2.6 – 0.3
2.19
2.1
p-CF3C6H4CDClCH2F
6.73 10–5
23.9 – 0.1
2.5 – 0.3
1.63
0.50
p-CF3C6H4CTClCH2F
4.22
10–5
24.2 – 0.2
2.6 – 0.6
3.26
10–2
18.6 – 0.1
–2.8 – 0.1
4.95
0.045
m-ClC6H4CDBrCH2Br
6.60
10–3
19.7 – 0.2
–2.6 – 0.2
2.02
0.0095
m-ClC6H4CTBrCH2Br
3.27 10–3
20.0 – 0.1
–2.8 – 0.4
m-ClC6H4CHBrCH2Br
a Data from Ref. [37]
0.072
0.068 3.75
0.27
0.0070
18.3 Proton Transfer Associated with Methoxide Promoted Dehydrohalogenation Reactions
The element effect has been used to replace the need to measure a heavy atom isotope effect like k35/k37 for chlorine; however, the chlorine isotope effect has the advantage that the nature of the leaving group does not change. Measuring k35/k37 for both the protium and deuterium compounds can distinguish between a reaction occurring by a concerted E2 mechanism or by the two-step process with internal return [35]. For the concerted reaction, the values of (k35/k37)HCl should equal those for (k35/k37)DCl; however, the two-step process will have a (k35/k37)HCl larger D than that for (k35/k37)DCl. This is due to the fact that kH 1 > k1 and the elimination step, kElim, has a larger role in the experimental rate constant, kobs = [k1kElim] / [k–1 + kElim], for HCl than for DCl. There is a large difference in the values k35/k37 obtained for methoxide-promoted dehydrochlorination of C6H5CiHClCH2Cl, (k35/ k37)HCl = 1.00978–0.00020 compared to (k35/k37)DCl = 1.00776–0.00020. Similar differences are obtained for the reaction using ethanolic sodium methoxide, and for the alkoxide-promoted dehydrochlorinations of C6H5CiHClCF2Cl, Table 18.3. These are very large values for chlorine isotope effects. McLennan was able to explain these values by calculating that a considerable lengthening of the C–Cl bond during the formation of the hydrogen-bonded carbanion, k1, would result in a (k35/k37) occurring for the proton-transfer step as well for the actual breaking of the C–Cl bond, kElim [36].
Table 18.3 Chlorine and hydrogen isotope effects, and element
effects associated with alcoholic sodium alkoxide-promoted dehydrochlorination ractions.[a] Compound
Solvent
k35/ k37 [C]
kH / kD [C]
kHBr / kHCl [C]
C6H5CHClCH2Cl
EtOH
1.00908 – 0.00008 [24]
4.24 [25]
35 [25]
1.00734 – 0.00012 [24]
C6H5CDClCH2Cl C6H5CHClCH2Cl
McOH
EtOH
1.01229 – 0.00047 [0]
MeOH
C6H5CDClCF2Cl
1.01255 – 0.00048 [20] 1.01025 – 0.00043 [20]
35 [25] 25 [25]
2.77 [0]
1.01003 – 0.00024 [0]
C6H5CDClCF2Cl C6H5CHClCF2Cl
3.83 [25]
1.00776 – 0.00020 [21]
C6H5CDClCH2Cl C6H5CHClCF2Cl
1.00978 – 0.00020 [21]
24 [25]
66 [0] 39 [0]
2.28 [25]
47 [25] 29 [25]
a Data from Ref. [35b].
Element effects for the hydrogen and deuterium compounds can also be used to distinguish between a concerted E2 mechanism and one with two steps and internal return, Scheme 18.2. Data in Table 18.2 can be used to calculate element effects comparing p-CF3C6H4CiHClCH2Cl and p-CF3C6H4CiHClCH2F where a
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18 Formation of Hydrogen-bonded Carbanions as Intermediates in Hydron Transfer
kHCl/kHF of 54 becomes a kDCl/kDF of 32. Similar results come from the ethoxidepromoted eliminations of C6H5CiHBrCH2Br, C6H5CiHBrCH2Cl and C6H5CiHBrCH2F: kHBr/kHCl = 35 and kDBr/kDCl = 16; kHCl/kHF = 67 and kDCl/kDF = 35 [37]. An element effect of kCl/kF = 68 had been previously reported for the ethoxide-promoted dehydrohalogenataions of C6H4CH2CH2X [38]. 18.4 Conclusion
Ritchie’s prediction that carbon acids whose conjugated bases have localized charge will show “kinetic acidities” greater than their thermodynamic acidities only needs to be changed slightly to read that the orbital of the carbanion is localized on that carbon atom. Density functional calculations using the natural population analysis allowed charge distributions to be calculated for the various anions. The negative charge for 9-PhFl– is highly p-delocalized to form an aromatic species with only 18% of the negative charge in the 9 position and this increases to 25% in the hydrogen-bonded species. The negative charge of the pentafluorophenyl anion, PFB–, cannot undergo p-delocalization and is thought to be localized in an sp2 orbital; however, the ipso carbon of PFB– only has 41% of the negative charge, which increases to 44% for the hydrogen-bonded species. Since only 41% to 44% of the negative charge is on the ipso carbon of PFB–, the charge is also delocalized by the field effects of five fluorine atoms in the benzene ring. 4) The case of CF3CCl2– is similar with 45% to 50% of the charge on the carbanion carbon in a localized sp3 orbital, and the remainder delocalized by field effects. The benzylic carbon atoms of Y-1– and Y-2– still retain 37% and 60% of the negative charge, but that charge is in a p-delocalized orbital. Both pentafluorobenzene and CHCl2CF3 exchange their protons much faster than expected from their gas phase acidities. The exchange reactions occur with large amounts of internal return, and there must be a mechanism that allows the exchange process to occur without having to form a free carbanion. Although the benzylic carbanions have about the same amount of the negative charge as those two anions they have much slower exchange reactions that also occur with large amounts of internal return resulting in near unity hydrogen isotope effects. The exchange of the 9-hydrogen of 9-phenylfluorene has a similar rate of exchange as benzylic compounds with similar gas phase acidities. The difference is that the reaction occurs with only a small amount of internal return and has a sizable hydrogen isotope effect. Gas-phase studies have been made to gain information about the intrinsic stability of hydrogen-bonded ionic intermediates of alcohols and carbon acids. Many anionic hydrogen-bonded complexes appear to be better when there is a good match of the gas-phase acidities of a neutral and the conjugate acid of the ion. 4) When this material was first presented at an
international conference, Paul Schleyer stated that a pentafluorophenyl anion is not a
localized carbanion, and this has certainly proven to be the case from our calculations.
References
However, it does not work for toluene and methanol which have comparable acidities, and Brauman’s group were not successful in their attempts to form the hydrogen-bonded complex of methoxide and toluene [39]. They were successful in the study of CHF3, which is slightly more acidic than toluene, and methanol complexes [40]. Studies of complexes between CHF3 and ethanol or isopropanol were also made, and the energies range from –21.1 to –23.5 kcal mol–1, which are larger than those that are typical ion-dipole complexes, 10–15 kcal mol–1. There is the same difference between the benzyl anion which is p-delocalized and –CF3 where the charge is in an sp3 orbital. The generality of concerted 1,2 eliminations was questioned by Bordwell [41], and supported by Saunders [42]. What it boils down to is what can be considered to be an intermediate during a chemical reaction. Jencks gives an excellent definition: “An intermediate is, therefore, defined as a species with a significant lifetime, longer than that of a molecular vibration of ~10–13 s, that has barriers for its breakdown to both reactants and products.” [43]. Bunnett has an excellent summation: “It is axiomatic that one cannot define a reaction mechanism absolutely. What one can do is to reject conceivable mechanisms that are not compatible with experimental evidence. When all conceivable mechanisms but one have been rejected, one is tempted to consider the mechanism to be established. However, such reasoning does not, and by definition cannot, take account of inconceivable mechanisms. At a later time, especially in the light of advances in the meanwhile, one or more further alternative mechanisms may be recognized, and the mechanism previously thought to be the only tenable one may be found to be incompatible with new experimental evidence. Such has happened many times in the history of mechanistic studies. The conservative scientist therefore refers to the better-understood mechanisms as generally accepted’ or well recognizes’ rather than as established’ or proven’.” [44].
References 1 C. D. Ritchie, J. Am. Chem. Soc. 1969,
91, 6749–6753. 2 A. Streitwieser, Jr., P. J. Scannon, N. M. Neimeyer, J. Am. Chem. Soc. 1972, 94, 7938–7937. 3 A. Streitwieser, Jr., J. A. Hudson, F. Mares, J. Am. Chem. Soc. 1968, 90, 648–650. 4 A. Streitwieser, Jr., W. B. Hollyhead, A. H. Pudjaatmake, P. H. Owens, T. L. Kruger, P. A. Rubenstein, R. A. MacQuarrie, M. L. Brokaw, W. K. C. Chu, H. M. Niemeyer, J. Am. Chem. Soc. 1971, 93, 5088–5096. 5 (a) R. P. Bell, Chem. Soc. Rev. 1974, 3, 513–544, (b) R. A. More O’ Ferrall,
6
7 8
9 10
Proton-Transfer Reactions, E. F. Caldin, V. Gold (Eds.), Chapman & Hall, London, 1975, pp. 216–227. L. Melander, Isotope Effects on Reaction Rates, Ronald Press, New York, 1960, pp. 24–32. F. H. Westheimer, Chem. Rev. 1961, 61, 265–273. C. G. Swain, E. C. Stivers, J. F. Reuwer, Jr, L. J. Schaad, J. Am. Chem. Soc. 1958, 80, 5885–5893. A. J. Kresge, Acc. Chem. Res. 1975, 9, 354–360. A. J. Kresge, A. C. Lin, J. Chem. Soc. Chem. Commun. 1973, 761.
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18 Formation of Hydrogen-bonded Carbanions as Intermediates in Hydron Transfer 11 D. J. Cram, D. A. Scott, W. D. Nielsen, 12
13
14 15
16
17 18
19 20
21 22
23
24 25
26
J. Am. Chem. Soc. 1961, 83, 3696–3707. A. Streitwieser Jr., W. B. Hollyhead, G. Sonnichsen, A. H. Pudjaatmake, C. J. Chang, T. L. Kruger, J. Am. Chem. Soc. 1971, 93, 5096–5102. H. F. Koch, J. C. Biffinger, M. Mishima, Mustanir, G. Lodder, J. Phys. Org. Chem. 1998, 11, 614–616. A. Streitwieser Jr., H. F. Koch, J. Am. Chem. Soc. 1964, 86, 404–409. H. F. Koch, J. G. Koch, N. H. Koch, A. S. Koch, J. Am. Chem. Soc. 1983, 105, 2388–2393. H. F. Koch, M. Mishima, H. Zuilhof, Ber. Bunsenges. Phys. Che. 1998, 102, 567–572. K. M. Ervin, V. F. DeTuri, V. F., J. Phys. Chem. A 2002, 9947–9956. V. F. DeTuri, H. F. Koch, J. G. Koch, G. Lodder, M. Mishima, H. Zuilhof, N. M. Abrams, C. E. Anders, J. C. Biffinger, P. Han, A. R. Kurl;and, J. M. Nichols, A. M. Ruminski, P. R. Smith, K. D. Vasey, J. Phys. Org. Chem. 2006, 19, 308–317. W. T. Miller, E. W. Fager, P. H. Griswold, J. Am. Chem. Soc. 1948, 70, 431–432. (a) J. Hine, R. Wiesboeck, R. G. Ghirardelli, J. Am. Chem. Soc. 1961, 83, 1291–1222; (b) J. Hine, R. Wiesboeck, O. B. Ramsay, J. Am. Chem. Soc. 1961, 83, 1222–1226. H. F. Koch, A. J. Kielbania Jr., J. Am. Chem. Soc. 1970, 92, 729–730. H. F. Koch, J. G. Koch, D. B. Donovan, A. G. Toczko, A. J. Kielbania Jr., J. Am. Chem. Soc. 1981, 103, 5417–5423. (a) C. Eaborn, D. R. M. Walton, G. Seconi, J. Chem. Soc., Perkin Trans. 2 1976, 1857–1861; (b) D. Macciantelli, G. Seconi, C. Eaborn, J. Chem. Soc., Perkin Trans. 2 1978, 834–838. H. F. Koch, A. S. Koch, J. Am. Chem. Soc. 1984, 106, 4536–4539. H. F. Koch, D. B. Dahlberg, G. Lodder, K. S. Root, N. A. Touchette, R. L. Solsky, R. M. Zuck, L. J. Wagner, N. H. Koch and M. A. Kuzemko, J. Am. Chem. Soc. 1983, 105, 2394–2398. E. D. Hughes, C. K. Ingold, S. Masterman, B. J. McNulty, J. Chem. Soc. 1940, 899–912.
27 J. F. Bunnett, E. W. Garbisch,
28 29 30
31 32 33 34 35
36 37
38 39 40 41 42 43 44
K. M. Pruitt, J. Am. Chem. Soc. 1957, 79, 385–391. R. A. Bartsch, J. F. Bunnett, J. Am. Chem. Soc. 1968, 90, 408–417. P. S. Skell, C. R. Hauser, J. Am. Chem. Soc. 1945, 67, 1661. H. F. Koch, D. B. Dahlberg, M. F. McEntee, C. J. Klecha, J. Am. Chem. Soc. 1976, 98, 1060–1061. H. F. Koch, D. B. Dahlberg, J. Am. Chem. Soc. 1980, 102, 6102–6107. V. J. Shiner, M. L. Smith, J. Am. Chem. Soc. 1961, 83, 593–598. V. J. Shiner, B. Martin, Pure Appl. Chem. 1964, 8, 371–378. Reference [31], p. 6106. (a) H. F. Koch, J. G. Koch, W. Tumas, D. J. McLennan, B. Dobson, G. Lodder, J. Am. Chem. Soc. 1980, 102, 7955–7956; (b) H. F. Koch, D. J. McLennan, J. G. Koch, W. Tumas, B. Dobson, N. H. Koch, J. Am. Chem. Soc. 1983, 105, 1930–1937. Reference [35b], pp. 1934–1935. H. F. Koch, G. Lodder, J. G. Koch, D. J. Bogdan, G. H. Brown, C. A. Carlson, A. B. Dean, R. Hage, P. Han, J. C. P. Hopman, L. A. James, P. M. Knape, E. C. Roos, M. L. Sardina, R. A. Sawyer, B. O. Scott, C. A. Testa, III, S. D. Wickham, J. Am. Chem. Soc. 1997, 119, 9965–9974. C. H. DePuy, C. A. Bishop, J. Am. Chem. Soc. 1960, 82, 2535–2537. G. C. Gatev, M. Zhong, J. I. Brauman, J. Phys. Org. Chem. 1997, 10, 531–536. M. L. Chabinyc, J. I. Brauman, J. Am. Chem. Soc. 1998, 120, 10863–10870. F. G. Bordwell, Acc. Chem. Res. 1972, 5, 374–381. W. H. Saunders, Jr., Acc. Chem. Res. 1976, 9, 19–25. W. P. Jencks, Acc. Chem. Res. 1980, 13, 161–169. J. F. Bunnett, in Techniques of Chemistry, Volume VI. Investigation of Rates and Mechanisms of Reactions, Part I, 3rd Edn. E. S. Lewis (Ed.), Wiley Interscience, New York, 1974, Ch. VIII, p. 369.
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19 Theoretical Simulations of Free Energy Relationships in Proton Transfer Ian H. Williams
19.1 Introduction
The observation of a rate equilibrium relationship, or equivalently a free energy relationship (FER), between logarithms of experimentally determined rate constants and equilibrium constants, raises questions concerning its validity, the possible significance of the slope of a linear correlation (LFER), or the origin of curvature, which are natural concerns for theoretical enquiry. Values of a Brønsted coefficient or a Marcus intrinsic barrier (see below) derived from empirical data are phenomenological parameters that of themselves do not provide satisfying explanations at a fundamental molecular level for observed or predicted reactivity trends. The subject of theoretical simulation involves the construction of FERs from the bottom up rather than from the top down: that is, it starts from microscopic models for chemical bonding and intermolecular interactions and proceeds, by way of explicit consideration of molecular structures for species undergoing chemical reaction, to evaluate energy changes governing the kinetic and thermodynamic aspects of a macroscopically observed process. However, since numerical computations alone rarely provide insight in a readily digestible form, it is common to seek interpretations of the results of theoretical simulations by means of simple analytical models involving parameters that may be understood in terms of fundamental molecular properties and chemical concepts. We begin by reviewing briefly some of the qualitative models for FERs before surveying some examples of simulated FERs for proton transfer (PT) reactions. These include molecular orbital (MO)-based studies of potential energy surfaces (PES) for gas-phase reactions and valence bond (VB)-based studies of free energy changes for reactions in condensed phases.
Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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19 Theoretical Simulations of Free Energy Relationships in Proton Transfer
19.2 Qualitative Models for FERs
Theory and experiment are inextricably linked in the development of models for chemical reactivity [1]. Since the 1930s, when the ideas of both transition-state (TS) theory [2] and of rate equilibrium relationships [3] were first promulgated, many distinguished scientists have contributed to the body of knowledge, concerning the relationships between barrier heights for simple group transfer processes and their reaction energies, sometimes referred to as the “Bema Hapothle” [4] – an acronym based upon the initials of a subset of these workers, namely Bell [5], Marcus [6], Hammond [7], Polanyi [8], Thornton [9] and Leffler [10]. Among other omissions from this short-list are the names of Jencks [11], More O’Ferrall [12], and Murdoch [13]. A general group transfer reaction (19.1a) may be considered as the sum of the two half-reactions 19.1b and 19.1c (in which homolysis or heterolysis is deliberately not specified). A–X + B fi A + X–B
(19.1a)
A–X fi A + X
(19.1b)
X + B fi X–B
(19.1c)
Evans and Polanyi [2c, 8] considered the energetics of each step separately: step (19.1b) could be described by an energy curve for bond dissociation of A–X as a function of the interatomic distance between A and X, and step (19.1c) could be described by an energy curve for association of atoms X and B (Fig. 19.1). The overall reaction could avoid the energetic cost of complete bond dissociation (to A + X + B) in step (19.1b) if there were an electronic reorganisation occurring at a particular distance between A and B that allowed a cross-over from the rising energy curve for step (19.1b) to the falling energy curve for step (19.1c). The barrier to reaction in this model, which assumes that the bond-breaking and bond-making processes are independent of each other, is given simply by the point of intersection of the two energy curves relative to the energy of the reactants, A–X + B. Since variation in the nature of B would not be expected to affect the energy curve for the bond-breaking step (19.1b), but would at least alter the energy of the products A + X–B relative to the reactants, the effect of changes in B (e.g. B1, B2 and B3 in Fig. 19.1) could be estimated by means of moving the curve for step (19.1c) up or down relative to that for step (19.1b). If the central part of each curve were reasonably linear, where the points of intersection occurred, then the change in the barrier height DE‡ would be expected to be proportional to the change in the reaction energy DErxn for reaction (19.1a), according to Eq. (19.2). DE‡ = a DErxn + C
(19.2)
19.2 Qualitative Models for FERs
Figure 19.1 Intersecting curves to illustrate the Bell–Evans–Polanyi Principle for a general group-transfer reaction (19.1a). Three members of a reaction series involving different acceptor groups Bi (i = 1, 2, 3) give separate energy curves for step (19.1c) each intersecting the energy curve for step (19.1b).
Bell [5] considered the case of X = H, representing proton transfer between a Brønsted acid and a base, and noted that, if DE‡ and DErxn were, respectively, proportional to log k and log K, Eq. (19.2) was equivalent to the Brønsted relation (Eq. (19.3)) where k is the rate constant and K is the equilibrium constant for the acid–base reaction of Eq. (19.4). log k = a log K + C¢
(19.3)
A–H + B fi A + H–B
(19.4)
These simple considerations yield several corollaries, sometimes known together as the Bell–Evans–Polanyi (BEP) principle [14]. First, there is an approximately linear relation between the barrier height and the reaction energy: this is the basis of the Brønsted relation (and other LFERs). Second, the proportionality constant a in Eq. (19.2) tends to be smaller for exothermic reactions (but larger for endothermic reactions). Third, the position of the crossing point between the curves lies closer to the reactants for more exothermic reactions: this is the basis of the Hammond postulate, that the TS for a more exothermic reaction more closely resembles the reactants (and that for a more endothermic reaction more closely resembles the products). Murdoch [15] pointed out that the quantitative barrier expressions given by London–Eyring–Polanyi–Sato [16], Johnston and Parr [17], Marcus [6, 18], Murdoch
585
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19 Theoretical Simulations of Free Energy Relationships in Proton Transfer
[13], Rehm and Weller [19], Agmon and Levine [20], Bell [21], le Noble [22], Lewis [23], Kurz [24], Thornton [9], Zavitsas [25], and Chatt and co-workers [26] all reduced to specific cases, or simple extensions, of Eq. (19.5). DE‡ = DEint‡ (1 – f2) + 12 DErxn (1 + f1)
(19.5)
Here DE‡ is the barrier for the reaction (or activation energy) in which the energy change (or reaction asymmetry) is DErxn, and DEint‡ is the intrinsic barrier for an identity reaction with DErxn = 0. The functions f1 and f2 are functions involving, respectively, only odd or even powers of DErxn and govern the relative contributions of the kinetic term DEint‡ (1 – f2) and the thermodynamic term 12 DErxn (1 + f1) to the overall barrier. Very exoergic reactions, for which DErxn is large and negative, f1 fi –1 and f2 fi +1, leading to DE‡ = 0. on the other hand, very endoergic reactions, for which DErxn is large and positive, f1 fi +1 and f2 fi +1, leading to DE‡ = DErxn. Near to thermoneutrality, reactions for which DErxn » 0 have both f1 and f2 » 0, yielding DE‡ = DEint‡ + 12 DErxn. The functions f1 and f2 serve to interpolate between the limiting cases of very high exoergicity and endoergicity. Changes in the structure or composition of the reactant species may affect both the kinetic term and the thermodynamic term in Eq. (19.5). If changes in the thermodynamic term dominate, or the changes in both terms are in the same direction, the BEP principle is likely to be upheld, with the more stable product being formed more quickly. However, if the kinetic term dominates and opposes changes in the thermodynamic term, then the BEP principle is expected to fail and a less stable product may be formed more quickly than a more stable product. The kinetic term determines the relative barrier heights for reactions having similar thermodynamic terms. If the interpolation functions in Eq. (19.5) take the values f1 = DErxn/4DEint‡ and f2 = (f1)2, this relationship between the barrier and the overall energy change for reaction becomes the Marcus relation, Eq. (19.6), whose range of applicability is | DErxn/DEint‡ | £ 4, corresponding to –1 £ f1 £ +1 [15]. DE‡ = DEint‡ [1 – (DErxn/4DEint‡)2] + 12 DErxn (1 + DErxn/4DEint‡) = DEint‡ + 12 DErxn + DErxn2/16DEint‡
(19.6)
It is well known [6, 14a, 27] that the Marcus relation may be derived from a model of intersecting parabolas for the reactant and product energy curves (Fig. 19.2). A parabola provides an unrealistic description of the energy profile for extension of an A–H bond far from its equilibrium length and towards complete dissociation: a Morse curve offers a better description. It is perhaps not too widely appreciated [28, 29] that transformation of a Morse function (Eq. (19.7)) from bond length (r) to bond order (n) coordinates (Eq. (19.8)) yields a parabola (Eq. (19.9)). E(r) = De exp[–b(r – re)] {exp[ – b(r – re)] – 2}
(19.7)
n = exp[–b(r – re)]
(19.8)
E(n) = De n (n – 2)
(19.9)
19.2 Qualitative Models for FERs
Figure 19.2 Intersecting parabolas of equal curvature.
Regardless of the choice of coordinates, consideration of an intersecting curves model in which the bond-breaking and bond-making processes are independent of each other implies that the reactant and product curves describe diabatic states of the system, i.e. there is no mixing between them that would allow for a smooth and gradual transformation from one to the other. Deformation of the reactant geometry without allowing for any electronic reorganisation from a reactant-like VB structure incurs an energetic penalty. The energy of the reactant diabatic state at the geometry corresponding to the energy minimum of the product is often known as the reorganisation energy, k; in Marcus theory, k= 4DEint‡. If the reactant and product diabatic states have equal curvature, then for a thermoneutral reaction k is also the energy of the product at the reactant geometry (Fig. 19.3). It is more realistic to allow the reactant-like and product-like states to interact with each other, rather than to consider them as being independent. Thus electronic reorganisation may accompany geometrical reorganisation along a reaction coordinate for proton transfer (PT). Mixing between the reactant and product diabatic states generates two new adiabatic states. The energy profile for PT follows the ground-state adiabatic curve that shows a smooth maximum passing through the geometry for which the diabatic curves intersect. Necessarily there is also an excited-state adiabatic curve containing an energy minimum with respect to the reaction coordinate. In the adiabatic model there is an avoided crossing between the reactant-like and product-like electronic arrangements. The degree of avoided crossing is given by the difference in energy Eres between the point of intersection of the diabatic curves and the maximum of the adiabatic curve (Fig. 19.3).
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19 Theoretical Simulations of Free Energy Relationships in Proton Transfer
Figure 19.3 Intersection of parabolic diabatic curves for reactant-like and product-like states, together with adiabatic energy curves arising from mixing of the diabatic states.
19.2.1 What is Meant by “Reaction Coordinate”?
The horizontal axis in diagrams such as Figs. 19.1–19.3, often labelled as the “reaction coordinate”, is usually not well defined. Figure 19.4 shows qualitatively a ground-state adiabatic PES for the PT (or hydrogen-atom transfer) reaction (19.4) as a function of two coordinates, the bond distances A···H and H···B. Let us first follow the Evans–Polanyi argument, outlined above, to trace an energy profile across this surface. We start near point y, where the H···B distance has some finite value, and elongate the A–H bond by traversing parallel to the A···H axis towards point z. Now we freeze the partially broken A–H bond but let the H···B distance decrease: we move parallel to the H···B axis towards point x. This path (dashed lines in Fig. 19.4) is continuous but its energy profile contains a cusp at point z, rather like the lower parts of the intersecting curves in Fig. 19.1. In this case the “reaction coordinate” of Fig. 19.1 contains two distinct segments, described by changes in different interatomic distances. The energy minimum along the path yz occurs at point r, corresponding to a reactant-like species A–H······B, which is not necessarily an energy minimum with respect to the H···B coordinate. Similarly, the product-like species A······H–B corresponding to point p (the energy minimum along path zx) which is not necessarily an energy minimum with respect to the A···H coordinate. A direct reaction path across the PES from r to p may be defined as a linear combination of the two coordinates,
19.2 Qualitative Models for FERs
(A···H) – (H···B). The energy profile along this path (diagonal dotted line in Fig. 19.4) is smooth and continuous but the species A···H···B corresponding to point s at the energy maximum is not a stationary point with respect to displacement in the perpendicular direction, defined by the linear combination (A···H) + (H···B). The energy minimum along the extension of the diagonal line zs occurs at point t, which is a saddle point with zero gradient in both degrees of freedom, corresponding to the true transition structure [A···H···B]‡. The points z, s and t lie, of course, in the dividing surface between reactants and products. The curved path passing through r, t and p (thick solid line in Fig. 19.4) corresponds to the minimum-energy reaction path for proton transfer between A and B. This path is described by some nonlinear combination of the two coordinates that cannot be simply predicted without prior knowledge of the shape of the PES. It is usually determined by following the “intrinsic reaction coordinate” from the saddle point towards both the reactants and products; obviously this requires the saddle point to have been located beforehand. A–H + B
A+H+ B
r
H…B
y
z s t
p A…H
A + H–B
x
Figure 19.4 Schematic potential energy surface to illustrate alternative reaction coordinates.
19.2.2 The Brønsted a as a Measure of TS Structure
The Marcus relation, Eq. (19.6), is clearly not a linear relationship between the activation energy and the reaction asymmetry but a quadratic one. The first derivative of DE‡ with respect to DErxn is equivalent to the Brønsted coefficient a in Eq. (19.2), but is itself a linear function of DErxn. dDE‡ / dDErxn = a = 12 + DErxn/8DEint‡
(19.10)
Leffler [10] had proposed that the slope of an empirical linear correlation between log k and log K (i.e. of DG‡ vs. DGrxn) could be identified as a parameter measur-
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19 Theoretical Simulations of Free Energy Relationships in Proton Transfer
ing the degree of resemblance of the TS to the products as compared with its resemblance to the reactants. Thus for a PT from an acid to a series of related bases, the value of a obtained from the linear correlation DG‡ = a DGrxn would be interpreted as a measure of the degree of transfer of the proton in the TS. A value of a = 0 would indicate a reactant-like TS in which essentially no PT had occurred from the acid to the base, a = 1 would indicate a product-like TS in which PT essentially complete, and a = 0.5 would indicate a TS in which the proton was about half transferred [30]. The use of the Brønsted a (and also the slopes of other structure–reactivity correlations) as measures of TS structure has been severely criticised [31], but has also been thoughtfully defended with appropriate cautionary notes [32]. It has long been recognised that there is a fundamental incompatibility within the Bema Hapothle collection of ideas that arise from TS theory: if the slope of a (genuinely) linear rate-equilibrium relationship is interpreted as some index of TS structure, it must reflect some constant property of the TS for the entire family of reactions used to construct the correlation; however, the BEP [2c, 5, 8] and Leffler [10] principles, Hammond postulate [7], and related notions all suggest that changing the reaction energetics should cause variation in TS structure within this same family.
19.3 FERs from MO Calculations of PESs
Modern computational chemistry offers a means by which the paradox between the existence of linear FERs and variation in TS structure may be resolved. For a particular reaction of a series of substituted compounds, the energetics and geometries of reactants, transition structures and products may be obtained from calculated PESs. Rate-equilibrium relationships may be constructed from plots of calculated DG‡ vs. DGrxn (or DH‡ vs. DHrxn) values. The merit of this approach is that the TS structure, deduced indirectly from the slopes of these plots, may be compared with directly determined transition structures [33]. 19.3.1 Energies and Transition States
Two comments are necessary before we proceed further. First, most of the preceding discussion of reaction energetics has been couched rather imprecisely in terms of undefined energy changes DE, whereas the logarithms of experimental rate constants or equilibrium constants are proportional to changes in Gibbs free energy DG. A linear rate-equilibrium relationship (DG‡ = a DGrxn) might arise as the result of: (a) DH‡ and DHrxn each being constant for all members of a series of related reactions; (b) DS‡ and DSrxn each being constant throughout the same series; or (c) enthalpy and entropy changes being linearly related to each other. With careful design of a theoretical simulation it is often possible to ensure that condition (b) is met satisfactorily, so that changes in free energy may be modelled ade-
19.3 FERs from MO Calculations of PESs
quately by changes in enthalpy. Moreover, within a series of related reactions which differ, for example, in regard to the nature of a remote substituent upon one reactant, it is also reasonable to approximate enthalpy changes DH by potential energy changes DE. In the remainder of this chapter we will consider examples of theoretical simulations of rate equilibrium relationships based upon changes in potential energy, enthalpy, and free energy. The second point is to clarify our usage of the terms “transition state” and “transition structure”. The latter term, transition structure, refers to the molecular geometry corresponding to a saddle point on a potential energy surface: this is a well-defined microscopic entity which may be located and characterized within a particular computational model. In contrast, the term transition state refers to the properties of an ensemble of molecular entities at a finite (nonzero) temperature: it may be associated with the maximum along a simulated free energy profile for an elementary step. We consider it useful to distinguish the two concepts in view of the significant difference between them: the one is microscopic and related to a feature of an (unobservable) PES; the other is macroscopic and related to phenomenological interpretation of empirical kinetic data. The connection between a transition structure and a TS involves statistical-mechanical averaging. Of course, the same distinction could be made for a stable molecule between its minimum energy structure and its equilibrium state at a given temperature and pressure. Perhaps the first example of a computationally simulated Brønsted correlation was the semiempirical MNDO study of Anhede, Bergman and Kresge (ABK) [34] for a series of PT reactions involving fluoroethanols, Eq. (19.11), with n = 0–3. CH(3–n)FnCH2OH + –OCH2CH3 fi CH(3–n)FnCH2O– + HOCH2CH3
(19.11)
The geometries of reactant and product ion–molecule complexes, together with transition structures, were completely optimized, and for each reaction the enthalpies of activation and of reaction were computed for the elementary step of PT between the reactant and product complexes. Each of the non-identity reactions (n = 1, 2, 3) was considered in both the forward and backward direction; together with the identity reaction (n = 0), this yielded seven pairs of values for a plot of computed DH‡ vs. DHrxn which showed noticeable curvature over a range –100
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19 Theoretical Simulations of Free Energy Relationships in Proton Transfer
riers and reaction energies were quantitatively reproduced by the Marcus equation for all systems and that there was fair agreement between the Brønsted a computed as the slope of the Marcus curve and as the position of the proton along the reaction coordinate in the transition structure. An intrinsic barrier of ~18 kJ mol–1 may be obtained by fitting a quadratic to the published data for the N···N distance (2.75 ) closest to that in the energy minimum of the double-well potential surface. The Brønsted plot for this transect is markedly curved, with a changing from 0.17 to 0.83 over a range of 93 kJ mol–1. Increasing the fixed N······N distance to 3.10 raises the intrinsic barrier (cf. Ref. [36]) to 77 kJ mol–1 and decreases the degree of curvature, with a changing from 0.4 to 0.6 over a range of 124 kJ mol–1. Scheiner and Redfern noted that the difficulties experienced a little previously, by Evleth and co-workers [37], in correlating similar ab initio SCF results for a range of PT reactions using the Marcus relation were due partly to the equation not being applied only to a single elementary step and partly to the estimation of intrinsic barriers from data on the symmetric systems AHA and BHB, where one of these was described by a single-well potential rather than a double well. Hoz, Yang and Wolfe (HYW) [38] made ingenious use of the gas-phase PES for the concerted addition of water to formaldehyde in order to obtain a Brønsted correlation for PT between oxygen atoms. PT from water to the carbonyl oxygen is endothermic in the reactant complex (Fig. 19.5, top left) but very exothermic in the zwitterionic species (bottom left) formed by nucleophilic attack at the carbonyl carbon, as shown by the More O’Ferrall–Jencks diagram. There is a single true
Figure 19.5 More O’Ferrall–Jencks diagram to illustrate how cross-sections of the potential energy surface for gas-phase hydration of formaldehyde yield a family of barriers from which a Brønsted correlation may be generated (cf. Ref. [38]).
19.3 FERs from MO Calculations of PESs
transition structure on this surface for hydration, as shown by the open arrow, but there are many energy maxima for PT along the cross-sections indicated by dotted lines in Fig. 19.5. The activation energy DE‡ and reaction aymmetries DErxn computed with both the semiempirical AM1 and ab initio HF/3-21G MO methods for each of several of these cross-sections were used to construct apparently very good linear Brønsted correlations. HYW argued that, although their computed energies fit the Marcus equation reasonably well, the linear fit was better. However, re-analysis of their published data actually suggests that a quadratic fit is slightly better than a simple linear correlation, with intrinsic barriers of ~96 kJ mol–1 (HF/3-21G) and ~143 kJ mol–1 (AM1). A larger matrix of related PT reactions was considered by Williams and Austin (WA) [39] using the semiempirical AM1 method. They modulated the proton affinities of donor and acceptor ammonia molecules in the complex (A-H···B)+ where A = B = NH3 by tuning the magnitude of external dipoles placed remotely along the N···N axis. This allowed a range of 4-substituted pyridines to be mimicked as both acids YPyH+ and bases PyX (X, Y = CN, Cl, H, Me, NMe2) thereby yielding 25 distinct reactions; geometries for all ion-dipole reactant/product complexes and transition structures were located with complete optimization (subject to a three-fold symmetry constraint). Figure 19.6 shows the Brønsted correlation generated by plotting – DHrxn against – DH‡ for intra-complex PT for each combination of donor and acceptor; to a good approximation this is equivalent to a plot of log k against log K, since changes in DSrxn and DS‡ are likely to be essentially constant for the whole set of reactions. A least squares fit of a quadratic to the 25 data points gives an excellent correlation (r2 = 0.999) with an intercept of 5.1 kJ mol–l, but a Marcus equation with intrinsic barrier DH‡int of 5.22 kJ mol–1 (= DH‡ for X = Y = H) provides an almost equally satisfactory fit to the AM1 calculated data. (Note that the coefficient of the quadratic term in the Marcus equation is a function of the constant and the coefficient of the linear term, and is therefore less flexible than a generalised second-order polynomial.) The slope of the curved Brønsted correlation for PT changes from 0 for the most exothermic to 1 for the most endothermic reactions, in accord with expectation [13a, 40], over a range of
Figure 19.6 Curved Brønsted correlation for gas-phase proton transfer between mimicked pyridine donors and acceptors; AM1 results from Ref. [39].
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19 Theoretical Simulations of Free Energy Relationships in Proton Transfer
46 kJ mol–1 corresponding to about 8DH‡int. The transition structures varied sensibly with the thermodynamic reaction asymmetry, and it was found that the slope of the Brønsted correlation provided an approximate measure of both the degree of PT and of charge development along the reaction coordinate between the reactant and product ion–dipole complexes. An analogous simulation for methyl transfer [39] between the same sets of donors and acceptors (now electrophiles and nucleophiles rather than acids and bases) gave an imperceptibly curved Brønsted correlation for which the Marcus intrinsic barrier was very high (152 kJ mol–1); this demonstrates that the apparent linearity of an LFER depends upon the fraction of 8DH‡int spanned by the range of thermodynamic reaction asymmetry covered by a simulation or by a series of experiments. The examples discussed above all employ MO theory to simulate gas-phase PT, and all yield energy minima and maxima along defined reaction paths across adiabatic PESs, as represented qualitatively by Fig. 19.4. Progress from a reactant ion– dipole complex through a transition structure (either fully optimized or subject to some constraint) towards a product ion–dipole complex is accompanied smoothly by changes in the shapes and energies of the MOs, corresponding to the changing charge distributions. All give results that correlate well with the Marcus equation. All show variation in geometry of the transition structure with changes in reaction energy, and all show curved Brønsted correlations. Closer examination of the WA data [39] is warranted in view of the fact that this simulation covered the whole range 0 £ a £1. It has often been noted that different values of a are obtained from apparently linear Brønsted correlations according to whether the acid is kept constant and the nature of the base is changed, or the acid is varied while keeping the base fixed [41], and this effect has been attributed to variation in the intrinsic barrier within a series of reactions. However, the WA intrinsic barriers vary by only 1 kJ mol–1. Selection from the WA data of the series with acid = +HPyH and bases PyX (X = CN, Cl, H, Me, NMe2) gives a linear correlation (r2 = 0.97) of DHrxn against DH‡ with a = 0.48; selection of the related series with base = PyH and acids +HPyY (Y = CN, Cl, H, Me, NMe2) gives a very similar linear correlation (r2 = 0.98) with a = 0.52. Each of these two series has a range of reaction enthalpies extending either side of the DHrxn = 0 by about the same amount. However, if one selects the series with acid = +HPyCN and the same five bases, a fair linear correlation (r2 = 0.81) of DHrxn against DH‡ is obtained with a slope of 0.24, whereas with base = PyCN and variation of the acid a good linear correlation (r2 = 0.98) with a slope of 0.76 is obtained. This marked difference in the value of the Brønsted coefficient arises not from variation in the intrinsic barrier but because the former series covers an exothermic range of DHrxn whereas the latter covers an endothermic range. To comment that neither a = 0.24 nor a = 0.76 can be taken as a measure of the position of the TS along the reaction coordinate does not add value beyond the understanding that the correlation is intrinsically curved in consequence of the continuously varying nature of the transition structure. The four examples of PT simulations discussed above employed a variety of MO methods, giving rise to wide variation in the intrinsic barriers. The large intrinsic
19.3 FERs from MO Calculations of PESs
barriers obtained by ABK [34] for ROH/–OR identity reactions ( DHint‡ = 65, 79, 74 and 69 kJ mol–1, respectively, for n = 0, 1, 2 and 3 in CH(3–n)FnCH2OH/CH(3–n) FnCH2O–) might arise purely from errors in the MNDO Hamiltonian, but they might also be due to overestimated O···O distances; ABK did not report their geometries. We have already noted that an increase of 0.35 in the N···N distance for PT in NH4+/RNH2 complexes [35] raises the HF/4-31G intrinsic barrier by 59 kJ mol–1; SR reported a barrier of 15.9 kJ mol–1 for the NH4+/NH3 identity reaction at the HF/4-31G with constrained geometry (N···N = 2.731 ) [35], as compared with 7.7 kJ mol–l for reaction through the true transition structure (N···N = 2.594 ) [37]. Intrinsic barriers are also very sensitive to the basis set and the degree of electron correlation. Table 19.1 collects values for MeOH/–OMe computed for HF/6-31G(d) optimised geometries [42]: p polarisation functions on hydrogen atoms lower the intrinsic barrier, whereas s and p diffuse functions on carbon and oxygen atoms raise it; inclusion of electron correlation at the MP2 level markedly reduces the intrinsic barrier; the values vary over an 18 kJ mol–1 range. Table 19.1 also contains data for NH3/–NH2 computed for MP2/6-31+G(d,p) optimised geometries [43]: extra polarisation functions may either raise or lower the intrinsic barrier, whereas improved methods for electron correlation give lower intrinsic barriers than Hartree–Fock theory; the values vary over a 24 kJ mol–1 range. Furthermore, inclusion of zero-point energy and the thermal energy correction for 298 K (using HF/6-31+G(d,p) frequencies scaled by 0.9) together serve to reduce the intrinsic barrier by about 14 kJ mol–1. The “best” estimate for the NH3/–NH2 intrinsic barrier [QCISD(T)/6-311+G(d,p)//MP2/6-31+G(d,p) + DEzpe + Ethermal(298 K)] is about 5 kJ mol–1. Wu, Shaik and Saunders [44] have used a VB method to analyse the factors contributing to intrinsic barriers for identity PTreactions between neutral acids A–H and anionic bases A–: they note that the reactant- and product-like covalent VB structures A–H A– and A– H–A alone do not provide an adequate description, and point out the importance of triple-ion VB structures A– H+ A– . In summary, these examples of MO simulations for gas-phase PT (and many more similar studies for hydrogen atom [45] or hydride transfer [46]) reactions clearly demonstrate the qualitative validity of quadratic FERs (such as the Marcus relation) over wide ranges of thermodynamic reaction asymmetry, and of approximately linear FERs over relatively narrow ranges. Quantitatively it remains a very demanding task for electronic structure methods to predict intrinsic barriers or kinetic activation energies with high accuracy: while feasible for single calculations, high-level calculations for families of PT reactions are not performed routinely even for gas-phase reactions, let alone in solution. Finally it may be noted that simulations yielding Brønsted coefficients outside the normal range of 0 > a > 1 (e.g. hydrogen-atom transfer in R–H + Cl (R = Me, Et, iPr, tBu) [45a]) or failure to obtain any sort of sensible FER at all (e.g. nucleophilic addition to a carbonyl group concerted with PT [47], cf. HYW [38]) probably indicates that the TSs involve structural features not present in either the reactants or products [48]. This type of behavior sometimes manifests itself in terms of large variations in Marcus intrinsic barriers [6c].
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19 Theoretical Simulations of Free Energy Relationships in Proton Transfer Tab. 19.1 Method dependence of intrinsic barriers calculated
with molecular orbital theory. Energy method
Intrinsic barrier / kJ mol–1
MeOH/–OMe [a] HF/6-31G(d)
9.2
HF/6-31G(d,p)
6.4
HF/6-31+G(d)
12.2
MP2/6-31G(d)
–1.8
MP2/6-31G(d,p)
–5.5
MP2/6-31+G(d,p)
0.1
H2NH/–NH2[b] basis set MP2/6-311+G(d,p)
16.3
MP2/6-311+G(2df,p)
13.8
MP2/6-311+G(3df,2p)
17.2
electron correlation HF/6-311+G(d,p)
37.7
MP2/6-311+G(d,p)
16.3
MP3/6-311+G(d,p)
20.5
MP4/6-311+G(d,p)
18.4
QCISD(T)/6-311+G(d,p)
18.8
thermodynamic corrections[c] DEzpe(0 K) DEthermal(298 K)
–10.0 –3.8
a Ref. 42; geometries calculated at HF/6-31G(d). b Ref. 43; geometries calculated at MP2/6-31+G(d,p). c Ref. 43; geometries calculated at HF/6-31+G(d,p)
19.4 FERs from VB Studies of Free Energy Changes for PT in Condensed Phases
19.4 FERs from VB Studies of Free Energy Changes for PT in Condensed Phases
Warshel and coworkers have employed the empirical valence-bond (EVB) method [49] to simulate FERs for PT [50] and other reactions [51]. The PT step between two water molecules in the mechanism of the reaction catalysed by carbonic anhydrase was described as an effective two-state problem involving “reactant-like” (HOH)(OH2) and “product-like” (HO-)(HOH2+) VB structures [50a]. Diabatic energy curves for these two VB structures were calibrated to reproduce the experimental free energy change DGrxn for autodissociation in water, and the mixing of the reactant-like and product-like states (cf. Eres in Fig. 19.3) was calibrated to reproduce the observed activation energy DG‡ for the uncatalysed reaction in water. The magnitude of the off-diagonal matrix element Eres that coupled the two diabatics to yield the ground-state adiabatic energy surface depended upon the value of the reaction coordinate. Classical free energy surfaces for reactions in aqueous solution or in an enzyme were evaluated by a combination of EVB with a free-energy perturbation/umbrella sampling method [51a]: within each of many overlapping windows along the reaction coordinate, a series of molecular dynamics trajectories were propagated to sample many configurations of the surrounding water or protein. The reaction coordinate used was not a geometrical parameter but rather the difference in energy between the reactant and product diabatic states. This approach did not attempt to evaluate PESs of reacting fragments but instead fit them to known experimental (or theoretical) results; however, it did focus upon the important issue of how changing the environment (from water to enzyme) affected the quantum mechanical region of the chemical reaction. It turns out that charge-transfer reactions, such as this, follow the linear response approximation in solution [51a, 52] and in enzymes [50a, 53], meaning that the diabatic energy curves are quadratic. Consequently, the (kinetic) activation free energy on the adiabatic surface is related to the (thermodynamic) reaction asymmetry according to Eq. (19.12). DG‡ = DGint‡ + 12 DGrxn + DGrxn2/16DGint‡ – Eres‡ + (EresR)2/(DGrxn + 4Gint‡)
(19.12) The first three terms on the right-hand side correspond to the Marcus relation for the nonadiabatic case where there is no coupling between the diabatic energy states (i.e. Eres = 0 at all values of the reaction coordinate). The fourth and fifth terms reflect the effect of the adiabatic coupling of the two surfaces on the transition state and reactant state, respectively, and EresR < 12|DGrxn + 4DGint‡|. The initial work of Warshel, Hwang and qvist [50a] for PT in water and in carbonic anhydrase (a zinc metalloenzyme) reported FERs simulated in two ways. First, the autodissociation in water catalysed by a metal ion was studied using explicit Zn2+, Mg2+, Ca2+ and Na+ cations. Second, the energy of the product diabatic curve (for the ionic VB structure) was shifted vertically in order to change
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19 Theoretical Simulations of Free Energy Relationships in Proton Transfer
the value of DGrxn for PT in both water and the enzyme active site. Both methods gave apparently linear Brønsted correlations, with the points for substitution of the catalytic metal ions lying on the same line as those for parametrically changing the reaction asymmetry in water. The slopes of both lines were similar (a » 0.5) but the intrinsic barriers at DGrxn = 0 were ~46 and ~21 kJ mol–1, respectively, for the reactions in water and catalysed by carbonic anhydrase; the lower value for the enzyme reflects stabilisation of the transition state. However, the reaction asymmetry is less endoergic in the enzyme than with the Zn2+-catalysed reaction in water, suggesting a thermodynamic component to the enzyme catalysis as well as a kinetic component. A later paper by Hwang and Warshel [50b] considered the role of quantum-mechanical nuclear motions using the quantized classical path approach: it was found that while these corrections could be quite large, they were not drastically different for PT in the enzyme than for PT in aqueous solution. This study found the reorganisation energies (Fig. 19.3) to be about 250 and 100 kJ mol–1, respectively, for the enzymic and nonenzymic reactions. These values correspond to Marcus intrinsic barriers (as given by the intersection of the diabatic curves for DGrxn = 0) of ~60 and 25 kJ mol–1, respectively. In contrast, the Marcus intrinsic barrier deduced by phenomenological fitting to experimental data for carbonic anhydrase gave a Marcus intrinsic barrier of only 6 kJ mol–1 [54]. The discrepancy was suggested to arise for two reasons: first, the reaction studied experimentally might involve more than an elementary step, and thus more than two intersecting parabolas; second, the conventional Marcus relation (Eq. (19.6)) might not be valid for reactions involving strong coupling between the reactant and product diabatic states, for which Eq. (19.12) would be more appropriate. Recently, Schutz and Warshel [50c] re-examined this problem and found that the FER reflected a much more complex situation than previously thought: they suggested the PT process involved three or more parabolic free energy surfaces rather than the two assumed in the simple Marcus treatment. Their analysis reproduced the strongly curved observed FER without using any adjustable parameters and, in contrast to the result obtained from application of a two-parabola Marcus treatment [54], they found the work function to have a negligible value. Their threestate EVB description considered PT from an active site Lys or His residue to the zinc-bound hydroxyl by means of a bridging water molecule, as in Eq. (19.13), with each of the elementary steps being treated by Eq. (19.12). BH+(H2O)b(OH–)aZn2+ fi B(H3O+)b(OH–)aZn2+ fi B(H2O)b(H2O)aZn2+
(19.13)
They argued that the Marcus-like behavior of the observed FER was not due to transition to the Marcus inverted region but to change in energy of the intermediate; as the overall PT becomes more exoergic, the reaction rate increases but then starts to decrease as the first step becomes rate limiting instead of the second step. Schutz and Warshel [50c] emphasised that their simulation approach was based on realistic molecular parameters obtained while starting from the the X-ray structure of the protein and reproducing the relevant pKas and reorganisation energy.
19.4 FERs from VB Studies of Free Energy Changes for PT in Condensed Phases
Interpretation of numerical simulations in terms of a (modified) Marcus treatment provides valuable insight owing to the important distinction between kinetic and thermodynamics factors in reactivity and catalysis. Feierberg, Cameron and qvist [55] applied the EVB methodology to simulate the reaction catalysed by glyoxalase I. They proposed the rate-limiting step to be PT from carbon on the substrate to a glutamate residue, forming a high-energy enolate intermediate. Simulated LFERs for the PT step revealed that the effect of an active-site divalent metal cation was mainly to reduce DGrxn with a rather smaller contribution to the activation energy reduction coming from a decrease in the reorganisation energy k. Kiefer and Hynes [56] have developed a quadratic FER for acid-base ionization PT reactions (Eq. (19.14)) in a polar environment in the proton adiabatic regime, in which the proton is treated quantum mechanically but does not tunnel. A–H···B fi A–···X–B+
(19.14)
Their approach is based on a two-state VB treatment involving neutral reactant and ionic product VB structures as in Eq. (19.14), and the reaction coordinate is a solvent coordinate. Strong electronic coupling between the VB states produces the ground electronically adiabatic surface on which the reaction occurs, similarly to Warshel’s EVB method. The underlying picture of PT is very different from the conventional view implicit in the examples discussed in Section 19.3. A PT reaction is driven by configurational changes in its surrounding polar environment and the activation free energy is largely determined by the reorganisaton of this environment rather than by the height of any potential barrier in the coordinate of the transferring proton. The rapidly vibrating proton adiabatically follows the slower rearrangement of the environment: evolution of the solvent coordinate leads to an evolving proton potential pattern, in which the proton is initially bound to a donor in the reactant state, to a TS with the proton delocalised to a degree between the donor and acceptor groups, and finally to the product state with the proton bound to the acceptor. In the proton adiabatic regime the quantised proton vibrational level lies above the proton barrier at the TS along the coordinate for rearrangement of the solvent environment: at the TS the proton potential is a double well, but the free energy barrier for PT is located along the solvent coordinate, not the proton coordinate. The resulting FER is given by Eq. (19.15), where a0 is the Brønsted coefficient at Grxn = 0 and a0¢ is the first derivative of the Brønsted coefficient also at DGrxn = 0. DG‡ = DGint‡ + a0Grxn + 12 a0¢DGrxn2
(19.15)
In this model the intrinsic barrier is governed by the solvent reorganisation, modulated by certain electronic structural changes, and the change in the combined zero-point energy (ZPE) of the proton and the hydrogen-bond vibrations to reach the TS in the solvent coordinate. Involvement of the proton ZPE in the intrinsic barrier is one key difference between this model and the conventional view of PT; in the latter there is no such contribution because the proton coordi-
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19 Theoretical Simulations of Free Energy Relationships in Proton Transfer
nate is the reaction coordinate, whereas in the former it is transverse to the reaction coordinate. Although application of this new approach to specific examples of PT is still awaited, nonetheless it is of considerable interest that the FER of Eq. (19.15), which is clearly related to the Marcus equation, is obtained from the proton adiabatic picture that differs so fundamentally from the traditional view of PT. A valuable aspect of the new approach is that it yields an analytical expression for the intrinsic barrier in terms of its microscopic ingredients, whereas usually in the Marcus treatment it is merely a phenomenological parameter with no clear relation to features of molecular structure and bonding.
19.5 Concluding Remarks
Among the many topics not dealt with in this chapter are intrinsic barrier asymmetry [57], disparity/tightness and their relation to observed Brønsted coefficients [45a, 58], the nitroalkane anomaly and role of additional VB states dissimilar from reactants and products [59], and several other interesting models for FERs [60, 61]. This reviewer was surprised at the lack, as yet, of applications of hybrid quantummechanical/molecular-mechanical methodology (other than EVB-based methods) for simulations of FERs for any chemical reactions, let alone PT. However, the subject is alive and well, and it is to be expected that many more theoretical simulations of FERs for PT will be performed in the relatively near future.
References 1 I. H. Williams, Chem. Soc. Rev. 1993, 22, 2
3 4 5 6
277–283. (a) H. Eyring, M. Polanyi, Z. Phys. Chem. 1931, 12B, 279–311; (b) R. A. Ogg, M. Polanyi, Trans. Faraday Soc. 1935, 31, 604–620; (c) M. G. Evans, M. Polanyi, Trans. Faraday Soc. 1935, 31, 875–894; (d) H. Eyring, J. Chem. Phys. 1935, 3, 107–115; Chem. Rev. 1935, 17, 65–77. L. P. Hammett, Chem. Rev. 1935, 17, 125–136. W. P. Jencks, Chem. Rev. 1985, 85, 511–527. R. P. Bell, Proc. R. Soc. London, Ser. A 1936, 154, 414–429. (a) R. A. Marcus, J. Phys. Chem. 1968, 72, 891–899; (b) A. O. Cohen, R. A. Marcus, J. Phys. Chem. 1968, 72,
7 8
9
10
4249–4256; (c) R. A. Marcus, J. Am. Chem. Soc. 1969, 91, 7224–7225. G. S. Hammond, J. Am. Chem. Soc., 1955, 77, 334–338. (a) M. G. Evans, M. Polanyi, Trans. Faraday Soc. 1936, 32, 1333–1360; (b) M. G. Evans, M. Polanyi, Trans. Faraday Soc. 1938, 34, 11–24. (a) E. R. Thornton, J. Am. Chem. Soc. 1967, 89, 2915–2927; (b) E. K. Thornton, E. R. Thornton, in Transition States of Biochemical Processes, Ed. R. D. Gandour, R. L. Schowen, Plenum, New York, 1978. J. E. Leffler, Science, 1953, 117, 340–341; J. E. Leffler, E. Grunwald, Rates and Equilibria of Organic Reactions, Wiley, New York, 1963.
References 11 (a) W. P. Jencks, Chem. Rev., 1972, 72,
705–718; (b) D. A. Jencks, W. P. Jencks, J. Am. Chem. Soc. 1977, 99, 7948–7960. 12 R. A. More O’Ferrall, J. Chem. Soc. B 1970, 274–277. 13 (a) J. R. Murdoch, J. Am. Chem. Soc. 1972, 94, 4410–4418; (b) J. R. Murdoch, D. E. Magnoli, J. Am. Chem. Soc. 1982, 104, 3792–3800. 14 M. J. S. Dewar, D. A. Dougherty, PMO Theory or Organic Chemistry, Plenum Press, New York, 1975. 15 J. R. Murdoch, J. Am. Chem. Soc. 1983, 105, 2159–2164. 16 S. Sato, J. Chem. Phys. 1955, 23, 592–593. 17 (a) H. S. Johnston, C. Parr, J. Am. Chem. Soc. 1963, 85, 2544–2551; (b) H. S. Johnston, Adv. Chem. Phys. 1960, 3, 131–170. 18 R. A. Marcus, J. Chem. Phys. 1956, 24, 966–978. 19 D. Rehm, A. Weller, Isr. J. Chem. 1970, 8, 259–271. 20 N. Agmon, R. D. Levine, J. Chem. Phys. 1979, 71, 3034–3041. 21 R. P. Bell, J. Chem. Soc., Faraday Trans. 2 1976, 2088–2094. 22 W. J. le Noble, A. R. Miller, S. D. Hamann, J. Org. Chem. 1977, 42, 338–342. 23 (a) E. S. Lewis, Top. Curr. Chem. 1978, 74, 31; (b) E. S. Lewis, C. C. Shen, R. A. More O’Ferrall, J. Chem. Soc., Perkin Trans. 2 1981, 1084–1088. 24 J. L. Kurz, Chem. Phys. Lett. 1978, 57, 243–246. 25 (a) A. A. Zavitsas, J. Am. Chem. Soc. 1972, 94, 2779–2789; (b) A. A. Zavitsas, A. A. Melikian, J. Am. Chem. Soc. 1975, 97, 2757–2763. 26 S. Ahrland, J. Chatt, N. R. Davies, A. A. Williams, J. Chem. Soc. 1958, 276–288. 27 V. G. Levich, R. R. Dogonadze, E. D. German, R. M. Kuznetsov, Y. I. Kharkats, Electrochim. Acta 1970, 15, 353–367. 28 (a) Footnote 44 in Ref. 14; (b) J. R. Murdoch, J. Mol. Struct. (THEOCHEM) 1988, 40, 447–476. 29 (a) R. B. Hammond, I. H. Williams, J. Chem. Soc., Perkin Trans. 2 1989, 59–66; (b) G. D. Ruggiero,
I. H. Williams, J. Chem. Soc., Perkin Trans. 2 2001, 448–458. 30 A. J. Kresge, in Proton-transfer reactions, Ed. E. F. Caldin, V. Gold, Chapman and Hall, London, 1975, pp. 179–199. 31 A. Pross, S. Shaik, Nouv. J. Chim. 1989, 13, 427–433. 32 W. P. Jencks, Bull. Soc. Chim. Fr. 1988, 218–224. 33 I. H. Williams, Bull. Soc. Chim. Fr. 1988, 192–198. 34 B. Anhede, N.-. Bergman, A. J. Kresge, Can. J. Chem. 1986, 64, 1173–1178. 35 S. Scheiner, P. Redfern, J. Phys. Chem. 1986, 90, 2969–2974. 36 S. Scheiner, Acc. Chem. Res. 1985, 18, 174–180. 37 H. Z. Cao, M. Allavena, O. Tapia, E. M. Evleth, J. Phys. Chem. 1985, 89, 1581–1592. 38 S. Hoz, K. Yang, S. Wolfe, J. Am. Chem. Soc. 1990, 112, 1319–1321. 39 I. H. Williams, P. A. Austin, Can. J. Chem. 1999, 77, 830–841. 40 A. J. Kresge, Chem. Soc. Rev. 1973, 2, 475–503. 41 R. P. Bell, Faraday Symp. Chem. Soc. 1975, 10, 7–19. 42 S. Wolfe, S. Hoz, C.-K. Kim, K. Yang, J. Am. Chem. Soc. 1990, 112, 4186–4191. 43 S. Gronert, J. Am. Chem. Soc. 1993, 115, 10258–10266. 44 W. Wu, S. Shaik, W. H. Saunders, J. Phys. Chem. A, 2002, 106, 11616–11622. 45 (a) H. Yamataka, S. Nagase, J. Org. Chem. 1988, 53, 3232–3238; (b) A. K. Chandra, V. Sreedhara Rao, Chem. Phys. 1995, 200, 387–393; (c) W. T. Lee, R. I. Masel, J. Phys. Chem. A 1998, 102, 2332–2341; (d) S. Gronert, C. Kimura, J. Phys. Chem. A 2005, 107, 8932–8938. 46 E.-U. Wrthwein, G. Lang, L. H. Schappele, H. Mayr, J. Am. Chem. Soc. 2002, 124, 4084–4092. 47 I. H. Williams, D. Spangler, G. M. Maggiora, R. L. Schowen, J. Am. Chem. Soc. 1985, 107, 7717–7723. 48 A. J. Kresge, J. Am. Chem. Soc. 1970, 92, 3210–3211. 49 A. Warshel, Computer Modeling of Chemical Reactions in Enzymes and Solutions, Wiley, Chichester, 1991.
601
602
19 Theoretical Simulations of Free Energy Relationships in Proton Transfer 50 (a) A. Warshel, J.-K. Hwang, J. qvist,
51
52
53
54
55 56
Faraday Discuss. 1992, 93, 225–238; (b) J.-K. Hwang, A. Warshel, J. Am. Chem. Soc. 1996, 118, 11745–11751; (c) C. N. Schutz, A. Warshel, J. Phys. Chem. B 2004, 108, 2066–2075. (a) J.-K. Hwang, G. King, S. Creighton, A. Warshel, J. Am. Chem. Soc. 1988, 110, 5297–5311; (b) A. Warshel, T. Schweins, M. Fothergill, J. Am. Chem. Soc. 1994, 116, 8437–8442; (c) Y. S. Kong, A. Warshel, J. Am. Chem. Soc. 1995, 117, 6234–6242. (a) R. A. Kuharski, J. S. Bader, D. Chandler, M. Sprik, M. L. Klein, R. W. Impey, J. Chem. Phys. 1988, 89, 3248–3257; (b) G. King, A. Warshel, J. Chem. Phys. 1990, 93, 8682–8692. (a) J. qvist, A. Warshel, J. Am. Chem. Soc. 1990, 112, 2860–2868; (b) A. Warshel, Pontif. Acad. Sci. Scr. Var. 1984, 55, 59–81; (c) A. Warshel, S. Russell, F. Sussman, Isr. J. Chem. 1987, 27, 217–224. D. N. Silverman, C. Tu, X. Chen, S. M. Tanhauser, A. J. Kresge, P. J. Laipis, Biochemistry 1993, 34, 10757–10762. I. Feierberg, A. D. Cameron, J. qvist, FEBS Lett. 1999, 453, 90–94. (a) P. M. Kiefer, J. T. Hynes, J. Phys. Chem. A 2002, 106, 1834–1849; (b) P. M. Kiefer, J. T. Hynes, J. Phys. Chem. A 2002, 106, 1850–1861.
57 (a) R. A. Marcus, Faraday Symp. Chem.
Soc. 1975, 10, 60–68; (b) G. W. Koeppl, A. J. Kresge, J. Chem. Soc., Chem. Commun. 1973, 371–373; (c) F. Wiseman, N. R. Kestner, J. Phys. Chem. 1984, 88, 4354–4358. 58 (a) M. M. Kreevoy, I.-S. H. Lee, J. Am. Chem. Soc. 1984, 106, 2550–2553; (b) E. Grunwald, J. Am. Chem. Soc. 1985, 107, 125–133. 59 (a) W. J. Albery, C. F. Bernasconi, A. J. Kresge, J. Phys. Org. Chem. 1988, 1, 29–31; (b) H. Yamataka, Mustanir, M. Mishima, J. Am. Chem. Soc. 1999, 121, 10223–10224; (c) J. R. Keefe, S. Gronert, M. E. Colvin, N. L. Tran, J. Am. Chem. Soc. 2003, 125, 11730–11745. 60 (a) S. J. Formosinho, J. Chem. Soc. Perkin Trans. 2 1987, 61–66; (b) L. G. Arnaut, S. J. Formosinho, J. Phys. Org. Chem. 1990, 3, 95–109; (c) L. G. Arnaut, A. A. C. C. Pais, S. J. Formosinho, M. Barroso, J. Am. Chem. Soc. 2003, 125, 5236–5246. 61 (a) S. Shaik, H. B. Schlegel, S. Wolfe, Theoretical aspects of Physical Organic Chemistry, Wiley, New York, 1992; (b) L. Song, W. Wu, K. Dong, P. C. Hiberty, S. Shaik, J. Phys. Chem. A 2002, 106, 11361–11370.
603
20 The Extraordinary Dynamic Behavior and Reactivity of Dihydrogen and Hydride in the Coordination Sphere of Transition Metals Gregory J. Kubas
20.1 Introduction 20.1.1 Structure, Bonding, and Activation of Dihydrogen Complexes
Transition metals can contain, within their coordination field, hydrogen in molecular (H2) and/or atomic (hydride) form. These types of metal–ligand complexes are unquestionably the most dynamic molecular systems known in terms of structural variability and atom motion/exchange processes. Until about 20 years ago, metals were known to contain only atomically bound hydrogen, that is, metal hydrides and metal hydride complexes (LnMHx, where L is an ancillary ligand). However the discovery by Kubas and coworkers [1] in 1983 of side-on coordination of a nearly intact dihydrogen molecule (H2) to a metal complex has led to a new paradigm in chemistry that is the subject of many review articles [2–10].
H
H LnM H η2-H2 complex
LnM H dihydride complex
Molecules containing only strong “inert” r bonds such as H–H in H2 and C–H in alkanes had previously been believed to be incapable of stable binding to a metal. However, dihydrogen complexes (referred to as g2-H2 or H2 complexes) that were only assumed to be unobservable intermediates in dihydride formation can be isolatable species, as exemplified by the first H2 complex, W(CO)3(PiPr3)2(H2) (Fig. 20.1) [1, 2]. The H–H distance is elongated to 0.89 here, versus 0.75 in free H2, indicating that the strong H–H bond is only partially broken. Hundreds of different H2 complexes with nearly every transition metal have now been established, and in many cases the nearly intact H2 ligand is reversibly bound, as in Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
604
20 Dynamic Behavior and Reactivity of Dihydrogen and Hydride
physisorbed H2. These species are part of a class of compounds called r complexes, which refers to the side-on 3-center interaction of the bonding electron pair in H–H or other X–H bonds with a transition metal center M (X = B, C, Si, etc) [2, 10]. The dihydrogen complexes are remarkable in that, aside from elemental H2 and materials containing weakly physisorbed H2, no other stable compounds containing H2 molecules had previously been known.
Figure 20.1 Molecular structure of W(CO)3(PiPr3)2(H2) showing intact H–H bond elongated to 0.82(1) . Lower phosphine is disordered. The actual H–H distance is longer (0.89 from solid state NMR) because rapid rotation of the H2 results in foreshortening of the neutron distance.
The metal-coordinated H2 is “activated,” a term used to describe the weakening of a chemical bond towards rupture when it is bound to a transition metal, as observed by the elongation of the H–H bond. This process, and indeed much of the structure/bonding/dynamic/exchange features of hydrogen in the coordination sphere of metals, can best be understood by examining the nature of the chemical bonding of H2 to metals. The nonclassical 3-center 2-electron bonding in M–H2 and other r-bond complexes is stabilized by backdonation (BD), that is the retrodative donation of electrons from a filled metal d orbital to the r* orbital of the H–H bond [2, 3]. This is analogous to the Dewar–Chatt–Duncanson model for olefin coordination in Scheme 20.1 [11]. BD is crucial in both increasing the strength of the M–H2 bonding and activating the H–H bond towards homolytic cleavage to dihydride [12] ligands. If the backbonding becomes too strong, for example if more electron-donating co-ligands are put on M, the r bond cleaves to form a
20.1 Introduction
dihydride because of overpopulation of H2 r*. The entire reaction coordinate for the activation and ultimate splitting of H2 on a metal can be mapped out and related to the degree of BD. This is dramatically demonstrated by the remarkable “stretching” of the H–H distance, dHH, as displayed within the large regime of known complexes with H2 bound to different metal–ligand fragments (Scheme 20.2) [2, 3]. A near continuum of dHH ranging from 0.82 to nearly 1.6 is observed by crystallographic (X-ray and neutron diffraction) and NMR methods for the hundreds of known stable H2 complexes. Much as in physisorbed H2, the dHH is relatively short ( 0.85–0.90 ) and the H2 is reversibly bound in “true” H2 complexes, sometimes referred to as Kubas complexes, as best exemplified by W(CO)3(PiPr3)2(H2). The elongated (or stretched) H2 complexes (dHH = 1.0–1.2 ) are the most dynamic species and the positions of the hydrogens are extremely delocalized [7], as will be shown below. Even longer dHH have been observed, at which point the complex is best viewed as a “compressed dihydride” containing weak H···H attractions. A type of complex originally synthesized in 1971 in Taube’s group, [Os(H2)(ethylenediamine)2(acetate)]+, shows a very long dHH [13] and is on the verge of becoming a dihydride, which it was originally believed to be! Complexes with dHH > 1.6 are considered to be hydrides, but even this is a subjective boundary. There is little H–H bonding interaction remaining when dHH becomes >1.1 , so intriguing questions arise such as “at what point is the bond broken?” By one criterion, the H–H bond can be considered “broken” when 1.34
H
+
H N
N
Os N
N OAc
σ*
π* –
– +
M +
C
+
+
π
–
C
+
–
– +
M +
–
H +
σ
H +
M–σ bond
M–π bond
Scheme 20.1
H–H BOND DISTANCES FROM CRYSTALLOGRAPHY AND NMR
H H
0.74 Å
M H 0.8-0.9 Å true H 2 complex
H
H
H
M
M
M H 1.0–1.2 Å
H M
H 1.36 Å
elongated H2 complex
H >1.6 Å hydride
Scheme 20.2
605
606
20 Dynamic Behavior and Reactivity of Dihydrogen and Hydride
dHH is twice the free molecule separation, 1.48 , at which point the bond order becomes zero [14]. Even before H2 complexes were discovered, Xa calculations performed in 1978 by Ginsberg [15] showed that significant H···H interactions occur even at dHH up to 1.9 and were believed to stabilize high coordination number polyhydrides such as [ReH9]2– and [ReH8(PR3)]–. Eisenstein also showed that weak long-range attractions exist between well-separated cis-hydride ligands [16]. The activation and splitting of H2 is very sensitive to the nature of the metal, the ancillary ligands, and the overall charge, all of which can affect the amount of electron BD to H2. Third-row metals, strongly donating ligands, and neutral charge favors elongation or splitting of the H–H bond (higher electron richness of metal increases BD), while first-row metals, electron-withdrawing ligands, and positive charge shortens the H–H distance. The binding site for hydrogen on a metal complex can thus be tuned electronically over a vast range, and the local ligand environment around the site can also be varied tremendously. Thus the activation process and associated hydrogen transfer processes on metal centers can feature extraordinary structural, bonding, and dynamic phenomena that are the subject of this chapter. 20.1.2 Extraordinary Dynamics of Dihydrogen Complexes
Long before the “nonclassical” dihydrogen complexes were discovered, classical polyhydride complexes had been known to be stereochemically nonrigid (also termed fluxional) in solution, as shown by investigations of complexes of the type MHn(PR3)4 (n = 1, 2, 4; M = Group 6, 8, and 9 metals) by Meakin, Muetterties and coworkers in the early 1970s [12]. All of these systems showed fluxional behavior, and low barriers for n = 1 or 2 were rationalized by a “tetrahedral jump” mechanism for rapid ligand exchange. The study of solution nuclear magnetic resonance line shapes was critical to the determination of mechanisms for intramolecular hydride exchange [12c]. Before H2 coordination was recognized, the fluxionality of polyhydrides was viewed as isolated H-atoms moving over the surface of the metal center. However, their association as H2 ligands as intermediate steps is now much more attractive, as will be discussed in detail. For example, for hydride site exchange in polyhydrides such as ML4H4 (M = Mo, W; L = P-atom donor), transient intermediates with a geometry very much like MH2(H2)L4 or trans-M(H2)2L4 with elongated dHH were considered possible, even in 1973 long before H2 complexes were actually discovered (Scheme 20.3). Since the dihydrogen ligand nearly freely rotates, that is, has a relatively low barrier to rotation (1–10 kcal mol–1), hydride ligand rearrangement could easily take place by rotating the intermediate H1–H2 ligand as shown. Many new examples of hydride fluxionality were later discovered, and the principle mechanistic aspects have been reviewed to include systems containing g2-H2 ligands [5a, 8, 17]. Fast exchange between terminal and bridging hydrides in dinuclear rhenium complexes has been shown calculationally to be facilitated by formation of dihydrogen-containing intermediates [18]. As will be shown, remarkably facile hydrogen site exchange between cis hydride and
20.1 Introduction
H1
H1...... H2
H2
P
P
P
P
P
M
P H3
H4
P M P H3 H4 rotate H1-H2
P
H2...... H1
H1
H2
P
P
P H3
H4
P
P
P M
M
P H3 H4
Scheme 20.3
H2 ligands can occur, even in the solid state at temperatures below 77 K, with activation barriers as low as 1.5 kcal mol–1! For the H2 ligand, the structure and dynamics are much more extensive and richer than for hydride ligands. These can include rotational/vibrational motion of g2-H2, binding and splitting of H2 (including equilibria between g2-H2/dihydride tautomers), transfer of hydrogen to substrates, heterolytic cleavage of H2, and r bond metathesis processes (Scheme 20.4). Several of these processes can occur simultaneously on a metal center and all will be discussed in more detail below. The dihydrogen ligand by itself is remarkably dynamic. Except for rare cases, g2-H2 rotates rapidly as in a propeller (librational motion is more accurate), even in the solid state. One of the key diagnostics for coordination of molecular H2 is in fact the observation by inelastic neutron scattering (INS) of rotational transitions for g2-H2 [19–22], which cannot exist for classical atomic hydrides. Most importantly, these extensive studies by Eckert and coworkers measure the barrier to rotation of H2 ligands and, as will be shown, consequently offer direct experimental proof of MfiH2 backdonation. The rotational transitions and barrier are very sensitive to even minor changes in ligand environment about M and provide valuable insight into the reaction coordinate for splitting of H2 on M and intramolecular interactions. Hydrogen reorientation among either identical or inequivalent sites is extremely complex because it can involve quantum-mechanical phenomena such as tunneling (in H2 rotation) and exchange coupling. As will be shown, the latter is an NMR effect in certain polyhydrides that undergo exchange of chemically-inequivalent hydrogens.
607
608
20 Dynamic Behavior and Reactivity of Dihydrogen and Hydride
H2 rotational and vibrational motion H
H
H
Ln M
LnM
H
H
LnM
H
binding and splitting of H2 (homolytic cleavage)
LnM +
H
LnM
H
H
H
LnM
H
H
exchange with cis ligands D
D M
H
H
H M
H M
H
H
D
transfer of H2 to substrates (hydrogenation) CH2
CH2
CH2CH3
H
M
M
H
H
M + CH3CH3
heterolytic cleavage of H2 LnM
−
H
LnM
H + H+
H σ bond metathesis L + M
H H
L M
H H
L M
+
H H
Scheme 20.4
20.1.2 Vibrational Motion of Dihydrogen Complexes
The vibrational motion of M–H2 complexes has been analyzed in depth both spectroscopically and by calculation [2, 23]. The vibrational modes are completely different from those for metal hydrides, which typically have only two fundamental modes: M–H stretches in the range 1700–2300 cm–1 and M–H deformations at 700–950 cm–1. When diatomic H2 combines with a M–L fragment to form a g2-H2, five “new” vibrational modes in addition to mHH are created which are related to the “lost” translational and rotational degrees of freedom for H2 (Scheme 20.5). mHH is still present, but shifted to much lower frequency and
20.1 Introduction
Scheme 20.5
becomes highly coupled with the m(MH2) modes. The bands shift hundreds of wavenumbers on isotopic substitution with D2 or HD, which greatly facilitates their assignment. The entire set of bands has been identified only in the first H2 complex, W(CO)3(PR3)2(H2) (R= Cy, iPr) [23a]. All but ms(MH2), observed in both the IR and Raman, are weak, and most of the bands tend to be obscured by other ligand modes. In the Nujol mull IR spectrum, four bands, m(HH) at 2690 cm–1, mas(MH2) at 1575 cm–1, ms(MH2) at 953 cm–1, and d(MH2)in-plane at 462 cm–1, can be observed and shift to lower frequency for the D2 analog. The band at 442 cm–1 in the D2 complex is assigned to d(WD2)out-of-plane. The modes for H2 rotation about the M–H2 axis, s(H2), and also (MH2)out-of-plane near 640 cm–1 are observable only by inelastic neutron scattering (INS) methods (see below). 20.1.3 Elongated Dihydrogen Complexes
In elongated H2 complexes, experimental and computational studies indicate that the g2-H2 ligand is greatly delocalized and cannot be envisaged as a fixed, rigid unit [7]. Rapid motion of two hydrogen atoms occurs on a flat potential energy surface with a shallow minimum at the neutron-diffraction determined position of 1.2 for trans-[OsCl(H2)(dppe)2]+. The potential energy surface for the H–H vibrational stretch is so flat for some complexes that the stretch of this bond can traverse the entire distance range
Cl P
+ P
Os
P H
P H
0.85-1.6 Å
609
610
20 Dynamic Behavior and Reactivity of Dihydrogen and Hydride
from 0.85 to 1.60 with attendant variation in dMH at an energy cost of merely 1 kcal mol–1! The motion of the hydrogens is approximated in cartoon-like fashion in Scheme 20.6. It is astonishing that a bond as strong as H–H can be weakened so as to be lengthened by 0.8 without a significant rise in energy. The m(HH) and m(MH2) vibrational stretches in fact lose their meaning and the “normal” stretching modes have to be redefined to one along the arrows shown in the middle drawing at the top of Scheme 20.4 (low-energy mode) and one orthogonal to it (top right, high-energy mode). Importantly, the soft vibrational mode parallels the reaction coordinate for metal-induced H–H bond splitting, an unprecedented situation in chemistry. H H
M
1.6 Å
0.85 Å H
H Scheme 20.6
20.1.4 Cleavage of the H–H Bond in Dihydrogen Complexes
Scheme 20.4 shows a set of dynamics involving the binding and splitting of H2 that essentially represent the reaction coordinate for homolytic H–H bond cleavage or in the reverse process, the formation of H2 from a dihydride species. Remarkably these can be equilibrium processes in certain cases. Solutions of the complex W(CO)3(PiPr3)2(H2) were observed by NMR spectroscopy to contain about a 4:1 ratio of dihydrogen to dihydride complex, proving that side-on bonded H2 complexes were the first step in formation of hydride complexes (Eq. (20.1); P = PiPr3) [1b, 2]. O C
O C
W
H H
H
CO
P
P
CO W
P C O
P
(20.1)
H C O
The structure of the dihydride tautomer could not be determined in the solid state because it is an equilibrium species that could not be isolated from solution (where it has a fluxional structure). However calculations indicated that a pentagonal bipyramid with distal hydrides is the lowest energy structure [24]. Thermodynamic and kinetic investigations of the equilibrium reactions of the tungsten complexes showed the following parameters [25].
20.1 Introduction
t1/2 = R3 P CO OC W H C O P R R
3.2 x 10-5 s +H2 –H2 1.5 x 10-3 s
R3 P CO H OC W H C O P R3
agostic ∆H = –10.1 kcal mol
0.04 s
R3 P CO
oxid addn
OC W .02 s
dihydrogen –1
∆ H = 1.2 kcal mol
H
(20.2)
H C O P R3 dihydrogen –1
The precursor for the dihydrogen complex here contains a so-called “agostic” interaction [26], that is an intramolecular interaction of a C–H bond with the metal that stabilizes the electronically (16-electron) and coordinatively unsaturated W(CO)3(PiPr3)2 species. It is noteworthy that the splitting/formation of the H–H bond is much slower here than its binding to and dissociation from the metal. The above processes are directly relevant to catalysis of either hydrogenation reactions or the production of hydrogen, both of which have been well studied in industrial and biological systems. Metal-catalyzed transfer of hydrogen to substrates, both in heterogeneous and homogeneous (solution) systems, is a welltreated area of immense size and importance in chemistry and will not be discussed in detail here. Several books and reviews have been devoted to just homogeneous catalysis using inorganic and organometallic complexes, where the reaction mechanisms for hydrogen transfer can be best studied [27]. A review on catalytic processes that specifically involve dihydrogen complexes and other sigma complexes has recently been published [4]. Direct transfer from coordinated dihydrogen ligands to organic or other substrates has been shown to take place in certain systems, as illustrated in Scheme 20.4 for olefin hydrogenation. Conclusive evidence for direct transfer of the hydrogens in an H2 ligand to co-bound substrates is limited, however, partly because it is difficult to prove that cleavage of the H–H bond to give a dihydride complex does not occur first [2, 4]. There are actually two different pathways for cleavage of H–H (and X–H bonds): homolytic cleavage to a dihydride as discussed above and also heterolytic cleavage, that is breaking the H–H bond into H+ and H– fragments (Scheme 20.4). Both paths have been identified in catalytic hydrogenation and are available for other r bond activations. Heterolytic cleavage is one of the oldest and most widespread reactions of H2 on metal centers [28, 29]. H2 can bind in stable fashion to very electron-deficient cationic metal complexes that favor heterolysis nearly as well as to more electron-rich M. A proton can then split off from the H2 ligand and migrate to either an external Lewis base B, a cis-ligand L, or an anion (A), as shown in Scheme 20.7 and discussed in detail in a recent review [30]. Especially on electron-poor cationic complexes, the H2 ligand becomes highly acidic, i.e. polarized towards Hd––Hd+ where the highly mobile H+ readily transfers. Free H2 is an extremely weak acid with a pKa near 35 in THF, but when H2 is bound to a
611
612
20 Dynamic Behavior and Reactivity of Dihydrogen and Hydride
+ A–
L M
H δ+
L
H δ–
M
L
–HA H
HA
H
M
intramolecular
L
+ A–
δ–
+ A–
H2
M
L:
H δ+ M
+ A–
LH M
H δ–
H
+ A–
–LH M
H
intramolecular –
–
+A
+A L
H δ+
M
H δ–
:B
L H M H
B –[HB+][A]–
L M
H
intermolecular = COORDINATIVELY UNSATURATED SITE (e.g. 16e) OR WEAK SOLVENT LIGAN D
Scheme 20.7
highly electrophilic cationic metal center, the acidity of H2 gas can be increased spectacularly, by up to 40 orders of magnitude. The pKa of H2 can become as low as –6 and thus the acidity of g2-H2 becomes as strong as that of sulfuric or triflic acid [31]. Intramolecular heterolysis involves proton transfer to a cis ligand L (e. g. H or Cl) or to the counteranion of a cationic complex. This can occur via the intermediacy of a so-called cis-interaction, which essentially is a hydrogen-bonding like interaction of H2 with a cis ligand, such as a hydride, that has a partial negative charge (d–) [2, 5a].
δ–
σ*
H
+ H δ
M H
cis-interaction This is essentially the reverse of the protonation reaction commonly used to synthesize H2 complexes (all the reactions in Scheme 20.7 can be reversible). The intermediate here, M–H···H–A, is held together by dihydrogen-bonding, also known as proton-hydride bonding, where the M–H hydrogen is hydridic and the HA hydrogen is protonic [5e, 32]. The unconventional hydrogen bonds here can
20.1 Introduction
be comparable in strength to classical X–H···(lone pair) hydrogen bonds (3–7 kcal mol–1). Proton-hydride exchange has recently been observed in the reaction of CpRuH(PP) (PP =diphosphine) with CF3CO2H that led to a dihydrogen bonded complex with an extremely short RuH···HO2CF3 interaction [32e]. The proton-transfer process could occur via an intermediate state between a dihydrogen bond and a coordinated dihydrogen molecule. H–A
HA Ru–H*
Ru–H*
Ru
H*
H* dihydrogen bond
–H*A
H
A
H
Ru
A
Ru–H
Ru–H H*–A
(20.3)
short dihydrogen bond
In this and a related Fe system [32h], the counteranion CF3CO2– (A) could change between the two hydrogen atoms of the dihydrogen bond, thus changing the nature of both in the manner represented here, which explains the observed protonhydride exchange. In this way, this extremely short dihydrogen bond behaves as a dihydrogen molecule polarized by the counteranion. As will be shown below, interactions similar to dihydrogen bonds can also occur between H and H2 ligands (cis interaction between Hb and Hc shown below) and other r ligands (H···Si–H) and play an important role in hydrogen transfer/exchange processes.
Ha P
Hb Hc
Fe P
Reversible proton transfer to pendant basic sites can also occur (Eq. (20.4)) [32f ] and is facilitated by dihydrogen bonding interactions, e.g. Eq. (20.4B) where the OH and IrH hydrogens scramble via rotation of the H2 ligand. + NH .. 2
N P Ir P
OH2
+
H
Ir P H δ–
H O δ+
H
Ir
H
H δ–
P P
+ NH3 P
δ+
P
H
H
(20.4A)
+ N
N
Ir
–H2O
+ P
N
N
H
N
NH .. 2
H2
P N H Ir P H H O
(20.4B)
613
614
20 Dynamic Behavior and Reactivity of Dihydrogen and Hydride
H2 heterolysis related to Eq. (20.4) also occurs via intramolecular proton transfer between nitrogens on Ru complexes containing phosphinopyridine ligands, Cp*RuH[PPh2(pyridine)]2 [32i]. Intramolecular heterolysis of H2 is closely related to the well-known r-bond metathesis processes (Scheme 20.4) that generally occur on less electrophilic centers, especially d0 systems [2, 5a]. Although the heterolytic process here is formally a concerted “ionic” splitting of H2, as often illustrated by a four-center intermediate with partial charges, the mechanism does not have to involve such charge localization. In other words the two electrons originally present in the H–H bond do not necessarily both go into the newly-formed M–H bond while a bare proton transfers onto L or, at the opposite extreme, an external base. The term r-bond metathesis is thus actually a better description and may comprise more transition states than the simple four-center intermediate shown in Scheme 20.4, for example initial transient coordination of H2 to the metal cis to L and dissociation of transiently bound H—L as the final step. Intermolecular heterolysis involves protonation of an external base B to give a metal hydride (H– fragment) and the conjugate acid of the base, HB+. The bases can be as weak as organic ethers, and the [HB]+ formed can relay the proton to internal or external sites. Such intermolecular heterolysis can be the key step in catalytic processes on highly electrophilic metal centers [4, 9, 30], where the reaction mechanism must, almost by definition, be considered to involve direct transfer of hydrogen (as H+) from coordinated dihydrogen ligands. Finally, heterolysis of H2 can occur via several mechanisms that may or may not involve H2 complexes as stable intermediates. Summarizing, the dynamics and transfer of hydrogen in the coordination sphere of metals is remarkably rich and complex, as illustrated above. The exact positions of the hydrogens, including critical parameters such as the H–H distance, cannot be determined accurately in many H2 complexes because of the usual difficulty of observing hydrogen in the coordination sphere of metals by X-ray crystallography. Furthermore, the rapid rotation of the H2 ligand can significantly foreshorten the observed dHH, even in neutron diffraction crystal structures, requiring application of imprecise correction factors [33]. Because of the diminutive size and extraordinary dynamics of hydrogen, it is often difficult or impossible to distinguish the detailed mechanistic features for transfer of hydrogens, both intramolecularly and intermolecularly. Several complexes still defy attempts to determine whether the dihydrogen is molecularly or atomically bound because rapid intramolecular exchange hinders spectroscopic diagnostics such as NMR methodologies. The following sections will examine in more detail several of the dynamical and hydrogen transfer processes summarized in Scheme 20.4.
20.2 H2 Rotation in Dihydrogen Complexes
20.2 H2 Rotation in Dihydrogen Complexes
The H2 ligand undergoes rapid two-dimensional hindered rotation about the M–H2 axis, that is it spins (librates) in propeller-like fashion with little or no wobbling. This phenomenon has been extensively studied by neutron scattering methods and computationally [19–22]. Significantly, there is always at least a small barrier to rotation, DE, brought about by MfiH2 r* backdonation (BD) (Scheme 20.8). The r-donation from H2 to M cannot give rise to a rotational barrier since it is completely isotropic about the M–H2 bond. The barrier actually σ* P O + C + H OC M + + σ C - H O P
P OC
∆E= barrier O C H
M C O
H P
M
∆E, kcal
Cr Mo
1.17 1.32
W
1.90
Scheme 20.8
arises from the disparity in the BD energies from the d orbitals when H2 is aligned parallel to P–M–P versus parallel to OC–M–CO, where BD is less (though not zero). DE varies with M and other factors and can be analyzed in terms of the BD and other forces that lead to it, both by calculation and by a series of experiments where metal–ligand (M/L) sets are varied. In most “true” H2 complexes with dHH < 0.9 , the barrier is only a few kcal mol–1 and observable only by neutron scattering methods. It can be as low as 0.5 kcal mol–1 for symmetrical ligand sets, for example all cis L are the same, but has never been measured to be zero because minor geometrical distortions or crystal lattice-related effects are usually present. In the case of complexes with elongated H–H bonds or where rotation is sterically blocked as in [Cp¢2M(H2)(L)]+ (M = Nb, Ta), much higher barriers of 3–12 kcal mol–1 are observed by INS (see below) or even solution NMR methods [22e, 34]. Interactions of g2-H2 with cis ligands can significantly lower the barriers as will be shown below. The hindered rotation of g2-H2 is thus governed by a variety of forces, which can be divided into bonded (electronic) and nonbonded interactions (“steric” effects). The direct electronic interaction between M and H2 results from overlap of the appropriate molecular orbitals. Nonbonded interactions such as van der Waals forces between the g2-H2 atoms and the other atoms on the molecule may vary as g2-H2 rotates.
615
616
20 Dynamic Behavior and Reactivity of Dihydrogen and Hydride
20.2.1 Determination of the Barrier to Rotation of Dihydrogen
The geometry and height of the barrier can be derived by fitting the rotational transitions observed by inelastic neutron scattering (INS) techniques to a model for the barrier. The simplest possible model for the rotations of a dumbbell molecule is one of planar reorientation about an axis perpendicular to the midpoint of the H–H bond in a potential of two-fold symmetry. Application of a barrier to rotation rapidly decreases the separation between the lowest two rotational levels, which may then be viewed as a split librational ground state. Transitions within this ground state as well as those to the excited librational state (often called torsions) may be observed by INS. The former occur by way of rotational tunneling [35] since the wave functions for the H2 in the two wells 180 apart overlap. This rotational tunneling transition has an approximately exponential dependence on the barrier height, and is therefore extremely sensitive to the latter. It is this property that is exploited to gain information on the origin of this barrier. Both the rotational tunneling transition and the transitions to the first excited librational state can readily be observed by INS techniques [19–22, 35]. Neutrons are extremely well suited as probes for molecular rotations when the motion involves mainly H atoms. The INS studies allow observation of low-lying transitions within the ground librational state of the g2-H2 (tunnel splitting), which corresponds to the para (I = 0, J = 0) to ortho (I = 1, J = 1) transition for free H2 (120 cm–1 in liquid hydrogen). INS measurements are typically carried out at ~5 K using ~1 g of polycrystalline H2 complex sealed under inert atmosphere in aluminum or quartz sample holders. This measurement can be performed without regard to other hydrogen-containing ligands, which do not have observable excitations at low temperatures in the energy range of those of the H2. Typical intensities of the tunneling peaks in these complexes are in fact about 0.25% or less than that of the intense central elastic peak (Fig. 20.2). In most cases the ground-state rotational tunnel splitting, as well as the two transitions to the split excited librational state, are observed. Because the tunnel splittings (typically 1–10 cm–1) can be measured with much better accuracy than the librational transitions, the value for the barrier height V2 is usually extracted from the former. Prior to the discovery of H2 complexes, the only systems known to contain hydrogen molecules were H2 gas or H2 that was barely affected by its surroundings (as in physisorbed H2). The smallest splittings between the ortho- and para H2 state that had previously been observed were 4.8–10.5 cm–1 for H2 in K-intercalated graphite [36], and 30.6 cm–1 for H2 in Co ionexchanged NaA Zeolite [37]. In both of these cases H2 is in all likelihood physisorbed as no indication of H–H bond activation could be found. However, for the M(g2-H2) ground librational state, splittings between 17 and 0.6 cm–1 are observed at temperatures as high as 200 K. The signals shift to lower energy and broaden but remain visible into the quasielastic scattering region (Section 20.4.2). Observation of rotational tunneling, which is a quantum mechanical phenomenon, at such a high temperature is extraordinary: in all previous studies of this type involving CH3 or [NH4]+ the transition to classical behavior occurs well below 100 K.
20.3 NMR Studies of H2 Activation, Dynamics, and Transfer Processes
Figure 20.2 Rotational tunneling spectra for the closely related series of complexes M(H2)(CO)3(PR3)2 where M = Mo and R = Cy (top) and M = W and R = Cy (middle) or iPr (bottom). Note the change in energy scale between top and middle figures and the high sensitivity of the spectra to changes in metal and minor changes in phosphine ligand. The sharp splitting in the peaks in the lower spectrum is believed to be due to the disordered phosphine in the crystal structure (see Fig. 20.1).
20.3 NMR Studies of H2 Activation, Dynamics, and Transfer Processes 20.3.1 Solution NMR
The solution and solid-state 1H NMR spectra of H2 complexes are normally quite distinctive compared to hydride complexes. In complexes containing both H2 and hydride ligands, facile exchange between the hydrogens nearly always occurs, especially if these ligands are cis (Scheme 20.4). Scrambling occurs via an M–H3 (trihydrogen) transient (see Section 20.4), where a deuteride (D) ligand differentiates the
617
618
20 Dynamic Behavior and Reactivity of Dihydrogen and Hydride
hydrogens in Scheme 20.4. In most cases an averaged broad singlet results, which may not decoalesce at low temperatures; many complexes are highly fluxional even below –100 C (barriers as low as 1 kcal mol–1). The tautomeric equilibria between H2 and dihydride forms in solution can be observed by NMR in about a dozen complexes, including W(CO)3(PR3)2(H2) 1. The 7-coordinate dihydride tautomer 2 exists in about 20% concentration in Scheme 20.9 for P = PiPr3 and is not isolatable but is detectable by IR and NMR, which shows separate signals for the H2 and hydride ligands at or below room temperature. Spin saturation transfer experiments using both 31P and 1H NMR confirm that these signals correspond to equilibrium species [38]. The relaxation time T1 for the broad H2 signal is much shorter than for the hydride signals, as will be described below. The inequivalency for both the hydride and phosphine signals in Scheme 20.9 is consistent with the calculated pentagonal bipyramid geometry (Eq. (20.1)) [24], which is also observed crystallographically in the dihydride MoH2(CO)(Et2PC2H4PEt2)2 [39]. O C
O C
W H H
Ha
solution
CO
P
Pa
P
~4:1 ratio
C O (1)
CO W Pb
Hb
C O (2)
JHD = 34 Hz
NMR
δ = –4.3 (H2) δ = 33.5 (P)
–92 oC toluene-d8
T1 = 4 ms (H2) νHH = 2695 cm–1
δ = –2.15 (Ha), –4.5 (Hb) δ = 30.8 (Pa), 39.5 (Pb) T1 = 1.67 s (Ha and Hb)
νCO = 1993, 1913, IR hexane 1867, 1828 cm–1
νCO = 1969, 1856 cm–1
Scheme 20.9
The tautomerization process in Scheme 20.9 has been studied theoretically in regard to the equilibrium isotope effect (EIE), which was studied by calculation and predicts that deuterium should bind more favorably than hydrogen to the nonclassical site at 300 K [24b]. The experimental EIE values for H2 versus D2 addition to metal complexes, KH/KD, are usually inverse over a large temperature range (260–360 K), showing that counter-intuitively D2 binds more strongly to metals than H2 [23]. KH
H MLn
H2 + MLn H KD
(20.5)
D MLn
D2 + MLn D
20.3 NMR Studies of H2 Activation, Dynamics, and Transfer Processes
This is due mainly to isotopic factors that relate to the large number of vibrational modes for molecularly-bound H2 or D2, which offset the weakness of the D–D bond relative to the H–H bond. The values of KH/KD observed thus far are 0.36– 0.77 for formation of H2 complexes and 0.47–0.85 for complete splitting of the H–H bond to form hydrides. The single most important NMR spectroscopic parameter is the scalar coupling constant, 1JHD, for the HD isotopomer of an H2 complex (JHD without the superscript is normally used here to refer to the one-bond coupling). The signal becomes a 1:1:1 triplet (D has spin 1) with much narrower linewidth and is direct proof of the existence of an H2 ligand, since classical hydrides do not show significant JHD because no residual H–D bond is present. JHD for HD gas is 43 Hz, the maximum possible value (dHD is 0.74 ). A lower value represents a proportionately shorter dHD. JHD determined in solution correlates well with dHH in the solid state via the empirical relationships developed by both Morris [40] and Heinekey [41]: dHH = 1.42 – 0.0167JHD
[Morris]
(20.6)
dHH = 1.44 – 0.0168JHD
[Heinekey]
(20.7)
The input data for formulating these expressions, which differ only slightly, include dHH from both diffraction and solid-state NMR measurements. Unusual behavior in the temperature dependence of JHD is found in three complexes with elongated dHH, [Cp*Ru(H···D)(dppm)]+ and trans-[OsX(H···D)(dppe)2]+ (X = H, Cl), and gave initial indications of the highly delocalized bonding (Scheme 20.6) in these and related species (Cp* = C5Me5; dppm = Ph2PCH2PPh2; dppe = Ph2PC2H4PPh2) [7, 42–45]. Subsequent NMR studies by Heinekey of the HD, HT, and DT isotopomers of [Cp*Ru(H2)(dppm)]+ show remarkably high isotope and temperature dependence of the bond distance of the coordinated dihydrogen isotopomer (ranging from 1.034 for dDT at 204 K to 1.091 for dHD at 286 K) as determined by the various NMR J couplings [44]. This is attributed to the extremely flat potential energy surface which defines the H–H and M–H interactions in this complex, which allows the zero point energy differences among the various isotopomers to be directly reflected in dHH. The striking change of dHH with small changes in temperature is due to the thermal population of vibrational excited states that are only slightly higher in energy than the ground state, an unprecedented situation in a readily isolable molecule. The results provide direct experimental verification of the conclusions of DFT (density functional theory) studies by Lledos, Lluch, and coworkers who predicted, for example, that the bond distance for the T–T complex would be 10% shorter than in the corresponding H–H species [46]. A small class of polyhydrides such as [CpIrH3L]+, CpRuH3L, and Cp2NbH3 with hydrides that are separated by approximately 1.7 exhibit quantum-mechanical exchange coupling (QEC) with extraordinarily large JHH that can exceed 1000 Hz in some cases [47]. Quantum-mechanical tunneling of two protons through a
619
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20 Dynamic Behavior and Reactivity of Dihydrogen and Hydride
vibrational potential surface accounts for QEC; covalent bonding between the hydrogens is not needed. Such a phenomenon is extremely rare and has been seen previously for heavy particles (non-electrons) only in studies of 3He at cryogenic temperatures. The current belief is that QEC and related hydride dynamics are simply a manifestation of quantum-mechanical delocalization of light particles in a soft potential energy surface where very slight changes in structure can lead to dramatic changes in dynamic behavior (see Scheme 20.6 and related discussion). An osmium complex best described as a “compressed dihydride” (dHH = 1.46 ) is a good example here [47e]. Another standard, though more problematic, method for determining dHH in solutions of H2 complexes involves measuring the minimum value of the relaxation time, T1min, for the H nuclei of the metal-bound H2. This provides a reasonably accurate dHH because dipolar relaxation of one H by its close neighbor, the partner H of the H2 ligand, is dominant and T1 is proportional to the sixth power of dHH. The broadness of NMR resonances for H2 ligands was attributed by Crabtree in 1985 to rapid dipole–dipole relaxation, which gives very short values for T1 (normally <50 ms compared to >>100 ms for classical hydrides) [48]. This became a useful criterion for g2-H2 versus dihydride complexes, although extensive refinements were needed. The theory for dipole–dipole relaxation shows that T1 varies with temperature and goes through a minimum. Subsequently Crabtree and Hamilton developed a quantitative method for extracting dHH from the experimentally determined T1min [49]. Because T1 depends on the sixth power of dHH, it is extremely sensitive to the presence of hydrogens that are close together as in an H2 complex, and values as low as 3 ms (at 300 MHz) are observed. Furthermore, the dipolar relaxation usually dominates the relaxation (e.g. >95% for FeH2(H2) (PEtPh2)3). However, there can be several interfering factors, particularly if the H2 is bound to certain metals with a high magnetogyric ratio such as Co, Re, and Mn that can make substantial contributions [50]. Also, in polyhydride complexes with cis-hydrogens, all hydride–hydride interactions need to be considered. Corrections for this can be made in some cases, and measurement of T1min for both the H2 and HD isotopomers can be used to cancel out relaxation caused by M. For example, using the T1min values of 15.2 and 116 ms determined, respectively, for [Mn(CO)(dppe)2(H2)]+ and its HD isotopomer, both dHH (0.91(2) , compared to 0.89(1) by solid state NMR [51]) and dMnH (1.64(3) ) can be calculated using this subtraction method [52]. The fast internal rotation of g2-H2 that causes crystallographic problems can also effect the calculation of dHH from T1min if the rotational rate is faster than molecular tumbling. Although the term “spinning” H2 is often used, the H2 does not really spin like a propeller but undergoes rapid libration combined with less
Ph2 H H P Mn P Ph2 CO
Ph2 P P Ph2
+
20.3 NMR Studies of H2 Activation, Dynamics, and Transfer Processes
frequent complete rotation. This reorientational motion can effect dipolar relaxation, which Morris addresses by viewing fast H2 rotation much like methyl group rotation studied by Woessner, where dHH calculated from T1min is corrected by a factor of 0.793 [53]. The formulas for calculation are: d(HH) = 5.81[T1min (slow)/m]1/6
(20.8)
d(HH) = 4.61[T1min (fast)/m]1/6
(20.9)
m = spectrometer frequency in MHz. This methodology can only set limits on dHH, a longer one when the H2 rotational frequency is lower than the spectrometer frequency and a shorter one when rotation is faster. Structural and spectroscopic data for a large series of cationic complexes, [MH(H2)(diphosphine)2]+ (M= Fe, Ru), strongly reinforce this supposition. These complexes show large values of JHD of 29.5–32.8 Hz, giving dHH = 0.87–0.94 from Eqs. (20.6) and (20.7), which is consistent with only the dHH calculated from the fast-rotation formula (0.86–0.90 versus 1.09–1.15 for slow rotation). The uncorrected neutron diffraction value of dHH is 0.82(3) for [RuH(H2)(dppe)2]+ (dHH corrected for H2 rotation is 0.94 ). While these complexes seem to require the fast time-scale correction factor, Gusev and Caulton [54] point out that a greater number do not, including W(CO)3(P-i-Pr3)2(H2) which clearly has a rapidly reorientating H2. To rationalize this, the character of H2 reorientation must be examined. Inelastic neutron scattering studies generally show a double minimum sinusoidal potential for rotation (Section 20.2.1), but a smaller 4-fold term is often added as a correction for non-sinusoidal behavior such as wobbling off the plane of rotation. However in some cases, e.g. four identical ligands cis to H2 as in [MH(H2)(diphosphine)2]+ species, a 4-fold component to rotation truly exists (90 rotation) giving very low rotational barriers near 0.5 kcal mol–1 and a faster spinning H2. 20.3.2 Solid State NMR of H2 Complexes
As established by Zilm and coworkers, solid state 1H NMR is very effective in accurately determining dHH because the measurement is unaffected by rotational or other motion of the bound H2 [55]. Only a small amount of solid in powder form is required to observe the g2-H2 signals using broad-line techniques (Fig. 20.3). The basic principles are well established: isolated pairs of nuclei in a rigid solid experience a mutual dipolar interaction directly proportional to the average of the inverse cube of the internuclear distance. For a powder sample of an H2 complex, a normal Pake doublet line shape results (Fig. 20.3C), which can be used to calculate internuclear H–H distances within 1%. The patterns are quite sensitive to anisotropic motion, that is hindered rotation or torsion of the side-bound H2 about the M–H2 axis. This will not affect the H2 dipolar splitting when this axis is parallel to the applied magnetic field. One pair of temperature-independent
621
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20 Dynamic Behavior and Reactivity of Dihydrogen and Hydride
Figure 20.3 A, Solid state 1H NMR spectrum for W(CO)3 (PCy3)2(H2) without suppression of the phosphine ligand signal. B, Same as A except using ligand suppression sequence. C, Same as B except using perdeuterated phosphine ligands.
discontinuities in the Pake pattern is thus unaffected and is used to calculate dHH. The protons in ancillary ligands such as PCy3, where 33 protons are present, can cause problems since they obscure the very wide Pake pattern for the H2. However this can be averted by deuterating the ligands (Fig. 20.3C) or using a hole-burning ligand suppression technique at 77 K to avoid costly deuteration. The latter method relies on the homogeneous line shape of the strongly coupled ligand protons that can be saturated by application of a several millisecond weak pulse. However, the inhomogeneous Pake doublet for g2-H2 is not saturated, a small hole is burned in the pattern, and the majority of the line shape is unaffected (Fig. 20.3B). The first complex studied, W(CO)3(PCy3)2(H2), showed a dHH of 0.890 – 0.006 [55a], a value that can be considered to be more reliable than the value from neutron diffraction [0.82(1) ], which must be corrected for the effects of librational motion. As will be discussed below (Section 20.4.1), solid state NMR can also be used to study the dynamics of extremely facile hydrogen exchange processes, such as in IrClH2(H2)(PiPr3)2 [56]. Limbach and coworkers have carried out extensive solid-state NMR studies of H2 complexes, particularly in regard to hydrogen exchange processes and their quantum mechanical behavior [57]. A unified description of the effects of the coherent and incoherent dihydrogen exchange on the NMR and INS spectra of transition metal hydrides based on the quantum-mechanical density matrix formalism of Alexander-Binsch [58] has been proposed [57a]. The dynamic parameters of the line shape analyses are the exchange couplings or rotational tunnel splittings J of the coherent exchange and the rate constants k of the incoherent exchange. The temperature dependent values J and k were determined for Cp*RuH3(PCy3), including the kinetic HH/HD/DD isotope effects on the incoherent exchange, determined by NMR, and for W(CO)3(PCy3)2(H2), determined by INS. The temperature depen-
20.4 Intramolecular Hydrogen Rearrangement and Exchange
dence of J and k was interpreted qualitatively in terms of a simple reaction scheme involving, at each temperature, a ground state and a dominant ro-vibrationally excited state. Using formal kinetics it was shown that a coherent exchange in the excited state contributes to J only if this exchange presents the rate limiting reaction step, i.e., if vibrational deactivation is fast. This is the case for levels located substantially below the top of the barrier. A very fast coherent exchange of levels located close to the top of the barrier contributes only to k. This result reproduces in a simple way the quantum-mechanical results of Szymanski and Scheurer et al. [59]. The results concerning the coherent and incoherent exchange processes in these complexes are discussed in terms of the simplified reaction model. Solid-state deuterium NMR has also been employed in these types of studies. The 2H NMR spectra and spin–lattice relaxation rates of W(CO)3(PCy3)2(D2) have been measured in the temperature regime of 50 K to 300 K [57b]. The spectra have been analyzed employing a model of a combination of homonuclear dipolar D–D interaction and deuterium quadrupolar interaction and a D–D distance of 0.89 – 0.1 . The linewidth of the spectra exhibits a weak temperature dependence at temperatures above 150 K. This temperature dependence is interpreted as a slight decrease in the quadrupolar coupling with increasing temperature, which is an indication of a change in the M–D2 distance with changing temperatures. The spin–lattice relaxation data of the complex exhibit pronounced deviations from simple Arrhenius behavior at lower temperatures, indicating the presence of a quantum-mechanical tunneling process. This process is analyzed in terms of a simple one-dimensional Bell tunnel model. A comparison with INS data from the H2 complex reveals a strong isotope effect of 2 103 for the exchange rates of the deuterons. Bakhmutov has also utilized 2H NMR to determine deuterium spin– lattice relaxation times of D2 ligands and analyzed them in terms of fast internal D2 motions, including free rotation, librations, and 180 jumps [60]. The results led to a criterion for using the relaxation data to distinguish fast-spinning dihydrogen ligands as discussed in Section 20.3.1.
20.4 Intramolecular Hydrogen Rearrangement and Exchange
Soon after the discovery of H2 complexes facile intramolecular site exchange of H atoms between H2 and hydride ligands was found to occur [61]. The 1H NMR signals of the cis H2 and hydride in [Ir(H2)H(bq)(PPh3)2]+ coalesce at 240 K because of exchange, and even the hydride trans to H2 in [Fe(H2)H(dppe)2]+ exchanges positions with the H atoms of g2-H2.
exchange
Ph 2 H H P Fe
Ph 2 P
P Ph 2
P Ph2
H
+
623
624
20 Dynamic Behavior and Reactivity of Dihydrogen and Hydride
Many new examples include more sophisticated systems with four or more H-donor ligands that display very complex dynamic processes. The complexes encompass early to late metal species such as [Cp*MoH4(H2)(L)]+ [62], [ReH4(CO)(H2)(L)3]+ [63], [RuH(H2)(CO)2(L)2]+ [64], and [TpIrH(H2)(L)]+ [65] (Tp = tris(pyrazolyl)borate; L = PR3). Ab initio calculations show that a variety of mechanisms are possible for the site exchange [62, 66]. For example a reductive elimination/oxidative addition pathway through a bis(H2) intermediate is proposed for the Re complex, but for cis-[FeH(H2)(L)4]+ and the Cp*Mo species, the preferred pathway is via an M–(H3) (trihydrogen) transition state (Scheme 20.10). The possible existence of g3-H3 ligands has been examined by Burdett in his detailed theoretical studies of polyhydrogen species, Hn (n = 3–13) [67]. “Open” (linear H3–) or “closed” (triangulo H3+) structures are possible. A trihydrogen complex has yet to be isolated, although there is experimental evidence for its intermediacy in facile tautomerization and exchange reactions (see Eq. (20.12) below and Section 20.4.1) [63a]. Polyhydrogen species are known mass spectrometer molecules, and H3+ has a closed (triangulo) structure with a calculated dHH of 0.87 [68] and can be viewed as an H2 complex of H+. However, a trihydrogen ligand is more likely to have an open linear structure best represented as H3–, as supported by calculations. The essential features of fluxionality among hydride and H2 ligands, including mechanistic aspects, are well reviewed by Gusev and others [8, 9, 17]. The intramolecular dynamics will thus only be summarized here and will mainly focus on g2-H2 containing systems. H*
H*
H
H M
M
or
M
H
H*
H
*H
H
H H
M
H rotate H M
H
H
H*
M
H
H
H*
M
H H*
open trihydrogen complex
closed trihydrogen complex
Scheme 20.10
For the simple H2/hydride situation, two general types of exchange mechanisms can be envisaged. The first is dissociative and involves homolysis of the H– H bond to produce a fluxional trihydride intermediate that facilitates intramolecular exchange of H atoms between either adjacent or distal H2 and H ligands. H Ln M
H*
H H
Ln M
H
H* H
Ln M
H
H H*
Ln M
H
(20.10) H*
20.4 Intramolecular Hydrogen Rearrangement and Exchange
H
H*
Ln M
Ln M
H
H
H
H
H H*
Ln M
H
H
Ln M
(20.11)
H*
H*
Equations (20.10) and (20.11) are controlled by the same factors that affect the kinetics of homolytic splitting of H2. The second mechanism is associative and implies a trihydrogen intermediate or transition state such as shown in Scheme 20.4. The complex [Re(H2)(H)2(PMe2Ph)3(CO)]+ provides the first and only good experimental evidence for an associative exchange mechanism that involves such a rotating H3 intermediate [63]. The latter could occur in other complexes such as Fe(H)2(H2)(PEtPh2)3, which contains a cis-interaction between H2 and a hydride that can be considered a nascent H3 ligand [69]. It is not possible to freeze out the JHD for the M(H)2(HD) isotopomer in such systems containing H2 plus two or more hydrides, even at the lowest attainable temperature for solution NMR. However even without NMR data, indirect evidence for unstable, fluxional H2 and/or H3 intermediates can be obtained merely from isotope exchange reactions using D2 gas. Before M–H2 complexes were discovered, Brintzinger proposed that a transient d0 complex, Cp*2ZrH2(D2), mediated H/D exchange in Cp*2ZrH2 via an associative transition state species [Cp*2Zr(H)(DDH)]‡ as in Eq. (20.12) [70]. H
H
D2
Cp* 2Zr
–D2
H
D
Cp* 2Zr
D H
‡
H D D
Cp* 2Zr H
(20.12) H
–HD Cp* 2Zr HD
D
Here the Zr center could not give a dissociative pathway because ZrVI is an unattainable oxidation state. This was one of the first examples of r-bond metathesis and postulation of a transient M–H3 species. In the six-hydrogen system, [CpM(H)4(H2)(PR3)]+ (M = Mo, W), stretching the H2 toward an adjacent hydride is a low energy process that also leads to a transition state with H3– character [62]. The calculated barriers for exchanges are thus only ~4 kcal mol–1 (for R = H), in agreement with the inability to decoalesce the hydride NMR signals, even at 133 K. Using 13C solution NMR, Heinekey measured the rate of cis H/H2 exchange in [RuH(H2)(13CO)2(PCy3)2]+ to be ~103 s–1 at 130 K, with DG‡120 = 5.5 kcal mol–1 [64]. Remarkably, decoalescence of the averaged 13CO signal does not occur until 130 K and rapid cleavage of the H–H bond occurs even for this relatively unactivated H2 complex (dHH = 0.9 ). This is consistent with a highly concerted exchange process with a Ru-trihydrogen-like transition state.
625
626
20 Dynamic Behavior and Reactivity of Dihydrogen and Hydride
Gusev and Berke highlight two types of principal motion that are often distinguishable in the dynamic behavior of metal hydrides [17]. These are a migratory (M) type and a replacement (R) type (Scheme 20.11). In the M-type exchange one or more ligands migrate from their original inequivalent positions to give inversion of the entire structure. Subsequent replacement of the migrated ligands by each other in their former coordination sites does not occur. The R-type exchange involves a physical rearrangement of identical atoms or ligands that exchange their exact positional coordinates. Hydride Ha replaces Hb at the same time Hb takes the former place of Ha. The simplest example of R exchange is rotation of g2-H2 as discussed above. The M and R mechanisms can be distinguished by NMR if they are not simultaneous events on the same time scale. Migratory (M) type exchange 131o
X
H1a
Ir
X
Ir Hb
H2b
o
156
H2a
Ha
73o
X
Ir H1b
Replacement (R) type exchange H1a
X
X
Ha
Ir
Ir
Hb
H2b IrH2X(PtBu2Ph)2
X
H1b Ir H2a
(X = Cl, Br, I)
Scheme 20.11
The R mechanism is important because polyhydrides can readily interchange cis-hydrides by transient formation of H2-like ligands where dHH is shortened to 1.3–1.4 (see Scheme 20.3). For example the 16 electron trihydrides OsH3X (PiPr3)2 (X = halide) have a structure with Ha and Hc exerting a strong mutual trans influence resulting in bending toward Hb (Eq. (20.13)). P aH
~60 2 bH
Ha
Os H 2c
1
P
P
P Hb
X
o
Os Hc
X
X
P
aH
2 cH 1
(20.13)
Os H 2b P
Formation of an intermediate with an elongated g2-H2 allows Hc to interchange position with Hb, which has been studied both experimentally and theoretically [71, 72]. The rate of site exchange increases slightly from X = I to X = Cl and the highest barrier, 8.8 kcal mol–1 (DG‡ at 205 K), is for the former. These complexes display large exchange couplings (QEC) between the hydrides (AB2 patterns) with J(H1–H2) values of 920 (Cl), 550 (Br), and 280 Hz (I) at –100 C (see Section
20.4 Intramolecular Hydrogen Rearrangement and Exchange
20.3.1). The observations indicate that exchange couplings can operate between such hydrogens if they are involved in R-type exchange [72]. A complex with an elongated H2 ligand, [Cp*OsH2(H···H)L]+, exchanges hydrogen apparently via a tetrahydride intermediate [22c]. 20.4.1 Extremely Facile Hydrogen Transfer in IrXH2(H2)(PR3)2 and Other Systems
Psuedo-octahedral complexes MXH2(H2)L2 with H2 cis to a hydride are extremely fluxional and show M-type exchange. A well-studied case is IrClH2(H2)(PiPr3)2 where INS studies showed the lowest barrier to H2 rotation (0.51(2) kcal mol–1) ever measured for a metal complex [73, 74]. Solid-state 1H NMR studies on a single crystal provided key initial information on the fluxional behavior [56]. A transition state with C2v symmetry is attained in these systems by stretching the H–H bond followed by concerted migration of metal-bound hydrogens. This transient structure inverts with Ha and Hb forming a new H2 ligand, all of which happens in the equatorial plane of the molecule (Eq. 20.14). Ha
Ha
Hb L
L X
M
X
Hb
M
Hc
L
L Hc
(20.14)
Hc
Hc
MH2(H2)L3 (M = Fe, Ru) MH2(H2)(CO)L2 (M = Ru, Os) IrH2(H2)XL2 (X = Cl, Br, I)
The NMR data indicate that the hydrogens remain as distinct pairs that do not cross the X–M–L plane, that is Hc does not exchange with the Ha site. Site exchange between Ha and Hb occurs via facile H2 rotation. Experimental and theoretical studies on IrXH2(H2)(PR3)2 has provided much insight into the mechanism of, and energy barriers to, exchange and attendant rotational dynamics of this system [74]. DFT calculations on model systems for X= Cl, Br, and I and R = H and Me determine the most favorable pathways and corresponding activation parameters for exchange as well as H2 rotational barriers that are similar in energy. Several mechanisms for exchange are possible in IrXH2(H2)(PR3)2 (including a bis-H2 intermediate), but calculations strongly support a pathway through a tetrahydride intermediate (Eq. (20.15). Ha
Ha L
Ha
L
Cl Ir Hb L 1.81 Hc Hc 0.836
Hb 1.61 L Hc H c 1.339 1.65
L = PH3
transition state
Cl
Ir
Cl L
L Hb
Ir 1.59 1.64 Hc Hc 1.754
intermediate
Ha Hb L Cl Ir Hc L Hc
(20.15)
627
628
20 Dynamic Behavior and Reactivity of Dihydrogen and Hydride
Exchange barriers of 1.9, 1.8, and 1.7 kcal mol–1 were calculated for X = Cl, Br, and I, respectively, (modeled using L= PMe3), in excellent agreement with the experimental value obtained by quasielastic neutron scattering studies for X = Cl (1.5 kcal mol–1) (Section 20.4.2). This low barrier pathway is consistent with the original solid state 1H NMR results that showed a barrier substantially less than 3 kcal mol–1 for the hydrogen exchange in IrClH2(H2)(PiPr3)2 but a much higher barrier for hydrogens crossing the Cl–Ir–P plane [56]. This is a remarkably low barrier for a solid state process, a process involving considerable rearrangement, yet facile enough to persist down to temperatures below 77 K. It is also significant that this is apparently a direct oxidativeaddition/reductive-elimination process, one of several possible mechanisms that must be considered in the fluxional behavior of other polyhydride complexes. The MH4L4 structural type is exceedingly dynamic, displaying both M and R exchanges. The cationic complexes [ReH4(CO)L3 ]+ (L = PMe3, PMe2Ph) exist in solution as two isomers A and C in equilibrium, each of which is highly fluxional (Scheme 20.12) [63]. The low-temperature 1H NMR spectra display one exchangeaveraged quartet in the hydride region for the tetrahydride C plus two decoalesced ReH2 and Re(H2) resonances for the H2 isomer A. 31P NMR shows that the phosphine skeleton is rigid in C but very fluxional in A. Because these species are thermally unstable above –40 C, X-ray structural data is not available. A dodecahedral structure is probable for C from 13C NMR evidence for the CO ligand. However the structure of A and the mechanism of exchange is controversial and two possibilities exist [17]. Crabtree proposed the pentagonal bipyramidal structure with H2 in equatorial position shown in Scheme 20.12. A pseudo-octahedral structure [Re(H3)(H)(PMe2Ph)3(CO)]+ with an H3 ligand was proposed as the intermediate or transition state of the exchange reaction within the H2-containing isomer. An H3 intermediate was also proposed earlier by Bianchini in [RuH(H2)(PP3)]+ containing a tripodal phosphine, although the evidence was less clear [75]. +
P P
P
P H
H
H
The DG‡ of 9.9 kcal mol–1 for the rate of H-atom exchange is the lowest measured among nearly 30 complexes (including the Ru species) and is consistent with a facile associative process [8]. Thus the H3 intermediate would be no more than 10 kcal mol–1 less stable than the H2/dihydride structure, suggesting that isolation of a trihydrogen complex may be attainable. Recent studies have been carried out on bis(cyclopentadienyl)Mo type complexes, the first complexes with d2 electronic configurations to have cis hydride-dihydrogen ligands. In contrast to [Cp2MoH3]+, which is a thermally stable trihydride complex, the ansa-bridged analogs [Me2X (C5R4)2MoH(H2)]+ (X = C, R = H; X = Si, R = Me) have been independently determined by both Heinekey [76] and Parkin [77] to be thermally labile dihydrogen/hydride complexes.
20.4 Intramolecular Hydrogen Rearrangement and Exchange
P P
Re
P
P
+ H
H*
H
fast
Re
P
H
C O
C O
+ P
C O
fast
H*
etc.
H
slow
H
fast
Re
H
H
B
A
P H
+ H
P
P
P H C O
C
H
fast
Re
H*
H*
+ P
P D
H
etc.
Scheme 20.12
+ H X
Mo
H H
X = C (1), Si (2)
For X = C [76], the presence of the carbon ansa bridge decreases the ability of the metallocene fragment to backdonate electrons to the hydrogen antibonding orbitals, thus stabilizing the g2-H2 unit. Partial deuteration of the hydride ligands allows observation of JH–D = 11.9 Hz in 1-d1 and 9.9 Hz in 1-d2 (245 K), indicative of a dihydrogen/hydride structure. A rapid dynamic process interchanges the hydride and dihydrogen moieties in 1, but it could be determined that the actual (non-averaged) value of JH–D is 30–36 Hz (dHH = 0.84–0.94 , compared to a DFT calculated value of 0.98 ). Low temperature 1H NMR spectra of 1 give a single hydride resonance, which broadens at very low temperature due to rapid dipole– dipole relaxation (T1 = 23 ms (750 MHz, 175 K). Low temperature 1H NMR spectra of 1-d2 allow the observation of decoalescence at 180 K into two resonances. The bound H2 ligand exhibits hindered rotation with DG‡150 = 7.4 kcal mol–1, comparable to previously reported observations in d2 Ta and Nb dihydrogen complexes [34d]. However H-atom exchange is still rapid at temperatures down to 130 K, and Scheme 20.13 depicts the dynamic process envisaged, with the central Mo-trihydrogen structure representing a transition state for atom transfer from one side of the molecule to the other. This process leads to isotopic scrambling of deuterium between hydride and H2 ligands, where there is a slight preference for deuterium to concentrate in the dihydrogen ligand. This system also apparently has very large exchange coupling (QEC) between the two H atoms of the bound
629
630
20 Dynamic Behavior and Reactivity of Dihydrogen and Hydride
H Mo *H
H H
Mo
H* H
Mo
H* H
*H
H
H
H*
Mo H
H
Mo H
Scheme 20.13
H2, estimated to be at least 24000 Hz, which rationalizes the observation of a single resonance for 1 at all accessible temperatures when no deuterium is incorporated in the hydride ligands. Rapid atom exchange combined with large exchange coupling when two H atoms are adjacent leads to the observed single resonance. Complex 2 which has an X = Si linker and methyl substituents on the ring carbons [77] offers an excellent comparison to 1. Low-temperature NMR studies enable direct determination of JH–D for the HD resonances in the Mo(HD)(H) (26.8 Hz) and Mo(HD)(D) (26.4 Hz) isotopomers, from which the H–H distance is estimated to be 0.98 by use of the dHH/JH–D correlation [41, 42]. The JH–D values are lower than those in 1, indicative of a more electron-rich metal center (methyl substituents on cyclopentadienyl carbons favor increased donation of electrons) and longer dHH. Although the proton NMR signal for the three H ligands of 2 is averaged into a singlet resonance at the lowest temperature studied (–95 C), studies on the MoH2D and MoHD2 isotopologs provide evidence for hindered rotation of the HD ligand as in 1. “Side-to-side” motion of the central hydrogen or deuterium atom as in Scheme 20.13, however, remains rapid on the NMR time scale at all temperatures studied. The principal reason why hindered rotation may not be observed for the H2 ligand is a consequence of a large JHH coupling constant as postulated in 1 and rapid “side-to-side” motion of the central hydrogen, the combination of which causes the highly second-order ABC spectrum to collapse to a singlet. The barrier to rotation of the H2 ligand is 9.0 kcal mol–1 at 25 C. As in 1, deuterium exhibits a greater preference than hydrogen to occupy dihydrogen sites in this system. In addition to altering the classical versus nonclassical nature of [Cp*2MoH3]+ and {[Me2Si(C5Me4)2]Mo(H2)(H)}+, the [Me2Si] ansa bridge also influences the stability of the complex with respect to elimination of H2 and dissociation of H+. Elimination of H2 from the ansa complex is more facile by a factor of ~300 in rate constant and also its acidity is greater than that of [Cp*2MoH3]+, as evidenced by the fact that the ansa complex is readily deprotonated by Cp*2MoH2 to form [Cp*2MoH3]+. All of the above behavior is rationalized by the ansa ligand being overall less electron donating than two unlinked cyclopentadienyl ligands, as proposed for 1. There are only a handful of bis-H2 complexes, which typically additionally have classical hydride ligands and present another example of the very low barriers for exchange of H2 and hydride ligands situated cis to each other around the equatorial plane of a complex. The complex [IrH2(H2)2(PCy3)2]+ is a good example, and separate 1H NMR resonances for the hydride and H2 ligands could be observed on cooling of the complex to 188 K [78]. These peaks coalesce at 200 K, and Morris [8] calculates the DG‡ at this temperature to be 8.4 kcal mol–1. Chaudret’s bis-H2 complex, RuH2(H2)2(PCy3)2, is also
20.4 Intramolecular Hydrogen Rearrangement and Exchange
+ R R R P H H2 Ir H2 H P R
R R
highly fluxional [79], as is his Tp*RuH(H2)2 complex with the hydride and two g2-H2 residing on the same side of the complex (Scheme 20.14) [80]. Although crystallographic evidence is unavailable, NMR data is compatible with averaging of the H positions in solution, and cis-interactions between the hydrogen/hydride ligands appear likely here. Calculations indicate that the ground state structure is H(H2)2 rather than a “pentahydrogen ligand,” which would have been a marvelous analog of the cyclopentadienyl ligand, which contains delocalized alternating single/double bonds between the 5-membered ring carbons. H
N N
Ru
N
H
H H H
H
Ru H
H
H
etc
H
H H Ru H H
H
Scheme 20.14
Transfer of H atoms between g2-H2 and a bridging hydride is seen whenever the two groups are cis to each other (Eq. (20.16)). H
H* H
H
H LnM
H* LnM
M' L'n
(20.16) M' L'n
Complexes include (L2)(H2)Ru(l-H)(l-Cl)2RuH(PPh3)2 (L2 = FeCp(1,2-C5H3(CHMeNMe2)(PiPr2)) [81] for which Morris [8] uses rate data to calculate DG‡(293 K) = 11.8 kcal mol–1, DH‡ = 15.3 kcal mol–1 and DS = 12 cal mol–1 K–1. Although this complex has a cis H2/H interaction that might assist the exchange [82], the DH‡ value is still higher than those for mononuclear complexes, apparently because a hydride must shift from its stable bridging position. Many, if not all, of the above hydrogen transfer/exchange processes can also involve other sigma ligands such as silanes where SISHA (secondary interactions between silicon and hydrogen atoms) [83] reduce the barriers to such processes much as for H/H2 exchanges above. Chaudret has studied r-ligand substitution mechanisms involving silanes and boranes, primarily for M = Ru [84]. H2
M H
L R
M H
–L
H
R
R= Si (H, B, C, etc)
L
M
H
H
H R
H
–RH
M H
H L
(20.17)
631
632
20 Dynamic Behavior and Reactivity of Dihydrogen and Hydride
The weak SISHA interactions (Si···H = 2.0–2.5 ) play an important role, as their breaking is responsible for the most energetically demanding step. They allow smooth variations leading to the formation of new r bonds without the necessity of decoordination of a ligand, which can be of considerable importance in catalytic reactions. Related intramolecular hypervalent interactions (IHI) between halosilyl ligands and hydrides are also relevant in this context [85]. 20.4.2 Quasielastic Neutron Scattering Studies of H2 Exchange with cis-Hydrides
Quasielastic neutron scattering (QNS) [86] is valuable for investigating the details of rapid H2–hydride atom exchange. QNS is actually a form of INS where experiments are carried out at higher temperatures in the regime where quantum-mechanical effects are in transition to classical dynamics (at for example T >100 K, but this varies). A complex with hydride(s) cis to H2 should show increasingly strong interaction between the ligands as a function of T, including possibly exchange. The former affects the rate of rotation of the H2 ligand as it becomes increasingly “aware” of the neighboring hydride’s electrons. This is reflected in non-Arrhenius-like behavior of the quasielastic linewidth, that is broadening of the intense narrow elastic line. QNS data collected at T up to 325 K on [FeH(H2)(dppe)2]BF4, 3, FeH2(H2)(PEtPh2)2, 4, IrClH2(H2)(PiPr3)2, 5, and RuH2(H2)2(PCy3)2, 6, show T dependence of the spectral linewidth that can be fitted to an Arrhenius law which gives an activation energy for the rotation of g2-H2 [33, 34, 87]. The latter values for compounds 3, 4, and 5 were determined to be 30–50% of the experimentally determined barriers to rotation. This is very surprising, as one would expect that at these T the rotation would be essentially classical, i.e. thermally activated rotational hopping over the barrier. It is therefore apparent that even at room T the rotational motion of g2-H2 is at least in part quantum-mechanical. Similar effects are known for the translational diffusion of hydrogen in metals, where in many cases experimentally determined activation energies can be substantially lower than potential well depths. Only the data for 3 could be fitted reasonably well to a model for stochastic rotation of a dumbbell molecule in a double-minimum potential, whereas the dynamics of H2 in 4 and 5 appear to differ substantially from that of 3. This difference may be attributable to interaction with the cis-hydride in 3 and the very rapid exchange between hydride and g2-H2 that is known to occur in 5. The variable temperature QNS data for 5 represents a breakthrough in showing the first experimental observation by INS of quasielastic scattering attributable to H2/hydride site exchange and its associated activation energy [74]. As T is increased above 100 K the rotational tunneling transitions for 5 broaden, shift to slightly lower frequencies, and decrease in intensity, while a very broad background appears beneath the peaks. Additionally, the narrow elastic line broadens progressively, indicating that another dynamic process is now fast enough to be observable within the frequency window (i.e. energy resolution) provided by the spectrometer of about 2 cm–1 FWHM. Although the intensity of the quasielastic component is quite low, it can be extracted by fit-
20.5 Summary
ting a Lorentzian convoluted with the measured gaussian resolution function over this part of the spectrum. The extracted Lorentzian linewidths are fitted to an Arrhenius law to effectively provide an activation energy of 1.5(2) kcal mol–1 for the exchange. This remarkably low barrier closely matches the DFT calculated activation barrier for site exchange of 1.9 kcal mol–1 and is consistent with the mechanistic features in Eq. (20.15) as discussed above. The bis-H2 complex, RuH2(H2)2(PCy3)2, 6, is also extremely fluxional, and NMR studies in Freon solvent mixtures at T as low as 143 K still give unresolvable spectra because of rapid exchange of hydrogens and a low H2 rotational barrier [87]. In agreement with this, calculations show that this complex has three isomeric structures within an energy range of only 2 kcal mol–1. The lowest energy structure has all H in the same plane, which is evidence for cis-interaction of H2 and hydride ligands that would promote exchange. Equation (20.18) shows one of many possibilities for exchange that might for example start with the known cis interaction between the g2-H2 and go through an OA/RE type mechanism as for 5. Hb
Hb L Ha
Ru
Hc Hd
L He
Hf
L
Ha
Hb Hc
Ha
L
Ru Hd
L Hf
He
Hc
Ru L Hf
Hd He
(20.18)
(6)
The INS spectrum of 6 below 50 K consists of the usual pair of bands on either side of the elastic peak corresponding to a low barrier to rotation of 1.1 kcal mol–1, which agrees with calculated barriers [87].
20.5 Summary
The dynamics and transfer of hydrogen within the coordination sphere of metals is astonishingly rich and complex and is much too extensive to fully address here. The metal-catalyzed transfer of hydrogen to organic and inorganic substrates is immensely important in industry, and hydrogenations are the world’s largest manmade chemical reactions. This chapter has explored only one facet of this area, that involving dihydrogen ligands, their splitting to hydride, and the exchange/transfer dynamics between these very important moieties that are the initial steps in catalytic hydrogenation. This alone has been a challenge to characterize and has been greatly aided by the extensive synergism between experiment and theory. Because of the diminutive size and extraordinary dynamics of hydrogen, it is often difficult or impossible to distinguish the detailed mechanistic features for transfer of hydrogens, both intramolecularly and intermolecularly. The past 20 years has witnessed surprising revelations such as the perplexing elongated dihydrogen complexes and novel quantum-mechanical phenomena such as
633
634
20 Dynamic Behavior and Reactivity of Dihydrogen and Hydride
rotational tunneling of H2 and NMR exchange coupling. The hydrogens can be extremely delocalized much as in the superdynamic molecule, CH5+ [88]. The future holds further intriguing discoveries as yet more sophisticated techniques are employed to increase our understanding of the marvelous behavior of hydrogen on metals at the molecular level. The surface has only been scratched: virtually everything discussed in this chapter applies also to heteronuclear X–H bonds containing hydrogen such as C–H, Si–H, B–H, and so forth. These all can bind to and transfer hydrogen atoms on metal centers analogously to H–H bonds; the possibilities are nearly endless!
Acknowledgments
We are grateful to the Department of Energy, Office of Basic Energy Sciences, Chemical Sciences Division and Los Alamos National Laboratory for funding.
References 1 (a) Kubas, G. J.; Ryan, R. R.; Swanson,
2
3 4 5
6
7 8 9
B. I.; Vergamini, P. J.; Wasserman, H. J. J. Am. Chem. Soc. 1984, 106, 451; (b) Kubas, G. J. Acc. Chem. Res. 1988, 21, 120. Metal Dihydrogen and r-Bond Complexes, Kubas, G. J., Kluwer Academic/Plenum Publishers: New York, 2001. Kubas, G.J. J. Organometal. Chem. 2001, 635, 37. Kubas, G.J. Catal. Lett. 2005, 104, 79. (a) Maseras, F.; Lleds, A.; Clot, E.; Eisenstein, O., Chem. Rev. 2000, 100, 601; (b) McGrady, G. S.; Guilera, G. Chem. Soc. Rev. 2003, 32, 383; (c) Jia, G.; Lin, Z.; Lau, C.P. Eur. J. Inorg. Chem. 2003, 2551; (d) Lin, Z.; Hall, M.B. Coord. Chem. Rev. 1994, 135/136, 845; (e) Bakhmutov, V. I. Eur. J. Inorg. Chem. 2005, 245. Recent Advances in Hydride Chemistry, Peruzzini, M.; Poli, R. (Eds.), Elsevier Science, Amsterdam, 2001. Heinekey, D.M.; Lleds, A.; Lluch, J.M. Chem. Soc. Rev. 2004, 33, 175. Jessop, P. G.; Morris, R. H. Coord. Chem. Rev. 1992, 121, 155. (a) Esteruelas, M. A.; Oro, L. A. Chem. Rev. 1998, 98, 577; (b) Esteruelas, M. A.; Oro, L. A. Adv. Organomet. Chem. 2001, 47, 1.
10 Crabtree, R. H. Angew. Chem. Int. Ed.
Engl. 1993, 32, 789. 11 (a) Dewar, M. J. S.; Bull. Soc. Chim. Fr.
1951, 18, C79; (b) Chatt, J.; Duncanson, L. A. J. Chem. Soc. 1953, 2929. 12 (a) Transition Metal Hydrides, E. L. Muetterties, E. L. (Ed.), Marcel Dekker, New York, 1971; (b) Meakin, P.; Guggenberger, L. J.; Peet, W. G.; Muetterties, E. L.; Jesson, J. P. J. Am. Chem. Soc. 1973, 95, 1467, and references therein; (c) Jesson, J. P.; Meakin, P. Acc. Chem. Res. 1973, 6, 269. 13 Hasegawa, T.; Li, Z.; Parkin, S.; Hope, H.; McMullan, R. K.; Koetzle, T. F.; Taube, H. J. Am. Chem. Soc. 1994, 116, 4352; Malin, J.; Taube, H. Inorg. Chem. 1971, 10, 2403. 14 Hush, N.S. J. Am. Chem. Soc. 1997, 119, 1717. 15 Ginsberg, A. P. Adv. Chem. Ser., 1978, 167, 201. 16 Jackson, S. A.; Eisenstein, O. J. Am. Chem. Soc. 1990, 112, 7203. 17 Gusev, D. G.; Berke, H. Chem. Ber. 1996, 129, 1143. 18 Bergamo, M.; Beringhelli, T.; D’Alfonson, G.; Mercandelli, P.; Sironi, A. J. Am. Chem. Soc. 2002, 124, 5117. 19 (a) Eckert, J.; Kubas, G. J., Dianoux, A. J. J. Chem Phys. 1988, 88, 466;
References
20 21 22
23
24
25
26
27
28 29
(b) Eckert, J.; Blank, H.; Bautista, M. T.; Morris, R. H. Inorg. Chem. 1990, 29747; (c) Eckert, J., Kubas, G. J.; Hall, J. H.; Hay, P. J.; Boyle, C. M. J. Am. Chem. Soc. 1990, 112, 2324. Eckert, J. Spectrochim. Acta, Part A, 1992, 48, 363. Eckert, J.; Kubas, G. J. J. Chem Phys. 1993, 97, 2378. (a) Eckert, J. Trans. Am. Crystallogr. Assoc. 1997, 31, 45; (b) Clot, E.; Eckert, J. J. Am. Chem. Soc. 1999, 121, 8855; (c) Webster, C. E.; Gross, C. L.; Young, D. M.; Girolami, G. S.; Schultz, A. J.; Hall, M. B.; Eckert, J. J. Am. Chem. Soc. 2005, 127, 15091. (a) Bender, B. R.; Kubas, G. J.; Jones, L. H.; Swanson, B. I.; Eckert, J.; Capps, K. B.; Hoff, C. D. J. Am. Chem. Soc. 1997, 119, 9179; (b) Janak, K.E.; Parkin, G. Organometallics 2003, 22, 4378; (c) Janak, K. E.; Parkin, G. J. Am. Chem. Soc. 2003, 125, 6889. (a) Toms, J.; Lleds, A.; Jean, Y. Organometallics 1998, 17, 4932; (b) Torres, L.; Moreno, M.; Lluch, J. M. J. Phys. Chem. A 2001, 105, 4676. Gonzalez, A. A.; Zhang, K.; Nolan, S. P.; de la Vega, R. L.; Mukerjee, S. L.; Hoff, C. D.; Kubas, G. J. Organometallics 1988, 7, 2429. (a) Wasserman, H. J.; Kubas, G. J.; Ryan, R. R.; J. Am. Chem. Soc. 1986, 108, 2294; (b) Brookhart, M.; Green, M.L.H.; Wong, L.-L. Progr. Inorg. Chem. 1988, 36, 1. See for example: (a) Homogeneous Hydrogenation , James, B. R., John Wiley and Sons, New York, 1973; (b) Harmon, R. E.; Gupta, S. K.; Brown, D. J. Chem. Rev. 1973, 73, 21; (c) Catalytic Transition Metal Hydrides, Slocum, D. W.; Moser, W. R. (Eds.), Ann. N. Y. Acad. Sci., 1983, 415; (d) Homogeneous Catalysis: Understanding the Art, van Leeuwen, P.W.N.M., Kluwer Academic Publishers, Boston, 2004. Brothers, P.J. Prog. Inorg. Chem. 1981, 28, 1. Morris, R. H. in Recent Advances in Hydride Chemistry, Peruzzini, M; Poli, R. (Eds.), Elsevier Science, Amsterdam, 2001, pp. 1–38.
30 Kubas, G. J. Adv. Inorg. Chem. 2004, 56,
127. 31 (a) Morris, R. H. Can. J. Chem. 1996, 74,
1907; (b) Jia, G.; Lau, C.-P. Coord. Chem. Rev.1999, 190–192, 83. 32 (a) Abdur-Rashid, K.; Gusev, D. G.; Landau, S. E.; Lough, A. J.; Morris, R. H. Organometallics 2000, 19, 1652; (b) Crabtree, R. H.; Siegbahn, P. E. M.; Eisenstein, O.; Rheingold, A. L.; Koetzle, T. F. Acc. Chem. Res. 1996, 29, 348; (c) Custelcean, R.; Jackson, J. E. Chem. Rev. 2001, 101, 1963; (d) Epstein, L. M.; Shubina, E. S.Coord. Chem. Rev. 2002, 231, 165; (e) Cayuela, E.; Jalon, F.A.; Manzano, B.R.; Espino, G.; Weissensteiner, W.; Mereiter, K. J. Am. Chem. Soc. 2004, 126, 7049; (f) Gruet, K.; Clot, E.; Eisenstein, O.; Lee, D.H.; Patel, B. P.; Macchioni, A.; Crabtree, R. H. New. J. Chem. 2003, 27, 80; (g) Jimenez-Tenorio, M.; Palacios, M.D.; Puerta, M. C.; Valerga, P. Organometallics 2005, 24, 3088; (h) Belkova, N. V.; Collange, E.; Dub, P.; Epstein, L. M.; Lemenovskii, D. A.; Lleds, A.; Maresca, O.; Maseras, F.; Poli, R.; Revin, P. O.; Shubina, E. S.; Vorontsov, E. V. Chem. Eur. J. 2005, 11, 873; (i) Jalon, F. A.; Manzano, B. R.; Caballero, A.; Carrion, M. C.; Santos, L.; Espino, G.; Moreno, M. J. Am. Chem. Soc. 2005, 127, 15364. 33 Kubas, G. J.; Burns, C. J.; Eckert, J.; Johnson, S.; Larson, A. C.; Vergamini, P. J.; Unkefer, C. J.; Khalsa, G. R. K.; Jackson, S. A.; Eisenstein, O. J. Am. Chem. Soc. 1993, 115, 569. 34 (a) Antinolo, A.; Carrillo-Hermosilla, F.; Fajardo, M.; Garcia-Yuste, S.; Otero, A.; Camanyes, S.; Maseras, F.; Moreno, M.; Lledos, A.; Lluch, J. M. J. Am. Chem. Soc. 1997, 119, 6107; (b) Jalon, F. A.; Otero, A.; Manzano, B. R.; Villasenor, E.; Chaudret, B. J. Am. Chem. Soc. 1995, 117, 10123; (c) Sabo-Etienne, S.; Chaudret, B.; Abou el Makarim, H.; Barthelet, J.-C.; Daudey, J.-C.; Ulrich, S.; Limbach, H.-H.; Moise, C. J. Am. Chem. Soc. 1995, 117, 11602; (d) Sabo-Etienne, S.; Rodriguez, V.; Donnadieu, B.; Chaudret, B.; el Makarim, H. A.; Barthelat, J.-C.; Ulrich, S.; Limbach,
635
636
20 Dynamic Behavior and Reactivity of Dihydrogen and Hydride
35 36
37 38
39 40
41 42
43
44 45 46
47
48 49 50
H.-H.; Mose, C. New J. Chem. 2001, 25, 55. Prager, M.; Heidemann, A. Chem. Rev. 1997, 97, 2933. Beaufils, J. P.; Crowley, T.; Rayment, R. K.; Thomas, R. K.; White, J. W. Mol. Phys. 1981, 44, 1257. Nicol, J. M; Eckert, J.; Howard, J. J. Phys. Chem., 1988, 92, 7117. Khalsa, G. R. K.; Kubas, G. J.; Unkefer, C. J.; Van Der Sluys, L. S.; Kubat-Martin, K. A. J. Am. Chem. Soc. 1990, 112, 3855. Kubas, G. J.; Ryan, R. R.; Unkefer, C. J. J. Am. Chem. Soc. 1987, 109, 8113. Maltby, P. A.; Schlaf, M.; Steinbeck, M.; Lough, A. J.; Morris, R.H.; Klooster, W. T.; Koetzle, T. F.; Srivastava, R. C. J. Am. Chem. Soc. 1996, 118, 5396. Luther, T. A.; Heinekey, D. M. Inorg. Chem. 1998, 37, 127. Klooster, W. T.; Koetzle, T.F.; Jia, G.; Fong, T.P.; Morris, R.H.; Albinati, A. J. Am. Chem. Soc. 1994, 116, 7677. Maltby, P. A.; Schlaf, M.; Steinbeck, M.; Lough, A. J.; Morris, R.H.; Klooster, W. T.; Koetzle, T. F.; Srivastava, R. C. J. Am. Chem. Soc. 1996, 118, 5396. Law, J.K.; Mellows, H.; Heinekey, D. M. J. Am. Chem. Soc. 2002, 124, 1024. Pons, V.; Heinekey, D. M. J. Am. Chem. Soc. 2003, 125, 8428. Gelabert, R.; Moreno, M.; Lluch, J. M.; Lleds, A. J. Am. Chem. Soc. 1997, 119, 9840. (a) Zilm, K. W.; Heinekey, D. M.; Millar, J. M.; Payne, N. G.; Demou, P., J. Am. Chem. Soc. 1989, 111, 3088; (b) Jones, D. H.; Labinger, J. A.; Weitekamp, D. P. J. Am. Chem. Soc. 1989, 111, 3087; (c) Sabo-Etienne, S.; Chaudret, B. Chem. Rev. 1998, 98, 2077; (d) Antinolo, A.; Carillo-Hermosilla, F.; Fajardo, M.; Fernandez-Baeza, J.; Garcia-Yuste, S.; Otero, A. Coord. Chem. Rev. 1999, 193–195, 43; (e) Schloerer, N.; Pons, V.; Gusev, D. G.; Heinekey, D. M. Organometallics 2006, 25, 3481. Crabtree, R. H.; Lavin, M. J. Chem. Soc., Chem. Commun. 1985, 1661. Crabtree, R. H. Acc. Chem. Res. 1990, 23, 95. Desrosiers, P. J.; Cai, L.; Lin, Z.; Richards, R.; Halpern, J. J. Am. Chem. Soc. 1991, 113, 4173.
51 King, W. A.; Luo, X-L.; Scott, B. L.;
Kubas, G. J.; Zilm, K. W. J. Am. Chem. Soc. 1996, 118, 6782. 52 King, W. A.; Scott, B. L.; Eckert, J.; Kubas, G. J. Inorg. Chem. 1999, 38, 1069. 53 Morris, R. H.; Wittebort, R. J. Magn. Reson. Chem. 1997, 35, 243; Woessner, D. E. J. Chem. Phys. 1962, 36, 1; 37, 647. 54 Gusev, D. G.; Kuhlman, R. L.; Renkema, K. H.; Eisenstein, O.; Caulton, K. G. Inorg. Chem. 1996, 35, 6775. 55 (a) Zilm, K. W.; Merrill, R. A.; Kummer, M. W.; Kubas, G. J. J. Am. Chem. Soc. 1986, 108, 7837; (b) Zilm, K. W.; Millar, J. M. Adv. Magn. Opt. Reson. 1990, 15, 163. 56 Wisniewski, L. L.; Mediati, M.; Jensen, C. M.; Zilm, K. W. J. Am. Chem. Soc. 1993, 115, 7533. 57 (a) Limbach, H.-H.; Ulrich, S.; Gruendemann, S.; Buntkowsky, G.; Sabo-Etienne, S.; Chaudret, B.; Kubas, G. J.; Eckert, J. J. Am. Chem. Soc. 1998, 120, 7929; (b) Wehrmann, F.; Albrecht, J.; Gedat, E.; Kubas, G. J.; Eckert, J.; Limbach, H.-H.; Buntkowsky, G. J. Phys. Chem. A 2002, 106, 2855. 58 Alexander, S. J. Chem. Phys. 1962, 37, 971; (b) Binsch, G. J. Am. Chem. Soc. 1969, 91, 1304; (c) Kleier, D. A.; Binsch, G. J. Magn. Reson. 1970, 3, 146. 59 (a) Szymanski, S. J. Chem. Phys. 1996, 104, 8216; (b) Scheurer, C.; Wiedenbruch, R.; Meyer, R.; Ernst, R. R. J. Chem. Phys. 1997, 106, 1. 60 Bakhmutov, V. I. Magn. Reson. Chem. 2004, 42, 66. 61 (a) Crabtree, R. H.; Lavin, M. J. Chem. Soc., Chem. Commun. 1985, 794; (b) Morris, R. H.; Sawyer, J. F.; Shiralian, M.; Zubkowski, J. D. J. Am. Chem. Soc. 1985, 107, 5581. 62 Bayse, C. A.; Hall, M. B.; Pleune, B.; Poli, R. Organometallics 1998, 17, 4309. 63 (a) Luo, X.-L.; Crabtree, R. H. J. Am. Chem. Soc. 1990, 112, 6912; (b) Luo, X.-L.; Michos, D.; Crabtree, R. H. Organometallics 1992, 11, 237; (c) Gusev, D.G.; Nietlispach, D.; Eremenko, I. L.; Berke, H. Inorg. Chem. 1993, 32, 3628. 64 Heinekey, D. M.; Mellows, H.; Pratum, T. J. Am. Chem. Soc. 2000, 122, 6498.
References 65 Oldham, W. J., Jr.; Hinkle, A. S.;
Heinekey, D. M. J. Am. Chem. Soc. 1997, 119, 11028. 66 (a) Maseras, F.; Duran, M.; Lledos, A.; Bertran, J. J. Am. Chem. Soc. 1992, 114, 2922; (b) Lin, Z.; Hall, M. B. J. Am. Chem. Soc. 1994, 116, 4446. 67 (a) Burdett, J. K.; Phillips, J. R.; Pourian, M. R.; Poliakoff, M.; Turner, J. J.; Upmacis, R. Inorg. Chem. 1987, 26, 3054; (b) Burdett, J. K.; Pourian, M. R. Organometallics 1987, 6, 1684; (c) Burdett, J. K.; Pourian, M. R. Inorg. Chem. 1988, 27, 4445. 68 (a) Pang T. Chem. Phys. Lett. 1994, 228, 555; (b) Farizon, M.; Farizon-Mazuy, B.; de Castro Faria, N. V.; Chermette, H. Chem. Phys. Lett. 1991, 177, 451. 69 Van Der Sluys, L. S.; Eckert, J.; Eisenstein, O.; Hall, J. H.; Huffman, J. C.; Jackson, S. A.; Koetzle, T. F.; Kubas, G. J.; Vergamini, P. J.; Caulton, K. G. J. Am. Chem. Soc. 1990, 112, 4831. 70 Brintzinger, H. H. J. Organomet. Chem. 1979, 171, 337. 71 Gusev, D. G.; Kuhlman, R. L.; Sini, O.; Eisenstein, O.; Caulton, K. G. J. Am. Chem. Soc. 1994, 116, 2685. 72 Clot, E.; LeForestier, C.; Eisenstein, O.; Pelissier, M. J. Am. Chem. Soc. 1995, 117, 1797. 73 (a) Eckert, J.; Jensen, C. M.; Jones, G.; Clot, E.; Eisenstein, O. J. Am. Chem. Soc. 1993, 115, 11056; (b) Eckert, J.; Jensen, C. M.; Koetzle, T. F.; Le-Husebo, T.; Nicol, J.; Wu, P. J. Am. Chem. Soc. 1995, 117, 7271. 74 Li, S.; Hall, M. B.; Eckert, J.; Jensen, C. M.; Albinati, A., J. Am. Chem. Soc. 2000, 122, 2903. 75 Bianchini, C.; Perez, P.J.; Peruzzini, M.; Zanobini, F.; Vacca, A. Inorg. Chem. 1991, 30, 279. 76 Pons, V.; Conway, S.L.J.; Green, M. L. H.; Green, J.C.; Herbert, B.J.; Heinekey, D.M. Inorg. Chem. 2004, 43, 3475.
77 Janak, K.E.; Shin, J.H.; Parkin, G. J. Am.
Chem. Soc. 2004, 126, 13054. 78 Lundquist, E. G.; Folting, K.; Streib, W.
E.; Huffman, J. C.; Eisenstein, O.; Caulton, K. G. J. Am. Chem. Soc. 1990, 112, 855. 79 (a) Sabo-Etienne, S.; Chaudret, B. Coord. Chem. Rev. 1998, 178–180, 381; (b) Grellier, M.; Vendier, L.; Chaudret, B.; Albinati, A.; Rizzato, S.; Mason, S.; Sabo-Etienne, S. J. Am. Chem. Soc. 2005, 127, 17592. 80 Moreno, B.; Sabo-Etienne, S.; Chaudret, B.; Rodriguez, A.; Jalon, F.; Trofimenko, S. J. Am. Chem. Soc. 1995, 117, 7441. 81 Hampton, C.; Cullen, W. R.; James, B. R. Charland, J.-P. J. Am. Chem. Soc. 1988, 110, 6918. 82 Jackson, S. A.; Eisenstein, O. Inorg. Chem. 1990, 29, 3910. 83 Delpech, F.; Sabo-Etienne, S.; Chaudret, B.; Daran, J.-C. J. Am. Chem. Soc. 1997, 119, 3167. 84 (a) Atheaux, I.; Delpech, F.; Donnadieu, B.; Sabo-Etienne, S.; Chaudret, B.; Hussein K.; Barthelat, J.-C.; Braun, T.; Duckett, S.B.; Perutz, R.N. Organometallics 2002, 21, 5347; (b) Lachaize, S.; Essalah, K.; Montiel-Palma, V.; Vendier, L.; Chaudret, B.; Barthelet, J.-C.; Sabo-Etienne, S.; Organometallics 2005, 24, 2935. 85 (a) Nikonov, G.I. J. Organometal. Chem. 2001, 635, 24; (b) Nikonov, G.I. Adv. Organomet. Chem. 2005, 53, 217. 86 Bee, M. Quasielastic Neutron Scattering Adam Hilger, Bristol,1988. 87 Rodriguez, V.; Sabo-Etienne, S.; Chaudret, B.; Thoburn, J.; Ulrich, S.; Limbach, H.-H. Eckert; J.; Barthelat, J.-C.; Hussein, K.; Marsden, C. J. Inorg. Chem. 1998, 37, 3475; Borowski, A. F.; Donnadieu, B.; Daran, J.-C.; SaboEtienne, S.; Chaudret, B. Chem. Commun. 2000, 543. 88 Thompson, K. C.; Crittenden, D. L.; Jordon, M. J. T. J. Am. Chem. Soc. 2005, 127, 4954, and references therein.
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21 Dihydrogen Transfer and Symmetry: The Role of Symmetry in the Chemistry of Dihydrogen Transfer in the Light of NMR Spectroscopy Gerd Buntkowsky* and Hans-Heinrich Limbach
21.1 Introduction
The concept of symmetry is one of the basic pillars of modern chemistry and physics. Many fundamental phenomena and laws of nature are related to symmetry or are describable with the help of symmetry arguments. Accordingly, the mathematical description of symmetry, the so-called group theory, is at the heart of both classical mechanics and quantum mechanics. Since the latter field is the basis of modern chemistry, symmetry is also of great importance for chemists. They employ symmetry arguments on a regular basis to help in the understanding of spectra or molecular structures and courses on group theory are a regular part of the chemical education syllabus. It is less well known that symmetry effects also play an important role in chemical kinetics, in particular when low mass particles like hydrogen or deuterium are involved in the reaction and quantum mechanical tunneling processes are present. Especially when dihydrogen exchange reactions are studied, the exchange of the two hydrogen atoms or more generally hydrons (i.e. 1H, 2H or 3H) is a perfect symmetry operation. This apparently trivial symmetry has far fetching consequences for the reaction dynamics. These consequences stem from two different aspects of symmetry: On the one hand basic quantum mechanics tells us that the wavefunctions of the hydrogen or deuterium atoms have to obey the spin dependent Fermi symmetrization rules: They have to be either symmetric (deuterium, spin 1) or anti-symmetric (hydrogen, spin 12). The result of this symmetrization is the formation of para- and ortho- states, which are the spin isotopomers of dihydrogen and dideuterium [1]. On the other hand group theory tells us that the eigenfunctions of the spatial Hamilton operator are now also eigenfunctions of the operator which exchanges the two hydrogen atoms. This implies that the eigenfunctions are either even or odd functions. As a consequence of this, the whole system behaves quantum mechanically. This is particularly visible at low temperatures when only the rotational ground states of the molecules are occupied. * Corresponding author
Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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21 Dihydrogen Transfer and Symmetry in the Light of NMR Spectroscopy
These symmetry related quantum effects are most important in the chemistry of non-classical transition metal hydrides with g2 -bonded dihydrogen ligands [2–24]. Following the pioneering work of Kubas et al., who found the first of these complexes a whole series of transition metal polyhydrides with hydrogen distances varying between 0.8 and 1.7 were synthesized [23, 25–29]. Understanding their chemistry has led to a better understanding of catalysis since they may be catalytic precursors or stable models for short lived intermediate steps in catalysis [15, 30–32]. They are of current interest in organometallic chemistry [33–36]. Due to the g2 -binding the two hydrogen atoms forming the dihydrogen part of the system exhibit a much higher mobility than hydrogen atoms in conventional hydride bonds. In particular their exchange is an exact symmetry operation, as discussed above. The mutual exchange of the hydrons is equivalent to a hindered 180 rotation around the axis intersecting the M–H2 angle [37–41]. The rotational barrier is caused mainly by the chemical structure, i.e. the binding between the two hydrogen atoms, the binding of the hydrons to the metal, effects of the ligands and sometimes also by crystal effects from neighboring molecules. For identical hydrogen isotopes, the above discussed quantum mechanical symmetry principles leads to the formation of para-states with anti parallel and ortho-states with parallel nuclear spins. The various energy levels of the system exhibit a tunnel splitting and the energy eigenfunctions split into two separate manifolds with even and odd symmetry. The height of the barrier determines the energy difference between the lowest even and odd symmetry. This so-called tunnel splitting can be expressed as a tunnel frequency tt. The size of the tunnel splitting depends strongly on the hindering potential. It varies from 1012 Hz for dihydrogen gas to a few Hz as the depth of the potential is increased. Due to this large range of tunnel frequencies no single spectroscopic technique is able to cover the whole dynamic range. While fast coherent tunneling in the frequency range of GHz to THz were studied by incoherent neutron scattering (INS) [19, 42], relatively slow tunneling processes in the frequency range of Hz to kHz are investigated by 1H liquid state NMR spectroscopy (see for example Refs. [19, 43–49] and many others) or 2H-liquid state NMR [50]. In these 1H liquid state NMR studies the tunnel frequency is usually termed “quantum exchange coupling”, due to the fact that the effect of the tunneling on the 1H liquid state NMR spectra is equivalent to the effect of an indirect spin coupling (J-coupling). At higher temperatures incoherent exchange processes are superimposed on the coherent tunneling. They are also visible in the NMR or INS spectra of these hydrides. An important application of these quantum mechanical symmetry principles is the so-called “Para Hydrogen Induced Polarization (PHIP)” experiment [51, 52]. If hydrogen gas (deuterium gas works similarly) is kept at low temperatures (typically liquid nitrogen or below), it converts after some time into the energetically favorable para-hydrogen, for example by contact with paramagnetic species [1] or adsorption to nuclear spins [53]. These para-hydrogen molecules are in a pure nuclear singlet state, which is associated via the Pauli exclusion principle with the
21.2 Tunneling and Chemical Kinetics
lowest rotational state. They are stable even in liquid solutions [54, 55]. Their high spin polarization can be utilized as an extremely sensitive monitor of the fate of the hydrogen in catalytically induced hydrogenation reactions (see for example Refs. [56–76]). The rest of the paper is organized as follows: The second chapter gives an introduction into the theoretical description of tunneling phenomena and chemical kinetics. After a short summary about the connection of symmetry and tunneling, the basic properties of coherent and incoherent rotational tunneling and their relation to NMR spectroscopy are discussed and the empiric Bell [77] tunnel model is introduced, which is a powerful semi-empirical tool for the description of chemical kinetics in the transition from the coherent to the incoherent regime. This model has been used for the description of Arrhenius curves of H-transfers as described in more detail in Chapter 6. The next two chapters show applications of these symmetry effects. First the para-hydrogen induced polarization (PHIP) experiments are discussed. There the symmetry induced nuclear spin polarization creates very unconventional NMR lineshape patterns, which are of high diagnostic value for catalytic studies. Then in Section 21.4 symmetry effects on NMR lineshapes and relaxation data of intramolecular hydrogen exchange reactions are discussed and examples from 1H-liquid state and 2H-solid state NMR are presented and compared to INS spectra. The last section gives an outlook on possible future developments in the field.
21.2 Tunneling and Chemical Kinetics
This section gives an introduction to the effects of symmetry and quantum mechanical tunneling on chemical reactions in general and hydrogen transfer in particular. 21.2.1 The Role of Symmetry in Chemical Exchange Reactions
Starting from the early days of quantum mechanics, when the dynamics of the ammonia molecule was analyzed by Hund [78], it is well known that there is a close relationship between the symmetry of a potential and the wavefunction of the system [79]. The eigenfunctions of the system have the symmetry of the irreducible representations of the corresponding symmetry group. This situation gets particularly simple if one considers the motion in a symmetric double well potential, as for example in the case of ammonia, where the three hydrogen atoms can be either at the left or the right side of the nitrogen atom.
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21 Dihydrogen Transfer and Symmetry in the Light of NMR Spectroscopy
21.2.1.1 Coherent Tunneling 21.2.1.1.1 Tunneling in a Symmetric Double Minimum Potential Basic textbook [80] quantum mechanics, already developed by Hund [78], tells us that we can associate two different wavefunctions j1i and j2i with these two states. ^ j2i ¼ 0 Both have the same energy E0. As long as the matrix element H12 ¼ h1jH between these two states is zero, they are degenerate eigenstates of the system and this is the end of the story. The situation changes dramatically if H12 „ 0, since then a level anti-crossing appears and j1i and j2i are no longer the eigenstates of the system. Instead the eigenfunctions are given by the symmetric (gerade) and anti-symmetric (ungerade) linear combinations of j1i and j2i. 1 1 j g i ¼ pffiffiffi ðj1i þ j2iÞ and jui ¼ pffiffiffi ðj1i j2iÞ 2 2
(21.1)
The corresponding energy levels are symmetrically split Ek ¼ E0 – jH12 j:
(21.2)
The lower energy level belongs to the symmetric and the upper energy level to the anti-symmetric state. Suppose now that we managed to prepare the system initially in the state j1i. Since j1i is no longer an eigenstate of the system there is a periodic motion from j1i to j2i and back, where the probabilities of finding the system in state j1i and j2i change according to pð1Þ ¼ cos 2 ðjH12 jtÞ and pð2Þ ¼ sin 2 ðjH12 jtÞ
(21.3)
The frequency of this oscillation mt , the so-called tunnel frequency, is given via mt ¼
2jH12 j jH12 j ¼ 2p p
(21.4)
This periodic motion is called the coherent tunneling of the system. It simply reflects the fact that the eigenstates of the system are given by Eq. (21.1). The size of the tunnel frequency depends strongly on the hindering potential.
21.2.1.1.2 Tunneling in a Symmetric Double Minimum Potential In the case of dihydrogen exchange, a linear exchange of the two hydrons is not possible and angular degrees of freedom must be taken into account. Thus the simplest realistic model is a one-dimensional hindered rotation of the two hydrons around their center of mass in a harmonic twofold potential, i.e. a onedimensional hindered quantum mechanical rotor. In this model it is assumed that the distance between the two hydrons, as well as their distance from the metal, does not change. In this case the angular position, described via an angle j, is
21.2 Tunneling and Chemical Kinetics
used as the only degree of freedom. The corresponding Schrdinger equation of a rigid rotor in a harmonic twofold potential is:
"2 d2 jWi V0 ð1 cos 2uÞjWi ¼ Ejwi 2lr 2 du2
(21.5)
where 2V0 describes the depth of the hindering potential and l is the reduced mass of the hydrogen. This differential equation is of the Matthieu type. For V0 ¼ 0 the dihydrogen is a free one-dimensional rotor with complex eigenfunctions of the type 1 jW k ðuÞi ¼ pffiffiffiffiffiffi expðikuÞ with k ¼ 0; –1; –2; . . . 2p
(21.6)
Since the corresponding energy eigenvalues Ek ¼
"2 k2 2mr 2
(21.7)
are doubly degenerate Eþk ¼ Ek , we can use equally well their real and imaginary linear combinations, which are simple sine and cosine functions, respectively a constant (k ¼ 1; 2; . . .) 1 jc0 ðuÞi ¼ pffiffiffiffiffiffi 2p 1 1 jck ðuÞi ¼ pffiffiffi ðjW k ðuÞi þ jW k ðuÞiÞ ¼ pffiffiffi cos ðkuÞ p 2
(21.8)
1 1 jsk ðuÞi ¼ pffiffiffi ðjW k ðuÞi jW k ðuÞiÞ ¼ pffiffiffi sin ðkuÞ p 2i
They have even respectively odd symmetry with respect to j: jck ðuÞi ¼ jck ðuÞi and jsk ðuÞi ¼ jsk ðuÞi:
(21.9)
For V0 > 0, they are no longer the eigenfunctions of the system. Employing them as base functions of the Hilbert space, the Schrdinger equation (21.5) is converted into a matrix equation, where the kinetic energy operator is diagonal and the only non-vanishing matrix elements are between pairs of even or pairs of odd, ^ jc–2 i ¼ p1ffiffi V0 and base functions which differ in the index k by –2, i.e. hc0 jV 2 ^ jcl i ¼ 1 V0 dk;lþ2 þ dk;l2 hck jV 2 ^ jsl i ¼ 1 V0 dk;lþ2 þ dk;l2 hsk jV 2
(21.10)
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21 Dihydrogen Transfer and Symmetry in the Light of NMR Spectroscopy
Thus the matrix is block diagonal and there are two sets of eigenfunctions (Fig. 21.1), namely cosine type functions and sine type functions jSn ðuÞi, which are linear combinations of the base functions (Eq. (21.9) jCn ðuÞi ¼
¥ X
an;k jck ðuÞi and jSn ðuÞi ¼
¥ X
k¼0
bn;k jsk ðuÞi
(21.11)
k¼1
The ground state wavefunction is always a cosine type state with even symmetry and the first excited state is always a sine type function with odd symmetry. The energy differences between different Cn(j) or Sn(j) depend strongly on the depth of the potential 2V0 and vary between zero and the order of typical rotational l wave or IR transitions (Fig. 21.2). At temperatures around 10 K only the lowest pair of eigenstates is thermally populated. For identical hydrons, the symmetry postulate of identical particles has to be fulfilled. For protons and tritons this means that the overall wave function must be antisymmetric under particle exchange and for deuterons it must be symmetric under particle exchange. Due to this correlation of spin and spatial state, the energy difference DE between the lowest two spatial eigenstates can be treated as a pure spin Hamiltonian, similar to the Dirac exchange interaction of electronic spins.
Cn(φ)
Sn(φ)
2V0
V(φ)
J0 −
π
0
π
−
π
0
π
2V0
644
J0 −
π
0
φ
π −π
0
φ
π
−
Figure 21.1 Eigenstates and energy eigenvalues of the Schrdinger equation of a rigid D2 rotor in a harmonic twofold potential for two different depths of the potential barrier (adapted from Ref. [40]). Upper panel: V0 = 107 MHz, J0 = 6.4 103 MHz, lower panel: V0 = 108 MHz, J0 = 60 Hz. Left : potential
π
0
φ
π
energy curve V(f); middle panel : cosine type eigenfunctions Cn(f), right panel: Sine type eigenfunctions Sn(f). The energy shift between cosine and sine functions is increased artificially to demonstrate the differences in Jn between energy levels of same n.
νt[Hz]
21.2 Tunneling and Chemical Kinetics 10
13
10
10
10
7
10
4
10
1
HH
10
DD
-2
0
100
200
300
400
500
600
700
2V0[meV] Figure 21.2 Tunnel frequency versus barrier [81]:Tunnel frequency and HH/DD isotope effect as a function of the barrier height 2V0 for a proton pair HH and a deuteron pair DD with RDD = 1.
Spin 12 case: For a Spin I ¼ 1=2 the eigenstates are 1 jS0 i ¼ pffiffiffi ðjab i jbaiÞ 2 jTþ1 i ¼ jaai
(21.12)
1 jT0 i ¼ pffiffiffi ðjabi þ jbaiÞ 2 jTþ1 i ¼ jbb i
The jS0 i state couples to the symmetric ground para-state to form a singlet manifold and the jTk i states couple to the odd ortho-state and forms the triplet manifold. The splitting between these states is described by the quantum mechanical exchange interaction, which was given by Dirac in the form ^ X ¼ X 1 1 þ 4~ I^2 H I^1~ 2
(21.13)
This Hamilton operator is the product of the energy splitting times the operator 0
^¼ P
1 2
^^ I2 1 þ 4~ I 1~
1 B0 B ¼@ 0 0
0 0 1 0
0 1 0 0
1 0 0C C 0A 1
(21.14)
^ is an example of a permutation operator in Permutation operator: The operator P spin space. It exchanges the coordinates of the two spins 1/2. In the product space
645
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21 Dihydrogen Transfer and Symmetry in the Light of NMR Spectroscopy
of the two spins the general definition of such an operator for arbitrary spins is given via ^ ~ P I^1 ;~ I^2 jl; mi ¼ jm; li
(21.15)
^ is found if symmetry An very useful alternate representation of the operator P adapted base functions jki are employed. In this base the permutation operator is diagonal with diagonal elements þ1 if the state has even and 1 if the state has odd symmetry. ^ ~ I^2 jki ¼ –jki P I^1 ;~
(21.16)
Employing these permutation operators it is easy to write down the exchange Hamiltonian for arbitrary spins. From the NMR point of view, the eigenfunctions of the spin 12 exchange Hamiltonian are identical to the eigenfunctions of the “normal” homonuclear spin–spin interaction, but the energy eigenvalues are shifted by a constant offset of X=2, since ^ X ¼ X þ 2X~ I^1~ I^2 H 2
(21.17)
X I^1~ I^2 ¼ þ JX~ 2
Thus for spin I ¼ 1=2 nuclei, the quantum mechanical exchange interaction is formally equivalent to an indirect spin–spin interaction. Accordingly the exchange of spin-1/2 particle is usually treated in NMR like a J-coupling (quantum exchange coupling), employing the more simple Hamiltonian ^ ¢X ¼ JX~ I^1~ I^2 H
(21.18)
These couplings are indeed directly visible in liquid state 1H-NMR spectra [46, 47]. Spin 1 case: For a Spin I ¼ 1 the nine eigenstates of a di-deuterium system are ja1 i ¼ jþþi
ja2 i ¼ j00i
ja3 i ¼ ji
1 ja4 i ¼ pffiffiffi ðjþi þ jþiÞ 2
1 ja5 i ¼ pffiffiffi ðjþ0i þ j0þiÞ 2
1 ja6 i ¼ pffiffiffi ðj0i þ j01iÞ 2
1 jb1 i ¼ pffiffiffi ðjþi jþiÞ 2
1 jb2 i ¼ pffiffiffi ðjþ0i j0þiÞ 2
1 jb3 i ¼ pffiffiffi ðj0i j01iÞ 2 (21.19)
The three b-states have odd and the six a-states have even symmetry. Since the deuterium nucleus is a boson, the overall wavefunction has to be symmetric and
21.2 Tunneling and Chemical Kinetics
the six even a-states couple to the even ground state and the three odd b-states ^ is calculated couple to the odd spatial state. The special form of the operator P from Eq. (21.15) or (21.16). For arbitrary base sets, a base independent operator representation of the permutation operator of spin 1 similar to the spin 12 case of Eq. (21.18) is useful. This representation can be found with the help of the following set of normalized single spin operators: 1 B1 ¼ pffiffiffiSx 2
1 B2 ¼ pffiffiffiSy 2
1 B3 ¼ pffiffiffiSz 2 1pffiffiffi 2 2 6 Sz B5 ¼ 2 3
1 B4 ¼ pffiffiffiE 2
1 B7 ¼ pffiffiffi Sx Sy þ Sy Sx 2 1 B9 ¼ pffiffiffi Sy Sz þ Sz Sy 2
1 B6 ¼ pffiffiffi S2y S2x 2
(21.20)
1 B8 ¼ pffiffiffiðSx Sz þ Sz Sx Þ 2
Employing these base operators the permutation operator of a homo nuclear spin 1 pair is given by X ^ ~ I^2 ¼ Bk Bk P I^1 ;~
(21.21)
k
where denotes the tensor or direct product of two vector spaces (see for example Refs. [80, 82]). As a result we find that in both the hydrogen and the deuterium case the ground state tunneling is describable by a pure spin tunnel Hamiltonian, which describes the tunnel splitting between the spatial pair of states of different symmetry. The implications are discussed in detail in Ref. [83]. Coherent tunneling at higher temperatures: If several pairs of tunnel levels are thermally populated, the thermal average of the different pairs of tunnel levels has to be calculated. As long as only a few levels far below the barrier are contributing, the values of the various tunnel frequencies Jn ¼ mtn will be small compared to the thermal exchange rates between the level pairs and the averaging can be done by summing up the individual values of mtn times their thermal population. This averaging can be approximated using the population of one of the connected levels: X E (21.22) mt ¼ mtn exp n kT n The situation becomes more difficult if the values of mt are comparable or greater than the thermal population rates or decay rates. In this regime, a transition from coherent to incoherent exchange will take place (see below), as was shown by density matrix theory [19].
647
648
21 Dihydrogen Transfer and Symmetry in the Light of NMR Spectroscopy
21.2.1.2 The Density Matrix As soon as large ensembles of particles with statistical populations of the eigenstates and incoherent exchange and relaxation processes between these states are investigated, quantum statistical tools are necessary to describe the system. In ^ has to be employed. For this situation the quantum mechanical density operator r the coherent evolution of the density operator under the influence of a Hamilto^ , the following differential equation is found [80] nian H d ^;r ^ ¼ i H ^ r dt
(21.23)
In this equation we have followed the NMR convention and set the constant " ¼ 1. This is equivalent to measuring energies in angular frequency units. Employing a suitable set of base functions of the Hilbert space, this equation can be converted into a set of linear differential equations for the matrix elements of ^. In the case of a single pair of tunnel levels the Hamiltonian of the two levels r with their tunnel splitting can be treated as a two-level system, employing ficti^ tious spin 1/2 operators, describable by the Hamiltonian H ^ ¼ H ¼
E1 0
0 E2
¼
E1 þ E2 1 0 E E2 1 0 þ 1 0 1 0 1 2 2
E1 þ E2 ^z ^ z ¼ E þ mt S þ ðE1 E2 ÞS 2
(21.24)
E1 þ E2 is the mean energy of the levels and mt ¼ ðE1 E2 Þ is the tunnel 2 frequency. This set of differential equations is most conveniently written by intro^ ^, which defines the Liouville space, ducing the so-called Liouville super operator L where the density matrix becomes a vector. The equation of motion of the density matrix is
Here E ¼
d ^^r ^ ¼ iL ^ r dt
(21.25)
The Liouville operator is constructed from the Hamiltonian via ^~ E ^^ ¼ H ^~ ^H ^ E L
(21.26)
^ is the unity matrix of Hilbert space. In the case of the tunnel Hamiltonian Here, E it is simply 0
0 B0 ^^ ^ B ^ L ¼ tt Sz ¼ tt @ 0 0
1 0 0 0 1 0 0C C 0 1 0 A 0 0 0
(21.27)
21.2 Tunneling and Chemical Kinetics
21.2.1.3 The Transition from Coherent to Incoherent Tunneling A rigorous quantum mechanical theory of the transition from coherent to incoherent tunneling was developed by Szymanski [84] and Scheurer [85]. The results of this elaborate theory can be reproduced by a combination of density matrix theory and formal kinetics as was shown in Ref. [19]. The transition from coherent to incoherent tunneling is most easily understood by considering the ground state of the system and the first excited state. In the systems under consideration the typical energy difference between the ground state and the first excited state is in the range 40–50 meV. At temperatures below 50 K practically only the ground state is populated (nb < 105 na ) and only a small population is found in the excited state. As a starting point let us see what happens, if we consider not only the ground state, but also the first excited state of the tunneling pairs. Both states are connected via thermal excitation with rates kab and kba . Since the transition between even and odd states is both symmetry and spin forbidden, these rates connect only states of the same symmetry and the spin is conserved in the transition. From the principle of detailed balance we find for the ratio of the rates kab E Ea << 1 ¼ exp b kba kB T
(21.28)
The coherent evolution of the density matrix is described by the corresponding Liouville operators: 0
0 B0 ^ B ^ La ¼ tta @ 0 0
1 0 0 0 0 0 1 0 0C 0 ^^ ¼ t B C and L B b tb @ 0 1 0 A 0 0 0 0 0
0 0 1 0 0 1 0 0
1 0 0C C 0A 0
(21.29)
The exchange between the levels connects the two Liouville spaces d ^ ¼ ðkab þ iLa Þ^ ^b ra þ kba r r dt a
(21.30) d ^a ^ ¼ ðkba þ iLb Þ^ r rb þ kab r dt b
In matrix form these coupled differential equations are 0
1 0 ra1 kab C B 0 dB r a2 B C¼B dt@ ra3 A @ 0 ra4 0
0 kab itta 0 0
0 0 kab þ itta 0
0 10 1 1 0 rb1 ra1 B B C C 0 C CB ra2 C þ kba B rb2 C @ rb3 A 0 A@ ra3 A ra4 rb4 kab
(21.31)
649
650
21 Dihydrogen Transfer and Symmetry in the Light of NMR Spectroscopy
and 1 0 kba rb1 C B dB B rb2 C ¼ B 0 dt@ rb3 A @ 0 rb4 0 0
0 kba ittb 0 0
0 0 kba þ ittb 0
10 1 1 0 rb1 0 ra1 C C B B 0 C CB rb2 C þ kab B ra2 C @ ra3 A 0 A@ rb3 A rb4 ra4 kba
(21.32) This system of equations can be greatly simplified by the fact that the excited state is only weakly populated. This allows us to use a quasi-stationary condition for the excited state by setting the derivative of the population of the excited state to zero. This converts the second differential equation into an algebraic one. 0
kba B 0 B @ 0 0
0 kba ittb 0 0
0 0 kba þ ittb 0
0 10 1 1 0 ra1 rb1 B B C C 0 C CB rb2 C þ kab B ra2 C ¼ 0 @ ra3 A 0 A@ rb3 A kba rb4 ra4
Solving for rb gives: 0 k 1 ab 0 1 kba ra1 rb1 B ab C B rb2 C B k kþit r C B C ¼ B ba tb a2 C @ rb3 A B kab r C @ kba ittb a3 A rb4 kab kba ra4
(21.33)
(21.34)
Inserting this expression into the equation for ra gives after some simple manipulations: 1 0 1 10 0 0 0 0 0 ra1 ra1 kab kba C B 0 kab itta þ k þit 0 0 CB ra2 C dB ba tb C CB B ra2 C ¼ B kba A@ ra3 A dt@ ra3 A @ 0 0 kab þ itta þ kkbaabit 0 tb ra4 ra4 0 0 0 0 (21.35) From the first and the last row it is evident that the density matrix elements ra1 and ra4 , which correspond to the populations of the levels, do not change. The center rows become: d r ¼ dt a2
kab kba r kba þ ittb a2
(21.36)
kab kba r kab þ itta þ kba ittb a3
(21.37)
kab itta þ
and d r ¼ dt a3
21.2 Tunneling and Chemical Kinetics
They can be rewritten as d r ¼ dt a2
kab t2 k k ra2 2 tb 2 i tta þ 2 ab ba2 ttb kba þ ttb kba þ ttb
(21.38)
kab t2 k k ra3 2 tb 2 þ i tta þ 2 ab ba2 ttb kba þ ttb kba þ ttb
(21.39)
and d r ¼ dt a3
The density matrix elements ra2 and ra3 represent coherent superpositions (coherences) between the para and ortho states, which evolve with the tunnelling frequency. Thus we find that the connection to the higher level causes a shift of the coherent tunnelling frequency to tta ¢ ¼ tta þ
kab kba t k2ba þ m2tb tb
(21.40)
and in addition a damping of the singlet triplet coherences by a relaxation rate kab t2 (21.41) r12 ¼ 2 tb 2 kba þ ttb For the interpretation of this relaxation rate it is useful to transform the Liouville operator in the localized base. The transformation matrix in Hilbert space is ^ ¼ p1ffiffiffi 1 1 (21.42) S 2 1 1 and the corresponding transformation super operator in Liouville space is calculated from the transformation matrix as [82] 0 1 1 1 1 1 B C ^^ ¼ S ^S ^ ¼ 1B 1 1 1 1 C S (21.43) 2@ 1 1 1 1 A 1 1 1 1 ^ is a real matrix. Employing this operator, the where we have used the fact that S equation in the localized base becomes
651
652
21 Dihydrogen Transfer and Symmetry in the Light of NMR Spectroscopy
0 1 1 0 1 ra1 0 0 0 0 ra1 B C B C 0 0C d ^^ B C^ B ra2 C ^^ B 0 r12 itta ¢ ^ 1 ^ ^ B ra2 C SB CS S C ¼SB B C @0 @ ra3 A dt @ ra3 A 0 r12 þ itta ¢ 0 A 0 0 0 0 ra4 ra4 0 0 1 1 1 1 0 0 r 2r12 2 12 B B C B B 0 12r12 12r12 0 C C C B B C 0 C 1 1 B @ 0 12r12 0 A C ra1 B C 2r12 B C 1 B C^B 0 0 12r12 ra2 C C 2r12 ^B ¼B S C B 0 1C B C 1 1 A @ r 0 t ¢ t ¢ 0 B C a3 ta ta 2 2 B B 1t ¢ CC 1 B C r 0 0 t ¢ a4 ta 2 ta C C B þ iB B 21 CC B 1 @ 2tta ¢ AA 0 0 @ 2tta ¢ 0 0 12tta ¢ 12tta ¢ 0
(21.44)
The first term has a very simple physical interpretation. It corresponds to an incoherent exchange of the localized particles with an exchange rate 1 1 kab t2tb (21.45) k12 ¼ r12 ¼ 2 2 k2ba þ t2tb between the localized states, i.e. an incoherent tunneling of the protons or deuterons from the left side to the right side of the potential. 0
k12 B 0 ^ B ^ K¼@ 0 k12
0 k12 k12 0
0 k12 k12 0
1 k12 0 C C 0 A k12
(21.46)
In the case of mtb >> kba this equation simplifies to 1 k12 ¼ kab 2
(21.47)
This result has a very intuitive explanation, which is sketched in Fig. 23.3. The rate kab is the transport rate from the ground state to the excited state. kab is much smaller then the decay rate kba . As soon as a molecule is excited to the higher state, the tunneling gets so fast that there is equal probability to find the particle on both sides, when it decays back into the ground state. Thus, depending on the size of the barrier height, the two hydrons will exhibit strong differences in their dynamic behavior. For a low barrier height, a large tunnel frequency is observed. The dihydrogen pair will be at least partially delocalized and acts more or less like a one-dimensional free quantum mechanical rotor, similar to p-H2 and o-H2, allowing coherent (i.e. strictly periodic) exchange processes of the individual hydrons with the tunnel frequency mt. For high potential barriers the tunnel splitting goes to zero, no coherent exchange processes take place, each hydron is located in a single potential minimum and the dihydrogen pair is fixed.
21.2 Tunneling and Chemical Kinetics
a)
Eb
b)
υtb
kba
kab
E − Ea k ab − k ba exp − b k BT
c)
k12 Ea
-π
0
π
Figure 21.3 Sketch of the transition from coherent to incoherent tunneling: (a) Quantitative four-level model [86]; (b) corresponding chemisty of coherent and incoherent dihydrogen exchange [19]; (c) dependence of coherent and incoherent rates [19].
In this situation, for an exchange of the two hydrons a coupling to external degrees of freedom is necessary. In this scenario the exchange of the two hydrogen atoms is describable as a thermally activated rate process. Compared to the previous coherent exchange, the thermally activated rate process corresponds to an incoherent exchange of the two hydrons, which leads to an exponentially decaying curve for the probability of finding one hydron on its initial position. 21.2.2 Incoherent Tunneling and the Bell Model
As we have seen in the previous section there is a transition from coherent to incoherent tunneling, caused by the coupling to external bath degrees of freedom. This second type of tunnel process is the classical forbidden penetration of a barrier (Fig. 21.4), as for example in the Gamow model of a-decay [87, 88] or the field emission of electrons of Condon [89, 90]. The probability of penetrating the barrier depends on the energy of the incident particle and the width, shape and height of the potential barrier. For most potentials only approximate solutions, as for example the well-known Wenzel [91], Kramers [92], Brillouin [93] WKB approximation (see for example the textbook [80]), or numerical calculations of the transition probability are possible. Analytically solvable exceptions include rectangular potential steps and parabolic potentials. While the former give only very crude approximations of a real world system, the latter gives reasonably good results, when compared to experimentally determined rate constants.
653
21 Dihydrogen Transfer and Symmetry in the Light of NMR Spectroscopy
Energy
654
V0
m W a
b
x
Figure 21.4 Tunneling through an energy barrier: While the particle m with energy W < V0 is classically reflected at a, quantum mechanics allows a tunneling through the barrier from a to b.
As soon as bound states are considered there are only discrete energy levels. Nevertheless it was shown by Bell [77] that it is possible to employ approximately a continuum of energy levels for the calculations of the tunnel rates, which is adequate for the description of many experimental systems. In the simplest form (see Fig. 21.5) of the Bell model, the potential barrier is an inverted parabola. This allows the use of the known solution of the quantum mechanical harmonic oscillator for the calculation of the transition probability through the barrier. The corresponding Schrdinger equation is
2 d 2m 1 2 2 mx jWi ¼ 0 (21.48) þ E x 0 2 dx 2 "2 The ground state energy level is 1 1 E0 ¼ "x0 ¼: mx20 a2 2 2
(21.49)
Here 2a is the width of the potential barrier at the ground state. Solving for m0 ¼ x0 =2 expresses the oscillation frequency via the ground state energy E0 and the width of the potential at E0 : 1 m0 ¼ pa
rffiffiffiffiffiffiffi E0 2m
(21.50)
If the oscillator potential is inverted as shown in Fig. 21.5(b)
d2 2m 1 2 2 mx jWi ¼ 0 þ E þ x 0 2 dx 2 "2
(21.51)
the previous solution can be reused by introducing the imaginary tunnel frequency 1 mt ¼ pa
rffiffiffiffiffiffiffi E0 2m
(21.52)
From this the probability for transition through the barrier
V W 1 GðWÞ ¼ 1 þ exp 0 hmt
(21.53)
21.3 Symmetry Effects on NMR Lineshapes of Hydration Reactions
is calculated. In typical chemical reactions large numbers of particles N0 are involved. They are modeled as a stream J = dN/dt of particles hitting the barrier. In thermal equilibrium the number of particles in energy interval [W, W + dW] is given by the Boltzmann distribution dN ¼ N0 pðWÞdW 1 W exp dW ¼ N0 kT kT
(21.54)
If TðWÞ is the transition probability at energy W, the number of particles per second, which pass the energy barrier is Z J ¼ J0
¥
pðWÞTðWÞdW
(21.55)
0
Quantum mechanically the transition rate JQM of the Bell model is calculated by inserting Eq. (21.53) into Eq. (21.55). W exp GðWÞdW kT 0
Z ¥ J W V W 1 1 þ exp 0 exp dW ¼ 0 kT hmt kT 0
JQM ¼
J0 kT
Z
¥
(21.56)
Comparing this to the classically allowed rate from Arrhenius law V Jc ¼ J0 exp 0 kT
(21.57)
one can define the tunnel correction: Qt ¼
JQM expðV0 =kTÞ ¼ kT Jc
Z
¥ 0
W GðWÞdW exp kT
(21.58)
For the numerical evaluation, Eq. (21.58) can be approximated by replacing the integration with a discrete sum over a set of energy levels. The result of such an evaluation is displayed in Fig. 21.5(d), which compares the classical Arrhenius rate with the quantum mechanical rates calculated from Eq. (21.56).
21.3 Symmetry Effects on NMR Lineshapes of Hydration Reactions
The symmetry effects associated with the Pauli principle provide an interesting diagnostic tool for the study of hydration and hydrogen transfer reactions. Employing spin-polarized parahydrogen (p-H2) gas in these reactions, a very
655
21 Dihydrogen Transfer and Symmetry in the Light of NMR Spectroscopy
a)
b)
V0
W -a
c)
J0
0
-a
a
0
a
d) 12 Jclass V0
log(k sec)
656
10 8
Quantummechanical
6 Plateau 4 0
Figure 21.5 The Bell tunnel model: (a) Quantum mechanical harmonic oscillator with its ground state wavefunctions. (b) Inverted harmonic oscillator potential. (c) A stream of particles with a Boltzmann distribution of energies hits the barrier. Classical only those particles with W > V0 can pass the barrier.
Classical 5
10 15 20 1000/T [K-1]
25
Quantum mechanically particles with W < V0 may also pass the barrier. (d) Comparison of classical Arrhenius rate and quantum mechanical corrected rate. While classically the rate goes to zero for Tfi0, quantum mechanically a finite plateau is approached (adapted after Bell [77]).
strong signal enhancement and thus selective spectroscopy of the reaction side is possible, as originally proposed by Bowers and Weitekamp [51, 56]. The origins of symmetry induced nuclear polarization can be summarized as follows: as mentioned above molecular dihydrogen is composed of two species, para-H2, which is characterized by the product of a symmetric rotational wavefunction and an antisymmetric nuclear spin wave function and ortho-H2, which is characterized by an antisymmetric rotational and one of the symmetric nuclear spin wavefunctions. In thermal equilibrium at room temperature each of the three ortho-states and the single para-state have practically all equal probability. In contrast, at temperatures below liquid nitrogen mainly the energetically lower para-state is populated. Therefore, an enrichment of the para-state and even the separation of the two species can be easily achieved at low temperatures as their interconversion is a rather slow process. Pure para-H2 is stable even in liquid solutions and para-H2 enriched hydrogen can be stored and used subsequently for hydrogenation reactions [54]. The transformation of this molecular rotational order into nuclear spin order during the hydrogenation reaction leads to typical polarization patterns in the NMR spectra of the hydrogenation products. Depending on whether the experiment is performed inside or outside of a magnetic field (see Fig. 21.6), these types of experiments have been referred to under the acronyms PASADENA (Parahydrogen and Synthesis Allow Dramatically Enhanced Nuclear Alignment) or
21.3 Symmetry Effects on NMR Lineshapes of Hydration Reactions
a) A2
b) A2 reaction
AX
reaction
A‘2
AX
|αα>
|αα>
|αβ>
|αβ>
|βα>
|βα>
K
|S0>
|ββ>
PASADENA Figure 21.6 Schemes of simple PHIP experiments in an AX-spin system [56]. (a) Ideal PASADENA experiment. With the reaction rate K the population of the para-H2 |S0> state is in a sudden change transferred to the jabi and jbai states, which are equally populated. (b) Ideal ALTADENA experiment.
|S0>
K
|S‘0>
|ββ>
ALTADENA With the reaction rate K the population of the para-H2 |S0. state is transferred to the |S¢0. state of the final product. From there the population is adiabatically transferred to the jbai state of the final product, resulting in a selective population of this level (adapted from Bowers et al. [56]).
ALTADENA (Adiabatic Longitudinal Transport after Dissociation Engenders Net Alignment) [56]. All variants are nowadays known under the more generally acronym of PHIP (Parahydrogen Induced Polarization) [52]. The basic theory of the PHIP effect in an AX-spin system was given in the review paper of Bowers and Weitekamp [56]. In the original work only a simple AX-spin system with pure coherent exchange was considered. In practice, however, the situation will be a lot more complicated because there are several coherent and incoherent reaction pathways in the course of a catalyzed hydrogenation reaction, as depicted in Fig. 21.7. To analyze these situations we first study analytically the PHIP effect for a general two spin system and then the effect of incoherent exchange on the PHIP line shape. 21.3.1 Analytical Solution for the Lineshape of PHIP Spectra Without Exchange
In the case of a simple reaction from the para-H2 state to the product state it is possible to derive analytical solution of the lineshape of PHIP spectra [65]. In the following an alternative derivation of the lineshape is given. For simplicity the reaction is assumed as a one-way reaction, i.e. no back reaction (kba=0, a, b denote the two different sites). For the para-H2 state, the Hamiltonian is given as a pure A2 spin system. ^ ^ a ¼ Ja~ H I^a~ Sa
(21.59)
657
658
21 Dihydrogen Transfer and Symmetry in the Light of NMR Spectroscopy
M + H2 + XC≡CY
C kCB
B
M + H2 + XC≡CY
M[XC≡CY] + H2
M [H2][XC≡CY]
kAB X
A M+
Ha M[H2] ≡ RM
Y C=C Hb Ha
Ha RM Hb
dihydrogen complex
Hb dihydride complex
Figure 21.7 Possible pathways of the catalyzed hydrogenation reaction of an unsaturated organic substrate involving various transition metal dihydrogen and/or dihydride intermediates [62]. The initial free dihydrogen is labeled as site C, the intermediates containing the dihydrogen pair as B, and the product containing the dihydrogen pair as A.
For the end product of the reaction a general liquid Hamiltonian is assumed ^ ^ zr þ mI ^Izr þ Jb~ ^ b ¼ mS S I^b~ H Sb ;
which has the following matrix representation 0 m þm J 1 b S I 0 0 0 2 þ 4 B C Jb Jb mS mI 0 0 C 2 þ 4 2 ^b ¼ B H B C Jb Jb mS þmI @ A 0 0 2 2 4 Jb mS mI þ 0 0 0 2 4
(21.60)
(21.61)
The initial condition of the problem is that at the beginning all hydrogen atoms are in the singlet S0 state of the para-H2. rð0Þ ¼ jS0 >< S0 j 1 ¼ jab ba >< ab baj 2 1 ~^~^ SI 4 0 1 0 0 0 0 1B0 1 1 0 C C ¼ B @ 0 1 1 0A 2 0 0 0 0 ¼
(21.62)
21.3 Symmetry Effects on NMR Lineshapes of Hydration Reactions
As a consequence of this the initial dynamics before any pulse is applied occurs only in the subspace spanned by the elements qa(22,23,32,33), qb(22,23,32,33) and the analysis of the dynamics can be restricted to this subspace. In the initial paraH2 state, the equation of motion is: d ^ a; r ^ a kab r ^a ^ ¼ i H r dt a
(21.63)
^ a commutes with r ^a ð0Þ, no oscillations of the coherences Since the Hamiltonian H are observed and the solution of the equation for qa(t) is simply given by an exponential decay ^a ðtÞ ¼ expðkab tÞ^ ra ð0Þ r
(21.64)
In the next step the differential equation for qb(t) has to be solved: d 1 ^ b; r ^b þ kab r ^a ^ ^ ¼ i H r r dt b T2b b 1 ^ b; r ^ a ð0Þexpðkab tÞ ^ ^b þ kab r r ¼ i H T2b b
(21.65)
For the solution of this differential equation it is advantageous to transform the matrix equation of Hilbert space into a vector equation in Liouville space (Eb is the identity matrix of the four-dimensional subspace): ^^ ¼ H ^b H ^ b Eb E ^b L b
(21.66)
^^ is The matrix representation of L b 0
1 Jb 0 J2b 0 2 B J Jb C 0 ^^ ¼ B 2b Dm 2C L B Jb C b @ 2 0 Dm J2b A Jb Jb 0 2 0 2
(21.67)
where we have introduced for abbreviation Dm ¼ mbS mbI . The inhomogeneous differential equation (21.65) becomes d 1 ^^ r ^ a ð0Þexpðkab tÞ ^ ^ ¼ 2ipL r r b ^ b þ kab r dt b T2b b
(21.68)
The solution of Eq. (21.68) is ^b ðtÞ ¼ r
1 ^^ þ k 1 2ipL kab b ab T2b ^^ 1 t expðk tÞ r ^a ð0Þ · exp 2ipL b ab T2b
(21.69)
659
660
21 Dihydrogen Transfer and Symmetry in the Light of NMR Spectroscopy
where the fact has been exploited that
^^ 1 þ k ; 2piL ^^ 1 ¼ 0 2piL b ab b T2b T2b
(21.70)
However, instead of directly evaluating Eq. (21.68) by Eq. (21.69) it is advantageous to combine the coherent evolution and the relaxation, i.e. the homogeneous part of Eq. (21.68) and transform the resulting matrix into a fictive spin –1/2 system, employing the normalized Pauli matrices as base vectors. The corresponding transformation is 0 1 1 0 0 1 p ffiffi ffi 1 0C ^^ ¼ 1 2B B0 1 C (21.71) S 1 0A 2 @ 0 1 1 1 0 0 1 ^^ becomes the block diagonal In this system, the matrix L b 0 1 1 T2b 0 0 0 B 2ipDt 0 C T12b C ^^ 1 ¼ B 0 L B C b 1 2ipJb A 2ipDt T2b T2b @ 0 0 0 2ipJb T12b
(21.72)
It can be diagonalized in a second step by transforming with the matrix 0
1 0 cC C sffiffi C p 2 2 2A 1ffiffi p sffiffi 0 pcffiffi2 p 2 2
1 B0 B ^ ^2 ¼ B S @0
0 s pcffiffi
0 0 p1ffiffi
(21.73)
Dm Jb with c ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi and s ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2 2 Dm2 þ Jb2 Dm þ Jb
The resulting matrix of the homogeneous part is 0
T12b B 0 B B B 0 B @ 0
0 T12b 0
0 0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi T12b þ 2ip Dt2 þ Jb2
0
0
0 0
1
C C C C ¼ ek dkl 0 C A ffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 T2b 2ip Dt2 þ Jb2
(21.74) Here the ek denote the eigenvalues.
21.3 Symmetry Effects on NMR Lineshapes of Hydration Reactions
Applying the same transformation to the inhomogeneous part of Eq. (21.68) ^ ^ ^2 S ^1 r ^): ^¼S yields (^ r denotes the density matrix in the transformed frame, i.e. r 0 pffiffiffi 1 p2ffiffiffi 1B 2C ^ ^ ^ ^ B Cexpðkab tÞ ^a ðtÞ ¼ S2 S1 ra ðtÞ ¼ @ r 2 c A c
(21.75)
With this the solution for the density matrix elements becomes (k = 1.4, index of eigenvalue ek ): rbk ðtÞ ¼
rak kab ðexpðkab tÞ expðek tÞÞ ek kab
(21.76)
Assuming that the oscillating matrix elements rb3 and rb4 disappear, a quasi-stationary limit of rbk can be calculated. If T2>>1/kab and T2>>1/(Dm2+Jb2)1/2 and kab <(Dm2+Jb2)1/2 it follows for t fi ¥: rb1 ð¥Þ ¼
1 pffiffiffi 2 2
rb2 ð¥Þ ¼ rb3 ð¥Þ ¼ 0
1 pffiffiffi Jb 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2 J 2 þ Dm2
(21.77)
b
rb4 ð¥Þ ¼ 0
Transforming back into the original frame gives: rb1 ð¥Þ ¼
1 DmJb 1 2 2 Jb þ Dm2
rb2 ð¥Þ ¼
J2 1 2 b 2 Jb þ Dm2
rb3 ð¥Þ ¼
J2 1 2 b 2 Jb þ Dm2
1 DmJb rb4 ð¥Þ ¼ 1þ 2 2 Jb þ Dm2
!
! (21.78)
The resulting spectral line can be calculated numerically from these elements of the density matrix. For the interpretation of the PHIP spectral line shape, the elements qb1 and qb4 are of particular interest, since they correspond to the level populations of the jabi and jbai states. Their dependence on Jb is shown in Fig. 21.8.
661
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21 Dihydrogen Transfer and Symmetry in the Light of NMR Spectroscopy
AB,Jb≈∆ν ρb4 AX
A2 ρb1
0
200
400
600
800
Jb [Hz]
Figure 21.8 Calculation [86] of qb1 and qb4, which are proportional to the populations of the jabi and jbai states in a PASADENA type PHIP experiment as a function of the coupling constant Jb. For a pure AX or A2 system the populations are equal, while for an AB system deviations exist, which are strongest for Jb » Dm. Calculation with Dm = 69 Hz.
21.3.2 Experimental Examples of PHIP Spectra
As mentioned above, PHIP is a versatile tool for the study of catalytic reactions. In the following three different experimental examples of this remarkable power, taken from recent work from the Bargon group followed by a theoretical example of reaction pathway sensitivity from our group are given. The experimental examples show a PHIP experiment performed under ALTADENA conditions, a PHIP experiment performed under PASADENA conditions and a PHIP experiment followed by a heteronuclear polarisation transfer from 1H to 13C.
21.3.2.1 PHIP under ALTADENA Conditions The first example (see Fig. 21.9) shows a 1H-PHIP spectrum of the hydration of perdeuterated styrene obtained under ALTADENA conditions, i.e. with hydration outside the NMR magnet taken from Ref. [94]. The spectrum of the hydration product ethyl-benzene exhibits the typical strong spin polarized signals at 1 ppm and 3 ppm. Between 5 ppm and 6 ppm there are additional spin polarized signals, which stem from a side reaction. In Ref. [94] it was shown that the ratio of hydration versus geminal exchange is controllable by addition of CO.
21.3.2.2 PHIP Studies of Stereoselective Reactions PHIP allows also the PASADENA investigation of the stereoselectivity of a reaction. A typical example is given in Ref. [70], where the stereoselective hydrogenation of 3-hexyne-1-ol under the influence of the cationic ruthenium complex [Cp*Ru(g4-
21.3 Symmetry Effects on NMR Lineshapes of Hydration Reactions
663
Figure 21.9 1H in situ PHIP NMR spectrum of the hydrogenation of styrene-d8 using H2Ru(PPh3)4 as catalyst measured under ALTADENA conditions (adapted from Ref. [94]).
CH3CH=CHCH=CHCOOH)][CF3SO3] is shown in a 1H-PHIP experiment (see Fig. 21.10). The spectrum reveals the characteristic PHIP polarization pattern of adsorptive and emissive lines. This polarization pattern proves the pair-wise transfer of the para-hydrogen to the substrate. The observed anti-phase coupling constant of 15.5 Hz is a typical value for an olefinic trans coupling constant and identifies the formation of the corresponding (E)-alkene by trans-hydrogenation of the substrate.
5.9
5.8
5.7
5.6
5.5
5.4
ppm(TMS) 1H
Figure 21.10 Olefinic region of a 200 MHz PHIP spectrum recorded during the hydrogenation of 3-hexyne-1-ol using Cp*Ru catalyst (adapted from Ref. [70]).
5.3
5.2
5.1
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21 Dihydrogen Transfer and Symmetry in the Light of NMR Spectroscopy
21.3.2.3 13C-PHIP-NMR The last experimental example shows that PHIP is also a powerful starting point for sensitivity enhancement of NMR spectroscopy of hetero nuclei in catalytic reactions. The homogeneously catalyzed hydrogenation of an unsaturated substrate with para-hydrogen leads not only to strong signal enhancements in 1H NMR spectra, but can also give rise to strong heteronuclear polarization, in particular in ALTADENA type experiments where the hydrogenation is carried out in low magnetic fields. As a typical example taken from Ref. [74], the polarization transfer from protons to 13C nuclei during the hydrogenation of 3,3-dimethylbut-1-yne with para-hydrogen and [Rh(cod)(dppb)]+ as catalyst is shown in Fig. 21.11. In the single shot 13C-NMR spectrum recorded in situ all 13C resonances can be observed with good to excellent signal-to-noise ratios. The enhanced SNR is due to the PHIP effect resulting from a transfer of the initial proton polarization of the parahydrogen to the carbon atoms.
ppm(TMS) Figure 21.11 13C in situ PHIP spectrum after hydrogenation with para-hydrogen and polarisation transfer from protons to carbons. Note the extremely high signal/noise ratio in the single shot spectrum, which is a measure for the strong signal enhancement obtained by PHIP (adapted from Ref. [74]).
21.3 Symmetry Effects on NMR Lineshapes of Hydration Reactions
Due to the ALTADENA procedure, nuclear polarization is transferred to all magnetically active nuclei, since all resonance frequencies are virtually the same for all nuclei at the very low magnetic field of the Earth. The corresponding spin systems are of a high order, i.e. the difference in the resonance frequencies between the carbons (13C) and the protons is small, compared with their coupling constants. This is an essential prerequisite for an efficient polarization transfer from protons to a large number of carbons. 21.3.3 Effects of Chemical Exchange on the Lineshape of PHIP Spectra
Equations (21.78) allow the calculation of PHIP spectra in the case of non-exchanging hydrogen atoms, i.e. for k12 ¼ 0. If k12 > 0, however, the lineshape of the PHIP spectra does depend on the chemical exchange. Interestingly this allows one to extract information about reaction intermediates, which are not directly visible in the NMR spectra [62] owing to their short lifetime or low concentration. Employing the quantum mechanical density matrix formalism it is possible to take into account the whole reaction pathway of Fig. 21.12 where both coherent and incoherent reaction pathways are present in the case of a PHIP experiment and convert the PHIP experiment into a diagnostic tool for all stages of a hydrogenation reaction. Such an analysis was performed in Ref. [62]. In these calculations the initial condition was that at the start of the reaction all molecules are in the p-H2 state of site C, i.e., a pure singlet spin state, represented as a circle in Fig. 21.12, which shows the different possible reaction pathways. Moreover, all intermolecular exchange reactions were treated as one-sided reactions, i.e. the rates of the back reactions were set to zero. Two different scenarios are analyzed, namely where the reaction goes as a twostep process, as depicted in Fig. 21.12(a) or where the reaction goes as a three-step process (Fig. 21.12(b)). Accordingly in Fig. 21.12(a) only two sites r = C or A are included. For simplicity, only the forward reactions are shown, but in the formalism the backward reactions are also included. In both sites C and A the possibility for incoherent exchange of the two hydrogen atoms Ha and Hb, characterized by the rate constants kCC and kAA is included. In addition, the parameter pCA is introduced, which describes the regio-selectivity of the reaction between C and A. It represents the probability of permutation of the two hydrogen atoms during the transfer from C to A and A to C, respectively. The step is completely regio-specific if pCA = 0 or 1 and completely non-selective when pCA = 0.5 and partially regio-selective for other values of pCA. In the latter two cases the reaction would lead to isotope scrambling if the reaction is performed with an HD pair as substrate. It is found that this regio-selectivity requires that the two protons are labeled prior to the reaction by different Larmor frequencies, otherwise it does not affect the results, as is the case if C corresponds to free dihydrogen; however, the regio-selectivity is important when an additional intermediate B is included in the more general case of Fig. 21.12(b) in which the two former para-H2 protons are chemically different.
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21 Dihydrogen Transfer and Symmetry in the Light of NMR Spectroscopy
Figure 21.12 Formal two-site (a) and three-site (b) reaction models of a single (a) and two-step (b) hydrogenation reaction [62]. prs = psr , r, s = A to C represents the parameter characterizing the probability of permutation of the two hydrogen atoms during the interconversion between r and s. The step is called regio-specific if prs = 0 or 1, non-regio-specific if psr = 0.5, and otherwise it is called regio-selective.
In the following, the effects of these exchange processes and isotope scrambling on the level populations and line shapes of the PHIP experiment are shown. Details of the numerical calculations are found in the original paper [62]. Figure 21.13 shows the dependence of the density matrix elements q22 and q33 on the mutual exchange rate kAA in a two-step experiment. It is evident that the mutual exchange removes the differences in the populations of the two levels jabi and jbai and thus will change the appearance of the PHIP spectra. Figure 21.14 displays this effect of an incoherent mutual exchange of the two protons in the product site A, characterized by the rate constant kAA on the PHIP spectra. Without mutual exchange there are strong differences in the line intensity pattern and the outer lines are higher than the inner ones. In the case of mutual exchange however, the intensity pattern of the normal NMR spectrum is obtained. These magnetization transfer effects are most pronounced in the case of the AB case where JA /DmA » 1, (bottom spectrum). By contrast, AX-type spectra are practically
21.3 Symmetry Effects on NMR Lineshapes of Hydration Reactions
JA = 2 Hz
ρb4
JA = 5 Hz
ρb4 ρb1
ρb1
0.2
0.4
0.6
0.8 kAA [sec-1]
JA = 10 Hz
ρb4
0.2
ρb4
ρb1
0.4
0.6
0.8 kAA [sec-1]
JA = 50 Hz
ρb1
0.2
0.4
0.6
0.8 kAA [sec-1]
0.2
0.4
0.6
0.8 kAA [sec-1]
Figure 21.13 Calculation of q22 and q33 in a PASADENA type PHIP experiment as a function of the self exchange rate ka for different spin systems [86]. In all cases the self-exchange leads to an averaging of the populations of q22 and q33.
a)
JA ∆υA
b)
c)
JA ∆υA
JA ∆υA
JA/∆υΑ
AX
0.10 0.25 0.50 0.75 1.00 Thermal Polarisation
kCA ≠0 , kAA =0
Figure 21.14 Calculated [62] NMR (a) and PHIP NMR (b,c) spectra of a two-proton spin system of compound A as a function of the ratio JA /DmA, produced in a PASADENA experiment with (p/4) x pulses by the two-site reaction C fi A (reaction time tr = 10 s; rate constant kCA = 1 s–1). (b) Without selfexchange. The ratios of the absolute outer
kCA ≠0 , kAA ≠0
AB
and inner line intensities differ from those of the normal NMR spectra (not shown). (c) a self-exchange of the two protons during the reaction time tr is introduced with kAA = 1 s–1 resulting in relative absolute PHIP-signal intensities corresponding to those of the normal NMR spectrum (a) (adapted from Ref. [62]).
667
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21 Dihydrogen Transfer and Symmetry in the Light of NMR Spectroscopy
not influenced by the exchange, neglecting the minor broadening effect of the lines which is not important for the present discussion. Calculations of the PASADENA pattern for regio-selecitvities pAB between 0 and 1 showed that the resulting density matrices and, therefore, the calculated PHIP spectra, are independent of this parameter. This is the expected result because in p-H2 the two protons are indistinguishable. Figure 21.15 shows the dependence of the density matrix elements qb1 and qb4 on the mutual exchange rate kAA in a three-step experiment. While the mutual exchange again removes the differences in the populations of the two levels jabi and jbai, the strength of the effect now depends on the lifetime of the reaction intermediate B. If this lifetime is short compared to the inverse exchange rate, the density matrix elements are only weakly affected. If the life time is long enough, however, both levels get equally populated (Fig. 21.15(b)). Moreover the regionselectivity of the reaction now also strongly influences the population numbers (Fig. 21.15(c),(d)). Again these changes in the population numbers have a strong influence on the appearance of the PHIP spectra. Figure 21.16 shows the resulting PHIP signal patterns of A formed in the three-site-reaction PASADENA of Fig. 21.12(b). The four sets of spectra illustrate the influence of kBB and of JB/DmB. If B constitutes an AX spin system (JB/DmB ), the resulting spectra show no depena)
b)
ρb4
ρb4
ρb1
ρb1
0
5
10
15 kBB [sec-1]
c)
0
d)
5
15 kBB [sec-1]
10
ρb4
ρb4 ρb1
0
Pab=0.5
5
10
ρb1 15 kBB [sec-1]
0
0.2
0.4
Figure 21.15 The calculation of q22 and q33 in a three-site PASADENA experiment as a function of the self-exchange rate kBB for an AB system for different production and decay rates: (a) completely regio-specific, Kcb = 1 s–1 Kba = 1 s–1; (b) completely region-specific, Kcb = 1 s–1 Kba = 100 s–1; (c) completely non-regio-specific; (d) dependence on the region selectivity parameter [86].
0.6
0.8 Pab
21.3 Symmetry Effects on NMR Lineshapes of Hydration Reactions
JB/∆υB
kBB=0.0 sec-1
kBB=0.2sec-1
0.10 0.25 0.50 0.75 1.00
JB/∆υB
kBB=0.5 sec-1
JA/∆υA=1
kBB=1.0 sec-1
0.10 0.25 0.50 0.75 1.00 Figure 21.16 Calculated PHIP signal patterns (adapted from Ref. [62]) of a hydrogenation product A resulting in a PASADENA experiment in the presence of the three-site reaction CfiBfiA as a function of the ratio JB/DmB. Note the differences in the line intensities (inner versus outer lines).
dence on kBB and the ratio between the absolute intensities of the outer and the inner lines corresponds to the normal spectrum. However, if B constitutes an AB spin system, as expected in the case of substantial but not too large exchange couplings, large effects are observed and the ratio between the absolute intensities of the outer and the inner lines has changed. Thus, in principle, the incoherent dihydrogen exchange, the exchange and magnetic couplings, and the chemical shifts of the two protons in the intermediate B, all leave fingerprints which can be deciphered from the PHIP pattern of A. In conclusion, the numerical simulations of the PHIP spectra show that the PHIP patterns do not only depend on the type of the experiment performed – e.g. ALTADENA in the absence and PASADENA in the presence of a magnetic field – but also on the properties of possible reaction intermediates where the reactants are bound to the employed transition metal catalyst. The important parameters of the intermediate are the chemical shifts and coupling constants of the former p-H2 protons, especially their exchange couplings, as well as the rate of an incoherent dihydrogen exchange. In addition, the regio-selectivity of the hydrogenation step is a factor determining the PHIP-patterns, whereby the individuality of the former p-H2 atoms arises from different chemical shifts in the intermediate. In summary the calculations presented in Ref. [62] represent the missing theoretical link between the phenomena of incoherent and coherent dihydrogen exchange in transition metal hydrides and the PHIP effect. Moreover, PHIP is identified as a powerful and sensitive tool to study reaction pathway effects via analysis of the polarization patterns of the final hydrogenation products.
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21 Dihydrogen Transfer and Symmetry in the Light of NMR Spectroscopy
21.4 Symmetry Effects on NMR Lineshapes of Intramolecular Dihydrogen Exchange Reactions
Symmetry induced tunneling effects influence not only hydration reactions but also intermolecular hydrogen exchange reactions. In the case of a dihydrogen exchange the spatial Schrdinger equation (Eq. (21.5)) and its solutions (Eq. (21.11)) were discussed in a previous section. Since the eigenfunctions obey the Pauli principle they couple to spin functions in accordance with their symmetry and the spin of the hydrogen isotope (i.e. 12 for 1H, 3H and 1 for 2H) and the whole dynamics of the system can again be described purely in a spin Hilbert space. The spin Hamiltonian of the system consists of three parts: The chemical shifts and/or quadrupolar interactions define the individual Hamiltonians of the spins ~ I^2 and the dipolar I^1 and ~ couplings and exchange interactions define the coupling ^ 1;2 ~ I^1 ;~ I^2 . The mutual exchange of the two nuclei corresponds to Hamiltonian H a permutation of the two nuclei which exchange their individual chemical shifts and/or quadrupolar couplings with exchange rates k12 ¼ k21 ¼ k. A relatively formal derivation in Ref. [11], which is based on the NMR lineshape analysis ideas of Alexander and Binsch [95, 96] shows that the whole dynamics is determined by the following Liouville von Neumann equation for the density matrix rg : d ^^ A þ K ^^ Þjrg Þ jr Þ ¼ ðW dt g
(21.79)
^ ^ ^ A is the sum of the Liouville super operator L ^A and the relaxation super Here W ^ ^ ^ ^ operator RA.K is the the self-exchange superoperator ^^ ¼ kð^^I d P ^^ 12 Þ K
(21.80)
which describes the exchange of the two nuclei in Liouville space. Its elements are ^ . The latter is calcu^ the identity operator ^^Id and the permutation superoperator P 12 ^ ^ ~ ^ ~ lated from the permutation operator in Hilbert space P I 1 ; I 2 (Eq. (21.16)) via * ^^ ¼ P ^ ~ ^ ~ P I^1 ;~ I^1 ;~ I^2 P I^2
(21.81)
* ^ ~ ^ ~ where P I^1 ;~ I^2 denotes the complex conjugate of operator of P I^1 ;~ I^2 . 21.4.1 Experimental Examples
The energy differences between the tunnel levels and thus the tunnel frequency depend very strongly on the hindering potential 2V0 and vary between zero and
21.4 Symmetry Effects on NMR Lineshapes of Intramolecular Dihydrogen Exchange Reactions
1012 Hz (see Fig. 21.2) i.e. over roughly twelve orders of magnitude. As a result of this extremely broad possible dynamic range, no single spectroscopic technique is able to cover the range of possible tunnel splitting. It follows that the experiment must be chosen according to the size of the expected tunnel frequency. While slow tunneling processes can be studied by 1H liquid state NMR spectroscopy, intermediate processes are accessible by 2H solid state NMR spectroscopy and relaxometry and fast processes are accessible by incoherent neutron scattering (INS). Fortunately the dynamic ranges of these techniques overlap partially. From this it follows that, at least in principle, a complete tunneling kinetics can be determined by combining some of these techniques. In the following three experimental examples of such quantum mechanical exchange processes are discussed. The examples are taken from liquid state NMR spectroscopy, solid state NMR spectroscopy and INS.
21.4.1.1 Slow Tunneling Determined by 1H Liquid State NMR Spectroscopy As discussed above in 1H liquid state NMR a tunnel splitting, i.e. exchange coupling, and a conventional magnetic J-coupling have the same influence on the 1H liquid state NMR spectra. This theoretical fact is nicely demonstrated in Fig. 21.17). It displays the superimposed experimental and calculated 1H liquid state NMR hydride signals of (C5Me5)RuH3(PCy3) (Cy = cyclohexyl) 1 dissolved in tetrahydrofuran-d8 [19]. At low temperatures site 2 exhibits a triplet splitting characterized by a temperature dependent exchange coupling constant J12 = J23. A coupling constant J24 with the 31P nucleus in site 4 cannot be resolved. Sites 1 and 3 are equivalent and exhibit the expected doublet splitting with the nucleus in site 2, as J12 = J23. Furthermore, each line component is split by scalar coupling with the 31P nucleus in site 4 with J14 = J34 = 32 Hz. In contrast to J14, corresponding to a magnetic coupling, J12 represents an exchange coupling which increases strongly with temperature, as revealed by the typical AB2X signal pattern. Above 210 K, line broadening and coalescence occurs, eventually leading to a doublet with an average splitting of J(1H–31P) = (J14 + J24 + J34)/3 = 22 Hz. This splitting indicates that the classical exchange process observed is purely intramolecular. By lineshape analysis the exchange coupling constants J12 and the rate constants kHH of the classical exchange are obtained.
21.4.1.2 Slow to Intermediate Tunneling Determined by 2H Solid State NMR Liquid state NMR experiments like above only allow the determination of slow coherent and incoherent tunnel rates, owing to the limited frequency range of the hydrogen chemical shifts. Faster tunneling processes can be studied by 2H solid state NMR spectroscopy [11, 40]. Figure 21.18 compares experimental 2H solid echo NMR spectra and the simulated 2H FID-NMR spectra of the Ru-D2 complex trans-[Ru(D2)Cl(dppe)2]PF6 (RuD2). At temperatures below 10 K the singularities of a satellite Pake pattern are visible as a splitting of the spectra at –60 kHz. This satellite Pake pattern is the
671
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21 Dihydrogen Transfer and Symmetry in the Light of NMR Spectroscopy
Figure 21.17 Superposed temperature dependent experimental and calculated 500 MHz 1H NMR hydride signals of (C5Me5)RuH3(PCy3) (Cy = cyclohexyl) 1 dissolved in tetrahydrofuran-d8 (adapted from Ref. [19]).
result of the coherent tunneling of the two g2-bound deuterons in the complex. While the satellite transitions are fairly narrow at 5.4 K they start to smear out at higher temperatures. This smearing out is the effect of the incoherent tunneling which starts to dominate the dihydrogen dynamics and thus the spectral lineshape at higher temperatures. At temperatures above 23 K the 2H NMR line corresponds to a typical 2H NMR quadrupolar Pake pattern with an asymmetry of g ¼ 0:2. The satellite pattern has completely disappeared. The width of the line decreases slowly with increasing temperature, which is an indication of a weakening of the g2-bond between the metal and dihydrogen. Assuming the simple harmonic potential of Eq. (21.5) the height of the rotational barrier can be estimated. Using the value of RHH = 1 , a rotational barrier of 2V0 ¼ 270 meV (6.22 kcal mol–1) is calculated.
21.4 Symmetry Effects on NMR Lineshapes of Intramolecular Dihydrogen Exchange Reactions
+ P
D-D P
PF6-
Ru P
Cl
P
230 K 103 K 64.7 K 36.7 K 31.4 K 8.8 K 6.2 K 5.8 K 5.4 K 100
0
-100
ν [kHz] Figure 21.18 Experimental solid echo 2H NMR spectra of the Ru-D complex 2 trans-[Ru(D2)Cl(dppe)2]PF6 (Ru-D2), measured in the temperature range 5.4 to 230 K. At temperatures below 8.8 K a splitting in the 2H NMR lineshape is clearly visible (arrows). This splitting can be explained by a coherent
tunneling of the two deuterons in the Ru-D2 sample (simulation as 2H FID-NMR experiment). The simulations were performed with qzz ¼ 80–3kHz (i.e. qcc ¼ 107–4kHz), g = 0 and a jump angle of 2b ¼ 90 between the two tensor orientations (adapted from Ref. [40]).
21.4.1.3 Intermediate to Fast Tunneling Determined by 2H Solid State NMR Faster incoherent tunnelling processes can be studied by 2H solid state NMR relaxometry [40, 41]. In these experiments the experimentally determined spin– lattice relaxation rates are converted into incoherent exchange rates. The latter are then evaluated, for example with the Bell tunnelling model described above. As a first experimental example, Fig. 21.19 displays the result of the T1 measurements on the same Ru-D2 complex trans-[Ru(D2)Cl(dppe)2]PF6 (Ru-D2) as above. Due to the low sensitivity of the sample the spin–lattice relaxation rates were measured only at some selected temperatures. The lowest T1 value (0.12–0.02 s) was found at 97 K. At low temperatures the T1 data show strong deviations from simple Arrhenius behavior. The exchange rates from the relaxation data are obtained for KEFG = 0.3p2(60 kHz)2 and the rate data from the spectra by lineshape analysis. As a second experimental example, Fig. 21.20 presents the experimental results of the temperature dependence of the 2H NMR spin–lattice relaxation time mea-
673
21 Dihydrogen Transfer and Symmetry in the Light of NMR Spectroscopy
Experiment qcc= 60kHz
100
1
+ D-D
P
P Ru
0
P
1
P
Cl
10
PF6-
T1 [sec]
log(T1 [sec])
2
0.1
-1
50
100
150 -1
1000/T [K ] Figure 21.19 T1relaxation data of the Ru-D2 complex ((adapted from Ref. [40]). Experimental points from lineshape analysis and relaxation measurements. The solid line is calculated from the exchange rates calculated from the modified Bell model using the value of KEFG = 0.3p2(60 kHz)2.
100
T1[sec]
674
10
1
P(Cy)3 CO D W
OC OC
5
10
1000/T
D
P(Cy)3
15
20
[K-1]
Figure 21.20 Experimental temperature dependence of the 2H spin–lattice relaxation in the W-D2 complex (adapted from Ref. [41]). The data exhibit deviations from Arrhenius behavior at low temperatures. The solid line is calculated from the exchange rates calculated from the Bell model.
surements on the W-D2 complex W(PCy3)2(CO)3(g2-D2), also known as the Kubas complex, together with a calculation of the relaxation times. The T1 measurements in the temperature regime from 50 to 230 K show a strong temperature dependence of T1 with a sharp minimum close to 110 K. At the minimum a T1
21.4 Symmetry Effects on NMR Lineshapes of Intramolecular Dihydrogen Exchange Reactions
relaxation time of (0:68–0:15) s is found. It is evident that in the low temperature branch of the spin–lattice relaxation curve there are again deviations from a simple Arrhenius behavior, visible in a flattening of the curve.
21.4.1.4 Fast Tunneling Determined by Incoherent Neutron Scattering Very fast coherent and incoherent tunneling processes can be studied by incoherent neutron scattering (INS). The basic mechanism of interpretation is closely related to the liquid state NMR experiment in the slow tunnel regime, however, now the energy scale of the tunnel splitting is of the order of fractions of meV, i.e. from 1010 to 1011 Hz. Here the INS lineshape of the energy gain and energy loss transitions are analyzed. They correspond to transitions between the singlet and triplet wavefunctions [19]. From this analysis the coherent tunnel frequency and the incoherent tunnel rates are determined and the spectral parameters J and k are elucidated. J determines the line position, k the increase in line width due to the presence of incoherent exchange. As an experimental example of such an INS lineshape analysis, the INS spectra of the protonated isotopomer of the same tungsten dihydrogen complex W(PCy3)(CO)3(g2-H2) are presented. The superimposed experimental and calculated spectra are depicted in Fig. 21.21. Here the lineshape associated with the two rotational tunnel transitions of the complex is simulated as a function of the parameters J and k. For the sake of clarity, plots of the calculated line shapes of the outer rotational tunnel transitions without the contribution of the quasi-elastic center line are included. J increases only slightly with increasing temperature, in contrast to the Lorentzian line widths W which increase strongly. In other words, the lines broaden with increasing temperature until they disappear. One notes that the relative intensity of the singlet–triplet and the triplet–singlet transitions are almost the same over the whole temperature range covered, in contrast to the case of a thermal equilibrium between the singlet and the triplet states. This indicates that the singlet–triplet conversion rates are very slow in the sample measured, and that the actual relative intensity of the two peaks is arbitrarily dependent on the history of the sample. 21.4.2 Kinetic Data Obtained from the Experiments
The above described experiments allow determination of the coherent and incoherent dihydrogen exchange rates of the two complexes.
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21 Dihydrogen Transfer and Symmetry in the Light of NMR Spectroscopy
OC OC
P(Cy)3 CO H W
H
P(Cy)3
Figure 21.21 Superposed experimental and calculated INS spectra of W(PCy)2 (CO)3(g-H2) as function of temperature (adapted from Refs. [19, 42, 97]). W is the total line width in meV; J is the rotational tunnel splitting in meV (1 meV = 2.318 1011 Hz = 8.065 cm–1).
21.4.2.1 Ru-D2 Complex In the case of the Ru-D2 complex the data from the lineshape analysis and the T1relaxation data are combined in Fig. 21.22 which shows an Arrhenius plot of the temperature dependence of X12 and k12 . While the temperature dependence of X12 is very weak and nearly linear in the temperature window between 5 and 20 K, the incoherent exchange rate k12 exhibits a strong non-Arrhenius behavior and varies from 5 · 103 s–1 at 5.4 K to ca. 2:5 · 106 s–1 at 103 K and ca. 1011 s–1 at 300 K. The rate data from both types of experiments overlap between 20 K and 100 K and there is an excellent agreement between the values. This indicates that both rates result from the same motional process. The simulation of the temperature dependence was performed assuming a thermally activated tunneling process, described by a Bell type of tunneling. The high temperature rate in the tunnel model was chosen as 4 · 1012 s–1, which is expected from the Eyring equation. Since the observed increase in k12 at low temperatures is not obtainable by a simple one-dimensional Bell model an effective power law potential was employed: 1 G T T01 Veff ðT 1 Þ ¼ VðT01 Þ þ ðVðT11 Þ VðT01 ÞÞ 1 (21.82) T1 T01
21.4 Symmetry Effects on NMR Lineshapes of Intramolecular Dihydrogen Exchange Reactions
12
k12 from T1
11
+
X12
P
X12(T)
8
D-D P
PF6-
9
10
Ru P
Cl
P
7
10
-1
10
10
[sec ]
log([sec-1])
k12 from spectra Bell
6 5
10 4 0
50
100
150
200
-1
1000/T [K ] Figure 21.22 Arrhenius plot of the temperature dependence of the coherent tunneling and incoherent exchange rates in the Ru-D2 sample (adapted from Ref. [40]), extracted from Fig. 21.18 and Fig. 21.19. The solid line is the result of a fit of the temperature dependence of the incoherent rates using a modified Bell tunnel model (see text). The dashed line is a simple linear fit of the coherent tunnel rates.
The best fit of the experimental rates (solid line in Fig. 21.22) was found for an exponent of G = 0.7. The effective potential varies between 268 meV(6.18 kcal mol–1) at 5.4 K and 129 meV (2.97 kcal mol–1) at 300 K. This effective potential gives a good reproduction of the experimental data. These rates were used to calculate the whole T1 dependence (solid line in Fig. 21.19). Moreover there is an excellent agreement between the low temperature value of 268 meV and the value of 270 meV extracted from the 2H NMR lineshape analysis. This temperature dependent effective potential shows that a complete description of the temperature dependence of the rates needs at least a two-dimensional model, where the average RHH and/or RRuH distances are functions of the temperature. 21.4.2.2 W(PCy)3(CO)3(g-H2) Complex In the case of the W-H2 complex NMR data from the deuterated complex and INS data from the protonated complex are available. This allows a comparison of the exchange rates and thus a determination of the H/D isotope effect of the reaction rate. For this the T1 values from Fig. 20.21 are converted to rate constants of the D–D exchange and plotted together with the rate data of the H–H exchange from the INS spectra. The resulting curve (Fig. 21.23) shows a deviation from simple Arrhenius behavior at low temperatures. This deviation is evidence for the presence of a quantum mechanical tunneling process at low temperatures, similar to the tunneling observed in the Ru-D2 sample. Comparison of these rate data with the H–H exchange rates determined from the lineshape analysis of the INS spectra of the protonated species reveals a strong isotope effect, which increases with lower temperatures.
677
21 Dihydrogen Transfer and Symmetry in the Light of NMR Spectroscopy
OC OC
P(Cy)3 CO H W
OC
H
OC
P(Cy)3
P(Cy)3 CO D W
D
P(Cy)3
13
10
k[sec-1]
678
W-H2, INS
11
W-D2, 2H-T1
10
9
10
7
10
5
10
5
10
15
20
1000/T [K-1] Figure 21.23 Arrhenius plot of the temperature dependence of the incoherent exchange rates in the W-D2 sample, extracted from the 2H T1 data (adapted from Ref. [41]). The data are compared to data obtained on the W-H2 complex, determined by INS. The solid lines are the results of fits of the temperature dependence of the incoherent rates using a Bell type tunnel model. The fits reveal a strong isotope effect, which is not solely attributable to a simple mass effect. The high temperature limit of the rates was chosen as 4 1012 s–1, according to the Eyring equation.
Calculations with the Bell tunnel model reveal that this isotope effect is not solely explainable by the differences of the masses of the two hydrogen isotopes. Thus the activation energy must also have changed. This change in the activation barrier may be caused by isotope effects on the M–D and D–D versus M–H and H–H distances and/or by differences in the zero point energy of the ground or an activated state, which serves as the transition state for the tunneling. At low temperatures the latter is probably the major contribution to the strong isotope effect, since the quadrupolar coupling constant of the low temperature spectra (not shown) is practically constant at low temperatures.
21.5 Summary and Conclusion
This chapter presents some effects symmetry has on the rates and mechanisms of chemical reactions. The reaction kinetics of low mass groups like dihydrogen or dideuterium, in particular at low temperatures, is strongly influenced by quantum mechanical tunneling processes and the Fermi postulate of the symmetry of the
References
wavefunction. These effects are particularly clearly manifested in NMR spectra, where coherent tunnel processes are visible as line splitting and incoherent tunnel processes are visible as line broadenings or relaxation rates. The complex kinetics of a superimposed coherent and incoherent exchange on both INS and NMR lineshapes is describable via two simple, temperature dependent spectroscopic parameters J and k, which are measures of the tunnel splitting and the incoherent exchange rate. Symmetry effects are also important for the diagnostic application of parahydrogen in para-hydrogen induced polarization (PHIP) effects. While the spinphysics of these isotopomers is well understood there is still a large field of possible applications. Probably the current biggest challenge in this field is the development of biophysical and medical applications of these spin-isotopomers. There the extremely high spin polarization could be employed for sensitivity enhancements in MRI or functional studies of hydrogenase and related enzymes. Finally, we wish to note that hydrogen is not the only small molecule, where molecular exchange symmetry causes the existence of a para- and an ortho- spin isotopomer. Water is another important example. In the gas phase it exists as para- or ortho-water. They are distinguishable by IR. Their concentration ratio is used in astronomy as a remote temperature sensor. The spin conversion mechanisms of these isotopomers are still an open field for future studies [98, 99].
Acknowledgements
This research has been supported by the Deutsche Forschungsgemeinschaft, Bonn, and the Fonds der Chemischen Industrie (Frankfurt).
References 1 A. Farkas, Orthohydrogen, Parahydrogen
2
3 4 5
6
and Heavy Hydrogen, Cambridge University Press, Cambridge, 1935. G. J. Kubas, R. R. Ryan, B. I. Swanson, P. J. Vergamini, H. J. Wasserman, J. Am. Chem. Soc. 116, 451 (1984). G. J. Kubas, Acc. Chem. Res. 21, 120 (1988). N. Aebischer, U. Frey, A. E. Merbach, Chem.Comm., 2303 (1998). G. Albertin, S. Antoniutti, S. Garciafontan, R. Carballo, F. Padoan, J. Chem. Soc., Dalton Trans., 2071 (1998). I. Alkorta, I. Rozas, J. Elguero, Chem. Soc. Rev. 27, 163 (1998).
7 V. I. Bakhmutov, Inorg. Chem. 37, 279
(1998). 8 T. Y. Bartucz, A. Golombek, A. J. Lough,
P. A. Maltby, R. H. Morris, R. Ramachandran, M. Schlaf, Inorg. Chem. 37, 1555 (1998). 9 M. G. Basallote, J. Duran, M. J. Fernandez-Trujillo, M. A. Manez, J. Chem. Soc., Dalton Trans., 2205 (1998). 10 C. Bohanna, B. Callejas, A. J. Edwards, M. A. Esteruelas, F. J. Lahoz, L. A. Oro, N. Ruiz, C. Valero, Organometallics, 373 (1998). 11 G. Buntkowsky, H.-H. Limbach, F. Wehrmann, I. Sack, H. M. Vieth,
679
680
21 Dihydrogen Transfer and Symmetry in the Light of NMR Spectroscopy R. H. Morris, J. Phys. Chem. A 101, 4679 (1997). 12 B. Chaudret, Coord. Chem. Rev. 180, 381 (1998). 13 A. C. Cooper, K. G. Caulton, Inorg. Chem. 37, 5938 (1998). 14 R. H. Crabtree, J. Organomet. Chem. 557, 111 (1998). 15 M. A. Esteruelas, L. A. Oro, Chem. Rev. 98, 577 (1998). 16 R. Gelabert, M. Moreno, J. M. Lluch, A. Lledos, J. Am. Chem. Soc. 120, 8168 (1998). 17 S. Grndemann, H.-H. Limbach, V. Rodriguez, B. Donnadieu, S. Sabo-Etienne, B. Chaudret, Ber. Bunsenges. Phys. Chem. 102, 344 (1998). 18 T. Hasegawa, Z. W. Li, H. Taube, Chem. Lett., 7 (1998). 19 H.-H. Limbach, S. Ulrich, S. Grndemann, G. Buntkowsky, S. Sabo-Etienne, B. Chaudret, G. J. Kubas, J. Eckert, J. Am. Chem. Soc. 120, 7929 (1998). 20 K. S. Macfarlane, I. S. Thorburn, P. W. Cyr, D. Chau, S. J. Rettig, B. R. James, Inorg. Chim. Acta 270, 130 (1998). 21 W. S. Ng, G. C. Jia, M. Y. Huang, C. P. Lau, K. Y. Wong, L. B. Wen, Organometallics 17, 4556 (1998). 22 P. L. A. Popelier, J. Phys. Chem. A 102, 1873 (1998). 23 S. Sabo-Etienne, B. Chaudret, Chem. Rev. 98, 2077 (1998). 24 S. S. Stahl, J. A. Labinger, J. E. Bercaw, Inorg. Chem. 37, 2422 (1998). 25 P. G. Jessop, R. H. Morris, Coord. Chem. Rev. 121, 155 (1992). 26 D. M. Heinekey, W. J. Oldham, J. Chem. Rev. 93, 913 (1993). 27 P. A. Maltby, M. Steinbeck, A. J. Lough, R. H. Morris, W. T. Klooster, T. F. Koetzle, R. C. Srivastava, J. Am. Chem. Soc. 118, 5396 (1996). 28 T. A. Luther, D. M. Heinekey, Inorg. Chem. 37, 127 (1998). 29 A. Toupadakis, G. J. Kubas, W. A. King, L. B. Scott, J. Huhmann-Vincent, Organometallics 17, 5315 (1998). 30 S. Q. Niu, L. M. Thomson, M. B. Hall, J. Am. Chem. Soc. 121, 4000 (1998).
31 M. E. Cucullu, S. P. Nolan,
T. R. Belderrain, R. H. Grubbs, Organometallics 17, 1299 (1998). 32 A. J. Lough, R. H. Morris, L. Ricciuto, T. Schleis, Inorg. Chim. Acta 270, 238 (1998). 33 F. Maseras, A. Lledos, E. Clot, O. Eisenstein, Chem. Rev. 100, 601 (2000). 34 J. Matthes, S. Grundemann, A. Toner, Y. Guari, B. Donnadieu, J. Spandl, S. Sabo-Etienne, E. Clot, H. H. Limbach, B. Chaudret, Organometallics 23, 1424 (2004). 35 A. Macchioni, Chem. Rev. 105, 2039 (2005). 36 S. Lachaize, W. Essalah, V. MontielPalma, L. Vendier, B. Chaudret, J. C. Barthelat, S. Sabo-Etienne, Organometallics 24, 2935 (2005). 37 H. H. Limbach, G. Scherer, M. Maurer, B. Chaudret, Angew. Chem., Int. Ed. Engl. 31, 1369 (1990). 38 H. H. Limbach, G. Scherer, M. Maurer, Angew. Chem. 104, 1414 (1992). 39 H. H. Limbach, G. Scherer, L. Meschede, F. Aguilar-Parrilla, B. Wehrle, J. Braun, C. Hoelger, H. Benedict, G. Buntkowsky, W. P. Fehlhammer, J. Elguero, J. A. S. Smith, B. Chaudret, in Ultrafast Reaction Dynamics and Solvent Effects, Experimental and Theoretical Aspects, Y,.Gauduel, P.J. Rossky (Eds.), American Institute of Physics., New York 1993, p. 225. 40 F. Wehrmann, T. Fong, R. H. Morris, H.-H. Limbach, G. Buntkowsky, Phys. Chem. Chem. Phys. 1, 4033 (1999). 41 F. Wehrmann, J. Albrecht, E. Gedat, G. J. Kubas, H. H. Limbach, G. Buntkowsky, J. Phys. Chem. A 106, 2855 (2002). 42 J. Eckert, G. J. Kubas, J. Phys. Chem. 97, 2378 (1993). 43 T. Arliguie, B. Chaudret, J. Devillers, R. Poilblanc, C. R. Acad. Sci. Paris, Ser. I 305, 1523 (1987). 44 D. M. Heinekey, N. G. Payne, G. K. Schulte, J. Am. Chem. Soc. 110, 2303 (1988). 45 D. M. Heinekey, J. M. Millar, T. F. Koetzle, N. G. Payne, K. W. Zilm, J. Am. Chem. Soc. 112, 909 (1990).
References 46 K. W. Zilm, D. M. Heinekey, J. M. Millar,
66 H. G. Niessen, D. Schleyer, S. Wiemann,
N. G. Payne, P. Demou, J. Am. Chem. Soc. 111, 3088 (1989). 47 D. Jones, J. A. Labinger, J. Weitekamp, J. Am. Chem. Soc. 111, 3087 (1989). 48 S. J. Inati, K. W. Zilm, Phys. Rev. Lett., 68, 3273 (1992). 49 M. T. Bautista, K. A. Earl, P. A. Maltby, R. H. Morris, C. T. Schweitzer, A. Sella, J. Am. Chem. Soc. 110, 7031 (1988). 50 G. A. Facey, T. P. Fong, D. G. Gusev, P. M. MacDonald, R. H. Morris, M. Schlaf, W. Xu, Can. J. Chem. 1899–1910 (1999). 51 C. R. Bowers, D. P. Weitekamp, Phys. Rev. Lett. 57, 2645 (1986). 52 T. C. Eisenschmidt, R. U. Kirss, P. P. Deutsch, S. I. Hommeltoft, R. Eisenberg, J. Bargon, J. Am. Chem. Soc. 109, 8089 (1987). 53 G. Buntkowsky, B. Walaszek, A. Adamczyk, Y. Xu, H.-H. Limbach, B. Chaudret, Phys. Chem. Chem. Phys. 8, 1929 (2006). 54 I. F. Silvera, Rev. Mod. Phys. 52, 393 (1980). 55 J. van Kranendonk, Solid Hydrogen, Plenum, New York 1983. 56 C. R. Bowers, D. H. Jones, N. D. Kurur, J. A. Labinger, M. G. Pravica, D. P. Weitekamp, Adv. Magn. Reson. 15, 269 (1990). 57 R. Eisenberg, T. C. Eisenschmid, M. S. Chinn, R. U. Kirss, Adv. Chem. Ser. D, 47 (1992). 58 S. B. Duckett, C. L. Newell, R. Eisenberg, J. Am. Chem. Soc. 116, 10548 (1994). 59 J. Barkemeyer, M. Haake, J. Bargon, J. Am. Chem. Soc. 117, 2927 (1995). 60 R. Eisenberg, J. Chin. Chem. Soc. 42, 471 (1995). 61 M. Haake, J. Barkemeyer, J. Bargon, J. Phys. Chem. 99, 17539 (1995). 62 G. Buntkowsky, J. Bargon, H.-H. Limbach, J. Am. Chem. Soc. 118, 867 (1996). 63 M. Jang, S. B. Duckett, R. Eisenberg, Organometallics 15, 2863 (1996). 64 S. B. Duckett, C. J. Sleigh, Progr. NMR. Spectrosc. 34, 71 (1999). 65 J. Natterer, O. Schedletzky, J. Barkemeyer, J. Bargon, S. J. Glaser, J. Magn. Reson. 133, 92 (1998).
J. Bargon, S. Steines, B. DriessenHoelscher, Magn. Reson. Chem. 38, 747 (2000). S. M. Oldham, J. F. Houlis, C. J. Sleigh, S. B. Duckett, R. Eisenberg, Organometallics 19, 2985 (2000). A. Eichhorn, A. Koch, J. Bargon, J. Mol. Catal. A 174, 293 (2001). A. Koch, J. Bargon, Inorg. Chem. 40, 533 (2001). D. Schleyer, H. G. Niessen, J. Bargon, New J. Chem. 25, 423 (2001). S. Wildschutz, P. Hubler, J. Bargon, Chem.Phys.Chem 2, 328 (2001). D. C. Bregel, S. M. Oldham, R. Eisenberg, J. Am. Chem. Soc. 124, 13827 (2002). A. Permin, R. Eisenberg, Inorg. Chem. 41, 2451 (2002). M. Stephan, O. Kohlmann, H. G. Niessen, A. Eichhorn, J. Bargon, Magn. Reson. Chem. 40, 157 (2002). L. D. Vazquez-Serrano, B. T. Owens, J. M. Buriak, Chem. Comm., 2518 (2002). H. Johannesson, O. Axelsson, M. Karlsson, Compt. Rend. Phys. 5, 315 (2004). R. B. Bell, The Tunnel Effect in Chemistry, Chapman &Hall, London & New York 1980. F. Hund, Z. Phys. 43, 805 (1927). F. A. Cotton, Chemical Applications of Group Theory, Wiley, New York 1963. C. Cohen-Tannoudji, B. Diu, F. Laloe, Mechanique Quantique, Hermann Editeurs, Paris 1977. G. Buntkowsky, Structural and Dynamical Studies with Dipolar and Quadrupolar Solid State NMR, Free University, Berlin 1999. R. Ernst, G. Bodenhausen, A. Wokaun, Principles of NMR in One and Two Dimensions, Clarendon Press, Oxford 1987. S. Szymanski, P. Bernatowicz, Annu. Rev. NMR 54, 1 (2005). S. Szymanski, J. Chem. Phys. 104, 8216 (1996). C. Scheurer, R. Wiedenbruch, R. Meyer, R. R. Ernst, D. M. Heinekey, J. Chem. Phys. 106, 1 (1997). G. Buntkowsky, unpublished results.
67
68 69 70 71 72
73 74
75
76
77
78 79 80
81
82
83 84 85
86
681
682
21 Dihydrogen Transfer and Symmetry in the Light of NMR Spectroscopy 87 G. Gamow, Z. Phys. Chem. 51, 204 88 89 90 91 92 93 94
(1927). G. Gamow, Z. Phys. Chem. 52, 510 (1928). E. U. Condon, R. W. Gurney, Nature 112, 439 (1928). E. U. Condon, R. W. Gurney, Phys. Rev. 33, 127 (1929). G. Wentzel, Z. Phys. 138, 518 (1926). H. A. Kramers, Z. Phys. 39, 828 (1926). L. Brillouin, C. R. Acad. Sci. 153, 24 (1926). H. G. Niessen, C. Ulrich, J. Bargon, J. Labelled Compd. Radiopharm. 43, 711 (2000).
95 S. Alexander, J. Chem. Phys. 37, 971
(1962). 96 G. Binsch, J. Am. Chem. Soc. 91, 1304
(1969). 97 J. Eckert, G. J. Kubas, A. J. Dianoux,
J. Chem. Phys. 88, 466 (1988). 98 V. I. Tikhonov, A. A. Volkov, Science 296,
2363 (2002). 99 H. H. Limbach, G. Buntkowsky,
J. Matthes, S. Grndemann, T. Pery, B. Walaszek, B. Chaudret, Chem.Phys.Chem. 7, 551 (2006).
683
Part VI Proton Transfer in Solids and Surfaces
In Part VI the environments in which H transfers take place become more complex. In Ch. 22 Sauer reviews the field of proton transfer of positively charged OH groups in zeolites to the carbon atoms of unsaturated organic molecules forming carbenium ions. These processes represent elementary steps of catalytic reactions. Using ab initio calculations and Carr Parinello Molecular Dynamic techniques the interactions of substrates with the inner pore surfaces as manifested by vibrational spectroscopy are elucidatedm as well as the different reaction steps and the associated reaction energy reaction profiles. Especially interesting is the role of water which enables the transport of protons via jumps from H3O+ to H2O. In Ch. 23 Kreuer reviews the mechanisms of proton conduction in solid electrolytes of fuel cells. During operation, a protonic current equivalent to the electronic current passing through the external load is driven through the electrolyte and parts of the heterogeneous electrode structures. It is the proton conducting properties of the diverse electrolytes which are the subject of this chapter. The proton conduction consists of a multitude of consecutive proton transfer reactions in hydrogen bonded chains embedded in channels of solid materials containing water, other hydrogen bonded liquids, or heterocyclic groups such as imidazole derivatives covalently bound to a polymer matrix. In Ch. 24 Aoki uses FT-IR reflection spectroscopy to monitor the transfer of protons and of water molecules from a layer of H2O ice to a layer of D2O ice as a function of time and external pressure. The H/D mutual diffusion coefficient measured at 400 K shows a monotonic decrease by two orders of magnitude as the pressure increases from 8 to 63 GPa. In order to separate molecular from protonic diffusion experiments were also carried out on H216O /H218O ice bilayer. Whereas molecular diffusion dominates under normal conditions, it is suppressed at high pressures. The protonic diffusion is assumed to take place via H3O+ and OH– ions which can, however, not be observed. Ch. 25 by Christmann is devoted to the interaction and reaction dynamics of hydrogen and simple molecules containing a hydroxy group such as water and methanol with transition metal surfaces. In particular, the possibility of H transfer via lateral diffusion or proton tunneling within the adsorbed layers is discussed. It is shown that lateral diffusion and transfer of H atoms does indeed occur via both Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
684
classical diffusion and tunneling. The growth and structure of the respective layers containing OH groups is largely governed by H bonding effects leading, in practically all of the investigated cases, to a relatively “open” network of water or alcohol molecules. Isotopic scrambling thereby indicates an extraordinarily high mobility of H or D atoms. Finally, Hempelmann and Skripov review in Ch. 25 hydrogen motions in metals important for the development of new hydrogen storage materials. While the behavior of hydrogen in a number of binary metal–hydrogen systems is well understood, a detailed microscopic picture of H diffusion in more complex compounds of practical importance has not yet evolved. A promising approach to investigation of these compounds is to combine a number of experimental techniques sensitive to different ranges of H jump rates such as NMR, QENS and inelastic relaxation with the neutron diffraction study of hydrogen positional parameters. The relation between the parameters of H motion and the structure of the hydrogen sublattice is emphasized.
685
22 Proton Transfer in Zeolites Joachim Sauer
22.1 Introduction – The Active Sites of Acidic Zeolite Catalysts
Catalysis is one of the fundamental principles in chemical reactivity and catalysis by acids is an important subclass common to homogeneous, enzymatic and heterogeneous catalysis. Among the solid acids used in industrial processes, acidic zeolites are most important because they combine the acidic function with selectivity due to their nanoporous crystalline structure. Every drop of gasoline we burn in our car has seen at least one zeolite catalyst on its way through the refinery. Many chemical products, from bulk polymers to fine chemicals, are built up from hydrocarbons in crude oil or natural gas with the help of zeolite catalysts. However, zeolites are of outstanding interest also from the fundamental point of view. Their well-defined crystalline structure makes them very good candidates for studying the role of proton transfer in acidic catalysis. Zeolites are three-dimensional crystalline networks of corner-sharing SiO4 and AlO4 tetrahedra. Because of the large flexibility of the Si–O–Si and Si–O–Al angles, a large variety of different frameworks with channels and cavities is possible, into which external molecules can penetrate. The negative charge of the framework (due to AlO4 tetrahedra) is compensated by extra-framework cations, and if the charge-compensating cation is a proton the zeolite is a solid acid. The proton attaches to one of the four oxygen atoms of the AlO4– tetrahedron, thus forming a bridging hydroxy group, Si–O(H)–Al, which acts as a strong Brønsted site (see formula below). The concentration of Al in the framework (and its distribution) are additional features by which different acidic zeolites can vary, however within limits. The Lwenstein rule forbids Al–O–Al links between AlO4– tetrahedra and the minimum Si/Al ratio is 1 (Lwenstein rule). Moreover, for low Si/Al ratios, not all charge-compensating cations can be protons and typically there are Na+ ions left. High-silica zeolites are particularly interesting catalysts, because they contain bridging hydroxy groups as perfectly isolated active sites. Two convincing experiments that use the n-hexane cracking activity as test reaction show this. For the H-MFI catalysts (trivial name H-ZSM-5) the activity changes linearly with the Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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22 Proton Transfer in Zeolites
-Si
+H/Al
-P
+H/Si
Si/Al ratio between 100 000 and 20 [1]. Two catalysts, H-FAU and H-MFI, with the same Si/Al ratio of 26 have nearly the same specific activities, 11.4 and 8.5 mmol g–1 min–1, respectively [2]. There is a third possible variation for acidic zeolite catalysts – the composition of the framework. The active Si–O(H)–AlO3 site in a high-silica zeolite is formally created from a nanoporous SiO2 polymorph by replacing Si by Al/H. If we consider an AlPO4 framework instead of an SiO2 framework (as we do when we go from the mineral quartz to berlinite) and then replace P by Si/H (see formula above), we obtain a catalyst with the same Si–O(H)–AlO3– active site but a different framework composition. Strictly, these catalysts are not zeolites (this name is reserved for aluminosilicates), but aluminumphosphates (AlPOs) or silicon-aluminumphosphates (SAPOs). It is indeed possible to synthesize acidic high-silica (H-SSZ-13) [3] and SAPO catalysts (H-SAPO-34) [4] with the same framework structure (CHA) [5].
22.2 Proton Transfer to Substrate Molecules within Zeolite Cavities
It is assumed that, after adsorption into the zeolite, the initial activation of substrate molecules for further conversion is by proton transfer from the zeolite, {AlO4}ZH + S fi ({AlO4}ZH · S > {AlO4–}Z · HS+) fi ({AlO4–}Z · HP+ > {AlO4}ZH · P) fi {AlO4}ZH + P
Inspired by the chemistry in superacidic media, it has been speculated that zeolites may be superacids and able to protonate even saturated hydrocarbon molecules to yield carbonium ions as a first step in catalytic cracking. Later, doubts have been raised as to whether carbenium ions obtained by protonation of unsatu-
22.2 Proton Transfer to Substrate Molecules within Zeolite Cavities
rated hydrocarbons are stable intermediates that can be found experimentally or if they are merely transition structures in the catalytic reaction cycle. From the theoretical point of view the question is: Are they minima (stable structures) or saddle points (transition structures) on the potential energy surface? However, even if they are minima, they may be separated by very small barriers from products or their neutral complex counterparts and, hence, transient species that are difficult to detect experimentally. There may also be additional deactivation channels for protonated species, for example carbenium ions can attach via C–O bonds to the zeolite framework and form alkoxides, as shown in Fig. 22.1 for isobutene.
Figure 22.1 Possible products of proton transfer from a zeolitic Brønsted site to isobutene.
Whether or not the neutral adsorption complex or the ion-pair structure is more stable depends on the energy of the proton transfer reaction, DEPT, {AlO4}ZH · S fi {AlO4–}Z · HS+
(22.1)
It can be decomposed into the deprotonation energy, EDP(Z) of the zeolite, {AlO4}ZH fi {AlO4–}Z + H+
the proton affinity of the substrate, –EPA(S),
(22.2a)
687
688
22 Proton Transfer in Zeolites
H+ + S fi HS+
(22.2b)
the binding energy of the substrate on the neutral zeolite surface, Eneutral(S), {AlO4}ZH + S fi {AlO4}ZH · S
(22.3a)
and the binding energy of its protonated counterpart on the deprotonated zeolite surfaces, EIP(SH+), {AlO4–}Z + HS+ fi AlO4–}Z · HS+ DEPT = EDP(Z) – EPA(S) – Eneutral(S) + EIP(SH+).
(22.3b) (22.4)
Nicholas and Haw concluded that stable carbenium ions in zeolites are observed by NMR if the parent compound (from which the carbenium ion is obtained by protonation) has a proton affinity of 875 kJ mol–1 or larger [6]. Simulations by quantum methods showed that this statement is more general and that proton transfer from a H-zeolite to a molecule or molecular cluster occurs if its proton affinity is about that of ammonia (854 kJ mol–1) or larger [7]. In the light of Eq. (22.4) this means that proton transfer occurs (DEPT £ 0)) if EDP(Z) – Eneutral(S) + EIP(SH+) is smaller than 854 kJ mol–1. Table 22.1 shows proton affinities and indicates in which cases and by which method protonated species have been detected.
22.3 Formation of NH4+ ions on NH3 adsorption
A common experimental means of characterizing the acidity of zeolites is the use of probe molecules. IR spectra leave no doubt that ammonium ions are formed upon adsorption of ammonia in zeolites, the OH band characteristic for bridging Si–O(H)–Al sites disappears and NH4+ bending bands appear [12]. The energy of ammonia desorption, {AlO4–}Z·NH4+ fi {AlO4}ZH + NH3
(22.5)
is used to characterize the acid strength of zeolites. Usually it is obtained from temperature-programmed desorption, but true equilibrium values require calorimetric measurements. The adsorption energy defined by the reverse of Eq. (22.5) is composed of the energy of the (hypothetical) desorption of NH4+ and a subsequent proton transfer from NH4+ to the AlO4– site on the zeolite, Ead(NH3) = EIP(NH4+) + EDP(Z) – EPA(NH3).
(22.6)
22.3 Formation of NH4+ ions on NH3 adsorption Tab. 22.1 Proton affinities, HPA(298) of molecules and clusters
(kJ mol–1) and observation of protonated species in zeolites. Parent compound [a]
Obsd.[a]
MP4[b]
water
691
benzene
750
746
propene
751
742
cyclopentene
766
759
methanol
754
toluene
784
isobutene
802
Proof ?
694
757
805
water dimer m-xylene
Other[c]
806 811 821[d]
3-methylphenyl-(2,4-dimethylphenyl)-methane water trimer ammonia
854
hexamethylbenzene
861
1-methylindene
DFT[d] 853
DFT[ f ]
858
IR[g] UV–vis[e] NMR[b]
878
methanol dimer
887
DFT[h]
water tetramer
895
DFT[ f ]
1,3-dimethylcyclopentadiene pyridine 1,5,6,6-tetramethyl-3-methylene-cyclohexa-1,4-diene 3,6-dimethylene-cyclohexa-1,4-diene
a b c d e f g h
Ref. [8]. Ref. [6], except where otherwise noted. MP2/DZP, unpublished data. Ref. [9]. Ref. [10]. Ref. [7, 11]. Ref. [12]. Ref. [30].
929
902
NMR[b]
917
IR, NMR
951
NMR[b]
1031[d]
DFT[d]
689
690
22 Proton Transfer in Zeolites
Quantum chemical studies (Table 22.2) confirm the formation of NH4+ ions on interaction of ammonia with Brønsted sites in zeolites. The proton transfer energies are around –30 kJ mol–1. No calculation that includes the full periodic structure of the zeolite has found a local minimum for a neutral adsorption complex. A hybrid QM/MM study considered high-silica zeolites with four different zeolite frameworks [13]. The energies of deprotonation indicate that H-FAU releases its proton most easily, yet the heat of NH3 adsorption (Eq. (22.6)) is largest for H-MOR. The reason is that binding of NH4+ onto the zeolite surface, EIP(NH4+), is less favorable in the large pore zeolite FAU (12-rings of SiO4/2 units) than in the smaller pores of the other zeolites (CHA, MOR, MFI) with 8- and 10-rings. These calculations assumed that the Brønsted site is created at the crystallographic T position at which Al is most stable. However, the energy differences for Al in different crystallographic T positions of a given framework are small, usually a few kJ mol–1. Moreover, the Al distribution can also be controlled by the synthesis process and the preferred positions are not known. For H-MOR DFT calculations have shown that the location of the Brønsted site can have a large effect on the
Tab. 22.2 Proton transfer energy, DEPT, deprotonation energy, EDP, hypothetical binding
energy of NH4+ on the deprotonated zeolite surfaces, EIP(SH+), and energy of ammonia adsorption, Ead(NH3), (kJ mol–1) for Brønsted sites in different zeolite frameworks [13]. Zeolite[a]
FAU (47)
CHA (11)
MOR (47)
MFI (95)
DEPT
–32
–35
–34
–29
EDP
1252
1271
1277
1283
EIP(NH4+)
–457 (2)
–476 (3)
–484 (2)
–480 (2)
–109
–109
–116
–106
–127
–128
–133
–123
–113
–114
–119
–109
–123; –133[ f ]
–126_ –128[ g] –152 [h]
–155
–160
Eads(NH3)[b] Eads(NH3),
HF+MP2[c]
Hads(NH3)[d] Eads(NH3), DFT Hads(NH3), obsd.[e]
a b c d e f g h
–115_–130
In parentheses: Si/Al ratio assumed in the calculations. Hartree–Fock results. Final electronic energy including electron correlation (MP2). Calculated heat of adsorption, includes estimates for zero-point vibrational energy and thermal corrections (298 K). See Ref. [13] and for MOR also Ref. [14] for the original references to microcalorimetry. B3LYP, Ref. [16]. PW91, Al in T1 and T2-sites, bidentate, Ref. [14]. PW91, Al in T3-site, tetradentate, Ref. [14].
–145;–150
22.4 Methanol Molecules and Dimers in Zeolites
heat of NH3 adsorption. Values of –126 to –128 kJ mol–1 (close to the results of Ref. [13]) are found for Al in sites 1 and 2, but for Al in site 3 a much larger value of –152 kJ mol–1 is obtained [14]. The reason is that in this case NH4+ can bind via four N–H···O bonds to the zeolite framework. It coordinates with three N–H bonds to oxygen atoms of an 8-ring and points with one N–H bond into the socalled side pocket of the MOR framework. Only for H-FAU are the calculated heats of adsorption in the range of reported calorimetric results. For H-CHA, H-MFI and H-MOR they are much lower. Even if adsorption in the side pocket is assumed for H-MOR, the predicted heat of adsorption would be about 20 kJ mol–1 too low. For adsorption of a series of structurally related molecules in the same zeolite, Eq. (22.6) implies a correlation between the measured heat of adsorption and the proton affinity of that molecule, provided that the ion-pair binding energy, EIP(MH+) is constant or changes with the proton affinity. For adsorption of ammonia and methyl-substituted amines on H-MFI and H-MOR such a correlation has indeed been reported [15] with two deviations: The heat of adsorption of trimethylamine is about 30 kJ mol–1 smaller than expected from the correlation, and that of n-butylamine is about 25 kJ mol–1 larger. Both can be explained by deviations from the prevailing adsorbate structure – interaction via two hydrogen bonds with the zeolite framework. Protonated trimethylamine can form only one hydrogen bond with the zeolite framework, and this explains a lower EIP(HN(CH3)3+). In the case of n-butylamine the van der Waals (dispersion) interaction of the butyl chain contributes to the binding on the zeolite surface in addition to the two hydrogen bonds. In conclusion, due to its high proton affinity (858 kJ mol–1) ammonia always is protonated in any H-zeolite. The hypothetical neutral adsorption complex, stabilized by hydrogen bonds, would be about 30 kJ mol–1 less stable [13] as measured by DEPT defined in Eq. (22.4).
22.4 Methanol Molecules and Dimers in Zeolites
The proton affinities (Table 22.1) of methanol (754 kJ mol–1) and water (691 kJ mol–1) are significantly lower than that of ammonia (854 kJ mol–1) and whether or not these molecules are protonated in H-zeolites has created lively debates in the literature. For H-zeolites with high Si/Al ratios DFT calculations showed that a single methanol molecule in a cavity with one bridging SiO(H)AlO3 site always forms a hydrogen-bonded complex and there is no proton transfer onto methanol. This was first shown for sodalite (SOD) [17] which has a small unit cell and is a hypothetical zeolite catalyst. Its proton form is not known and there is no way that methanol could penetrate into sodalite cages through its six-ring windows. Chabasite (CHA) also has a small unit cell, but is experimentally relevant (H-SSZ-13) [4] and methanol in H-CHA has been studied by Haase et al. [18, 19]. In contrast to the result for sodalite, for chabasite an ion-pair structure of protonated methanol
691
692
22 Proton Transfer in Zeolites
within an 8-ring was found by DFT (energy minimization) [20]. This caused speculations [21] that “a direct correlation between zeolite structure and chemical activation of the adsorbate” might exist which could not be confirmed. Subsequent Car Parrinello molecular dynamics (CPMD) simulations for CHA [18] revealed that the ion-pair complex is a stationary point on the potential energy surface that is reached during MD only 4 times within 2.5 ps for a very short time. The global minimum structure is the neutral complex which is 18 kJ mol–1 more stable, see Ref. [22] for a later confirmation. Later studies addressed zeolites with large unit cells, FER and MFI [22] or TON, FER and MFI [19], and all found neutral adsorption structures. The calculated (PW91 functional) heat of adsorption in MFI, 131 kJ mol–1, is close to the experimental value, 115–5 kJ mol–1 [23]. Only for methanol adsorption in H-FER [19, 22] did the two DFT studies not lead to a consistent picture. Both simulations find a neutral adsorption complex of methanol in the 10-ring channel. In addition, Stich et al. [22] find a neutral adsorption structure for methanol in the 8-ring channel of FER. However in a dynamics run at 300 K proton transfer occurs and the average structure corresponds to the CH3OH2+ ion with two almost equal OM–H distances [22]. It is presently not clear if this result reflects special properties of the FER framework or more technical difficulties. Use of a unit cell with a very short cell parameter in the c direction could have an effect, but a test with a doubled cell showed that this is probably not the case. The two simulations differed in the location of the bridging hydroxy group in the framework. Stich et al. [22] assume Al in the T4 position and the proton sits on O6, while Haase and Sauer [19] assume Al in the more stable T2 position with the proton on O1. Al in T2 is 38 kJ mol–1 more stable than in T4 [24]. For the less stable Al(4)O(6) site, the energy of deprotonation is 29 kJ mol–1 lower than for the more stable Al(2)O(1) site [19], and this could explain the tendency to protonate methanol at higher temperatures, cf. Eq. (22.4). Unfortunately, the Al-distribution in the experimental samples is unknown. All these studies tell us is that it is not enough to look at the stationary points on the PES. Because of the flatness of the potential energy surface and similar energies of neutral and ion-pair adsorption structures, the dynamics of the system at realistic temperatures needs to be considered. The average structures obtained under these conditions may deviate significantly from the equilibrium structures. We will come back to this point in the water adsorption section. The observed 1H NMR chemical shift for methanol in H-ZSM-5 (9.4 ppm) was much larger than for liquid methanol (4.7 ppm) and in the same range as the shift observed for methanol in the FSO3H–SbF5–SO2 superacid (9.4 ppm) [25]. As it was known that methanol forms stable oxonium species in superacids this was hinting at the formation of methoxonium species in H-zeolites although the authors have been cautious enough not to exclude alternative interpretations. Assignment to a methoxonium species was possible because there was not enough information about its chemical shift when interacting via hydrogen bonds with the zeolite surface. However, quantum calculations could provide such information. Figure 22.2 shows the 1H NMR chemical shifts calculated for methanol and the methoxonium ion, both hydrogen-bonded to the zeolite surface [26]. The
22.4 Methanol Molecules and Dimers in Zeolites
HM
HZ NC
HM
HZ
(0.0)
(2.9)
7.0
14.6
IP
NC
10.8
IP free
(6.2)
Calcd
17.4
Figure 22.2 1H NMR chemical shifts (ppm) for methanol (neutral complex – NC) and methoxonium (ion pair complex – IP) interacting with the zeolite surface. HM – methanol proton, HZ – zeolite proton in the neutral adsorption complex. Results for the free methanol and methoxonium species are also given.
methoxonium protons undergo a huge downfield shift when interacting with the zeolite surface in the ion-pair complex. The calculated shift of 17.4 ppm is much larger than the observed value 9.4 ppm [25, 27]. In the neutral complex the Brønsted site proton also undergoes a similarly large shift due to the strong hydrogen bond, while the methanol proton extends a weaker hydrogen bond to the zeolite framework and its NMR signal shifts less. Due to a fast exchange of the zeolite and methanol protons an average shift of 10.8 ppm is obtained [26] which is close to the observed value. Support for a neutral hydrogen-bonded adsorption complex comes also from a measurement of the distance between the methanol and the zeolite protons in H-MOR by wide line 1H NMR at 4 K [28].
rHH
693
694
22 Proton Transfer in Zeolites
The result of 193–200 pm [28] is in good agreement with the calculated equilibrium distances for H-CHA (188 pm) [18], TON (189, 192 pm) and H-FER (190 pm) [19], while the H–H distance calculated for methoxonium adsorbed in CHA is much smaller, 158 pm [18]. The agreement of spectroscopic parameters with predictions for neutral adsorption complexes, of course, does not exclude the possibility that surface methoxonium ions would exist as a minority species in equilibrium. That the methoxonium ion is not a (metastable) local minimum structure but a transition structure is concluded from the quantum calculations mentioned above. For the adsorption of two methanol molecules per bridging hydroxy groups (2:1 loading) studies on all zeolites, SOD [29], CHA [22, 30], FER [22] agree that a protonated methanol dimer is formed (Fig. 22.3). The obvious reason is the high PA of the methanol dimer that exceeds even the PA of ammonia (Table 22.1).
Figure 22.3 Protonated methanol dimer in zeolite chabasite (CHA) as predicted by CPMD simulations [30].
22.5 Water Molecules and Clusters in Zeolites
High-silica zeolites are known to be hydrophobic and it has also been long known that the water uptake at a given pressure is a function of the aluminum content, i.e. of the number of Brønsted sites [31–33]. At standard temperature and modest water pressure (e.g., p/p0 = 0.6) typically four water molecules per Al are adsorbed, suggesting formation of a H9O4+ species. Computationally, the interaction of water molecules with H-zeolites was first studied for cluster models of Brønsted sites [34, 35]. These calculations showed that the neutral adsorption complex is a minimum on the PES (stable structure), while the hydroxonium ion corresponds to a transition structure for proton exchange. Infrared spectra obtained for a loading level of a single water molecule per Brønsted site have been interpreted as due either to a neutral hydrogen-bonded molecule or to the formation of a hydroxonium ion. The calculations showed [34] that an ion-pair complex cannot explain
22.5 Water Molecules and Clusters in Zeolites
the characteristic pair of bands in the hydrogen-bond region (2877 and 2463 cm–1, see Fig. 22.4) while the neutral adsorption complex can, if one assumes that this pair of bands is due to a Fermi-resonance. Due to hydrogen bonding with the adsorbed H2O molecule the zeolitic OH stretching is strongly red-shifted, and resonance with the overtone of the in-plane SiOH bending creates a window at the overtone position (see Ref. [36] for a recent model calculation). Figure 22.4 shows the observed spectrum [37] and the assignment based on MP2 frequency calculations [34]. The predicted position of the zeolitic OH stretch band (red-shifted and broadened due to hydrogen bonding) falls close to the predicted position of the overtone of the in-plane SiOH bending. The bands at 3698 and 3558 are assigned to OH stretch of the free and hydrogen-bonded protons of the adsorbed H2O molecule, and the bands at 1629 and 1353 to the HOH and SiOH bendings. The crucial experiment was the isotope substitution (18O) of water [37] which showed no effect on the pair of bands at 2877 and 2463 cm–1 and thus clearly supported their assignment to vibrations of the zeolitic Brønsted site. While these computational studies [34] were awaiting publication, a neutron diffraction study on H-SAPO-34 provided evidence for a protonated water molecule [38]. Whereas comments in the more popular press [39] stressed the apparent disagreement with previous calculations (“much of the confusion about how zeolites work stems from quantum calculations”) and used the entertaining title “Quantum mechanics proved wrong”, a comment to the original paper in the same issue
∆ν OHz
OHf OHb
2δ ZOH
δ HOH δZOH
Si δ ZOH
O Hz
Al
O Hf
Figure 22.4 IR spectrum of H216O and H218O adsorbed on H-ZSM-5 (adapted from Fig. 2 in Ref. [37]). Shown is the assignment based on frequency calculations for models of the neutral adsorption complex [34]. The overtone of the in-plane SiOH bending (dZOH) falls onto the red-shifted OH stretching frequency of the bridging hydroxy group of the zeolite, mOHZ.
O
Si
Hb δ HOH
695
696
22 Proton Transfer in Zeolites
pointed out that a loading higher than one H2O molecule per Brønsted site may be responsible for protonation of water in the experimentally studied system [40]. Indeed, both cluster studies mentioned [34, 35] and a DFT study applying periodic boundary conditions [29] found that a second water molecule per Brønsted site yields H5O2+ attached to the surface as an energy minimum structure. Subsequently, two periodic DFT simulations have been made of the H2O/H-SAPO-34 system [7, 41] which analyzed the role of an increasing number of water molecules in detail. To match the composition of the experimental sample as closely as possible, a double cell of the CHA structure was chosen with one Brønsted site in one cell and two in the other cell [7] . Even for a loading of two water molecules (per two OH groups in one cell), the neutral water dimer proved to be the energy minimum structure, while H5O2+ showed up only a few times during the 2 ps of the MD simulation at room temperature (Fig. 22.5). The lowest energy H5O2+ structure is 18 kJ mol–1 above the neutral adsorption structure.
1.49
1.9
1.44 1.46 1.62
Figure 22.5 CPMD simulation (PW 91 functional) of two H2O molecules per two Brønsted sites in H-SAPO (the other cell contains only one Brønsted site and one H2O molecule) [7]. One of the Brønsted protons is residing on the SAPO-framework all the time, the distance of the other Brønsted proton to O of the nearest H2O molecule shows large variations (upper curve). The lower curve
shows the OH distance in this water molecule that is not involved in a H-bond with the second water molecule. Equal OH distances indicate formation of a protonated water dimer (H5O2+). Most of the time the distance between the zeolitic proton and the nearest water molecule is much longer – corresponding to an adsorbed H2O dimer shown at bottom left. Distances are given in .
22.5 Water Molecules and Clusters in Zeolites
When a simulation with four H2O molecules per three Brønsted sites was made, something very interesting happened: One water molecule moved from the cage with one OH group into the cage with two OH groups and the three molecules together have a high enough proton affinity to form a H7O3+ cluster stabilized by H-bonds with the wall of the SAPO material:
This perfectly fits our picture that the proton transfer depends on the proton affinity of the adsorbed molecule: the proton affinity of the water trimer (853 kJ mol–1, Table 22.1) is about that of ammonia (858 kJ mol–1). For a single cell of H-SAPO with one Brønsted site, hydrogen-bonded H2O was found for a loading of one molecule per site by CPMD simulations. For two molecules per site hydrogen-bonded H2O dimers and protonated dimers, H5O2+, were found [41]. Virtually identical energies of adsorption were obtained for both situations (Table 22.3). If the CHA framework is not aluminum phosphate, as in H-SAPO-34, but silica as in H-SSZ-13, for a loading of two to four molecules per site the ion-pair structure is found to be more stable (Table 22.3) [11]. Because of the small energy differences between the neutral complex and the ion-pair structure, the detailed answer depends on the specific density functional applied in the calculations. Table 22.3 shows that the Becke-Lee-Yang-Parr (BLYP) functional yields smaller adsorption energies and gives more weight to neutral adsorption complexes than the Perdew-Wang 91 (PW91) and Perdew-Burke-Ernzerhofer (PBE) functionals. The latter two belong to the same “family” of functionals and are expected to yield very similar results. For a loading of two molecules per site, BLYP predicts the neutral complex to be slightly more stable than the ion-pair structure, but the adsorption energies differ only by about 1 kJ mol–1.
697
698
22 Proton Transfer in Zeolites
Tab. 22.3 Energy of water adsorption per molecule, Ead(H2O) (kJ mol–1) on Brønsted sites in zeolites
and aluminumphosphates with chabasite (CHA) structure for different H2O loadings. H/Al-SiO2 (H-SSZ-13)
H/Si-AlPO4(H-SAPO-34)
Loading, n H2O/m H(Al)
BLYP[a]
Average
Cell1;Cell2
NC
IP
NC
IP
NC
1/1
1/1
62
–
76
–
81
2/1
2/1
46
45
–
61
67
2/1
2/1;2/1
48
47
–
63
2/1
1/1;3/1
49
3/1
3/1
–
45
–
59
4/1
4/1
–
45
–
60
PBE[a]
PW91[b] IP
67
63
a Ref. [11]. b Ref. [41].
For this loading, another interesting result is obtained, if a double cell is used for the simulation. A heterogeneous distribution of one molecule per site in the first cell and three molecules per site in the second cell is energetically slightly more stable than (BLYP) or equally stable as (PBE) the homogeneous distribution. This may have implications for the interpretation of experiments. For example, an IR spectrum obtained for an average loading of 2:1 may be composed of spectra for 1:1 (neutral hydrogen-bonded) and 3:1 complexes (ion-pair structures). Table 22.4 summarizes the energies of adsorption for the first water molecule on a Brønsted site. The most reliable calculations have been made for H-CHA and Tab. 22.4 Energy and enthalpy of water adsorption, Ead(H2O) and
Hads(H2O) (kJ mol–1) on Brønsted sites in zeolites for a loading of 1 H2O/1 H(Al).
Method
Model
Ead(H2O)
Hads(H2O)
Ref.
MP2
cluster
58
45 (0 K)
34
70
60 (0 K)
35
B3LYP B3LYP/MNDO B3LYP
cluster cluster/CHA CHA
72 82 84
16
PBE
CHA
75
42
MP2/PBE
cluster/CHA
78
calorimetry isotherms
MFI MFI
73 (298 K)
42
90 – 10 80 – 10
23 33
22.5 Water Molecules and Clusters in Zeolites
the most accurate value has been obtained by an MP2/PBE hybrid method and extrapolated to the complete basis set limit [42]. The predicted heat of adsorption at 298 K, 73 kJ mol–1, can be compared with heats of adsorption of 80 – 10 and 90 – 10 kJ mol–1 obtained from isotherms [33] and calorimetric measurements [23], respectively, for a different zeolite, H-ZSM-5. Comparison of DFT calculations with the most reliable computational result, MP2/PBE, indicates that PBE gives more reliable results than BLYP. For loadings of two to four water molecules, DFT adsorption energies are rather constant and about 15 kJ mol–1 lower than for a loading of one molecule per site (Table 22.4). This is in agreement with the observed decrease of the heat of adsorption for H-ZSM-5 from 80 – 10 (n = 1) to 63 – 10 (n = 2–4). Figure 22.6 (top, right) shows the energy minimum structure of the protonated water trimer in H-CHA [11]. It is an open trimer structure which is protonated on a terminal molecule, H3O+(H2O)2, rather than on the central molecule as in the corresponding gas phase species (Fig. 22.6, top of insert bottom right). This is obviously a consequence of the stabilization by a strong hydrogen bond with the negatively charged AlO4– framework site nearby. The H2O(H3O+)H2O structure is
Figure 22.6 CPMD simulation (BLYP functional) of three H2O molecules per one Brønsted site of H-CHA [11]. Left: characteristic distances along a 4 ps trajectory for the hydrogen bond between the Brønsted site and a terminal H2O molecule of the trimer and between the terminal and central H2O molecules of the trimer (bottom). The bottom right insert shows the protonated H2O trimer in the gas phase with the H3O+ in the center, and the corresponding structure in H-CHA, which is a local minimum. Distances are given in .
699
700
22 Proton Transfer in Zeolites
a local minimum in H-SSZ-13 (Fig. 22.6, insert bottom right), 14 kJ mol–1 above the global minimum structure. Molecular dynamics simulations on a DFT potential energy surface (CPMD) show frequent proton jumps between the water trimer and the zeolite. Figure 22.6 (left) shows several atomic distances along the MD trajectory. Soon after starting the bh proton leaves the water cluster and makes several attempts to jump back. However, after only about 2 ps proton transfer occurs again and the proton stays for the rest of the simulation time on the water cluster. The consequences for the average structure at 350 K is a shortening of the O1(zeolite)–Oh distance from 258 to 256 pm, and a lengthening of the Oh–Hbh distance from 104 to 113 pm, which means a shift of the bridging proton bh from the water cluster (Oh) to the zeolite (O1). The distances between the “left” (Oh) and the central water molecules (Ow) are given in the left bottom part of Fig. 22.5. There are several attempts by the bw proton to jump to the central water molecule, but they are not successful. The average Oh–Ow distance along the trajectory is 256 nm, while the energy minimum distance is 247 pm. This increase in the intermolecular distance is accompanied by a shortening of the Oh–Hbw bond from 111 pm (minimum structure) to 108 pm at 350 K. Hence, even at higher temperature, there is no indication for a proton transfer to the central water molecule. In turn, trajectories started at the H2O(H3O+)H2O local minimum structure never reached the global minimum structure. This confirms the H3O+(H2O)2 structure for the protonated water trimer in H-SSZ-13 and points to the important role of the environment in the structure of protonated water clusters. We also conclude that proton transfer between the water trimer and the zeolitic Brønsted site occurs on the picosecond time scale.
22.6 Proton Jumps in Hydrated and Dry Zeolites
In previous sections we have considered proton transfer between the zeolitic Brønsted site and adsorbed proton accepting molecules or clusters. For an unloaded zeolite, there are four oxygen sites around Al to which the proton can be attached. In most zeolites proton affinities are different for these oxygen sites and some will be preferred. For zeolite FAU, two OH frequencies and two 1H NMR shift signals can be experimentally resolved; these are unequivocally assigned to O1H and O3H sites. This is in agreement with quantum calculations for isolated sites (Si/Al = 47) which yield the stability sequence (relative energies, kJ mol–1, in parentheses) O1 (0.0) < O3 (9.5) < O4 (10.0) < O2 (18.3) [43]. For higher temperatures, on-site proton jumps between the different oxygen atoms of an AlO4– site may be possible. Translational proton motion through the zeolite lattice appears to be much less likely because the proton has to leave the Al(–)–O–Si site and move to Si–O–Si sites that have a lower proton affinity. Hence, it is expected that the barriers for “intersite” jumps that occur between neighboring TO4 tetrahedra with T = Al–, Si are
22.6 Proton Jumps in Hydrated and Dry Zeolites
on-site
inter-site
higher. DFT calculations for a typical Brønsted site in H-MFI (Si/Al = 95) [44] yield an inter-site barrier of 127 kJ mol–1 for leaving the AlO4 site. The highest barrier for proton transfer from AlO4 site to AlO4 site along a path of Si–O–Si sites is 202 kJ mol–1. From impedance spectroscopy effective barriers of 100 to 126 kJ mol–1 have been inferred for Si/Al ratios between 75 and 500 and temperatures above 423 K. If impedance spectroscopy probes complete translational proton motion between neighboring Brønsted sites the calculated barriers deviate by as much as 70–100 kJ mol–1 from the observed ones. This raises the question as to whether defects are responsible for the effective barriers derived from experiments. In contrast to on-site jumps, a “vehicle” mechanism cannot explain this discrepancy because addition of even 3 vol% of water reduces the barrier by not more than 20 kJ mol–1 [44]. Quantum calculations for the six different on-site jump paths between the oxygen atoms of the AlO4– site (Fig. 22.7) have been made for three different framework structures, CHA, FAU and MFI [43]. For CHA and FAU there is only one crystallographically distinct AlO4– site, while for H-MFI there are 12, and one of them (Al7) has been chosen as a representative site for the calculations. For all three structures the barriers vary widely between 70 and 102 kJ mol–1 for CHA, between 68 and 106 kJ mol–1 for FAU, and between 52 and 98 kJ mol–1 for MFI (values include zero-point vibrational energy contributions) [43]. The fact, that the O–Al–O angle substantially narrows in the transition structure (Fig. 22.7(a)) raised speculations that the barrier height may correlate with this angle, either in the transition structure or in the initial structure. However, the calculations for different zeolite frameworks [43] could not confirm that and rather pointed to the importance of (i) the local framework flexibility that allows the Al–O–Al angle to close up to 76–80 without too much energy penalty, together with (ii) the overall flexibility of the zeolite lattice, and (iii) stabilization of the proton in the transition structure by interactions with neighboring oxygen atoms of the framework. All three factors together show up in a plot of the barrier height against the size of the alumosilicate ring that the proton has to pass for a particular jump path
701
702
22 Proton Transfer in Zeolites
125 pm
(a)
98 pm
77° 107°
∆ E‡ ∆ Er
(b)
∆ E‡
∆ Er
Figure 22.7 Reaction profile for on-site proton jumps on an AlO4H site with inequivalent proton positions for dry zeolites (a) and hydrated zeolites (1:1 loading) (b). DE‡ – barrier height, DEr – reaction energy.
(Fig. 22.8). For all zeolites, proton jumps occurring within six-membered rings have the lowest barriers, while higher barriers are found for five- and four-membered rings (due to lower flexibility), but also for eight-membered and larger rings due to fewer oxygen atoms nearby that could stabilize the proton. For jumps from the most stable proton sites transition state theory yields rates of the order of 1–100 s–1 at room temperature and of the order of 105–106 at 500 K [43]. Experimentally, proton jumps have been studied using various variable temperature 1H NMR techniques [45, 46], but the proton jump barriers reported for H-FAU (61–78 kJ mol–1) and H-MFI (18–45 kJ mol–1) vary widely and are significantly lower than the calculated barriers (68–106 and 52–98 kJ mol–1, respectively). Tunneling cannot be the reason, because the crossover temperature above which tunneling becomes negligible, Tx, is around room temperature [43] and the NMR experiments are carried out above room temperature. The experiments agree in reporting lower barriers for H-MFI than for H-FAU and this is also found in the calculations. The 1H-NMR experiments are based on averaging the dipolar Al–H interaction, which requires that the proton visits all four oxygen atoms of the AlO4– site starting from the most stable position. For H-FAU there is no such
22.7 Stability of Carbenium Ions in Zeolites 120
E‡ (kJ/mol)
110 100 90 80 70 60 50
4T
5T
6T
8T
> 8T
Ring Size Figure 22.8 Dependence of the proton jump energy barriers on ring size nT for H-CHA (j), H-FAU (r) and H-MFI (~) zeolites.
path with a barrier lower than 93 kJ mol–1, while for H-MFI there is a path with the highest barrier of 64 kJ mol–1. The most likely explanation for the discrepancy between calculated and NMRderived barrier heights is the presence of residual amounts of small molecules like water or ammonia left over from the preparation process. Such molecules may significantly reduce measured barriers for proton motion by a vehicle mechanism (Fig. 22.7 (b)). A simple calculation shows that already for a coverage of Brønsted sites with water molecules at the ppm level the kinetics is dominated by the very much faster H2O assisted jumps [47]. A careful computational study (which goes beyond DFT for the H2O–Brønsted site complex, but includes the full periodic zeolite at the DFT level) yields barriers (including zero-point vibrational contributions) of 65 and 20 kJ mol–1 for O1–O2 jumps in dry and water-loaded H-CHA (1:1), respectively [42]. At room temperature, this increases the jump rate by eight orders of magnitude from 40 to 30 108 per second. The nanosecond time scale at which H2O-assisted proton jumps can hence be expected is not accessible by CPMD simulations, which typically are run for picoseconds. This explains that during CPMD simulations for the 1:1 H2O/H-CHA system mentioned above, proton jumps from one framework oxygen to another one via a hydroxonium transition structure (Fig. 22.7(b)) have not been observed.
22.7 Stability of Carbenium Ions in Zeolites
Carbenium ions can be formed by proton transfer from the Brønsted site to an unsaturated hydrocarbon which requires a negative proton transfer energy, Eq. (22.4). {AlO4}ZH + CnHm–2 fi {AlO4–}Z · CnHm–1+
(22.7)
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22 Proton Transfer in Zeolites
Alternatively, carbenium ions can be formed by hydride abstraction from a saturated hydrocarbon, {AlO4}ZH + CnHm fi {AlO4–}Z · CnHm–1+ + H2
(22.8)
The lifetime of the carbenium ion formed will be limited by transferring a proton back to the zeolite, thus completing the dehydrogenation of the hydrocarbon. Hydride abstraction from xylene is assumed to be the initial step in its disproportionation into toluene and trimethylbenzene [9]. The parent compound (7, Fig. 22.9) of the carbenium ion formed (6) has such a high proton affinity (1031 kJ mol–1, Table 22.1) that proton transfer back to the zeolite does not occur at all. However, the lifetime of carbenium ions in zeolites is not only limited by proton transfer, but also formation of a C–O bond between the carbenium ion and a framework oxygen atom, yielding an alkoxide, needs to be considered. In ferrierite (FER) the alkoxide of 6 is found to be 50 to 60 kJ mol–1 more stable than the carbenium ion [9]. Table 22.1 lists three examples of cyclic alkenyl carbenium ions that live long enough in zeolites to be detected by NMR [6]. Obviously, alkoxide formation is not favored and the proton affinities of their parent hydrocarbon compounds are so large that they win the competition with the zeolite framework for the proton. An obvious candidate for a stable noncyclic carbenium ion is the tert-butyl cation observed in superacidic media. Even if the proton affinity of isobutene (Table 22.1) does not make it very likely that tert-butyl cations will exist in zeolites, several quantum chemical studies have localized stationary points for tert-butyl cations in zeolite and found that they are less stable than the adsorption complex, but are similar in stability to surface butoxides. Because of technical limitations vibrational analysis, which could prove that this cation is a local minimum on the potential energy surface, that is a metastable species, have only recently been made. Within a periodic DFT study of isobutene/H-FER a complete vibrational analysis for all atoms in the unit cell was made [48], and as part of a hybrid QM/MNDO study on an embedded cluster model of isobutene/H-MOR a vibrational analysis was made with a limited number of atoms [49]. Both reached the
+ H+ - H2
- H+
(6)
Figure 22.9 Carbenium ion, 6, obtained by hydride abstraction from xylene and its deprotonation product, 7.
(7)
22.7 Stability of Carbenium Ions in Zeolites
conclusion that the tert-butyl cation is a local minimum (Fig. 22.10 (b)) and, hence, a possible intermediate with a stability comparable to that of isobutoxide. However, care has to be taken when applying DFT to hydrocarbon species in zeolites. The currently available functionals do not properly account for dispersion, which is a major stabilizing contribution for hydrocarbon–zeolite interactions. Due to the size of the systems it is difficult to apply wavefunction-based methods such as CCSD(T) or MP2. Thanks to an effective MP2/DFT hybrid approach and an extrapolation scheme energies, including the dispersion contribution, are now available for the different hydrocarbon species of Fig. 22.1 [50]. Fig. 22.10(c) shows the following surprising results: (i) The predicted energy of adsorption (70 kJ mol–1 at 0 K) is of the same order of magnitude as estimates based on experiments for related molecules (50–63 kJ mol–1). (ii) With respect to isobutene in the gas phase separated from the zeolite, the tert-butyl cation is much less stable (–17 kJ mol–1) than the isobutoxide (–48 kJ mol–1). The reason is that dispersion contributes substantially less to the stabilization of the tert-butyl cation than to the stabilization of the adsorption complex or the isobutoxide. As result, the proton transfer energy increases from 24 kJ mol–1 (DFT) to 59 kJ mol–1 (MP2/DFT) and it seems very unlikely that the tert-butyl cation will be detected in zeolites, even as a short-lived species. (a)
174
190
(b) isobutene + H-FER
- 27 - 63 -74
t-butyl cation (4) isobutoxide (5)
adsorbed isobutene (2) Figure 22.10 Energy profile for possible products of proton transfer from a zeolitic Brønsted site to isobutene, see Fig. 22.1. Standard heats of formation for intermediates 2, 4 and 5 obtained by hybrid MP2/DFT calculations [50], barriers between them are tentative, after Ref. [49]. Structures of (a) adsorbed isobutene (2) and (b) tert-butyl cation (4) [48] are also shown.
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References 1 W. O. Haag, R. M. Lago, P. B. Weisz,
Nature (London) 1984, 309, 589. 2 J. R. Sohn, S. J. DeCanio, P. O. Fritz, J. H. Lunsford, J. Phys. Chem. 1986, 90, 4847. 3 S. I. Zones, J. Chem. Soc., Chem. Commun. 1995, 2253. 4 L. J. Smith, L. Marchese, A. K. Cheetham, J. M. Thomas, Catal. Lett. 1996, 41, 13. 5 W. M. Meier, D. H. Olson, Atlas of Zeolite Structure Types, 3rd Revised Edn., Butterworths-Heinemann, London, 1992, http://www.iza-sc.ethz.ch/ IZA-SC/. 6 J. B. Nicholas, J. F. Haw, J. Am. Chem. Soc. 1998, 120, 11804. 7 V. Termath, F. Haase, J. Sauer, J. Hutter, M. Parrinello, J. Am. Chem. Soc. 1998, 120, 8512. 8 E. P. Hunter, S. G. Lias, in NIST Chemistry WebBook, NIST Standard Reference Database Number 69, (http://webbook.nist.gov), P. J. Linstrom, W. G. Mallard (Eds.), National Institute of Standards and Technology, Gaithersburg MD, 20899, 2005. 9 L. A. Clark, M. Sierka, J. Sauer, J. Am. Chem. Soc. 2003, 125, 2136. 10 M. Bjorgen, F. Bonino, S. Kolboe, K.-P. Lillerud, A. Zecchina, S. Bordiga, J. Am. Chem. Soc. 2003, 125, 15863. 11 M. V. Vener, X. Rozanska, J. Sauer, Phys. Chem. Chem. Phys. 2006; in preparation. 12 Y. Yin, A. L. Blumenfeld, V. Gruver, J. J. Fripiat, J. Phys. Chem. B 1997, 101, 1824. 13 M. Brndle, J. Sauer, J. Am. Chem. Soc. 1998, 120, 1556. 14 T. Bucko, J. Hafner, L. Benco, J. Chem. Phys. 2004, 120, 10263. 15 C. Lee, D. J. Parrillo, R. J. Gorte, W.E. Farneth, J. Am. Chem. Soc. 1996, 118, 3262. 16 X. Solans-Monfort, M. Sodupe, V. Branchadell, J. Sauer, R. Orlando, P. Ugliengo, J. Phys. Chem. B 2005, 109, 3539.
17 E. Nusterer, P. E. Blchl, K. Schwarz,
Angew. Chem., Int. Ed. 1996, 35, 175; Angew. Chem. 1996, 108, 187. 18 F. Haase, J. Sauer, J. Hutter, Chem. Phys. Lett. 1997, 266, 397. 19 F. Haase, J. Sauer, Microporous Mesoporous Mater. 2000, 35–36, 379. 20 R. Shah, J. D. Gale, M. C. Payne, J. Phys. Chem. 1996, 100, 11688. 21 R. Shah, M. C. Payne, M.-H. Lee, J. D. Gale, Science 1996, 271, 1395. 22 I. Stich, J. D. Gale, K. Terakura, M. C. Payne, J. Am. Chem. Soc. 1999, 121, 3292. 23 C. C. Lee, R. J. Gorte, W. E. Farneth, J. Phys. Chem. B 1997, 101, 3811. 24 P. Nachtigall, M. Davidova, D. Nachtigallova, J. Phys. Chem. B 2001, 105, 3510. 25 M. W. Anderson, P. J. Barrie, J. Klinowski, J. Phys. Chem. 1991, 95, 235. 26 F. Haase, J. Sauer, J. Am. Chem. Soc. 1995, 117, 3780. 27 M. Hunger, T. Horvath, J. Am. Chem. Soc. 1996, 118, 12302. 28 L. Heeribout, C. Doremieux-Morin, L. Kubelkova, R. Vincent, J. Fraissard, Catal. Lett. 1997, 43, 143. 29 E. Nusterer, P. E. Blchl, K. Schwarz, Chem. Phys. Lett. 1996, 253, 448. 30 J. Sauer, M. Sierka, F. Haase, in Transition State Modeling for Catalysis, D. G. Truhlar, K. Morokuma (Eds.), ACS Symposium Series 721, American Chemical Society, Washington, 1999, p. 358. 31 N. Y. Chen, J. Phys. Chem. 1976, 80, 60. 32 D. H. Olson, W. O. Haag, R. M. Lago, J. Catal. 1980, 60, 390. 33 D. H. Olson, W. O. Haag, W. S. Borghard, Microporous Mesoporous Mater. 2000, 35–36, 435. 34 M. Krossner, J. Sauer, J. Phys. Chem. 1996, 100, 6199. 35 S. A. Zygmunt, L. A. Curtiss, L. E. Iton, M. K. Erhardt, J. Phys. Chem. 1996, 100, 6663. 36 V. V. Mihaleva, R. A. van Santen, A. P. J. Jansen, J. Chem. Phys. 2004, 120, 9212.
References 37 F. Wakabayashi, J. N. Kondo, K. Domen,
38
39 40 41
42 43 44
C. Hirose, J. Phys. Chem. 1996, 100, 1442. L. J. Smith, A. K. Cheetham, R. E. Morris, L. Marchese, J. M. Thomas, P. A. Wright, J. Chen, Science 1996, 271, 799. Chem. Ind. 1996, 117. J. Sauer, Science 1996, 271, 774. Y. Jeanvoine, J. G. Angyan, G. Kresse, J. Hafner, J. Phys. Chem. B 1998, 102, 7307. C. Tuma, J. Sauer, Chem. Phys. Lett. 2004, 387, 388. M. Sierka, J. Sauer, J. Phys. Chem. B 2001, 105, 1603. M. E. Franke, M. Sierka, U. Simon, J. Sauer, Phys. Chem. Chem. Phys. 2002, 4, 5207.
45 H. Ernst, D. Freude, T. Mildner,
46
47 48
49 50
H. Pfeifer, Proceedings of the 12th International Zeolite Conference, Vol. 4, M. M. J. Treacy, B. K. Marcus, M. E. Bischer, J. B. Higgins (Eds.), 1998, Baltimore, Maryland, Materials Research Society, Warrendale, PA, 1999, p. 2955. P. Sarv, T. Tuherm, E. Lippmaa, K. Keskinen, A. Root, J. Phys. Chem. 1995, 99, 13763. J. A. Ryder, A. K. Chakraborty, A. T. Bell, J. Phys. Chem. B 2000, 104, 6998. C. Tuma, J. Sauer, Angew. Chem., Int. Ed. 2005, 44, 4769; Angew. Chem. 2005, 117, 4847. M. Boronat, P. M. Viruela, A. Corma, J. Am. Chem. Soc. 2004, 126, 3300. C. Tuma, J. Sauer, Phys. Chem. Chem. Phys. 2006, 8, 3955.
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23 Proton Conduction in Fuel Cells Klaus-Dieter Kreuer
23.1 Introduction
Fuel cells are devices which electrochemically convert the chemical free energy of gaseous, and sometimes also liquid, reactants into electrical energy. As in a battery the reactants are prevented from reacting chemically by separating them with an electrolyte, which is contacted with electrochemically active porous electrode structures. Apart from effectively separating the anode and cathode gases and/or liquids the electrolyte mediates the electrochemical reactions taking place at the electrodes by conducting a specific ion at very high rates during the operation of the fuel cell. Proton conducting electrolytes are used chiefly as separators for low and intermediate temperature fuel cells such as PEMFCs (polymer electrolyte membrane or proton exchange membrane fuel cells), DMFCs (direct methanol fuel cells), PAFCs (phosphoric acid fuel cells), and AFCs (alkaline fuel cells), but proton conducting oxides [1] and plasic acidic salts of oxo-acids [2] have also been considered recently for fuel cell applications at somewhat higher temperature. The main features of a fuel cell, including the electrochemical reactions taking place for the most simple case of hydrogen and oxygen as reacting gases, are shown schematically in Fig. 23.1. During operation, a protonic current equivalent to the electronic current passing through the external load is driven through the electrolyte and parts of the heterogeneous electrode structures, and it is the proton conducting properties of the diverse electrolytes which are the subject of this chapter. Since the scope of this Handbook is rather broad, this chapter also gives a more general description of proton conduction phenomena in electrolytes which are currently used in fuel cells or which have the potential to be used for this purpose in the near future. For those readers who are interested in the whole variety of available electrolytes and the specific aspects of their operation in fuel cell environments, appropriate references are given. Of course, this chapter is intended to be complementary to the other chapters in this Handbook with its main focus on the features of proton conduction in fuel cell electrolytes. Many of these electrolytes contain water or other hydrogen bonded liquids, or are hydrogen bonded solid stuctures, which are also discussed in other chapters from different perspectives. Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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23 Proton Conduction in Fuel Cells
Figure 23.1 Schematic representation of a hydrogen / oxygen fuel cell, comprising the proton conducting separator (electrolyte) and the heterogeneous gas electrodes. The transport of protons and electrons, the electrode reactions and the total reaction are indicated.
For the non-fuel cell expert, Section 23.2 provides a brief introduction to prototypical proton conducting fuel cell electrolytes including the rationales for their choice for particular fuel cell systems. Since the key feature of all these electrolytes is their proton conductivity, that is the long range transport of protonic charge carriers, this is first discussed in general in Section 23.3 before describing the proton conduction mechanisms of specific homogeneous media, which have some relevance as the conducting part of heterogeneous separator materials. Indeed, many fuel cell separators exhibit nano-heterogeneities, and the corresponding confinement and interfacial effects sometimes lead to the appearance of qualitatively new features, which are discussed in Section 23.4. The discussion in all the sections makes use of many results from simulations. For a brief introduction to the underlying models and techniques the interested reader is referred to Ref. [3].
23.2 Proton Conducting Electrolytes and Their Application in Fuel Cells
The fuel cell concept has been known for more than 150 years. It was Christian Friedrich Schnbein who recognized and described the appearance of “inverse electrolysis” [4] shortly before Sir William Grove, the inventor of the platinum/ zinc battery, constructed his first “gas voltaic battery” [5]. Grove used platinum electrodes and dilute sulfuric acid as a proton conducting electrolyte. Sulfuric acid is still used today for the impregnation of porous separators serving as the electrolyte in direct methanol laboratory fuel cells [6], but the most commonly used fuel cell electrolytes today are hydrated acidic ionomers. As opposed to aqueous sulfuric acid, where the dissociated protons and the diverse sulfate anions (conjugated
23.2 Proton Conducting Electrolytes and Their Application in Fuel Cells
bases) are mobile, such ionomers are polymers containing covalently immobilized sulfonic acid functions. The immobilization reduces anion adsorption on the platinum cathode, which may lead to reduced exchange current densities for oxygen reduction in the case of sulfuric acid as electrolyte. Among the huge number of sulfonic acid bearing polymers [7–12], the most prominent representative of this class of separators is DuPont’s Nafion [13, 14]. Such polymers naturally combine, in one macromolecule, the high hydrophobicity of the backbone (green in Fig. 23.2(a)) with the high hydrophilicity of the sulfonic acid functional group, which gives rise to a constrained hydrophobic/hydrophilic nano-separation. The sulfonic acid functional groups aggregate to form a hydrophilic domain that is hydrated upon absorption of water (blue in Fig. 23.2(a)). It is within this continuous domain that ionic conductivity occurs: protons dissociate from their anionic counter ion (SO3–) and become solvated and mobilized by the hydration water (red in Fig. 23.2(a)). Water typically has to be supplied to the electrolyte through humidification of the feed gases and is also produced by the electrochemical reduction of oxygen at the cathode. This is the reason for two serious problems relevant to the use of such membranes in fuel cells. Since high proton conductivity is only obtained at high levels of hydration, the maximum operating temperature is limited approximately to the condensation point of water, and any protonic current also leads to transport of water through the membrane (as a result of electroosmotic drag; see also Section 23.4.1) and, if methanol dissolves in the membrane, this is transported at virtually the same rate [12]. The limited operating temperature and the acidity of the electrolyte makes it necessary to use platinum or platinum alloys (the most active but also the most expensive electrocatalysts) to promote the electrochemical reactions in the anode and cathode structures. However, even with platinum, only rather pure hydrogen can be oxidized at sufficient rates. Nevertheless, such acidic polymers are currently very popular as separator materials in PEM fuel cells because they allow very high electrical power densities (up to about 0.5 W cm–2). The smaller conductivities of basic electrolytes (the highest proton conductivities are observed for aqueous KOH solutions) actually limit the power density of AFCs, but the efficiency of such fuel cells is significantly higher than for fuel cells based on acidic electrolytes, the latter showing higher overpotentials for the oxygen reduction reaction. At the operation temperature of state-of-the-art PEM-fuel cells (usually below 90 C), the rate of direct oxidation of methanol (which is frequently considered an environmentally friendly fuel) is not sufficient for high power applications, and even trace amounts of CO present in any hydrogen-rich reformate (for instance produced by steam reforming of methanol or methane) poison platinum-based catalysts by blocking the reaction sites. The humidification requirements, along with the high electroosmotic drag of water and methanol in solvated acidic ionomers, complicates the water and heat management of the fuel cell and leads to a significant chemical short-circuiting, this is parasitic chemical oxidation of methanol at the cathode. These disadvantages are overcome by using phosphoric acid as the electrolyte in PAFCs. Phosphoric acid keeps its high protonic conductivity even at high temperature (up to about 200 C) and low humidity. In PAFCs, phosphoric acid is usually adsorbed
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23 Proton Conduction in Fuel Cells
23.2 Proton Conducting Electrolytes and Their Application in Fuel Cells
Figure 23.2 Schematic representation of the nanostructures of (a) hydrated acidic ionomers such as Nafion, (b) complexes of an oxo-acid and a basic polymer such as PBI·n H3PO4 and (c) proton solvents fully immobilized via flexible spacers (in this particular case the proton solvent (phosphonic acid) also acts as a protogenic group). Note, that there are different types of interaction between the polymeric matrices (green) and the liquid or liquid-like domains (blue). The protonic charge carriers (red) form within the liquid or liquid-like domain, where proton conduction takes place.
by a porous silicon carbide separator, but more recently adducts of basic polymers (for instance polybenzimidazole) and phosphoric acid have also become a focus of atttention (for reviews see Refs. [15, 16]). The microstructure of such separator materials is illustrated in Fig. 23.2(b), showing the polymer matrix (green) which is protonated by phosporic acid, resulting in the formation of a stable nonconducting complex. It is the excess amount of phosphoric acid absorbed by this complex which leads to the appearance of proton conductivity. Leaching out of phosphoric acid in the presence of water and the poor oxygen reduction reversibility on platinum-based cathodes in the presence of phosphate species are inherent drawbacks of fuel cells using such electrolytes. Therefore, there is currently tremendous effort to develop separator materials which conduct protons in the absence of any low molecular weight solvent such as water or phosphoric acid (for a review see Ref. [17]). One of the recent approaches is illustrated in Fig. 23.2(c): protogenic groups (here phosphonic acid) are immobilized to an inert matrix (green) via flexible spacers. It is within the domain formed by the protogenic groups that proton conductivity occurs. In this type of electrolyte the only mobile species is the proton.
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23 Proton Conduction in Fuel Cells
23.3 Long-range Proton Transport of Protonic Charge Carriers in Homogeneous Media
Despite the diversity of proton conducting electrolytes there have been attempts to describe the underlying elementary reactions. Initially the proton was considered to interact chemically with only two electronegative nearest neighbors (mostly oxygen or nitrogen) via hydrogen bonding before the electrostatic interaction with the more distant proton environment was included by considering the environment as a simple dielectric continuum (for a review of the different approaches see Ref. [11]). Such simple concepts did not include any chemical or structural details other than the chemical nature of the proton donor and acceptor, and the donor / acceptor separation. Also the dynamics of the proton environment was either reduced to the variations of the donor / acceptor separation [19–21] or described qualitatively as being solid-like or liquid-like [22]. However it turned out that the structural, chemical and dynamical details are essential for complex descriptions of long-range proton transport. These parameters appear to be distinctly different for different families of compounds, preventing proton conduction processes from being described by a single model or concept as is the case for electron transfer reactions in solutions (described within Marcus’ theory [23]) or hydrogen diffusion in metals (incoherent phonon assisted tunneling [24]). A common feature of most proton conduction mechanisms is the conflict between high rates of proton transfer and structural reorganization, which are both required to establish long-range proton transport. This has to do with the characteristics of the hydrogen bond interaction which not only provides a path for proton transfer but also has pronounced structure forming properties. Rapid proton transfer is actually favored by short, strong hydrogen bonds, while structural reorganization, requiring the breaking of hydrogen bonds, is hindered by strong hydrogen bonding. This is especially true for small clusters such as the simple proton / acceptor system H5O2+. For this the proton transfer barrier equals the energy needed to break the central hydrogen bond at a donor / acceptor separation Q » 300 pm, where both energies are of the order of 1 eV, which is significantly higher than the activation enthalpy of proton mobility in bulk water (» 0.1 eV) [25]. Obviously, it is the mutual interaction of many particles in bulk water, which is essential for the appearance of high rates of proton transfer and structural reorganization, which are both required for fast proton conduction. This is not surprising considering that the regions around protonic defects (excess or defect protons) in condensed matter frequently show pronounced relaxation effects, which in turn suggests a strong coupling of proton conductance to the dynamics of its environment [18]. In the following, details of such complex proton conduction mechanisms are presented for homogeneous media, where effects from confinement and interaction with other phases are not yet considered. These media comprise aqueous solutions, phoshoric (phosphonic) acid and heterocycles such as imidazole, which form the molecular environments in proton conducting electrolytes used or considered for fuel cell applications.
23.3 Long-range Proton Transport of Protonic Charge Carriers in Homogeneous Media
23.3.1 Proton Conduction in Aqueous Environments
The dominant intermolecular interaction in water is hydrogen bonding. The introduction of an excess proton (i.e. the formation of a protonic defect) leads to the contraction of hydrogen bonds in the vicinity of such a defect. This corresponds to the well-known structure forming properties of excess protons in water (see for example Ref. [26]). Thus the isolated dimer H5O2+ finds its energetic minimum at an O / O separation of only 240 pm [27, 28] with an almost symmetrical single well potential for the excess proton in the center of the complex. But due to the presence of additional hydrogen bonds, the central bond of such complexes is weakened to some extent [18] with some small barrier building up in bulk water. In other words, the binding power of a water molecule depends on the number of hydrogen bonds it is already involved in. This also leads to relaxation effects in neighboring hydrogen bonds as a response to hydrogen bond formation or cleavage: when a hydrogen bond is formed, the surrounding bonds are weakened, while the cleavage of a hydrogen bond leads to a strengthening of neighboring bonds. As a consequence, the effective energy for breaking a hydrogen bond in bulk water is significantly lower than the average hydrogen bond energy. This is evidenced, for instance, by the evolution of the fraction of broken hydrogen bonds with temperature for pure bulk water [29]. The apparent activation energy for hydrogen bond cleavage at room temperature only amounts to 50 meV, which is significantly lower than the average hydrogen bond energy (» 180 meV). On the other hand the effective activation energy increases to about 100 meV at the critical temperature, although the average hydrogen bond energy decreases with temperature. At such high temperatures the number of intact hydrogen bonds is small, with little interaction remaining between hydrogen bonds. Consequently, the full energy of a hydrogen bond is required to break the bond. For the well-connected hydrogen-bond network present at low temperature this bond interaction leads to a significant softening of the intermolecular interaction and therefore to strong variations in the hydrogen bond length as well as a rapid breaking and forming of hydrogen bonds. The above-described features are reproduced in a high level quantum-molecular-dynamics simulation of an excess proton in water [30, 31]. In accordance with results from several other groups, this finds the excess proton either as part of a dimer (H5O2+, “Zundel”-ion) or as part of a hydrated hydronium ion (H9O4+, “Eigen”-ion) (Fig. 23.3). Interestingly, the center of the region of excess charge coincides with the center of symmetry of the hydrogen bond pattern [25], i.e. apart from the bonds with the common shared proton, each water molecule of the Zundel-ion acts as a proton donor through two hydrogen bonds, and each of the three outer water molecules of the Eigen-ion acts as a proton donor in two hydrogen bonds and as an acceptor for the hydronium ion and an additional water molecule (Fig. 23.3). Changes to these hydrogen bond patterns through hydrogen bond breaking and forming processes displaces the center of symmetry in space and therefore also the center of
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23 Proton Conduction in Fuel Cells
Figure 23.3 Proton conduction mechanism in water. The protonic defect follows the center of symmetry of the hydrogen-bond pattern, which “diffuses” by hydrogen-bond breaking and forming processes. Therefore, the mechanism is frequently termed “structure diffusion”. Note that the hydrogen bonds in the region of protonic excess charge are
contracted, and the hydrogen bond breaking and forming processes occur in the outer parts of the complexes (see text). Inserted potentials correspond to nonadiabatic transfer of the central proton in the three configurations (atomic coordinates taken from Ref. [30, 31] with kind permission from Chemical Reviews.
the region of excess charge. In this way a Zundel-ion is converted into an Eigenion, which then transfers into one of three possible Zundel-ions (Fig. 23.3). This type of mechanism may be termed “structure diffusion” (as suggested by Eigen for a similar mechanism [32, 33]) because the protonic charge follows a propagating hydrogen bond arrangement or structure. The sum of all proton displacements involved in the hydrogen bond breaking and forming processes and the proton displacements within the hydrogen bonds of the Zundel- and Eigen-ions then corresponds to the net displacement of one unit charge by just a little more than the separation of the two protons in a water molecule (i.e. @ 200 pm). Although there are no individual exceptionally fast protons, even on a short time scale, the fast diffusion of protonic defects leads to a slight increase in the physical diffusion of all protons in the system. This is indeed observed for aqueous solutions of hydrochloric acid, for which mean proton diffusion coefficients were found to be up to 5% higher than the diffusion coefficient of oxygen as measured by 1H- and 17O-PFG-NMR [34] reflecting the slight decoupling of proton and oxygen diffusion in acidic media. Another interesting feature of this mechanism is that the hydrogen bond breaking and forming (hydrogen bond dynamics) and the translocation of protons within the hydrogen bonds take place in different parts of the hydrogen bond network,
23.3 Long-range Proton Transport of Protonic Charge Carriers in Homogeneous Media
albeit in a highly concerted fashion. This is the most thermodynamically favorable transport path, because the hydrogen bonds in the center of the two charged complexes are contracted to such an extent as to allow an almost barrierless proton translocation while the hydrogen bond breaking and forming processes take place in the weakly bonded outer parts of the complexes. This contraction of the center of the complex is probably a direct consequence of the lower coordination of the involved species (3 instead of about 4). The activation enthalpy of the overall transport process is dominated by the hydrogen bond breaking and forming, which also explains the strong correlation of the proton transport rate and the dielectric relaxation [2]. The Zundel- and Eigen-complexes are just limiting configurations, and the simulations indeed produce configurations that can hardly be ascribed to one or the other [36]. The time-averaged potential surfaces for proton transfer in such contracted hydrogen bonds are almost symmetrical (especially for the Zundel-ion) without significant barriers, and the proton is located close to the center of the bond. Whether its location is off-center at any time mainly depends on the surrounding hydrogen bond pattern, and it is the change in this pattern that alters the shape (and asymmetry) of this potential and therefore the position of the proton within the hydrogen bond (see Fig. 23.3 top). In other words, the proton is transferred almost adiabatically with respect to the solvent coordinate [18]. This has important consequences for the mechanism when static asymmetric potential contributions are introduced, for instance by chemical interactions or the presence of ionic charges (see below). The very low barriers are also the reason why the mechanism can be well described classically with respect to the motion of the nuclei (especially the proton), in particular, proton tunneling has only a minor effect on the rate of transfer. Nevertheless, the protonic defect (region of protonic excess charge) may become delocalized through several hydrogen bonds owing to quantum fluctuations [36, 37]. The mechanism also provides insight into the extent to which proton transfer in water is a cooperative phenomenon. In many physical chemistry textbooks one still finds cartoons showing the concerted transfer of protons within extended hydrogen bonded water chains (Grotthuss mechanism) in order to explain the unusually high equivalent conductivity of protons in this environment. However, the creation of the corresponding dipolar moment in an unrelaxed high dielectric constant environment costs far too much energy to be consistent with a very fast process [18, 38]. As anticipated in Ref. [18], the propagation of a protonic defect in a low-dimensional water structure surrounded by a low dielectric environment is obviously between “concerted” and “step-wise” in mechanism [39, 40], but in bulk water the cooperation is restricted to the dynamics of protons in neighboring hydrogen bonds (see also Fig. 23.2). One should also keep in mind that water is a liquid with a high self-diffusion coefficient (DH2O = 2.25 10–5 cm2 s–1 at room temperature) and that the diffusion of protonated water molecules makes some contribution to the total proton conductivity (vehicle mechanism [41]). But, as suggested by Agmon [42], the diffusion of H3O+ may be retarded owing to the strong hydrogen bonding in its first hydration shell.
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Of course, the relative contributions of “structure diffusion” and “vehicular diffusion” depend on temperature, pressure and the concentrations and kinds of ions present. With increasing temperature, “structure diffusion” is attenuated and with increasing pressure the contribution of “structure-diffusion” increases until it reaches a maximum around 0.6 GPa (6 kbar) [18]. Especially relevant for the later discussion of proton transport in hydrated polymeric fuel cell electrolytes is the observation that structure diffusion strongly decreases with increasing acid concentration [43] which is probably due to changes in the hydrogen bond pattern (there are progressively more proton donors than corresponding proton acceptor “sites”) and a consequence of the biasing of the hydrogen bonds in the electrostatic field of the ions suppressing the proton transfer mechanism illustrated in Fig. 23.3. Since basic aqueous solutions also have some relevance for fuel cell applications (in AFCs, where aqueous KOH solutions are used as electrolyte) the conduction mechanism of defect protons (OH–) is also summarized here. As opposed to Zundel- and Eigen-complexes, in which the central species are only three-fold coordinated (under-coordinated with respect to water in pure water which is probably the reason for the bond contraction in these complexes, see above) on the average, the hydroxide ion is found to be coordinated by about 4.5 water molecules in an almost planar configuration with the OH proton pointing out of the plane [44]. This is considered to be a true quantum effect and contradicts the common understanding of a threefold coordination [45]. This “hyper-coordination” is suggested to prevent proton transfer from an H2O to the OH–, because this would produce an unfavorable H–O–H bond angle of 90. The proton transfer only occurs when the OH– coordination is reduced to 3 by breaking one of the 4 hydrogen bonds within the plane and some rearrangement of the remaining bonds, which allows the direct formation of a water molecule with a tetrahedral geometry. Surprisingly, the ground-state coordination of the most favorable configurations around excess protons appears to be close to the coordination of the transition state for the transport of defect protons. However, it should be noted that “hyper-coordination” of the OH– is still the subject of controversial debate. The statistical mechanical quasichemical theory of solutions suggests that tricoordinated OH– is the predominant species in the aqeous phase under standard conditions [46, 47]. This finding seems to be in agreement with recent spectroscopic studies on hydroxide water clusters, and is in line with the traditional view of OH– coordination. It should also be mentioned that OH– “hyper-coordination” is not found in concentrated solutions of NaOH and KOH [48]. In contrast to acidic solutions where structure diffusion is suppressed with increasing concentration the transference number of OH– (for example in aqueous KOH solutions) remains surprisingly high (approximately 0.74) for concentrations up to about 3 M. In pure water, excess protons (H3O+, H5O2+) and defect protons (OH–) are present in identical concentration, but owing to their low concentration (10–7 M under ambient conditions) and the high dielectric constant of bulk water the diffusion of these defects is quasi-independent.
23.3 Long-range Proton Transport of Protonic Charge Carriers in Homogeneous Media
The complexity of the above-discussed many-particle conduction mechanisms of excess and defect protons in water reduces the effective activation enthalpy for the long-range transport of protonic defects, but it is also responsible for the relatively low pre-exponential factor of this process, which probably reflects the small statistical probability to form a transition state configuration in this environment. 23.3.2 Phosphoric Acid
The proton conduction mechanism in phosphoric acid has not been investigated to the same extent as is the case for aqueous solutions, but it is evident that the principal features exhibit both similarities and important differences. Above its melting point, Tm = 42 C, neat phosphoric acid (H3PO4) is a highly viscous liquid with extended intermolecular hydrogen bonding. But in contrast to the situation in water, there are more possible donor than acceptor sites and the amphoteric character is significantly more pronounced: phosphoric acid may act as both a Brønsted acid and base. In terms of equilibrium constants both Ka and Kb are reasonably high (Ka of the conjugate base is low). Consequently, phosphoric acid shows a very high degree of self-dissociation (auto-protolysis) of about 7.4% [49] along with some condensation, H2PO4–, H4PO4+, H3O+ and H2P2O72– being the main dissociation products. Because of their high concentrations, the separation of the overall conductivity into charge carrier concentration and mobility terms is problematic. Nevertheless, the proton mobility has been calculated from total conductivities by the Nernst–Einstein equation by taking concentrations from Ref. [49]; and the values have been found to be almost two orders of magnitude higher than the values for the diffusion coefficient of the diverse phosphate species obtained directly by 31P PFG-NMR [50] and estimated from viscosity measurements via the Stokes–Einstein relation. Pure phosphoric acid is a liquid with a low diffusion coefficient of phosphate species but an extremely high proton mobility, which must involve proton transfer between phosphate species and some structural rearrangements. The contribution to the total conductivity is about 98%, in other words, phosphoric acid is an almost ideal proton conductor. The total conductivity at the melting point (42 C) is 7.7 10–2 S cm–1 with an estimated proton mobility of 2 10–5 cm2 s–1 [50]. Extremely high proton mobilities have also been indirectly determined with 1H-PFG-NMR and were found to be even higher (by a factor of 1.5–2.3). This has been explained by the correlated motion of the oppositely charged defects (H2PO4–, H4PO4+) when they are close to one another (this is the case just after their formation (by dissociation of H3PO4) and before their neutralization). Correlation effects are actually quite common in proton conductors with high concentrations of charge carriers and they are even more pronounced in other systems with lower dielectric constant [51, 52]. Molecular details of the “structure diffusion“ mechanism with the hydrogen bond breaking and forming and the proton transfer between the different phosphate species (essentially H2PO4–, H3PO4, H4PO4+) have not been investigated
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yet, but the high degree of self-dissociation suggests that the proton transfer events are even less correlated than in water (the system is more tolerant towards protonic charge density fluctuations). The transfer events are probably almost barrierless as indicated by negligible H/D effects of the diffusion coefficients in mixtures of H3PO4 and D3PO4 [53]. The principal proton transport mechanism seems to be essentially unchanged with the addition of some water with a conductivity increase up to 0.25 S cm–1 under ambient conditions. A 1H and 31P-PFG-NMR study also showed an 85 wt% phosphoric acid system to be an almost ideal proton conductor with 98% of the conductivity originating from the structure diffusion of protons [54]. The combination of high intrinsic charge carrier concentration and mobility gives the possiblility of very high conductivities in these systems. In particular, there is no perturbation from extrinsic doping, that is there is no suppression of structure diffusion despite the high concentration of protonic charge carriers. On the other hand, attempts to increase the conductivity of phosphoric acid based systems by doping have expectedly failed [55]. It should be mentioned, that the transport properties of phosphonic acid, which has recently been used as protogenic group in fully polymeric proton conductors (see Section 23.4.2), seem to be similar to these of phosphoric acid 23.3.3 Heterocycles (Imidazole)
Historically, the interest in hydrogen bonding and proton conductivity in heterocycles has its roots in speculation about the participation of hydrogen bonds in energy and charge transfer within biological systems [56, 57]. Even Zundel has worked in the field [58] and it is not surprising that his view of the proton dynamics in imidazole is closely related to that of water. He suggested a high polarizability of the protons within intermolecular hydrogen bonds and, as a consequence, a very strong coupling between hydrogen bonds, as indicated by the intense IR continuum in the NH stretching regime. Surprisingly, he did not suggest the existence of any complex similar to the Zundel complex in water [58] (see Section 23.3.1), whereas Riehl [59] had already suggested “defect protons” or “proton holes” as requirements to maintain a current in solid imidazole. Early conductivity measurements were focused on crystalline monoclinic imidazole, which has a structural hydrogen bond length of 281 pm [60]. The measured conductivities were typically low (approximately 10–8 S cm–1) with very poor reproducibility [56, 61, 62]. Later tracer experiments [63] and a 15N-NMR study [64] raised doubts about the existence of proton conductivity in pure crystalline imidazole. The conductivity of liquid imidazole, however, was found to be several orders of magnitude higher (about 10–3 S cm–1 at the melting point Tm = 90 C [56]) but the conduction mechanism was investigated much later. It was the search for chemical environments different from water in fuel cell membranes that brought heterocycles back into focus. The potential proton donor and acceptor functions (amphoteric character), the low barrier hydrogen bonding between the highly
23.3 Long-range Proton Transport of Protonic Charge Carriers in Homogeneous Media
polarizable nitrogen atoms, and the size and shape of the molecule were the reasons why Kreuer et al. started to investigate the usefulness of heterocycles as proton solvents in separator materials for fuel cells [65]. This work also comprises the study of the transport properties of neat and acidified liquid imidazole, pyrazole, and later benzimidazole [66]. An important finding was that the transport coefficients (mobility of protonic charge carriers and molecular diffusion coefficients) are close to those of water at a given temperature relative to the melting point. This is particularly true for their ratio: the proton mobility is about a factor of 4.5 higher than the molecular diffusion coefficient at the melting point of imidazole [65]. This is a direct indication of fast intermolecular proton transfer and the possibility of structure diffusion in this environment. Subsequently, details were revealed by a CP-MD simulation [67]. In contrast to earlier suggestions of concerted proton transfer in extended chains of hydrogen bonds [56, 58] (analagous to the proton conduction mechanism in water presented in most textbooks at that time [38]) a structure diffusion mechanism similar to that for water (Fig. 23.3) was found. The region containing the excess proton (intentionally introduced) is an imidazole with both nitrogens protonated and acting as proton donors towards the two next nearest imidazoles in a configuration Imi – Imi+ – Imi with hydrogen bonds (approximately 273 pm) slightly contracted compared to the average bond length of the system but still longer than the bonds in the isolated complex (in the gas phase) [69]. The position of the protons within these hydrogen bonds depends mainly on the hydrogen bonding between the nearest and next nearest solvating imidazoles (Fig. 23.4). The hydrogen bonded structure in imidazole is found to be chain-like (low-dimensional) with two possible orientations of the hydrogen bond polarization within segments which are separated by imidazoles with their protonated nitrogen directed out of the chain. This may even form a “cross-linking” hydrogen bond with a nonprotonated nitrogen of a neighboring strand of imidazole. The simulation data revealed the existence of imidazole mol-
Figure 23.4 Proton conduction mechanism in liquid imidazole as obtained by a CP-MD simulation [67]. As in water, changes in the second solvation shell of the protonic defect (here imidazolium) drive the long-range transport of the defect.
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ecules close to the protonic defect in hydrogen bond patterns, which rapidly change by bond breaking and forming processes. Similar to water, this shifts the excess proton within the region and may even lead to complete proton transfer as displayed in Fig. 23.4. There is no indication of the stabilization of a symmetrical complex (Imi – H – Imi)+: there always seems to be some remaining barrier in the hydrogen bonds with the proton being on one side or the other. As for the CP-MD simulation of water, the simulated configuration is artificial, because there is no counter charge compensating for the charge of the excess proton. This is necessary, methodologically, since self-dissociation is unlikely to occur within the simulation box used (8 imidazole molecules with a single excess proton) and the accessible simulation time (approximately 10 ps). The self-dissociation constants for heterocycles (in particular imidazole) are actually much higher than for water, but degrees of self-dissociation (concentration of protonic charge carriers) around 10–3 are still about two orders of magnitude lower than for phosphoric acid (see Section 23.3.2). Site-selective proton diffusion coefficients (obtained by 1H-PFG-NMR of different imidazole-based systems) show surprisingly high diffusion coefficients for the protons involved in hydrogen bonding between the heteroatoms (nitrogen) [70]. Depending on the system, they are significantly higher than calculated from the measured conductivities corresponding to Haven ratios (rD/r) of 3–15. This indicates some correlation in the diffusion of the proton, which may be due to the presence of a counter charge neglected in the simulation. In pure imidazole, regions containing excess protons must be charge compensated by proton deficient regions with electrostatic attraction between these regions (defects) that depends on their mutual separation distance and the dielectric constant of the medium. Under thermodynamic equilibrium such defects are steadily formed and neutralized. Formally, the creation of a protonic defect pair is initiated by a proton transfer from one imidazole to another with the subsequent separation of the two charged species with a diffusion mechanism as described above (see also Fig. 23.4). However, this transfer is against the electrostatic field of the counter charge, favoring a reversal of the dissociation process. But since the two protons of the positively charged imidazolium (Imi+) are equivalent, there is a 50% chance that another proton will be transferred back, provided that the orientational coherence between the dissociating molecules is completely lost. If the same proton is transferred back, the transient formation and neutralization of an ion pair contributes neither to the proton diffusion nor to the proton conductivity. But if the other proton is transferred back, the protons interchange their positions in the hydrogen bond network, which generates diffusion but no conductivity, since the transient charge separation is completely reversed. The sum of all proton translocation vectors then forms a closed trajectory which is reminiscent of cyclic intermolecular proton transfer reactions known to take place in certain organic pyrazole containing complexes [71] and proton diffusion in hydroxides [51, 52].
23.4 Confinement and Interfacial Effects
23.4 Confinement and Interfacial Effects
As described in Section 23.2, the proton conducting media discussed in Section 23.3 are dispersed within matrices (usually polymers), which not only give the separator material its morphological stability and gas separating properties but also modify the charge carrier distribution and transport properties within the conducting domain as a result of confinement and interaction. Such effects are described in the following for the three type of separator materials illustrated in Fig. 23.2. 23.4.1 Hydrated Acidic Polymers
The hydrophilic domain of hydrated acidic polymers contains only water and excess protons (Fig. 23.2(a)), which is reminiscent of the situation illustrated in Fig. 23.3, but both species interact chemically and electrostatically with the immobile negatively charged sulfonic groups. Traditionally, the distribution of charge carriers within the corresponding space charge layer is described by the Gouy– Chapman theory, which has been developed for semi-infinite geometries, or by numerically solving the Poisson–Boltzmann equation for specific geometries [72]. In either case, one obtains a monotonically decreasing concentration of protonic charge carriers as one moves from the hydrophobic/hydrophilic interface (where the anion charge resides) towards the center of the hydrated hydrophilic domain. This picture, however, is not complete because these continuum theories neglect any structural inhomogeneity in the vicinity of the electrified interface. In the Gouy–Chapman approach, even a homogeneous distribution of the counter charge over the interface is assumed, but the fact that the separation of neighboring sulfonic acid groups (approximately 0.8 nm) and the typical extension of the hydrophilic domain (a few nm) is of similar order does not justify this assumption. Also the assumption of a homogeneous dielectric constant of the aqueous phase breaks down for such dimensions and is indeed not backed up by dielectric measurements as a function of the water content in the microwave (i.e. GHz) range [73, 74]. As known for the near surface region of bulk water or any interface with water on one side, the dielectric constant of the hydrated hydrophilic phase is significantly reduced close to the hydrophobic/hydrophilic interface. In addition, the specific interaction of the sulfonic acid group with water (hydration) also decreases the dielectric constant. Therefore, the spatial distribution of the dielectric constant within hydrated domains depends strongly on the width of the channels (degree of hydration) and the separation of the dissociated sulfonic acid functional groups. This is evidenced by an equilibrium statistical thermodynamic modeling of the dielectric saturation in different types of hydrated polymers [75]. According to these calculations, the dielectric constant reaches the bulk value (81) in the center of the channel (pore) for water contents higher than about 10 water molecules per sulfonic acid group, corresponding to a domain width of about
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1 nm, while for lower degrees of hydration even in the center of the channel the dielectric constant is lower than the bulk value. The calculations did not account for specific chemical interactions between the water and the polymer backbone, which are expected to further reduce the dielectric constant at the hydrophilic/ hydrophobic interface. The general picture arising from this simulation is that the majority of excess protons are indeed located in the central part of the hydrated hydrophilic nano-channels where the enthalpy of the proton hydration is anticipated to be highest, as a result of the high dielectric constant. It should be mentioned that a multistate empirical valence bond (MS-EVB) simulation finds a marked preference of excess protons for the hydrophilic/hydrophobic interface suggesting an amphiphilic character for the excess proton [76]. However, the experimentally obtained proton conductivities are in favor of a charge carrier stabilization in the center of the channels. In this region the water is bulk-like (for not too low degrees of hydration) with local proton transport properties similar to those described for water in Section 23.3.1. Indeed, the experimentally found activation enthalpies of both proton mobility and water diffusion are close to those of bulk water and only increase slightly with decreasing degree of hydration for intermediate water contents [43, 77–79]. Apart from the slight retardation of the local proton mobility (Dr) and water diffusion (DH2O) within the hydrophilic domain, the decrease in the macroscopic transport coefficients with decreasing degree of hydration therefore mainly reflects the decreasing percolation within the water-like domain. At the highest degrees of hydration the major proton conduction mechanism is actually structure diffusion (Dr > DH2O, Fig. 23.5). With decreasing water content the concentration of excess protons in the aqueous phase increases, which in turn increasingly suppresses intermolecular proton transfer and therefore structural diffusion, an effect which is well known for aqueous solutions [80]. Consequently, proton mobility at intermediate and low degrees of hydration is essentially vehicular in nature. Nonequilibrium statistical mechanics-based calculations of the water and hydronium self-diffusion coefficients in Nafion membranes have addressed this conductivity contribution, and they clearly show that the diffusion of water (vehicle) and hydrated protons (H3O+) are retarded for intermediate degrees of hydration as a result of the interaction with the negatively charged sulfonate groups [81]. For very low degrees of hydration (for instance Nafion membranes with less than about 3 water molecules per sulfonic acid group) the decreasing solvent (water) activity leads to a decreasing dissociation of the sulfonic acid group, that is an increasing exclusion of protons from the transport in the aqueous phase. When methanol enters the hydrophilic domain (for example in a direct methanol fuel cell) the proton conductivity may dramatically decrease, even at higher degrees of solvation [12], simply because of an increased ion pairing (decreased dissociation) as a result of the lowering of the dielectric constant. As discussed above, proton conduction is related to the transport and the local dynamics of water. This water transport shows up not only as water self diffusion, chemical diffusion and permeation [3], but also as electroosmotic drag, which is the transport of water coupled to the drift velocity of protonic defects in an electri-
23.4 Confinement and Interfacial Effects
Figure 23.5 Proton conductivity and water diffusion coefficient (Dr and DH2O) of hydrated Nafion as a function of its water volume fraction. Data are taken from Refs. [12, 43, 77, 78, 108–116] , unpublished data from the author’s laboratory are also included.
cal field and is usually expressed as the number of water molecules transported per protonic charge carrier. This is a pronounced effect in hydrated acidic polymers, because the only mobile charge carriers are protonic defects (for example hydronium ions) strongly interacting with the water, while the corresponding hydrated counter ions (sulfonic anion)) are immobilized by covalent bonding to the polymer. The classical mechanistic theory of electroosmosis dates back to the time of Helmholtz [82], Lamb [83], Perrin [84] and Smoluchowski [85] who assumed that transport takes place only close to the wall in electrical double layers of low charge carrier concentration and with extent significantly less than the pore (channel) diameter. The corresponding theories qualitatively describe the electroosmotic drag in wide pore systems, such as clay plugs, but both model assumptions are not valid for typical PEM materials such as Nafion. The width of the hydrated (solvated) channels is orders of magnitude smaller than the Debye length of water and the concentration of charge carriers is very high (typically around 5 M within the hydrophilic domain). For this type of system, Breslau and Miller developed a model for electroosmosis from a hydrodynamic point of view [86]. Recently, electroosmotic drag coefficients became accessible by electrophoretic NMR [3, 12, 87, 88] for a wide range of polymer–solvent volume ratios, and the results clearly confirm the hydrodynamic nature of electroosmosis, particularly at high degrees of solvation. The data presented in Fig. 23.6 [3, 89–95] essentially
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Figure 23.6 Electoosmotic drag coefficient Kdrag for Nafion as a function of its solvent (water and/or methanol) volume fraction; data from Refs. [12, 87, 88, 117–123] and unpublished data from the author’s laboratory. The normalized drag coefficients for water and methanol are plotted together because they are virtually identical. (Reproduced with kind permission from Chemical Reviews.)
show two things: (i) at low degrees of hydration the electroosmotic drag coefficient approaches a value of one but does not fall below this value, and (ii) with increasing solvent fraction (increasing channel width) the drag coefficient dramatically increases and reaches about 50% of the maximum possible value (dashed line), which corresponds to an identical drift velocity for all solvent molecules and protonic charge carriers. Considering that at high degrees of hydration about half of the conductivity is carried by structure diffusion, as indicated by the proton mobility (proton self-diffusion coefficient) being about twice the water self diffusion coefficient, almost all water molecules appear to drift at approximately identical velocity (about half of the drift velocity of protonic charge carriers) in extremely swollen samples. This situation corresponds to minor relative motion of water molecules with respect to one another, that is the transport is clearly of a collective nature. The decrease in the drag coefficient with decreasing water content roughly scales with the 4th power of the channel diameter, which is reminescent of Hagen–Poisseuille type behavior with continously increasing “stripping off” of the water molecules. This stripping comes to an end at low degrees of hydration, where the motion of one water molecule remains strongly coupled to the motion of the excess proton (K ~ 1). This is also expected from the high enthalpy of primary hydration (stability of H3O+) and the proton conduction mechanism, which is the diffusion of H3O+ in a water environment (vehicle mechanism).
23.4 Confinement and Interfacial Effects
There is no quantitative model yet that describes the observed electroosmotic drag coefficients as a function of the degree of hydration and temperature. However, the available data provide strong evidence for a mechanism which is: (i) hydrodynamic in the high solvation limit, with the dimensions of the solvated hydrophilic domain and the solvent–polymer interaction as the major parameters, and (ii) diffusive at low degrees of solvation, where the excess proton essentially drags its primary solvation shell (e.g. H3O+). 23.4.2 Adducts of Basic Polymers with Oxo-acids
To date the most relevant materials of this type are adducts (complexes) of polybenzimidazole (PBI) and phosphoric acid. as illustrated in Fig. 23.2(b). In contrast to water, which exhibits a high mobility for protonic defects but a very low intrinsic concentration of protonic charge carriers, phosphoric acid shows both high mobility and concentration of intrinsic protonic defects (see Section 23.3.2). Phosphoric acid is intrinsically a very good proton conductor with a very small Debye length, and its charge carrier density is hardly affected by the interaction with PBI. Indeed, a strong acid–base reaction occurs between the nonprotonated, basic nitrogen of the PBI repeat unit and the first phosphoric acid absorbed. The transfer of one proton leads to the formation of a benzimidazolium cation and a dihydrogenphosphate anion forming a stable hydrogen bonded complex, as shown by infrared spectroscopy [96, 97]. It is a common observation for all systems of this type that their conductivity strongly increases upon further addition of an oxo-acid, approaching the conductivity of the pure acid for high acid concentrations. In particular, there is no indication of participation of the polymer in the conduction process. Although no microstructural information is available to date, the macroscopic transport has been investigated in the related system poly (diallyldimethylammonium-dihydrogenphosphate)–phosphoric acid (PAMA+ H2PO4–) · n H3PO4 [98]. The proton mobility (Dr) and the self-diffusion coefficient of phosphorus (Dp) as a measure of the hydrodynamic diffusion of the system is shown in Fig. 23.7 for a given temperature as a function of the polymer/acid ratio. Similar to pure phosphoric acid, the mobility of protonic charge carriers is significantly higher than the self-diffusion coefficient of the phosphate species and both transport coefficients decrease with increasing polymer content, virtually in the same manner. Therefore, the main effect is just the decreasing percolation within the liquid-like part of the phosphoric acid domain, which is reminiscent of the situation in hydrated acidic polymers. At very small acid contents, when all the phosphoric acid is immobilized in the 1:1 complex, only very little conductivity is left. As expected, the confinement of phosphoric acid in the PBI matrix does not give rise to any relevant electroosmotic drag. Of course, the main reason is the fact that proton conductivity is dominated by structure diffusion, that is the transport of protonic charge carriers and phosphoric acid are effectively decoupled. The other reason is that protonic charge carriers are produced by self-dissociation of the proton solvent (phoshoric acid), that is the number of positively and negatively
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Figure 23.7 Proton conductivity diffusion coefficient (Dr) and self-diffusion coefficient of phosphorous for poly-(diallyldimethylammoniumdihydrogenphosphate)-phosphoric acid ((PAMA+H2PO4–)·n H3PO4) as a function of the phosphoric acid content [98]. Note that the ratio Dr/DP remains almost constant (see text).
mobile charged defects in the liquid-like domain are virtually identical (see also Section 23.3.2). As for pure phosphoric acid, the transport properties of PBI and phosphoric acid also depend on the water activity, this is on the degree of condensation (polyphosphate formation) and hydrolysis. There is even indication that these reactions do not necessarily lead to thermodynamic equilibrium, and hydrated orthophosphoric acid may coexist with polyphosphates in heterogeneous gel-like microstructures [99]. There is not much known on the mechanism of proton transport in polymer adducts with polyphosphates and/or low hydrates of orthophosphoric acid. Whether the increased conductivity at high water activities is the result of the plasticizing effect of the water on the phosphate dynamics, thereby assisting proton transfer from one phosphate to the other, or whether the water is directly involved in the conduction mechanism has not been elucidated. 23.4.3 Separated Systems with Covalently Bound Proton Solvents
Both types of heterogeneous systems discussed above comprise a polymeric domain and a low molecular weight liquid-like domain containing the proton sol-
23.4 Confinement and Interfacial Effects
vent (H2O, H3PO4) with weak ionic or hydrogen bond interaction between the two domains. But there are other proton solvents such as heterocycles and phosphonic acid, which allow covalent immobilization. Apart from the proton donor and acceptor sites, such solvents contain sites, which may be used for covalent “grafting” to polymeric structures. If these are hydrophobic (nonpolar), a similar separation as in hydrated acidic polymers may occur, however with covalent bonding bridging the nonpolar/polar “interface” (Fig. 23.2(c)) This approach has been implemented in order to obtain systems with high proton conductivity with structure diffusion as the sole proton conduction mechanism. Of course, the covalent bonding across the nonpolar/polar “interface” mediates a significant influence of the nonpolar part of the structure on the structure and dynamics of the polar proton-conducting domain. If heterocycles are used as proton solvent the two hetero-nitrogens act equally as proton donor and acceptor. Any covalent immobilization must avoid reduction of this symmetry, which is best achieved by using the carbon between the two nitrogens (C2 in imidazole or C4 in pyrazole) for covalent bonding (of course symmetry reduction is not a problem for the covalent bonding of phosphonic groups via C–P bonds). It is interesting to note that the symmetry is broken in the case of histidine, an imidazole-containing amino acid, which is frequently involved in proton translocation processes within biological systems [57]. However, the energetic asymmetry is very small (about 20 meV) in this particular case [100]. The type of bonding appears to be more important, that is only single bonds allow rapid reorientation of the bonded proton solvent, which is a persistent element in the proton conduction mechanism. But even for single bonds, significant barriers appear for the rotation of the proton solvent around this bond of the isolated (non-hydrogen bonded) alkane segment, with higher barriers for the phosphonic acid (~ 0.10 eV) compared to heterocycles (~ 0.04 eV) [101]. In order to minimize the constraints in the dynamical aggregation of the heterocycles, immobilization via flexible spacers, such as alkanes or ethylene oxide (EO) segments, appears to be favoured [17, 102]. The optimum spacer length is then given by the optimum balance between heterocycle aggregation and heterocycle density, on the one hand, and the dynamics of the hydrogen bond network formed by the heterocycles on the other hand. Di-imidazole (a brittle solid with a high melting point), is perfectly aggregated by strong static hydrogen bonding with negligible proton conductivity. Separating the two imidazoles by a soft EOspacer leads to the appearance of significant proton conductivity and a decrease in the melting point and glass transition temperature with increasing spacer length [103]. The conductivity then displays typical VTF behavior and, for a given concentration of excess protons (dopant), it is very similar for all spacer lengths when plotted versus 1/(T – To) where To is closely related to Tg [17]. For very high spacer lengths, the dilution of the heterocycles by the spacer segments tends to reduce aggregation of the heterocycles and, therefore, once again reduce proton mobility. Corresponding oligomers terminated by phosphonic acid usually show higher melting points, and in the liquid state the conductivity somehow scales with the concentration of the phoshonic fuctional group [104], which resembles the high temperature behavior of heterocycle-based systems.
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The aggregation of imidazole leading to a continuous static hydrogen bonded structure in crystalline Imi-2 (two imidazole spaced by two ethylene oxide repeat units) is shown in Fig. 23.8(a) [17]. Upon melting, the situation in most parts of the material is more like that shown in Fig. 23.8(b). This result comes from an NMR study [105] demonstrating that liquid Imi-2 exhibits ordered domains (similar to the crystalline form), a disordered but still aggregated domain with dynamical hydrogen bonding, and a certain fraction of nonbonded molecules. It is only within the disordered domain (Fig. 23.8(b)) that fast proton mobility is observed, again demonstrating the delicate balance of aggregation and dynamics in hydrogen bonded structures with high proton mobility. Recently, fully polymeric systems with side chain architectures have been developed that still exhibit high proton mobility despite complete long-range immobili-
Figure 23.8 Hydrogen-bonded structure of Imi-2 (two imidazoles spaced by two ethylene oxide (EO) repeat units): (a) in the crystalline state as revealed by a X-ray structure alaysis [103] and b) in the liquid state (schematical) as suggested by an NMR study [105]. Note, that the hydrogen bonds in the solid state are long lived, whereas the hydrogen bonding in the molten state is highly dynamic (see text).
23.5 Concluding Remarks
zation of imidazole [106] or phosphonic acid SSPC, this is Dr/Dsolvent = ¥. This finding is of paramount importance since it demonstrates that complete decoupling of the long-range transport of protons and the proton solvent is possible. This is directly evidenced by the echo attenuation of the proton resonance in PFGNMR experiments of phosphonic acid functionalized oligomer [104]. Only the echo of the phosphonic protons is attenuated while the echo of the oligomer protons is only slightly affected by the magnetic field gradient (Fig. 23.9). The reader may recall that complexation of phosphoric acid and a basic polymer does not show any sign of this effect (see Fig. 23.7), which opens the way to the development of true single ion conductors.
Figure 23.9 Echo attenuation of the proton resonance in PFG-NMR experiments of a phosphonic acid funtionalized oligomer [104]. Only the echo of the phosphonic protons is attenuated while the echo of the oligomer protons is only slightly affected by the magnetic field gradient.
One of the problems associated with the use of heterocycles as proton solvent in fuel cell separators is that the intrinsic concentration of protonic charge carriers can only be moderately increased through acid doping. This is particularly the case when the dynamics within the hydrogen-bonded domain is highly constrained through immobilization (especially in fully polymeric systems), which is probably the direct consequence of the reduced dielectric constant. This also leads to a further increase in the Haven ratio DH/Dr as discussed in Section 23.3.3. Similar Haven ratios are also observed for phosphonic acid functionalized oligomers and polymers, but the observed proton conductivities are generally about one order of magnitude higher than for heterocycle-based systems. This is simply the result of the higher amphotericity and therefore higher degree of self-dissociation (in the dry state), that is the higher intrinsic concentration of protonic defects.
23.5 Concluding Remarks
High efficiency and power density of PEM fuel cells are closely related to high proton conductivity and the gas separating property of the used electrolyte (separa-
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23 Proton Conduction in Fuel Cells
tor). High proton conductivity, that is the long-range diffusion of protonic defects, is preferentially observed in the liquid state of hydrogen-bonded structures, because these provide the proper balance of the structure forming and dynamical properties of the intermolecular hydrogen bond interaction [25]. Aqueous solutions were indeed used as electrolyte in the first fuel cells, and even state of the art separator materials still have a liquid domain (usually water or phosphoric acid) providing the generally heterogeneous structures with their high proton conductivity (Fig. 23.10), while the inert matrix gives the material its separating properties. However, the vapor pressure of molecular liquids, their miscibility with water and/or methanol and their viscous properties, lead to severe limitations in current fuel cell technology (see Section 23.2). Therefore, the development of non-liquid electrolytes with proton conduction properties close to these of hydrogen-bonded liquids is a key issue of current PEM fuel cell research. However, the fuel cell requirements do not allow much of a compromise with respect to proton conductivity, which should not drop below about r = 5 10–2 S cm–1. Such high conduc-
Figure 23.10 Proton conductivity of a few prototypical proton conducting separator materials: Nafion as a representative of hydrated acid ionomers (see also Fig. 23.2(a) [43, 78], a complex of PBI (polybenzimidazole) and phosphoric acid as a representative of adducts of basic polymers and oxo-acids (see also Fig. 23.2(b)) [16], phosphonic acid covalently immobilized via an alkane spacer at a siloxane backbone (see also Fig. 23.2(c)) [127], the acid salt CsHSO4 [125] and an Y-doped BaZrO3 [126].
References
tivities are several orders of magnitude higher than is known for the proton conductivity of biological systems, for instance transmembrane proteins [18, 57]. The conducting volume increments of such systems contain relatively ordered hydrogen-bonded structures of protein residues and water molecules and exhibit high selectivity for the transport of protonic charge carriers but this is only possible at the expense of high conductivity. The complete decoupling of the transport of protonic charge carriers from their solvating environment in fully polymeric systems with conductivities up to about 10–2 S cm–1 (Fig. 23.10) is, therefore, a fundamental achievement. However, much is left to be done for the development of competitive fuel cell separators free of any liquid phase. Apart from a further increase in the proton conductivity, stability and the electrochemical reactivity requirements are making this a challenging but also an appealing task [107].
Acknowledgment
The authors thank J. Fleig (Max-Planck-Insitut fr Festkrperforschung) and the external reviewers for carefully reading the proofs and for fruitful discussions. We thank A. Fuchs for assisting in producing the figures and the Deutsche Forschungsgemeinschaft (KR 794), the Bundesministerium fr Bildung und Forschung (0329567) and the Stifung Energie Baden-Wrttemberg (A 19603) for financial support.
References 1 K. D. Kreuer, Annu. Rev. Mater. Res. 33, 2
3
4 5 6
7 8 9 10
333 (2003). S. M. Haile, D. A. Boysen, C. R. I. Chisholm, S. M. Merle, Nature 410, 910 (2001). K. D. Kreuer, S. J. Paddison, E. Spohr, M. Schuster, Chem. Rev. 104, 4637 (2004). C. F. Schnbein, Philos. Mag. 14, 43 (1839). W. R. Grove, Philos. Mag. 14, 127 (1839). E. Peled, T. Duvdevani, A. Aharon, A. Melman, Electrochem. Solid State Lett. 3, 525 (2000). O. Savadogo, J. New Mater. Electrochem. Syst. 1, 47 (1998). Q. Li, R. He, J. O. Jensen, N. J. Bjerrum, Chem. Mater. 15, 4896 (2003). M. Rikukawa, K. Sanui, Progr. Polym. Sci. 25, 1463 (2000). J. Rozire, D. J. Jones, Annu. Rev. Mater. Res. 33, 503 (2003).
11 P. Jannasch, Curr. Opin. Colloid Interface
Sci. 8, 96 (2003). 12 K. D. Kreuer, in Handbook of Fuel Cells –
13 14 15 16
17 18 19
Fundamentals, Technology and Applications, W. Vielstich, A. Lamm, H. A. Gasteiger (Eds.), John Wiley & Sons, Chichester, p. 420, 2003. M. Doyle, G. Rajendran, in Ref. 12, p.351. K. A. Mauritz, R. B. Moore, Chem. Rev. 104, 4535 (2004). R. He, Q. Li, G. Xiao, N. J. Bjerrum, J. Membr. Sci., 226, 169 (2003). Y. L. Ma, J. S. Wainright, M. H. Litt, R. F. Savinell, J. Electrochem. Soc. A 151, 8 (2004). M. F. H. Schuster, W. H. Meyer, Annu. Rev. Mater. Res. 33, 233 (2003). K. D. Kreuer, Chem. Mater. 8, 610 (1996). K. D. Kreuer, A. Fuchs, J. Maier, Solid State Ionics 77, 157 (1995).
733
734
23 Proton Conduction in Fuel Cells 20 W. Mnch, K. D. Kreuer, U. Traub,
46 D. Asthagiri, L. R. Pratt, J. D. Kress,
J. Maier, J. Mol. Struct. 381, 1 (1996). 21 W. Mnch, G. Seifert, K. D. Kreuer, J. Maier; Solid State Ionics 97, 39 (1997). 22 K. D. Kreuer, Solid State Ionics 94, 55 (1997). 23 R. A. Marcus, J. Chem. Phys. 24, 966 (1956). 24 C. P. Flynn, A. M. Stoneham, Phys. Rev. B1, 3966 (1970). 25 K. D. Kreuer, Solid State Ionics 136/137, 149 (2000). 26 W. A. P. Luck, Fortschr. Chem. Forsch., 4, 653 (1964). 27 X. Duan, S. Scheiner, J. Mol. Struct. 270, 173 (1992). 28 R. Janoschek, J. Mol. Struct., 321, 45 (1994). 29 W. A. P. Luck, Ber. Bunsenges. Phys. Chem. 69, 626 (1965). 30 M. E. Tuckerman, K. Laasonen, M. Sprike, M. Parrinello, J. Chem. Phys. 103, 150 (1995). 31 M. E. Tuckerman, D. Marx, M. L. Klein, M. Parrinello, Science 275, 817 (1997). 32 M. Eigen, L. De Maeyer, Proc. R. Soc. (London), Ser. A 247, 505 (1958). 33 M. Eigen, Angew. Chem. 75, 489 (1963). 34 T. Dippel, K. D. Kreuer, Solid State Ionics 46, 3 (1991). 35 B. Cohen, D. Huppert, J. Phys. Chem. A 107, 3598 (2003). 36 D. Marx, M. E. Tuckerman, J. Hutter, M. Parrinello, Nature 397, 601(1999). 37 R. Vuilleumier, D. Borgis, Chem. Phys. Lett. 284, 71 (1998). 38 K. D. Kreuer, Solid State Ionics 94, 55 (1997). 39 R. R. Sadeghi, H. P. Cheng, J. Chem. Phys. 111, 2086 (1999). 40 Q. Cui, M. Karplus, J. Phys. Chem. B 107, 1071(2003). 41 K. D. Kreuer, A. Rabenau, W. Weppner, Angew. Chem. Int. Ed. Engl. 21, 208 (1982). 42 N. Agmon, J. Chim. Phys. Phys. – Chim. Bio. 93, 1714 (1996). 43 K. D. Kreuer, T. Dippel, W. Meyer, J. Maier, Mater. Res. Soc. Symp. Proc. 293, 273 (1993). 44 M. E. Tuckerman, D. Marx, M. Parrinello, Nature 417, 925 (2002). 45 B. L. Trout, M. Parrinello, J. Phys. Chem. B 103, 7340 (1999).
M. A. Gomez, Chem. Phys. Lett. 380, 530 (2003). 47 D. Asthagiri, L. R. Pratt, J. D. Kress, M. A. Gomez, Proc Nat. Acad. Sci (USA) 101, 7233 (2004). 48 B. Chen, J. M. Park, I. Ivanov, G. Tabacchi, M. L. Klein, M. Parrinello, J. Am. Chem. Soc. 124, 8534 (2002). 49 R. A. Munson, J. Phys. Chem. 68, 3374 (1964). 50 T. Dippel, K. D. Kreuer, J. C. Lassgues, D. Rodriguez, Solid State Ionics 61, 41 (1993). 51 M. Spaeth, K. D. Kreuer, T. Dippel, J. Maier, Solid State Ionics 97, 291 (1997). 52 M. Spaeth, K. D. Kreuer, J. Maier, J. Solid State Chem. 148, 169 (1999). 53 T. Dippel, N. Hainovsky, K. D. Kreuer, W. Mnch, J. Maier, Ferroelectrics 167, 59 (1995). 54 S. H. Chung, S. Bajue, S. G. Greenbaum, J. Chem. Phys. 112, 8515 (2000). 55 A. Schlechter, R. F. Savinell, Solid State Ionics 147, 181 (2002). 56 A. Kawada, A. R. McGhie, M. M. Labes, J. Chem. Phys. 52, 3121 (1970). 57 T. E. Decoursey, Physiol. Rev. 83, 475 (2003). 58 G. Zundel, E. G. Weidemann, Eur. Biophys. Congr., Proc., 1st 6, 43 (1971). 59 N. Riehl, Trans. N.Y. Acad. Sci. 27,772 (1965). 60 G. Will, Z. Krist. 129, 211 (1969). 61 G. P. Brown, S. Aftergut, J. Chem. Phys. 38, 1356 (1963). 62 K. Pigon, H. Chojnacki, Acta Phys. Pol. 31, 1069 (1967). 63 A. R. McGhie, H. Blum, M. M. Labes, J. Chem. Phys. 52, 6141 (1970). 64 B. S. Hickman, M. Mascal, J. J. Titman, I. G. Wood, J. Am. Chem. Soc. 121, 11486 (1999). 65 K. D. Kreuer, A. Fuchs, M. Ise, M. Spaeth, J. Maier, Electrochim. Acta 43, 1281 (1998). 66 K.D. Kreuer, Solid State Ionics and Technology, B.V.R. Chowdari et al. (Eds.), World Scientific, Singapore, pp. 263–274, 1998. 67 W. Mnch, K. D. Kreuer, W. Silvestri, J. Maier, G. Seifert, Solid State Ionics 145, 437 (2001).
References 68 J. T. Daycock, G. P. Jones, J. R. N. Evans,
J. M. Thomas, Nature 218, 67 (1968). 69 W. Tatara, M. J. Wojcik, J. Lindgren, M. Probst, J. Phys. Chem. A 107, 7827 (2003). 70 Unpublished results from the author’s laboratory. 71 F. Toda, K. Tanaka, C. Foces-Foces, A. L. Llamas-Saiz, H. H. Limbach, F. Aguilar-Parrilla, R. M. Claramunt, C. Lpez, J. J. Elguero, J. Chem. Soc. Chem. Commun. 1139 (1993). 72 M. Eikerling, A. A. Kornyshev, J. Electroanal. Chem. 502, 1 (2001). 73 S. J. Paddison, G. Bender, K. D. Kreuer, N. Nicoloso, T. A. Zawodzinski, J. New Mater. Electrochem. Syst. 3, 291 (2000). 74 S. J. Paddison, D. W. Reagor, T. A. Zawodzinski, J. Electroanal. Chem. 459, 91 (1998). 75 S. J. Paddison, Annu. Rev. Mater. Res. 33, 289 (2003). 76 M. K. Petersen, S. S. Iyengar, T. J. F. Day, G. A. Voth, J. Phys. Chem. B 108, 14804 (2004). 77 K. D. Kreuer, Solid State Ionics 97, 1 (1997). 78 T. A. Zawodzinski, T. E. Springer, J. Davey, R. Jestel, C. Lopez, J. Valerio, S. Gottesfeld, J. Electrochem. Soc. 140, 1981 (1993). 79 M. Cappadonia, J. W. Erning, S. M. S. Niaki, U. Stimming, Solid State Ionics 77, 65 (1995). 80 T. Dippel, K. D. Kreuer, Solid State Ionics 46, 3 (1991). 81 S. J. Paddison, R. Paul, K. D. Kreuer, Phys. Chem. Chem. Phys. 4, 1151 (2002). 82 H. Helmholtz, Weid. Ann. 7, 337 (1879). 83 H. Lamb, Philos. Mag. 5, 52 (1888). 84 J. Perrin, J. Chim. Phys. 2, 601 (1904). 85 M. Smoluchowski, Handbuch der Elektrizitt und des Magnetismus, Vol. II, Barth, Leipzig, 1914. 86 B. R. Breslau, I. F. Miller, Ind. Eng. Chem. Fundam. 10, 554 (1971). 87 M. Ise, PhD Thesis, University Stuttgart, 2000. 88 M. Ise, K. D. Kreuer, J. Maier, Solid State Ionics 125, 213 (1999). 89 T. Okada, S. Moller-Holst, O. Gorseth, S. Kjelstrup, J. Electroanal. Chem. 442, 137 (1998).
90 X. Ren, S. Gottesfeld, J. Electrochem.
Soc. 148, A87 (2001). 91 T. A. Zawodzinski, J. Davey, J. Valerio,
S. Gottesfeld, Electrochim. Acta 40, 297 (1995). 92 T. A. Zawodzinski, C. Derouin, S. Radzinski, R. J. Sherman, V. T. Smith, T. E. Springer, S. Gottesfeld, J. Electrochem. Soc. 140, 1041 (1993). 93 T. A. Zawodzinski, C. Derouin, S. Radzinski, R. J. Sherman, V. T. Smith, T. E. Springer, S. Gottesfeld, J. Electrochem. Soc. 140, 1041 (1993). 94 G. Xie, T. Okada, J. Electrochem. Soc. 142, 3057 (1995). 95 T. F. Fuller, J. Newman, J. Electrochem. Soc. 139, 1332 (1992). 96 X. Glipa, B. Bonnet, B. Mula, D. J. Jones, J. J. Rozire, Mater. Chem. 9, 3045 (1999). 97 R. Bouchet, E. Siebert, Solid State Ionics 118, 287 (1999). 98 A. Bozkurt, M. Ise, K. D. Kreuer, W. H. Meyer, G. Wegner, Solid State Ionics 125, 225 (1999). 99 B. C. Benicewicz, presented as a poster during the Gordon Research Conference on “Fuel Cells” 2003. 100 W. Mnch, unpublished result. 101 S. J. Paddison, K. D. Kreuer, J. Maier, in preparation. 102 K. D. Kreuer, J. Membr. Sci. 185, 29 (2001). 103 M. F. H. Schuster, W. H. Meyer, M. Schuster, K. D. Kreuer, Chem. Mater. 16, 329 (2004). 104 M. Schuster, T. Rager, A. Noda, K. D. Kreuer, J. Maier, Fuel Cells, in press. 105 G. R. Goward, M. F. H. Schuster, D. Sebastiani, I. Schnell, H. W. Spiess, J. Phys. Chem. B 106, 9322 (2002). 106 H. G. Herz, K. D. Kreuer, J. Maier, G. Scharfenberger, M. F. H. Schuster, W. H. Meyer, Electrochim. Acta 48, 2165 (2003). 107 K. D. Kreuer, ChemPhysChem 3, 771 (2002). 108 C. A. Edmondson, P. E. Stallworth, M. E. Chapman, J. J. Fontanella, M. C. Wintersgill, S. H. Chung, S. G. Greenbaum, Solid State Ionics 135, 419 (2000).
735
736
23 Proton Conduction in Fuel Cells 109 C. A. Edmondson, P. E. Stallworth,
117 T. Okada, S. Moller-Holst, O. Gorseth,
M. C. Wintersgill, J. J. Fontanella, Y. Dai, S. G. Greenbaum, Electrochim. Acta 43, 1295 (1998). 110 M. C. Wintersgill, J. J. Fontanella, Electrochim. Acta 43, 1533 (1998). 111 T. A. Zawodzinski, M. Neeman, L. O. Sillerud, S. Gottesfeld, J. Phys. Chem. 95, 6040 (1991). 112 C. A. Edmondson, J. J. Fontanella, S. H. Chung, S. G. Greenbaum, G. E. Wnek, Electrochim. Acta 46, 1623 (2001). 113 C. A. Edmondson, J. J. Fontanella, Solid State Ionics 152–153, 355 (2002). 114 J. J. Fontanella, M. G. McLin, M. C. Wintersgill, J. P. Calame, S. G. Greenbaum, Solid State Ionics 66, 1 (1993). 115 X. Ren, T. E. Springer, T. A. Zawodzinski, S. Gottesfeld, J. Electrochem. Soc. 147, 466 (2000). 116 S. Hietala, S. L. Maunu, F. Sundholm, J. Polym. Sci B: Polym. Phys. 38, 3277 (2000).
S. Kjelstrup, J. Electroanalytical Chem. 442, 137 (1998). 118 X. Ren, S. Gottesfeld, J. Electrochem. Soc. 148, A87 (2001). 119 T. A. Zawodzinski, J. Davey, J. Valerio, S. Gottesfeld, Electrochim. Acta 40, 297 (1995). 120 T. A. Zawodzinski, C. Derouin, S. Radzinski, R. J. Sherman, V. T. Smith, T. E. Springer, S. Gottesfeld, J. Electrochem. Soc. 140, 1041 (1993). 121 X. Ren, W. Henderson, S. Gottesfeld, J. Electrochem. Soc. 144, L267 (1997). 122 G. Xie, T. Okada, J. Electrochem. Soc. 142, 3057 (1995). 123 T. F. Fuller, J. Newman, J. Electrochem. Soc. 139, 1332 (1992). 124 H. Rssler, M. Schuster, K. D. Kreuer, presented at SSPC-12, Uppsala, 2004. 125 A. I. Baranov, L. A. Shuvalov, N. Shchagina, JETP Lett. 36, 459 (1982). 126 K. D. Kreuer, Solid State Ionics 125, 285 (1999). 127 H. Steininger, M. Schuster, K. D. Kreuer, J. Maier, Solid State Ionics, in press and electronically available 2006.
737
24 Proton Diffusion in Ice Bilayers Katsutoshi Aoki
24.1 Introduction 24.1.1 Phase Diagram and Crystal Structure of Ice
Ice is one of the most familiar substances to human beings and has attracted interest in a wide range of research fields including chemistry, physics, biology and earth or planetary science [1]. The chemical and physical properties specific to ice arise from its bonding nature, that is, hydrogen bonding. Each water molecule is linked to four nearest neighboring molecules tetrahedrally coordinated and the molecules construct a three-dimensional hydrogen-bonded network, geometrically similar to that in diamond. A hydrogen bond has a directional nature like a covalent bond but also has much flexibility in the bond length and bond angle. A free water molecule has an H–O–H angle of 104.52 and an O–H distance of 0.09572 nm. The molecular geometry is modified by a few percent on crystallization into ice [2]. The hydrogen bond is flexible due to its complex bonding nature involving a covalently bonded hydrogen nucleus and electrostatic interactions as a major contribution. The flexible hydrogen bond results in a rich phase behavior in the pressure– temperature diagram of ice, as illustrated schematically in Fig. 24.1. Each phase has a local structure of tetrahedrally coordinated water molecules connected by hydrogen bonds although a slight change in the bond length or angle leads to modification of the unit cell parameters. A dramatic change in molecular packing takes place along with the phase transition from VI to VII in the high temperature region and also to VIII in the low temperature region. The high pressure phases VII and VIII appear at pressures above 2 Gpa and have dense structures consisting of interpenetrating diamondlike sublattices [3], while all the low pressure phases, below 2 Gpa, have essentially diamond structures with a large empty space. The interpenetration of sublattices leads to a body centered cubic (bcc) arrangement of oxygen atoms and smears out the empty space (Fig. 24.2). In the phase VII, for instance, each oxygen atom has Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
24 Proton Diffusion in Ice Bilayers
Temperature (K)
738
Pressure (GPa) Figure 24.1 The outline of the phase diagram of ice on a logarithmic scale.
eight nearest neighbors at the corners of a cube but is tetrahedrally linked by hydrogen bonds to four of them. Ice VII is present over a wide area of the phase diagram and hence is an appropriate candidate for study of the structural or physical properties modified largely by applying pressure [4–8].
+
Figure 24.2 Crystal structure of the high pressure phase of ice VII consisting of interpenetrated sublattices (bottom). The free spaces, which can be seen as the empty cubes in the sublattices with a diamond-like geometry (top), are filled with the counterpart sublattice.
24.1 Introduction
24.1.2 Molecular and Protonic Diffusion
Another characteristic feature of ice is the migration of water molecules in it. The diamond structure with the large empty space and the flexible hydrogen bond may allow even whole water molecules to move by either a vacancy or an interstitial mechanism. Molecular diffusion has been a major subject in research on the crystal growth of ice. The diffusion coefficient for the molecular migration has been determined using various techniques such as the isotopically labeled molecule method [9–11]. A tracer labeled with 2H or 18O is placed on one face of an ice block and then held for a certain fixed time. The analysis of the tracer concentration as a function of the depth of penetration allows us to derive the diffusion coefficient under some assumptions for the boundary conditions. The diffusion coefficients measured at temperatures of 233–273 K range from 10–16 to 10–14 m2 s–1 with an activation energy of 0.6~0.7 eV. The water molecules can move relatively fast in ice, at a rate of 10–100 nm s–1 on average. In contrast to the well studied molecular diffusion, proton diffusion is less well understood. Protons can move in the hydrogen-bonded network of water molecules by transfer in a hydrogen bond and a successive jump into another hydrogen bond by molecular rotation, as illustrated in Fig. 24.3. This diffusion processis oversimplified but well highlights the dominant proton motions involved. Although the model was proposed a half century ago [12], its process has eluded experimental investigation. The competitive molecular diffusion shades the protonic diffusion. The protonic diffusion coefficient is estimated to be the order of 10–20 m2 s–1 for ambient-pressure ice at 263 K, which is four to five orders of magnitude less than the molecular diffusion coefficient. The dielectric property and electrical conductivity, from which we can derive the protonic diffusion coefficient, have been measured for pure and doped ices.
(a)
(b)
(c)
Figure 24.3 Diffusion process model: an excess proton is located at an ionic defect (a). The proton transfers along the hydrogen bond (b) and then jumps to an adjacent hydrogen bond with molecular rotation (c).
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24 Proton Diffusion in Ice Bilayers
24.1.3 Protonic Diffusion at High Pressure
The protonic diffusion is considered to be enhanced significantly at high temperature and high pressure, realized in planets such as jupiter. Theoretical studies have consistently predicted the presence of a superionic (or superprotonic) phase characterized by a fast protonic diffusion with a coefficient of ~10–8 m2 s–1 at extremely high temperatures and pressures [13,14]. The superionic state would appear at about 1000 K and 20 GPa and to move to higher temperatures ranging from 2000 to 4000 K above 100 GPa. At such high temperatures and pressures, the protons move to occupy the midpoints between the adjacent oxygen atoms and hence water molecules can no longer be recognized. The protons likely move fast by jumping successively between their neighboring occupation sites in the crystal lattice, consisting solely of oxygen atoms (as shown in Fig. 24.2 the oxygen atoms form a bcc lattice). This implies that the two-step diffusion process proposed for the molecular crystalline ice changes to a single-step process in dense ices with the bcc lattice of oxygen. Such a superionic phase can be characterized as a partially melted state and compared with an ionic fluid or a fully melted state in which neutral or ionized water molecules diffuse freely. The superionic phase of ice may play a crucial role in the generation of the magnetic fields in giant planets as well as their metallic fluid [14–17] The experimental fact of the small diffusion rate at ambient pressure and the theoretical prediction of a superprotonic state under extreme conditions point us to diffusion measurements for “hot ice” in which protons are thermally activated to move faster. The high pressure techniques enable us to generate an extreme condition around 1000 K and 20 GPa where ice is predicted to enter the superprotonic state. As seen in Fig. 24.1, ice VII exists over a wide pressure span above 2 GPa. The interpenetrated dense structure would prevent water molecules from moving and allow measurement of the protonic diffusion at high temperatures beyond the melting point of 273 K at ambient pressure [18]. Ice VII thus provides a great advantage for protonic diffusion measurement. A diamond-anvil-cell (DAC) is a small high pressure cell most suitable for the spectroscopic measurement of molecular or atomic diffusion. The DAC is used for various kinds of spectroscopic investigations on liquids and solids at pressures up to several tens of GPa [19–22]. The optically transparent nature of diamond over a wide wavelength span allows in situ optical measurements in combination with conventional equipment such as visible light or infrared spectrometers. The protonic diffusion in ice is measured by a traditional diffusion-couple method, in the present case, with an H2O/D2O ice bilayer. The mutual diffusion of hydrogen (H) and deuteron (D) in the ice bilayer is monitored by measuring the infrared vibrational spectra. The experimental details are described in the following sections.
24.2 Experimental Method
24.2 Experimental Method 24.2.1 Diffusion Equation
For the bilayer configuration of H2O/D2O ice, the equation of diffusion can be described with an analytical form under appropriate boundary conditions. The protons (deuterons) initially contained in the H2O (D2O) ice layer diffuse into the D2O (H2O) ice layer by H/D exchange reaction. The initial distribution of proton, which is described with a step-function as shown in Fig. 24.4, deforms gradually with time and eventually reaches a homogeneously distributed state. Starting with Fick’s second law, we can derive a one-dimensional diffusion equation for the concentration of H at time t and location x under the following boundary and initial conditions [23]. ¶CH ðx; tÞ ¶2 CH ðx; tÞ ¼D ¶t ¶x2 ¶CH ðx ¼ 0; tÞ ¶CH ðx ¼ ‘; tÞ ¼ ¼0 ¶x ¶x 1 ð0 £ x £ lH Þ CH ðx; t ¼ 0Þ ¼ 0 ðlH £ x £ l Þ
CH ðx; tÞ ¼
¥ npx np2 lH X 2 nplH þ cos Dt sin exp l l np l l n¼1
(24.1)
Here the mutual diffusion coefficient D is assumed to be the same for the proton and deuteron migrations. Since the lighter element hydrogen can move faster than deuterium which has twice the mass of H, the coefficient D might correspond to the diffusion coefficient for the rather slowly moving deuterium. For the isotope concentrations at the outer back surface of the bilayer, x = l, the equation can be deduced to be a simple function described with time t alone. The proton concentration at the back surface of the D2O ice layer CH is now presented by ¥ X l 2 nplH np 2 exp CH ð0; tÞ ¼ H þ Dt (24.2) sin l l np l n¼1 where lH and lD are the initial thicknesses of theH2O and D2O ice layers, respectively. Their sum gives the total thickness of the bilayer, l: l = lH + lD. The exponential term containing time t determines the essential shape of the CH vs. t curve. The proton concentration CH rises rapidly in the initial stage of the diffusion process and approaches gradually the steady value given by lH/l, the first term on the right-hand side in Eq. (24.2). The counterpart equation can readily be derived for the deuteron concentration CD at the back surface of the H2O ice layer or x = 0.
741
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24 Proton Diffusion in Ice Bilayers
cH (x,t) 1 H2O
D2O
lH
lD
x
0 l
Figure 24.4 The initial state of an H2O/D2O ice bilayer used for measuring the mutual diffusion of H and D. CH: concentration of hydrogen, lH: thickness of H2O ice layer, lD: thickness of D2O ice layer. The diffusion process along the x-axis can be derived within a one-dimensional approximation as described in the text.
24.2.2 High Pressure Measurement [24]
The optically transparent nature of diamond allows in situ measurement of infrared absorption spectra in association with the excitation of vibrational states. The pressure accessible with a DAC reaches a very high pressure of around 100 GPa for a temperature range of 0–1000 K. The size of a sample pressurized with DAC depends on the pressure desired for each experiment, ranging from a few hundred to ten microns in diameter. The DAC is ordinarily used in combination with a microscope system to focus the probe light on a small sample. Figure 24.5 shows an optical setup for high-pressure diffusion measurement with a DAC. An H2O/D2O ice bilayer is already prepared in the sample chamber. The dimension of each ice layer is typically 120 lm in diameter and 20 lm in thickness. The detailed procedure for preparing the ice bilayer has been described in the literature [24]. The surface concentration of proton, CH, at x = l can be
H 2O
D2O
Figure 24.5 Schematic drawing of the optical configuration for measuring the infrared reflection spectra: (left) a diamond anvil cell containing an ice bilayer and (right) a reflection objective for focusing incident infrared lights. (From Ref. [24]).
24.2 Experimental Method
obtained from infrared reflection spectra measured at the interface between the diamond and the D2O ice. The protons initially contained in the H2O ice layer penetrate through the D2O ice layer by the H/D exchange reaction and eventually reach the back surface. The surface concentration CH can be related to the peak intensity of the OH stretch vibration, which shows a gradual growth with time until the diffusion process reaches the steady state, as analyzed with a bilayer model in the previous sections. A reflection objective is used to introduce the incident infrared light to the ice–diamond surface and also the reflected light to a detector. It has magnification of 16 and a numerical aperture of 0.6. 24.2.3 Infrared Reflection Spectra
Reflection spectra measured by focusing incident light on the ice/diamond interface involve the extrinsic components arising from the reflection and absorption of the diamond anvil. The incident light is reflected from the air/diamond interface and then absorbed while passing through the diamond anvil. The reflected light from the ice surface undergoes absorption and reflection as well in the back track. Spectral correction is hence an essential procedure for deriving the intrinsic spectral features of the specimen. The spectral features of diamond, which range over a wavenumber region roughly from 1600 to 2600 cm–1, can be eliminated practically and effectively by subtracting an appropriate reference spectrum from each raw spectrum. Spectral correction is well made using a reference spectrum taken for the DAC filled with potassium bromide, KBr (Fig. 24.6). Peak intensity calibration is another essential procedure required for correct determination of the isotope concentrations from the observed spectra. Here we should note that the peak intensity per one OH bond is not necessary equal to that per one OD bond. Calibration spectra are taken for an ice specimen containing homogeneously distributed H and D isotopes prepared by freezing an
Reflectance (arb. units)
OH stretch OD stretch
(c)
(b) (a)
2000
3000
4000 -1
Wavenumber (cm )
Figure 24.6 Infrared reflection spectra: (a) a reference spectrum measured for the KBr-diamond interface with a DAC, (b) a representative raw spectrum measured for the D2O back surface of an ice bilayer specimen, (c) a reflection spectrum of ice obtained by dividing the raw spectrum by the reference spectrum. The OD and OH stretch peaks are located approximately at 2400 and 3400 cm–1, respectively. (From Ref. [24].)
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24 Proton Diffusion in Ice Bilayers
H2O(50%)–D2O(50%) solution and are used to determine practically the relative peak intensities between the OH and OD stretch peaks. The reflection spectra measured at pressures from 9.5 to 16.2 GPa reveal that each peak height remains nearly independent of pressure. The ratio of the OH peak height with respect to the OD peak height ranges from 1.32 to 1.48, yielding an average value of 1.40. This value is used for conversion of the peak heights to the isotope concentrations. Infrared reflection spectra are measured with a microscope FT-IR spectrometer mounted with a reflection objective, with which the incident lights are focused onto the diamond/ice interface and the reflected lights are introduced to a MCT detector cooled by liquid nitrogen. A wavenumber region of 700–5000 cm–1 is covered. The reflected lights are focused on the path to the detector to make a magnified real image of the specimen, which is trimmed into a 40 40 lm2 square in its real scale with an optical mask. Reflection spectra are thus measured for the central sample area; the one side of the masking square 40 lm corresponds to one third of the sample diameter. Equation (24.1) and (24.2) are derived for a bilayer specimen with an infinite radius. The trimming of the measuring area leads to elimination or reduction of undesirable wall effects involved in the actual diffusion process. 24.2.4 Thermal Activation of Diffusion Motion
The high-pressure experiment enables us to investigate the protonic diffusion process thermally enhanced by heating. The diffusion rate of ambient-pressure ice is estimated to be of the order of 10–20 m2 s–1 at 258 K [1], indicating that 1000 years is required for the protons to pass through an ice layer of 20 lm in thickness. Thermal annealing is an effective way to increase the diffusion rate, even by several orders in magnitude. At ambient pressure heating ice is limited to the melting point of 273 K; the diffusion coefficient might increase by only one order, insufficient to reduce the astronomical figures. The melting temperature rises rapidly on applying pressure, reaching, for instance, 690 K at 10 GPa. This temperature is 400 K higher than that at ambient pressure and sufficient to accelerate the diffusion rate so that it can be detected within a laboratory scale time. Thermal annealing of the sample is simply achieved by warming the DAC itself in an electric oven. An appropriate annealing temperature and time are examined with a bilayer sample and chosen to be 400 K and several tens of hours, respectively. Infrared reflection spectra are measured with the DAC taken out of the oven and cooled quickly to room temperature. Thermal annealing and successive spectral measurement are repeated several tens of times until the spectral change is complete. The accumulated annealing time required for one experimental run ranges from several hundreds to a thousand hours. The DAC is warmed up to 400 K and cooled down to 298 K in a few minutes, negligibly short compared with a thermal annealing time of several tens of hours. No correction for the transient time is required in accumulation of the annealing time.
24.3 Spectral Analysis of the Diffusion Process
24.3 Spectral Analysis of the Diffusion Process 24.3.1 Protonic Diffusion
The protonic diffusion process in the ice bilayer is clearly monitored by the vibrational spectroscopic measurement. The reflection spectra measured after annealing at 400 K and 10.2 GPa are shown in Fig. 24.7. Panels A and B present the spectral changes with time measured for the back surfaces of D2O and H2O ice layers, respectively. The OH stretch peak is located around 3200 cm–1, whereas the OD stretch peak is located around 2500 cm–1, lower by a factor of approximately 1/2, as expected from a square root of the mass ratio mH/mD [5]. The H/D mutual diffusion process is demonstrated as gradual changes in the peak height in the opposite directions with time. For instance, at the back surface of the D2O ice layer, the OD peak shows a gradual decrease in height with time, while the OH peak shows a gradual increase. The spectra measured for both back surfaces become equivalent after 1287 h, indicating homogeneous distribution of H and D over the ice specimen as a result of the mutual diffusion. A diffusion coefficient can be derived from the variation of the peak height or the surface concentration of hydrogen (deuteron) with time. The deuteron concentration CD at the back surface of the H2O ice layer shows an exponential increase with time, as expected from Eq. (24.2), as displayed in Fig. 24.8. It rises abruptly after a small time lag of several hours (not able to be seen in Fig. 24.8 plotted with a full time-scale of 1200 h) and approaches a steady value of 0.52. The fitting of the experimental results yields a diffusion coefficient of 6.2 10–16 m2 s–1. This (b)
(a)
OH
2000
3000
Wavenumber (cm-1)
OH
Reflectance (arb. units)
Reflectance (arb. units)
OD
4000
110 201
OD
2000
0 19 46
1287
3000
Wavenumber (cm-1)
Figure 24.7 Variation of infrared reflection spectra with time measured for the outer surface of D2O ice layer (A) and for that of H2O ice layer (B). The numbers attached to the spectra give the accumulated annealing time in hours. (From Ref. [24].)
4000
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24 Proton Diffusion in Ice Bilayers
(b)
(a)
OD
OH
2000
OH
Reflectance (arb. units)
Reflectance (arb. units)
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4000 -1
Wavenumber (cm )
110 201
OD
2000
0 19 46
1287
3000
4000
Wavenumber (cm-1)
Figure 24.8 Variation of deuteron concentration CD with time measured for the back surface of an H2O/D2O ice bilayer annealed at 400 K at 10.2 GPa. The solid line represents a fit to the diffusion equation. (From Ref. [24].)
value is larger by a factor of 104 than that estimated for ambient pressure ice at 258 K. The diffusion motion is significantly enhanced at 400 K by thermal activation. The exact diffusion equation is described in terms of an infinite series of n as given in Eqs. (24.1) and (24.2). The equation with n = 100 is capable of reproducing satisfactorily all the features of the concentration variation measured: an abrupt rise in the initial stage of diffusion and a subsequent gradual increase toward the steady value. The CD–t curve thus reproduced with the coefficient of 6.2 10–16 m2 s–1 is represented by a solid line. 24.3.2 Molecular Diffusion
As described in Section 24.1.2, molecular diffusion is dominant in ambient-pressure ice and there still remains the possibility that the spectral change observed is brought about by migration of whole molecules of H2O and D2O. Molecular diffusion is therefore carefully examined in an H216O /H218O ice bilayer. The substitution of oxygen isotopes does not influence the molecular vibrations, since the difference in atomic mass between 16O and 18O is very small compared with that between 1H and 2D. The resultant frequency difference is estimated to be approximately 20 cm–1 for the stretch vibrations. Molecular diffusion is suppressed in the high pressure phase of ice VII. No signal for molecular diffusion is detected. Reflection spectra measured for the back surfaces of an H216O /H218O ice bilayer are shown in Fig. 24.9. The annealing temperature and pressure are 400 K and 10.2 GPa, respectively, the same as those for the protonic diffusion measurement. The abscissa axis is expanded to emphasize the peak positions of the 16OH and 18OH stretch vibrations. Separation by
24.3 Spectral Analysis of the Diffusion Process
Reflectance
H218O surface
H216O surface 3050
3100
3150
3200
3250
Wavenumber (cm-1) Figure 24.9 Infrared reflection spectra collected from the back surfaces of an H216O/H218O ice bilayer (dashed lines) annealed at 400 K and 10.2 GPa for 600 h. The spectra measured for an ice specimen once melted at 298 K by releasing pressure and then compressed again to 10.2 GPa showed the peak shifts to the midpoint (solid lines). (From Ref. [24].)
20 cm–1 is clearly seen, in agreement with the estimation. Thermal annealing at 400 K results in no spectral change. The stretch peaks remain in the initial positions even after 600 h annealing, indicating that molecular diffusion does not take place. To confirm this, the ice specimen is once melted at 298 K by releasing the pressure carefully (ice melts at 0.9 GPa at room temperature after passing through another high pressure phase of ice VI) and frozen by increasing the pressure quickly to 10.2 GPa. The spectra measured again for the back surfaces show the peak shifts to the midpoint between the original positions. H218O and H216O molecules are homogeneously mixed by fast molecular diffusion in the liquid state. 24.3.3 Pressure Dependence of Protonic Diffusion Coefficient [25]
The protonic diffusion coefficients measured for ice VII in a pressure range 2.1–63 GPa are shown in Fig. 24.10. Around 60 GPa, the O–H...O bond length decreases to a critical value of 0.24 nm, at which the hydrogen atoms move to occupy the midpoint between the neighboring oxygen atoms, that is, the hydrogen bond becomes symmetric with equal O–H and H–O distances [4–9, 26]. In other words, the molecular crystal is converted to a nonmolecular crystal at this critical pressure. Such a significant change in the hydrogen bond would influence the
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24 Proton Diffusion in Ice Bilayers
protonic motions and hence result in some anomalous feature in the diffusion coefficient. The diffusion coefficients measured at 400 K show a monotonic decrease by two orders of magnitude with increasing pressure up to 63 GPa (Fig. 24.10). The influence of pressure on the diffusion is phenomenologically described by D = D0exp(–cP/kT), where c represents the magnitude of the pressure influence on the activation energy for the protonic diffusion motion. Fitting to the experimental results gives 0.003 eV GPa–1 for c. Although no experimental data are available for the activation energy at ambient pressure, DE0, we may assume it to correspond to that determined from the electric conductivity measurement on pure ice at ambient pressure [27]. The activation energy, DE = DE0 + cP, is finally rewritten as DE = 0.70+ 0.003P, where DE and DE0 are in eV and P in GPa. 10
-14
400 K Diffusion coefficient (m2/s)
748
-15
10
10
-16
10
-17
10
-18
0
10
20
30
40
50
60
70
Pressure (GPa) Figure 24.10 Variation of the protonic diffusion coefficient with pressure measured for ice VII. Open and solid circles represent those obtained from reflection spectra measured for the H2O and D2O back surfaces of H2O/D2O bilayer, respectively. (From Ref. [25].)
The variation of the diffusion coefficient with pressure appears contrary to that expected from the distinct change in the hydrogen bonding state in association with the molecular to nonmolecular transition. In the molecular state at low pressures, the protonic diffusion proceeds by two steps: transfer in a hydrogen bond and a successive jump into another hydrogen bond. For ambient-pressure ice, the activation energies are determined experimentally by infrared absorption measurements to be 0.41 eV for the transfer and 0.52 eV for the jump [28]. In the nonmolecular region around 60 GPa, a small energy barrier still exists at the midpoint and hence a double minimum shape of potential remains slightly. The proton, however, can transfer almost freely by tunneling or thermal activation between two occupation sites and form statistically ionized molecular species [29–32]. The
References
diffusion motion would be alternated with a single-step process involving a proton jump alone, and would be expected to be accelerated by an increase in population of the ionized molecular species such as H3O+ and OH–. Nevertheless, the diffusion coefficient still shows a decrease around this pressure region. The potential barrier for the proton jump between the adjacent oxygen sites likely rises with pressure as the molecules approach, and consequently the one-step diffusion motion might be inhibited.
24.4 Summary
Protonic diffusion in ice has been investigated by a spectroscopic method. This method is based on the isotope effect on molecular vibrations. The mass difference between hydrogen and deuteron results in a frequency difference by a factor of 2 for the stretch mode. The peak positions are well separated in the spectra and hence their heights are converted to the H(D) concentrations with good accuracy. The diffusion process is monitored by measuring the reflection spectra of an H2O/ D2O ice bilayer, for which the equation of diffusion is described in analytical form. The H/D mutual diffusion coefficient measured at 400 K shows a monotonic decrease by two orders of magnitude as the pressure increases from 8 to 63 GPa. The spectroscopic method can be applied to other substances, for instance, solid acids such as CsHSO4 and polymer electrolytes. The range of diffusion rate covered by the present method could be extended by the use of an advanced infrared lightsource and detector. The diffusion coefficient of 10–16 to 10–14 m2 s–1 is currently accessible using a conventional Fourier-transform infrared spectrometer mounted with a ceramics-heater light-source and an MCT detector. A synchrotron radiation facility provides brilliant light in the infrared region; the intensity is higher by several orders of magnitude than that of a conventional light source. Infrared array detectors such as the HgCdTe device provide parallel detection without moving parts and spectral rates much higher than with a FT-IR system.
References 1 V. F. Petrenko, R. W. Whitworth, Physics
4 R. J. Hemley, A. P. Jephcoat,
of Ice, Oxford University Press, New York, 1999. 2 E. Whalley, Hydrogen Bond, Vol. 3, P. Schuster, G. Zundel, C. Sabdorfy (Eds.), North-Holland, Amsterdam, p. 1425 (1976). 3 W. F. Kuhs, J. L. Finney, C. Vettier, D. V. Bliss, J. Chem. Phys. 81, 3612 (1984).
H. K. Mao,L. W. Finger, D. E. Cox, Nature 330, 737 (1987). 5 M. Song, H. Yamawaki, M. Sakashita, H. Fujihisa, K. Aoki, Phys. Rev. B 60, 12644 (1999). 6 Ph. Pruzan, E. Wolanin, M. Gaythier, J. C. Chervin, B. Canny, J. Phys. Chem. B 101, 6230 (1997).
749
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24 Proton Diffusion in Ice Bilayers 7 A. F. Goncharov, V. V. Struzhkin,
8
9 10 11 12 13 14
15 16
17
18 19 20
H. K. Mao, R. J. Hemley, Phys. Rev. Lett. 83, 1998 (1999). M. Song, H. Yamawaki, H. Fujihisa, M. Sakashita, K. Aoki, Phys. Rev. B 68, 014106 (2003). H. Blicks, O. Dengel, N. Riehl, Phys. Kondens. Materie 4, 375 (1966). R. O. Ramseier, J. Appl. Phys. 38, 2553 (1967). K. Itagaki, J. Phys. Soc. Jpn. 22, 427 (1967). N. Bjerrum, Science 115, 385 (1952). P. Demontis, R. LeSar, M. L. Klein, Phys. Rev. Lett. 60, 2284 (1988). C. Cavazzoni, G. L. Chiarotti, S. Scandolo, E. Tosatti, M. Parrinello, Science 283, 44 (1999). D. J. Stevenson, Rep. Prog. Phys. 46, 555 (1983). W. J. Nellis, D. C. Hamilton, N. C. Holmes, H. B. Radousky, F. H. Ree, A. C. Mitchell, M. Nicol, Science 240, 779 (1988). W. J. Nellis, N. C. Holmes, A. C. Mitchell, D. C. Hamilton, J. Chem. Phys. 107, 9096 (1997). F. Datchi, P. Loubeyre, R. LeToullec, Phys. Rev. B 61, 6535 (2000). S. Block, G. J. Piermarini, Phys. Today 29, 44 (1976). A. Jayaraman, Rev. Mod. Phys. 55, 65 (1983).
21 H. K. Mao, R. J. Hemley, A. L. Mao, in
22
23 24
25
26
27 28 29 30 31
32
High-Pressure Science and Technology, S. C. Schmidt, J. W. Shaner, G. A. Samara, M. Ross (Eds.), AIP, New York, 1613 (1993). M. I. Eremets, High Pressure Experimental Methods, Oxford University Press, New York, 1996. J. Crank, The Mathematics of Diffusion, Clarendon, Oxford, 1975. K. Aoki, Eriko Katoh, H. Yamawaki, H. Fujihisa, and M. Sakashita, Rev. Sci. Instrum. 74, 2472 (2003). E. Katoh, H. Yamawaki, H. Fujihisa, M. Sakashita, K. Aoki, Science 295, 1264 (2002). P. Loubeyre, R. LeToullec, E. Wolanin, M. Hanfland, D. Hausermann, Nature 397, 503 (1999). V. F. Petrenko, R. W. Whitworth, J. Phys. Chem. 87, 4022 (1983). W. B. Collier, G. Ritzhaupt, J. P. Devlin, J. Phys. Chem. 88, 363 (1984). K. S. Schweizer, F. H. Stillinger, J. Chem. Phys. 80, 1230 (1984). P. G. Johannsen, J. Phys.: Condens. Matter. 10, 2241 (1998). M. Benoit, D. Marx, M. Parrinello, Nature 392, 258 (1998); M. Benoit, D. Marx, M. Parrinello, Solid State Ionics 125, 23 (1999). W. B. Holzapfel, Physica B 265, 113 (1999).
751
25 Hydrogen Transfer on Metal Surfaces Klaus Christmann
25.1 Introduction
Among the definitions of the term “hydrogen bond” one can find the following explanations: A weak bond involving the sharing of an electron with a hydrogen atom; hydrogen bonds are important in the specificity of base pairing in nucleic acids and in the determination of protein shape; or: A hydrogen bond is a chemical bond in which a hydrogen atom of one molecule is attracted to an electronegative atom, especially a nitrogen, oxygen, or fluorine atom, usually of another molecule. A somewhat closer look into the chemical bonding situation reveals that a hydrogen bond is the consequence of an attractive intermolecular force between two partial electric charges of opposite sign, whereby an H atom participates. The simplest and most common example is perhaps an H atom located between the two oxygen atoms of two neighboring water molecules: This H atom can build up a bond to either oxygen atom, thus forming a bridge between these O atoms. This is the reason why, in the German notation, this particular type of bonding is called “Wasserstoff-Brcken-Bindung”. It is not necessarily an intermolecular bond; considering large molecules such as proteins, it is also possible that H bonds are formed between two parts of the same molecule. These intramolecular bonds often decisively influence the shape of the respective molecular entity, they are, for example, responsible for the folding of proteins etc. Accordingly, the significance of H bonding in biochemistry or, more generally, in life sciences cannot be overestimated. The strength of an H bond is usually larger than the common intermolecular (van-der-Waals-like) forces, however, it cannot compete with the strength of typical covalent or ionic bonds. This “intermediate” bond strength is certainly the reason behind the pronounced variability of H bonding effects and their importance in the life sciences. While one could further expand greatly on the specifics of H bonds, one of their prominent characteristics is that the H atom involved can easily be transferred from one electronegative heteroatom (nitrogen, oxygen, chlorine...) to another, and the question arises as to how this transfer process proceeds and where the H atom is actually located or which electronegative center it is associated with. Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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25 Hydrogen Transfer on Metal Surfaces
Indeed, the respective H atom may be considered entirely delocalized between the two negatively polarized atoms or functional groups. Due to its small size it can even tunnel through the potential energy barrier which exists between the two negative centers. Since liquid water is the most common solvent, a wealth of investigations has been carried out to specify hydrogen bonding in water and/or hydrophilic systems (unnecessary to say that just these systems are the dominating ones in biochemistry). The respective studies involve both experimental and theoretical work and often focus on a particularly important aspect, namely, the transfer of hydrogen. Detailed information on the energetics and dynamics of this hydrogen transfer is required to understand the mechanisms of the biochemical reactions and processes. Unfortunately, these reactions mostly (if not always) occur in three-dimensional condensed phases (preferably in liquid systems) and usually involve large and complicated molecules. Nevertheless, studies with very simple (in most cases admittedly too simple) model systems can be advantageous to disentangle selective reaction steps of hydrogen transfer. Studies on surfaces, for example, are often quite helpful to reduce the dimension or the symmetry of a problem, and it is not purely by chance that the “inventors” of the scanning tunneling microscope soon after its invention tried to image a biomolecule (DNA) deposited on a surface [1]. In order to learn something about hydrogen transfer it is therefore a legitimate approach and, in addition, quite helpful, to deposit molecules on solid surfaces and scrutinize, e.g., the migration and exchange of H atoms between two molecular entities. We recall that two-dimensional systems involving H bonding and H transfer also play a decisive role in heterogeneous catalysis, in thin solid or liquid films, in micelles and (fuel cell) membranes. At a first glance, these systems may be considered less complex than H bonding in three-dimensional liquid or solid–liquid systems. While this may be true in a few cases, the details of H transfer are nevertheless also complicated in 2D systems, due to the variability of possible routes of interaction. On the other hand, the transition from 2D to 3D systems can be accomplished by continuously increasing the amount of molecules deposited on the surface template until condensation occurs. During the respective multilayer growth process, the change in the system’s properties can be followed and attributed to the characteristics of the 3D aggregation. An approach that has been pursued very successfully in the past is to simplify the system under consideration even further and to consider the interaction of gases with geometrically and electronically well defined two-dimensional singlecrystal surfaces. Metal surfaces are comparatively well understood with respect to both geometrical and electronic structure. This includes simple processes occurring during the interaction of reactive gases (hydrogen, oxygen, carbon monoxide) with these surfaces. Focusing here on dihydrogen interaction with metal surfaces in general, numerous review reports exist [2–4] which provide detailed information on thermodynamic and kinetic properties (hydrogen adsorption and desorption energies, sticking probabilities, frequency factors and activation energies, vibrational frequencies, electronic levels and dipole moments). The experimental studies have been accompanied by an almost equal number of theoretical calculations and simulations [5], often with quite satisfactory agreement between experiment
25.1 Introduction
and theory. One might argue that the interaction of a molecule as simple as H2 with a metal surface should lead to a very clear and distinct view. However, just the interaction of hydrogen bears a variety of complications which are caused, among others, by the small physical size of hydrogen, its quantum-mechanical properties and the ability of many metals to spontaneously dissociate dihydrogen. Instead of a simple one-point adsorption step (which nevertheless occurs in quite a number of instances) the very reactive H atoms formed upon dissociation can (and often will) cause consecutive reactions with the metal surface: Among others, the relatively large heat of hydrogen adsorption can enable metal surface atoms to move and geometrically rearrange themselves to energetically more favorable lattice positions, thus causing a new lateral periodicity of the entire surface (a process referred to as “surface reconstruction”). In a next step, this rearrangement may produce surface channels through which H atoms can more easily enter subsurface or even bulk sites (dissolution and absorption of hydrogen) ending up with metal– hydrogen compounds, i.e., hydridic phases. Metals like palladium, vanadium, titanium, niobium or tantalum are well known to absorb appreciable quantities of H atoms under appropriate thermodynamic conditions [6]. How a dihydrogen molecule can interact with metal surfaces, including absorption and solution, is schematically sketched in the (one-dimensional) potential energy diagram of Fig. 25.1.
Figure 25.1 One-dimensional potential energy diagram illustrating the changes in the potential energy of a hydrogen molecule which approaches a metal (the location of the surface is indicated by the hatched area). The following processes may occur: – Trapping of a H2 molecule in a shallow physisorption minimum of depth EH2 – Dissociation of the H2 molecule and formation of a stable chemisorptive bond between each H atom and the surface;
release of adsorption energy EH. Full line: Sparsely H-covered surface; dashed line: fully H-covered surface (consideration of coverage-dependent interaction potentials, cf. Fig. 25.5) – Migration of H atoms into subsurface sites, with a (coverage-dependent – full and dashed lines) sorption energy ESS. – (Possible) absorption of H atoms in interstitial sites with heat of solution Esol. The activation energy of diffusion of the respective H atoms, Ediff., is indicated.
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25 Hydrogen Transfer on Metal Surfaces
A brief outline as to how this chapter is organized may be helpful. In our attempt to consider H bonding and related effects on and at metal surfaces we will largely exclude the aforementioned complications such as surface reconstruction, subsurface-site population or hydrogen sorption effects, since they may obscure the essential H transfer and bonding phenomena. First, in Section 25.2 we shall familiarize the reader with some general terms and elementary processes that can occur during the interaction of gaseous dihydrogen with metal surfaces and that are crucial in order to understand the details of H transfer on these kinds of surfaces. They include processes like physisorption and chemisorption, activated and nonactivated adsorption and desorption, a priori and a posteriori energetic heterogeneity, formation of phases with longrange order, and others. In Section 25.3, we will discuss the elementary steps of hydrogen transfer on a metal surface. In the simplest case, this is just the diffusion of H atoms or H2 molecules from one lattice site of a homogeneous periodic surface to another site on the same surface, whereby the H species may travel over distances on the microscopic (a few nanometers) or on the macroscopic scale (micrometers to millimeters). Especially for the lightest hydrogen isotope 11 H, the classical’ diffusion may be accompanied (or even replaced) by quantum tunneling processes which can dominate the transport at lower temperatures. Relevant, too, is hydrogen transfer on a heterogeneous surface (especially in the area of technical catalysis). Generally, such a surface may consist of different compounds and/or elements arranged in patches of different size and surface geometry and actually represents quite a complex system. Focusing on metallic surfaces (as we do here), we consider alloy or bimetallic surfaces in the first instance (the latter consisting of immiscible components), where one component is active with respect to hydrogen adsorption (dissociation) and the other is not. There arises an immediate question: Will the H atoms formed on the active part of the bimetallic surface remain trapped on the sites belonging to the active patch, or will they, once formed, be able to migrate also to sites located on the inactive surfaces? This so-called spillover effect is believed to be a crucial property in various hydrogenation reactions over metal and supported metal catalyst surfaces [7]. Finally, in Section 25.4 homogeneous surfaces will be considered that are (partially) covered with negatively polarized molecules containing hydroxy (OH) groups. In this context, the adsorption and especially the condensation and network formation of water or alcohol molecules at surfaces deserves interest, because a monitoring of the respective growth processes allows conclusions to be drawn on the two-dimensional « three-dimensional phase transition and the network formation mainly caused by hydrogen bonding effects.
25.2 The Principles of the Interaction of Hydrogen with Surfaces: Terms and Definitions
25.2 The Principles of the Interaction of Hydrogen with Surfaces: Terms and Definitions
A hydrogen molecule arriving from the gas phase first feels’ the (generally slightly attractive) force fields of the surface and can experience three processes, depending on the strength of the interaction potential: If the H2 molecule is merely trapped by weak van-der-Waals forces, it undergoes “physical” adsorption; this genuine physisorption of hydrogen usually involves interaction energies of merely a few kJ mol–1, and temperatures as low as 15–20 K are already sufficient to make the molecules leave the surface again by thermal desorption. Physisorptive interaction is the rule with chemically inactive surfaces (e.g., alkali metal halide or graphite surfaces) and, accordingly, hydrogen molecules do not adsorb at common temperatures (T ‡ 300 K) on those materials. Only close to the freezing point of solid molecular hydrogen, i.e., in the temperature interval between, say, 5 and 20 K is it possible to precipitate and condense liquid or solid H2 layers on these surfaces. In a few special cases the H2 molecule may interact somewhat more strongly with metal surfaces, provided the respective system offers sites with higher geometrical coordination and a peculiar electronic structure; in this case, interaction energies up to ~ 20 kJ mol–1 are involved, leading to markedly elevated hydrogen desorption temperatures between 60 and 90 K. Examples of this weak molecular chemisorption have been reported for stepped Ni surfaces [8] and for some fcc(210) surfaces (Pd, Ni) [9, 10]. The molecular nature of the adsorbed hydrogen is clearly proven by vibrational loss (observation of the H–H stretching vibration) and isotope exchange measurements, in that the isotopic scrambling (observation of HD besides H2 and D2) does not take place. In Fig. 25.2 we present, as an example, thermal desorption spectra of H2, D2, and HD after a mixed’ exposure of a Pd(210) surface to hydrogen gas and deuterium gas at ~40 K. Obviously, there is only a vanishingly small HD contribution, ruling out significant isotopic scrambling [9]. The still low desorption temperatures of the molecular hydrogen thereby reflect the weak interaction forces which are, on the other
Figure 25.2 Thermal desorption spectrum of hydrogen deuteride (HD, mass 3) from a Pd(210) surface that had received a simultaneous exposure of hydrogen, H2, and deuterium, D2, at 40 K. The b states represent atomically adsorbed hydrogen (deuterium), while the c states are due to the molecular species. Apparently, practically no isotopic scrambling occurs in the c states (absence of HD), while the exchange is complete in the atomic b states. After Schmidt et al. [9,10].
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25 Hydrogen Transfer on Metal Surfaces
hand, responsible for the appreciable mobility of the H2 molecules while being trapped on the surface. In other words, easy hydrogen transfer (H2) is achieved with these systems. More common and important, however, is the chemisorption of hydrogen, with the interaction energies ranging from ~ 50 to 150 kJ mol–1. In this case, the H2 molecules undergo homolytic dissociation into two H atoms, either spontaneously (nonactivated adsorption) or, much more slowly, in an activated step (activated adsorption). Which process actually dominates depends on the electronic structure of the metal in question, see below. Activated H adsorption greatly reduces the rate of H uptake at lower temperatures, but this rate increases strongly with temperature T, since then more molecules exist having the required activation energy. In Fig. 25.3, spontaneous and activated adsorption are illustrated by a simple Lennard-Jones potential energy diagram. Note that only in the case of activated
Figure 25.3 Lennard-Jones potential energy diagram of a H2 molecule interacting with an active (full line) and an inactive metal surface (dotted line) as a schematic one-dimensional description of the activated (non-activated) hydrogen adsorption. The dashed line indicates the potential energy U(z) for a pre-dissociated H2 molecule (shifted by the dissociation energy Ediss, with respect to energy zero)
and for the two isolated, reactive, H atoms as they approach the surface. The deep potential energy well (EMe–H) represents the energy of the metal–H bond formed (which is gained twice). In the activated case the intersection between the dotted and dashed curves leads to an activation barrier of height E* that a H2 molecule getting in contact with the surface has to overcome in order to be chemisorbed.
25.2 The Principles of the Interaction of Hydrogen with Surfaces: Terms and Definitions * . adsorption does the H2 molecule have to overcome an activation barrier, Ead Examples are coinage metal surfaces (Cu, Ag, Au), where barriers of up to 50 kJ mol–1 have been determined [11] and other free electron’ metals (alkali, alkaline earth and earth metals) or various elemental semiconductor surfaces (Si, Ge) with barriers of similar height [12, 13]. Even more illustrative is a two-dimensional representation of the homolytic dissociation reaction (elbow’ plot), see Fig. 25.4, where the internuclear H–H distance x is plotted against the distance y of the H2 molecule with respect to the surface. The resulting elbow-like equipotential lines indicate that only close to the surface are the forces operating between the substrate and the H atoms strong enough to sufficiently stretch the inner-molecular bond and to make it dissociate. We add here that a wealth of theoretical work has been carried out to develop appropriate quantum-chemical models which can explain both the spontaneous and activated hydrogen dissociation [14–16]. Following Harris [16], dissociation generally requires weakening of the H–H bond, and both filling the empty anti-bonding 2r* molecular orbital (MO) of the H2 molecule with electrons, or emptying its filled 1r bonding MO can cause the respective bond weakening effect. In addition, since the H2 molecule is a closed-shell unit, the Pauli repulsion between the filled, delocalized metallic s,p bands of the substrate and the occupied 1r hydrogen MO is responsible for the appearance of an activation barrier as the H2 molecule is brought closer to the surface. Only if empty d electron states with similar energy to that of the sp electrons are available, can rehybridization help to circumvent the Pauli repulsion. Harris, who has theoretically modeled this rehybridization, states explicitly that the sp electrons of the metal can escape’ into the empty d state [16]. From this it is immediately apparent why transition metals (with their high density of empty d states, right at the Fermi level EF) are active and coinage metals (with their filled d bands lying ~ 2–3 eV below EF) are inactive with respect to spontaneous H2 dissociation.
Figure 25.4 Two-dimensional representation (“elbow” plots) of the potential energy situation when a H2 molecule interacts with an active metal surface. The coordinate x describes the internuclear H–H distance, y is the distance of the H2 molecule from the surface. Two possible trajectories are indicated: (1) represents a reflection trajectory (unsuccessful event) with no chemisorption, (2) a successful approach
that leads to dissociation. The saddle point P can be located either in the entrance’ channel (relatively far away from the surface, left-hand side) or in the exit’ channel (closer to the surface, righthand side). In the first case, the H2 molecule needs mainly translational energy for a successful passage across the barrier, while vibrational excitation is advantageous in the second case.
757
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25 Hydrogen Transfer on Metal Surfaces
Once the H atoms have reached the bottom of the deep potential energy well (cf., Fig. 25.1 and Fig. 25.3) two metal–H bonds, each with energy EMe–H, are formed and, in addition, the excess energy is released as adsorption energy, Ead, or heat of hydrogen adsorption. This quantity can easily be measured experimentally as will be pointed out further below. From the overall energy balance EMeH ¼
1 ðE þ Ediss Þ 2 ad
(25.1)
(Ediss = heat of H2 dissociation = 432 kJ mol–1), the energy of a metal–H bond, EMe–H can immediately be deduced. Generally, Ead is a crucial property of any H–metal interaction system, and numerous experimental and theoretical studies have been, and still are being, devoted to the determination of this quantity. Concerning the experimental methods, Ead can either be determined by means of equilibrium measurements, for example by taking hydrogen adsorption isotherms [17], or by analyzing thermal desorption data [9]. Many different theoretical methods are used to obtain hydrogen–metal binding and adsorption energies, such as tight-binding, cluster and slab (supercell) approaches. Particularly powerful are calculations based on density functional (DFT) methods plus generalized gradient approximations (GGA); for more details we refer to reviews and monographs [3, 5]. In view of H transport across surfaces, it is worth mentioning that Ead also decisively governs this transport. The reason is that quite generally the heat of adsorption is internally correlated with the activation energy for (classical) lateral diffusion: An empirical relation states that for any adsorbate system the activation energy for diffusion, i.e. for hopping events from one surface site to another, is about one tenth of the adsorption energy, i.e., the depth of the adsorbate–surface interaction potential. Therefore one can get at least a crude estimate of the magnitude of the lateral diffusion energies (see Section 3.1) from known Ead values. In Table 25.1 [3] we present some experimental values for Ead along with values for EMe–H calculated according to Eq. (25.1). Interestingly, these latter numbers are relatively similar for different systems, because the fairly large heat of dissociation of the H2 molecule is always involved. The Ead data thereby refer to vanishing hydrogen coverages, since elevated H surface concentrations can and will induce lateral H–H interactions between adjacent adsorbed H atoms. Usually, these interactions are repulsive (since the adsorbed H atoms share the charge density of the metal atom(s) underneath), in a few cases, however, they may also be attractive and, hence, support H chain or H island formation, the H-on-Ni(110) system being a good example [17]. The respective lateral interactions have quantumchemical origin [19–21] and can significantly alter the potential energy situation across the surface as illustrated schematically in Fig. 25.5. For a single adsorbed H atom, see Fig. 25.5(a), there is a regular sinusoidal potential energy situation along the x,y-direction leading to entirely equivalent adsorption sites; for a pair of adjacent H atoms, repulsive lateral interactions of size x lower the adsorption energy Ead (Fig. 25.5(b)), while attractive interactions lead to an increase in Ead in the
25.2 The Principles of the Interaction of Hydrogen with Surfaces: Terms and Definitions
759
Tab. 25.1 Adsorption energies of hydrogen on selected metal single crystal surfaces [3].
Surface orientation [hkl]
Fe(110)
Ni(100)
Cu(110)
Mo(100)
Ru(0001)
Rh(100)
Adsorption energy [kJ mol–1]
109 – 5[a]
96.3[b]
77.1 – 1[c]
101.3[d]
125[e]
79.9 – 2[ f ]
Metal–hydrogen binding energy [kJ mol–1]
270.5
264.1
254.6
266.7
278.5
255.9
Surface orientation [hkl]
Pd(100)
Ag(111)
W(110)
Re(0001)
Pt(111)
Adsorption energy [kJ mol–1]
102.6[g]
43.6[h]
146.4[i]
134[ j]
71[k]
Metal–hydrogen binding energy [kJ mol–1]
267.3
237.8
289.2
283.0
251.5
a Bozso, F., Ertl., G., Grunze, M., Weiss, M., Appl. Surf. Sci. 1 (1977) 103; b Christmann, K., Schober, O., Ertl, G., Neumann, M., J. Chem. Phys. 60 (1974) 4528; c Goerge, J., Zeppenfeld, P., David, R., Bchel, M., Comsa, G., Surf. Sci. 289 (1993) 201; d Zaera, F., Kollin, E. B., Gland, J. L., Surf. Sci. 166 (1986) L149; e Feulner, P., Menzel, D., Surf. Sci.154 (1985) 465; f Kim, Y., Peebles, H. C., White, J. M., Surf. Sci. 114 (1982) 363; g Behm, R. J., Christmann, K., Ertl, G., Surf. Sci. 99 (1980) 320; h Parker, D. H., Jones, M. E., Koel, B. E., Surf. Sci. 233 (1990) 65; i Nahm, T.-U., Gomer, R., Surf. Sci. 380 (1997) 434; j He, J.-W., Goodman, D. W., J. Phys. Chem. 94 (1990) 1502; k Poelsema, B., Mechtersheimer, G., Comsa, G., Proc. IVth Int. Conf. Solid Surfaces and IIIrd ECOSS, eds. Degras, D. A., Costa, M., (Cannes 1980), p. 834.
local area of the H–H pair (Fig. 25.5(c)). This modification of x also has, of course, an effect on the activation energy for diffusion; i.e., the lateral periodic potential is modulated by the Had–Had pair potential, an energetic heterogeneity is induced (a posteriori heterogeneity). For comparison, there exist surfaces (e.g. crystallographically open’ (high-Miller-index) surfaces such as Pd(210) [9, 10]) which possess inherently energetically different adsorption sites. Likewise, alloys with chemically different constituents can exhibit energetically heterogeneous surfaces, see Section 3.2. In the course of adsorption, the respective energetically inequivalent sites become successively filled by hydrogen. The overall phenomenon is called a priori heterogeneity and sensitively influences the lateral mobility of adsorbed H atoms or molecules. The aforementioned lateral interactions are also responsible for the formation of H (H2) phases with two-dimensional long-range order, since the repulsive or attractive forces between the adsorbed H atoms or H2 molecules can force the spe-
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25 Hydrogen Transfer on Metal Surfaces
Figure 25.5 Variation of the potential energy of an adsorbed H atom parallel to the surface, E(x,y). Three different cases are shown: (a) single particle adsorption with no lateral interactions; equivalence of all adsorption sites; (b) repulsive interactions, x, between neighboring adsorbed H atoms with the consequence of energetically inhomogeneous adsorption sites; (c) attractive interactions, x, between neighboring H atoms leading to energetically more favorable adsorption sites in the direct vicinity of an already adsorbed H atoms.
cies into periodic lattice sites at sufficiently low temperatures. Examples exist for both H atoms on metal and H2 molecules on graphite surfaces, whereby the latter systems often exhibit a wealth of complicated structures [22]. Ordered phases of H atoms on metal surfaces and their thermal stability are interesting subjects to study, since they allow (via statistical mechanics) conclusions on the sign and magnitude of the mutual H–H interaction forces [23, 24]. An example for ordered H phases is given in Fig. 25.6 which displays the phase diagram of the three ordered H structures reported for the Ru(0001) surface below a temperature of ~ 75 K [25]. Raising the temperature to values above the critical value, Tc, destroys
Figure 25.6 Phase diagram (T–H diagram) for the H-on-Ru(0001) adsorption system. Three different ordered H phases are formed: A p(33)R30 phase around H = 0.33; a p(21) phase at H = 0.50, and a (22)-3H phase at H = 0.75 with critical temperatures of 74 K, 68 K, and 72 K, respectively. After Sokolowski et al. [25].
25.3 The Transfer of Hydrogen on Metal Surfaces
the long-range order and leads to two-dimensional lattice gas behavior. This can conveniently be followed by means of temperature-dependent LEED experiments (LEED = low-energy electron diffraction) and evaluated (e.g., by using Monte Carlo calculations) with respect to order parameters, critical exponents, and lateral interaction energies [26]. Another frequently studied example of an ordered H phase is the c(22)-2H structure on the Ni(111) surface with a critical temperature of TC = 273 K and a characteristic asymmetric phase diagram [27, 28]. It is worth noting that for systems with chemisorption energies at the upper end (120–150 kJ mol–1) the H chemisorption process is frequently accompanied by the aforementioned structural changes (reconstruction) and the consecutive processes of H sorption and hydride formation [29]. In addition, for systems with normal’ chemisorption energies (80–120 kJ mol–1] elevated hydrogen pressures and temperatures may also favor these more vigorous interactions and increasing chemical attack towards hydrogenation. Surfaces which can form volatile hydrides (Li, Al etc.) can therefore easily be chemically eroded by exposure to hydrogen, especially at elevated temperatures, despite the large activation barrier for spontaneous H2 dissociation [30]. Similar effects have been reported for semiconductor surfaces (Si, Ge, GaAs), which can undergo successive hydrogenation and form volatile hydrides, i.e., SiH4 (silane), GeH4 (germane), GaH3 (gallane) and AsH3 (arsine), as soon as reactive H atoms are available at the surface [31, 32].
25.3 The Transfer of Hydrogen on Metal Surfaces 25.3.1 Hydrogen Surface Diffusion on Homogeneous Metal Surfaces
The most efficient process for transferring hydrogen at surfaces is diffusion – the only requirement is that the H atoms or H2 molecules are trapped in the respective chemisorption or physisorption potentials and possess a sufficient residence time, s, in this state – this can be achieved by choosing the appropriate surface temperature, T. Weakly bonded hydrogen species require low, sometimes very low, temperatures, whereas strongly chemisorbed H atoms remain trapped, even at elevated temperatures. Slowing down the lateral diffusion by lowering T leads to immobile’ adsorption, where the H atoms or H2 molecules remain in their local sites, whilst higher temperatures (below the desorption temperatures though) favor the mobility of the H adlayer. Generally, surface diffusion of adsorbed particles is crucial for many processes occurring on and at surfaces; among others, it influences the rate of adsorption and desorption, the formation of phases with long-range order and, finally, the turn-over numbers of catalytic processes. For the sake of brevity, bulk diffusion phenomena will be excluded here, although they also involve transfer of particles from the surface region to the bulk of a crystal and often play an important role just in hydrogen–metal interaction systems: note that certain metals (e.g., V, Ti,
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25 Hydrogen Transfer on Metal Surfaces
Zr, Nb, Pd and Ta) can absorb large quantities of hydrogen and, therefore, act as hydrogen storage materials. We note that Pd surfaces especially show a rich diffusion scenario involving overlayer–underlayer (surface–subsurface) transitions and interstitial diffusion leading to absorption and hydride formation processes. For more details here we recommend the respective literature [6]. Concerning genuine surface diffusion, articles by Morris et al. [33] and Naumovets and Vedula [34] reviewed the state of the art until the mid-eighties (including a description of experimental methods) and gave, in addition, a useful description of the general laws and relationships as well as mechanistic details of the diffusion process(es). For a brief introduction, we refer again to Fig. 25.5(a), which immediately for an atom (or a molecule) to reveals that it requires an activation energy of Ediff be transferred from a site “A” to another, geometrically identical site “B” on the same periodic surface. In the classical view, this two-dimensional diffusion process can be thought of as a sequence of individual and statistical hopping’ events , as pointed out, for example, by of frequency m, each activated with an energy Ediff Roberts and McKee [35]. The inverse of this frequency then yields the residence time, s¢, of the particle in the respective site. For thermally equilibrated particles, the temperature dependence of the classical surface diffusion is described by the well-known Arrhenius relation E DðTÞ ¼ D0 exp diff kT
(25.2)
with D0 being the pre-exponential factor [cm2 s–1], and D(T) the temperature-dependent diffusion coefficient. The pre-exponential factor may be associated with an attempt frequency to overcome the activation barrier. According to Fick’s first law which assumes stationary diffusion, i.e., a constant concentration gradient ¶c ¶x t , D(T) can be expressed as the ratio of the particle flux through the concentration front and the actual concentration gradient at time t. Alternatively, the diffusion progress with time t can be monitored by the mean square displacement hx 2 i of a given particle on a surface, based on Einstein’s equation: pffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi hx 2 i ¼ 2Dt
(25.3)
Another frequently used expression is based on random walk events between fixed sites and relates the pre-exponential factor D0, to the jump length a and the vibrational frequency parallel to the surface, m. For a surface with fourfold symmetry one has 1 D0 ¼ a2 m 4
(25.4)
The factor 14 arises from the four possible diffusion probabilities on this surface. Depending on the surface structure and corrugation, there may exist easy’ and difficult’ pathways for diffusion with low and high activation barriers, respectively; hence, on a crystallographically well defined single crystal surface, the diffu-
25.3 The Transfer of Hydrogen on Metal Surfaces
sion coefficient is usually strongly direction-dependent. Most of the experiments focus on a determination of activation energies for diffusion and diffusion coefficients, whereby, as mentioned above, the classical’ regime must be distinguished from the (low-temperature) regime, in which quantum tunneling dominates, as will be shown further below. Confining our considerations to hydrogen surface diffusion, the mobility’ of a hydrogen diffusion front’ was studied already 50 years ago in Gomer’s laboratory on Pt and W field emitters [36, 37]. At 4.2 K, a sharp front of adsorbed hydrogen (presumably consisting of H2 (D2) molecules) was produced by partially exposing a Pt field emitter tip to hydrogen (deuterium) [37]. As the tip temperature was raised to 20 K, the front became very mobile, in that the hydrogen molecules spread over the entire tip area. Pre-dissociating the low-temperature hydrogen layer led to a more strongly bound species (very likely chemisorbed H atoms), whose front became mobile only around 105 K tip temperature. Using the relations (25.3) and (25.4) and assuming x » 600 , a = 6 and 1012 attempts s–1 for the jump frequency m the authors concluded on an activation energy for H diffusion of ~ 4.5 kcal mol–1 (= 19 kJ mol–1). From the known H2 adsorption energy of 16 kcal mol–1 (= 67 kJ mol–1), a value of 58 kcal mol–1 (» 243 kJ mol–1) was deduced for the depth of the Pt–H potential-energy well – thus basically confirming the aforementioned 10:1 relation between the adsorption and diffusion energy. Some years later, the field emission fluctuation method was developed in Gomer’s laboratory, a powerful technique to determine diffusion coefficients and activation energies, especially for H on W surfaces. For more details about the sophisticated technique we refer to the original work by DiFoggio and Gomer [38]. In 1972, Ertl and Neumann introduced the laser-induced thermal desorption technique to determine the rate of diffusion [39]; later, this method was further refined by Seebauer and Schmidt [40] and Mak and collaborators [41–43]: In principle, the technique is based on the hole refilling’ phenomenon and is relatively straightforward: A laser beam of known cross section is incident on an adsorbatecovered, well-defined patch on the surface, whereby the power of the laser beam is just sufficient to thermally desorb all the particles in the illuminated area. After the laser shot, refilling of the hole from the cold, H-rich surrounding sets in, which can be followed as a function of time by subsequently fired laser pulses into the same spot. The refilling signal, which is monitored with a fast and sensitive mass spectrometer, is then expressed in terms of Fick’s second law of diffusion. Despite its simplicity, this technique bears some problems, among which are the appropriate adjustment of the beam power and the determination of the surface temperature within the burnt hole; furthermore, it is difficult to consider directional and coverage dependences of the diffusion fluxes [44]. Mak and George have published a simplified method to determine the coverage dependence of surface diffusion coefficients [42]. In Table 25.2, we have compiled some diffusion coefficients and activation energies for this classical’ atomic H diffusion on metal surfaces. So far we have not considered the most prominent property of an H atom, viz., its peculiar quantum character. This is based on the light mass of the proton (or
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25 Hydrogen Transfer on Metal Surfaces
Tab. 25.2 Activation energies of hydrogen diffusion on selected metal single
crystal surfaces [3]. Surface orientation [hkl]
Ni(100)
Cu(100)
Diffusion energy [kJ mol–1]
16.7 – 2[a] 19.0[b]
Ru(0001) Rh(111)
W(100) at T>220
W(100) at T=140
Pt(111) Pt(111) FEM tip
16.7[c]
> 16.7[e]
> 4.2[e]
18.8[ f ]
15.5[d]
> 29.3[g]
a George, S. M., DeSantolo, A. M., Hall, R. B., Surf. Sci. 159 (1985) L425; b Lauhon, L. J., Ho, W., Phys. Rev. Lett. 85 (2000) 4566; c Mak, C. H., Brand, J. L., Deckert, A. A., George, S. M., J. Chem. Phys. 85 (1986) 1676; d Seebauer, E. G., Kong, A. C. F., Schmidt, L. D., J. Chem. Phys. 88 (1988) 6597; e Daniels, E. A., Gomer, R., Surf. Sci. 336 (1995) 245; f Lewis, R., Gomer, R., Surf. Sci. 17 (1969) 333; g Seebauer, E. G., Schmidt, L. D., Chem. Phys. Lett. 123 (1986) 129.
the neutral H atom), i.e., mH = 1.67 10–27 kg, only heavier than an electron by a factor of 1836. Just this property, compared to the other elements, is specific for hydrogen. In addition, the availability of two significantly heavier hydrogen isotopes deuterium 21 H, and tritium 31 H, allows one to perform comparison diffusion experiments and to judge directly the influence of tunnel processes. Particularly revealing is, of course, a measurement of the T dependence of the diffusion rate: Note that for genuine tunnel processes the temperature coefficient should tend to zero. On the other hand a distinct dependence of the tunnel probability on the mass of the hydrogen isotope used is to be expected. Isotope experiments of this kind have been frequently performed in the past, especially with W surfaces; again, Gomer’s work has to be mentioned in the first instance: Careful studies of atomic hydrogen (deuterium, tritium) adsorbed on W single crystal surfaces at different temperatures and coverages revealed detailed insight into the dynamics of adsorbed H atoms on these surfaces. On W(110), DiFoggio and Gomer [38] and Auerbach et al. [45] found an anomalous isotope dependence of the hydrogen (deuterium) diffusion rates in the low-coverage regime: Low temperature tunneling diffusion showed an isotope effect several orders of magnitude smaller than predicted by simple rigid-lattice models, and high-temperature (activated) diffusion exhibited an inverse isotope effect several orders of magnitude larger than expected from the rigid lattice model. These effects were explained by peculiar W lattice–hydrogen interactions, i.e., by a large difference in the time scales of the motions of hydrogen and the tungsten lattice. Activated diffusion was described as a many-phonon process in which the vibron is thermally excited as a result of phonon–vibron coupling. The interesting data are reproduced in Fig. 25.7, taken from Auerbach’s et al. work [45]. Returning to the possibility of quantum delocalization, one could expect that the light H atoms adsorbed on a surface would behave similar to the electrons in free-electron metal surfaces, provided the energy barrier for the H atoms to move , is very small. This barrier has to across the surface, i.e., the diffusion barrier Ediff
25.3 The Transfer of Hydrogen on Metal Surfaces
Figure 25.7 Arrhenius-type plot of the diffusion coefficient D [cm2 s–1] versus the inverse temperature [1/K] for the three hydrogen isotopes (H, D, and T) adsorbed on the tungsten (110) surface (low coverage regime (H = 0.1)). Clearly evident is that (T-independent) tunneling dominates in the low temperature range, whereas classical diffusion takes over at higher temperatures. After Auerbach et al. [45].
be compared with the vibrational energy associated with a H atom adsorbed in a given surface site. For many H-on-metal systems, these vibrational ground state energies are of the order of 50–150 meV and, hence, compete with the diffusion * , which amount to 200–300 meV (~20–30 kJ mol–1), cf., Table 25.2. It barriers, Ediff is therefore by no means surprising that experimental evidence of hydrogen’s quantum character has been searched for by LEED and, especially, vibrational loss measurements. On certain (preferentially densely packed) metallic surfaces the lateral H–metal potential is often sufficiently flat as to suggest the possibility of efficient tunneling between neighboring adsorption sites. In an extreme view, this is equivalent to the existence of protonic bands, thus underlining the delocalized character of H atoms adsorbed in the respective surface sites. This behavior was first concluded for the Ni(111) + Had system in conjunction with LEED experiments to explain the observed structural disorder [27]; if diffusion barriers are neglected, the de Broglie wavelength resulting from the thermal energy of H atoms moving parallel to the surface is of the order of 1 only. This motion parallel to the surface was proposed to occur in a band-like fashion with band gaps caused by diffraction of H atoms from the two-dimensional periodic potential. The principal idea can be taken from Fig. 25.8 which shows the potential energy situation both parallel (Fig. 25.8(a)) and perpendicular to the surface (Fig. 25.8(b)) with the delocalized protonic bands and the band gaps indicated [27]. A few years later, the idea was picked up again by Puska et al. and subjected to a detailed theoretical consideration using the effective medium theory [46, 47]. In Fig. 25.9 we present the respective results for H adsorbed on a Ni(100) surface:
765
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25 Hydrogen Transfer on Metal Surfaces
Figure 25.8 Schematic representation of the atomic band structure for H atoms chemisorbed on a metal surface (assumed adsorption energy ~ 2.8 eV = 270 kJ mol–1) with very low diffusion barriers between the adsorption sites. Top: Atomic band structure parallel to the surface; bottom: Total atomic band structure with the motion perpendicular to the surface. Bands and band gaps are sketched. After Ref. [27].
Shown is the band structure (i.e., the E(k) relation) for hydrogen chemisorbed on the Ni(100) surface along the high-symmetry directions of the surface Brillouin zone (shown in the upper right). Apparently, bands formed by delocalized H wavefunctions can be distinguished, which are separated by gaps of several tens of meV. Particularly the higher excited bands show noticeable dispersion. The calculations revealed that the bandwidth of the ground state is a few meV only, whereas those of the excited states can reach several tens of meV. The authors also pointed out that the motion of H perpendicular to the surface should significantly couple to the parallel motion because of the anharmonicity of the combined perpendicu-
25.3 The Transfer of Hydrogen on Metal Surfaces
Figure 25.9 The band structure of hydrogen atoms adsorbed on a Ni(100) surface (E(~ k) relation) along the high-symmetry –X –M and C . Only directions of the surface Brillouin zone, C the states belonging to the A1 representation of the C4v point group are shown. After Puska et al. [46].
lar and parallel potentials in conjunction with the delocalized nature of the H adsorption. Somewhat more recent theoretical considerations on the quantum diffusion of hydrogen on metal surfaces have been published by Whaley et al. [48]. The authors present a quantum mechanical theory for the low-temperature diffusion of hydrogen atoms on metal surfaces based upon a band model for the hydrogen motion. At low coverages the hydrogen band motion is restricted by collisions between the adsorbate particles causing a lowering of the diffusion coefficient with increasing concentration. Additional features of H–H interactions have to be introduced to explain the coverage dependence at higher surface concentrations. The model satisfactorily reproduces the experimental observations for the coverage dependence of H, D, and T diffusion on W(110) surfaces by Gomer et al. [38, 49]. In principle, vibrational loss measurements (mostly and conveniently performed by high-resolution electron-energy loss spectroscopy (HREELS)) should be capable of detecting this band-like behavior, but it took several years until appropriate (electron energy loss) spectrometers with sufficient resolution and sensitivity were available to prove the respective excitations. The first experimental evidence came from a study by Mate and Somorjai focusing on the H(D)-onRh(111) system [50]. At H coverages of ~ 0.4 monolayers, the authors observed a prominent loss peak at 450 cm–1 which they attributed to transitions from the ground-state band to the first excited-state band for the motion of the H atoms on the Rh(111) surface. This conclusion was mainly motivated by a comparison with the aforementioned theoretical report by Puska et al. [46, 47] who calculated for the H-on-Ni(111) system (a surface with the same geometry as Rh(111)) that the first excited band for H motion parallel to the surface has E symmetry and is located ~ 320 cm–1 above the ground-state band, close to the 450 cm–1 observed for Rh(111)/H. Furthermore, the absence of dipole scattering contributions in this band (as expected for excitations of E-type symmetry) was also taken as evidence for the aforementioned assignment, as well as the absence of this band in the deuterium loss spectra. Besides the 450 cm–1 band, there appeared also (weak) loss features at higher energies which were, according to the model, interpreted as
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25 Hydrogen Transfer on Metal Surfaces Figure 25.10 Calculated eigenvalues and eigenstates lead to a series of vibrational states with quantum numbers (n, k); for the k = 0 state the Bloch orbitals of each branch were examined. At low energies, the respective orbitals are mainly confined around the fcc, top, or hcp sites of the Pt(111) surface. The figure shows for selected bands the localization/delocalization of the orbitals n = 1 (Fig. 25.9(a, b)); n = 3 (Fig. 25.9 (c, d)); n = 4 (Fig. 25.9 (e, f)); n = 26 (Fig. 25.9 (g, h)); n = 15 (Fig. 25.9 (k, l)), and n = 16 (Fig. 25.9 (m, n)), whereby the right sequence of graphs displays the probability density q(r) in transversal sections. Ten equidistant contour lines are used in each graph. After Badescu et al. [55].
reflecting excitations from the ground-state band to the higher excited states. In full agreement with the protonic band model, no ordered H overlayer was found in LEED at 80 K adsorption temperature, which led the authors to call the delocalized adsorbed H layer a hydrogen fog’. In addition, the extended line widths of the vibrational bands could be taken as a hint to nonlocal properties of the adsorbed H atoms. The next study to be mentioned here was concerned with time-of-flight scattering and recoiling spectroscopy of hydrogen adsorbed on a W(211) surface and included also an effective-medium-theoretical treatment [51]. This shows a shallow H–W potential, with an activation barrier to motion along the [1-1-1] troughs of only 100 meV. The lowest excited states correspond to vibrations parallel to the surface with large amplitudes, fill a large portion of the trough and can be populated thermally. At 450 K, the calculations reveal that the H atoms are delocalized to a greater extent than expected from the shadow-cone radius of a W atom arising from the ion scattering. In 1992, Astaldi et al. took coverage-dependent vibrational loss spectra of H and D adsorbed at 110 K on a Cu(110) surface and concluded that there was a protonic band structure at low coverages (H £ 0.15), while the H atoms were more localized at higher coverages [52]. The HREELS measurements were supported by parallel LEED observations: Below H = 0.15 there was no H-induced superstructure visible, pointing to a disperse lattice-gas H phase, whilst for H > 0.15 extra’ spots of a (13) phase appeared, indicating rather more localized H atoms in the troughs of the Cu(110) surface. Particularly revealing were the isotope effects: spectra taken with deuterium showed a much lower coverage dependence. About four years later Takagi et al. published vibrational loss data for H and D adsorbed (likewise in low concentrations) at 90 K on a Pd(110) surface [53] and performed parallel model calculations from which they also concluded that the delocalized protonic band model was valid. The latest work dealing with that issue appeared in 2001, when Badescu et al. studied the H-on-Pt(111) system by means of high-resolution electron-energy loss spectroscopy (HREELS) at 85 K and again found vibrational bands and systematic excitations in the respective energy range which were attributed to the existence of protonic bands and the respective excitation. From their most recent experimental and theoretical work [54, 55] we reproduce in Fig. 25.10 their orbital model with the probability density of the protonic orbitals’ for low excited (n = 1, 3 and 4) and high excited states
"
25.3 The Transfer of Hydrogen on Metal Surfaces
769
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25 Hydrogen Transfer on Metal Surfaces
(n = 15, 16, and 26), the H coverage being 1 monolayer. Other more recent experimental [56] and theoretical work [57] also favored at least a partial delocalization of adsorbed H atoms on transition metal surfaces. Quite recently, an exhaustive review article appeared on the issue of quantum delocalization of hydrogen on metal surfaces [58] which is recommended for further reading. It should be mentioned here, however, that the concept of highly delocalized hydrogen has also been questioned several times, and there exist various reports for a variety of metal surfaces, in which it is denied that quantum delocalization plays a dominant role in hydrogen adsorption [59, 60]. As a good example, we refer to a recent study by Kostov et al. [61] on the H-on-Ru(0001) system, where very careful measurements of H-induced vibrational bands were performed (including angle dependences and linewidths) and a thorough discussion conducted concerning the evidence for or necessity to assume delocalization. Actually, the (0001) surface of the hexagonal close-packed (hcp) system with its shallow corrugation represents an ideal candidate’ for delocalized hydrogen. However, Kostov et al. pointed out explicitly that all their observed vibrational phenomena and isotope effects could be consistently explained by classical’ adsorption of H atoms in distinct sites of the Ru(0001) surface. In concluding this paragraph, one can state that more (and more careful) vibrational measurements are required to shed more light on the (undoubtedly interesting) issue of quantum motion of hydrogen on metallic surfaces. Turning to classical diffusion again, significant progress in understanding the mechanism of this diffusion has been achieved since the late eighties and early nineties by performing scanning tunneling microscopy (STM) experiments and watching the adsorbed particles during their hopping and site exchange events [62–64]. A direct counting and subsequent statistical analysis of the number of migrating N (O) atoms on a Ru surface as a function of time and coverage revealed much insight into the principal surface hopping, diffusion, and lateral ordering phenomena of O and N atoms at and around room temperature. By performing rapid scans it was even possible to make an STM movie of the dynamical surface scenario during oxygen atom migration [64]. However, in order to watch diffusing hydrogen atoms with their appreciably larger diffusion rate, the surfaces have to be kept at significantly lower temperatures; a possible solution is provided by performing STM observations in combination with inelastic electron tunneling spectroscopy (IETS) in a 4 K-STM [65, 66]. Recently, there arose much interest in single atom diffusion and its direct observation. Details of this novel technique which is being developed in the laboratory of W. Ho with emphasis on hydrogen adsorbed layers can be taken from the internet site http://www.physics.uci.edu/ ~wilsonho/stm-iets.html. The space limitations do not allow us to expand further on both experimental and theoretical investigations on hydrogen diffusion. There exist numerous theoretical articles dealing with diffusive H motion on surfaces, many of them focusing on the interesting nonthermally activated quantum tunneling processes [67, 68].
25.3 The Transfer of Hydrogen on Metal Surfaces
25.3.2 Hydrogen Surface Diffusion and Transfer on Heterogeneous Metal Surfaces
While the foregoing section was concerned only with homogeneous, elemental metal surfaces (consisting of a single kind of atoms only), the admixture of a second (guest) metal can change the situation significantly, depending on the chemical differences between the host and guest metal. As far as the interaction of hydrogen with the respective alloy or bimetallic’ surface is concerned, these changes include both the dissociation probability of a H2 molecule and the adsorption energy of the H atoms in a given adsorption site. Certainly also affected will be, of course, the shape and height of the activation barriers for H diffusion (transfer) parallel to the surface, especially in the vicinity of the admixed guest atoms and, hence, the overall H transfer. Alloy or bimetallic systems (often in conjunction with oxidic support materials) are of utmost importance in heterogeneous catalysis, because they can supply hydrogen atoms for reactions with co-adsorbed molecules which either simply add the H atoms to unsaturated bonds (hydrogenation) or use the H atoms to cleave internal bonds, preferentially C–C bonds (hydrogenolysis), see below. In recent years, however, other technical applications have also led to an enormous interest in physisorption and chemisorption of hydrogen on a variety of mixed metal surfaces, either in dispersed form on a support or in a more compact fashion. We recall the development of gas sensors, where often Pd (or Pd alloys) is deposited on tin oxide or other semiconducting surfaces and used to activate molecular hydrogen which can then, in conjunction with the surface oxide, dehydrogenate hydrides and hydrocarbons [69]. Even more important is the application of Pt group metals and their alloys in fuel cell technology. Fuel cells serve as very clean electricity sources in that they electrochemically oxidize a fuel, typically hydrogen, and, at the same time, reduce oxygen to give water. In this respect, they can be assigned as proton pumps’. The basic ingredients of a fuel cell are (i) the electrolyte, usually a proton conducting membrane (NAFION), which is embedded in a sandwich-like fashion between (ii) two gas-porous electrodes which contain the redox catalysts [70]. In low-temperature fuel cells, very often Pt is the essential part of the catalyst material, however, it is mostly doped with other metals (Cr, Co, Ni) to enhance the catalyst’s activity for both oxidation and reduction reactions. Therefore, the interaction of hydrogen with Pt-based alloys is frequently being investigated with respect to H2 dissociation, H binding states, and H-induced surface restructuring phenomena. Since, however, both Pt and Ni readily dissociate hydrogen and the H atoms formed are chemisorbed with similar adsorption energies it is not at all easy to distinguish chemically between the two constituents of the alloy and their specific interaction with both H2 molecules and H atoms. In some cases the vibrations of the respective different H–metal chemisorption complexes, i.e., H–Pt and H–Ni, are different, an analysis of the local H–metal vibrations can yield some insight into the local distribution and filling of the respective adsorption sites. For surfaces with larger areas, inelastic neutron scattering (INS) is a unique analytical tool to study the vibrational dynamics of hydrogen-containing materials including
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dihydrogen. Therefore, this technique can be applied for dispersed, polycrystalline catalyst materials. More information can be taken from work by Mitchell et al. who have, among others, used Pt and PtRu alloys deposited on carbon supports and studied the adsorbed states of dihydrogen and H spillover to the C surface by means of INS [71, 72]. However, there exists one particularly interesting class of materials which we shall expand on in the following section, namely binary alloys that consist of a hydrogen-active’ and a hydrogen-inactive’ metal: As pointed out in Section 2, the chemical affinity of hydrogen with respect to a noble’ metal (NM) containing only filled, deep-lying, d-bands (Cu, Ag, Au) differs largely from that of a transition metal (TM) with its high density of d electron states right at the Fermi level (Ni, Pd, Pt etc.). Within this class of materials, it is reasonable to further distinguish (i) homogeneous alloys with completely miscible components forming a continuous series of solid solutions (Cu+Ni, Ag+Pd), (ii) miscible components which form stoichiometric intermetallic compounds and phases with long-range order (Cu+Pd, Cu+Pt), and (iii) constituents that are immiscible in the bulk (Cu+Ru, Ag+Ru, Au+Ru). In all three cases both the electronic structure of the alloy surface (density of electronic states) and its topography can, and often will, be greatly modified by the mutual concentrations of the constituents. In addition, surface enrichment may occur, whereby the more volatile constituent usually segregates at the surface [73]. Taking an example from sub-category (i), we consider an alloy between Ni and Cu, where Ni is the active’ and Cu the inactive’ component. Depending on the composition and heat treatment, a certain statistical distribution of Cu atoms in a Ni matrix will arise, and ensembles containing few or many Cu atoms are formed in the surface. In the simplest case, a given Cu atom will arithmetically block an H adsorption site of the Ni. More often, however, it induces a long-range effect in that it spoils’ (i.e., deactivates) fairly large ensembles of active Ni atoms. The hydrogen adsorption capacity of this ensemble is then greatly reduced or even completely extinguished by a single Cu atom (ensemble effect’). On the other hand, a Cu atom in the direct vicinity of a Ni atom can also be electronically activated by a local charge transfer and then, despite its inherent inactivity, be activated to bind H atom(s) (ligand effect’). Both ensemble and ligand effect are decisive and well-known issues in heterogeneous catalysis [74, 75]. Similar scenarios are encountered with (ii) alloys which form ordered superlattices and/or intermetallic compounds with a defined stoichiometry, for instance Cu/Pd or Cu/Pt alloys. Depending on the copper concentration, either Cu-rich Cu3Pd (Cu3Pt) or Pd(Pt)-rich alloys (Pd3Cu (Pt3Cu) can be adjusted. These materials often exhibit a regular surface distribution of the constituents and, hence, form geometrically well-defined ensembles which enables the researcher to relate the ensemble size and geometry with the adsorption property of a given bimetallic surface [76–78]: For a regular Cu3Pt(111) surface, a given Pt atom is actually surrounded by 6 Cu atoms and, hence, geometrically isolated from its next Pt neighbors. In a LEED experiment, extra’ diffraction spots indicate a defined surface composition and geometry, and, in recent years, scanning tunneling microscopy
25.3 The Transfer of Hydrogen on Metal Surfaces
(STM) with atomic resolution could sometimes directly image the distribution of the elements in the surface alloy, provided there is sufficient chemical contrast’ between the two elements [79]. For CO adsorption on Pt-Co alloys, direct STM investigations made it possible to pinpoint the ligand effect for the first time [80]. In technical catalysis, bimetallic systems (category (iii)) often play a more important role than homogeneous alloys. With these systems, a limited thermodynamic miscibility controls the lateral dispersion of the NM deposit on the TM substrate and often leads to a very inhomogeneous two-dimensional distribution in that extended islands of the NM are formed on top of the TM surface, with additional adatom, edge and kink sites which may provide particular centers of chemical activity. Typical experiments aiming at the determination of ensemble effects and hydrogen spill-over (see below) date back to the sixties and seventies: Sinfelt from Exxon laboratories was one of the first who developed the so-called bimetallic cluster catalysts and pointed out their peculiar catalytic activity concerning hydrogenation and hydrogenolysis reactions [81–83]. By appropriate co-precipitation and calcination, a cluster of a catalytically active transition metal (Ni or Ru) was partially covered with an inactive coinage metal (Cu, Ag, or Au), whereby the coinage metal existed in the form of a flat, raft-like’ surface array [84]. Therefore, surface scientists became interested in modeling these bimetallic cluster catalysts and prepared, especially, Cu deposits on a flat Ru(0001) surface [85–95]. A survey of the scientific activities focusing on bimetallic surface chemistry has been given by Campbell [96]. In this context it is also of vital interest to scrutinize the influence of nonmetallic, often strongly polarized, additives to metal surfaces, such as oxygen, chlorine, sulfur, or phosphorus (electronegative species) or alkali metals (Na, K, Cs etc., electropositive species) on the adsorption properties of a metal single crystal surface. Here we refer to Goodman’s review [97] in which the influence of electronegative, neutral, and electropositive impurity atoms is discussed in terms of promoting or inhibiting effects for catalytic reactions involving hydrogen and/or carbon monoxide. Mostly, electronic effects (ligand, ensemble effects) are invoked to explain the observed poisoning which is, for a Ni(100) surface, stronger with sulfur than with chlorine or phosphorus; mainly, the hydrogen uptake is suppressed, likely due to a reduction of the hydrogen sticking probability. Returning to the interaction of an alloy or bimetallic surface with hydrogen, both the hydrogen adsorption/desorption kinetics and the energetics of adsorption and diffusion can be affected. A typical kinetic effect occurs, if the H2 sticking coefficient is modified by the alloy’s surface topography (which is frequently the case). Since theories of the H2–surface interaction dynamics [98] predict a strong influence of hydrogen dissociation on the local geometry of an adsorption site, defined ensembles of adjacent TM atoms are believed to be required for nonactivated H2 dissociation. This effect has been proven many times by recording the H uptake as a function of the alloy composition (TM)x(NM)y. Increasing the concentration of the NM resulted in an over-proportional decrease in the H uptake [86, 87, 94], and it was concluded that ensembles of up to four adjacent TM atoms are required to dissociate the H2 molecule and to appropriately adsorb the formed H atoms. Very recently, this expectation was directly confirmed by observing the H2 disso-
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ciation reaction on a Pd(111) surface with atomic resolution by means of low-temperature STM. Three adjacent Pd atoms were found to form an active’ ensemble for H2 dissociation [99]. At this point the important question arises as to whether H atoms formed by dissociation on the active part of a surface will be able to spill over’ to empty sites or patches of the inactive deposit. Many researchers assume that hydrogen transfer of this kind does indeed occur. On heterogeneous catalyst materials consisting of small Ni, Ru, Pd, Ir or Pt clusters dispersed on a silica, alumina, titania, zirconia or carbon support, H spillover has frequently been reported [72, 100–103]. It should be noted here that the literature available for the issue “spill-over of hydrogen” certainly fills several book shelves [100], and there are very important novel aspects of energy technology where the transfer of hydrogen, e.g., from transition metal nanoparticles to carbon nanotubes is considered in order to develop new materials (carbon–metal composites) for hydrogen storage and fuel cell applications [72, 73, 103]. For alloys or bimetallic systems, fewer reports exist in favor of H spill-over. Cruq et al. measured hydrogen adsorption isotherms on pure Ni and (polycrystalline) Cu–Ni alloys and observed hydrogen adsorption on mixed ensembles of Cu and Ni atoms via a spill-over mechanism; H2 molecules were assumed to dissociate only over Ni ensembles [104]. Shimizu et al. studied the adsorption of hydrogen on Cu+Ru(0001) surfaces and could not detect significant transfer of hydrogen atoms from Ru sites to Cu sites at 100 K adsorption temperature [86]. A couple of years later, the same system was re-investigated by Goodman and Peden, and these authors reported non-negligible H spill-over to Cu by raising the adsorption temperature to 230 K; apparently, H transfer from the active Ru sites to the less active Cu sites required a slightly thermally activated surface diffusion step [88]. We reproduce, from their work, the experimental evidence of spill-over, cf. Fig. 25.11. Shown are three H2 thermal desorption traces obtained from a Ru(0001) surface covered with 0.7 monolayers of Cu: curve (a) refers to a H2 saturation exposure at 100 K, (b) to a saturation exposure at 230 K, and (c) is the difference curve (b) – (a) and clearly shows the amount of spillover hydrogen at 230 K. Apparently, it is possible for H2 molecules to dissociate on Ru sites into H atoms which can then migrate to Cu sites where they chemisorb with a binding energy close to that found with genuine Cu(111) surfaces, i.e., ~65 kJ mol–1 [105–107]. Note that this binding (adsorption) energy does not really deviate from the respective values measured for typical transition metals such as Ni or Pd – this suggests that the crucial elementary step is the dissociation (and not the adsorptive binding) which is activated on the noble metal (Cu, Ag, Au...) and nonactivated on the transition metal. From the (slight) thermal activation energy for H migration from Ru to Cu sites suggested by the data of Goodman and Peden [88] it turns out, however, that a H atom chemisorbed on a bimetallic surface can definitely distinguish between TM and NM sites which are apparently separated from each other by slight diffusion barriers.
25.4 Alcohol and Water on Metal Surfaces: Evidence of H Bond Formation and H Transfer Figure 25.11 Selected hydrogen thermal desorption traces obtained from a bimetallic Cu–Ru surface (Cu coverage = 0.7 monolayers on a Ru(0001) surface) as a function of adsorption temperature: The top curve (a) was obtained after the system had received a saturation exposure at 100 K; curve (b) H2 desorption trace after a saturation exposure at 230 K. The dashed line indicates the direct superposition of (a) onto (b). The bottom curve (c) represents the difference (b) – (a) and, hence, is equal to the amount of hydrogen spilled over from Ru to Cu sites at 230 K. After Goodman and Peden [88].
25.4 Alcohol and Water on Metal Surfaces: Evidence of H Bond Formation and H Transfer 25.4.1 Alcohols on Metal Surfaces
In this section some features of hydrogen transfer will be discussed in conjunction with the interaction (adsorption and partial dissociation) of water and aliphatic alcohols (methanol CH3OH, in particular) with selected metal surfaces. Common to these molecules is that they contain a hydroxy group which is (formally) coupled to either a H atom (water) or to an organic rest, for example a methyl group CH3. In the hydroxy group we realize the basic principle of a hydrogen bond mentioned in the introductory section: the close vicinity of an H atom to a strongly electronegative atom, here the oxygen atom (atom “A”). As another electronegative atom (in the simplest case the oxygen atom “B” of an adjacent water or alcohol molecule) is brought close to the H atom in question, the latter can be split off and transferred to the atom “B”, depending on the mutual distance H–B. The situation “A–H–B” is typical for H bonding with its characteristic doublepotential well. Of course, nitrogen, sulfur, or phosphorus atoms can also play the part of the second electronegative atom “B” with the consequence that the double potential well is no longer symmetric. If a hydroxy group-containing molecule interacts with a metal surface, several effects can occur, depending on temperature, on the nature of the adsorbing metal and the adsorbate’s surface concentration. Besides mere adsorption of the molecular entity in various bonding configurations and without or with long-range
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order, dissociation reaction(s) may readily take place. In quite a number of cases, the hydroxy hydrogen atom is actually split off leaving behind either a nude hydroxy group (in the case of water) or an aliphatic oxide (for example, methoxide in the case of methanol). Thermodynamically decisive here is the affinity of the metal surface with respect to adsorbing the split-off hydrogen. The overall energy gain (including the release of the hydrogen adsorption energy) determines whether or not the dissociation process is thermodynamically favored. However, even if the free enthalpy gain of the system suggests the dissociation path, possible kinetic barriers may still prevent a spontaneous dissociation or at least greatly slow down the rate of H transfer to the surface. Looking at Table 25.1, spontaneous O–H dissociation processes of this kind are principally possible with most transition metal surfaces, among others with Ni, Ru, Rh, Pd, Ir or Pt , and have indeed been reported in quite a number of cases. Relatively easy to survey is the adsorption of alcohols on surfaces, because the progress of the O–H dissociation can be followed conveniently by monitoring the molecular orbitals of the fragments by means of UV photoemission or by following their characteristic vibrations by means of electron-energy loss spectroscopy. To some extent, this holds also for the dissociation of water on surfaces, where X-ray photoelectron spectroscopy (XPS), thermal desorption and vibrational loss measurements have been used to prove the existence of the dissociation products – although the respective features are somewhat more difficult to unravel. In 1977 Rubloff and Demuth investigated the interaction of methanol with a Ni(111) surface by means of UV photoemission (UPS) and reported on the formation of a methoxide species, CH3O, plus adsorbed hydrogen [108]; this conclusion was somewhat later confirmed by HREELS measurements [109]. Christmann and Demuth studied the adsorption and decomposition of methanol on a Pd(100) surface [110,111] using UPS, HREELS, work function (Dj) and thermal desorption spectroscopy (TDS) measurements. At 120 K, a small fraction of methanol underwent dissociation into CH3O and H, while the major part adsorbed molecularly in a disordered fashion. During the formation of multilayers, however, TD spectra revealed hints of hydrogen bonding effects, and the formation of a chain-like network made up by H-bonded CH3OH units as displayed in Fig. 25.12 was concluded. Ehlers et al. used infrared reflection–absorption spectroscopy (IRAS) and UPS in conjunction with TDS to follow the interaction of methanol with Pt(111)
Figure 25.12 Schematic sketch of the formation of a H-bonded chain of methanol molecules on a Pd(100) surface as deduced from the energetic and kinetic behavior of the CH3OH thermal desorption spectra. After ref. [110].
25.4 Alcohol and Water on Metal Surfaces: Evidence of H Bond Formation and H Transfer
and reported on the formation of a first undissociated CH3OH layer with the molecules being strongly chemisorbed at their oxygen end, while the IR data suggested strong hydrogen bonding within the second and third monolayer phase [112]. In view of the increasing use of methanol in fuel cells (DMFC = direct methanol fuel cell) the interaction of CH3OH with metal surfaces, especially Pd and Pt surfaces, has been extensively studied in recent years [113–119], based on the idea that the electrooxidation of methanol on the Pt or PtRu anode is one of the decisive reactions in the DMFC. The first step will certainly be the adsorption of methanol on the metal surface, followed by a subsequent dehydrogenation of the hydroxo and/or the methyl group. Stuve et al. [113] have reviewed some of the recent gas phase adsorption and decomposition studies of methanol interaction with metal surfaces and concluded that either a hydroxymethyl (CH2OH) or a methoxide (CH3O) intermediate can be formed on the Pt (PtRu) surface. Both species will then further react with oxygen via other short-living intermediates. After the removal of water a transient CO species is obtained which is then oxidized to the final stable product CO2. An important point in this reaction scenario is whether or not the C–O bond of the methanol molecule is actually cleaved. Here, some discrepancy exists with respect to the electro-oxidation reaction in the condensed phase (DMFC application) and the reaction sequence reported for methanol adsorbed under ultra-high vacuum (UHV), conditions, see below. Chen et al. [118] showed for CH3OH vapor adsorbed on a Pd(111) surface that the dissociation of the C–O bond requires methanol coverages close to one monolayer: Upon heating, most of the methanol (75%) desorbs, but the remaining part (25%) becomes partially dehydrogenated, while some other fraction of CH3OH molecules undergo a bimolecular reaction via 2 CH3OH = CH3O + CH3 + H2O,
whereby the C–O bond is opened. A hydrogen bridge between the two methanol molecules was considered essential for this C–O bond scission reaction. The same system was recently re-investigated by Schennach et al. (combining experimental (TDS) and theoretical (DFT) work) [119]; these authors, too, pointed out that a hydrogen bond between two neighboring methanol molecules adsorbed on a Pd(111) surface is necessary to break the C–O bond. In continuation of the work of Ehlers et al. [112] H bonding effects for methanol monolayers adsorbed on a Pt(111) surface have been deduced from combined Dj and IRAS studies by Villegas and Weaver [117] who emphasized that adsorbed CH3OH layers provided a particularly suitable solvent’ to model a double layer network on a surface, since both the O–H stretching (mOH) and the C–OH stretching vibrations (mC–OH) are sensitive to the local coordination environment. At low coverages, CH3OH adsorbs on Pt(111) in the form of monomers, while at higher coverages clusters stabilized by H bonding are formed. In a recent DFT study Desai et al. [116] have calculated the routes of interaction of methanol with a Pt(111) surface and considered the two reaction channels mentioned above, viz.,
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the dissociation of chemisorbed methanol into either methoxide CH3O plus H or into hydroxyl methyl CH2OH plus H fragments. Intact methanol adsorbs on Pt(111) in an atop site at 25% surface coverage with an adsorption energy of ~ 43.2 kJ mol–1; this relatively weak van-der-Waals-like Pt–CH3OH bonding is concluded also from the rather extended (calculated) Pt–O bond length of 2.59 . The methoxy intermediate, on the other hand, favorably adsorbs in a three-fold hollow site at low coverages H (~ 10% of total monolayer) and switches to the Pt–Pt bridge site as soon as H reaches 25%. The adsorption energy then yields the rather considerable value of 161 kJ mol–1. In this configuration, the CH3O intermediate interacts with the Pt surface through the oxygen atom, forming two Pt–O bonds with 2.51 bond length. The internal C–O bond is tilted by an angle of 65 with respect to the surface plane. In another theoretical contribution by Greeley and Mavrikakis [120] who performed a periodic, self-consistent, DFT calculation, likewise the gas-phase decomposition of methanol on Pt(111) was explored. The reaction starts with O–H dissociation (the rate-limiting step) and proceeds via sequential hydrogen abstraction from the methoxy intermediate towards the final products CO and hydrogen. For several decomposition pathways, the authors present a potential energy diagram as a function of the reaction coordinate. The long-standing controversy in methanol electro-oxidation over Pt and Pd surfaces as to whether the scission of the hydroxy group or the cleavage of a C–H bond of a methyl group (leading to CH2OH) is the primary step has already been touched upon. Davis and Barteau point out [121] that thermodynamic arguments favor the latter mechanism, since the energy required to break a C–H bond is 393 kJ mol–1, whereas 435 kJ mol–1 is the dissociation energy of an O–H bond. However, and this underlines the important role of hydrogen bonding effects, there is – at least for reactions in a condensed aqueous environment – a tendency of the OH group to be solvated by as many as three water molecules [122] which keeps it away from the Pt electrode surface and thus increases the probability that the reaction proceeds via the methyl end of the molecule. Without going further into any details, we simply refer the reader to Franaszczuk et al.’s exhaustive comparison of the electrochemical and gas-phase decomposition pathways of methanol on Pt surfaces [122]. 25.4.2 Water on Metal Surfaces
While these considerations should just illustrate the importance of H bonding effects in electro-catalysis of methanol (which is, as pointed out before, essential for mimicking the oxidation of methanol on the Pt-containing catalyst-electrodes of the DMFC), we move on now to the interaction of water with metal surfaces which is largely dominated by H bonding and H transfer processes. Based on the importance of water in all kinds of biochemical systems a voluminous literature has been accumulated in the past concerning soft’ biological systems which contain water in all kinds of aggregations. Because of space limitations we are unable to enter this (admittedly interesting) field; instead we focus on some of the UHV
25.4 Alcohol and Water on Metal Surfaces: Evidence of H Bond Formation and H Transfer
work on the interaction of H2O with metal surfaces. The state of the art in this field until 1987 has been reviewed by Thiel and Madey [123]; in 2002 Henderson [124] revisited the same topic in an exhaustive review article the reader is referred to for further details. Again, we examine some typical transition metal surfaces, especially the 4d and 5d TMs (Ru, Rh, Pd, Ir, Pt), and pay particular attention to evidence of H bonding and H transfer. As with the alcohol adsorption studies, the experimental techniques of UV photoelectron spectroscopy and especially vibrational loss spectroscopy (HREELS) have proven to be very sensitive tools to identify adsorbed water and its fragments and to monitor the structure of the H2O surface phases formed. As will be shown below these are dominated by H bonding effects. Pioneering HREELS reports about water adsorption on platinum surfaces appeared already in 1980 when Ibach and Lehwald studied the H2O/Pt(100) [125] and Sexton [126] the H2O/Pt(111) system. The observation of three different O–H stretching vibrations at 2850 cm–1, 3380 cm–1 and 3670 cm–1 for water adsorbed on the Pt(100) surface in submonolayer quantities was interpreted as indicating H bonding to Pt, H bonding between oxygen atoms, and O–H bonding in free’ OH groups, respectively [125]. For the Pt(111) surface, Sexton likewise inferred evidence for H bonding from both the presence of a broad librational region between 100 and 1000 cm–1 in the HREEL spectra of water and the exposure (coverage) dependences of the water bending and stretching modes. While the bending (d) modes were almost invariant with coverage (since their frequency is not strongly affected by the O–H bond strength), there was a marked frequency downshift of the stretching (m) modes, caused by a continuous weakening of the O–H bonds due to H bonding [126]. As an example of the water clustering induced by H bonding, we present Ibach’s and Lehwald’s structure model in Fig. 25.13. Structures of this kind are typical for H-bonded water networks and ice formed by continuous exposure of cold metal surfaces to water vapor. Griffiths et al. [127] followed, by means of infrared absorption spectroscopy, the development of the H bonded O–H stretch as a function of water coverage on three different metal surfaces, Ni(110); Pt(100) and Al(100). Only on Ni(110), could H2O monomers be detected, whereas on Pt(100) water clustering very readily took place at 130 K and even at low coverages. On Al(100), a broad distribution of H2O cluster sizes was found which was taken as evidence for a restricted mobility of the adsorbing water molecules after sticking to the surface. In a sense, these observations are symptomatic for the water interaction with metal surfaces, whereupon clustering and network formation far below the monolayer coverage take place, often in the form of bilayers representing a buckled hexagonal arrangement of water molecules interconnected by H bonds. An important observation was communicated by Sexton [126] who found, by means of isotopic labeling (co-adsorption of H2O and D2O), that complete isotopic exchange of hydrogen occurred, indicating a very high mobility of the H and D atoms in the adsorbed water layers. Although isotope exchange is not unusual for ice at room temperature [128], it is nonetheless surprising that such rapid isotopic scrambling takes place within a network of H bonded water molecules on a Pt surface kept at a temperature as low as 100 K. This observation underlines the
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Figure 25.13 Sketch of the structure of water adsorbed at 150 K on a Pt(100) surface stabilized by H bonding. Top: Formation of a (tilted) cyclic water hexamer that accommodates to the Pt surface by forming a “chair”-like arrangement known from the cyclohexane molecule. Bottom: Structure of the network formed by a monolayer of water on the Pt surface: The oxygen atoms are held at distance to the Pt surface atoms by H bonds, thereby forming an open bilayer structure. The lone pair orbitals of the O atoms are indicated. After Ibach and Lehwald [125].
possibility of rapid H transfer even within water clusters or water networks on metal surfaces despite their rigid structure. A more recent HREELS study of the H2O/ Pt(111) system over a wide exposure range and with improved vibrational resolution was reported by Jacobi et al. [129]. They followed the development of networks of H-bonded water molecules from monomers to three-dimensional ice. On Pt(111), a H2O bilayer is formed, and two perpendicular vibrational modes could be distinguished for the top H2O molecules (266 cm–1) and the bottom molecules in contact with the Pt surface (133 cm–1). Very extensive and revealing studies of water interaction with the Ru(0001) surface were performed by Thiel et al. [130, 131] using a variety of techniques (TDS, AES, HREELS, UPS, and ESDIAD = electron-stimulated desorption ion angular distribution). The authors observed several binding states in their TD spectra which develop simultaneously with H2O exposure, again indicating that a first and a second water layer grow at the same time, whereby the second layer is H-bonded to the first layer. In other words, H2O clusters are formed even at low exposures, in agreement with the observations for the Pt surfaces discussed above. The respective bilayer of H2O on Ru(0001) even gave rise to the formation of an ordered p(33)R30 phase with a well-developed diffraction pattern. Accordingly, a careful structure determination of adsorbed D2O on Ru(0001) was performed by Held and Menzel [132] by analyzing the LEED intensities of the p(33)R30 structure. The main result was that the D2O bilayer is almost flat, caused by a periodic displacement of surface Ru atoms in anti-correlation to the
25.4 Alcohol and Water on Metal Surfaces: Evidence of H Bond Formation and H Transfer
water molecules. The construction principle of the bilayer was confirmed to contain chemical bonds between the Ru surface atoms and the O atoms of the closer water molecules, and H bondings from the latter to the other D2O molecules. Apparently, the strength of the Ru–O bonding compares somewhat with the Ru–Ru bond strength leading to the situation that the underlying metal surface must no longer be regarded as a rigid lattice but represents a system that responds dynamically to the presence of adsorbing D2O molecules. The adsorption of water (D2O) on the Rh(111) surface at 20 K has been studied by Yamamoto et al. [133] by means of IRAS, and again, the development of amorphous ice layers beginning with the formation of water monomers, dimers and larger clusters (D2O)n with 3 < n < 6 , via subsequent two-dimensional islands and three-dimensional clusters and ending with bulk amorphous ice layers. The vibrational data were collected with high resolution and sensitivity and carefully assigned to the various stretching and bending frequencies for D2O clusters of different aggregations, n. Interesting conclusions could be drawn with respect to the mobility of the individual water clusters on the Rh surface in comparison to Pt(111) and Ni(111) surfaces: On Rh(111), the migration of water molecules is claimed to be especially hindered, leading to comparatively small 2D islands. This brings us to another peculiar property of adsorbed water molecules and clusters in conjunction with the formation of H bonds, namely, their mobility and dynamical behavior in the adsorbed state. The respective studies are closely tied to the possibility to directly image adsorbed water molecules and clusters by means of scanning tunneling microscopy (STM). The application of this technique to adsorbed water requires low-temperature studies and an appropriately designed low-T-scanning tunneling microscope. Pioneering studies here were communicated by Morgenstern who examined in a sequence of papers the principles of imaging water molecules on Ag(111) surfaces by means of STM [134–136]. In agreement with the studies mentioned above she found that the H2O molecules form simultaneously H-bonded networks of different dimensionalities, in addition to an apparently zero-dimensional structure consisting of a cyclic hexamer with the molecules being adsorbed in on-top positions on the Ag surface [135]. The adsorption, clustering and diffusion of water molecules adsorbed at 40 K on a Pd(111) surface were then followed by means of low-T-STM by Mitsui et al. [137]. At low exposures, water adsorbs in the form of isolated molecules which laterally diffuse and collide with adjacent monomers. H bonding then leads to dimers, trimers, tetramers etc. The most interesting observation was, however, that the mobility of these aggregates on the Pd(111) surface increased by several orders of magnitude for the tetramers, but decreased again for larger aggregates (pentamers etc.). Cyclic hexamers were found to be particularly stable, in agreement with Morgenstern’s observations for H2O on Ag(111). With increasing exposure these hexamers combine to a hexagonal honeycomb network that is commensurate to the underlying Pd(111) surface, forming the same p(33)R30 structure described above for the Ru(0001) surface. The large mobility of small water clusters is explained by a combination of strong H bonding between molecules and the misfit between the O–O distance in the dimer, which is 2.96 in the gas phase, but
781
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25 Hydrogen Transfer on Metal Surfaces
only 2.75 (= the nearest Pd–Pd distance) for the O atoms of an adsorbed H2O dimer (if these O atoms are assumed to be bonded in atop positions on adjacent Pd atoms). The respective observations underline the change in relative strength between intermolecular hydrogen bonds and molecule–substrate bonds as a function of water cluster size and are related to the (macroscopic) wetting properties of a metal surface. A final point remains to be discussed, namely, the ability of the various metal surfaces to dissociate the adsorbing water molecules into OH and H, whereby the split-off H atoms could be transferred to other (co-adsorbed) species – certainly a catalytically very relevant issue, because the respective H transfer is necessary for hydrogenation reactions. Various previous studies into the dissociation properties of water adsorbed on metal surfaces agree insofar as spontaneous dissociation is a relatively unlikely event on the classical’ transition metal surfaces, whereby crystallographically open’ surfaces are expected to be more active with respect to dissociation than flat low-index surfaces. For more reactive materials, e.g., the Al(100) surface, thermally activated water dissociation has been reported [127]. Wittrig et al. investigated the interaction of water with the (12)-reconstructed Ir(110) surface [138] and found that at most ~ 6% of the adsorbed H2O molecules dissociated at 130 K. Similar results were obtained for other surfaces, i.e., spontaneous water dissociation is apparently not a favored route on TM surfaces, regardless of their crystallographic orientation. However, the situation changes considerably, if oxygen atoms are pre-adsorbed. In this case, O–HOH complexes may easily be formed, interconnected by H bonds. From HREELS data, the existence of these complexes was deduced by Thiel et al. [135] for the Ru(0001) surface, from the appearance of certain vibrational losses. Furthermore (and more importantly), a dramatic increase in the water dissociation probability into O and OH was found in the presence of preadsorbed oxygen, for example for the Pt(111)+O system by Fisher and Gland [139, 140] or for the Ir(110)(12) surface by Wittrig et al. [138] using X-ray photoelectron spectroscopy (XPS). The respective distinction was based on the position of the oxygen 1s orbital energy level: For the species (OH2)ad, (OH)ad, and Oad on Pt(111) Fisher and Gland reported orbital energies at 532.2, 530.5, and 528.8 eV, respectively [140]. Another possibility to dissociate water into H and OH is provided by illumination with UV light: As was demonstrated by Gilarowski et al. [141], H2O dissociation could be achieved on a Pt(111) surface by shining the light of a xenon arc lamp (wave length cut-off at 190 nm) on the water-covered surface and watching the development of various vibrational frequencies within the adsorbed layer. A two-route reaction was emphasized. The irradiation led to molecular desorption of water on the one hand, but also to increasing dissociation into OH and H fragments, as monitored by the gradual development of new vibrational losses characteristic of OH bending and the hindered translation of OH. Furthermore, the appearance of a new peak in the thermal desorption spectra could be associated with the OH + H recombination reaction. Energetic arguments suggest that the mechanism of the photo-dissociation with a threshold of 5.2 eV occurs via a substrate excitation.
References
25.5 Conclusion
The interaction of hydrogen and simple molecules containing a hydroxy group (water, methanol) with transition metal surfaces has been surveyed with respect to the possibility of H transfer via lateral diffusion or proton tunneling within the respective adsorbed layers. It was shown that lateral diffusion and transfer of H atoms does indeed occur via both classical diffusion and tunneling. The growth and structure of the respective layers containing OH groups is largely governed by H bonding effects leading, in practically all of the investigated cases, to a relatively open’ network of water or alcohol molecules. Isotopic scrambling thereby indicates an extraordinarily high mobility of H or D atoms.
Acknowledgements
The author gratefully acknowledges financial support of the Deutsche Forschungsgemeinschaft (through SPP 1091) and helpful discussions with Chr. Pauls.
References 1 Bar , A. M., Miranda, R., Alam n, J.,
2
3 4
5 6
7
8
Garcia, N., Binnig, G., Rohrer, H., Gerber, Ch., Carrascosa, J. L., Nature 315 (1985) 253. Knor, Z., in Catalysis Vol.3, J. R. Anderson, M. Boudart (eds.), Springer, Berlin 1982, p.231. Christmann, K., Surf. Sci. Rep. 9 (1988) 1. Davenport, J.W., Estrup, P.J., in The Chemical Physics of Solid Surfaces and Heterogeneous Catalysis, D.A. King, D.P. Woodruff, (eds.), Vol. 3A, Elsevier, Amsterdam 1990, p.1. Groß, A., Theoretical Surface Science, Springer-Verlag, Berlin 2003. Alefeld, G., V lkl, J. (eds.), Hydrogen in Metals, Springer-Verlag, Berlin 1978, Vol. 1 and 2. Conner, Jr., W. C., in Hydrogen Effects in Catalysis, Z. P al, P. G. Menon, (eds.), Marcel Dekker, New York 1988, Ch. 12, p.311 ff. M rtensson, A.S., Nyberg, C., Andersson, S., Phys. Rev. Lett. 57 (1986) 2045.
9 Schmidt, P.K., Christmann, K., Kresse,
10 11
12
13 14 15
16 17
18
G., Hafner, J., Lischka, M., Groß, A., Phys. Rev. Lett. 87 (2001) 096103. Schmidt, P. K., Ph.D. Thesis, FU Berlin 2002. Balooch, M., Cardillo, M. J., Miller, D. R., Stickney, R. E., Surf. Sci. 46 (1974) 358. Kolasinski, K. W., Nessler, W., Bornscheuer, K.-H., Hasselbrink, E., Surf. Sci. 331-333 (1995) 485. Bratu, P., H fer, U., Phys. Rev. Lett. 74 (1995) 1625. Groß, A., Wilke, S., Scheffler, M., Phys. Rev. Lett. 75 (1995) 2718. Eichler, A., Hafner, J., Groß, A., Scheffler, M., Phys. Rev. B59 (1999) 13297. Harris, J., Appl. Phys. A 47 (1988) 63. Christmann, K., Schober, O., Ertl, G., Neumann, M., J. Chem. Phys. 60 (1974) 4528. Alemozafar, A. R., Madix, R. J., Surf. Sci. 557 (2004) 231.
783
784
25 Hydrogen Transfer on Metal Surfaces 19 Einstein, T. L., Schrieffer, J. R., Phys. 20 21 22 23 24
25 26 27
28 29 30 31
32 33
34 35
36
37 38 39
Rev. B 7 (1973) 3629. Grimley, T. B., Proc. Phys. Soc. (London) 90 (1967) 751. Grimley, T. B., Proc. Phys. Soc. (London) 92 (1967) 776. Cui, J. H., Fain, S. C., Phys. Rev. B 39 (1989) 8628. Roelofs, L. D., Hu, G. Y., Ying, S. C., Phys. Rev. B 28 (1983) 6369. Roelofs, L. D., Einstein, T. L., Bartelt, N. C., Shore, J. D., Surf. Sci. 176 (1986) 295. Sokolowski, M., Koch, T., Pfnr, H., Surf. Sci. 243 (1991) 261. Sandhoff, M., Pfnr, H., Everts, H.-U., Surf. Sci. 280 (1993) 185. Christmann, K., Behm, R. J., Ertl, G., van Hove, M. A., Weinberg, W. H., J. Chem. Phys. 70 (1979) 4168. Behm, R. J., Christmann, K., Ertl, G., Solid State Commun. 25 (1978) 763. Christmann, K., Z. Phys. Chem. (NF) 154 (1987) 145. Hara, M., Domen, K., Onishi, T., Nozoye, H., J. Phys. Chem. 95 (1991) 6. Wagner, H., Butz, R., Backes, U., Bruchmann, D., Solid State Commun. 38 (1981) 1155. Butz, R., Memeo, R., Wagner, H., Phys. Rev. B 25 (1982) 4327. Morris, M. A., Bowker, M., King, D. A., Simple Processes at the Gas–Solid Interface, in Chemical Kinetics, Vol. 19, Bamford, C.H., Tipper, C.F.H., Compton, R.G., (eds.), Elsevier, Amsterdam 1984, Ch. I. Naumovets, A. G., Vedula, Y. S., Surf. Sci. Rep. 4 (1984) 365. Roberts, M. W., McKee, C. S., Chemistry of the Metal–Gas Interface, Clarendon Press, Oxford 1979, p.92. (a) Wortman, R., Gomer, R., Lundy, R., J. Chem. Phys. 27 (1957) 1099; (b) Gomer, R., Field Emission and Field ionization, Harvard University Press, Cambridge 1961. Lewis, R., Gomer, R., Surf. Sci. 17 (1969) 333. DiFoggio, R., Gomer, R., Phys. Rev. B 25 (1982) 3490. Ertl, G., Neumann, M., Z. Naturforsch.a 27 (1972) 1607.
40 Seebauer, E. G., Schmidt, L. D., Chem.
Phys. Lett. 123 (1986) 129. 41 Mak, C. H., Brand, J. L., Deckert, A. A.,
George, S. M., J. Chem. Phys. 85 (1986) 1676. 42 Mak, C. H., George, S. M., Surf. Sci. 172 (1986) 509. 43 Mak, C. H., Brand, J. L., Koehler, B. G., George, S. M., Surf. Sci. 191 (1987) 108. 44 Mann, S. S., Seto, T., Barnes, C. J., King, D. A., Surf. Sci. 261 (1992) 155. 45 Auerbach, A., Freed, K. F., Gomer, R., J. Chem. Phys. 86 (1987) 2356. 46 Puska, M. J., Nieminen, R. M., Chakraborty, B., Holloway, S., Nørskov, J. K., Phys. Rev. Lett. 51 (1983) 1083. 47 Puska, M. J., Nieminen, R. M., Surf. Sci. 157 (1985) 413. 48 Whaley, K. B., Nitzan, A., Gerber, R. B., J. Chem. Phys. 84 (1986) 5181. 49 Wang, S. C., Gomer, R., J. Chem. Phys. 83 (1985) 4193. 50 Mate, C. M., Somorjai, G. A., Phys. Rev. B 34 (1986) 7417. 51 Grizzi, O., Shi, M., Rabalais, J. W., Rye, R. R., Nordlander, P., Phys. Rev. Lett. 63 (1989) 1408. 52 Astaldi, C., Bianco, A., Modesti, S., Tosatti, E., Phys. Rev. Lett. 68 (1992) 90. 53 Takagi, N., Yasui, Y., Takaoka, T., Sawada, M., Yanagita, H., Aruga, T., Nishijima, M., Phys. Rev. B 53 (1996) 13767. 54 Badescu, S. C., Salo, P., Ala-Nissila, T., Ying, S. C., Jacobi, K., Wang, Y., Bedrftig, K., Ertl, G., Phys. Rev. Lett. 88 (2002) 136101. 55 Badescu, S. C., Jacobi, K, Wang, Y., Bedrftig, K., Ertl, G., Salo, P., Ala-Nissila, T, Ying, S. C., Phys. Rev. B 68 (2003) 205401; 209903. 56 Okuyama, H., Ueda, T., Aruga, T., Nishijima, M., Phys. Rev. B 63 (2003) 233403; 233404 57 Nobuhara, K., Kasai, H., Nakanishi, H., Okiji, A., Surf. Sci. 507-510 (2002) 82. 58 Nishijima, M., Okuyama, H., Takagi N., Aruga, T., Brenig, W., Surf. Sci. Rep. 57 (2005) 113. 59 Lopinski, G. P., Prybyla, J. A., Estrup, P. J., Surf. Sci. 296 (1993) 9. 60 Sprunger, P. T., Plummer, E. W., Phys. Rev. B 48 (1993) 14436.
References 61 Kostov, K. L., Widdra, W., Menzel, D.
Surf. Sci. 560 (2004) 130. 62 Zambelli, T., Trost, J., Wintterlin, J., Ertl, G., Phys. Rev. Lett. 76 (1996) 795. 63 Trost, J., Zambelli, T., Wintterlin, J., Ertl, G., Phys. Rev. B 54 (1996) 17850. 64 Wintterlin, J., Trost, J., Renisch, S., Schuster, R., Zambelli, T., Ertl, G., Surf. Sci. 394 (1997) 159. 65 Stipe, B. C., Rezaei, M. A., Ho, W., J. Chem. Phys. 107 (1997) 6443. 66 Stipe, B. C., Rezaei, M. A., Ho, W., Science 280 (1998) 1732. 67 Freed, K. F., J. Chem. Phys. 82 (1985) 5264. 68 Baer, R., Zeiri, Y., Kosloff, R., Surf. Sci. 411 (1998) L783. 69 Kohl, D., J. Phys. D: Appl. Phys. 34 (2001) R125. 70 Carette, L., Friedrich, K. A., Stimming, U., Fuel Cells 1 (2001) 5. 71 Mitchell, P. C. H., Parker, S. F., Tomkinson, J., Thompsett, D., J. Chem. Soc., Faraday Trans. 94 (1998) 1489. 72 Mitchell, P. C. H., Ramirez-Cuesta, A. J., Parker, S. F., Tomkinson, J., Thompsett, D., J. Phys. Chem. B 107 (2003) 6838. 73 Watanabe, K., Hashiba, M., Yamashina, T., Surf. Sci. 61 (1976) 483. 74 Sachtler, W. M. H., Le Vide 164 (1973) 67. 75 Ertl, G., in The Nature of the Surface Chemical Bond, Rhodin, T. N., Ertl, G. (eds.), North-Holland, Amsterdam 1979, p. 335. 76 Schneider, U., Castro, G. R., Wandelt, K., Surf. Sci. 287/288 (1993) 146. 77 Linke, R., Schneider, U., Busse, H., Becker, C., Schr der, U., Castro, G. R., Wandelt, K., Surf. Sci. 307–309 (1994) 407. 78 Holzwarth, A., Loboda-Cackowic, J., Block, J. H., Christmann, K., Z. Phys. Chem. 196 (1996) 55. 79 Hebenstreit, E. L. D., Hebenstreit, W., Schmid, M., Varga, P., Surf. Sci. 441 (1999) 441. 80 Gauthier, Y., Schmid, M., Padovani, S., Lundgren, E., BuÐ, V., Kresse, G., Redinger, J., Varga, P., Phys. Rev. Lett. 87 (2001) 036103. 81 Sinfelt, J. H., Bimetallic Catalysis, Wiley & Sons, New York 1983.
82 Sinfelt, J. H., Acc. Chem. Res. 10 (1977)
15. 83 Sinfelt, J. H., Lam, Y. L., Cusamano,
84 85 86 87 88 89
90
91 92
93
94 95 96 97 98
99
100
101 102 103
J. A., Barnett, A. E., J. Catal. 42 (1976) 227. Prestridge, E. B., Via, G. H., Sinfelt, J. H., J. Catal. 50 (1977) 115. Christmann, K., Ertl, G., Shimizu, H., J. Catal. 61 (1980) 397 {Cu on Ru}. Shimizu, H., Christmann, K., Ertl, G., J. Catal. 61 (1980) 412 {Cu on Ru}. Vickerman, J. C., Christmann, K., Surf. Sci. 120 (1982) 1 {Cu on Ru}. Goodman, D. W., Peden, C. H. F., J. Catal. 95 (1985) 321 {Cu on Ru}. Yates Jr., J. T., Peden, C. H. F., Goodman, D. W., J. Catal. 94 (1985) 576 {Cu on Ru}. Houston, J. E., Peden, C. H. F., Blair, D. S., Goodman, D. W., Surf. Sci. 167 (1986) 427 {Cu on Ru}. Houston, J. E., Phys. Rev. Lett. 56 (1986) 375. Harendt, C., Christmann, K., Hirschwald, W., Vickerman, J. C., Surf. Sci. 165 (1986) 413 {Au on Ru}. Goodman, D. W., Yates, Jr., J. T., Peden, C. H. F., Surf. Sci. 164 (1985) 417 {Cu on Ru}. Lenz, P., Christmann, K., J. Catal. 139 (1993) 611 {Ag on Ru}. Lenz-Solomun, P., Christmann, K., Surf. Sci. 345 (1996) 41 {Ag on Ru}. Campbell, C. T., Annu. Rev. Phys. Chem. 41 (1990) 775 {review}. Goodman, D. W., Annu. Rev. Phys. Chem. 37 (1986) 425 {review}. Groß, A., Theoretical Surface Science – A Microscopic Perspective, Springer, Berlin 2003, p. 148 ff., and references given therein. Mitsui, T., Rose, M. K., Fomin, E., Ogletree, D. F., Salmeron, M., Nature 422 (2003) 705. Spillover and Migration of Surface Species on Catalysis, Proc. 4th Intern. Conf. on Spillover, Dalian, China, Can Li, Quin Xin, (eds.), Elsevier, Amsterdam 1997. Baumgarten, E., Denecke, E., J. Catal. 95 (1985) 296. Jung, K.-W., Bell, A. T., J. Catal. 193 (2000) 207. Yang, F. H., Lachawiec, Jr., J., Yang, R. T., J. Phys. Chem. B (2006) 6236.
785
786
25 Hydrogen Transfer on Metal Surfaces 104 Cruq, A., Degols, L., Lienard, G., Fren-
105 106 107 108 109 110 111 112 113
114 115 116 117 118
119 120 121 122
net, A., in Proceedings of the First International Symposium on the Spillover of Adsorbed Species, G. M. Pajonk, S. J. Teichner, J. E. Germain, (eds.), Elsevier, Amsterdam 1983, p. 137. Greuter, F., Plummer, E. W., Solid State Commun. 48 (1983) 37. Anger, G., Winkler, A., and Rendulic, K. D., Surf. Sci. 220 (1989) 1. Luo, M. F., MacLaren, D. A., Allison, W., Surf. Sci. 586 (2005) 109. Rubloff, G. W., Demuth, J. E., J. Vac. Sci. Technol. 14 (1977) 419. Demuth, J. E., Ibach, H., Chem. Phys. Lett. 60 (1979) 395. Christmann, K., Demuth, J. E., J. Chem. Phys. 76 (1982) 6308. Christmann, K., Demuth, J. E., J. Chem. Phys. 76 (1982) 6318. Ehlers, D. H., Spitzer, A., Lth, H., Surf. Sci. 160 (1985) 57. Jarvi, T. D., Stuve, E. M., in Electrocatalysis, Lipkowski, J., Ross, P. N., (eds.), Wiley-VCH, Weinheim 1998, p. 75. Hartmann, N., Esch, F., Imbihl, R., Surf. Sci. 297 (1993) 175. Solymosi, F., Berk , A., T th, Z., Surf. Sci. 285 (1993) 197. Desai, S. K., Neurock, M., Kourtakis, K., J. Phys. Chem. B 106 (2002) 2559. Villegas, I., Weaver, M. J., J. Chem. Phys. 103 (1995) 2295. Chen, J.-J., Jiang, Z.-C., Zhou, Y., Chakraborty, B. R., Winograd, N., Surf. Sci. 328 (1995) 248. Schennach, R., Eichler, A., Rendulic, K. D., J. Phys. Chem. B 107 (2003) 2552. Greeley, J., Mavrikakis, M., J. Am. Chem. Soc. 124 (2002) 7193. Davis, J. L., Barteau, M. A., Surf. Sci. 187 (1987) 387. Franaszczuk, K., Herrero, E., Zelenay, P., Wieckowski, A., Wang, J., Masel, R. I., J. Phys. Chem. 96 (1992) 8509.
123 Thiel, P. A., Madey, T. E., Surf. Sci. Rep.
7 (1987) 211–365. 124 Henderson, M. A., Surf. Sci. Rep. 46
(2002) 1–308. 125 Ibach, H., Lehwald, S., Surf. Sci. 91
(1980) 187. 126 Sexton, B. A., Surf. Sci. 94 (1980) 435. 127 Griffiths, K., Kasza, R. V., Esposto, F. J.,
Callen, B. W., Bushby, S. J., Norton, P. R., Surf. Sci. 307–309 (1994) 60. 128 Water, Franks, F., (ed.), Vol. 2, Plenum Press New York 1973. 129 Jacobi, K., Bedrftig, K., Wang, Y., Ertl, G., Surf. Sci. 472 (2001) 9. 130 Thiel, P. A., Hoffmann, F. M., Weinberg, W. H., J. Chem. Phys. 75 (1981) 5556. 131 Thiel, P. A., Hoffmann, F. M., Weinberg, W. H., Phys. Rev. Lett. 49 (1982) 501. 132 Held, G., Menzel, D., Surf. Sci. 316 (1994) 92. 133 Yamamoto, S., Beniya, A., Mukai, K., Yamashita, Y., Yoshinobu, J., J. Phys. Chem. B109 (2005) 5816. 134 Morgenstern, K., Rieder, K.-H., Chem. Phys. Lett. 358 (2002) 250. 135 Morgenstern, K., Surf. Sci. 504 (2002) 293. 136 Morgenstern, K., Nieminen, J., J. Chem. Phys. 120 (2004) 10786. 137 Mitsui, T., Rose, M. K., Fomin, E., Ogletree, D. F., Salmeron, M., Science 297 (2002) 1850. 138 Wittrig, T. S., Ibbotson, D. E., Weinberg, W. H., Surf. Sci. 102 (1981) 506. 139 Fisher, G. B., Gland, J. L., Surf. Sci. 94 (1980) 446. 140 Fisher, G. B., Sexton, B. A., Phys. Rev. Lett. 44 (1980) 683. 141 Gilarowski, G., Erley, W., Ibach, H., Surf. Sci. 351 (1996) 156.
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26 Hydrogen Motion in Metals Rolf Hempelmann and Alexander Skripov
26.1 Survey
Many metals dissociatively dissolve hydrogen [1–6]. At low H content the metal host lattice is unchanged (apart from a slight lattice expansion), and the hydrogen atoms occupy random sites in the interstitial lattice (e.g. octahedral interstices in Pd or tetrahedral interstitial sites in Nb). In the metal/H phase diagram this regime is called the solid-solution (a) phase. At higher H concentration stoichiometric hydride phases appear, in which the hydrogen atoms form an interstitial lattice with long-range order and in which the host lattice structure may differ from the empty’ host lattice. The hydrogen atom on its interstitial site in the metal (or metal alloy or intermetallic compound) generally may perform motional processes on very different time scales. At very short times the H atom vibrates against its metallic neighbors which, due to their much heavier masses, do not participate in these high frequency vibrations. Depending on H concentration and H–H interaction they can be considered either as local or optical modes. On the time scale of acoustic vibrations of the host lattice, the H atoms move more or less adiabatically according to the distortion pattern imposed by the host phonons and mirror the host density of states. This type of motion is also called a band mode. At much longer times the hydrogen is able to leave its interstitial site and to perform jumps’ to other sites. The quantum mechanical nature of these jumps’ and their spatial/temporal evolution in the lattice are denoted as hydrogen diffusion in metals, and the present chapter is focused on this type of hydrogen motion. Experimentally, hydrogen diffusion can be studied either by measuring appropriate concentration dependent macroscopic physical properties while a metal hydrogen system, starting from a nonequilibrium situation approaches the new equilibrium, or by methods which are sensitive to single jumps. From the latter methods the most relevant ones – anelastic relaxation, nuclear magnetic resonance and quasielastic neutron scattering, are explained in Section 26.2. Experimental results for hydrogen diffusion coefficients and their relevance for the kinetics of hydrogen absorption are presented in Section 26.3. Section 26.4 Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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26 Hydrogen Motion in Metals
deals with the diffusion mechanism, i.e. the evolution of the jump processes on atomistic scales of time and space, for hydrogen in systems of increasing complexity and disorder: pure metals, alloys, intermetallic compounds, and amorphous metals. Section 26.5 is devoted to the single hydrogen site change event (jump’) which due to the light mass of hydrogen at all temperatures is governed by quantum mechanical tunneling (quantum diffusion) instead of thermally activated over-barrier jumps (classical diffusion). Some highlights are the hydrogen tunneling experiments on Nb doped with impurities and on a-MnHx as well as the measurements of rapid low-temperature hopping of hydrogen in a-ScHx(Dx) and in TaV2Hx(Dx). In the concluding remarks of Section 26.6 the essential features of hydrogen motion, particularly in metals, are briefly summarized.
26.2 Experimental Methods
In this section we present a brief overview of experimental methods used to study hydrogen motion in metals. The methods giving microscopic information on the hydrogen jump motion are emphasized. We restrict ourselves to a discussion of the basic principles of these methods only. More detailed consideration of the application of different methods to studies of the hydrogen diffusion in metals can be found in the reviews [7–14]. 26.2.1 Anelastic Relaxation
When a hydrogen atom occupies an interstitial site, it causes an expansion of the host–metal lattice. If the site symmetry is lower than cubic, such a local lattice distortion can be characterized by its orientation. In the case of uniaxial distortion the strain field is described in terms of the strain tensor with the principal components k1, k2 and k3 = k2. Such defects can interact with a shear stress to produce reorientational relaxation (the Snoek effect) [7, 15]. Before application of the stress, equivalent sites with different orientations have the same energy, so that hydrogen atoms are equally distributed among them. Depending on orientation, the applied stress splits the site energies and initiates a relaxation to a new equilibrium hydrogen configuration with preferential occupation of sites with lower energy. Thus, the reorientational relaxation involves local hydrogen jumps between the sites with different orientations of the strain field. If a constant stress is applied, a metal–hydrogen system responds with an immediate elastic strain ee followed by the anelastic strain ea which grows with time to the limiting value ea0. The ratio ea0/ee is a convenient measure of the magnitude of the relaxation; it is called the relaxation strength DR. For the Snoek effect, DR is proportional to (k1–k2)2. The Snoek effect is usually probed in the dynamical regime, for example, by deforming the sample at a certain frequency and measuring the mechanical
26.2 Experimental Methods
damping (internal friction) as a function of temperature. The maximum damping is expected to occur at the temperature at which the reorientation jump rate sR–1 becomes equal to the circular frequency x of the external excitation. In particular, the condition xsR = 1 determines the position of the sound attenuation peak in ultrasonic experiments. In the simple case of a reorientation relaxation with a single type of reorientation jumps, the ultrasonic loss 1/Qu is given by the Debye expression 1 xsR ¼ DR Qu 1 þ x2 s2R
(26.1)
Using Eq. (26.1) it is possible to obtain the temperature dependence of the hydrogen jump rate from the experimental data on ultrasonic loss. The Snoek relaxation measurements are especially informative if they are performed at a number of excitation frequencies. It should be noted that the Snoek effect can be observed only for sufficient elastic anisotropy, k1–k2, of hydrogen sites. For hydrogen in pure b.c.c. metals, the Snoek effect has not been found [16], in spite of the uniaxial symmetry of tetrahedral sites occupied by hydrogen in these materials. It is believed that the absence of the observable Snoek effect is due to the small value of k1–k2 for hydrogen in the tetrahedral sites of b.c.c. metals. Another method using mechanical relaxation for studies of hydrogen motion in metals is based on the dilatational relaxation caused by the long-range hydrogen diffusion (the Gorsky effect) [17, 18]. The Gorsky relaxation is usually measured quasi-statically as an elastic after-effect. The relaxation is initiated by bending a bulk sample of suitable shape (wire, ribbon, disk, etc.). On application of the bending stress, the instantaneous elastic deformation is followed by an additional deformation which is caused by a redistribution of hydrogen atoms over the sample volume. In fact, the stress gives rise to the flow of hydrogen atoms from the compressed side to the stretched side of the sample. Since H atoms cause the lattice expansion, such a process of uphill’ diffusion results in the additional (delayed) deformation. The relaxation is complete when the flow of H atoms caused by the stress is compensated by the diffusion flow due to the H concentration gradient. The chemical diffusion coefficient Dch of hydrogen can be obtained from the relaxation time sG of the elastic after-effect. For example, for a strip of thickness d, the relation between sG and Dch is given by sG = d2/p2Dch
(26.2)
In contrast to the Snoek effect, the Gorsky effect does not depend on the elastic anisotropy. The relaxation strength determined from the Gorsky effect measurements is proportional to the square of the trace of the strain tensor, i.e. to (k1+2k2)2. The measured relaxation strength also contains important information on the thermodynamic factor ¶l/¶c [19], where l is the chemical potential of hydrogen and c is the hydrogen concentration. The relation between the chemical diffusion coefficient Dch (as determined by macroscopic methods employing
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26 Hydrogen Motion in Metals
H concentration gradients) and the tracer diffusion coefficient D (as determined by microscopic methods at equilibrium conditions) is given by [20] Dch ¼
cD ¶l fc kB T ¶c
(26.3)
where fc is the correlation factor (or Haven’s ratio). For small c the value of fc is 1; with increasing H concentration, fc decreases down to values typically between 0.5 and 0.8. Since both Dch and ¶l/¶c can be determined from the same Gorsky relaxation experiment, the Gorsky effect measurements allow one to obtain the tracer diffusion coefficient D. Therefore, these measurements provide a bridge between the macroscopic and microscopic methods of investigation of hydrogen motion. 26.2.2 Nuclear Magnetic Resonance
Nuclear magnetic resonance (NMR) is widely used to evaluate the parameters of hydrogen motion in metals. All three hydrogen isotopes as well as many host-metal nuclei can be employed as natural probes of hydrogen motion. The only serious limitation of applicability of NMR to studies of hydrogen motion is that the samples cannot be magnetically ordered or strongly paramagnetic. There are basically two types of NMR experiments probing the motional behavior of hydrogen: (i) measurements of the NMR linewidths and the nuclear spin relaxation rates giving information on the jump rate of hydrogen atoms, and (ii) measurements of the spin-echo attenuation in applied magnetic field gradients allowing one to determine the tracer diffusion coefficient D. The former type of experiments are based on the sensitivity of NMR parameters to fluctuations of the local magnetic and electric fields. These fluctuations originate from the jump motion of hydrogen atoms. For protons (1H) and tritium nuclei (3T) having nuclear spin I = 12, the motional contributions to the spin relaxation rates are determined by the modulation of the magnetic dipole–dipole interaction between nuclear spins. Since the deuterium (2D, I = 1) and host-metal nuclei with I > 12 have nonzero electric quadrupole moments, they can also interact with fluctuating electric-field gradients. Therefore, for these nuclei the fluctuating electric quadrupole interaction gives an important contribution to the nuclear spin relaxation rates. Measurements of the nuclear spin–lattice (or longitudinal) relaxation rate R1 are most commonly used to obtain information on the hydrogen jump rates. In favorable cases such measurements allow one to trace the changes in the hydrogen jump rate over the range of four decades. However, the measured values of R1 normally also contain additive contributions not related to hydrogen motion, for example, the contribution due to the hyperfine interaction between nuclear spins and conduction electrons. The motional contribution to the spin–lattice relaxation rate, R1m, can be extracted using the difference in the temperature and frequency
26.2 Experimental Methods
dependences of different contributions to R1 [12]. Such a procedure may be effective if the R1 measurements are performed over wide ranges of temperature and resonance frequency. The motional contribution is described by a sum of several terms, each of the general form [12] R1m = <M2>J(xI, xS, sc)
(26.4)
where <M2> is the part of the interaction (dipole–dipole or quadrupole) of the nuclear spin with its environment that fluctuates due to the motion, and J(xI, xS, sc) is the spectral density function that describes the dependence of the fluctuations in M on the resonance frequencies xI and xS of the resonant and nonresonant nuclei, respectively, and on the correlation time sc of the fluctuations. For hydrogen diffusion in metals, sc is approximately equal to the mean residence time sd of a hydrogen atom in an interstitial site. The characteristic feature of the temperature dependence of R1m is the maximum that occurs when xIsd » 1. In other words, the R1m maximum is observed at the temperature at which the hydrogen jump rate sd–1 becomes nearly equal to the (circular) resonance frequency xI. In the limit of slow motion (xIsd >> 1) R1m is proportional to xI–2sd–1, and in the limit of fast motion (xIsd << 1) R1m is proportional to sd, being frequency-independent. Since, for long-range diffusion, the appropriate spectral densities J(xI, xS, sc) cannot be calculated in the analytic form, in order to extract sd–1(T) from the R1m data, one has to rely either on the results of numerical (Monte Carlo) calculations [21–23] or on the model spectral densities [24–26]. The most widely used model is that based on the Lorentzian form of the spectral densities, as introduced by Bloembergen, Purcell and Pound (BPP) [24]. The BPP model correctly describes the main features of the R1m data (including the asymptotic behavior in the limits of fast and slow motion) and provides rather simple expressions relating R1m and sd. Comparison of the BPP results with those of more sophisticated calculations shows that although the absolute sd values derived from the BPP model analysis may be in error by as much as a factor of 2, their relative temperature-dependent behavior is usually far more reliable, resulting in diffusion activation energies that agree to within about 10% with those obtained by other techniques [8]. The range of the jump rates sd–1 that can be effectively probed by the spin–lattice relaxation measurements is 106–1010 s–1. Measurements of the rotating-frame spin relaxation rate R1q are more demanding from the experimental point of view than the R1 measurements. In metal– hydrogen systems, R1q can usually be measured only for protons (1H). However, measurements of R1q are sensitive to much lower jump rates than those of R1; the typical range of sd–1 that can be probed by R1q is 103–107 s–1. Qualitatively, the behavior of R1q in metal–hydrogen systems is similar to that of R1. The maximum of R1q(T) is determined by the condition x1sd » 1, where x1 is the circular frequency of nuclear spin precession in a (weak) rf magnetic field. Since the typical values of x1 are three orders of magnitude smaller than those of the NMR frequency xI, the maximum of R1q is observed at much lower temperature than that of R1. The maximum value of R1q is much higher than that of R1; therefore, the contributions not related to hydrogen motion appear to be less important for R1q.
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26 Hydrogen Motion in Metals
NMR methods of measuring the tracer diffusion coefficient are based on registration of an additional attenuation of the spin-echo signal due to displacement of nuclear spins in an external magnetic field gradient. The application of the field gradient serves to set a spatial scale in a certain direction. In most of the modern experiments, the magnetic field gradient is not static; it is applied in the form of two or more gradient pulses. The fundamental aspects of this pulsed field gradient (PFG) technique are discussed in [8]. The echo attenuation is usually measured as a function of the strength or the length of the gradient pulses. This attenuation is simply related to the displacement of nuclear spins along the direction of the gradient during the time interval between the gradient pulses. Therefore, the PFG technique provides a direct way of measuring the tracer diffusion coefficient D. In metal–hydrogen systems, the range of D values that can be measured by the PFG technique is typically 10–8–10–4 cm2 s–1. The lower limit is determined mainly by the maximum values of the gradient available from the pulse circuitry and by the spin–spin (transverse) relaxation limiting the characteristic time of the echo decay. Modern NMR-PFG spectrometers can generate field gradients up to 250 mT kG cm–1 [27]. The most serious difficulty in applying the PFG technique to metal–hydrogen systems is the presence of the background’ field gradients associated with nonuniform sample magnetization in a static magnetic field [8]. These background’ gradients may be considerable for powder samples with high magnetic susceptibility. The tracer diffusion coefficient and the jump rate are related by the expression D = ftL2/6sd
(26.5)
where L is the jump length of the migrating atoms and ft is the tracer correlation factor. The value of ft is very close to 1 for dilute metal–hydrogen systems, while for concentrated hydrides it may drop to about 0.7. Using the PFG measurements of D and the nuclear spin relaxation measurements of sd for the same sample, it is possible to evaluate the jump length L from Eq. (26.5). Thus, the two types of NMR experiments can be combined to obtain information on the diffusion path. 26.2.3 Quasielastic Neutron Scattering
One of the advantages of quasielastic neutron scattering (QENS) experiments over the relaxation and resonance measurements described above is that they provide information on spatial as well as temporal aspects of elementary processes of diffusion [14, 28, 29]. This is due to the fact that the wavelength of thermal and cold neutrons is comparable to interatomic distances, and at the same time their energy is of the order of typical solid state excitations. Furthermore, the neutron– nucleus interaction is weak. As a consequence neutrons penetrate deeply into matter and are sensitive to bulk properties; multiple scattering processes which, for example, dominate electron scattering because of the strong Coulomb interaction, are only second-order contributions. The proton exhibits a very large incoherent neutron scattering cross section (rinc = 79.9 barn) which is more than one
26.2 Experimental Methods
order of magnitude larger than the incoherent or coherent scattering cross sections of all other nuclei. Incoherent QENS contains information on self-diffusion. Collective hydrogen diffusion, which can be elucidated from coherent QENS on the D isotope, is beyond the scope of the present chapter. For H in metals the measured QENS intensity, after the necessary raw data corrections (background subtraction, detector efficiency, etc.) is proportional to the incoherent scattering function Sinc(Q, x) which can be written as the two-fold Fourier transform (in space and time) of the single-particle, space-time van Hove correlation function, Gs(r,t), Gs(r,t) — FT in space fi Is(Q,t) — FT in time fi Sinc(Q,x)
(26.6)
where Is(Q,t) denotes the self-part of the intermediate scattering function. Gs(r,t) means the probability of finding a particle at r after time t has elapsed since it (the same particle!) started from the origin (r = 0). For translational long-range jump diffusion of a lattice gas the stochastic theory (random walk, Markov process and master equation) [30] eventually yields the result that Gs(r,t) can be identified with the solution (for a point-like source) of the macroscopic diffusion equation, which is identical to Fick’s second law of diffusion but with the tracer (self-diffusion) coefficient D instead of the chemical or Fick’s diffusion coefficient, Gs(r,t) = (4pD |t| )–3/2 exp (– r2/4D |t|) .
(26.7)
Spatial Fourier transformation of the self-correlation function (Eq. (26.7)) yields the intermediate scattering function, Is (Q,t) = exp (–DQ2t)
(26.8)
which is a measure of the probability of finding a H atom, which has been at a certain site at t = 0, still at that site after time t has elapsed; after sufficiently long time this probability vanishes. Subsequent temporal Fourier transformation of the self-part of the intermediate scattering function (Eq. (26.8)) yields a Lorentzian shape for the incoherent scattering function Sinc ðQ; xÞ ¼
1 K p K2 þ ð"xÞ2
(26.9)
with the width (half width at half maximum, HWHM) K = "DQ2
(26.10)
Thus a plot of K vs. Q2 yields a straight line, and from its slope the self-diffusion coefficient is derived. This so-called Q2 law (valid for sufficiently small Q) is indicative of translational diffusion.
793
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26 Hydrogen Motion in Metals
In some intermetallic compounds clusters of isoenergetical sites occur which are well separated from other sites, see for instance the case of TaV2Hx in Fig. 26.4, and which form closed loops; on those loops the H atom performs a spatially restricted jump motion (jump rotation) for some time until, by thermal fluctuations, eventually it is able to jump into the neighboring loop. For rotational diffusion over a loop of N sites after sufficiently long time the H atom can be found on any of the N sites with equal finite probability. The time-independent (i.e. long-time) contribution to Is(Q,t) yields an elastic contribution (x = 0) after temporal Fourier transformation: 2 1 X Is ðQ; ¥Þ ¼ 2 expðiQ Rj Þ ¼ Sinc ðQ; 0Þ N j
(26.11)
sites
this quantity is called the elastic incoherent structure factor, EISF. Although incoherent neutron scattering is single-particle scattering, in this case it bears structural information, namely information about the spatial arrangement of the sites which the H atom visits in the course of its rotational motion. Experimentally, the EISF is the fraction of the total quasielastic’ intensity contained in the purely elastic peak. For an exact’ experimental determination of the EISF the neutron spectra have to be fitted with the correct scattering function which consists of the elastic and a series of quasielastic terms (see [14, 28, 29]). Approximately, however, the EISF can be determined in a kind of model-independent data evaluation by fitting the neutron spectrum with a single Lorentzian plus an elastic term. Although in this way the line shape is not correct (except for N = 2 and 3), the EISF thus obtained allows statements to be made about the geometry for the localized motion. For the present chapter two EISFs, both spatially averaged (for powder samples), are of particular relevance: N = 2 (dumb-bell) hEISF2 i ¼
1 sin ðQsÞ 1 1þ ¼ ð1 þ j0 ðQsÞÞ 2 Qs 2
(26.12)
where s denotes the distance between the two sites; N = 6 (hexagon) hEISF6 i ¼
pffiffiffi i 1h 1 þ 2j0 ðQr Þ þ 2j0 Qr 3 þ j0 ð2Qr Þ 6
(26.13)
where six sites are equally spaced on a circle of radius r. The complete scattering functions for different situations of rotational diffusion can be found in Ref. [29]. QENS is a particularly powerful technique for the investigation of highly ordered metal hydrogen systems. A precondition is a single crystal as a sample, which for intermetallic compounds and their hydrides in most cases is not available up to now. The theoretical description is outlined in Section 26.4.1. QENS is
26.2 Experimental Methods
also very useful for the study of diffusion in disordered systems. A very general and widely used approach is the so-called two-state model; this model was originally developed by Singwi and Sjlander [31] in order to describe the diffusion of water molecules in liquid water and later adapted by Richter and Springer [32] for the diffusion of hydrogen in metals in the presence of impurities. The resulting incoherent scattering function consists of two Lorentzians and bears information about the following spatial and temporal quantities: s1 jump rate over undisturbed parts of the lattice escape rate from the impurities acting as traps s1 0 trapping rate s1 1 ‘ jump length in the undisturbed past of the lattice s distance between two traps This model has been applied by Richter and Springer [32] for H diffusion in Nb doped with nitrogen impurities, by Hempelmann [33] for H diffusion in some intermetallic compounds and by Richter et al. [34] for H diffusion in amorphous metals. 26.2.4 Other Methods
The determination of diffusion coefficients Dch from the evaluation of concentration profiles (mostly after a high temperature diffusion period and subsequent quenching to room temperature), as is common in the investigation of metal atom diffusion in metals or ion diffusion in ionic crystals, is hardly feasible for hydrogen in metals. A very special exemption is the in situ resistance measurement, where a unidirectional flow of hydrogen is detected by measuring the temporal variation of the electrical resistance of a number of sections of a long specimen [35]. Instead, two main types of experiments are possible which enable the macroscopic measurements of hydrogen diffusion in metals, namely relaxation methods and permeation methods. In relaxation experiments, starting from the metal hydride sample in an “old” equilibrium, at t = 0 suddenly a “new” thermodynamic state is created, and it is observed how the sample approaches the “new” equilibrium. For this purpose, the time dependence of any physical property which is concentration dependent can be measured. A special example is the Gorsky effect (elastic after-effect) described in Section 26.2.2 . In an analogous way magnetic aftereffect measurements are possible if the metal hydride is ferromagnetic [36]. These two techniques have the advantage that they are not influenced by surface dependent effects. In other cases the change in the chemical potential is produced by a change in the H concentration, initiated by a step-change of the hydrogen gas pressure. Then the time dependence of the hydrogen absorption process can be followed gravimetrically or volumetrically. In order to be able to extract the hydrogen diffusion coefficient from these data, bulk diffusion (and not, e.g., surface penetration) must be the rate determining step of the complex hydrogen absorption and desorption process. Gravimetric or volumetric mea-
795
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26 Hydrogen Motion in Metals
surements are useful for brittle systems which disintegrate into powder upon hydrogenation. If bulk diffusion is the slow step, the hydrogen content nt at time t of spherical powder particles with radius r is obtained as a solution of Fick’s second law [37]: ¥ nt 6 X 1 m2 p2 Dch t ¼1 2 exp p m¼1 m2 r2 n¥
(26.14)
If t is not too small, the higher-order terms can be neglected and the reaction rate constant is given by kdiff = p 2Dch/r2
(26.15)
In permeation methods, the temporal variation of a diffusion flow into or out of a specimen is measured after a sudden application or removal of an external driving force – the hydrogen pressure or the hydrogen electrochemical potential [38, 39]. A diffusion foil separates two vessels representing the “entrance” and “detection” side. A change in hydrogen concentration or in hydrogen influx rate at the entrance side – starting from a uniform hydrogen distribution within the foil – appears with a certain time lag at the detection side. For instance for a step-change of the surface H concentration at the “entrance” side and an electrochemical detection of the surface H concentration at the “detection” side, the time-lag or breakthrough time tb is related to the diffusion coefficient by tb = 0.755d 2/p 2Dch
(26.16)
where d is the thickness of the foil. A common difficulty of permeation methods is that, in many cases, the surface of the sample acts as a barrier to the flow of hydrogen, and the overall flow rate depends on the surface conditions. This difficulty can be removed, to some extent, by sputter-deposition of a Pd film in ultrahigh vacuum [40]. Usually, possible surface effects are checked by performing experiments on samples of different thicknesses [41].
26.3 Experimental Results on Diffusion Coefficients
Extensive compilations of experimental data on hydrogen diffusion coefficients in binary metal–hydrogen systems have been published by Vlkl and Alefeld [9] and Wipf [42]. These reviews can be referred to as sources of information on H diffusivities in different M–H systems. In this section we shall discuss some general features of H diffusivity in metals resulting from numerous experimental studies.
26.3 Experimental Results on Diffusion Coefficients
For most of the studied metal–hydrogen systems, the temperature dependence of the measured tracer diffusion coefficient of hydrogen follows the Arrhenius law, D = D0 exp(–Ea/kBT)
(26.17)
over wide ranges of T. Here Ea is the activation energy for hydrogen diffusion. Usually Eq. (26.17) is associated with the classical over-barrier jump mechanism of diffusion, Ea being the height of the energy barrier between the potential wells at the nearest-neighbor interstitial sites. However, in many metal–hydrogen systems the experimental values of Ea appear to be considerably lower than the actual depth of the corresponding potential wells. This indicates that tunneling through the barriers should play an important role in the processes of hydrogen diffusion in metals, even at temperatures of the order of room temperature. In fact, the quantum-mechanical theories of diffusion of light particles [10, 43] predict a temperature dependence of the form of Eq. (26.17) for phonon-assisted tunneling at temperatures above about half of the Debye temperature. However, the nature of Ea in these quantum-mechanical approaches differs from that in the classical theory; moreover, the apparent value of Ea in the regime of so-called nonadiabatic transitions (lower temperatures) is expected to be lower than that in the regime of adiabatic transitions (higher temperatures) [10, 43]. We shall emphasize here the following features of hydrogen diffusivity in metals: (i) the strong dependence of D on the host-metal structure, (ii) deviations from the Arrhenius-type temperature dependence of D, and (iii) isotope effects on hydrogen diffusivity. Comparison of the available experimental data on the hydrogen diffusivity (at low H concentrations) in b.c.c. and f.c.c. metals shows that the values of D in b.c.c. metals are generally much higher than in f.c.c. metals, and the corresponding activation energies for H diffusion in b.c.c. metals are lower than in f.c.c. metals. For example, the measured value of D(300 K) in b.c.c. V is 5.410–5 cm2 s–1 and Ea = 0.045 eV (143–667 K), whereas in f.c.c. Pd the corresponding values are D(300 K) = 4.010–7 cm2 s–1 and Ea = 0.23 eV (230–900 K) [42]. The same trend has also been found for metals which can exist in both b.c.c. and f.c.c. modifications. In fact, the transition from the high-temperature c (f.c.c.) phase to the low-temperature a (b.c.c.) phase of Fe leads to considerable increase in the H diffusivity and to an order of magnitude decrease in Ea [9]. Even more spectacular results have been reported [9, 44] for hydrogen diffusion in the Pd0.47Cu0.63 alloy that can have either an ordered b.c.c. structure or a disordered f.c.c. structure in the same range of T including room temperature. The measured value of D(300 K) in the b.c.c. modification appears to be 4 orders of magnitude higher than that in the f.c.c. modification, and the value of Ea in the b.c.c. phase is an order of magnitude lower than that in the f.c.c. phase. The strong difference between the H diffusion parameters in b.c.c. and f.c.c. metals is believed to originate mainly from the geometry of hydrogen sublattices. In b.c.c. metals hydrogen usually occupies tetrahedral interstitial sites which form the sublattice with short nearest-neighbor distances (1.0–1.2 ). Therefore, the energy barriers between
797
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26 Hydrogen Motion in Metals
such sites are expected to be low, and the matrix elements for hydrogen tunneling may be relatively large. On the other hand, in f.c.c. metals hydrogen usually occupies octahedral interstitial sites; the nearest-neighbor distances between these sites are at least a factor of two greater than those for the tetrahedral sites in b.c.c. metals. High H diffusivities and low activation energies have also been found for hydrogen dissolved in many Laves-phase intermetallic compounds [45]. The sublattice of interstitial sites partially occupied by hydrogen in Laves phases is characterized by short nearest-neighbor distances (1.0–1.2 ). Thus, short intersite distances are definitely favorable for the occurrence of fast hydrogen diffusion. The geometry of the hydrogen sublattice in Laves phases will be discussed in Section 26.4.2. For a number of metal–hydrogen systems the temperature dependence of D has been found to deviate from the Arrhenius law at low T. As an example of the data, Fig. 26.1 shows the temperature dependences of the diffusion coefficients of hydrogen isotopes H, D and T in b.c.c. metals V, Nb and Ta, as determined from the Gorsky effect measurements [46]. All the data correspond to very low hydrogen concentrations. It can be seen that there is a marked break in the slopes of the Arrhenius plots for H diffusion in Nb and Ta near 200–250 K. A somewhat less pronounced break in the slope of the Arrhenius plot is also observed for H diffusion in V near 300 K. However, for the diffusion of heavier hydrogen isotopes (D and T) in these metals such breaks in the slope have not been found. It is believed that the break in the slope of the Arrhenius plots for H diffusion reflects the transition from the adiabatic regime of tunneling at high temperatures to nonadiabatic tunneling at lower temperatures. As mentioned above, such a transition is expected to result in a decrease in the apparent activation energy. For heavier hydrogen isotopes this transition should occur at considerably lower temperatures (presumably, out of the actual experimental temperature range). The break in the slope of the Arrhenius plots has also been found for H diffusion in a number of Laves-phase intermetallic compounds where the hydrogen diffusivity is very high. As an example of the data, Fig. 26.2 shows the behavior of D for hydrogen diffusion in the cubic (C15-type) Laves-phase compounds ZrCr2H0.2 and ZrCr2H0.5, as determined from the pulsed-field-gradient NMR measurements [47]. It can be seen that the change in the slope of the Arrhenius plots for these compounds occurs below ~ 200 K. The solid lines in Fig. 26.2 represent the fits of the sum of two Arrhenius-like terms (with different activation energies and pre-exponential factors) to the data. The origin of this effect is assumed to be the same as in the case of H diffusion in b.c.c. metals. We now turn to the discussion of isotope effects in hydrogen diffusivity. The classical diffusion theory predicts that the pre-exponential factor D0 in Eq. (26.17) is inversely proportional to the square root of the mass of a diffusing particle, while the activation energy does not depend on this mass. to these prepffiffiAccording ffi dictions, the diffusion coefficient of D atoms should be 2 times lower than that of H atoms over the entire temperature range. However, the isotope dependence of hydrogen diffusivity in all metal–hydrogen systems studied so far shows deviations from the predictions of the classical theory. In particular, the measured effec-
26.3 Experimental Results on Diffusion Coefficients
Figure 26.1 The diffusion coefficients of hydrogen isotopes H, D and T in b.c.c. metals V, Nb and Ta as functions of the inverse temperature (from Ref. [46]). Note that the vertical scales for the three metals are shifted with respect to each other.
tive activation energy appears to depend on the mass of a diffusing particle. This effect is clearly seen for b.c.c. metals V, Nb and Ta (Fig. 26.1) where EaH < EaD,T. Because of the difference between the activation energies for H and D, the ratio of the diffusion coefficients for H and D in these metals increases with decreasing temperature. These results are consistent with the concept of phonon-assisted hydrogen tunneling. Moreover, the numerical calculations based on this concept [43, 48, 49] show a surprisingly good agreement with the experimental data on hydrogen diffusion coefficients in Nb and Ta. The isotope dependence of the hydrogen diffusivity in f.c.c. metals differs from that in the case of b.c.c. metals. While the ratio of the pre-exponential factors
799
26 Hydrogen Motion in Metals 10-5 C15-ZrCr2H0.2 C15-ZrCr2H0.5
-6
Diffusivity (cm2/s)
800
10
10-7
10-8
10-9
2
3
4
5
6
7
8
103/T (K-1) Figure 26.2 The hydrogen diffusivities in C15-type ZrCr2H0.2 and ZrCr2H0.5 as functions of the inverse temperature (from Ref. [47]). The solid lines represent the fits of the sum of two Arrhenius terms to the data.
pffiffiffi D0H/D0D for f.c.c. metals is usually close to 2 (as predicted by the classical theory), the activation energy for deuterium in a number of f.c.c. metals appears to be lower than that for H. For example, the activation energy for deuterium in Pd derived from the Gorsky effect measurements [50] is 0.206 eV (~220–350 K). This value should be compared to that for H in Pd, EaH = 0.23 eV. Because of the inequality EaD < EaH, the diffusion coefficient of the heavier isotope becomes higher than that of the lighter isotope below a certain temperature (~ 600 K for Pd). The diffusivity of tritium in Pd near room temperature has also been found to exceed that of H [51]. The inequality EaD < EaH has also been reported for hydrogen diffusion in other f.c.c. metals (Cu, Pt, Ni) [42, 52]. A plausible qualitative explanation of the inverse isotope effect on Ea is based on the idea that some excited vibrational states of hydrogen may play an important role in the process of transitions between the interstitial sites in f.c.c. metals [53]; the excitation energy for D is expected to be lower than that for H. In contrast to binary metal–hydrogen systems, little is known about isotope effects on the hydrogen diffusivity in intermetallic compounds. In most of the studied Laves-phase hydrides [54–58] the long-range H(D) diffusion is characterized by the inequality EaD > EaH; in this case the diffusive motion of D atoms is slower than that of H atoms (normal isotope effect). The inverse isotope effect corresponding to the inequality EaD < EaH has been found only for concentrated Laves-phase hydrides HfV2Hx(Dx) and ZrV2Hx(Dx) with x > 3.5 [55]. However, the inverse isotope effect in these systems is likely to result from the difference between the occupancies of inequivalent sites for the hydrides and deuterides [55]. Thus, the origin of this inverse isotope effect may differ from that in f.c.c. metals.
26.4 Experimental Results on Hydrogen Jump Diffusion Mechanisms
26.4 Experimental Results on Hydrogen Jump Diffusion Mechanisms
Detailed atomistic information of the elementary process of jump diffusion can be obtained from QENS at Q values comparable with the inverse jump distances, i.e. at large’ Q [14, 28, 29]. Hydrogen in the a-phases of the cubic f.c.c. and b.c.c. metals Pd, Nb, Ta and V was investigated very early, and the quite detailed results which are now available will be outlined first in Section 26.4.1. One of the rare cases where a hydride single crystal was available is b-V2H, and the corresponding QENS study will be presented in some more detail in the second part of Section 26.4.1. The theoretical basis of all these QENS studies is the Chudley–Elliott model [59], which in its basic form involves the following postulates. 1. All sites involved in the diffusion process are crystallographically and thus also energetically equivalent (Bravais sublattice). 2. All jumps (to nearest neighbor sites only) have the same jump length , and are characterized by jump vectors si, i = 1, .., z where z is the coordination number and |si| = , for all i. 3. The particle stays at a site for a mean residence time s; then instantaneously it jumps to a neighboring site; i.e. the jump time is negligibly small compared to the residence time; C ¼ ðzsÞ1 denotes the jump rate. 4. Successive jumps are uncorrelated, i.e. the jump direction is completely random. This physical picture has been cast into a mathematical model in the form of a so-called master equation z n o ¶ 1 X Pðr; tÞ P r þ sj ; t Pðr; tÞ ¼ ¶s z s j¼1
(26.18)
which says that the temporal change of the occupation probability P of site r (lefthand side of Eq. (26.18)) is due to jumps away from that site (first term on the right-hand side of Eq. (26.18)) and jumps into that site from the neighboring sites r + sj which all exhibit the same occupancy P. Solution of Eq. (26.18) in Fourier space and subsequent spatial Fourier transformation yields a single Lorentzian for the incoherent scattering function (Eq. (26.9)) with the HWHM KðQÞ ¼
z " X 1 expðiQsj Þ zs j¼1
(26.19)
In this basic form the Chudley–Elliott model describes the H diffusion in f.c.c. Pd. A first generalization of the Chudley–Elliott model has been developed in order to deal with crystallographically different hydrogen sites. Crystallographically different sites occur, e.g., for H diffusion over the tetrahedral interstices in b.c.c. metals like Nb. In this case the hydrogen sublattice consists of six superimposed b.c.c.
801
802
26 Hydrogen Motion in Metals
lattices, and the single master equation (Eq. (26.18)) becomes a six-fold differential equation system, which also can be solved in Fourier space yielding a 66 Hermitean jump matrix and eventually an incoherent scattering function consisting of a superposition of six Lorentzians; the negative eigenvalues of the jump matrix are the linewidths whereas the respective weights are given by the eigenvectors. It is practically impossible to fit an individual experimental QENS spectrum with six Lorentzians and to determine six half-widths in this way, but one has to record many QENS spectra (at many |Q| values) in a number of different crystallographic directions and then perform one simultaneous fit of the Q and x dependences in order to extract the atomistic diffusional information. A further generalization of the Chudley–Eliott model allows the sites to be not only crystallographically but also energetically different. In this case the forth and back jump rates Cmn and Cnm between two sites m and n are not equal; they are, however, related by the detailed balance condition to the different site energies, C
En Em ¼ C exp exp nm mn kB T kB T
(26.20)
where Em and En are the potential energies of sites m and n, respectively. The system of differential equations (master equation) can again be transformed into a jump matrix which in this case, however, is not Hermitean; but anyway eigenvalues and eigenvectors can be determined and transformed into the line widths and weights of the set of Lorentzians which represents the incoherent scattering function. Experimentally, again a single crystal as a sample and QENS spectra recorded in different crystallographic directions are necessary to extract atomistic diffusional information which in this case also involves the energetical differences of the sites involved. 26.4.1 Binary Metal–Hydrogen Systems
The very first quasielastic neutron scattering experiments to study the diffusive motion of hydrogen in metals were performed by Skld and Nelin [60] on polycrystalline Pd in the diluted disordered a-phase where the hydrogen atoms occupy octahedral sites. Later Rowe et al. [61] performed a more detailed study in two symmetry directions (<100> and <110>) using single crystals. The resulting line widths are in excellent agreement with the predictions of the Chudley –Elliott model. For reasons of comparison with other methods the resulting mean residence times s taken from a number of quasielastic neutron scattering experiments and from permeation Gorsky effect and NMR measurements are extrapolated to a hydrogen concentration c = 0. The comparison shows that there is fairly good agreement and consistency of these data. In contrast to f.c.c. Pd, striking discrepancies were found for K(Q) for hydrogen in the a-phases of b.c.c. metals, in particular in Nb where hydrogen occupies tetrahedral sites. For hydrogen in the a-phases of b.c.c. metals it was observed by Rowe
26.4 Experimental Results on Hydrogen Jump Diffusion Mechanisms
et al. [62, 63], and Lottner et al. [64, 65] that the experimental linewidths K(Q) at large Q are considerably lower than expected according to the Chudley–Elliott model. This could formally be attributed to effective jump distances considerably larger than expected for jumps into adjacent sites. Lottner et al. [64] have proposed a two-state model: the hydrogen atom alternates between a state of high mobility, the so-called free state, and an immobilized state, the trapped state; in the free state it stays for a time s1 and performs during this time a sequence of transport’ jumps to the respective nearest neighbour sites with transport jump rate’ s–1; in the trapped state the hydrogen stays well localized on a site for a relatively long time s0. The corresponding change-over rates are the trapping rate s1 1 and the . The physical reason for this seemingly strange behavior is the escape rate s1 0 metal lattice relaxation around an occupied hydrogen site (local lattice expansion) which lowers the local site energy but takes some time. The relaxed sites represent the traps; once the hydrogen has managed (by thermal fluctuations) to escape from such a site, it jumps quickly over unrelaxed sites until, after time s1, somewhere apart again lattice relaxation takes place and the hydrogen is trapped. At high hydrogen concentration metal–hydrogen systems form ordered hydrides, particularly at lower temperatures. b-V2H is an example, and its structure is shown in Fig. 26.3. The hydrogen atoms occupy sets of octahedral sites with nearly tetragonal point symmetry which form sheets in (110) directions in pseudocubic notation. The actual symmetry is monoclinic [66]. In this way occupied sheets alternate with empty layers, see Fig. 26.3. A vacancy diffusion mechanism on the hydrogen sublattice, as mentioned above, is ineffective in this case. Actually, as will be explained below, hydrogen diffusion in b-V2H proceeds via an interstitial mechanism on two interstitial sublattices: some hydrogen atoms
Figure 26.3 Structure of b-V2H, explanation in the text.
803
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26 Hydrogen Motion in Metals
occupy sites in the forbidden layer, i.e. anti-structure sites or, in other words, they form Frenkel defects. These are the hydrogen atoms which are significant for the diffusion process; usually, however, they cannot be investigated by means of QENS since their number is too small. In b-V2H, however, the situation is fortunate: with increasing temperature more and more of the sites in the forbidden’ layers are occupied, and at 448 K an order–disorder transition to the e-phase occurs in which the hydrogen atoms are randomly distributed over both types of layers. At 390 K £ T £ 440 K, the temperatures of the QENS study of Richter et al. [67], the number of H atoms on anti-structure sites turned out to be sufficient to be detectable by means of QENS. The master equation system for H diffusion in b-V2H is given by 4 4 ¶Pðr; tÞ 1 1 1 X 1 X ¼ þ Pðr; tÞ þ Pðr þ Si ; tÞ þ U r þ S0i ; t ¶t s s0 4s i¼1 4s1 i¼1
(26.21)
4 4 ¶U ðr; tÞ 1 1 1 X 1 X ¼ U ðr; tÞ þ þ U ðr þ Si ; tÞ þ P r þ S0i ; t (26.22) ¶t su s1 4su i¼1 4s0 i¼1
Here P(r,t) and U(r,t) denote the probabilities of finding a hydrogen in the occupied and unoccupied layers, respectively; s –1 and s1 u are the jump rates within the occupied and unoccupied layers, respectively (both along the jump vectors S1 1 to S4), and s1 0 and s1 are the change-over rates from the occupied to the empty layer and vice versa, respectively (both along the jump vectors S01 to S04 ). This jump model yields a 22 jump matrix and subsequently an incoherent scattering function consisting of two Lorentzians. The quantitative data evaluation in terms of this model allowed the derivation of the four jump rates and led to the following picture: Let us consider a hydrogen atom starting in the filled layer. Then, depending on temperature (in the temperature range 390 K £ T £ 440 K), the jump probability to change into the empty layer is 6 to 3 times higher than to move among the occupied sites. If the hydrogen has changed into the empty layer, then on average it performs 5 to 2 jumps before it drops back into a vacancy in one of the adjacent filled layers. Thus the diffusion parallel to the sheets consists of repeated trapping and release processes between the filled and empty layers. In particular, at lower temperatures, where the ratio between the fast jump rate in the empty layer and all other rates is the largest, hydrogen diffusion is strongly anisotropic. 26.4.2 Hydrides of Alloys and Intermetallic Compounds
In alloys and intermetallic compounds the sublattices of interstitial sites usually have rather complex structures. Furthermore, hydrogen atoms dissolved in alloys and intermetallics can occupy a number of inequivalent types of interstitial sites.
26.4 Experimental Results on Hydrogen Jump Diffusion Mechanisms
These features may give rise to a coexistence of several types of H motion with different characteristic jump rates. Here we shall discuss the experimental results on hydrogen jump diffusion mechanisms in a number of representative intermetallic compounds. A comprehensive review of the experimental studies in this field before 1992 can be found in Ref. [11]. Among intermetallics, hydrogen diffusion has been most extensively studied in Laves phases AB2 which can have either the cubic (C15-type) or the hexagonal (C14-type or C36-type) structures. Many of the Laves-phase compounds are known to absorb considerable amounts of hydrogen forming solid solutions AB2Hx with wide homogeneity ranges [68, 69]. NMR experiments on TiCr1.8Hx (C15) and TiCr1.9Hx (C14) [70] and on C15-type ZrV2Hx and HfV2Hx [71] have revealed significant deviations of the measured nuclear spin relaxation rates from the behavior expected for a single frequency scale of H motion. The unambiguous evidence for the coexistence of two hydrogen jump processes with different characteristic frequencies in a cubic Laves phase was found in the series of NMR measurements on the C15-type TaV2 – H(D) system [54, 72, 73]. These measurements have revealed the temperature dependence of the nuclear spin–lattice relaxation rate R1 with two well-separated peaks. The two frequency scales of H jump motion may be related to the structural features of the sublattice of interstitial sites. In cubic Laves phases, H atoms usually occupy only 96g sites (coordinated by [A2B2] tetrahedra) at low and intermediate hydrogen concentrations (up to x » 2.5) [68, 69]. In particular, only g sites are occupied by H(D) atoms in TaV2Hx(Dx) over the entire range of attainable H(D) concentrations (x £ 1.7) [74]. For cubic Laves phases absorbing greater amounts of hydrogen, 32e sites (coordinated by [AB3] tetrahedra) start to be filled at x > 2.5. The spatial arrangement of interstitial g and e sites in the C15-type lattice is shown in Fig. 26.4. The sublattice of g sites consists of regular hexagons lying in the planes perpendicular to the <111> directions. Each g site has three nearest neighbors: two g sites (on the same hexagon) at a distance r1 and one g site (on the adjacent hexagon) at a distance r2. The ratio r2/r1 is determined by the positional parameters (Xg and Zg) of hydrogen atoms at g sites. Examination of the available neutron diffraction data for cubic Laves-phase deuterides reveals strong changes in the ratio r2/r1 from one compound to another. For example, the value of r2/r1 is 1.45 for TaV2Dx [76], 1.07 for ZrCr2Dx [77] and 0.78 for YMn2Dx [78]. In the case of TaV2Dx(Hx), the g-site hexagons are well separated from each other. Therefore, a hydrogen atom is expected to perform many jumps within a hexagon before jumping to another hexagon. In this case, the faster jump rate sl–1 can be attributed to the localized hydrogen motion within g-site hexagons, and the slower jump rate sd–1 can be associated with hydrogen jumps from one g-site hexagon to another. The results of QENS measurements for TaV2Hx [76] are consistent with this microscopic picture of H motion. First, on the frequency scale of sl–1 the measured QENS spectra S(Q, x) are well described by the sum of a narrow elastic line and a broader quasielastic line having Q-dependent intensity, but Q-independent width. These features are typical of the case of spatially-confined (localized) motion [14].
805
26 Hydrogen Motion in Metals
Figure 26.4 The spatial arrangement of interstitial g sites (dark spheres) and e sites (light spheres) in the C15-type lattice [75].
Second, the Q-dependence of the measured elastic incoherent structure factor (EISF) appears to be in excellent agreement with the predictions of the model of localized atomic motion over a hexagon (Eq. (26.13)) with the distance between the nearest-neighbor sites equal to the experimental r1 value. As an example of these results, Fig. 26.5 shows the behavior of the EISF for TaV2H1.1 as a function of Q at several temperatures. The solid curves represent the fits of the six-site model to the data. In these fits the distance between the nearest-neighbor sites has been fixed to its value resulting from the structure, r1 = 0.99 , so that the 1.2
TaV2H1.1 1.0 0.8
EISF
806
0.6
0.2
105 K 200 K 250 K 300 K
0.0 0.0
0.5
0.4
1.0
1.5
2.0
2.5
Q (A-1) Figure 26.5 The elastic incoherent structure factor for TaV2H1.1 as a function of Q at T = 105, 200, 250 and 300 K [76]. The solid lines represent the fits of the six-site model with the fixed r1 = 0.99 to the data.
26.4 Experimental Results on Hydrogen Jump Diffusion Mechanisms
only fit parameter is the fraction p of H atoms participating in the fast localized motion. The results presented in Fig. 26.5 indicate that the fraction p increases with increasing temperature. A similar microscopic picture of hydrogen motion has been observed for other cubic Laves-phase hydrides with exclusive g-site occupation and r2/r1 > 1: ZrCr2Hx [77], ZrMo2Hx [79], HfMo2Hx [80] and ZrV2Hx [81]. However, in these systems the difference between the two frequency scales of H motion appears to be smaller than in TaV2Hx. For example, at 300 K the value of sd/sl is 5.2103 for TaV2Hx, 240 for ZrV2Hx and 20 for ZrCr2Hx [45]. This decrease in sd/sl correlates with the decrease in r2/r1 [45]. Furthermore, the observed variations of r2/r1 caused by changes in the positional parameters of hydrogen atoms at g sites can be rationalized in terms of the metallic radii RA and RB of elements A and B forming the AB2 intermetallic. In fact, since g sites are coordinated by two A and two B atoms, one may expect that the positional parameters Xg and Zg (and hence, r2/r1) are related to RA/RB. The experimental values of r2/r1 for paramagnetic C15-type hydrides AB2Hx(Dx) where both A and B are transition metals exhibit nearly a linear decrease with increasing RA/RB [45]. Thus, the ratio RA/RB gives a key to understanding the systematics of the two frequency scales of H motion in cubic Laves-phase hydrides. In particular, the highest value of sd/sl for TaV2Hx can be related to the anomalously low RA/RB ratio (= 1.090) for TaV2. For cubic Laves-phase compounds with RA/RB > 1.35, the r2/r1 ratio becomes less than 1. In this case, each g site has only one nearest neighbor lying at the adjacent hexagon. Such a transformation of the g-site sublattice may lead to a qualitative change in the microscopic picture of H jump motion: the faster jump process is expected to be transformed into the back-and-forth jumps within pairs of g sites belonging to adjacent hexagons. The results of recent QENS experiments [78] on YMn2Hx (RA/RB = 1.425, x = 0.4, 0.65 and 1.26) are consistent with these expectations. At high H content (x > 2.5) hydrogen atoms start to occupy e sites in C15-type hydrides, the relative occupancy of e sites increasing with x. Each e site has three nearest-neighbor g sites (see Fig. 26.4) at a distance r3 comparable to the g–g distances r1 and r2; the exact value of r3 depends on the positional parameters of H atoms at e sites (Xe) and g sites (Xg, Zg). The partial e-site filling makes the microscopic picture of H motion less tractable. However, one may generally expect that the partial occupation of e sites leads to an increase in the long-range H mobility due to the opening of new diffusion paths. This effect is well documented for ZrV2Hx [55, 82]. The coexistence of at least two frequency scales of hydrogen jump motion has also been found in a number of hexagonal (C14-type) Laves-phase hydrides [77, 83, 84]. As an example of the data, Fig. 26.6 shows the temperature dependences of sl–1 and sd–1 obtained from QENS measurements for C14-type HfCr2H0.74 [84]. It can be seen that in the studied temperature range the behavior of both sl–1(T) and sd–1(T) is satisfactorily described by the Arrhenius relation; the values of the activation energies derived from the Arrhenius fits are 122 meV for sl–1 and 148 meV for sd–1. The microscopic picture of H motion in C14-type compounds
807
26 Hydrogen Motion in Metals 1012 HfCr2H0.74 -1
τl
1011
-1
-1
(s-1)
τd
1010
τ
808
109 2
3
4
5
6
103/T (K-1) Figure 26.6 The hydrogen jump rates sl–1 and sd–1 in C14-type HfCr2H0.74 as functions of the inverse temperature. The jump rates are obtained from QENS experiments [84]. The solid lines are the Arrhenius fits to the data.
has been addressed in the QENS study of ZrCr2Hx [77] (note that ZrCr2 may exist in the form of either the hexagonal or the cubic C15 modification). At low hydrogen concentrations H atoms occupy the tetrahedral sites with [A2B2] coordination. In contrast to the C15 structure where all [A2B2] sites are equivalent (g sites), in the C14 structure there are four inequivalent types of [A2B2] site (h1, h2, k and l). The sublattice of [A2B2] sites in the C14 structure [85] also consists of hexagons; however, these hexagons are formed by inequivalent sites: h1 – h2 – h1 – h2 – h1 – h2 (type I hexagons) and k – l – l – k – l – l (type II hexagons). All the distances between the nearest sites within the hexagons appear to be shorter than the distances between the nearest sites on different hexagons [77]. Therefore, the general features of the microscopic picture of H motion in C14-ZrCr2Hx are expected to be similar to those of H motion in C15-type compounds with g-site occupation and r2/r1 > 1. The experimental QENS results for C14-ZrCr2H0.5 [77] have been interpreted in terms of the model neglecting the small difference between type I and type II hexagons and the difference between the l–l and k–l distances in type II hexagons. The observed Q-dependence of the EISF for C14-ZrCr2H0.5 is well described by the model of localized H motion over hexagons with the intersite distance = 1.16 , where is the weighted average of the intersite distances for type I and type II hexagons. Since the sublattice of [A2B2] sites in C14-type compounds is more complex than that in C15-type compounds, the detailed microscopic picture of H motion in hexagonal Laves phases may imply more than two frequency scales. In order to clarify the systematics of H jump processes in hexagonal Laves-phase hydrides, further QENS experiments (combined with neutron diffraction studies of hydrogen positions) are required. Another important class of hydrogen-absorbing intermetallics is represented by LaNi5 and the related materials (the hexagonal CaCu5-type structure). The detailed microscopic picture of H motion in this lattice has been investigated by QENS on
26.4 Experimental Results on Hydrogen Jump Diffusion Mechanisms
single-crystalline samples of a-LaNi5Hx [86]. Figure 26.7 shows the structure of a-LaNi5Hx. Hydrogen atoms can occupy two types of sites: 3f (corresponding to lower site energy) and 6m (higher site energy). While the sublattice of 3f sites forms infinite layers in the basal planes, the sublattice of 6m sites consists of regular hexagons well separated from each other (Fig. 26.7). The sublattices of f and m sites are interconnected by jump vectors such that a diffusing H atom can reach eight m sites from each f site and four f sites from each m site. Since the studied a-LaNi5Hx samples were single-crystalline, the analysis of the QENS data [86] benefited from the possibility to direct the neutron momentum-transfer vector Q either parallel or perpendicular to the c axis. It has been found that the faster jump process in this system corresponds to localized H motion within the hexagons formed by m sites. The slower frequency scales are associated with H jumps between the sublattices of f and m sites and with H jumps in the f-site layers. Another example of an interesting H jump diffusion mechanism has been reported for hydrogen dissolved in the cubic A15-type compound Nb3Al [87]. In this compound H atoms occupy the tetrahedral 6d sites coordinated by four Nb atoms. The 6d sites form three sets of nonintersecting chains in the <100>, <010> and <001> directions. The distance between the nearest-neighbor d sites in the
Figure 26.7 (a) The structure of a-LaNi5Hx. A–D denote four possible jumps between neighboring interstitial sites. Host metal atoms are partially omitted for clarity. (b) The geometrical representation of the hydrogen sublattice. The 3f sites form infinite layers in the basal plane. The 6m sites are grouped to form regular hexagons in the z = 12 plane (from Ref. [86]).
809
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26 Hydrogen Motion in Metals
chains is 22% shorter than the shortest distance between d sites on different chains. In this case the faster jump process corresponds to one-dimensional H diffusion along the chain, while the slower process implies H jumps from one chain to another. Other well-documented examples of two coexisting frequency scales of H jump motion include the high-temperature cubic phase of Mg2NiH4 [88], the cubic Ti2Ni-type compounds Ti2CoHx [89] and the rhombohedral Th2Zn17-type compound Pr2Fe17H5 [90]. The motion of hydrogen dissolved in disordered alloys is usually described in terms of broad distributions of H jump rates [91, 92]. 26.4.3 Hydrogen in Amorphous Metals
Hydrides of amorphous metals have been investigated to some extent in the last twenty years, mainly for their potential use in hydrogen storage technology; see, for instance Ref. [93] and references therein. Pressure–composition isotherms, for example of Zr–Ni alloys, deviate strongly from Sievert’s law at higher H concentration. These positive deviations have been attributed to a distribution of site energies in the amorphous structure, and H atoms entering successively higherenergy states. This behavior is reviewed by Kirchheim [93] and brought into correlation with diffusion. Generally, interstitial H diffusion is more or less strongly dependent on the H concentration, where this dependence is due to site energy disorder giving rise to a saturation effect of low-energy sites. In the simplest approach, a Gaussian site-energy distribution is assumed [39]. Additionally it is assumed that the energy levels of the potential barriers (in the picture of classical over-barrier jumps) have the same energy value throughout the sample, i.e. do not exhibit an energetic distribution (constant saddle-point energy). In the literature this model is known as the Gaussian model. Kondratyev et al. [94] have analyzed the available experimental data of hydrogen diffusion in amorphous alloys and presented a review of the existing theoretical approaches noting that the influence of short range order on the hydrogen diffusion was not properly taken into account in previous studies. They propose a model with specific features of the respective amorphous structure and derive general expressions for the diffusion coefficient of hydrogen in amorphous metals and binary alloys with f.c.c.-like short-range crystalline order. QENS studies of H in amorphous metal hosts give contradictory results. While Schirmacher et al. [95] interpret their results on H diffusion in amorphous (a) Zr76Ni24 in terms of a broad continuous distribution of activation energies, Richter et al. [34] find the existence of energetically well-separated interstitial sites in a-Pd85Si15H7.5. So-called anomalous diffusion [96] means that in the time scale of interest the mean square distance walked by the diffusing particle increases sublinearly instead of linearly with time. Also the conjecture that the network of diffusion paths exhibits fractal character leads to such a sublinear time dependence: hr 2 ðtÞit2=ð2þHÞ , where H describes the range dependence of the diffusion coefficient on the fractal network Dr H [97]. For the Q dependence of the quasielastic
26.4 Experimental Results on Hydrogen Jump Diffusion Mechanisms
linewidth K this implies K Q 2þH , i. e. K is expected to grow faster than Q2. The experimental observation of K Q 1:54 does not support the assumption of anomalous diffusion or of a dominating fractal structure for the diffusion paths. The QENS data on amorphous Pd85Si15H7.5 could successfully be evaluated in terms of a diffusion and trapping model. Figure 26.8 shows the Q dependences of the weight of the narrow component and of both line widths. The temperature dependence of the weight shows that the hydrogen atoms are activated from energetically more stable sites, which could be called traps, into a state of high mobility. (a)
(b)
Figure 26.8 (a) Weight of narrow QENS component of H in a-Pd85Si15H7.5 as a function of temperature and momentum transfer. (b) T and Q dependences of the linewidths. The solid lines represent a fit of the two-state model to these data. Inset: magnification of the small Q behaviour of the linewidths at 373 K (dashed line: HWHM Q2) (from Ref. [34]).
811
812
26 Hydrogen Motion in Metals
From the Q dependence a mobility range of about 10 is obtained. For the mobile state the isotropic Chudley–Elliott model is assumed. The result of a fit with this two-state model is shown by the solid line in Fig. 26.8; obviously a reasonable agreement between model and fit is achieved. In particular, the diffusion process in between traps is considerably faster than in crystalline Pd, whereas, as a consequence of trapping, the long-range diffusion coefficient is of the same order. At small Q the character of the narrow mode already crosses over from diffusive (KQ 2 ) to localized behavior ðK1=s0 Þ; this explains a Q exponent smaller than 2, as found experimentally. The observation of two well-separated regimes of jump rates is evidence for the existence of two different kinds of interstices. Actually, by means of neutron vibrational spectroscopy [98], vibrational modes typical for octahedral and tetrahedral sites have been detected. Schirmacher [99] and Wagner and Schirmacher [100] interpret their QENS data on a-Zr76Ni24H8 in terms of an effective medium description of anomalous diffusion in disordered systems with a broad distribution of activation energies. On the other hand, Apih et al. [101] in their NMR study of the hydrogen tracer diffusion coefficient in a Zr69.5Cu12Ni11Al7.5 metallic glass have observed an Arrhenius law for the temperature dependence, which suggests a well-defined hydrogen site energy, and they have not found any appreciable H concentration dependence of the diffusion coefficient.
26.5 Quantum Motion of Hydrogen
While a rigorous description of elementary H jumps in metals should imply tunneling even at room temperature [6, 43], for most of the studied systems the experimental data on hydrogen jump rates can still be approximated by the Arrhenius-like temperature dependences over extended T ranges. In this section we shall discuss the behavior of hydrogen in a number of systems where a quantummechanical description is essential for understanding the basic features of hydrogen motion. Hydrogen dynamics in these systems is characterized either by unusual temperature dependences of the jump rates or by quantum delocalization of hydrogen. For particles moving in a periodic crystal field, one may expect the formation of Bloch states at very low temperatures. However, such a long-range coherent tunneling dynamics has not been observed for hydrogen in metals, most probably because of lattice distortions and interactions between interstitial atoms that prevent the formation of band-like states for relatively heavy particles (as compared to electrons). On the other hand, the effects of quantum delocalization of hydrogen over small groups of closely-spaced interstitial sites have been found experimentally in some metal–hydrogen systems to be discussed below. The simplest model describing general features of hydrogen tunneling is that of a particle in a double-well potential (Fig. 26.9). If the positions of the two minima are close to each other, and the barrier between them is not too high, one may expect an overlap of the ground-state wavefunctions of a particle oscillating in
26.5 Quantum Motion of Hydrogen
Figure 26.9 Schematic representation of a double-well potential with asymmetry e. The tunnel-split ground state levels of hydrogen are shown by solid horizontal lines.
either of the two wells. In this case, the wavefunctions of the system are given by linear combinations of the wavefunctions of a particle oscillating in the left (WL0) and right (WR0) wells: Ws = aWL0 + bWR0
(26.23)
Wa = aWR0 – bWL0 .
(26.24)
For a symmetric double-well potential, a2 = b2 = 12, so that the particle is delocalized and equally distributed over both potential wells. In analogy to the binding and antibinding orbitals of the H2 molecule, the symmetric and antisymmetric wavefunctions exhibit slightly different energy eigenvalues, and this small energy difference is called the tunnel splitting J. The value of J is determined by the matrix element of the Hamiltonian between the states WL0 and WR0 in the localized representation; it can be calculated for some specific shapes of the doublewell potential [53, 102, 103]. All these results imply that J decreases exponentially with the increasing barrier height, particle mass, and well separation, although precise numerical factors change from one model to another. If the double-well potential is characterized by the asymmetry e (see Fig. 26.9), the splitting of the ground state is given by DE = (J2 + e2)1/2
(26.25)
and the normalization factors, a2 + b2 = 1, are related as 2 a J 2 þ e2 ¼ b J2
(26.26)
Thus, the asymmetry of the potential leads to the increase in the splitting and to the partial localization of the particle in the minimum with lower energy. The tunnel splitting of the ground-state energy level of hydrogen can be directly probed by inelastic neutron scattering (INS). If DE >> kBT, the energy exchange between neutrons and the tunneling system corresponds to the transitions between the two well-defined states. In this case, the INS spectrum is expected to
813
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26 Hydrogen Motion in Metals
show two peaks at the energy transfer of –DE (in addition to the elastic peak at zero energy transfer). The intensities of these two peaks are related by the condition of detailed balance, and the width of the peaks is determined by the coupling of the tunneling system to its environment (phonons and conduction electrons). The expressions for the double differential neutron scattering cross-section in the case of a tunneling system interacting with its environment were derived and discussed in Refs. [104, 105]. 26.5.1 Hydrogen Tunneling in Nb Doped with Impurities
Hydrogen trapped by interstitial impurities (O, N or C) in niobium represents a particularly interesting case of localized motion governed by quantum-mechanical effects. The impurity atoms occupy the octahedral interstitial sites in the b.c.c. lattice of Nb, and the trapped hydrogen can jump between a small number of nearby tetrahedral sites. Most probably, the localized H motion occurs between two equivalent tetrahedral sites (at a distance of » 1.17 from each other) located at a distance of » 3.40 from the trapping atom [42]. It should be noted that in impurity-free b.c.c. Nb hydrogen diffusion can hardly be studied below 100 K, since in this temperature range all hydrogen atoms are in the precipitated hydride phase. The trapping of hydrogen by interstitial impurities provides an alternative to the phase separation preventing the precipitation of the hydride. Certainly, this scenario is operative only for small hydrogen/impurity concentrations (up to approximately 1 at.%). The existence of internal excitations in these systems involving very small energies was first revealed in heat capacity measurements at low temperatures [106, 107]. These measurements have demonstrated that the heat capacity anomalies below 2 K previously observed in V, Nb and Ta are, in fact, due to the presence of small amounts of dissolved hydrogen. Moreover, the strong effect of isotope (H«D) substitution on the heat capacity anomaly suggests the possibility of some tunneling motion of hydrogen. Subsequent measurements of the heat capacity of Nb samples doped with O(N) and H(D) [108–110] have clarified the nature of the low-temperature excitations. It has been shown that the low-temperature heat capacity results are consistent with the model of H(D) tunneling in a double-well potential produced by a trapping atom. The quantitative analysis taking into account a distribution of the energy shifts e for the hydrogen ground-state levels due to lattice distortions yields the following values of the tunnel splitting [110]: J = 230–10 leV for H trapped by O and J = 170–10 leV for H trapped by N. For deuterium the values of the tunnel splitting derived from the heat capacity data appear to be an order of magnitude smaller than those for H (20–1 leV for D trapped by O and 14–1 leV for D trapped by N). The strong isotope dependence of the tunnel splitting is also consistent with the ultrasonic attenuation data for Nb with N traps [111]; however, the absolute value of J for the trapped hydrogen obtained from the ultrasonic experiments is about 20% smaller than that found from the heat capacity measurements.
26.5 Quantum Motion of Hydrogen
Direct evidence for the existence of the tunnel-split hydrogen states has been obtained from the high-resolution neutron spectroscopic experiments [104, 105, 112, 113]. These experiments have revealed well-defined peaks at the energy transfer of ~ 0.2 meV in the low-temperature neutron spectra of Nb(OH)x, Nb(NH)x and Nb(CH)x. As an example of the data, Fig. 26.10 shows the neutron spectra of Nb(OH)0.0002 at 0.2 K and 4.3 K [112]. The peak at the energy transfer of ~ 0.2 meV (which at T = 4.3 K is clearly seen both for the neutron energy loss and the neutron energy gain) originates from excitations between the tunnel-split ground states of hydrogen. The values of the tunnel splitting obtained from the neutron scattering measurements are in good agreement with those derived from the analysis of the heat capacity data. In particular, the tunnel splitting for hydrogen trapped by N or C is found to be about 15% smaller than that for hydrogen trapped by O. Figure 26.10 also demonstrates that the width of the 0.2 meV peaks strongly depends on the state of conduction-electron system. In fact, since the superconducting transition temperature for niobium is 9.2 K, in zero magnetic field the spectra at both 0.2 K and 4.3 K correspond to the superconducting state. However, a magnetic field of 0.7 T suppresses the superconductivity, so that the sample is in the normal-conducting state at both 0.2 K and 4.3 K. As can be seen from Fig. 26.10, the 0.2 meV peaks in the normal state are considerably broader than those in the superconducting state at the same temperature; this effect is more pronounced at 4.3 K. These results show that, in Nb(OH)x samples with very small x, conduction electrons play a dominant role in the damping of the tunnel-split H states at low tempera-
Figure 26.10 Neutron spectra of a Nb(OH)0.0002 sample at 0.2 K (a) and 4.3 K (b). For both temperatures, the spectra are taken in the superconducting (0 T) and normal-conducting (0.7 T) electronic state. The thick and thin solid lines represent the fit curves for the total and inelastic scattering intensity, respectively. The broken lines are for the elastic intensity (from Ref. [112]).
815
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26 Hydrogen Motion in Metals
tures. The width of the 0.2 meV peaks is also found to increase with increasing defect concentration x [104, 105]. This is believed to result from distributions both in e and J which are introduced by lattice distortions. As the temperature increases above ~ 5 K, the well-defined tunnel-split H states are progressively destroyed, and hydrogen starts to perform diffusive jumps between the two nearest-neighbor tetrahedral sites (incoherent tunneling). This is reflected in the following transformation of the neutron spectra: the inelastic peaks (corresponding to excitations between the tunnel-split states) broaden and merge into the quasielastic line. In the regime of local jump motion, the width of the quasielastic line is proportional to the jump rate. Figure 26.11 shows the temperature dependence of the H jump rate derived from the measured width of the quasielastic line in Nb(OH)x and Nb(NH)x [114, 115]. The most striking feature of the data is that in the temperature range 10–70 K the hydrogen jump rate increases with decreasing temperature both for Nb(OH)x and Nb(NH)x. Such behavior has been attributed to nonadiabatic effects in the interaction between hydrogen and conduction electrons [43, 116, 117]. The strength of the nonadiabatic coupling between hydrogen and conduction electrons is described by the dimensionless Kondo parameter K; in the case of weak coupling (K << 1) the theory [43, 118, 119] gives the jump rate sl–1 as s1 ¼ l
1 CðKÞ J 2pkB T 2K1 2 Cð1 KÞ " J
(26.27)
where C(x) denotes the gamma function and J is the tunnel splitting in the normal-conducting state for T fi 0. As can be seen from Fig. 26.11, the observed temperature dependence of sl–1 below 60 K is consistent with the T 2K–1 power law; the value of K derived from the experimental data is 0.055. At T < 60 K the hydrogen jump rates in the case of N traps are lower than those in the case of O traps. This is also consistent with Eq. (26.27), since the measured values of J for H trapped by N are smaller than those for H trapped by O. The dashed and solid lines in Fig. 26.11 show the results of calculations based on Eq. (26.27) with the values of J and K determined from the neutron scattering measurements for Nb(OH)x and Nb(NH)x at T < 10 K (without any adjustable parameters). It can be seen that the values of J and K found from experiments in the regime of H tunneling also provide a good description of the data in the regime of H jump motion, at least up to 60 K. Thus, for hydrogen trapped by interstitial impurities in Nb, the scenario of H tunneling in a double-well potential with nonadiabatic coupling between hydrogen and conduction electrons appears to be self-consistent. Above 70 K the hydrogen jump rate starts to increase with increasing temperature (Fig. 26.11). In this temperature range the interaction between hydrogen and phonons is believed to become the dominant one, so that Eq. (26.27) no longer describes the data. The appropriate theoretical description of H motion in this range is given in terms of phonon-assisted incoherent tunneling [43]. As the temperature increases above ~ 150 K, there is an increasing probability that a hydrogen atom can leave its trap site. The detrapped H atom is expected to perform a
26.5 Quantum Motion of Hydrogen
Figure 26.11 The jump rates of trapped hydrogen in Nb(OH)x (open symbols, circles: x = 0.002, triangles: x = 0.011) and Nb(NH)x (full symbols, diamonds: x = 0.0005, triangles: x = 0.004, polycrystalline sample, circles: x = 0.004, singlecrystalline sample) as functions of the temperature. The broken (O traps) and solid (N traps) lines are the theoretical predictions based on Eq. (26.27) (from Ref. [115]).
long-range diffusive motion before it is trapped again by another impurity atom. In this regime the hydrogen jump motion is characterized by two different jump rates corresponding to the localized motion in the trapped state and to the longrange diffusion in the free state. These two jump rates, as well as the ratio of the mean lifetimes of a hydrogen atom in the free and trapped states, have been determined from QENS measurements on Nb(OH)0.011 in the range 150–300 K [118]. It has been found that at 150 K the hydrogen jump rate for the localized motion is considerably higher than that for the long-range diffusion; however, above 250 K these two jump rates are nearly the same. It should be noted that low-temperature dynamical processes were also observed for hydrogen trapped by some substitutional impurities (Ti, Zr) in niobium using the internal friction [119, 120] and heat capacity [121] measurements. In particular, the heat capacity of a NbTi0.05 alloy doped with H(D) shows considerable hydrogen- or deuterium-induced contributions between 0.05 and 2 K [121]. However, the available experimental information is not sufficient to elucidate the microscopic picture of hydrogen motion in these systems. The same also refers to the low-temperature dynamical processes of hydrogen in b.c.c. V and Ta [106, 107, 122]. 26.5.2 Hydrogen Tunneling in a-MnHx
Neutron scattering studies of hydrogen dynamics in solid solutions of hydrogen in a-manganese [123, 124] have revealed a remarkable tunneling effect. This is the
817
26 Hydrogen Motion in Metals
first well-documented case of intrinsic (that is, not related to impurities) coherent H tunneling in a metal–hydrogen system. The maximum solubility of hydrogen in a-Mn increases from about 0.3 at.% at ambient pressure to a few at% at hydrogen pressures of 0.6–0.9 GPa [125]. The solid solutions a-MnHx (x £ 0.073) obtained by high-pressure quenching retain long-term stability at room temperature after the pressure release [123]. The neutron diffraction study of a-MnH0.07 [123] has shown that H atoms randomly occupy the interstitial sites 12e of the space group I 43m in the complex cubic unit cell of a-Mn composed of 58 manganese atoms. The sublattice of 12e sites consists of pairs of closely-spaced sites, the distance between the sites in a pair being only 0.68 (see inset in Fig. 26.12). Because of such a small intersite distance, each pair can accommodate only one hydrogen atom. On the other hand, these pairs are well-separated from each other, the distance between the centers of the pairs being about 4.5 . It is evident that this configuration of 12e sites is favorable for hydrogen tunneling.
S(Q,ω) (arb. units)
818
0 74
6.4
0
50
107
100
190 meV
130
150
200
Energy transfer (meV) Figure 26.12 The inelastic neutron scattering spectrum of a-MnH0.07 measured at 23 K on the TFXA spectrometer (Rutherford-Appleton Laboratory). Inset: the arrangement of closely spaced pairs of 12e sites in the unit cell of a-Mn [126].
Inelastic neutron scattering (INS) studies of a-MnH0.07 [123, 124] have revealed that, in addition to the band of hydrogen optical vibrations (peaks at 74, 107 and 130 meV), there is a strong peak at the energy transfer of 6.4 meV (Fig. 26.12). The intensity of the 6.4 meV peak corresponding to the neutron energy loss is found to decrease with increasing temperature. At temperatures near 200 K this peak shows relaxation behavior merging into the quasielastic line. The 6.4 meV peak has been attributed [123, 124] to the excitation between the tunnel-split vibrational ground-state levels of hydrogen. This conclusion is supported by the following observations [124].
26.5 Quantum Motion of Hydrogen
1. The position of the peak is found to depend strongly on the isotope (H«D) substitution. In fact, for a-MnD0.05 the low-energy peak appears at 1.6 meV. Because of a certain H contamination of the deuterated sample in experiments [124] and the large incoherent neutron scattering cross-section of H, the peaks at both 1.6 meV and 6.4 meV are present in the INS spectra of a-MnD0.05. As an example of the data, Fig. 26.13 shows the INS spectra (neutron-energy gain side) of a-MnD0.05 at a number of temperatures. The observed isotope effect on the splitting J of the vibrational ground states is consistent with the estimates (JH = 5 meV, JD = 1.5 meV) based on the theoretical model [127], if the actual parameters for a-MnHx(Dx) are used [124]. 2. The temperature dependences of the integrated intensities of the 6.4 meV and 1.6 meV peaks are well described in terms of the Boltzmann thermal population factors of the split ground-state levels, both for the neutron-energy gain and neutron-energy loss. On the other hand, the observed temperature dependences of the peak intensities differ qualitatively from those expected for phonons or harmonic oscillators [124]. 3. The behavior of the intensity of the 6.4 meV peak in a-MnH0.07 as a function of momentum transfer, Q, is consistent with that expected in the case of tunneling between two sites [105], SðQ; xtun Þ
1 sin Qd expðQ 2 u2 Þ 2 2Qd
(26.28)
where d is the distance between two sites and u2 is the effective mean-square displacement due to vibrations of H atoms. Figure 26.14 shows the Q-dependence of the 6.4 meV peak intensity measured at 20 K using the MARI neutron spectrometer at the Rutherford-Appleton Laboratory [124]. As can be seen from Fig. 26.14, Eq. (26.28) with the fixed experimental value d = 0.68 and a realistic mean-square displacement (u2 = 0.0256 2) gives a satisfactory description of the data. It should be noted that the splitting due to H tunneling in a-MnHx is anomalously large (about 30 times larger than for H trapped by impurities in b.c.c. metals). Because of its large magnitude, the splitting is observed up to temperatures exceeding 100 K, which is very unusual for such quantum effects. Moreover, the a-MnDx system gives the unique possibility to observe the level splitting due to tunneling of deuterium. The tunneling modes in a-MnHx are found to be suppressed by elastic stresses [128]. In fact, the INS peak due to tunneling disappears at a pressure of 0.8 GPa in a quasi-hydrostatic regime of a sapphire anvil cell. On the other hand, the appli-
819
26 Hydrogen Motion in Metals
S(Q,ω) (arb. units)
820
44 K
29 K
15 K 2K
-8
-6
-4
-2
0
Energy transfer (meV) Figure 26.13 The difference between the INS spectra (neutron-energy gain side) of a-MnD0.05 and a-Mn measured on the IN6 spectrometer (Institute Laue-Langevin). The spectra corresponding to different temperatures are shifted along the vertical axis. The a-MnD0.05 sample is contaminated with about 0.5 at.% H which manifests itself by the peak at 6.4 meV [126].
Figure 26.14 The H tunneling peak intensity in the INS spectrum of a-MnH0.07 measured at 20 K as a function of Q [124]. The solid line shows the result of a fit based on Eq. (26.28) with the fixed d = 0.68 .
cation of the same pressure under purely hydrostatic conditions does not cause any changes in the parameters of the 6.4 meV peak [128]. The suppression of the hydrogen tunneling modes by applied inhomogeneous elastic stresses is believed to result from a shift of the energy levels in the adjacent potential wells caused by static displacements of atoms.
26.5 Quantum Motion of Hydrogen
26.5.3 Rapid Low-temperature Hopping of Hydrogen in a-ScHx(Dx) and TaV2Hx(Dx)
The behavior of hydrogen in Sc and the related h.c.p. metals Y and Lu shows a number of unusual features. In contrast to most binary metal–hydrogen systems, hydrogen in ScHx, YHx, and LuHx is not precipitated into a hydride phase at low temperatures; it remains in the solid-solution (a) phase up to x = 0.2–0.3. It is believed that the a-phase stabilization is related to the peculiar short-ranged ordering of hydrogen [129, 130], which develops with decreasing temperature. Neutron diffraction [131] and diffuse scattering [129, 130] measurements have shown that hydrogen occupies only the tetrahedral interstitial sites in the h.c.p. Sc lattice and tends to form next-nearest-neighbor pairs with a bridging metal atom in the c axis direction. As the temperature is lowered, these pairs arrange themselves into a longer-range structure, predominantly along the c direction. However, truly longrange order is not achieved in these systems. The dynamical properties of hydrogen in Sc are also quite remarkable. NMR measurements of the proton spin–lattice relaxation rate R1 in a-ScHx [132] have revealed a localized H motion with the characteristic jump rate sl–1 of about 108 s–1 at 50 K. This localized motion is evident from an additional frequency-dependent R1 peak at low temperatures (35–80 K). The structure of the sublattice of tetrahedral interstitial sites in a h.c.p. metal suggests that the localized H motion corresponds to jumps between two nearest-neighbor sites separated by about 1.0 in the c direction. QENS measurements on a-ScHx [133, 134] have revealed the existence of a still faster localized motion with the jump rate passing through a minimum of approximately 71010 s–1 near 100 K and increasing to 1012 s–1 at 10 K. This result is illustrated by Fig. 26.15 showing the width of the quasielastic component of the QENS spectrum for ScH0.16 as a function of temperature. Since this width is proportional to the H jump rate, it can be seen that the temperature dependence of the H jump rate for a-ScHx is similar to that for Nb(OH)x and
Figure 26.15 The full width at half-maximum of the Lorentzian quasielastic line for ScH0.16 as a function of temperature. The solid line shows the fit based on of Eq. (26.27) to the data below 100 K.
821
822
26 Hydrogen Motion in Metals
Nb(NH)x (see Fig. 26.11). In particular, the power law (26.27) also appears to describe the temperature dependence of the H jump rate for ScH0.16 below 70 K (the solid line in Fig. 26.15); the corresponding fit parameters are K = 0.039 and J = 0.32 meV [133]. The Q-dependence of the elastic incoherent structure factor for ScH0.16 is consistent with H jumps between two sites separated by ~ 1.0 . The temperature dependence of the quasielastic line intensity indicates that the fraction p of H atoms participating in the fast localized motion (on the frequency scale determined by the energy resolution of the QENS experiments, ~ 70 leV) decreases with decreasing temperature; for ScH0.16 this fraction is less than 5% below 50 K. It has been suggested [133, 134] that the immobile fraction, 1–p, corresponds to H atoms forming pairs with a bridging Sc atom, while the mobile fraction p is associated with the unpaired H atoms. It should be noted that, because of the limited energy resolution (70 leV), the QENS experiments [133, 134] could not detect the slower H motion found by NMR [132]. This slower motion cannot be attributed to H atoms involved in the pairing, since the NMR results show that only a small fraction of protons participate in this motion, while most of the H atoms are paired at low temperatures. Therefore, it is difficult to elucidate the nature of this slower motion. Note that the long-range H diffusion in a-ScHx is completely frozen out’ on the NMR frequency scale at T < 300 K. Subsequent NMR measurements of the 45Sc spin-lattice relaxation rates in a-ScHx(Dx) [135, 136] have revealed strong isotope effects on the localized hydrogen motion. For 45Sc the main motional contribution to R1 originates from the electric quadrupole interaction modulated by H(D) hopping. Since, for the quadrupole interaction, only charge fluctuations are important, H and D atoms are expected to give the same contributions to the host-metal relaxation rate, if their motional parameters are the same. However, the measured amplitude of the low-temperature R1Sc peak for a-ScDx samples appears to be much higher than for a-ScHx samples with comparable hydrogen content [135, 136]. This unusual isotope effect indicates that the fraction of D atoms participating in the localized motion in a-ScDx on the frequency scale of 108–109 s–1 is considerably larger than the corresponding fraction of H atoms in a-ScHx. The whole set of the 1H, 2D and 45Sc spin–lattice relaxation measurements at different resonance frequencies [135, 136] and the high-resolution (~ 1.2 leV) QENS measurements [136] is consistent with the following picture of localized hydrogen motion in a-ScHx(Dx). The motion of D atoms in a-ScDx is characterized by a distribution of the jump rates sl–1; the most probable value of sl–1 decreases with decreasing temperature (following an Arrhenius-like law with an activation energy of ~ 50 meV) and passes through the NMR frequency (~ 108 s–1) near 100 K. It should be noted that the temperature of the ultrasonic attenuation peak observed for a-ScD0.18 (50 K in the frequency range of 1 MHz) [137] is in agreement with the NMR data for a-ScDx. For H atoms in a-ScHx, the distribution of the jump rates appears to be shifted to much higher frequencies, so that only a tail of this distribution can be probed by NMR measurements. A large difference between the characteristic jump rates of H and D atoms is consistent with a quantum origin of the localized hydrogen motion in scandium.
26.5 Quantum Motion of Hydrogen
Another example of fast low-temperature hydrogen hopping is the localized H(D) motion over g-site hexagons (see Section 26.4.2) in cubic Laves phases. This motion has been most extensively investigated for the TaV2–H(D) system (where it is the fastest among the studied Laves phases). Therefore, the discussion in this section will be based on the experimental results obtained for TaV2Hx(Dx). Three interesting features of the localized hydrogen motion will be emphasized: (i) the strong dependence of the jump rate sl–1 on hydrogen concentration, (ii) the isotope effects on the parameters of the localized motion, and (iii) the non-Arrhenius temperature dependence of the jump rate at low T. The hydrogen jump rate sl–1 in TaV2Hx(Dx) has been found to increase strongly with decreasing H(D) content [54, 72, 73]. In NMR measurements, this is reflected in the marked shift of the position of the low-T maximum of R1 to lower temperatures. For example, at the frequency of 90 MHz the low-T maximum of the proton R1 is observed at 187 K for TaV2H1.33, at 125 K for TaV2H0.87 [54] and at 45 K for TaV2H0.06 [73]. The strong dependence of sl–1 on x has also been found in the QENS measurements on TaV2Hx [76] and in the ultrasonic experiments on TaV2Dx [138]. Qualitatively, such a dependence is consistent with the fact that the distance between the nearest-neighbor sites in the hexagon, r1, becomes shorter with decreasing x due to the decrease of the lattice parameter. In this case, the hydrogen jump rate sl–1 should be extremely sensitive to changes in r1, which suggests that the localized H motion is governed by tunneling transitions. As in the case of a-ScHx(Dx), NMR measurements of the host-metal (51V) spin– lattice relaxation rate in TaV2Hx(Dx) [54] have revealed a strong isotope effect: the amplitude of the low-temperature R1V peak for TaV2Dx is nearly three times higher than that for TaV2Hx with the same x. These results also suggest that the fraction of D atoms participating in the fast localized motion is considerably larger than that of H atoms. Measurements of the ultrasonic attenuation in TaV2Hx(Dx) in the frequency range of 1 MHz [58, 138, 139] have found even more dramatic isotope effects. For example, for TaV2D0.17 the ultrasonic attenuation shows a distinct peak near 20 K which can be attributed to localized D motion; however, for TaV2H0.18 the low-T attenuation peak is observed near 1 K, and its amplitude is about 8 times lower than that for TaV2D0.17 [138]. These results demonstrate that, at low temperatures, the jump rate of H atoms is at least an order of magnitude faster than that of D atoms for similar concentrations. The ultrasonic data [138] are also consistent with the temperature-dependent fraction of mobile’ atoms, the value of p decreasing with decreasing temperature. The temperature dependence of the jump rate sl–1 for both H and D in TaV2Hx(Dx) is found to be strongly non-Arrhenius. The behavior of sl–1(T) obtained from the proton R1 measurements in TaV2Hx [54] is reasonably described by the exponential function, sl–1 = s0–1 exp(T/T0)
(26.29)
over the temperature range 30–200 K. At low temperatures this dependence is much weaker than the Arrhenius one. Although the relation given by Eq. (26.29)
823
26 Hydrogen Motion in Metals
should be considered as empirical, it is worth noting that a similar term in the jump rate has been found in the framework of the quantum diffusion theory taking into account the effects of barrier fluctuations [140]. While for protons the behavior of the measured spin–lattice relaxation rate at low T is affected by the temperature dependence of p [76], the 2D spin–lattice relaxation rates can be measured separately for the mobile’ and static’ fractions [72]. Therefore, the temperature dependence of sl–1 derived from the 2D relaxation data for the mobile’ fraction of D atoms should be more reliable. Figure 26.16 shows the behavior of sl–1(T) obtained from the 2D relaxation rate data for TaV2D0.5 and TaV2D1.3 [72]. It can be seen that sl–1(T) for D atoms is satisfactorily described by Eq. (26.29). The corresponding fit parameters are T0 = 38 and 33 K, s0–1 = 2.0107 and 1.5106 s–1 for TaV2D0.5 and TaV2D1.3, respectively. For comparison, the low-temperature behavior of sl–1 for H in TaV2H0.56 (the dashed line in Fig. 26.16) is described by T0 = 50.3 K, s0–1 = 1.1108 s–1 [54]. It should be noted that Eq. (26.29) with the values of T0 and s0–1 derived from the 2D NMR data for TaV2D0.5 also gives a reasonable description of the ultrasonic attenuation results for TaV2D0.5 [138]. The ultrasonic experiments on TaV2Hx with low x [138] show that the hydrogen jump rate sl–1 remains finite down to the lowest temperature of the measurements (0.3 K), being well above the ultrasound frequency of ~ 1 MHz. Inspection of the experimental data for the systems with fast localized hydrogen motion suggests that the applicability of Eq. (26.29) is not restricted to hydrogen in Laves phases. In particular, this equation appears to describe the behavior of sl–1(T) for the trapped hydrogen in Nb(OH)0.011 [118] in the range 100–300 K and for the mobile’ H atoms in a-ScH0.16 [133] in the range 125–300 K. The values of T0 estimated from these data are 130 K for Nb(OH)0.011 and 146 K for a-ScH0.16. 10
10
TaV2D0.5 TaV2D1.3
9
-1
(s )
10
8
-1
10
τl
824
7
10
6
10
0
50
100
150
200
T (K) Figure 26.16 The temperature dependence of the jump rates sl–1 for deuterium in TaV2D0.5 and TaV2D1.3, as determined from the 2D spin lattice relaxation data [72]. The solid lines show the fits of Eq. (26.29) to the data. The dashed line represents the behavior of sl–1(T) for H in TaV2H0.56, as derived from the fit of Eq. (26.29) to the proton spin–lattice relaxation data (Ref. [54]).
26.6 Concluding Remarks
26.6 Concluding Remarks
Information on hydrogen diffusion rates is of crucial importance for the applicability of materials for reversible hydrogen storage. The understanding of hydrogen diffusion processes in metals is expected to contribute to the development of new hydrogen storage materials with fast kinetics of hydrogen release/uptake at moderate temperatures. Therefore, the theoretical and experimental investigation of H motion in metals remains a very active field of research. The present chapter gives a brief review of experimental studies of the mechanisms and parameters of hydrogen diffusion in metals. We emphasize the relation between the parameters of H motion and the structure of the hydrogen sublattice. The general experimental trend is to investigate systems of increasing structural complexity. While the behavior of hydrogen in a number of binary metal–hydrogen systems is well understood, a detailed microscopic picture of H diffusion in complex compounds of practical importance has not yet evolved. A promising approach to investigation of these compounds is to combine a number of experimental techniques sensitive to different ranges of H jump rates (such as NMR, QENS and anelastic relaxation) with the neutron diffraction study of hydrogen positional parameters. A new challenge is to elucidate the mechanisms of H diffusion in nanocrystalline materials which are used for hydrogen storage. Further studies are also necessary to understand the processes of H tunneling and low-temperature hopping. Recent work [141] has demonstrated the potential of the first-principles density functional theory accurately predicting the rates of activated hopping and quantum tunneling of H in b.c.c. Nb and Ta. Progress in numerical methods may lead to application of the first-principles calculations to H motion in more complex systems. From the experimental side, in the near future one may anticipate the discovery of new compounds showing high H mobility down to low temperatures.
Acknowledgement
We are grateful to the Alexander von Humboldt Foundation for awarding a Research Fellowship to A.S. The present chapter results from a number of research visits of A.S. (supported by the Humboldt Foundation) to the University of Saarbrcken.
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26 Hydrogen Motion in Metals
References 1 G. Alefeld, J. Vlkl (Eds.), Hydrogen in 2 3 4
5
6 7
8
9
10 11
12
13
14
15 16 17 18 19
20
Metals I, Springer, Berlin, 1978. G. Alefeld, J. Vlkl (Eds.), Hydrogen in Metals II, Springer, Berlin, 1978. H. Wipf (Ed.), Hydrogen in Metals III, Springer, Berlin, 1997. L. Schlapbach (Ed.), Hydrogen in Intermetallic Compounds I, Springer, Berlin, 1988. L. Schlapbach (Ed.), Hydrogen in Intermetallic Compounds II, Springer, Berlin, 1992. Y. Fukai, The Metal-Hydrogen System, Springer, Berlin, 1993. A. S. Nowick, B. S. Berry, Anelastic Relaxation in Crystalline Solids, Academic Press, London, 1972. R. M. Cotts, in Hydrogen in Metals I, G. Alefeld, J. Vlkl (Eds.), Springer, Berlin, 1978, p. 227. J. Vlkl, G. Alefeld, in Hydrogen in Metals I, G. Alefeld, J. Vlkl (Eds.), Springer, Berlin, 1978, p. 321. Y. Fukai, H. Sugimoto, Adv. Phys. 1985, 34, 263–326. D. Richter, R. Hempelmann, R. C. Bowman, in Hydrogen in Intermetallic Compounds II, L. Schlapbach (Ed.), Springer, Berlin, 1992, p. 97. R. G. Barnes, in Hydrogen in Metals III, H. Wipf (Ed.), Springer, Berlin, 1997, p. 93. D. K. Ross, in Hydrogen in Metals III, H. Wipf (Ed.), Springer, Berlin, 1997, p. 153. R. Hempelmann, Quasielastic Neutron Scattering and Solid State Diffusion, Clarendon Press, Oxford, 2000. J. L. Snoek, Physica 1939, 6, 591. J. Buchholz, J. Vlkl, G. Alefeld, Phys. Rev. Lett. 1973, 30, 318–321. G. Schaumann, J. Vlkl, G. Alefeld, Phys. Rev. Lett. 1968, 21, 891–893. J. Vlkl, Ber. Bunsenges. Phys. Chem. 1972, 76, 797. H. Wagner, in Hydrogen in Metals I, G. Alefeld , J. Vlkl (Eds.), Springer, Berlin, 1978, p. 5. G. E. Murch, Philos. Mag. A 1982, 45, 685–692.
21 L. D. Bustard, Phys. Rev. B 1980, 22,
1–11. 22 D. A. Faux, D. K. Ross, C. A. Sholl,
J. Phys. C 1986, 19, 4115–4133. 23 D. A. Faux, C. K. Hall, Z. Phys. Chem.
N. F. 1989, 164, 859–864. 24 N. Bloembergen, E. M. Purcell,
R. M. Pound, Phys. Rev. 1948, 73, 679–712. 25 H. C. Torrey, Phys. Rev. 1953, 92, 962–969. 26 C. A. Sholl, J. Phys. C 1988, 21, 319–324. 27 P. Galvosas, F. Stallmach, G. Seiffert, J. Krger, U. Kaess, G. Majer, J. Magn. Reson. 2001, 151, 260. 28 T. Springer, Quasielastic Neutron Scattering for the Investigation of Diffusive Motions in Solids and Liquids, Springer Tracts in Modern Physics, Vol. 64, Springer, Berlin, 1972. 29 M. B e, Quasielastic Neutron Scattering. Principles and Applications in Solid State Chemistry, Biology and Materials Science, Adam Hilger, Bristol, 1988. 30 N. G. van Kampen, Stochastic Processes in Physics and Chemistry, Elsevier, Amsterdam, 1992. 31 K. S. Singwi, A. Sjlander, Phys. Rev. 1960, 119, 863–871. 32 D. Richter, T. Springer, Phys. Rev. B 1978, 18, 126–140. 33 R. Hempelmann, J. Less-Common Met. 1984, 101, 69. 34 D. Richter, G. Driesen, R. Hempelmann, I. S. Anderson, Phys. Rev. Lett. 1986, 57, 731–734. 35 K. Watanabe, Y. Fukai, J. Phys. F: Met. Phys. 1980, 10, 1795–1801. 36 H. Kronmller, in Hydrogen in Metals I, G. Alefeld, J. Vlkl (Eds.), Springer, Berlin, 1978, p. 291. 37 J. Crank, The Mathematics of Diffusion, Oxford University Press, Oxford, 1975. 38 E. Wicke, H.Brodowsky, in Hydrogen in Metals II, G. Alefeld, J. Vlkl (Eds.), Springer, Berlin, 1978, pp. 73–155. 39 R. Kirchheim, Acta Metall. 1982, 30, 1069. 40 H. Zchner, in Hydrogen in Metals (Japan Institute of Metals, Sendai 1980): Trans. JIM (Suppl.) 1980, 21, 101.
References 41 R. Kirchheim, R. B. McLellan, 42
43
44
45 46 47
48 49 50
51 52 53
54
55
56
57
58 59
J. Electrochem. Soc. 1980, 127, 2419. H. Wipf, in Hydrogen in Metals III, H. Wipf (Ed.), Springer, Berlin, 1997, pp. 51–91. H. Grabert, H. R. Schober, in Hydrogen in Metals III, H. Wipf (Ed.), Springer, Berlin, 1997, pp. 5–49. J. Vlkl, H. C. Bauer, U. Freudenberg, K. Kokkinidis, G. Lang, K. A. Steinhauser, G. Alefeld, in Internal Friction and Ultrasonic Attenuation in Solids, R. R. Hasiguti, N. Mikoshiba (Eds.), University of Tokyo Press, Tokyo, 1977, p. 485. A.V. Skripov, Defect Diffus. Forum 2003, 224–225, 75–92. Zh. Qi, J. Vlkl, R. Lsser, H. Wenzl, J. Phys. F 1983, 13, 2053–2062. W. Renz, G. Majer, A. V. Skripov, A. Seeger, J. Phys.: Condens. Matter 1994, 6, 6367–6374. A. Klamt, H. Teichler, Phys. Status Solidi (b) 1986, 134, 503. H. R. Schober, A. M. Stoneham, Phys. Rev. Lett. 1988, 60, 2307–2310. J. Vlkl, G. Wollenweber, K. H. Klatt, G. Alefeld, Z. Naturforsch.A 1971, 26, 922. G. Sicking, M. Glugla, B. Huber, Ber. Bunsenges. Phys. Chem. 1983, 87, 418. L. Katz, M. Guinan, R. J. Borg, Phys. Rev. B 1971, 4, 330–341. K. Kehr, in Hydrogen in Metals I, G. Alefeld, J. Vlkl (Eds.), Springer, Berlin, 1978, pp. 197–226. A. V. Skripov, S. V. Rychkova, M.Yu. Belyaev, A. P. Stepanov, J. Phys.: Condens. Matter 1990, 2, 7195–7208. A. V. Skripov, M.Yu. Belyaev, S. V. Rychkova, A. P. Stepanov, J. Phys.: Condens. Matter 1991, 3, 6277–6291. A. V. Skripov, Yu. G. Cherepanov, B. A. Aleksashin, S. V. Rychkova, A. P. Stepanov, J. Alloys Compd. 1995, 227, 28–31. G. Majer, W. Renz, A. Seeger, R. G. Barnes, J. Shinar, A. V. Skripov, J. Alloys Compd. 1995, 231, 220–225. K. Foster, R. G. Leisure, A. V. Skripov, Phys. Rev. B 2001, 64, 214302. C. T. Chudley, R. J. Elliott, Proc. Phys. Soc. 1961, 77, 353.
60 K. Skld, G. Nelin, J. Phys. Chem. Solids
1967, 28, 2369. 61 J. M. Rowe, J. J. Rush, L. A. de Graaf,
62 63
64
65
66
67
68 69
70
71 72
73 74
75
76
77
78
G. A. Ferguson, Phys. Rev. Lett. 1972, 29, 1250–1253. J. M. Rowe, J. J. Rush, H. E. Flotow, Phys. Rev. B 1974, 9, 5039–5045. J. M. Rowe, K. Skld, H. E. Flotow, J. J. Rush, J. Phys. Chem. Solids 1971, 32, 41–54. V. Lottner, J. W. Haus, A. Heim, K. W. Kehr, J. Phys. Chem. Solids 1979, 40, 557. V. Lottner, H. R. Schober, W. J. Fitzgerald, Phys. Rev. Lett. 1979, 42, 1162–1165. V. A. Somenkov, I. R. Entin, A. Y. Chervyakov, S. Sh. Shil’stein, A. A. Chertkov, Sov. Phys. Solid State 1972, 13, 2178. D. Richter, S. Mahling-Ennaoui, R. Hempelmann, Z. Phys. Chem. N. F. 1989, 164, 907–920. V. A. Somenkov, A. V. Irodova, J. Less-Common Met. 1984, 101, 481–492. K. Yvon, P. Fischer, in Hydrogen in Intermetallic Compounds I, L. Schlapbach (Ed.), Springer, Berlin, 1988, pp. 87–138. R. C. Bowman, B. D. Craft, A. Attalla, J. R. Johnson, Int. J. Hydrogen Energy 1983, 8, 801–808. J. Shinar, D. Davidov, D. Shaltiel, Phys. Rev. B 1984, 30, 6331–6341. A. V. Skripov, A. V. Soloninin, V. N. Kozhanov, Solid State Commun. 2002, 122, 497–501. A. L. Buzlukov, A. V. Skripov, J. Alloys Compd. 2004, 366, 61–66. P. Fischer, F. Fauth, A. V. Skripov, A. A. Podlesnyak, L. N. Padurets, A. L. Shilov, B. Ouladdiaf, J. Alloys Compd. 1997, 253–254, 282–285. U. Eberle, G. Majer, A. V. Skripov, V. N. Kozhanov, J. Phys.: Condens. Matter 2002, 14, 153–164. A. V. Skripov, J. C. Cook, D. S. Sibirtsev, C. Karmonik, R. Hempelmann, J. Phys.: Condens. Matter 1998, 10, 1787–1801. A. V. Skripov, M. Pionke, O. Randl, R. Hempelmann, J. Phys.: Condens. Matter 1999, 11, 1489–1502. A. V. Skripov, J. C. Cook, T. J. Udovic, M. A. Gonzalez, R. Hempelmann,
827
828
26 Hydrogen Motion in Metals
79
80
81 82
83
84
85
86
87
88 89
90 91
92
93 94
95
V. N. Kozhanov, J. Phys.: Condens. Matter 2003, 15, 3555–3566. A. V. Skripov, J. C. Cook, C. Karmonik, V. N. Kozhanov, Phys. Rev. B 1999, 60, 7238–7244. A. V. Skripov, J. C. Cook, T. J. Udovic, V. N. Kozhanov, Phys. Rev. B 2000, 62, 14099–14104. D. J. Bull, D. P. Broom, D. K. Ross, Chem. Phys. 2003, 292, 153–160. G. Majer, U. Kaess, M. Stoll, R. G. Barnes, J. Shinar, Defect Diffus. Forum 1997, 143–147, 957–962. R. Hempelmann, D. Richter, A. Heidemann, J. Less-Common Met. 1982, 88, 343–351. A. V. Skripov, A. V. Soloninin, A. L. Buzlukov, L. S. Voyevodina, J. C. Cook, T. J. Udovic, R. Hempelmann, J. Phys.: Condens. Matter 2005, 17, 5011–5025. J. J. Didisheim, K.Yvon, D. Shaltiel, P. Fischer, Solid State Commun. 1979, 31, 47–50. C. Schnfeld, R. Hempelmann, D. Richter, T, Springer, A. J. Dianoux, J. J. Rush, T. J. Udovic, S. M. Bennington, Phys. Rev. B 1994, 50, 853–865. A. V. Skripov, A. V. Soloninin, A. P. Stepanov, V. N. Kozhanov, J. Phys.: Condens. Matter 2000, 12, 9607–9616. D. Nor us, L. G. Olsson, J. Chem Phys. 1983, 78, 2419–2427. A. L. Buzlukov, A. V. Soloninin, A. V. Skripov, Solid State Commun. 2004, 129, 315–318. E. Mamontov, T. J. Udovic, O. Isnard, J. J. Rush, Phys. Rev. B 2004, 70, 214305. L. Lichty, J. Shinar, R. G. Barnes, D. R. Torgeson, D. T. Peterson, Phys. Rev. Lett. 1985, 55, 2895–2898. D. S. Sibirtsev, Yu. G. Cherepanov, A. V. Skripov, J. Alloys Compd. 1998, 278, 21–28. R. Kirchheim, Defect Diffus. Forum 1997, 143–147, 911–925. V. V. Kondratyev, A. V.Gapontsev, A. N.Voloshinskii, A. G.Obukhov, N. I.Timofeyev, Int. J. Hydrogen Energy 1999, 24, 819–824. W. Schirmacher, M. Prem, J.-B. Suck, A. Heidemann, Europhys. Lett. 1990, 13, 523.
96 R. Kutner, A. Pekalski, K. Sznajd-Weron
(Eds.), Anomalous Diffusion: From Basics to Applications, Lecture Notes in Physics Vol. 519, Springer, Berlin, 1999. 97 Y. Gefen, A. Aharony, S. Alexander, Phys. Rev. Lett. 1983, 50, 77–80. 98 J. J. Rush, T. J. Udovic, R. Hempelmann, D. Richter, G. Driesen, J. Phys.:Condensed Matter 1989, 1, 1061–1070. 99 W. Schirmacher, Ber. Bunsenges. Phys. Chem. 1991, 95, 368. 100 M. Wagner, W. Schirmacher, Ber. Bunsenges. Phys. Chem. 1991, 95, 983. 101 T.Apih, M. Bobnar, J. Dolinsek, L. Jastrow, D. Zander, U. Koester, Solid State Commun. 2005, 134, 337–341. 102 T. P. Das, J. Chem. Phys., 1957, 27, 763. 103 W. A. Phillips, Amorphous Solids: Low Temperature Properties, Springer, Berlin, 1981. 104 H. Wipf, A. Magerl, S.M. Shapiro, S.K. Satija, W. Thomlinson, Phys. Rev. Lett. 1981, 46, 947–950. 105 A. Magerl, A. J. Dianoux, H. Wipf, K. Neumaier, I. S. Anderson, Phys. Rev. Lett. 1986, 56, 159–162. 106 G. J. Sellers, M. Paalanen, A. C. Anderson, Phys. Rev. B 1974, 10, 1912–1915. 107 G. J. Sellers, A. C. Anderson, H. K. Birnbaum, Phys. Rev. B 1974, 10, 2771–2776. 108 C. Morkel, H. Wipf, K. Neumaier, Phys. Rev. Lett. 1978, 40, 947–950. 109 H. Wipf, K. Neumaier, Phys. Rev. Lett. 1984, 52, 1308–1311. 110 P. Gutsmiedl, M. Schikhofer, K. Neumaier, H. Wipf, in Quantum Aspects of Molecular Motions in Solids, A. Heidemann, A. Magerl, M. Prager, D. Richter, T. Springer (Eds.), Springer, Berlin, 1987, p. 158. 111 W. Morr, A. Mller, G. Weiss, H. Wipf, B. Golding, Phys. Rev. Lett. 1989, 63, 2084–2087. 112 H. Wipf, D. Steinbinder, K. Neumaier, P. Gutsmiedl, A. Magerl, A. J. Dianoux, Europhys. Lett. 1987, 4, 1379–1384. 113 K. Neumaier, D. Steinbinder, H. Wipf, H. Blank, G. Kearley, Z. Phys. B 1989, 76, 359–363.
References 114 D. Steinbinder, H. Wipf, A. Magerl,
115
116 117 118
119 120
121
122
123
124
125
126
127
D. Richter, A. J. Dianoux, K. Neumaier, Europhys. Lett. 1988, 6, 535–540. D. Steinbinder, H. Wipf, A. J. Dianoux, A. Magerl, K. Neumaier, D. Richter, R. Hempelmann, Europhys. Lett., 1991, 16, 211–216. J. Kondo, Physica B 1984, 125, 279. K. Yamada, Progr. Theor. Phys. 1984, 72, 195–201. K. Cornell, H. Wipf, J. C. Cook, G. J. Kearley, K. Neumaier, J. Alloys Compd. 1999, 293–295, 275–278. G. Cannelli, R. Cantelli, M. Koiwa, Philos. Mag. A 1982, 46, 483. G. Cannelli, R. Cantelli, F. Cordero, K. Neumaier, H. Wipf, J. Phys. F 1984, 14, 2507–2515. K. Neumaier, H. Wipf, G. Cannelli, R. Cantelli, Phys. Rev. Lett. 1982, 49, 1423–1426. S. G. O’Hara, G. J. Sellers, A. C. Anderson, Phys. Rev. B 1974, 10, 2777–2781. V. K. Fedotov, V. E. Antonov, K. Cornell, G. Grosse, A. I. Kolesnikov, V. V. Sikolenko, V. V. Sumin, F. E. Wagner, H. Wipf, J. Phys.: Condens. Matter 1998, 10, 5255–5266. A. I. Kolesnikov, V. E. Antonov, S. M. Bennington, B. Dorner, V. K. Fedotov, G. Grosse, J. C. Li, S. F. Parker, F. E. Wagner, Physica B 1999, 263–264, 421–423. V. E. Antonov, T. E. Antonova, N. A. Chirin, E. G. Ponyatovsky, M. Baier, F. E. Wagner, Scr. Mater. 1996, 34, 1331–1336. A. I. Kolesnikov, V. E. Antonov, V. K. Fedotov, A. J. Dianoux, B. Dorner, A. Hewat, A. S. Ivanov, G. Grosse, F. E. Wagner, ILL Annual Report 1999. S. I. Drechsler, G. M. Vujicic, N. M. Plakida, J. Phys. F 1984, 14, L243–L246.
128 V. E. Antonov, V. P. Glazkov,
D. P. Kozlenko, B. N. Savenko, V. A. Somenkov, V. K. Fedotov, JETP Lett. 2002, 76, 318–320. 129 M. W. McKergow, D. K. Ross, J. E. Bonnet, I. S. Anderson, O. Schrpf, J. Phys. C 1987, 20, 1909–1923. 130 O. Blaschko, J. Pleschiutschnig, P. Vajda, J. P. Burger, J. N. Daou, Phys. Rev. B 1989, 40, 5344–5349. 131 C. K. Saw, B. J. Beaudry, C. Stassis, Phys. Rev. B 1983, 27, 7013–7017. 132 L. R. Lichty, J. W. Han, R. Ibanez-Meier, D. R. Torgeson, R. G. Barnes, E. F. W. Seymour, C. A. Sholl, Phys. Rev. B 1989, 39, 2012–2021. 133 I. S. Anderson, N. F. Berk, J. J. Rush, T. J. Udovic, R. G. Barnes, A. Magerl, D. Richter, Phys. Rev. Lett. 1990, 65, 1439–1442. 134 N. F. Berk, J. J. Rush, T. J. Udovic, I. S. Anderson, J. Less-Common Met. 1991, 172–174, 496–508. 135 J. J. Balbach, M. S. Conradi, R. G. Barnes, D. S. Sibirtsev, A. V. Skripov, Phys. Rev. B 1999, 60, 966–971. 136 A. V. Skripov, A. V. Soloninin, D. S. Sibirtsev, A. L. Buzlukov, A. P. Stepanov, J. J. Balbach, M. S. Conradi, R. G. Barnes, R. Hempelmann, Phys. Rev. B 2002, 66, 054306. 137 R. G. Leisure, R. B. Schwarz, A. Migliori, D. R. Torgeson, I. Svare, Phys. Rev. B 1993, 48, 893–900. 138 J. E. Atteberry, R. G. Leisure, A. V. Skripov, J. B. Betts, A. Migliori, Phys. Rev. B 2004, 69, 144110. 139 K. Foster, J. E. Hightower, R. G. Leisure, A. V. Skripov, J. Phys.: Condens. Matter 2001, 13, 7327–7341. 140 Yu. Kagan, J. Low Temp. Phys. 1992, 87, 525. 141 P. G. Sundell. G. Wahnstrm, Phys. Rev. Lett. 2004, 92, 155901.
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Part VII Special Features of Hydrogen-Transfer Reactions
Volume 2 of this work is closed by Part VII, three articles that address special features of hydrogen-transfer reactions. Truhlar and Garrett review the application of variational transition-state theory to hydrogen transfer in Ch. 27. This modern extension and improvement of more traditional forms of the transition-state theory has proven powerful in the development of deep understanding of how the reactions occur, whether in simple gas-phase reactions of small molecules or in large enzyme active sites. The subject thus spans the entire range of levels of organization and complexity that this work encompasses. In Ch. 28, K. U. Ingold leads the reader through the experimental and theoretical developments, largely from his own laboratory, that put a firm underpinning beneath the phenomenology of hydrogen-atom tunneling under highly characterized conditions. The precision and reliability of the observations were such as to provide a good foundation for the theoretical views that continue to play an important role. Smedarchina, Siebrand, and Fernndez-Ramos in Ch. 29 then introduce a novel theoretical approach to the problem of multiple proton transfers and the degree to which proton motions are coupled, making use of experimental results described in other chapters of these volumes.
Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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27 Variational Transition State Theory in the Treatment of Hydrogen Transfer Reactions Donald G. Truhlar and Bruce C. Garrett
27.1 Introduction
Transition state theory (TST) [1–4] is a widely used method for calculating rate constants for chemical reactions. TST has a long history, which dates back 70 years, including both theoretical development and applications to a variety of reactions in the gas phase, in liquids, at interfaces, and in biological systems. Its popularity and wide use can be attributed to the fact that it provides a theoretical framework for understanding fundamental factors controlling chemical reaction rates and an efficient computational tool for accurate predictions of rate constants. TST provides an approximation to the rate constant for a system where reactants are at equilibrium constituted by either a canonical ensemble (thermal equilibrium) or a microcanonical ensemble (corresponding to a fixed total energy). Two advances in TST have contributed significantly to its accuracy: (i) the variational form of TST in which the optimum dividing surface is determined to minimize the rate constant and (ii) the development of consistent methods for treating quantum mechanical effects, particularly tunneling. TST in a classical mechanical world can be derived by making one approximation – Wigner’s fundamental assumption [3]. With this assumption, the net reactive flux through a dividing surface separating reactants and products is approximated by the equilibrium oneway flux in the product direction. In a classical world this approximation leads to an overestimation of the rate constant, since all reactive trajectories are counted as reactive, but some nonreactive ones also contribute to the one-way flux. In variational TST (VTST), the dividing surface is optimized to give the lowest upper bound to the true rate constant [5–7]. The need to include quantum mechanical effects in reaction rate constants was realized early in the development of rate theories. Wigner [8] considered the lowest order terms in an "-expansion of the phase-space probability distribution function around the saddle point, resulting in a separable approximation, in which bound modes are quantized and a correction is included for quantum motion along the reaction coordinate – the so-called Wigner tunneling correction. This separable approximation was adopted in the standard ad hoc procedure for quanHydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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27 Variational Transition State Theory in the Treatment of Hydrogen Transfer Reactions
tizing TST [1]. In this approach, partition functions for bound modes are treated quantum mechanically, usually within a harmonic approximation, and a correction for tunneling through the potential barrier along the reaction coordinate is included. Even though more accurate treatments of tunneling through parabolic barriers have been presented [9], beyond the expansion through "2 of Wigner, tests of TST using accurate quantum mechanical benchmarks have shown that this nonseparable approximation is inadequate for quantitative predictions of rate constants when quantum mechanical effects are important [10, 11]. Breakthroughs in the development of quantum corrections for VTST, particularly tunneling, came from comparing the adiabatic theory of reactions [12–14] with VTST for a microcanonical ensemble (microcanonical variational theory). Even though the two theories are based upon very different approximations, they predict the same reaction rates when the reaction coordinate is defined in the same way in both theories and motion perpendicular to it is treated classically [7] or by an identical quantum mechanical approximation [15]. Consequently, quantum mechanical treatments of reaction-coordinate motion for the adiabatic theory provide a starting point for developing quantal corrections for VTST that include the nonseparable, multidimensional nature of tunneling [16–24]. In these approaches, the multidimensional character of the tunneling is included by specifying an optimal tunneling path through the multidimensional space. This approach was pioneered by Marcus and Coltrin [25], who developed the first successful nonseparable tunneling correction for the collinear H + H2 reaction, for which only one mode is coupled to the reaction coordinate. H-transfer reactions are of great interest because they play important roles in a variety of systems, from gas-phase combustion and atmospheric reactions of small molecules to complex catalytic and biomolecular processes. Many enzyme reactions involve proton or hydride transfer in the chemical step [26], and we know from experience with simpler reactions that multidimensional treatments of the tunneling process are essential for quantitative accuracy and sometimes even for qualitative understanding. From a theoretical point of view H transfer reactions are of great interest because they provide opportunities to study the importance of quantum mechanical effects in chemical reactions and are a good testing ground to evaluate approximate theories, such as TST approaches. There is a long history of applications of TST to H-transfer reactions starting with the H + H2 reaction and its isotopic variants. A comprehensive review of the early literature for the H + H2 reaction appeared over 30 years ago [27]. In the 1960s it was being debated whether quantum mechanical tunneling was important in the H + H2 reaction (see Ref. [28], pp. 204–206]). Since then studies on gas-phase H-atom transfer reactions, particularly using TST methods, have shown definitively that treatment of quantum mechanical effects on both bound modes and reaction coordinate motion is important in the treatment of light-atom transfer reactions, such as hydrogen atom, proton, and hydride transfers. This point is strongly supported by two comprehensive reviews of TST and applications of TST approaches to chemical reactions, including H transfer, that have been published over the past 20 years [4].
27.2 Incorporation of Quantum Mechanical Effects in VTST
Kinetic isotope effects (KIEs) have played an important role in using experiments to unravel mechanisms of chemical reactions from experimental data [29]. The primary theoretical tool for interpreting KIEs is TST [29, 30]. The largest KIEs occur for hydrogen isotopes, for which it is critical to consider quantum mechanical effects. It has also been shown that effects of variationally optimizing the dividing surface can have significant effects on primary hydrogen KIEs [31]. VTST with multidimensional tunneling (MT) provides a more complete theory of kinetic isotope effects, which has recently been demonstrated by its ability to predict kinetic isotope effects in complex systems, such as hydride transfer in an enzymatic reaction [32]. Calculations of reaction rates with variationally determined dynamical bottlenecks and realistic treatments of tunneling require knowledge of an appreciable, but still manageably localized, region of the potential energy surface [33]. In this chapter we assume that such potentials are available or can be modeled or calculated by direct dynamics, and we focus attention on the dynamical methods. In this chapter we provide a review of variational transition state theory with a focus on how quantum mechanical effects are incorporated. We use illustrative examples of H-transfer reactions to assist in the presentation of the concepts and to highlight special considerations or procedures required in different cases. The examples span the range from simple gas-phase hydrogen atom transfer reactions (triatomic to polyatomic systems), to solid-state and liquid-phase reactions, including complex reactions in biomolecular enzyme systems.
27.2 Incorporation of Quantum Mechanical Effects in VTST
An important consideration in developing variational transition state theory is the definition of the dividing surface separating reactants from products. A convenient choice is to consider a one-parameter sequence of dividing surfaces that are defined to be orthogonal to a reaction path [7, 34], rather than to allow more arbitrary definitions. This procedure has a few advantages. First, the variational optimization is performed for one parameter defining the dividing surfaces, even for complex, multidimensional reactions. Second, the reaction path can be uniquely defined as the path of steepest descent in a mass-weighted or mass-scaled coordinate system [35, 36], e.g., the minimum energy path (MEP), and this choice of reaction path has further advantages as discussed below. Third, use of a reaction path allows connection to the adiabatic theory of reactions, which provides the basis for including consistent, multidimensional tunneling corrections into VTST. With this choice of dividing surfaces, a generalized expression for the transition state theory rate constant for a bimolecular reaction is given by: VMEP ðsÞ k T Q GT ðT; sÞ (27.1) kGT ðT; sÞ ¼ r B exp kB T h U R ðT Þ where T is temperature, s is the distance along the reaction path with the convention that s = 0 at the saddle point and s < 0 (> 0) on the reactant (product) side of
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27 Variational Transition State Theory in the Treatment of Hydrogen Transfer Reactions
the reaction path, r is a symmetry factor, kB is Boltzmann’s constant, h is Planck’s constant, Q GT ðT; sÞ is the generalized transition state partition function for the bound modes orthogonal to the reaction path at s, UR ðT Þ is the reactant partition function per unit volume and includes the translational partition function per unit volume for the relative motion of the two reacting species, and VMEP(s) is the potential evaluated on the MEP at s. The symmetry factor r accounts for the fact that the generalized transition state partition function is computed for one reaction path, and for reactions with equivalent reaction paths this partition function needs to be multiplied by the number of equivalent ways the reaction can proceed. In computing the vibrational frequencies that are required to evaluate QGT(T,s) at a value s of the reaction coordinate, we use a projection operator to project seven degrees of freedom out of the system’s Hessian so that the frequencies correspond to a space orthogonal to the reaction coordinate and to three overall translations and three overall vibrations [37–40]. Canonical variational theory (CVT) is obtained by minimizing the generalized transition state rate expression kGT ðT; sÞ with respect to the location s of the dividing surface along the reaction coordinate: kCVT ðT Þ ¼ min kGT ðT; sÞ ¼ kGT T; sCVT ðT Þ s
(27.2)
where sCVT ðT Þ is the location of the dividing surface that minimizes Eq. (27.1) at temperature T. Sometimes it is convenient to write Eq. (27.1) as [16] kGT ðT; sÞ ¼
. i kB T zo h K exp DGGT;o ðsÞ RT T h
(27.3)
where K‡o is the reciprocal of the standard-state concentration for bimolecular reactions (it is unity for unimolecular reactions), R is the gas constant, and DGTGT;o is the standard-state generalized-transition-state theory molar free energy of activation. Then Eq. (27.2) becomes kCVT ðTÞ ¼
. kB T zo K exp DGCVT;o RT T h
(27.4)
where CVT DGCVT;o ¼ DGGT;o s T T
(27.5)
is the standard-state quasithermodynamic molar free energy of activation at temperature T. Although we have described the theory in terms of taking the reaction path as the MEP in isoinertial coordinates, this can be generalized to arbitrary paths by methods discussed elsewhere [41]. The treatment of the reaction coordinate at geometries off the reaction path also has a significant effect on the results; one can use either rectilinear [34, 37–39] or curvilinear [40, 42] coordinates for this pur-
27.2 Incorporation of Quantum Mechanical Effects in VTST
pose, where the latter are more physical and more accurate. In particular, the vibrational modes are less coupled in curvilinear coordinates, and therefore anharmonic mode–mode coupling, which is hard to include, is less important. Recently a method has been presented for including anharmonicity in rate constant calculations of general polyatomics using curvilinear coordinates [43]. An expression similar to Eq. (27.1), but for a microcanonical ensemble (fixed energy instead of temperature) can be obtained for the generalized transition-state microcanonical rate constant. Optimizing the location of the dividing surface for this microcanonical expression at each energy and then performing a Boltzmann average of the microcanonical rate constants yields a microcanonical variational theory expression for the temperature-dependent rate constant. Canonical variational theory optimizes the dividing surface for each temperature, whereas microcanonical variational theory optimizes the dividing surface for each energy, and gives a rate constant that is lower than or equal to the CVT one [7, 15]. The improved canonical variational theory (ICVT) [16] is a compromise between CVT and the microcanonical theory, which only locates one optimum dividing surface for each temperature, but removes contributions from energies below the maximum in the ground-state adiabatic potential. The proper treatment of the reaction threshold in the ICVT method recovers most of the differences between the CVT and microcanonical theory. In most cases, CVT and ICVT give essentially the same predicted rate constants. Equations (27.1) and (27.2) are “hybrid” quantized expressions in which the bound modes orthogonal to the reaction coordinate are treated quantum mechanically, that is, the partition functions Q GT ðT; sÞ and UR ðT Þ are computed quantum mechanically for the bound degrees of freedom, although the reaction coordinate is still classical. In recent work we often use the word “quasiclassical” to refer to this hybrid. Others, mainly organic chemists and enzyme kineticists, often call this “semiclassical,” but chemical physicists eschew this usage because “semiclassical” is often a good description for the WKB-like methods that are used to include tunneling. The “hybrid” or “quasiclassical” approach is very old [1]. As the next step we go beyond the standard treatment, and we discuss using the adiabatic theory to develop a procedure for including quantum effects on reaction coordinate motion. A critical feature of this approach is that it is only necessary to make a partial adiabatic approximation, in two respects. First, one needs to assume adiabaticity only locally, not globally. Second, even locally, although one uses an adiabatic effective potential, one does not use the adiabatic approximation for all aspects of the dynamics. 27.2.1 Adiabatic Theory of Reactions
The adiabatic approximation for reaction dynamics assumes that motion along the reaction coordinate is slow compared to the other modes of the system and the latter adjust rapidly to changes in the potential from motion along the reaction coordinate. This approximation is the same as the Born–Oppenheimer electronically adiabatic separation of electronic and nuclear motion, except that here we
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27 Variational Transition State Theory in the Treatment of Hydrogen Transfer Reactions
use the vibrationally adiabatic approximation for an adiabatic separation of one coordinate, the reaction coordinate, from all other nuclear degrees of freedom [1, 14, 44]. The Born–Oppenheimer approximation is justified based on the large mass difference between electrons and atoms. It is less clear that the adiabatic approximation should be valid for separating different nuclear degrees of freedom, although a general principle for applying this to chemically reactive systems near the dynamical bottleneck would be that near the reaction threshold energy (which is the important energy range for thermally averaged rate constants), the reaction coordinate motion is slow because of the threshold condition. As we discuss below, the vibrationally adiabatic approximation can provide a useful framework for treating quantum mechanical tunneling. For chemical reactions, the adiabatic approximation is made in a curvilinear coordinate system where the reaction coordinate s measures progress along a curved path through Cartesian coordinates, and the remainder of the coordinates u are locally orthogonal to this path. Note that the effective mass for motion along the reaction coordinate is unambiguously defined by the transformation from Cartesian to curvilinear coordinates. The effective mass may be further changed by scaling of the coordinates and momenta. When one scales a coordinate um by a constant c1/2, one must change the reduced mass lm for that coordinate by a factor of c–1 so that the kinetic energy, 12 lm l_ 2m , where an overdot denotes a time derivative, stays the same [45]. We are free to choose the value of the reduced mass for each coordinate, and we choose it consistently to be the same value l for all coordinates because this makes it easier to write the kinetic energy for curved paths and for paths at arbitrary orientations with respect to the axes, and it makes it easier to make physical dynamical approximations. Coordinate systems in which the reduced masses for all motions are the same are called isoinertial. In the present article we call the constant reduced mass l and set it equal to the mass of the hydrogen atom to allow easier comparison of intermediate quantities that depend on the reaction coordinate. A convenient choice of the reaction path is the MEP in isoinertial coordinates, because by construction the gradient of the potential V(s,u) is tangent to s and there is no coupling between s and u through second order. Therefore the potential can be conveniently approximated by V ðs; uÞ ¼ VMEP ðsÞ þ Vu ðu; sÞ » VMEP ðsÞ þ
X
ui Hij ðsÞuj
(27.6)
i;j
where the Hessian matrix for a location s along the reaction coordinate is given by ¶2 V Hij ðsÞ ¼ (27.7) ¶ui ¶uj s;ui ¼uj ¼0
and we choose the origin for the u coordinates to be on the MEP. Although the potential energy term in these coordinates is simple, the kinetic energy term is complicated by factors dependent upon the curvature of the reaction path [13, 14,
27.2 Incorporation of Quantum Mechanical Effects in VTST
37, 46]. As a first approximation we will assume that the reaction-path curvature can be neglected, but we will eliminate this approximation after Eq. (27.22) because the curvature of the reaction path is very important for tunneling. Treating bound modes quantum mechanically, the adiabatic separation between s and u is equivalent to assuming that quantum states in bound modes orthogonal to s do not change throughout the reaction (as s progresses from reactants to products). The reaction dynamics is then described by motion on a one-mathematicaldimensional vibrationally and rotationally adiabatic potential Va ðn; K; sÞ ¼ VMEP ðsÞ þ eGT int ðn; K; sÞ
(27.8)
where n and K are quantum numbers for vibrations and rotations, respectively, and eGT int ðn; K; sÞ is the vibrational-rotational energy of quantum state (n,K) of the generalized transition state at s. In a rigid-body, harmonic approximation, the generalized transitive-state energy level is given by
X 1 eGT ð n; K; s Þ ¼ "x ð s Þ n þ (27.9) þ eGT m m int rot ðK; sÞ 2 m where the harmonic vibrational frequencies xm(s) are obtained from the nonzero eigenvalues of the Hessian matrix in Eq. (27.7), and the rotational energy level eGT rot ðK; sÞ is determined for the rigid-body geometry of the MEP at location s. Six of the eigenvalues of the Hessian will be zero (for a nonlinear system), corresponding to three rotations and three translations of the total system. If the reaction coordinate is treated classically, the probability for reaction on a state (n,K) at a total energy E is zero if the energy is below the maximum in the adiabatic potential for that state, and 1 otherwise: PCA ðn; K; E Þ ¼ h E VaA ðn; KÞ (27.10) where VaA ðn; KÞ is the absolute maximum of the adiabatic potential Va ðn; K; sÞ and h(x) is a Heaviside step function such that h(x) = 0 (1) for x < 0 (> 0). Since the classical reaction probability is determined entirely by whether the energy is above the adiabatic barrier or not, the neglect of reaction-path curvature in the kinetic energy term does not matter. We shall see below that this is not true when the reaction path is treated quantum mechanically, in which case the curvature of the reaction path must be included. An expression for the rate constant can be obtained by the proper Boltzmann average over total energy E and sum over vibrational and rotational states Z X 1 dE expðE=kB T Þ kA ðT Þ ¼ hUR ðT Þ PCA ðn; K; E Þ (27.11) n;K
which can be reduced for a bimolecular reaction to kA ðT Þ ¼
kB T X exp VaA ðn; KÞ=kB T R hU ðT Þ n;K
(27.12)
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27 Variational Transition State Theory in the Treatment of Hydrogen Transfer Reactions
Like Eq. (27.2), Eqs. (27.11) and (27.12) are also hybrid quantized expressions in which the bound modes are treated quantum mechanically but the reaction coordinate motion is treated classically. Whereas it is difficult to see how quantum mechanical effects on reaction coordinate motion can be included in VTST, the path forward is straightforward in the adiabatic theory, since the one-dimensional scattering problem can be treated quantum mechanically. Since Eq. (27.12) is equivalent to the expression for the rate constant obtained from microcanonical variational theory [7, 15], the quantum correction factor obtained for the adiabatic theory of reactions can also be used in VTST. 27.2.2 Quantum Mechanical Effects on Reaction Coordinate Motion
A fully quantum mechanical expression for the rate constant within the adiabatic approximation is given by replacing the classical reaction probabilities in A ðn; K; E Þ corresponding to oneEq. (27.11) with quantum mechanical ones PQ dimensional transmission through the potential Va(n,K,s). Note that, at the energies of interest, tunneling and nonclassical reflection by this potential are controlled mainly by its shape near the barrier top, that is, near the variational transiA ðn; K; sÞ only requires the assumption of local vibrational adiation state. Thus PQ baticity along with the observation that reactive systems pass through the dynamical bottleneck region in quantized transition states [47]. The quantum mechanical vibrationally and rotationally adiabatic rate constant can be expressed in terms of the hybrid expression in Eq. (27.12) by kVA ðT Þ ¼ kVA ðT Þ kA ðT Þ
(27.13)
where the transmission coefficient is defined by R¥ k ðT Þ ¼ VA
0 R¥ 0
dE expðE=kB T Þ dE expðE=kB T Þ
P n;K
P n;K
A ðn; K; E Þ PQ
(27.14) PCA ðn; K; E Þ
Rather than compute the reaction probabilities for all quantum states that contribute significantly to the sum in Eq. (27.14), we approximate the probabilities for all excited states by the probabilities for the ground state with the energy shifted by the difference in adiabatic barrier heights (relative to a single overall zero of energy) for the excited state, VaA ðn; KÞ, and ground state, VaAG [16]: A AG PQ ðn; K; E Þ ¼ PQ E VaA ðn; KÞ VaAG
(27.15)
AG where PQ ðE Þ is the reaction probability for the ground-state adiabatic potential. This approximation assumes that adiabatic potentials for excited states are similar in shape to the ground-state potential. Although this approximation is not valid in
27.2 Incorporation of Quantum Mechanical Effects in VTST
general, it works surprisingly well for calculating the transmission coefficient because at low temperatures the transmission coefficient is dominated by contributions from the ground state or states energetically similar to the ground state, and at high temperatures, where classical mechanics becomes valid, it correctly goes to a value of one. With this approximation the transmission coefficient takes the form R¥ k
VAG
ðTÞ ¼
0 R¥ 0
AG dE expðE=kB T ÞPQ ðEÞ
(27.16) dE expðE=kB T ÞPCAG ðEÞ
AG A ðn; K; EÞ with n, K in where G in general denotes the ground state, PQ ðEÞ is PQ AG AG the ground state, and PC ðEÞ is like PQ ðEÞ for all degrees of freedom except the reaction coordinate, but with the reaction coordinate motion classical. Then
PCAG ðEÞ ¼ h E VaAG
(27.17)
where VaAG ¼ VaA ½ðn; KÞ ¼ G
(27.18)
This yields kVAG ðT Þ ¼ ðkB T Þ1 exp V AG kB T
Z¥ AG dE expðE=kB T ÞPQ ðE Þ
(27.19)
0
We first consider the case where the reaction probabilities are computed for the adiabatic model with the reaction-path curvature neglected, the so-called vibrationally adiabatic zero-curvature approximation [36]. We approximate the AG ðE Þ for the one-dimenquantum mechanical ground-state probabilities PQ sional scattering problem by a uniform semiclassical expression [48], which for E < V AG is given by PSAG ðE Þ ¼ f1 þ exp½2hðE Þg1
(27.20)
where the imaginary action integral is hðE Þ ¼ "
1
Zs>
1 ds 2l VaG ðsÞ E 2
(27.21)
s<
l is the mass for motion along the reaction coordinate, VaG ðsÞ is the ground-state adiabatic potential, that is Va ðn; K; sÞ for n = K = 0, and s< and s> are the classical turning points, that is the locations where VaG ðsÞ = E. The uniform semiclassical
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27 Variational Transition State Theory in the Treatment of Hydrogen Transfer Reactions
approximation can be extended to energies above the ground-state barrier maximum for a parabolic barrier [48] PSAG V AG þ DE ¼ 1 PSAG V AG DE
(27.22)
and we use this method to obtain reaction probabilities for energies above the barrier maximum up to 2V AG – E0, where E0 is the maximum of the reactant and product zero-point energies. For higher energies the probability is set to one. When one uses CVT, one must replace PCAG ðEÞ by an approximation that is consistent with the threshold implicitly assumed by CVT. In particular we replace VaAG by VaG ½sCVT ðTÞ in Eq. (27.17). This then yields for the rate constant with tunneling kCVT=MT ðTÞ ¼ kðTÞkCVT ðTÞ
(27.23)
where R¥ kðTÞ ¼
0
AG dðE=kB T ÞexpðE=kB T ÞPQ
exp VaG ½sCVT ðTÞ
(27.24)
and where MT can be SCT, LCT, or OMT. The inability of the zero-curvature tunneling (ZCT) approximation to provide reliable rate constants has been known for over 30 years [10, 36], and over the last 25 years significant progress has been made in developing approaches to treat the multidimensional effect of reaction-path curvature in adiabatic calculations of reaction probabilities. The most successful methods for including the multidimensional effect of reaction-path curvature in adiabatic calculations of reaction probabilities specify a tunneling path that cuts the corner’ and shortens the tunneling length [18]. Marcus and Coltrin [25] found the optimum tunneling path for the collinear H + H2 reaction by finding the path that gave the least exponential damping. General multidimensional tunneling (MT) methods, applicable to polyatomic reactions, have been developed that are appropriate for systems with both small [17, 18, 22, 24] and large [20, 23, 34] reaction path curvature, as well as more general methods that optimize tunneling paths by a least-imaginary-action principle [20, 39]. In practice it is usually sufficient to optimize the imaginary action from among a small set of choices by choosing either the small-curvature tunneling (SCT) approximation or the large-curvature tunneling (LCT) approximation, whichever gives more tunneling at a given tunneling energy; this is called microcanonical optimized multidimensional tunneling (lOMT), or, for short, optimized multidimensional tunneling (OMT) [23, 49]. These methods are discussed below in more detail in the context of illustrative examples of H-transfer processes, but we anticipate that discussion and the later discussion of con-
27.3 H-atom Transfer in Bimolecular Gas-phase Reactions
densed-phase reactions by noting that all MT approximations generalize Eq. (27.24) to R¥ kðTÞ ¼
0
dðE=kB T ÞexpðE=kB T ÞPðV1 ; V2 jE Þ
exp V2 s ðTÞ kB T
(27.25)
where V1 is the effective multidimensional potential energy surface, V2 is the effective one-dimensional adiabatic potential energy curve, and s*(T) is the variational transition state location at temperature T. In the ZCT and SCT approximations, one need not specify V1, that is the tunneling depends only on the effective one-dimensional adiabatic potential energy curve, but in the LCT and OMT approximations we need to know more about the potential energy surface than just the information contained in V2(s). For gas-phase reactions, V2(s) is just VaG ðsÞ, and V1 is the full potential energy surface.
27.3 H-atom Transfer in Bimolecular Gas-phase Reactions
Gas-phase reactions of two interacting reactants have provided a fertile ground for developing and testing methods for treating H-transfer reactions. In particular, triatomic reactions like H + H2 have been instrumental in this development and in helping us understand the limits of validity of the approximations used in these methods, because accurate quantum mechanical results are available for comparison. We present three examples of reactions that help us present details of the methods as well as features displayed by H-atom transfers. 27.3.1 H + H2 and Mu + H2
The H + H2 reaction and its isotopic variants have been extensively studied over the years. Muonium (Mu) is one of the most interesting isotopes studied for this reaction because Mu (consisting of a positive muon and an electron) has a mass that is about 8.8 times smaller than that of H and has the potential to exhibit very large kinetic isotope effects. Even though both reactions, H + H2 and Mu + H2, involve the transfer of a H atom, the presence of the much lighter Mu atom drastically changes the nature of the quantum mechanical effects on the H-transfer process. Calculations of H- and Mu-transfer rate constants are illustrated here using the Liu–Siegbahn–Truhlar–Horowitz (LSTH) potential energy surface [50]. The traditional treatment of KIEs is based upon conventional TST [29, 30], in which the dividing surface is placed at the saddle point of the reaction, with tunneling effects generally included by a separable approximation such as the Wigner
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27 Variational Transition State Theory in the Treatment of Hydrogen Transfer Reactions
correction or Bell parabolic tunneling. Using this approach with the harmonic approximation, the Mu/H KIE is determined by kMu kW URH QMu ¼ Mu W kH kH URMu QH
(27.26)
The Wigner correction for tunneling depends only on the imaginary frequency xs;X for the unbound mode at the saddle point [8] 12 0 " x s;X 1 @ A kX ¼ 1 þ 24 kB T
(27.27)
Reactant vibrational and rotational partition functions are the same for both reactions (i.e., those for H2) and the ratio of reactant partition functions reduces to the ratio of translational partition functions, which depends only on the reduced masses for the relative motion of the reactants 3 URH mH ðmMu þ 2mH Þ 2 ¼ » 15:5 mMu ð3mH Þ URMu
(27.28)
The ratio of partition functions for bound modes at the saddle point is determined by the frequencies for those modes, Y sinh "xMu;i =2kB T QMu F1 ¼ QH i¼1 sinh "xH;i =2kB T
(27.29)
where F is the number of vibrational modes. With the rate constant for the reaction with the light mass in the numerator, a KIE is termed normal’ if it is greater than one. Because of the large difference in masses, the saddle point frequencies for the Mu reaction are larger than those of the H reaction, and the ratio of saddle point partition functions is less than one. The imaginary frequency for the reaction coordinate motion is also higher for the Mu reaction than for the H reaction, so that the ratio of tunneling factors is greater than one as well as the ratio of reactant partition functions. The saddle point frequencies for these two reactions using the LSTH potential energy surface are (2059, 909, and 1506 i cm–1) and (4338, 1382, and 1784 i cm–1) and for the (stretch, bend, and unbound) modes for H + H2 and Mu + H2, respectively. Using these frequencies in harmonic transition state theory with Wigner tunneling gives a KIE less than one, which is termed inverse, as shown in Fig. 27.1, where the TST/W results are compared with experiment [51]. Although TST with Wigner tunneling gives the right qualitative trend, both the magnitude and slope are inaccurate. We next discuss the other curves in Fig. 27.1, which present improvements in the treatment of quantum mechanical effects for the hydrogen transfer process.
27.3 H-atom Transfer in Bimolecular Gas-phase Reactions
Figure 27.1 Kinetic isotope effects for the Mu/H + H2 reaction as a function of temperature.
A first consideration is the treatment of the bound vibrational modes, which in the TST/W results shown in Fig. 27.1, use the harmonic approximation. The total harmonic zero-point energy at the saddle point (for stretch and bend vibrations) is much higher for the Mu reaction, 10.2 kcal mol–1, than for the H reaction, 5.5 kcal mol–1. As shown in Fig. 27.2, the stretching vibration extends to larger distances and higher energies for the Mu reaction than for the H reaction, and therefore accesses more anharmonic parts of the potential. In this situation methods for including anharmonicity must be considered [52, 53]. The straight lines through the saddle point end at the classical turning points for the harmonic approximation to the stretch potential at the saddle point. For the symmetric H + H2 reaction the harmonic turning points extend just past the 12 kcal mol–1 contour, and on the concave side, it is very close to the accurate anharmonic turning point, calculated using a WKB approximation [53]. For the Mu + H2 reaction the harmonic turning point on the concave side falls short of the anharmonic turning point, which is near the 16 kcal mol–1 contour, and it extends past the 20 kcal mol–1 contour on the convex side of the turning point, clearly indicating that the potential for this mode is quite anharmonic. Comparison of the curves label TST/W (harmonic treatment) and TST/W (WKB) in Fig. 27.1 shows the importance of anharmonicity in the quantum treatment of bound states. When the vibrational modes at the saddle point are treated more accurately using a WKB method [53], the Mu rate constants are increased by about a factor of two, while the H rate constants change only slightly, leading to a larger disagreement with experiment for the KIE. A more accurate treatment of the reaction uses variational TST, in which the dividing surface is allowed to move off the saddle point, or equivalently, uses the adiabatic theory as described in Section 27.2. The vibrationally adiabatic potential
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27 Variational Transition State Theory in the Treatment of Hydrogen Transfer Reactions
Figure 27.2 Potential energy contours (thin solid curves) at 4, 8, 12, 16, and 20 kcal mol–1 are shown for collinear A–HH geometries (A = H or Mu) with HH and AH distances represented by R1 and R2, respectively. The solid diamond denotes the saddle point. Thick solid and dashed curves are for
the H and Mu reactions, respectively. Harmonic stretch vibrational modes are the straight lines through the saddle point. Minimum energy paths are the curved lines through the saddle point. The curved lines on the concave side of the MEP are paths of turning points for the anharmonic stretch vibration.
curves for the two reactions are shown in Fig. 27.3 and are compared with the potential along the MEP. The MEPs for the two reactions, as shown in Fig. 27.2, are very close to each other, so that the potentials along the MEP are also about the same. Note that the MEPs are paths of steepest descent in a mass-weighted or mass-scaled coordinated system, and therefore, the MEPs for the H and Mu reactions are slightly different. The largest differences are seen in the entrance channel (large R1) where the reaction coordinate is dominated by either H or Mu motion relative to H2, while in the exit channel (large R2) the reaction coordinate for both reactions is an H atom moving relative to the diatomic product (either H2 or MuH). The reaction coordinate in Fig. 27.3 is defined as the arc length along the MEP through mass-weighted coordinates. To facilitate comparisons of potential curves for the two reactions, we use the same effective mass for the mass weighting – the mass of the hydrogen atom. Because the mass of Mu is so much lighter than H, the scale of s on the reactant side is contracted when the same mass weighting is used for both reactions, leading to a steeper increase for Mu. The ground-state adiabatic potential curves in Fig. 27.3 are constructed by adding accurate anharmonic zero-point energies for the stretch and bend modes to VMEP. On the reactant side the shapes of VMEP and VaG are very similar with the adiabatic potential being shifted up by approximately the zero-point energy for the H2 stretch vibrations, 6.2 kcal mol–1. Near the saddle point this contribution decreases markedly for the H + H2 reaction, to 2.9 kcal mol–1, causing the adia-
27.3 H-atom Transfer in Bimolecular Gas-phase Reactions
Figure 27.3 Potential along the MEP (VMEP, lower pair of curves) and ground-state adiabatic potential (VaG , upper pair of curves) as a function of reaction coordinate s for the H + H2 reaction (solid lines) and Mu + H2 reaction (dashed line).
batic potential to be less peaked than VMEP for this reaction. Contributions from the bending vibration near the saddle point are about 2.6 kcal mol–1, otherwise the adiabatic potential curve would be even flatter near the saddle point. The zeropoint energy for MuH is 13.4 kcal mol–1, which accounts for the large difference in the H and Mu adiabatic curves in the product region and the shift of its maximum toward products. The difference in the maximum of the adiabatic curve and its value at the saddle point is about 2.3 kcal mol–1, which leads to a decrease by about a factor of 10 in the Mu rate constant at 500 K. This is the main reason for the large shift in the curve labeled ICVT/SCSAG (WKB) relative to the TST/W (WKB) curve in Fig. 27.1. We now turn our attention to the issue of quantum mechanical tunneling in these H-atom transfer reactions. The Wigner and Bell tunneling methods use the shape of VMEP at the saddle point to estimate the tunneling correction. The effective mass for the reaction coordinate in Fig. 27.3 is the same for both reactions, therefore, tunneling is treated as the motion of a particle with the mass of a hydrogen atom through the potentials in the figure. The similarity in the VMEP curves for H and Mu indicates why the tunneling correction using these methods gives similar results for the H and Mu reactions. For example, Wigner tunneling gives corrections for Mu that are less than 30% higher those for H for 300 K and higher temperatures. The shapes of the adiabatic curves exhibit greater differences with the curve for the Mu reaction having a narrow barrier near the maximum. When reaction-path curvature is neglected, the tunneling correction factors for Mu are factors of 2.5 and 1.6 higher than those for H at temperatures of 300 and 400 K.
847
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27 Variational Transition State Theory in the Treatment of Hydrogen Transfer Reactions
As discussed above, the most accurate methods for treating tunneling include the effects of reaction-path curvature. The original small-curvature tunneling (SCT) method [17] provides an accurate description of the H-transfer process in these triatomic H-atom transfer reactions. In the Marcus–Coltrin method [25] the tunneling occurs along the path of concave-side turning points for the stretch vibration orthogonal to the reaction coordinate. Figure 27.2 shows paths of turning points tstr(s) for the stretch vibration for the H/Mu + H2 reactions, where the turning points are obtained for the anharmonic potential at the WKB zero-point energy. Tunneling along this path shortens the tunneling distance and the effect of the shortening of the path can be included in the calculation of the action integral by replacing the arc length along the MEP ds in Eq. (27.15) by the arc length along this new path dn, or equivalently by including the Jacobian dn/ds in the integrand of Eq. (27.15). An approximate expression for dn/ds can be written in terms of the curvature of the MEP and vibrational turning points [17, 18]. The MEP is collinear for the H + H2 reaction and the curvature coupling the bend vibration to the reaction coordinate is zero for collinear symmetry. Therefore, the Jacobian can be written just in terms of the one mode
2
dn dtstr 2 » ½1 kðsÞtstr ðsÞ2 þ ds ds
(27.30)
The SCT method extends the Marcus–Coltrin idea in a way that eliminates problems with the Jacobian becoming unphysical. Rather than including the Jacobian factor, the reduced mass for motion along the reaction coordinate l is replaced by leff(s) in Eq. (27.21), where leff(s) is given by ( "
#) leff ðsÞ dtstr 2 » min 1; exp 2aðsÞ ½aðsÞ2 þ l ds
aðsÞ ¼ kðsÞtstr ðsÞ
(27.31)
(27.32)
where j(s) is the curvature coupling between the reaction coordinate motion and the stretch vibrational motion [37]. Note that the signs of j(s) and tstr(s) are chosen so that the path lies on the concave side of the path and their product a(s) is positive. The reaction-path curvature is given by the coupling of the stretch vibration to the reaction coordinate in the mass-weighted coordinate system, not the coordinate system used to display the paths in Fig. 27.2. The reaction Mu + H2 has smaller reaction-path curvature than the H + H2 reaction, by about a factor of two in the region near the peak of the adiabatic barriers, and the enhancement of the tunneling from corner cutting is much less for the Mu reaction. Neglect of reaction-path curvature gave tunneling factors for the Mu reaction that are much higher than those for the H reaction and including the effects of the curvature greatly reduces this large difference. In fact, at 300 K without curvature the Mu reaction
27.3 H-atom Transfer in Bimolecular Gas-phase Reactions
has a tunneling factor that is 2.5 times larger than the H reaction and this is reduced to an enhancement of only 2% when curvature is included with the SCT method. For temperatures from 400 to 600 K, the SCT tunneling factors for the Mu reaction are lower than those for the H reaction by about 9%. When these effects are included the predicted KIEs are in good agreement with the experimental results, being only 30–40% low, as shown in Fig. 27.1. The H/Mu + H2 reactions are examples of H-atom transfers with relatively small reaction-path curvature and provide a good example of how the description of the hydrogen transfer process is effected by quantization of bound modes, variational optimization of the location of the dividing surface, and inclusion of quantum mechanical effects on reaction coordinate motion. The magnitude of the reaction-path curvature for an H-atom transfer reaction is often correlated with the skew angle, where the skew angle is defined as the angle between the gradient along the reaction path in the product channel with that in the reactant channel. For the H-atom transfer reaction AH + B fi A + BH this angle is defined by cos b skew ¼
mA mB ðmA þ mH ÞðmB þ mH Þ
1=
2
(27.33)
where A and B can be atomic or polyatomic moieties with masses mA and mB. Skew angles for the H and Mu reactions are 60 and 77, respectively, and we saw above how the larger curvature in the system with the smaller skew-angle system resulted in greater tunneling. When the masses of A and B are much larger than the mass of H, the skew angle can become very small, resulting in large reactionpath curvature. These systems require tunneling methods that go beyond the small-curvature approach used here. 27.3.2 Cl + HBr
The collinear Cl + HBr reaction provides an example of a system with a very small skew angle. Figure 27.4 shows potential energy contours for this collinear reaction in mass-scaled coordinates x and y for the potential energy surface of Babamov et al. [54], where x is the distance from Cl to the center of mass of HBr and y is a scaled HBr distance. The kinetic energy is diagonal in this coordinate system and the scaling of y is chosen so that the effective masses for x and y motion are the same. Therefore, reaction dynamics in this coordinate system can be viewed as a single mass point moving on the potential energy contours in Fig. 27.4. The skew angle, which in this coordinate system is the angle between the minimum energy path in the asymptotic reactant channel and the asymptotic product channel, is only 12. Regions of large reaction-path curvature, which can be seen near the saddle point, lead to a breakdown of the approximations used in the SCSAG method. The approximation of vibrational adiabaticity is valid in the entrance and exit channels where the stretch vibration is dominated by motion of the hydrogen
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27 Variational Transition State Theory in the Treatment of Hydrogen Transfer Reactions
Figure 27.4 Potential energy contours (thin solid curves) from –10 to 20 kcal mol–1 (spaced every 5 kcal mol–1) are shown for the collinear Cl–H–Br reaction as a function of internal coordinates x and y (see text). A solid diamond denotes the saddle point and the thick straight line through the saddle point is the anharmonic vibrational mode. The thick solid curve is the minimum energy path. The classical turning point on the groundstate adiabatic potential energy curve at
9 kcal mol–1 is indicated by the unfilled symbol in the entrance channel. Turning points for adiabatic potential curves with the stretch vibration in its ground state (n = 0) and excited state (n = 2) are shown as an unfilled circle (n = 0) and square (n = 2) in the exit channel. Dashed lines connect the turning point for the ground-state adiabatic potential curve in the entrance channel with the turning points for n = 0 and 2 in the exit channel.
atom. At the saddle point the vibrational motion more nearly resembles the relative motion of the two heavy atoms leading to a low vibrational energy (e.g., only 0.4 kcal mol–1 at the saddle point compared to 3.8 kcal mol–1 for reactants). The thick straight line through the saddle point shows the extent of the vibrational motion. Because of the large reaction-path curvature, the regions of vibrational motion in the reactant valley on the concave side of the MEP, just before the bend in the MEP, overlap with the vibrational motion at the saddle point. This complication, and the strong coupling of the reaction coordinate motion to the vibration orthogonal to it, argues against an adiabatic treatment of hydrogen atom tunneling in the saddle point region. For this type of system the LCT method is more appropriate [19, 20, 22, 39, 49, 55], and we describe it briefly here. A key aspect of LCT methods is that the tunneling depends on more aspects of the potential energy surface than just VaG ðsÞ, and that is why we introduced the multidimensional potential energy surface in Eq. (27.25). In the vibrationally adiabatic approximation, tunneling at a fixed total energy is promoted by motion along the reaction coordinate and initiates from the classical turning point on the adiabatic potential. The physical picture in the LCT method is that the rapid vibration of the hydrogen atom promotes transfer of the hydrogen atom between the reactant and product valleys and this hopping begins from turning points in the vibrational coordinate on the concave side of the MEP. For a given total energy, tunneling can take place all along the entrance channel, up to the adiabatic turning point, as the reactants approach and recede. Tunneling is assumed to occur along straight-line paths from the reactant to product valleys, subject to the constraint that adiabatic energies in the reactant and product channels are the same. Figure 27.4 illustrates the LCT tunneling paths, where the straight dashed line is the tunneling path connecting points, denoted by open cir-
27.3 H-atom Transfer in Bimolecular Gas-phase Reactions
cles, along the MEP for which the ground-state adiabatic potential curve has an energy of 9 kcal mol–1. In the large-curvature ground state approximation, version 3 or version 4 [22, 39, 49], the straight-line path used to specify a given tunneling path initiates and terminates on the MEP rather than at the turning points for the vibrational motion. This assumption simplifies the extension of the method to polyatomic reactions, and it yields results that are similar to earlier versions of the method with more complicated specifications. In current work one should always use the latest version (version 4) of the LCT method because it incorporates our most complete experience on how to embed the physical approximations in a stable algorithm, although the differences between the versions are small in most cases. Although the LCT method does not rely on the adiabatic approximation in the region where it breaks down (i.e., the nonadiabatic region), it does use the approximation in the reactant and product channels to determine the termini for the straight-line tunneling paths. Figure 27.5 shows adiabatic potential curves in the reactant and product regions and the potential along the MEP. This reaction is exoergic by about 16 kcal mol–1 with a barrier over 10 kcal mol–1 higher than the minimum of the reactant valley. Because of the large exoergicity and rapid decrease of the potential along the MEP on the product side, the value of the
Figure 27.5 Potential along the minimum energy path (lowest continuous curve) and adiabatic potential segments in the reactant and product regions for n = 0 (solid curve), 1 (long dashed curve) and 2 (short dashed curve) as a function of reaction coordinate for the collinear Cl + HBr reactions. The values of the adiabatic potential curves in the asymptotic reactant and product regions are
shown as short straight-line segments on the left and right of the plot. The gray shaded area around the saddle point is a region where the adiabatic approximation is not valid (see text). The 3 small tick marks at s = 0 are the values the 3 adiabatic potential curves would have at the saddle point. The bullets are turning points for a total energy of 9 kcal mol–1.
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27 Variational Transition State Theory in the Treatment of Hydrogen Transfer Reactions
ground-state adiabatic potential at the edge of the nonadiabatic region on the product side is already quite low (near 0). The vibrationally adiabatic approximation requires that vibrational quantum numbers remain constant throughout a reaction. The strong coupling induced by the reaction-path curvature can lead to appreciable nonadiabaticity and population of excited states in the product channel, and this effect is included in the LCT method. (As mentioned above, the SCT approximation does not imply global vibrational adiabaticity either, but it does assume adiabaticity for the effective potential during the entire tunneling event itself; the LCT approximation includes vibrational nonadiabaticity even for the effective potential during the tunneling event.) Figure 27.5 shows the product-channel segments of the adiabatic potential curves for the ground and first two excited states. The product-side turning point for the first excited adiabatic curve also falls within the nonadiabatic region like the ground-state one, and on the scale of the plot is not discernible from the ground-state turning point. The energies of the n = 2 adiabatic curve are sufficiently high that the turning points occur well out into the product region (around s = 1 a0 for a tunneling energy of 9 kcal mol–1). Figure 27.4 shows the tunneling path corresponding to these turning points. This path is seen to cut the corner significantly. The barrier to tunneling along this path is comparable to the adiabatic barrier and the shorter tunneling path offered by this corner cutting greatly enhances the tunneling. The LCT method was extended to account for contributions from tunneling into excited states of products [55], and for this reaction, the contribution to the tunneling correction factor is dominated by tunneling into the n = 2 state. The small-curvature (SC) and large-curvature (LC) methods were developed to treat tunneling in the cases of two extremes of reaction-path curvature. In the SC methods, the effective tunneling path (which is implicit but never constructed and not completely specified, since it need not be) is at or near the path of concave-side turning points for the bound vibrational motions that are coupled to the reaction coordinate motion. In the LC methods, the effective tunneling paths (which are explicit) are straight-line paths between the reactant and product valleys. The optimum tunneling paths for reactions with intermediate reaction-path curvature may be between these two extremes, and for these reactions the leastaction tunneling (LAT) method [20, 39, 56] is most appropriate. In the LAT method, we consider a sequence of tunneling paths depending on a single parameter a such that for a = 0 the tunneling path is the MEP and for a = 1 it is the LCT tunneling path. The optimum value of a (yielding the optimum tunneling path) for each tunneling energy is determined to minimize the imaginary-action integral and thereby maximize the tunneling probability. Figure 27.6 compares rate constants computed by the ICVT method, including tunneling by SCT, LCT, and LAT methods, with accurate quantum mechanical ones [55] for the collinear Cl + HBr reaction. The adiabatic method (SCT) cannot account for the large probability of populating the n = 2 excited product state and underestimates the accurate rate constants by factors of 3 to 6 for temperatures from 200 to 300 K. The LCT and LAT methods agree to within plotting accuracy, and are therefore shown as one
27.3 H-atom Transfer in Bimolecular Gas-phase Reactions
Figure 27.6 Rate constants as a function of temperature for the collinear Cl + HBr reaction. Accurate quantum mechanical rate constants (solid line with bullets) are compared with those computed using improved canonical variational theory (ICVT) with tunneling included by SCSAG (dotted line) and LCG3 and LAG (long dashed line).
curve, indicating that the optimum tunneling paths for this reaction are the straight-line paths connecting the reactant and product valleys. These methods underestimate the accurate rate constants by only 10–25% for T from 200 to 300 K and agree to within 50% over the entire temperature range from 200 to 1000 K. The excellent agreement with accurate rate constants for this model system indicates the good accuracy provided by the LCT and LAT methods for this type of small skew angle reaction. The physical picture of tunneling in this system provided by the approximate, yet accurate, tunneling methods is very different than descriptions of tunneling in simpler conventional models of tunneling. In the Wigner and Bell tunneling approximations, properties of the potential near the saddle point determine the tunneling correction factors. As illustrated in Fig. 27.4, barriers along straight-line paths, which connect the reactant and product channels, control the actual tunneling in this small-skew angle system, and these paths are significantly displaced from the saddle point. 27.3.3 Cl + CH4
The higher dimensionality of polyatomic reactions makes them more of a challenge to treat theoretically. Variational transition state theory with multidimensional tunneling has been developed to allow calculations for a wide variety of polyatomic systems. In this section we consider issues that arise when treating polyatomic systems. The Cl + CH4 reaction provides a good system for this pur-
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27 Variational Transition State Theory in the Treatment of Hydrogen Transfer Reactions
pose because the accurate SPES potential energy surface of Corchado et al. [57] is available and a variety of experimental results [58] exist to validate the methods. Hydrogen transfer between Cl and CH3 corresponds to a heavy–light–heavy mass combination and this reaction has a small skew angle of about 17 and regions of large curvature along the reaction path. The reaction is endoergic by 6.1 kcal mol–1 on the analytical potential energy surface with its barrier in the product valley (the HCl bond length at the saddle point is only 0.08 longer than HCl in products while the CH bond length is 0.30 longer at the saddle point than in the reactants). Figure 27.7 shows the potential along the MEP and the ground-state adiabatic potential for this reaction, harmonic frequencies xi(s), and components ji(s) of reaction-path curvature along the reaction coordinate. Although there are 11 vibrational modes orthogonal to the reaction path, only 3 have significant curvature components. Relative motion of the two heavy moieties CH3 and Cl dominates the reaction coordinate in the reactant and product regions, while in the interaction region, where the curvature is largest, motion of the H atom between CH3 and Cl characterizes reaction coordinate motion. The mode that couples most strongly to reaction coordinate motion mirrors this behavior and is denoted the reactive mode. It originates as a nondegenerate CH stretch in the reactants, transforms into motion that is dominated by C–Cl vibration in the region of strong coupling, and ends as an HCl stretch in the products. Note that regions of large reaction-path curvature also coincide with regions where the har-
Figure 27.7 (a) Potential energy and ground-state adiabatic potential curves as a function of reaction coordinate for the Cl + CH4 reaction using the SPES surface. (b) Nine highest harmonic frequencies for modes orthogonal to the reaction coordinate. Doubly degenerate modes are shown as dashed curves. The two lowest frequency transition modes are not shown. (c) Components of reaction-path curvature (solid lines) for 3 vibrational modes and two approximations for turning points along the curvature vector (dashed curves) as a function of reaction coordinate. Short dashed curve is ^(s)· t(s) approximation and the long dashed curve is t(s) (see text). the j
27.3 H-atom Transfer in Bimolecular Gas-phase Reactions
monic frequencies change rapidly and we observe crossings of modes. Because of the late barrier, the largest curvature occurs well before the saddle point (between s = –0.6 and –0.4 a0), where the potential along the MEP is only about half the value at the barrier maximum and the adiabatic potential exhibits a local minimum. The peak in the curvature and dip in the adiabatic potential are a result of the transformation of the reactive mode from a high-frequency CH stretching mode (2870 cm–1 in the reactants) to a lower frequency mode (~1300 cm–1 at s = –0.5 a0) with contributions from CCl motion. A second region of large curvature occurs near the saddle point where this low-frequency mode transforms into a high frequency HCl vibration (2990 cm–1 at products). A second mode, corresponding to a methyl umbrella mode, also shows significant coupling to the reaction coordinate, and the value of curvature coupling for this mode is larger than the reactive mode near s = 0). A third mode, corresponding to a high-frequency CH stretching mode throughout the reaction, exhibits much smaller, but still significant, coupling near s = –0.5 a0). Accurate treatment of tunneling in this reaction requires consideration of how the curvature in multiple dimensions is taken into account. First we consider how the SCT method is defined to consistently treat reactions with curvature coupling in multiple modes. In SCT, we assume that the corner cutting occurs in the direction along the curvature vector j(s) in the space of the local vibrational coordinates Q. To emphasize this, the final version of the SCT method was originally called the centrifugaldominant small-curvature approximation [22]. In this method, we make a local rotation of the vibrational axes so that j(s) lies along one of the axes, u1, and by construction the curvature coupling in all other vibrational coordinates, ui, i = 2 to F – 1, are zero in this coordinate system. Defining tðsÞ as the turning point for zero-point motion in the potential for the ui coordinate, the effective mass in the imaginary action integral is given by the SCT expression for one mode coupled to the reaction coordinate, as written in Eq. (27.31), with a(s) replaced by aðsÞ ¼
F1 X
!12 2
½ki ðsÞ
tðsÞ
(27.34)
i¼1
where F is the number of vibrational modes, ti(s) is the turning point for mode i on the concave side of the MEP. The definition of tðsÞ is provided in previous work for a harmonic description of the vibrational modes [22]. We illustrate here how it works for the Cl + CH4 reaction. As discussed above, only three modes contribute significantly to the reactionpath curvature in the Cl + CH4 reaction, and the coupling for two of the modes is much greater than for the third. Figure 27.8 shows a contour plot of the two harmonic vibrational modes with the largest coupling where the frequencies are those at s = –0.49 a0. Turning points in these modes, t1(s) and t2(s), are indicated by ^(s), a unit vector, of the curvature-coupling the square and triangle. The direction j vector j(s) is shown as a straight line and this line defines the u1 axis. The line ^(s)·t(s) = j1(s)t1(s) + j2(s)t2(s). This approximation extends out to a value equal to j to the turning point in u1 (which is what one would use if one allowed independent corner cutting in every generalized normal mode) gives a value that is too
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27 Variational Transition State Theory in the Treatment of Hydrogen Transfer Reactions
Figure 27.8 Potential energy contours for two harmonic vibrational modes, which are orthogonal to the reaction coordinate, for the Cl + CH4 reaction at s = –0.49 a0 on the reaction coordinate. The straight line is the direction u1 of the reaction-path curvature vector and the symbols are turning points for zero-point harmonic motion along Q1 (square), Q2 (triangle), and u1 (circle).
high when compared with value of tðsÞ for the SCT method, which is indicated by ^(s)·t(s) along the reacthe circle. Figure 27.7 presents a comparison of tðsÞ and j ^(s)·t(s) approximation is tion path and shows that the value obtained using the j consistently larger than tðsÞ. For systems with many modes contributing significantly to the reaction-path curvature, the overestimate of the turning point that one would obtain by allowing independent corner cutting in every generalized normal mode is even larger and unphysical. Equation (27.34) gives a consistent procedure to extend the SCT approach to multidimensional systems. As was the case with the Cl + HBr reaction, the small skew angle and concomitant large reaction-path curvature in the Cl + CH4 reaction require consideration of methods beyond the small-curvature approximation. It might be argued that the SCT method is adequate because the region of largest curvature falls outside the region where tunneling contributes significantly to the thermal rate constant. However, the only true test is to perform calculations that treat corner cutting more accurately for large-curvature systems. Previous work on this system has shown that the optimum tunneling paths are the straight-line paths used in the LCT method [57]. Consistent procedures have been presented for extending largecurvature methods to multidimensional systems [22, 39, 49]. In the LCG3 and LCG4 versions of the LCT method the tunneling paths are uniquely defined as straight lines between points on the MEP in the reactant and product valleys, and the key to their success is the definition of the effective potentials along these tunneling paths. As mentioned previously, the SCT and LCT methods represent approaches that are most appropriate for two extremes and the most general and optimal way to interpolate between these extremes is the least-action method. A simpler optimized tunneling (OMT) approach [23, 59] is obtained by using the SCT and LCT reaction probabilities and choosing the one that gives the largest tunneling probability at each energy. In this case the OMT probability is given by PSCT ðE Þ (27.35) POMT ðE Þ ¼ max PLCT ðE Þ
27.4 Intramolecular Hydrogen Transfer in Unimolecular Gas-phase Reactions
and the microcanonical optimized multidimensional tunneling (lOMT) tunneling correction factor is obtained by substituting this expression for the probability into Eq. (27.13). Rate constants and kinetic isotope effects for the Cl + CH4 reaction, its reserve, and its isotopic variants, computed using lOMT on the potential of Corchado et al. agree well with experiment [57].
27.4 Intramolecular Hydrogen Transfer in Unimolecular Gas-phase Reactions
Intramolecular hydrogen transfer is another important class of chemical reactions that has been widely studied using transition state theory. Unimolecular gasphase reactions are most often treated using RRKM theory [60], which combines a microcanonical transition state theory treatment of the unimolecular reaction step with models for energy redistribution within the molecule. In this presentation we will focus on the unimolecular reaction step and assume that energy redistribution is rapid, which is equivalent to the high-pressure limit of RRKM theory. Unimolecular hydrogen transfer reactions require additional considerations beyond those discussed for bimolecular reactions. The expression for the thermal rate constant takes the same form as Eq. (27.1), but the reactant partition function per unit volume in the bimolecular expression is replaced by a unitless partition function for the vibrations and rotations of the reactant molecule. More serious considerations are required in treating quantum mechanical effects, particularly tunneling. For bimolecular reactions, quantum mechanical tunneling can be initiated by relative translational motion along the reaction coordinate or by vibrational motion in small skew-angle systems. For unimolecular reactions, vibrational motion alone promotes tunneling. For bimolecular reactions, heavy–light–heavy mass combinations require the reaction coordinate to have regions of large reaction-path curvature to connect the reaction paths in the asymptotic entrance and exit channels. (If the barrier occurs in the region of high curvature, large-curvature tunneling may dominate small-curvature tunneling.) Such a general statement cannot be made for unimolecular reactions, and the type of reaction-path curvature in unimolecular H-transfer reactions can vary from small-curvature to large-curvature. Initiation of tunneling by vibrational motion in the reaction coordinate motion requires modification to the expression used to obtain the thermally averaged tunneling correction factor, Eq. (27.19). For unimolecular processes tunneling does not occur for a continuum of translational energies, but from discrete energy levels in the bound wells of the adiabatic potential. In this case the integral in Eq. (27.19) should be replaced by a sum over discrete states plus contributions from continuum energies above the barrier [61, 62] X dev AG kVA ðT Þ ¼ ðkB T Þ1 exp V AG =kB T P ðe Þ expðev =kB T Þ dv Q v v þ ðkB T Þ1 exp V AG =kB T
Z¥ AG dE PQ ðE ÞexpðE=kB T Þ V AG
(27.36)
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27 Variational Transition State Theory in the Treatment of Hydrogen Transfer Reactions
where the sum is over all bound states along the reaction coordinate motion in AG ðE Þ for enerthe reactant well, ev is the energy of state v in the reactants, and PQ gies above the barrier are given by Eq. (27.22) up to 2V AG – E0 and are set to one above that energy. Equations (27.19) and (27.36) are equivalent for a sufficiently large density of states in the reactant well. We provide two examples of intramolecular hydrogen transfer reactions in polyatomic systems to illustrate the convenience and value of VTST methods for treating these types of reactions. 27.4.1 Intramolecular H-transfer in 1,3-Pentadiene
The [1,5] sigmatropic rearrangement reaction of cis-1,3-pentadiene proceeds via hydrogen transfer from C-5 to C-1, and a primary kinetic isotope effect has been observed experimentally [63]. The large number of degrees of freedom (33 vibrational modes at the reactants) and types of motions involved in the rearrangement process, including torsional motions and vibrations of the carbon skeletal modes, as well as H atom motions, complicate theoretical treatment of this reaction. For this reason, approaches based on reduced-dimensional models [64] have difficulty capturing the correct dynamics of the rearrangement process. Variational transition state theory with multidimensional tunneling has been applied to this reaction in its full dimensionality to provide a complete understanding of the dynamics of the rearrangement process and the importance of tunneling in it [24, 65]. These studies used the direct dynamics approach [33, 66] in which electronic structure calculations of energies, gradients, and Hessians are performed as needed. The reactant configuration of 1,3-pentadience is the s-trans conformer. Denoting the dihedral angles for C1–C2–C3–C4 and C2–C3–C4–C5 as f1 and f2, respectively, motion along the MEP out of the reactant well corresponds to rotation of f1 around the C2–C3 single bond from 180 to a value of about 30. The change in energy for this motion along the reaction coordinate is relatively small compared to the barrier height of 39.5 kcal mol–1. Once the ethylene group (C1–C2) approaches the C5 methyl group, the second dihedral angle changes in a concerted manner with f1, that is, f2 increases from a value of zero as f1 continues to decrease. The potential along the MEP is shown in Fig. 27.9, and the left most extreme of the reaction coordinate (s = –3 a0) is approximately the value of the reaction coordinate where f2 starts to change. Much closer to the saddle point (within about 0.5 a0) the reaction coordinate motion is characterized by H-atom motion (relative to C1 and C5) accompanied by rearrangement in the C–C distances, with the largest changes in the C1–C2 and C4–C5 distances. The saddle point is a cyclic structure with Cs symmetry; the transferring H atom is equidistant from the C1 and C5 carbon atoms with a bent C–H–C configuration. Analysis of the frequencies along the minimum energy path allows identification of the modes that are most strongly coupled to the reaction coordinate and have the largest participation in the tunneling process. Figure 27.9 shows all 32
27.4 Intramolecular Hydrogen Transfer in Unimolecular Gas-phase Reactions
Figure 27.9 (a) Potential energy and ground-state adiabatic potential curves (solid curves) and SCT effective mass (dashed curve) as a function of reaction coordinate for the intramolecular H-tranfer in 1,3-pentadiene. (b) Harmonic frequencies for modes orthogonal to the reaction coordinate.
frequencies and the one mode that shows the most rapid change near the saddle point is that with the largest curvature coupling. This reactive mode starts as a CH vibration in reactants and transforms into the C2–C3–C4 asymmetric stretch near the saddle point. This mode accounts for the largest single component to the reaction-path curvature at the saddle point, varying from about 1/3 to 2/3 of the total contribution in the region between s = – 0.3 and 0.3 a0. The highest frequency modes (those above 3000 cm–1 at the saddle point) contribute less than a couple of percent and the lowest frequency modes (those below about 700 cm–1 at the saddle point) only contribute between 15 and 20% to the reaction-path curvature. This analysis shows the shortcomings of simple reduced-dimensional models of this complicated rearrangement and tunneling process. First, it is difficult to guess, a priori, the mode or modes that are critical for an accurate description of the multidimensional tunneling process [64]. Second, even when the dominant mode is discovered, there are 20 other modes in the range 800 to 2000 cm–1 that do contribute significantly to the curvature, and an accurate treatment of tunneling needs to account for motion in those degrees of freedom. For this reaction, both LCG3 and SCT methods were applied to calculate tunneling correction factors [24]. The SCT method gave larger tunneling probabilities,
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27 Variational Transition State Theory in the Treatment of Hydrogen Transfer Reactions
indicating that reaction-path curvature is small to intermediate for the region of the reaction coordinate over which tunneling is important. The adiabatic potential used in the SCT ground-state tunneling calculations is shown in Fig. 27.9. For temperatures around 460 K (the bottom of the range for experimental measurements) the maximum contribution to the tunneling integral occurs about 2.5 kcal mol–1 below the adiabatic barrier maximum. At this energy the turning points in the adiabatic potential occur for s = – 0.26 a0. These values are inside the two places where the maximum curvature occurs (around s = – 0.6 a0) and this is reflected in the values of the effective mass (also shown in Fig. 27.9), which are in the range 0.7–0.9 of the reduced mass in this region. Even with these moderate values for the effective mass, the SCT tunneling factor at 460 K is over 70% larger than the one neglecting reaction-path curvature. 27.4.2 1,2-Hydrogen Migration in Methylchlorocarbene
The 1,2-hydrogen migration in methylchlorocarbene converts it to chloroethene: H3CCCl fi H2CC(H)Cl. Calculations were carried out using direct dynamics [67]. At 365 K, tunneling lowers the gas-phase Arrhenius activation energy from 10.3 kcal mol–1 to 8.5 kcal mol–1, and at 175 K the drop is even more dramatic, from 10.2 kcal mol–1 to 2.0 kcal mol–1.
27.5 Liquid-phase and Enzyme-catalyzed Reactions
Placing the reagents in a liquid or an enzyme active site involves new complications. Since it is not presently practical to treat an entire condensed-phase system quantum mechanically one begins by dividing the system into two subsystems, which may be called solute and solvent, reactive system and bath, or primary subsystem and secondary subsystem. The “primary/secondary” language is often preferred because it is most general. For example, in a simple liquid-phase reaction the primary subsystem might consist of the reactive solute(s) plus one or more strongly coupled solvent molecules, and the secondary subsystem would be the rest of the solvent. In an enzyme-catalyzed reaction, the primary subsystem might be all or part of the substrate plus all or part of a cofactor and possibly a part of the enzyme and even one or a few solvent molecules, whereas the secondary subsystem would be all the rest. The solvent, bath, or secondary subsystem is sometimes called the environment. The secondary subsystem might be treated differently from the primary one both in terms of the potential energy surface and the dynamics. For example, with regard to the former aspect, the primary subsystem might be treated by a quantum mechanical electronic structure calculation, and the secondary subsystem might be treated by molecular mechanics [68] or even approximated by an electrostatic field or a continuum model, as in implicit solvation modeling [69]. The par-
27.5 Liquid-phase and Enzyme-catalyzed Reactions
tition into primary and secondary subsystems need not be the same for the potential energy surface step and the dynamics step. Since the present chapter is mainly concerned with the dynamics, we shall assume that a potential energy function is somehow available, and when we use the “primary/secondary” language, we refer to the dynamics step. Nevertheless the strategy chosen for the dynamics may be influenced by the methods used to obtain the potential function. This is of course true even for gas-phase reactions, but the interface between the two steps often needs to be tighter when one treats condensed-phase systems, because of their greater complexity. We will distinguish six levels of theory for treating environmental aspects of condensed-phase reactions. These levels may be arranged as follows in a hierarchy of increasingly more complete coupling of primary and secondary subsystems: . separable equilibrium solvation VTST (SES-VTST) . potential-of-mean-force VTST (PMF-VTST) based on a distinguished reaction-coordinate, which is also called single-reaction-coordinate PMF-VTST (SRC-PMF-VTST) . equilibrium solvation path VTST (ESP-VTST) . nonequilibrium solvation path VTST (NES-VTST) . ensemble-averaged VTST with static secondary zone (EA-VTST-SSZ) . ensemble-averaged VTST with equilibrium secondary zone (EA-VTST-ESZ) In practical terms, though, it is easier to consider these methods in terms of two parallel hierarchies. The first contains SES, ESP, and NES; the second contains PMF-VTST, EA-VTST-SSZ, and EA-VTST-ESZ. There is, however, a complication. While the first five rungs on the ladder correspond to successively more complete theories, the final rung (ESZ) may be considered an alternative to the fifth rung (SSZ), which may be better or may be worse, depending on the physical nature of the dynamics. An example of a system in which both solute coordinates and solvent coordinates must be treated in a balanced way is the autoionization of water. One way to describe this process is to consider a cluster of at least a half dozen water molecules as the solute, and the rest of the water molecules as the solvent. One requires solute coordinates to describe the nature of the hydrogen bond network in the solute plus at least one solvent fluctuation coordinate; the latter may describe the direction and strength of the electric field on a critical proton or protons of the solute [70] as quantified, for example, by the energy gap between arranging the solvent to solvate the reactant and arranging it to solvate the product. Molecular dynamics simulations, though, indicate that a conventional energy gap coordinate is not necessarily the best way to describe the collective solvent re-organization. A detailed comparison of different kinds of collective solvent coordinates is given elsewhere [71]. The NES-VTST method is well suited to using collective solvent coordinates whereas EA-VTST is more convenient when explicit solvent is used. The SES, ESP, and PMF methods can easily be used with either kind of treatment of the solvent.
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27 Variational Transition State Theory in the Treatment of Hydrogen Transfer Reactions
The PMF-VTST approach may be understood in terms of a general molecular dynamics calculation of the equilibrium one-way flux from a reactant region of phase space through a dividing surface [5–7, 72, 73]. When the no-recrossing approximation is valid at the dividing surface and when one neglects quantum effects, it may be viewed as the most efficient way to calculate the rate constant from an ensemble of trajectories. However, for reactions involving hydrogenic motion in the reaction coordinate, classical mechanics is not quantitatively accurate, and the transition state formulation provides a much more convenient way to include quantum effects than does a trajectory calculation. (Note that many workers use the term “molecular dynamics” to refer to classical trajectory calculations.) In the rest of this section we briefly review the six rungs of the condensed-phase VTST ladder. In Section 27.6 we provide two examples that illustrate the application of the general theory. 27.5.1 Separable Equilibrium Solvation
The simplest way to include solvation effects is to calculate the reaction path and tunneling paths of the solute in the gas phase and then add the free energy of solvation at every point along the reaction path and tunneling paths. This is equivalent to treating the Hamiltonian as separable in solute coordinates and solvent coordinates, and we call it separable equilibrium solvation (SES) [74]. Adding tunneling in this method requires a new approximation, namely the canonical mean shape (CMS) approximation [75]. The gas-phase rate constant of Eqs. (27.4) and (27.23) is replaced in the SES approximation by kSES=MT ðTÞ ¼ kðTÞkSES ðTÞ
(27.37)
and kSES ðTÞ ¼
n h io kB T zo K min exp DGGT;o ðsÞ þ DDGoS ðsjT Þ T s h
(27.38)
where DDGoS ðsjT Þ is the difference between the standard-state free energy of solvation of the generalized transition state at s and that of the reactants. The transmission coefficient is given by Eq. (27.25), and all that is done to extend the SCT, LCT, and OMT approximations from the gas phase to liquid reactions is to generalize V1 and V2. In the SES approximation, V1 is taken as V1(R|T) = U(R|T)
(27.39)
27.5 Liquid-phase and Enzyme-catalyzed Reactions
where R denotes the complete set of solute coordinates, and U(R|T) is the CMS potential given by UðRjTÞ ¼ WðRjTÞ þ ð1=TÞ
¶WðRjTÞ ¶ð1=TÞ
(27.40)
and W(R|T) is the potential of mean force (PMF) on the primary subsystem, which will be called the solute in the rest of this Subsection and in Subsection 27.5.3. The PMF is defined by eWðR¢jTÞ=kB T ¼ eH=kB T dðR R¢Þ T
(27.41)
where H is the total system Hamiltonian, dðR R¢Þ is a multidimensional delta function that holds the solute coordinates fixed at R¢, and hLiT denotes a normalized average over the phase space of the entire system. Colloquially, W(R|T) is the free energy surface of the solute. The function U(R|T) is the enthalpy-like component of W(R|T). In practice the second term of Eq. (27.40) is harder to approximate than the first term, and we can use the zero-order CMS approximation (CMS-0), which is UðRjTÞ @ WðRjTÞ
(27.42)
In the SES approximation, WðRjTÞ ¼ VðRÞ þ DGoS ðRjTÞ
(27.43)
where DGoS ðRjTÞ is the standard-state free energy of solvation. Since we will only need differences of W, e.g., its R dependence, it is not a matter of concern that different standard state choices correspond to changing the zero of W(R|T) by R-independent amounts. Finally, the SES approximation for the effective adiabatic potential is V2 ðsjTÞ ¼ URP ðsjTÞ þ eGT int ðG; sÞ
(27.44)
where URP(s|T) is U(R|T) evaluated along the reaction path, and eGT int ðG; sÞ is the ground-state value of the second term of Eq. (27.8) for the solute modes. As for V1, one can use any convenient zero of energy for V2(s|T) since the results are independent of adding a quantity independent of s. The final protocol for an SES calculation with the CMS-0 approximation reduces to the following: Calculate a gas-phase MEP and carry out generalized normal mode analyses along the MEP to obtain eGT int ðG; sÞ for the solute. (In an LCT calcuð n „ G; K ¼ G; sÞ.) Now add the free energy of solvation lation one also requires eGT int along the MEP to find the variational transition state rate constant and tunneling paths, and add the free energy of solvation along the tunneling paths to obtain an effective potential that is used to calculate the tunneling probabilities.
863
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27 Variational Transition State Theory in the Treatment of Hydrogen Transfer Reactions
27.5.2 Equilibrium Solvation Path
In the equilibrium solvation path (ESP) approximation [74, 76], we first find a potential of mean force surface for the primary subsystem in the presence of the secondary subsystem, and then we finish the calculation using this free energy surface. Notice a critical difference from the SES in that now we find the MEP on U rather than V, and we now find solute vibrational frequencies using U rather than V. 27.5.3 Nonequilibrium Solvation Path
The SES and ESP approximations include the dynamics of solute degrees of freedom as fully as they would be treated in a gas-phase reaction, but these approximations do not address the full complexity of condensed-phase reactions because they do not allow the solvent to participate in the reaction coordinate. Methods that allow this are said to include nonequilibrium solvation. A variety of ways to include nonequilibrium solvation within the context of an implicit or reduceddegree-of-freedom bath are reviewed elsewhere [69]. Here we simply discuss one very general such NES method [76–78] based on collective solvent coordinates [71, 79]. In this method one replaces the solvent with one or more collective solvent coordinates, whose parameters are fit to bulk solvent properties or molecular dynamics simulations. Then one carries out calculations just as in the gas phase but with these extra one or more degrees of freedom. The advantage of this approach is its simplicity (although there are a few subtle technical details). A difficulty with the nonequilibrium approach is that one must estimate the time constant or time constants for solvent equilibration with the solvent. This may be estimated from solvent viscosities, from diffusion constants, or from classical trajectory calculations with explicit solvent. Estimating the time constant for solvation dynamics presents new issues because there is more than one relevant time scale [69, 80]. Fortunately, though, the solvation relaxation time seems to depend mostly on the solvent, not the solute. Thus it is very reasonable to assume it is a constant along the reaction path. Another difficulty with the NES model is not knowing how reliable the solvent model is and having no systematic way to improve it to convergence. Furthermore this model, like the SES and ESP approximations, assumes that the reaction can be described in terms of a reaction path residing in a single free energy valley or at most a small number of such valleys. The methods discussed next are designed to avoid that assumption. The ESP method was applied to the reaction mentioned in Subsection 27.4.2, namely 1,2-hydrogen migration in chloromethylcarbene. Tunneling contributions are found to be smaller in solution than in the gas phase, but solvation by 1,2-dichloroethane lowers the Arrhenius activation energy at 298 K from 7.7 kcal mol–1 to 6.0 kcal mol–1 [67].
27.5 Liquid-phase and Enzyme-catalyzed Reactions
27.5.4 Potential-of-mean-force Method
In the PMF method one identifies a reaction coordinate on physical grounds rather than by calculating an MEP. For example, the reaction coordinate might be z = rDH – rAH
(27.45)
where rDH is the distance from the transferred hydrogen to the donor atom, and rAH is the distance from the transferred hydrogen to the acceptor atom. Then one calculates a one-dimensional potential of mean force (W(z|T)), and the classical mechanical rate constant for a unimolecular reaction in solution is given by Eq. (27.4) with [81] DGCVT;o ¼ max ½WðzjTÞ þ Wcurv ðzjTÞ GRn T z
(27.46)
where Wcurv(z|T) is a kinematic contribution [81], usually small, at least when the reaction coordinate is a simple function of valence coordinates as in Eq. (27.45), and GRn [82] is the free energy of the reaction-coordinate motion of the reactant. Like the SES and ESP approximations, PMF-VTST involves a single reaction coordinate. Even within the equilibrium-solvation approximations and neglecting recrossing effects, the classical mechanical result of Eq. (27.46) needs to be improved in two ways. First one needs to quantize the vibrations transverse to the reaction coordinate. A method for doing this has been presented [83], and including this step converts Eq. (27.46) to a quasiclassical result. Second, one must include tunneling. The inclusion of tunneling is explained in the next subsection, and it involves partitioning the system into primary and secondary subsystems. Note that any reasonable definition of the primary subsystem would include the three atoms involved in the definition of the reaction coordinate given in Eq. (27.45). Thus, in the present section, if one uses Eq. (27.45), the secondary subsystem does not participate in the reaction coordinate. 27.5.5 Ensemble-averaged Variational Transition State Theory
Ensemble-averaged VTST [82, 84] provides a much more complete treatment of condensed-phase reactions. Originally developed in the context of enzyme kinetics, it is applicable to any reaction in the liquid or solid state. First one carries out a quasiclassical PMF-VTST calculation as explained in Subsection 27.5.4. This is called stage 1, and it involves a single, distinguished reaction coordinate. Then, in what is called stage 2, one improves this result with respect to the quality of the reaction coordinate (allowing the secondary subsystem to participate), with respect to averaging over more than one reaction coordinate, and by including tunneling.
865
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27 Variational Transition State Theory in the Treatment of Hydrogen Transfer Reactions
Stage 2 consists of a series of calculations, each one of which corresponds to a randomly chosen member of the transition state ensemble. For this purpose the transition state ensemble consists of phase points from the quasiclassical PMF calculation with the value of z in a narrow bin centered on the variational transition state, which is the value of z that maximizes the quantized version of the right-hand side of Eq. (27.46). In practice one uses the version of Eq. (27.46) in which quantization effects of modes orthogonal to z [83] are added to W. For each member of the transition state ensemble, one now optimizes the primary subsystem to the nearest saddle point in the field of the frozen secondary subsystem, and then one computes a minimum energy path through the isoinertial coordinates of the primary subsystem, with the secondary subsystem frozen. Based on this MEP one carries out a VTST/MT rate constant calculation, just as in the gas phase except for three differences. First, one does not need the reactant partition function. Second, one freezes the secondary subsystem throughout the entire calculation. Third, the projection operator discussed below Eq. (27.1) is replaced by one that just projects out the reaction coordinate because the frozen secondary subsystem removes translational invariance, converting the overall translations and rotations to librations. (The same simplified projection operator is also used for treating solid-state reactions [61].) The calculations described in the previous paragraph yield, for each ensemble member ‘, a free energy of activation profile DGGT ‘ ðT; sÞ and a transmission coefficient k‘ ðTÞ, where ‘ = 1,2,...,L, and L is the number of MEPs computed. The standard EA-VTST/MT result, called the static-secondary-zone result, is then given by kEA-VTST/MT = c(T)kQPMF(T)
(27.47)
where kQPMF is the result from stage 1, based on the quantized PMF and identical to the result of Subsection 27.5.4, and c is a transmission coefficient given by c¼
L 1 X C ðTÞk‘ ðTÞ L ‘¼1 ‘
(27.48)
where
C ‘ ¼ exp DGGT T; s* ;‘ DGGT T; s0;‘ RT ‘ ‘
(27.49)
where s* ;‘ is the value of s that maximizes DGGT ‘ ðT; sÞ, and s0;‘ is the value of s corresponding to the value of z that maximizes the PMF of stage 1. The physical interpretation of C ‘ is that, by using a more appropriate reaction coordinate for each secondary-zone configuration, one is correcting for recrossing of the original, less appropriate dividing surface defined by z = constant. An alternative, more expensive way to do this is by starting trajectories at the dividing surface and counting their recrossings, if any [6, 15, 72]. More expensive is not necessarily more accurate though because the trajectories may lose their quantization before they recross.
27.6 Examples of Condensed-phase Reactions
In the equilibrium-secondary-zone approximation [82, 85] we refine the effective potential along each reaction path by adding the charge in secondary-zone free energy. Thus, in this treatment, we include additional aspects of the secondary subsystem. This need not be more accurate because in many reactions the solvation is not able to adjust on the time scale of primary subsystem barrier crossing [86].
27.6 Examples of Condensed-phase Reactions 27.6.1 H + Methanol
References for a large number of SES calculations are given in a previous review [69], but there have been far fewer calculations using the ESP and NES approximations. The ESP and NES approximations based on collective solvent coordinates have, however, been applied [78] to (R1) H + CH3OH fi H2 + CH4OH, (R2) D + CH3OD fi DH + CH2OD, and (R3) H + CD3OH fi HD + CD2OH. The resulting rate constants for reaction (R1) are shown in Table 27.1. In this particular case the NES results are accidentally similar to the SES ones, but that is not of major importance. What is more significant is that the true equilibrium solvation results differ from the SES ones by about a factor of two, and nonequilibrium solvation decreases the rate constants in solution by more than a factor of two as compared to the equilibrium solvation effect. If the solute–solvent coupling is decreased, the NES result becomes closer to the equilibrium solvation result, and it is difficult to ascertain how realistic the best estimates of the coupling strength actually are. Perhaps more interesting though is that if the coupling is made four times stronger, the calculated rate constant drops by another factor of three. Since ionic reactions might have much stronger solute–solvent coupling than this free radical reaction, we conclude that nonequilibrium effects might be larger for many reactions in aqueous solution. Table 27.2 shows the kinetic isotope effects [78, 87]. Although the solvation effects are smaller than for the rate constants themselves, they are not negligible.
Tab. 27.1 Rate constants (10–15 cm3 molecule–1 s–1) at various levels of
dynamical theory for H + CH3OH fi H2 + CH2OH in aqueous solution at 298 K [78]. Gas
SES
ESP
NES
CVT
0.7
0.9
1.9
0.81
CVT/SCT
8.3
8.7
16.6
6.5
CVT/OMT
12.9
12.7
25.9
12.4
867
868
27 Variational Transition State Theory in the Treatment of Hydrogen Transfer Reactions Tab. 27.2 Kinetic isotope effects for H + CH3OH fi H2 + CH2OH at various
levels of dynamical theory in aqueous solution at 298 K (CVT/OMT [78, 87]). Gas R1/R2 R1/R3
0.68 21.1
SES 0.48 21.3
ESP 0.51 20.2
NES 0.37 19.5
Although a more recent calculation [88] indicates a barrier height about 2 kcal mol–1 higher than that on the potential energy surface used for these studies, the qualitative conclusions still hold if they are regarded as based on a realistic model reaction. 27.6.2 Xylose Isomerase
Xylose isomerase catalyzes a hydride transfer reaction as part of the conversion of xylose to xylulose. This reaction has been calculated [32] by the EA-VTST/MT method using Eq. (27.45) as the reaction coordinate and using L = 5 in Eq. (27.48). The primary zone had 32 atoms, and the secondary zone had 25 285 atoms. The average value of C ‘ was 0.95. The fact that this is so close to unity indicates that the reaction coordinate of Eq. (27.45) is very reasonable for this reaction, even though the reaction coordinate is strongly coupled to a Mg–Mg breathing mode. The transmission coefficient c was calculated to be 6.57, with about 90% of the reactive events calculated to occur by tunneling. Calculations were also carried out for deuteride transfer. The kinetic isotope effect was calculated to be 1.80 without tunneling and 3.75 with tunneling. The latter is within the range expected from various experimental [89] determinations. 27.6.3 Dihydrofolate Reductase
The ensemble-averaged theory has also been applied to several other enzyme reactions involving transfer of a proton, hydride ion, or hydrogen atom, and the results are reviewed elsewhere [84, 90]. More recently than these reviews, the method has been applied to calculate [91] the temperature dependence of the rate constant and kinetic isotope effect for the hydride transfer catalyzed by E. coli dihydrofolate reductase (ecDHFR). In earlier work [92] we had calculated a primary KIE in good agreement with experiment [93] and also predicted a secondary KIE that turned out to be in good agreement with a later [94] experiment. In both studies [91, 92], we treated the dynamics of 31 atoms quantum mechanically. The primary KIE had also been calculated by Agarwal et al. [95], also in good agreement with experiment, but they could not calculate the secondary KIE because they treated the dynamics of only one atom quantum mechanically. In the new
27.8 Concluding Remarks
work [91] we predicted the temperature dependence of the KIE and found that it is small. In previous work by other groups, new mechanisms had been invoked when temperature-independent or nearly temperature-independent KIEs had been observed. The importance of the new work [91] is not so much the actual predicted small temperature dependence of the KIE (because the quantitative results may be sensitive to improving the calculation) but rather the demonstration that even nearly temperature-independent KIEs can be accommodated by VTST/MT theory, and one need not invoke new theoretical concepts.
27.7 Another Perspective
For another perspective we mention a second approach of which the reader should be aware. In this approach the dividing surface of transition state theory is defined not in terms of a classical mechanical reaction coordinate but rather in terms of the centroid coordinate of a path integral (path integral quantum TST, or PI-QTST) [96–99] or the average coordinate of a quantal wave packet. In model studies of a symmetric reaction, it was shown that the PI-QTST approach agrees well with the multidimensional transmission coefficient approach used here when the frequency of the bath is high, but both approaches are less accurate when the frequency is low, probably due to anharmonicity [98] and the path centroid constraint [97]. However, further analysis is needed to develop practical PI-QTST-type methods for asymmetric reactions [99]. Methods like PI-QTST provide an alternative perspective on the quasithermodynamic activation parameters. In methods like this the transition state has quantum effects on reaction coordinate motion built in because the flux through the dividing surface is treated quantum mechanically throughout the whole calculation. Since tunneling is not treated separately, it shows up as part of the free energy of activation, and one does not obtain a breakdown into overbarrier and tunneling contributions, which is an informative interpretative feature that one gets in VTST/MT. Other alternative approaches for approximating the quantum effects in VTST calculations of liquid-phase [4] and enzyme reactions [90] are reviewed elsewhere.
27.8 Concluding Remarks
In the present chapter, we have described a formalism in which overbarrier contributions to chemical reaction rates are calculated by variational transition state theory, and quantum effects on the reaction coordinate, especially multidimensional tunneling, have been included by a multidimensional transmission coefficient. The advantage of this procedure is that it is general, practical, and well validated.
869
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27 Variational Transition State Theory in the Treatment of Hydrogen Transfer Reactions
It is sometimes asked if a transmission coefficient is a “correction” and therefore less fundamental than other ways of including tunneling in the activation free energy. In fact, this is not the case. The transmission coefficient is a general way to include tunneling in the flux through the dividing surface. We can see this by writing the exact rate constant as a Boltzmann average over the exact rate constants for each of the possible initial states (levels) of the system, where these initial levels are labeled as n(initial): D E k ” knðinitialÞ
(27.50)
We can then replace this average by an average over systems that cross the transition state in various levels of the transition state, each labeled by n(VTS): D E k ” knðVTSÞ
(27.51)
We can write this as D k”
E knðVTSÞ kTST n kTST n
(27.52)
where we have multiplied and divided by an average over transition-state-theory rates for each n(VTS). The VTST rate constant can easily be written [15] in the is just kVTST. form of the average that we have inserted into Eq. (27.52), so kTST n The fraction in Eq. (27.52) is easily recognized as the transmission coefficient j, and therefore we have the following expression, which is exact: k ” k kVTST
(27.53)
In practice, we approximate the exact transmission coefficient by a mean-fieldtype of approximation; that is we replace the ratio of averages by the ratio for an “average” or effective potential. For gas-phase reactions with small reaction-path curvature, this effective potential would just be the vibrationally adiabatic groundstate potential. In the liquid phase and enzymes we generalize this with the canonical mean-shape approximation. In any event, though, the transmission coefficient should not be thought of as a perturbation. The method used here may be thought of as an approximate full-dimensional quantum treatment of the reaction rate. At the present stage of development, we have well validated methods available for calculating reactive rates of hydrogen atom, proton, and hydride transfer reactions in both gaseous and condensed phases, including reliable methods for multidimensional tunneling contributions. The accuracy of calculated rate constants is often limited more by the remaining uncertainties in potential energy surfaces and practical difficulties in including anharmonicity than by the dynamical formalism per se.
References
Acknowledgments
This work was supported in part at both Pacific Northwest National Laboratory (PNNL) and the University of Minnesota (UM) by the Division of Chemical Sciences, Office of Basic Energy Sciences, U. S. Department of Energy (DOE), and it was supported in part (condensed-phase dynamics) at the University of Minnesota by the National Science Foundation. Battelle operates PNNL for DOE.
References 1 H. Eyring, J. Chem. Phys. 3 (1935) 107;
S. Glasstone, K. J. Laidler, H. Eyring, The Theory of Rate Processes, McGrawHill, New York, 1941. 2 H. Eyring, Trans. Faraday Soc. 34 (1938) 41; B. C. Garrett, D. G. Truhlar, in Encyclopedia of Computational Chemistry, P. v. R. Schleyer, N. L. Allinger, T. Clark, J. Gasteiger, P. A. Kollman, H. F. Schaefer, III (Eds.), John Wiley & Sons, Chichester, 1998. 3 E. Wigner, Trans. Faraday Soc. 34 (1938) 29. 4 D. G. Truhlar, W. L. Hase, J. T. Hynes, J. Phys. Chem. 87 (1983) 2664; D. G. Truhlar, B. C. Garrett, S. J. Klippenstein, J. Phys. Chem. 100 (1996) 12771. 5 E. Wigner, J. Chem. Phys. 5 (1937) 720; J. Horiuti, Bull. Chem. Soc. Jpn. 13 (1938) 210; J. C. Keck, J. Chem. Phys. 32 (1960) 1035; D. G. Truhlar, B. C. Garrett, Annu. Rev. Phys. Chem. 35 (1984) 159. 6 J. C. Keck, Adv. Chem. Phys. 13 (1967) 85. 7 B. C. Garrett, D. G. Truhlar, J. Phys. Chem. 83 (1979) 1052. 8 E. Wigner, Z. Phys. Chem. B 19 (1932) 203. 9 R. P. Bell, The Proton in Chemistry, Chapman and Hall, London, 1973. 10 D. G. Truhlar, A. Kuppermann, Chem. Phys. Lett. 9 (1971) 269. 11 W. H. Miller, Acc. Chem. Res. 9 (1976) 306. 12 J. O. Hirschfelder, E. Wigner, J. Chem. Phys. 7 (1939) 616; H. Eyring, J. Walter, G. E. Kimball, Quantum Chemistry,
Wiley, New York, 1944; R. A. Marcus, J. Chem. Phys. 43 (1965) 1598; R. A. Marcus, J. Chem. Phys. 45 (1966) 4450; D. G. Truhlar, J. Chem. Phys. 53 (1970) 2041. 13 G. L. Hofacker, Z. Naturforsch. A 18 (1963) 607. 14 R. A. Marcus, J. Chem. Phys. 45 (1966) 4493. 15 B. C. Garrett, D. G. Truhlar, J. Phys. Chem. 83 (1979) 1079. 16 B. C. Garrett, D. G. Truhlar, R. S. Grev, A. W. Magnuson, J. Phys. Chem. 84 (1980) 1730. 17 R. T. Skodje, D. G. Truhlar, B. C. Garrett, J. Phys. Chem. 85 (1981) 3019. 18 R. T. Skodje, D. G. Truhlar, B. C. Garrett, J. Chem. Phys. 77 (1982) 5955. 19 B. C. Garrett, D. G. Truhlar, A. F. Wagner, T. H. Dunning, Jr., J. Chem. Phys. 78 (1983) 4400; D. K. Bondi, J. N. L. Connor, B. C. Garrett, D. G. Truhlar, J. Chem. Phys. 78 (1983) 5981. 20 B. C. Garrett, D. G. Truhlar, J. Chem. Phys. 79 (1983) 4931. 21 B. C. Garrett, T. Joseph, T. N. Truong, D. G. Truhlar, Chem. Phys. 136 (1989) 271. 22 D.-h. Lu, T. N. Truong, V. S. Melissas, G. C. Lynch, Y.-P. Liu, B. C. Garrett, R. Steckler, A. D. Isaacson, S. N. Rai, G. C. Hancock, J. G. Lauderdale, T. Joseph, D. G. Truhlar, Comput. Phys. Commun. 71 (1992) 235. 23 Y.-P. Liu, D.-h. Lu, A. Gonzalez-Lafont, D. G. Truhlar, B. C. Garrett, J. Am. Chem. Soc. 115 (1993) 7806.
871
872
27 Variational Transition State Theory in the Treatment of Hydrogen Transfer Reactions 24 Y.-P. Liu, G. C. Lynch, T. N. Truong,
42 B. C. Garrett, D. G. Truhlar, J. Chem.
D.-h. Lu, D. G. Truhlar, B. C. Garrett, J. Am. Chem. Soc. 115 (1993) 2408. 25 R. A. Marcus, M. E. Coltrin, J. Chem. Phys. 67 (1977) 2609. 26 C. J. Walsh, Enzyme Reaction Mechanisms, Freeman, New York, 1979. 27 D. G. Truhlar, R. E. Wyatt, Annu. Rev. Phys. Chem. 27 (1976) 1. 28 H. S. Johnston, Gas Phase Reaction Rate Theory, Ronald, New York, 1966. 29 L. Melander, Isotope Effects on Reaction Rates, Ronald Press, New York, 1960; L. Melander, W. H. Saunders, Reaction Rates of Isotopic Molecules, Krieger Publishing, Malabar, FL, 1987. 30 J. Bigeleisen, M. Wolfsberg, Adv. Chem. Phys. 1 (1958) 15. 31 B. C. Garrett, D. G. Truhlar, J. Am. Chem. Soc. 102 (1980) 2559. 32 M. Garcia-Viloca, C. Alhambra, D. G. Truhlar, J. Gao, J. Comput. Chem. 24 (2003) 177. 33 D. G. Truhlar, M. S. Gordon, Science 249 (1990) 491. 34 B. C. Garrett, D. G. Truhlar, J. Chem. Phys. 70 (1979) 1593. 35 R. E. J. Weston, J. Chem. Phys. 31 (1959) 892; I. Shavitt, J. Chem. Phys. 49 (1968) 4048; R. A. Marcus, J. Chem. Phys. 49 (1968) 2617; K. Fukui, in The World of Quantum Chemistry, R. Daudel, B. Pullman (Eds.), Reidel, Dordrecht, 1974; H. F. Schaefer, III, Chem. Brit. 11 (1975) 227. 36 D. G. Truhlar, A. Kuppermann, J. Am. Chem. Soc. 93 (1971) 1840. 37 W. H. Miller, N. C. Handy, J. E. Adams, J. Chem. Phys. 72 (1980) 99. 38 A. D. Isaacson, D. G. Truhlar, J. Chem. Phys. 76 (1982) 1380. 39 D. G. Truhlar, A. D. Isaacson, B. C. Garrett, in Theory of Chemical Reaction Dynamics, M. Baer (Ed.), CRC Press, Boca Raton, FL, 1985. 40 C. F. Jackels, Z. Gu, D. G. Truhlar, J. Chem. Phys. 102 (1995) 3188. 41 S. J. Klippenstein, R. A. Marcus, J. Chem. Phys. 87 (1987) 3410; J. Villa, D. G. Truhlar, Theor. Chem. Acc. 97 (1997) 317; P. L. Fast, D. G. Truhlar, J. Chem. Phys. 109 (1998) 3721; J. R. Pliego, W. B. De Almeida, Phys. Chem. Chem. Phys. 1 (1999) 1031.
Phys. 72 (1980) 3460; G. A. Natanson, B. C. Garrett, T. N. Truong, T. Joseph, D. G. Truhlar, J. Chem. Phys. 94 (1991) 7875; G. A. Natanson, Theor. Chem. Acc. 112 (2004) 68. 43 A. D. Isaacson, J. Phys. Chem. A 110 (2006) 379. 44 R. A. Marcus, J. Chem. Phys. 46 (1967) 959; R. A. Marcus, J. Chem. Phys. 49 (1968) 2610. 45 D. G. Truhlar, B. C. Garrett, J. Phys. Chem. A 107 (2003) 4006. 46 R. A. Marcus, J. Chem. Phys. 41 (1964) 2614; G. L. Hofacker, N. Rsch, Ber. Bunsen- Ges. Phys. Chem. 77 (1973) 661. 47 D. C. Chatfield, R. S. Friedman, D. G. Truhlar, B. C. Garrett, D. W. Schwenke, J. Am. Chem. Soc. 113 (1991) 486; D. C. Chatfield, R. S. Friedman, D. W. Schwenke, D. G. Truhlar, J. Phys. Chem. 96 (1992) 2414; D. C. Chatfield, R. S. Friedman, S. L. Mielke, G. C. Lynch, T. C. Allison, D. G. Truhlar, D. W. Schwenke, in Dynamics of Molecules and Chemical Reactions, R. E. Wyatt, J. Z. H. Zhang (Eds.), Marcel Dekker, New York, 1996, p. 323. 48 J. N. L. Connor, Mol. Phys. 15 (1968) 37; B. C. Garrett, D. G. Truhlar, J. Phys. Chem. 83 (1979) 2921. 49 A. Fernandez-Ramos, D. G. Truhlar, J. Chem. Phys. 114 (2001) 1491. 50 D. G. Truhlar, C. J. Horowitz, J. Chem. Phys. 68 (1978) 2466. 51 A. A. Westenberg, N. De Haas, J. Chem. Phys. 47 (1967) 1393; K. A. Quickert, D. J. Leroy, J. Chem. Phys. 53 (1970) 1325; I. D. Reid, L. Y. Lee, D. M. Garner, D. J. Arseneau, M. Senba, D. G. Fleming, Hyperfine Interact. 32 (1986) 801. 52 B. C. Garrett, D. G. Truhlar, J. Phys. Chem. 83 (1979) 1915; D. G. Truhlar, A. D. Isaacson, R. T. Skodje, B. C. Garrett, J. Phys. Chem. 86 (1982) 2252; D. G. Truhlar, J. Comput. Chem. 12 (1991) 266. 53 B. C. Garrett, D. G. Truhlar, J. Chem. Phys. 81 (1984) 309. 54 V. K. Babamov, V. Lopez, R. A. Marcus, Chem. Phys. Lett. 101 (1983) 507; V. K. Babamov, V. Lopez, R. A. Marcus, J. Chem. Phys. 78 (1983) 5621;
References V. K. Babamov, V. Lopez, R. A. Marcus, J. Chem. Phys. 80 (1984) 1812. 55 B. C. Garrett, N. Abusalbi, D. J. Kouri, D. G. Truhlar, J. Chem. Phys. 83 (1985) 2252. 56 T. C. Allison, D. G. Truhlar, in Modern Methods for Multidimensional Dynamics Computations in Chemistry, D. L. Thompson (Ed.), World Scientific, Singapore, 1998. 57 J. C. Corchado, D. G. Truhlar, J. Espinosa-Garcia, J. Chem. Phys. 112 (2000) 9375. 58 M. S. Zahniser, B. M. Berquist, F. Kaufman, Int. J. Chem. Kinet. 10 (1978) 15; M. L. Pohjonen, J. Koskikallio, Acta Chem. Scand. Ser. A 33 (1979) 449; J. J. Russell, J. A. Seetula, S. M. Senkan, D. Gutman, Int. J. Chem. Kinet. 20 (1988) 759; T. J. Wallington, M. D. Hurley, Chem. Phys. Lett. 189 (1992) 437; W. R. Simpson, A. J. Orr-Ewing, R. N. Zare, Chem. Phys. Lett. 212 (1993) 163; Y. Matsumi, K. Izumi, V. Skorokhodov, M. Kawasaki, N. Tanaka, J. Phys. Chem. A 101 (1997) 1216; A. J. Orr-Ewing, W. R. Simpson, T. P. Rakitzis, S. A. Kandel, R. N. Zare, J. Chem. Phys. 106 (1997) 5961; S. A. Kandel, R. N. Zare, J. Chem. Phys. 109 (1998) 9719; G. D. Boone, F. Agyin, D. J. Robichaud, F. M. Tao, S. A. Hewitt, J. Phys. Chem. A 105 (2001) 1456. 59 D. G. Truhlar, D.-h. Lu, S. C. Tucker, X. G. Zhao, A. Gonzalez-Lafont, T. N. Truong, D. Maurice, Y.-P. Liu, G. C. Lynch, in Isotope Effects in Gas-Phase Chemistry, J. A. Kay (Ed.), American Chemical Society, Washington, D. C., 1992. 60 R. G. Gilbert, S. C. Smith, Theory of Unimolecular and Recombination Reactions, Blackwell, Oxford, 1990; T. Baer, W. L. Hase, Unimolecular Reaction Dynamics, Oxford University Press, New York, 1996. 61 J. G. Lauderdale, D. G. Truhlar, Surf. Sci. 164 (1985) 558. 62 G. C. Hancock, C. A. Mead, D. G. Truhlar, A. J. C. Varandas, J. Chem. Phys. 91 (1989) 3492; B. M. Rice, B. C. Garrett, M. L. Koszykowski, S. M. Foiles, M. S. Daw, J. Chem. Phys. 92 (1990) 775; S. E. Wonchoba, W. P. Hu,
D. G. Truhlar, Phys. Rev. B 51 (1995) 9985; P. S. Zuev, R. S. Sheridan, T. V. Albu, D. G. Truhlar, D. A. Hrovat, W. T. Borden, Science 299 (2003) 867. 63 W. R. Roth and J. Knig, Liebigs Ann. Chem. 699 (1966) 24. 64 L. Chantranupong, T. A. Wildman, J. Am. Chem. Soc. 112 (1990) 4151. 65 Y. Kim, J. C. Corchado, J. Villa, J. Xing, D. G. Truhlar, J. Chem. Phys. 112 (2000) 2718. 66 K. K. Baldridge, M. S. Gordon, R. Steckler, D. G. Truhlar, J. Phys. Chem. 93 (1989) 5107; B. C. Garrett, M. L. Koszykowski, C. F. Melius, M. Page, J. Phys. Chem. 94 (1990) 7096; D. G. Truhlar, in The Reaction Path in Chemistry: Current Approaches and Perspectives, D. Heidrich (Ed.), Kluwer, Dordrecht, 1995. 67 T. V. Albu, B. J. Lynch, D. G. Truhlar, A. C. Goren, D. A. Hrovat, W. T. Borden, R. A. Moss, J. Phys. Chem. A 106 (2002) 5323. 68 J. Gao, M. A. Thompson, Combined Quantum Mechanical and Molecular Mechanical Methods, American Chemical Society, Washington, DC, 1998; H. Lim, D. G. Truhlar, Theor. Chem. Acc. in press, online DOI: 10.1007/s00214-006-0143-z. 69 C. J. Cramer, D. G. Truhlar, Chem. Rev. 99 (1999) 2161. 70 R. A. Marcus, J. Chem. Phys. 24 (1956) 966; P. L. Geissler, C. Dellago, D. Chandler, J. Hutter, M. Parrinello, Science 291 (2001) 2121. 71 G. K. Schenter, B. C. Garrett, D. G. Truhlar, J. Phys. Chem. B 105 (2001) 9672. 72 C. H. Bennett, in Algorithms for Chemical Computation, R. E. Christofferson (Ed.) American Chemical Society, Washington, DC, 1977. 73 K. Hinsen, B. Roux, J. Chem. Phys. 106 (1997) 3567. 74 Y.-Y. Chuang, C. J. Cramer, D. G. Truhlar, Int. J. Quantum Chem. 70 (1998) 887. 75 D. G. Truhlar, Y.-P. Liu, G. K. Schenter, B. C. Garrett, J. Phys. Chem. 98 (1994) 8396.
873
874
27 Variational Transition State Theory in the Treatment of Hydrogen Transfer Reactions 76 B. C. Garrett, G. K. Schenter, Int. Rev.
Phys. Chem. 13 (1994) 263. 77 B. C. Garrett, G. K. Schenter, in Structure and Reactivity in Aqueous Solution, C. J. Cramer, D. G. Truhlar (Eds.), American Chemical Society, Washington, DC, 1994. 78 Y.-Y. Chuang, D. G. Truhlar, J. Am. Chem. Soc. 121 (1999) 10157. 79 S. Lee, J. T. Hynes, J. Chem. Phys. 88 (1988) 6863; D. G. Truhlar, G. K. Schenter, B. C. Garrett, J. Chem. Phys. 98 (1993) 5756; M. V. Basilevsky, G. E. Chudinov, D. V. Napolov, J. Phys. Chem. 97 (1993) 3270. 80 I. Ohmine, H. Tanaka, J. Chem. Phys. 93 (1990) 8138; G. K. Schenter, R. P. McRae, B. C. Garrett, J. Chem. Phys. 97 (1992) 9116; M. Maroncelli, J. Mol. Liq. 57 (1993) 1; M. Maroncelli, V. P. Kumar, A. Papazyan, J. Phys. Chem. 97 (1993) 13; M. Cho, G. R. Fleming, S. Saito, I. Ohmine, R. M. Stratt, J. Chem. Phys. 100 (1994) 6672; M. F. Ruiz-Lopez, A. Oliva, I. Tunon, J. Bertran, J. Phys. Chem. A 102 (1998) 10728; B. Bagchi, R. Biswas, Adv. Chem. Phys. 109 (1999) 207; J. Li, C. J. Cramer, D. G. Truhlar, Int. J. Quantum Chem. 77 (2000) 264. 81 G. K. Schenter, B. C. Garrett, D. G. Truhlar, J. Chem. Phys. 119 (2003) 5828. 82 C. Alhambra, J. Corchado, M. L. Sanchez, M. Garcia-Viloca, J. Gao, D. G. Truhlar, J. Phys. Chem. B 105 (2001) 11326. 83 M. Garcia-Viloca, C. Alhambra, D. G. Truhlar, J. Gao, J. Chem. Phys. 114 (2001) 9953. 84 D. G. Truhlar, J. Gao, C. Alhambra, M. Garcia-Viloca, J. Corchado, M. L. Sanchez, J. Villa, Acc. Chem. Res. 35 (2002) 341; D. G. Truhlar, J. L. Gao, M. Garcia-Viloca, C. Alhambra, J. Corchado, M. L. Sanchez, T. D. Poulsen, Int. J. Quantum Chem. 100 (2004) 1136. 85 T. D. Poulsen, M. Garcia-Viloca, J. Gao, D. G. Truhlar, J. Phys. Chem. B 107 (2003) 9567. 86 G. van der Zwan, J. T. Hynes, J. Chem. Phys. 78 (1983) 4174; J. T. Hynes, in Solvent Effects and Chemical Reactivity,
87
88 89
90 91 92 93
94
95
96
97
98 99
O. Tapia, J. Bertrn (Eds.), Kluwer, Dordrecht, 1996. Y.-Y. Chuang, M. L. Radhakrishnan, P. L. Fast, C. J. Cramer, D. G. Truhlar, J. Phys. Chem. A 103 (1999) 4893. J. Z. Pu, D. G. Truhlar, J. Phys. Chem. A 109 (2005) 773. C. Lee, M. Bagdasarian, M. Meng, J. G. Zeikus, J. Biol. Chem. 265 (1990) 19082; H. van Tilbeurgh, J. Jenkins, M. Chiadmi, J. Janin, S. J. Wodak, N. T. Mrabet, A.-M. Lambeir, Biochemistry 31 (1992) 5467; P. B. M. van Bastelaere, H. L. M. Kerstershilderson, A.-M. Lambeir, Biochem. J. 307 (1995) 135. J. Gao, D. G. Truhlar, Annu. Rev. Phys. Chem. 53 (2002) 467. J. Pu, S. Ma, J. Gao, D. G. Truhlar, J. Phys. Chem. B 109 (2005) 8851. M. Garcia-Viloca, D. G. Truhlar, J. L. Gao, Biochemistry 42 (2003) 13558. C. A. Fierke, K. A. Johnson, S. J. Benkovic, Biochemistry 26 (1987) 4085. R. S. Sikorski, L. Wang, K. A. Markham, P. T. R. Rajagopalan, S. J. Benkovic, A. Kohen, J. Am. Chem. Soc. 126 (2004) 4778. P. K. Agarwal, S. R. Billeter, S. Hammes-Schiffer, J. Phys. Chem. B 106 (2002) 3283. M. J. Gillan, J. Phys. C 20 (1987) 3621; G. A. Voth, D. Chandler, W. H. Miller, J. Chem. Phys. 91 (1989) 7749; G. R. Haynes, G. A. Voth, Phys. Rev. A 46 (1992) 2143; G. A. Voth, J. Phys. Chem. 97 (1993) 8365; M. Messina, G. K. Schenter, B. C. Garrett, J. Chem. Phys. 98 (1993) 8525; G. K. Schenter, G. Mills, H. Jnsson, J. Chem. Phys. 101 (1994) 8964; G. Mills, G. K. Schenter, D. E. Makarov, H. Jonsson, Chem. Phys. Lett. 278 (1997) 91. R. P. McRae, G. K. Schenter, B. C. Garrett, G. R. Haynes, G. A. Voth, G. C. Schatz, J. Chem. Phys. 97 (1992) 7392. R. P. McRae, B. C. Garrett, J. Chem. Phys. 98 (1993) 6929. S. Jang, C. D. Schwieters, G. A. Voth, J. Phys. Chem. A 103 (1999) 9527.
875
28 Quantum Mechanical Tunneling of Hydrogen Atoms in Some Simple Chemical Systems K. U. Ingold
Not only is it difficult to prove that a given reaction proceeds via tunneling, it is even difficult to define the term tunneling unambiguously. The hydrogen atoms themselves, one presumes, are unaware that they are tunneling: from their vantage point the barrier is, like beauty, only present in the eye of the observer. Moreover, not all observers will see the barrier but only those that have not yet overcome their classical prejudices. Willem Siebrand 1984
28.1 Introduction
In 1933 Bell [1] predicted that, due to quantum mechanical effects, the rate of transfer of a hydrogen atom (H-atom) or proton would become temperature independent at low temperatures. Since that time, kineticists have embraced the concept of quantum mechanical tunneling (QMT) so enthusiastically that it is frequently invoked on the flimsiest of experimental evidence, often using data obtained at, or above, room temperature. At such elevated temperatures, conclusive evidence that the rate of an H-atom or proton transfer is enhanced above that due to “over the top of the barrier” thermal activation, and can only be explained by there being a significant contribution from QMT, is rare. Significant has been italicized in the foregoing sentence because QMT will always make some contribution to the rate of such transfers. The QMT contribution to the transfer rate becomes more obvious at low temperatures. For this reason, the unequivocal identification of QMT in simple chemical systems requires that their rates of reaction be measured at low temperatures. In this chapter, a few simple unimolecular and bimolecular reactions will be described in which the rates of H-atom motion were measured down to very low temperatures. These kinetic measurements provide unequivocal evidence that QMT dominates the reaction rates over a wide range of temperatures. There are two common themes. First, all the experimental data were generated in my own Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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28 Quantum Mechanical Tunneling of Hydrogen Atoms in Some Simple Chemical Systems
laboratory where QMT became one research focus between 1974 and 1990. The second theme is that all the kinetic data were generated using electron paramagnetic resonance (EPR) spectroscopy.
28.2 Unimolecular Reactions 28.2.1 Isomerization of Sterically Hindered Phenyl Radicals 28.2.1.1 2,4,6-Tri–tert–butylphenyl
The lifetimes of many classes of free radicals can be dramatically increased by attaching two (or more) tert-butyl groups close to the radical center [2]. This sterically induced increase in free radical persistence was subject to a severe challenge with phenyl radicals because both their H-atom abstraction and addition reactions with organic substrates are exothermic and very rapid. Nevertheless, 2,4,6-tri–tert– butylphenyl, 1H , produced by reaction of 1HBr with photochemically generated Me3Sn (or Me3Si ) radicals in liquid cyclopropane in the cavity of an EPR spectrometer was found to be fairly long-lived at ambient and lower temperatures [3] hm
Me3SnSnMe3 ! 2 Me3Sn
Me 3Sn +
(28.1)
Me 3SnBr +
Br
(28.2)
1H (1D)
1HBr (1DBr)
On interrupting the photolysis, 1H decayed with first-order kinetics and with rate constants from –30 to –90 C that were independent of the concentrations of 1Br, ditin and cyclopropane [3]. The product, also identified by EPR, was the 3,5-di-tertbutylneophyl radical, 2 , that itself decayed with second-order kinetics.
k3
(28.3)
1H (1D)
2H (2D)
2 2H
2H -2H
(28.4)
28.2 Unimolecular Reactions
Reaction (28.3) was found to have a surprisingly low Arrhenius pre-exponential factor (log (AH/s–1) = 5.3). 1D Br was synthesized in which the three tert-butyl groups had been essentially fully deuterated (2H content > 99%) [4]. Under similar conditions in the EPR an even more persistent 1D radical was obtained. This also D decayed with first-order kinetics and yielded kH 3 /k3 » 50 at –30 C. It was thought probable that reaction (28.3) would provide one of the first clear and unequivocal examples of QMT in an H-atom transfer. This reaction and related reactions were therefore examined in considerable detail [4, 5]. The decay of 1H generated from 1H Br with Me3Sn (reaction (28.2)) and by the photolysis of 3 (reaction (28.5)) occurred with “clean” first-order kinetics and at
C(O)OOBu t
hν
CO2
1H
(28.5)
3
identical rates in liquid cyclopropane, propane, isopentane and toluene and at temperatures from 247 to 113 K [4]. 1D also decayed by reaction (28.3) with “clean” first-order kinetics from 293 to 124 K [4]. Arrhenius plots of both sets of kinetic data are curved (see Fig. 28.1) implying QMT of both H- and D-atoms. When 1H or 1D were generated from 1Br using Me3Si radicals formed via reaction (28.6) hv
Me3 SiH
ButOOBut ! ButO ! ButOH + Me3Si
(28.6)
the decay rates were the same as for the Me3Sn method at 245 K but were significantly greater at lower temperatures. These faster reactions were attributed to the intermolecular reaction (28.7) becoming competitive with the intramolecular isomerization, reaction (28.3) [4]. 1 + Me3SiH ! 1-H + Me3Si
(28.7)
The unimolecular isomerization of 1 to 2 involves a relatively inflexible and nonpolar species. This suggested that the isomerization rate might not be affected by changing from the liquid to the solid phase. If this were the case, the reaction could be studied at temperatures below 113–K where the effects of QMT should become even more pronounced. Benzene, perdeuteriobenzene and neopentane were used as the solid matrices and kinetic measurements on the isomerization of 1H were made over a range of temperatures down to the boiling points of liquid nitrogen (77 K) and liquid neon (28 K) [5]. In the overlapping temperature range, the rate constants for isomerization of 1H were essentially the same for reactions in the solid state and in solution, see Fig. 28.1. Measurements of the rates of isomerization of 1D were made only after sufficient time had elapsed for any incompletely deuterated radical to have decayed completely (Fig. 28.1). Unfortunately, the 1D isomerization became too slow to measure (in any reasonable time) at temperatures below 123 K.
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28 Quantum Mechanical Tunneling of Hydrogen Atoms in Some Simple Chemical Systems
2 1 0
log [k /s-1]
878
-1 -2 -3 -4 -5 -6 2.5
12.5
22.5
1000/[T /K]
32.5
Figure 28.1 Arrhenius plots of the rate constants for the isomerization of 2,4,6-tri-tert-butylphenyl. Key: 1H isomerization in solution (s) and in matrices, d; 1D isomerization in solution (h) and in matrices. (j)
The isomerization reaction: 1 fi 2 , exhibits all the phenomena characteristic of a hydrogen atom motion in which QMT dominates the rate. These phenomena are: 1. Large deuterium kinetic isotope effects (DKIEs). When QMT makes only an insignificant contribution to the rate, the DKIE arises only from differences in the zero-point energies (ZPEs) of the H- and D-containing reactants and their transition states. The DKIE will be maximized when all the ZPE in the reactants is lost in the transition state. In such a case, the difference in the ZPEs of the H- and D-containing reactants will equal the difference in the activation enthalpies, ED – EH . For the breaking of a C–H/C–D bond, ED – EH £ 1354 cal mol–1, provided that the ZPEs of both stretching and bending vibrations are lost in the transition state [6]. Thus, for the “classical” rupture of a C–H/C–D bond, i.e., in the absence of significant QMT, the maximum possible DKIEs (kH /kD ) are, for example, 17, 53 and 260 at 243, 173 and 123 K, respectively. The experimentally measured DKIEs for the 1 !2 isomerization were always much larger than these calculated values, viz., 80, 1400 and 13000 at 243, 173 and 123 K. Admittedly, in the case of the 1D isomerization there will be a small additional contribution to the DKIE from secondary DKIEs but these are unlikely to be greater than 2 at 243 K and 6 at 123 K [4].
28.2 Unimolecular Reactions
2. Nonlinear Arrhenius plots. QMT will become relatively more important as the temperature is decreased and this will lead to curved Arrhenius plots with the curvature being more pronounced for H transfer than for D transfer. This is clearly seen in Fig. 28.1. Moreover, if the reaction rate can be monitored at sufficiently low temperatures, there will be little or no thermal activation and the reaction will only occur because of QMT. This means that at very low temperatures the rate should become essentially independent of the temperature. This is clearly the case for 1H isomerization (see Fig. 28.1) and presumably would also have been true for 1D had it been possible to make measurements at lower temperatures. 3. Large differences in Arrhenius activation enthalpies and pre-exponential factor for H and for D transfer. Both of these criteria of QMT are commonly employed when the kinetic measurements are confined to such a narrow range that curvature of the Arrhenius plots is not as obvious as it is for 1H and 1D (see Fig. 28.1). Although neither of these criteria is required to conclude that QMT plays a dominant role in the isomerization of 1 , it is worth noting that the “leastsquares” Arrhenius plots using only the kinetics measured in solution yielded ED= 6.4, EH = 2.5 kcal mol–1 (difference: 3.9 kcal mol–1), and AD= 105.1, AH = 103.1 s–1 [4]. The experimental rate constants for the isomerization of 1 were analyzed [4, 5] in the manner customary in the 1970s [7]. This assumed that passage through the transition state could be described by the motion of a particle of constant mass along a single, separable, coordinate. According to this one-dimensional model [7], the temperature dependence of the rate constant, k(T), could be represented by: k(T) = AC(T)e–Vo =RT
(28.I)
where Vo is the height of the potential barrier, R is the gas constant, A is the approximate temperature-independent frequency of mass point collisions with the barrier, and C(T) is the ratio of the quantum mechanical to the classical barrier transmission rates of a Boltzmann distribution of incident mass-point kinetic energies. The barrier heights and widths were determined by finding the best fit of both the 1H and 1D kinetic data to a common barrier using three differently shaped potential barriers known as the Eckart, Gaussian and truncated parabolic barriers. The results of these computations [4, 5] will not be reported here because they are irrelevant from today’s perspective. The problem is that these types of potential energy barriers are single “bumps” on an otherwise flat, constant energy, reaction coordinate extending from minus to plus infinity. These are certainly not realistic barriers for any H-atom transfer reaction.
879
28 Quantum Mechanical Tunneling of Hydrogen Atoms in Some Simple Chemical Systems
Fortunately, Siebrand and coworkers [8] developed a new and much more satisfying approach to processes involving QMT that avoided the usual tunneling formalism. Instead of formulating the H-atom transfer in terms of barrier penetration, it was described as a radiationless transition between potential energy surfaces. An explicit barrier shape is not employed, though one can be obtained from the vibrational potentials determining the initial (reactant) and final (product) states and the interaction operator which allows the H-atom transfer to occur. These are also one-dimensional barriers like those described above and, not too surprisingly, they can fail to account for the experimental transfer kinetics. These inconsistencies were removed by including low-frequency, nonhydrogenic modes which cause barrier oscillations and periodically favorable transfer conditions. This generalized model yielded satisfactory descriptions of the temperature and isotope dependence of some reported transfer rate constants [9]. The calculated rate constants, plotted as an exponential function of T rather than 1/T, show a constant part at low temperatures followed by a quasi-linear part at higher temperatures. Siebrand et al. [9] applied their procedure to a number of intramolecular H- and D-atom transfers for which some experimental data were available. This included the isomerizations of the tri-tert-butylphenyl radicals, 1H and 1D . The curves obtained [9] using an anharmonic low frequency motion (which was superior to the harmonic version) are shown in Fig. 28.2. These curves give very satisfactory fits to the experimental rate constants. The calculated, limiting, low temperature QMTonly, DKIE is ~ 50000! It appears to be worthy of the Guinness Book of Records [28]. 2 1 0 -1
log[k /s-1]
880
-2 -3 -4 -5 -6 -7 -8 0
100
200
300
T /K Figure 28.2 Plots of the rate constants for the isomerization of 2,4,6-tri-tert-butylphenoxyl, 1H and 1D , against T (K). The symbols are the same as those in Fig. 28.1. The solid lines depict the calculated rate constants for H-atom and D-atom transfer in these 1 ! 2 reactions.
28.2 Unimolecular Reactions
28.2.1.2 Other Sterically Hindered Phenyl Radicals 2,4,6-Tri(1¢-adamantyl)phenyl, [4] 4H , and octamethyloctahydroanthracen-9-yl, [5] 5H , have also been generated from their parent bromides and observed by EPR spectroscopy. Both of these radicals decayed with “clean” first-order kinetics. Ad
Ad
(28.8) Ad 5H
4H (Ad = 1-adamantyl)
Arrhenius plots of their decay rate constants show pronounced curvature, see Fig. 28.3. By analogy with the 1H fi2H isomerization it can be concluded that 4H and 5H decay by intramolecular H-atom transfers involving 5-center cyclic transition states with QMT playing a dominant role. Unfortunately, product radicals could only be observed in the case of 2H , those from 4H and 5H could not be detected at any temperature. This is because these two product radicals have a very large number of individual EPR lines which would have made their detection extremely difficult. At the same temperature, 4H and 5H are more persistent than 1H [4, 5] (cf. Fig. 28.1 and 28.3). This was attributed to the fact that the minimum distance that the hydrogen atom must “jump” is considerably less for 1H (1.34 , assuming normal bond lengths and angles) than for the other two hindered phenyl radicals (e. g., 1.84 for 4H ) [4, 5]. Attempts to further confirm the importance of QMT in the isomerization of 4H and 5H by studying these reactions in frozen matrices at really low temperatures were frustrated by poor resolution of the phenyl radicals’ EPR spectra in the 2
0
-1
log [k /s ]
1
-1 -2 -3 -4 3
5
7
1000/[T /K]
9
Figure 28.3 Arrhenius plots of the rate constants for the isomerization of 2,4,6-tri(1¢-adamantyl)phenyl, 4H (s) and for the isomerization of octamethyloctahydroanthracen-9-yl, 5H ().
881
882
28 Quantum Mechanical Tunneling of Hydrogen Atoms in Some Simple Chemical Systems
solids. The compound 5D Br in which all eight methyl groups were perdeuterated was therefore synthesized and converted to 5D using tri-n-butyltin radicals (generated by photolysis of hexa-n-butyl ditin) [5]. As expected, 5D decayed with first-order kinetics and more slowly than 5H . However, the DKIE increased only from ca. 20 to ca. 50 over a temperature range from 323 to 173 K. Moreover, in contrast to the isomerization of 5H where the rates were independent of the ditin concentration and solvent (cylclopropane, propane, isopentane, isooctane), the rates of “isomerization” of 5D were dependent on the ditin concentration and solvent (faster in isopentane than in cyclopropane) [5]. Obviously, 5D decays not by an intramolecular D-atom QMT but by an intermolecular H-atom abstraction from the surrounding medium. This is unfortunate but does have a positive side: Because 5H is so much shorter lived than 5D it cannot be reacting with the surrounding medium to any significant extent. That is, 5H must decay by intramolecular H-atom QMT. The much less sterically hindered phenyl radicals 6H , 7H and 8H were generated
(28.9)
6H
7H
8H
9H
10H
from their parent bromides in the usual ways but did not give EPR detectable signals [4, 5]. That 6H and 7H were being produced was demonstrated by the addition of tetramethylgermane. The (very sharp) EPR signals due to ðCH3 Þ3 GeCH2 could then be readily detected, e.g., 7H + (CH3)4Ge ! 7H H + (CH3)3GeCH2
(28.10)
That 8H was formed was obvious from the appearance, even at 113 K, of the EPR signal due to a neophyl-type radical. This must arise from a fast intramolecular H-atom abstraction via a 6-center cyclic transition state.
8H
(28.11)
The phenyl radicals 9H and 10H could be detected by EPR spectroscopy but were much less persistent than 1H [5]. They decayed with first-order kinetics in cyclopropane but their rates of decay were proportional to the concentration of hexabutyl ditin. Generation of 9H by direct photolysis of 9H Br decreased the rate of its decay significantly and the addition of (CH3)4Ge gave rise to the ðCH3 Þ3 GeCH2 EPR signal.
28.2 Unimolecular Reactions
Radicals 9H and 10H were prepared with the hope of increasing phenyl radical persistence by increasing the distance the H-atom must “jump” in a 5-center intramolecular H-atom abstraction in comparison with the distances involved for 1H and 4H e.g., 2.25 for 9H. This approach was unsuccessful (in solution) because of intermolecular H-atom abstraction by the more exposed radical centers. However, these experiments did serve to define the requirements necessary to most readily observe unequivocal examples of QMT in intermolecular H-atom abstractions, viz., relatively “fixed” and relatively close spatial coordinates for the H-atom donor and the H-atom receiver, see final section in this chapter. 28.2.2 Inversion of Nonplanar, Cyclic, Carbon-Centered Radicals
The vast majority of trivalent carbon-centered radicals are planar (single energy minimum) or, if not strictly planar, they generally have negligible barriers to inversion, e.g., Me3 C [10]. However, nonplanar trivalent carbon-centered radicals with significant barriers to inversion exist when the radical center has strongly electron-withdrawing atoms directly attached, e.g., F3 C [11], or forms a part of a three-membered ring, e.g. cyclopropyl [12]. Although an inversion may not always be considered to be a chemical “reaction” they can provide very nice examples of systems in which QMT plays a dominant role in the inversion kinetics.
28.2.2.1 Cyclopropyl and 1-Methylcyclopropyl Radicals Both of these cyclopropyls are nonplanar at their radical centers and have a similar degree of deviation from planarity [12]. They are therefore likely to have similar “classical” barriers to inversion. For cyclopropyl, 11H , the four ring hydrogen atoms are magnetically equivalent on
Rα
Hanti
Hsyn
R k 12
Hsyn
Hanti
R
Hanti
Rα Hanti
11 (R α = H, D, Me)
k 12
Hsyn Hsyn (28.12)
the EPR time scale at the lowest temperatures explored (89 K in ethane as solvent) [13]. This was also true for 11D [13] In contrast, for 1-methylcyclopropyl the four ring hydrogen atoms are only equivalent at temperatures down to 183 K. At still lower temperatures, the syn and anti hydrogen become magnetically unequivalent [13]. The experimental spectra were simulated through the coalescence tempera-
883
28 Quantum Mechanical Tunneling of Hydrogen Atoms in Some Simple Chemical Systems
ture range. The calculated values of the inversion rate constant, k12 , gave an excellent (linear) Arrhenius plot: –1 –1 log (kMe 12 /s ) = 13.1 – 3.1/2.3RT (kcal mol )
(28.II)
The magnitude of the pre-exponential factor provides further confirmation that methyl inversion is essentially a “classical” process, as expected for such a massive group. However, because 11H and 11Me are expected to have roughly the same inversion barriers, the failure to resolve the syn and anti hydrogen atoms in 11H and even in 11D is a strong indication that QMT dominates both H and D inversions.
28.2.2.2 The Oxiranyl Radical As was the case with 11Me , the rates of inversion of the oxiranyl radicals, 12H and 12D could be measured by EPR line broadening over a wide range of temperatures Hsyn
R
Hanti
R
Hsyn
k 13
Hanti
O
Rα
k 13
Rα O
(28.13)
12 (R α = H, D)
[14]. The results are shown as Arrhenius plots in Fig. 28.4. In view of the large DKIE, there can be little doubt that QMT dominates the H-atom inversion. Furthermore, the Arrhenius plot for H-atom inversion is curved and the rate con-
8
-1
log [k /s ]
884
7
6
5
4.4
5.4
6.4
7.4
1000/[T /K]
8.4
9.4
Figure 28.4 Arrhenius plots of the rate constants for the inversion of oxiranyl, 12H (s) and a-deuteriooxiranyl, 12D (d). The solid and dashed lines depict the calculated rate constants for H-atom and D-atom inversion, respectively.
28.2 Unimolecular Reactions 6 –1 stant for inversion, kH 11 , reaches a limiting value of ca. 7 10 s at temperatures below ca. 140 K. Unfortunately, the rate of D-atom inversion became too slow to measure at temperatures lower than ca. 140 K. The available data for D-atom inversion can be fitted reasonably well to the Arrhenius equation: –1 –1 log (kD 13 /s ) = 10.9 – 3.6/2.3RT (kcal mol )
(28.III)
However, the pre-exponential factor in this equation is roughly 2 orders of magnitude smaller than would be expected for a “classical” (over the barrier) inversion (compare with Eq. (28.II)). It is therefore highly probable that QMT is also important in the D-atom inversion over the temperature range covered. To interpret the kinetic results for oxiranyl inversion quantitatively, the structure and vibrational force field were, in the absence of experimental data, determined by ab initio molecular orbital calculations [14]. The minimum-energy path for inversion was found to involve not only components perpendicular to the COC plane but also components parallel to the plane. Moreover, atoms other than the inverting hydrogen were found to undergo substantial displacements so that the calculation of accurate inversion rate constants would have required a multidimensional potential energy surface. For practical reasons only a one-dimensional effective potential was employed. The frequency associated with the effective potential was taken to be that of the inverting H-atom, Ha, in 12H because this has the lowest frequency and will contribute the most to the temperature dependence of kH 13 at low temperatures. This yielded only a partial potential, defined only at stationary points and could not be used to calculate kH 13 (T) directly. The observed inversion rate constants were therefore employed to derive a one-dimensional empirical, double-minimum potential energy surface that was reasonably close to the theoretical potential at its stationary points. The empirical barrier height was 6.8 kcal mol–1 in excellent agreement with the experimental barrier height for inversion of 2,3-dimethyloxiranyl [15], which amounts to 7.0 kcal mol–1 after correction for the zero point energy [14]. It is noteworthy that only a one-dimensional potential is required for the inversion of 12 rather than the two-dimensional potential required for the isomerization of 1 . Note also that the rate constants for D-atom inversion smoothly fit a curved Arrhenius plot that has its strongest curvature at lower temperatures than for the H-atom inversion (see Fig. 28.4). This is because the frequency of the outof-plane bending mode is lower for 12D than for 12H, so that 12D ’s excited states start contributing to the tunneling at lower temperatures. The limiting rate 4 –1 [14]. Thus, the limiting, constant, kD 13 , at 0 K was calculated to be 6.9 10 s 6 QMT-only, DKIE for oxiranyl inversion is 7 10 /6.9 104 » 100. This limiting DKIE is comparable to that calculated for the inversion of the dioxolanyl radical [16] (vide infra), but is much smaller than that obtained for 2,4,6-tri-tert-butylphenyl isomerization (~50000, vide supra) and that which could be estimated for reaction (28.14) in matrices (vide infra). CH3 + CH3OH (CD3OD) fi CH4 (CH3D) + CH2 OH ( CD2OD)
(28.14)
885
28 Quantum Mechanical Tunneling of Hydrogen Atoms in Some Simple Chemical Systems
28.2.2.3 The Dioxolanyl Radical The EPR spectrum of 1,3-dioxolan-2-yl, 13H , showed no detectable line broadening Hsyn
Hanti R k 15
O Rα
Hanti
O O
R k 15
Rα
(28.15)
Hsyn
O 13 (R α = H, D)
down to 93 K [16]. However, for 13D, the syn and anti hydrogen atoms at C-4 and C-5 are not magnetically equivalent at low temperatures and values of kD 15 have been calculated from 191 to 99 K [16]. An Arrhenius plot of these data provides a very nice example of D-atom tunneling in an inversion. The methods of calculation used for the 12H and 12D oxiranyl inversions were applied to the dioxolanyl radicals and provided the lines shown in Fig. 28.5. These calculations imply that the QMT-only inversion rate constant for 13H, is only just too great for measurement by EPR line broadening. During inversion the Ca and Ha atoms move in opposite directions while the remaining atoms move very little. This inversion is therefore “double-hinged” so that the Ca motion reduces the Ha (or Da) tunneling path length compared, for example, to the oxiranyl radical, leading to faster tunneling for 13, than for 12 although the barrier heights for these two radicals are rather similar (vide infra). 8.5 8.0 -1
log [k /s ]
886
7.5 7.0 6.5 6.0
5
6
7
8
1000/[T /K]
9
10
Figure 28.5 Arrhenius plot of the rate constants for the inversion of [2D]-1,3-dioxolan-2-yl, 13D . The solid line depicts the calculated rate constant for this process. The broken line depicts the calculated rate constants for inversion of the nondeuterated radical,13H .
28.3 Bimolecular Reactions
28.2.2.4 Summary The inversion of cyclic carbon-centered radicals provides some very nice examples of H- and D-atom QMT. For purposes of comparison [16], approximate values of: (i) the pyramidyl angles at the radicals’ centers are 39, 45, and 42; (ii) the barrier heights are 3.0, 6.8, and 7.7 kcal mol–1; and (iii) the limiting, QMT-only, DKIEs are 8, 100, and 50; for cyclopropyl, oxiranyl and dioxolan-2-yl, respectively. The EPR line broadening method allowed the rate constants for H- and D-atom inversion in oxiranyl and D-atom inversion in dioxolan-2-yl to be measured over a wide range of temperatures. However, as a consequence of QMT, both H- and D-atom inversion in cyclopropyl and H-atom inversion in dioxolanyl occurred too rapidly for their rate constants to be determined by this technique even at the lowest temperatures.
28.3 Bimolecular Reactions 28.3.1 H-Atom Abstraction by Methyl Radicals in Organic Glasses
Methyl radical decay in simple organic glasses made from acetonitrile [7, 17], methyl isocyanide [18] and methanol [19], at low temperatures, e.g., 77 K (liquid N2) commonly occur by H-atom abstraction from a molecule in the glass: CH3 + CH3G fi CH4 + CH2 G
(28.16)
These processes were generally regarded as outstanding examples of reactions in which QMT dominates the thermally activated process. This is undoubtedly true (vide infra) but the interpretation of the experimental results from all these systems suffered from two difficulties. First, in these glasses reaction (28.16) did not follow (pseudo-)first-order kinetics. Second, the rates of deuterium transfer from CD3G were generally too slow to measure accurately. Indeed CD3 radicals in CD3CN [17] and in CD3NC [18] disappear by reactions other than D-atom abstraction from the glass, leading to the term “all-or-nothing isotope effects” [18]. If methyl radical decay in glasses followed first-order kinetics its concentration would decrease according to exp(–k16t). However, it has been convincingly demonstrated [20] that in several glasses the decay actually follows a rate law of the form exp(–ct1/2). The meaning of the constant c was not made clear and no plausible kinetic scheme supporting such a rate law had been put forward. This unsatisfactory state of affairs changed in 1984 with a proposal [21] that these abnormal kinetics were a consequence of the inhomogeneity of the matrix. In the experiments that were carried out [21], the methyl radicals were produced in a methanol glass from methyl halides by photo-induced electron capture using traces of diphenylamine, reaction (28.17). It was suggested [21] that the radicals
887
888
28 Quantum Mechanical Tunneling of Hydrogen Atoms in Some Simple Chemical Systems hv
CH3 X
Ph2NH ! e– ! CH3 + X–
(28.17)
were formed in a distribution of sites in the glass. This meant that decay would occur with a distribution of first-order rate constants arising from a distribution of H-atom transfer distances. It was found that when the irradiation time used to generate the CH3 was short (10 s) relative to the decay times, the plot of log[ CH3 ] vs. t1/2 at 77 K was indeed linear for a 200-fold decrease in the radical’s concentration, a decrease which occurred over 1600 s [21]. However, when a reduced light intensity and a long irradiation time (~10000 s) were employed the plot of log[ CH3 ] vs. t1/2 was nonlinear, being strongly curved downwards towards the t1/2 axis. These preliminary results [21] were satisfactorily accommodated within a simple model. The range of first-order rate constants in the different sites in the glass was found to extend over roughly two orders of magnitude and was attributed to a distribution of H-atom transfer distances (and thus was indirectly related to the structure of the glass). The different decay kinetics found for long and short irradiation times arise because the methyls in the more reactive sites had mostly decayed before the measurements were started. In subsequent publications [22] this model was refined and a great deal more kinetic data on reaction (28.14) and partially deuterated versions of this reaction were reported. Measurements were made over as wide a range of temperatures as was experimentally possible. This was 5–89 K for CH3OH and 77–97 K for CD3OD glasses, the upper temperature being set by the softening of the glass (phase transition at 103 K) and the 77 K lower limit for CD3OD glass by the extreme slowness of the D-atom abstraction at lower temperatures [22b]. For each site where the methyl radicals are trapped, the H- or D-atom transfer rate is, of course, governed only by the local properties of the glass, irrespective of other sites. The first-order rate constant for each site is determined by the distance from the center of the radical to the nearest methanolic methyl hydrogen atom. Since short-range order is conserved in the glass, this distance, governed by the van der Waals radii of the methyl group and methyl radical, will vary only slightly from site to site. Since, on the time scale of the experiments, methyl rotation and tumbling are rapid at these temperatures, the distribution of transfer distances will be narrow and random. The rate constants of this distribution were analyzed theoretically to obtain a quantitative relation between rate and equilibrium distance for H- and D-atom transfer. The model used was based on QMT and a twodimensional barrier. One dimension, associated with C–H stretching in the CH3OH, accounts for the observed large DKIE, the other associated with the lattice mode, is mainly responsible for the temperature dependence. Some of the parameters employed in these computations were independently known, e.g., the C–H stretching frequency. Other parameters were computed by determining the best fit to the experimental data. The numerical values of these “adjustable” parameters were found to be physically reasonable, e.g., 3.9 for the most probable equilibrium distance between the methyl radical and the methyl group, a distance that can be compared with 4.0 for the sum of their van der Waals radii (there-
28.3 Bimolecular Reactions
fore, the most probable equilibrium tunneling distance is » 3.9 – 2 1.09 » 1.7 ), and a lattice frequency of 140 cm–1 which is close to the Debye frequency for ice of 133 cm–1. The experimental nonexponential decay of the EPR signal due to the methyl radical yield k0, the maximum in the distribution of first-order rate constants, i.e., the “most probable” rate constant [22]. Values of k0 plotted against T and the computed rate constants are shown in Fig. 28.6 for the CH3OH and CD3OH glasses [22b,c] The good fit of theory to experiment using realistic parameters lends credence to the validity of the interpretation and to the tunneling distances deduced from it. The strongest deviations occur at very low temperatures where methyl rotations may reduce to librations with the favored orientations relatively unfavorable to QMT. There was also evidence that methyl radical generation was not instantaneous near 5 K [22b]. The EPR spectra of methyl radicals trapped in methanol glasses show “forbidden” lines as satellites of the main 1:3:3:1 quartet lines [23]. These are due to dipolar coupling of the unpaired electron with protons of neighboring methanol molecules. Comparison of the relative intensities of these satellites in CH3OH, CH3OD, CHD2OD, CD3OH and CD3OD indicate that around the trapped methyl radical the structure is similar to the (disordered) b-phase crystal structure of methanol, with the radical replacing a methanol molecule and occupying a position close to its methyl position [23]. The calculated methyl–methyl distances from these experiments [23] are compatible with the distance previously calculated from the methyl radical decay kinetics [22]. -2
-1
log [k0 /s ]
-3 -4 -5 -6 0
20
40
T /K
60
80
100
Figure 28.6 Plots of the “most probable” rate constants for H-atom (s) and D-atom (d) abstraction by methyl radicals in CH3OH and CD3OD glasses, respectively, against T (K). The solid lines depict the calculated rate constants for the two reactions.
889
890
28 Quantum Mechanical Tunneling of Hydrogen Atoms in Some Simple Chemical Systems
The measured rates of decay of methyl radicals embedded in glasses made from CH2DOD over a range of temperatures [22c], and from mixtures of CH3OH and CD3OH at 77 K [24] were also consistent with the distribution of trapping sites/ distribution of first-order kinetics model. However, decay rates in the isotopomerically mixed glasses showed that the static picture was inadequate [24]. At 77 K, the radical had to be able to diffuse through the glass on the time scale of the kinetic measurements. Such diffusion allows the radical to encounter more CH3OH molecules than would be expected for the static structure on a statistical basis. That is, the effective (reactive) mole fraction of CH3OH in the mixtures was higher than the analytical concentration. For example, with 5% CH3OH in CD3OH, the radical encounters, on average, ca. 26 methanol molecules before abstraction occurs which corresponds to diffusion over roughly 11 . 28.3.2 H-Atom Abstraction by Bis(trifluoromethyl) Nitroxide in the Liquid Phase
The convincing evidence given above for the dominant role of QMT in the rates of H-atom abstractions, both intramolecular, e.g., 1H fi2H , and intermolecular, e.g., methyl radical decay in glassy methanol, were obtained in systems involving only a limited number of transferable hydrogen atoms around the radical center. Furthermore, those transferable H-atoms were fairly rigidly held (at tunneling distances) away from the radical center, and the transfers were strongly exothermic. Convincing experimental evidence for QMT’s involvement in any intermolecular H-atom abstraction in the liquid phase had not been presented and represented an interesting challenge in the 1980s (and to this day, so far as the author is aware). If H-atom tunneling is to be identified in the generalized reaction (28.18) X + RH !XH + R
(28.18)
in solution, considerable difficulties would have to be overcome. A kinetic EPR spectroscopic study would have to meet the following criteria: 1. X must be observable by EPR. 2. Reaction (28.18) must be (relatively) rapid, i.e. X must be highly reactive and/or RH must be a “good” H-atom donor. 3. Reaction (28.18) must be irreversible 4. X must be destroyed only by reaction (28.18), i.e. there must be products), no bimolecular self-reaction of X (2 X no unimolecular rearrangement or scission of X ( X
products), and no reaction of X with
the solvent (X + solvent
products).
5. The solvent must have an extremely low freezing point, as close to 77 K as is compatible with it being liquid over a wide range of temperatures.
28.3 Bimolecular Reactions
The radical that appeared to meet the criteria for X most closely was (CF3)2NO and the desired solvent properties were most closely met by some of the Freons (chlorofluorocarbons). The radical was generated photochemically via reactions (28.19) and (28.20) in solvent containing the RH substrate. Initial experiments hv
CF3OOCF3 ! 2 CF3O
(28.19)
CF3O + (CF3)2NOH !CF3OH + (CF3)2NO
(28.20)
[25] were rather encouraging despite the difficulties experienced in keeping the samples at a constant low temperature for times between 2 weeks and 4 months! In these initial experiments, rate constants for reaction (28.21) were measured from 327 down to 123 K for toluene and from 345 to 183 K for toluene-d8. D kH 21 ðk21 Þ
(CF3)2NO + C6H5CH3(d8) ! (CF3)2NOH(D) + C6H5CH2 (d7 ) v fast
(CF3)2NO + C6H5CH2 (d7 )! (CF3)2NOCH2C6H5(d7)
(28.21) (28.22)
Arrhenius plots exhibited slight curvature for the H-atom transfer at low temperatures. If these low temperature points were ignored, the plots yielded AH21 » AD 21 = 104 M–1 s–1, a pre-exponential factor that is well below the 108.5–0.5 M–1 s–1 found for the vast majority of intermolecular H-atom abstractions [26], and H –1 [25]. The (possibly) curved Arrhenius plot, the low A ED 21 – E21 = 1.6 kcal mol factors and the differences in activation enthalpies between D-and H-atom abstraction all suggested a significant role for QMT in reaction (28.21). Follow-up work [27] revealed that the CF3OOCF3/(CF3)2NOH method for generating (CF3)2NO radicals that had been employed [25] had problems. This method necessarily involves low [(CF3)2NO ]/[(CF3)2NOH] ratios and not all R were trapped by (CF3)2NO (e.g., reaction (28.22)). Some R radicals were lost by reaction (28.23). R + (CF3)2NOH ! RH + (CF3)2NO
(28.23)
This leads to a decrease in the measured rate constant as the reaction progresses (and the [(CF3)2NO ]/[(CF3)2NOH] ratio decreases. The loss of (CF3)2NO could be seen not to follow (pseudo-)first-order kinetics if the decay was monitored for 3 or more half-lives. To overcome this problem, in the new work the (CF3)2NO radical itself was employed [27]. Rate constants for H-atom abstraction from 11 new substrates yielded Arrhenius pre-exponential factors ranging from a low of 104.2 M–1 s–1 for diethyl ether (temperature range 297–178 K) to a high of 106.5 M–1 s–1 for 1,4-cyclohexadiene (296– 192 K). In addition, the rate constants were measured for a reaction in which QMT could not be involved. This was the addition of (CF3)2NO to CH2=CCl2.
891
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28 Quantum Mechanical Tunneling of Hydrogen Atoms in Some Simple Chemical Systems
(CF3)2NO + CH2=CCl2 ! (CF3)2NOCH2CCl2
(28.24)
The Arrhenius plot yielded a pre-exponential factor, A24, that was only 105.3 M–1 s–1 that is also much lower than the expected [26] 108.5 M–1 s–1. The measured rate constants [27] should be reliable (except for the earlier toluene data [25]) and they yielded Arrhenius plots that were linear over a wide range of temperatures. Moreover, for H- and D-atom abstraction from C6H5CHO and C6H5CDO the pre-exponential factors were equal within experimental error (AH = 105.3–0.3, AD = 105.1–0.5 M–1 s–1) and, although the DKIE was large, viz. 15 at 298 K, it was not so large that it could only be accounted for by there being a significant role for QMT in the H-atom abstraction. It was, therefore, (reluctantly) concluded that in none of these, quite extensive, H-atom abstraction experiments with (CF3)2NO in the liquid phase was there unequivocal evidence that QMT played a significant role. Another conclusion that could be drawn is that it is going to be extremely difficult, if not impossible, to prove that QMT is truly important in any bimolecular H-atom abstraction in the liquid phase by the one certain test, a curved Arrhenius plot and a rate constant that is independent of the temperature.
References 1 . Bell, R. P. Proc. R. Soc. London, Ser. A
2 3
4
5
6 7 8
9
1933, 139, 466–474; see also: Bell, R. P. Proc. R. Soc. London, Ser.A 1935, 148, 241–250. Griller, D.; Ingold, K. U. Acc. Chem. Res. 1976, 9, 13–19. Barclay, L. R. C.; Griller, D.; Ingold, K. U. J. Am. Chem. Soc. 1974, 96, 3011–3012. Brunton, G.; Griller, D.; Barclay, L. R. C.; Ingold, K. U. J. Am. Chem. Soc. 1976, 98, 6803–6811. Brunton, G.; Gray, J. A.; Griller, D.; Barclay, L. R. C. ; Ingold, K. U. J. Am. Chem. Soc. 1978, 100, 4197–4200. Bell, R. P. Chem. Soc. Rev. 1974, 3, 513–544. LeRoy, R. J.; Sprague, E. D.; Williams, F. J. Phys. Chem. 1972, 76, 546–551. Laplante, J.-P.; Siebrand, W. Chem. Phys. Lett. 1978, 59, 433–436; Siebrand, W.; Wildman, T. A.; Zgierski, M. Z. J. Am. Chem. Soc. 1984, 106, 4083–4089. Siebrand, W.; Wildman, T. A.; Zgierski, M. Z. J. Am. Chem. Soc. 1984, 106, 4089–4096.
10 Griller, D; Ingold, K. U.; Krusic, P. J.;
11
12 13
14
15 16
17 18
Fischer, H. J. Am. Chem. Soc. 1978, 100, 6750–6752. Griller, D; Ingold, K. U.; Krusic, P. J.; Smart, B. E.; Wonchoba, E. R. J. Phys. Chem. 1982, 86, 1376–1377. Johnston, L. J.; Ingold, K. U. J. Am. Chem. Soc. 1986, 108, 2343–2348. Deycard, S.; Hughes, L.; Lusztyk, J.; Ingold, K. U. J. Am. Chem. Soc. 1987, 109, 4954–4960. Deycard, S.; Lusztyk, J.; Ingold, K. U.; Zerbetto, F.; Zgierski, M. Z.; Sieband, W. J. Am. Chem. Soc. 1988, 110, 6721–6726. Itzel, H.; Fischer, H. Helv. Chim. Acta. 1976, 59, 880–901. Deycard, S.; Lusztyk, J.; Ingold, K. U.; Zerbetto, F.; Zgierski, M. Z.; Siebrand, W. J. Am. Chem. Soc. 1990, 112, 4284–4290. Sprague, E. D.; Williams, F. J. Am. Chem. Soc. 1971, 93, 787–788. Wang, J-T.; Williams, F. J. Am. Chem. Soc. 1972, 94, 2930–2934.
References 19 Campion, A.; Williams, F. J. Am. Chem.
Soc. 1972, 94, 7633–7637. 20 Bol’shakov, B. V.; Tolkatchev, V. A. Chem. Phys. Lett. 1976, 40, 468–470; Stepanov, A. A.; Tkatchenko, V. A.; Bol’shakov, B. V; Tolkatchev, V. A. Int. J. Chem. Kinet. 1978, 10, 637–648; Bol’shakov, B. V; Doktorov, A. B.; Tolkatchev, V. A.; Burshtein, A. I. Chem. Phys. Lett. 1979, 64, 113–115; Bol’shakov, B. V; Stepanov, A. A.; Tolkatchev, V. A. Int. J. Chem. Kinet. 1980, 12, 271–281. 21 Doba, T.; Ingold, K. U.; Siebrand, W. Chem. Phys. Lett. 1984, 103, 339–342. 22 (a) Doba,T.; Ingold, K. U.; Siebrand, W.; Wildman, T. A. Chem. Phys. Lett. 1985, 115, 51–54; (b) Doba, T.; Ingold, K. U.; Siebrand, W.; Wildman, T.A. Chem. Phys. Lett. 1984, 88, 3165–3167; (c) Doba,T.; Ingold, K. U.; Siebrand, W.; Wildman, T. A. Faraday Discuss. Chem. Soc. 1984, 78, 175–191.
23 Doba,T.; Ingold, K. U.; Reddoch, A. H.;
24
25 26 27 28
Siebrand, W.; Wildman, T. A. J. Chem. Phys. 1987, 86, 6622–6630. Doba, T.; Ingold, K. U.; Lusztyk, J.; Siebrand, W.; Wildman, T. A. J. Chem. Phys. 1993, 98, 2962–2970. Malatesta, V.; Ingold, K. U. J. Am. Chem. Soc. 1981, 103, 3094–3098. Benson, S. W. Thermochemical Kinetics, 2nd edn., Wiley, New York, 1976 Doba, T.; Ingold K. U. J. Am. Chem. Soc. 1984, 106, 3958–3963. Computational methods now exist that include contributions from all vibrational modes to the H/D-transfer process, thus eliminating the need to introduce any empirical parameters, e.g., variational transition state theory with semiclassical tunneling corrections (Truhlar, D. G.; Garett, B. C.; Klippenstein, S. J. J. Phys. Chem. 1996, 100, 12771) and the approximate instanton method (Siebrand, W.; Smedarchina, Z.; Zgierski, M. Z.; Fernndez-Ramos, A. Int. Rev. Chem. Phys. 1999, 18, 5).
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29 Multiple Proton Transfer: From Stepwise to Concerted Zorka Smedarchina, Willem Siebrand, and Antonio Fernndez-Ramos
29.1 Introduction
It is well recognized that reactions involving the transfer of a proton or hydrogen atom are special in that these particles can tunnel through classically forbidden regions [1]. The wave-like properties also add a new element to reactions in which two or more protons transfer, since under appropriate conditions, they may allow the protons to move as a single particle. In this contribution we review the dynamics of such reactions [2], focusing on double proton transfer for simplicity. In particular, we probe how the motion of one proton influences that of the other and which conditions lead to weak or strong correlation between their motions. Generally speaking, no correlation results in independent transfer and weak correlation in stepwise transfer. Strengthening the correlation will ultimately lead to concerted transfer and may give rise to synchronous transfer if the transferred particles are equivalent. While proton–proton correlation is a unifying concept that allows us to classify and understand the various multiproton transfer mechanisms, it is not a quantity that is easily measured or calculated. In dealing with a specific reaction, one tends to use a simpler approach based on the search for a transition state, i.e. a configuration along the transfer path characterized by a first-order saddle point representing a vibrational force field with one imaginary frequency. More generally, the presence of two mobile particles implies that the potential energy surface contains stationary states with zero, one, or two imaginary frequencies, representing, respectively, a stable intermediate, a transition state, and a state with a secondorder saddle point. A stable intermediate roughly halfway along the trajectory implies barriers separating it from the equilibrium configurations. Such a potential favors stepwise transfer under conditions where the intermediate is thermally accessible. This basically reduces the dynamics to that appropriate for single proton transfer, but leaves open the question of how to deal with transfer at low temperature. A barrier corresponding to a single transition state, similar to that observed for single proton transfer, implies concerted transfer of the two protons. This again can Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H. H. Limbach, and R. L. Schowen Copyright 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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29 Multiple Proton Transfer: From Stepwise to Concerted
be treated by the methods developed for single proton dynamics [1, 3]. However, if, instead, this barrier corresponds to a second-order saddle point, it represents concerted motion along two proton coordinates. This situation does not immediately reveal the nature of the corresponding transfer process, but it drives home the point that the presence of two mobile protons allows at least two transfer mechanisms. On a potential energy surface with more than one saddle point, there will in general be multiple pathways along which the potential has a doubleminimum profile. To analyze the transfer dynamics governed by such a potential, we need an approach that goes beyond the question whether the transfer is concerted or stepwise. To elucidate the effect of proton–proton correlation on the transfer mechanism, we approach the problem from two sides. On the one hand, we develop in Section 29.2 a theoretical model based on two identical single proton transfer potentials subject to proton–proton coupling represented by a simple bilinear function. On the other hand, we consider a representative range of two- and multi-proton transfer processes for which the proton dynamics has been studied experimentally and/or theoretically, typical examples being dimeric carboxylic acids [4–7], porphyrins [8–11] and porphycenes [12–14], naphthazarins [15], and transfer catalyzed by proton conduits such as chains of water molecules [16–18]. Our own calculations on several of these systems are based on the approximate instanton method (AIM) [3, 19], which we review in Section 29.3 and extend to transfer along two reaction coordinates in Section 29.4. Experimental information on multiple proton transfer is available in the form of (state-specific) level splittings and/or thermal rate constants. The observation of a level splitting implies concerted transfer between levels of the same energy. It does not necessarily imply that the potential has a single saddle point or that the transfer can be described in terms of a single trajectory. This question is analyzed in Section 29.4 for a model two-dimensional potential relevant to double proton transfer, with explicit evaluation of tunneling probabilities along various paths. The observation of deuterium (and tritium) isotope effects on level splittings and thermal rate constants provides valuable information on the transfer mechanism [2]. However, whereas in single proton transfer a large isotope effect indicates transfer dominated by tunneling, such an observation may be ambiguous for multiple proton transfer because of the proportionality of zero-point energy shifts with the number of protons. In this connection, generalization of the Swain– Schaad relation between H, D, and T transfer [20] so as to include tunneling [21], offers an alternative method. In the remaining sections, we apply these theoretical approaches to systems for which transfer data are available. We use these results to probe to what extent it is possible to predict the mechanisms contributing to multiproton transfer reactions in a given system, on the basis of known physical properties such as symmetry, geometry, transfer distance and hydrogen bond strength, in an attempt to arrive at a coherent picture of the present state of our understanding of these reactions.
29.2 Basic Model
29.2 Basic Model
Our basic model for double proton transfer is a molecule or complex in which two equivalent protons (hydrogen atoms) can transfer between equivalent positions. We arrange the four carrying atoms X (oxygen, nitrogen, carbon, etc.) in a rectangle with sides a and b, such that any hydrogen bonding takes place along a, the hydrogen bonds being separated by b, as illustrated in Fig. 29.1. This allows us to vary the strength of the hydrogen bonds by varying a, and the strength of their correlation by varying b. The separation a may vary during the transfer in the case of hydrogen bonding and this in turn may affect the correlation. In Fig. 29.1(a) the protons are arranged as in the formic acid dimer, i.e. according to an equilibrium structure belonging to point group C2h . The alternative structure of Fig. 29.1(b) belonging to point group C2v would be realized in the case of double proton transfer between ethane and ethylene moieties in a parallel arrangement. The two arrangements transform into each other through single proton transfer. To keep the notation simple, we use in this section dimensionless units by expressing the coordinates in units r=2, where r is the transfer distance of each proton, i.e. the distance between its two equilibrium positions, and expressing the energies in units 2U0 , where U0 is the barrier height for single proton transfer along the XH X bonds. For any symmetric double-minimum potential we have U0 r 2 and for the linear X–H X bond of Fig. 29.1 we have r ¼ a 2RXH , where RXH is the X–H bond length. First we consider the case where b is so large that the correlation between the two protons is negligible. Then we can write the transfer potential as the sum of two double minimum potentials, which we represent by quartic potentials 1 Uðx1 ; x2 Þ ¼ ½ð1 x12 Þ2 þ ð1 x22 Þ2 2
Figure 29.1 Schematic representation of the basic model of double-proton transfer along parallel equivalent hydrogen bonds in a symmetric system with C2h (a) or C2v (b) symmetry.
(29.1)
897
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29 Multiple Proton Transfer: From Stepwise to Concerted
The corresponding potential-energy surface has a maximum U ¼ 1 at x1 ¼ x2 ¼ 0, where the two protons are in the center of their paths, and four equivalent minima U ¼ 0 at jx1 j ¼ jx2 j ¼ 1 where the protons are in their equilibrium positions x1;2 ¼ –1; two of these correspond to the structure of Fig. 29.1(a) and two to that of Fig. 29.1(b). The minima along each coordinate are separated by a barrier U ¼ 1=2 at x1 ¼ 0; jx2 j ¼ 1 and jx1 j ¼ 1; x2 ¼ 0. We now introduce a weak coupling between the two protons. To derive a functional form for this coupling, we note that it should be symmetric in the two coordinates and sensitive to their sign. The simplest coupling term that meets these requirements will be proportional to x1 x2 . This bilinear term is likely to be the leading term in any expansion of the coupling between symmetric local potentials, irrespective of the coupling mechanism. It will create a difference in energy between the structures of Figs. 29.1(a) and 29.1(b). We choose the structures x1 ¼ x2 ¼ –1 as those of the equilibrium configurations. Adopting this coupling and omitting constant terms, we arrive at the potential 1 Uðx1 ; x2 Þ ¼ ½ð1 x12 Þ2 þ ð1 x22 Þ2 2Gx1 x2 2
(29.2)
where G ‡ 0 is the coupling parameter (in units 2U0 ), which formally represents the interaction between the two XH X hydrogen bonds. To illustrate the nature of this coupling, we first consider the simple case that it is dominated by electrostatic interactions between the XH X hydrogen bonds with dipole moments jl1;2 j ¼ f jx1;2 j, where f is the fractional charge of the proton. For the model of Fig. 29.1(a), the interaction is attractive when both protons are in the equilibrium position (x1 ¼ x2 ¼ –1), repulsive when one of the protons has transferred (x1 ¼ x2 ¼ –1), and zero when the protons are in the center of their path (x1 ¼ x2 ¼ 0). For two dipoles separated by a distance R this behavior can be simulated by the function K.
l~1 l~2 jl1 jjl2 j cos f f 2r2 ¼ ¼ 3 x1 x2 3 3 R R R
(29.3)
where we used the fact that the angle f between the dipoles is 0 or p when they are parallel or antiparallel, respectively. The separation R is expressed in the distances b and a according to 1 1 . 3 ½1 aðx1 x2 Þ2 ; 3 R b
a ¼ 3ða 2RXH Þ2 =2b2 :
(29.4)
Addition of this coupling to Eq. (29.1) yields 1 Uðx1 ; x2 Þ ¼ ½ð1 x12 Þ2 þ ð1 x22 Þ2 2Gx1 x2 ½1 aðx1 x2 Þ2 2
(29.5)
29.2 Basic Model
where G ¼ f 2 r 2 =16b3 U0 may be a weak function of a through the implicit rdependence of U0 noted above. Equation (29.5) reduces to Eq. (29.2) when b exceeds a such that b >> a 2RXH . While such a simple electrostatic picture yields qualitatively correct results for, e.g., dimeric formic acid, it is clearly inadequate for, e.g., naphthazarin, illustrated in Fig. 29.2, where the interaction is governed by the skeletal p-electrons. Nevertheless, the work of de la Vega et al. [15] indicates that a potential of the form of Eq. (29.2) remains a suitable first approximation for this molecule as well. Although, in general, higher-order interaction terms will be necessary to obtain
Figure 29.2 Illustration of stepwise and concerted double proton transfer in naphthazarin, showing the equilibrium configurations (MIN), the (unstable) intermediates (INT), the second-order saddle point (SP2), and the location of the first-order saddle points (SP1).
899
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29 Multiple Proton Transfer: From Stepwise to Concerted
quantitative results for specific molecules, especially if the coupling is strong, the leading bilinear coupling term used in Eq. (29.2) should be adequate to map out the various distinguishable transfer mechanisms. To obtain the stationary points and their curvature for the potential (29.2), we calculate the first and second derivatives with respect to the two coordinates. From the sums and differences of the first derivatives ¶U ¼ 2½x1 ðx12 1Þ Gx2 ¼ 0; ¶x1
¶U ¼ 2½x2 ðx22 1Þ Gx1 ¼ 0 ¶x2
(29.6)
we obtain the expressions ðx1 þ x2 Þ½ðx1 x2 Þ2 þ x1 x2 ð1 þ GÞ ¼ 0; ðx1 x2 Þ½ðx1 þ x2 Þ2 x1 x2 ð1 GÞ ¼ 0
(29.7)
which define the following stationary points: pffiffiffiffiffiffiffiffiffiffiffiffi 1. two global minima x1 ¼ x2 ¼ – 1 þ G, with zero energy 2. the global maximum x1 ¼ x2 ¼ 0, which is a saddle point of second order, with energy ð1 þ GÞ2 pffiffiffiffiffiffiffiffiffiffiffiffi 3. two minima x1 ¼ x2 ¼ – 1 G with energy 4G, which represent stable intermediates p with one proton transferred ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2 ¼ ð1– 1 4G2 Þ=2 with energy 4. two transition states x1;2 ð1 þ 2GÞ2 =2, which represent the barriers for single proton transfer The minima (3) disappear for G ‡ 1, at which point they coincide with the absolute maximum (1). From the second derivatives ¶2 U ¼ 6x12 2; ¶x12
¶2 U ¼ 6x22 2 ¶x22
(29.8)
it follows that the extrema (3) are minima only for G < 2=3. The energy of the transition states (4) exceeds that of the extrema (3) if G ‡ 1=2, a limit that contradicts the limit obtained for the existence of a stable minimum (3). Clearly, the local representation fx1 ; x2 g becomes inadequate for couplings G ‡ 1=2. For coupling in this range we therefore switch to collective coordinates. Defining normal coordinates as plus and minus combination of the local coordinates: xp ¼ ðx1 þ x2 Þ=2;
xm ¼ ðx1 x2 Þ=2
(29.9)
we obtain the potential (29.1) for uncoupled protons in the form 2 2 2 2 Uðxm ; xp Þ ¼ ð1 xp2 Þ2 þ ð1 xm Þ þ 6xm xp 1 2 4 ðxp2 1=3Þ þ xm ¼ ð1 xp2 Þ2 þ 6xm
(29.10)
29.2 Basic Model
Introduction of the coupling of Eq. (29.2) leads to 2 4 Uðxm ; xp Þ ¼ ðxp2 n2p Þ2 þ 6xm ðxp2 n2m Þ þ xm
(29.11)
where n2p ¼ 1 þ G and n2m ¼ ð1 GÞ=3. This yields first derivatives ¶U 2 ¼ 12xp ½ðxp2 n2p Þ=3 þ xm ¼ 0; ¶xp
(29.12)
¶U 2 ¼ 12xm ½ðxp2 n2m Þ þ xm =3 ¼ 0 ¶xm
and second derivatives ¶2 U 2 ¼ 12½ðxp2 þ xm Þ n2p =3; ¶xp2
¶2 U 2 ¼ 12½ðxp2 þ xm Þ n2m 2 ¶xm
(29.13)
In this representation the global minima retain the same formpas in the local coorffiffiffiffiffiffiffiffiffiffiffiffi dinate representation, (1) turning into xm ¼ 0; xp ¼ –np ¼ – 1 þ G. The global maximum (2), i.e. xp ¼ xm ¼ 0, retains its character as a second-order saddle point up to G ¼ 1. For larger coupling, it turns into a simple first-order saddle point when the derivative with respect to xm goes to zero. This eliminates the second reaction coordinate xm and results in one-dimensional synchronous motion of the twopprotons. The intermediate configuration (3) corresponding to xp ¼ 0; pffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffi xm ¼ –nm 3 ¼ – 1 G is a minimum p forffiffiffiffiffiffiffiffiffiffiffiffiffiffi G < ffi1; it is separated from pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi the global minima by transition states (4) at xp ¼ – 1 2G=2; xm ¼ – 1 þ 2G=2. It ceases to be a stable minimum and turns into a saddle point with ¶2 =¶xp2 < 0 for 1=2 < G < 1, under which conditions the two transition states (4) disappear. The coordinates and energies of these extrema are collected in Table 29.1.
Table 29.1 Parameters of the most characteristic configurations of model surface (29.11).
Parameter Global minima (1)
Maximum (2)
Intermediate (3)
Transition state (4)
Bifurcation point
0 pffiffiffiffiffiffiffiffiffiffiffiffi 1G
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 2G=2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ 2G=2
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 GÞ=3
2jxp j=r
pffiffiffiffiffiffiffiffiffiffiffiffi 1þG
0
2jxm j=r
0
0
U=2U0
0
2
ð1 þ GÞ
4G
0 2
ð1=2Þð1 þ 2GÞ
ð4=9Þð1 þ 2GÞ2
It follows that the model potential (29.11) can reproduce three types of potential energy surfaces relevant to double proton transfer, as illustrated in Fig. 29.3(a)–(c). For G < 1=2 (“weak coupling”) it leads to surface (a) that supports a stable intermediate. For 1=2 < G < 1 (“intermediate coupling”) it leads to surface (b) without
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29 Multiple Proton Transfer: From Stepwise to Concerted
29.2 Basic Model 3 Figure 29.3 Schematic two-dimensional potential energy surfaces appropriate to double proton transfer for weak (a), intermediate (b) and strong (c) proton–proton correlation, respectively, where the labeling is that used in Fig. 29.2.
a stable intermediate, but with two types of saddle points, one of first and one of second order. For G > 1 (“strong coupling”) it leads to surface (c) with a single transition state along the coordinate for concerted motion. The model surface (29.11) is defined by three parameters: r, U0 and G. In practice, the potential energy surface and the vibrational force field will be calculated quantum-chemically, which should lead to a more accurate description than that given by the present model potential. We note, however, that the calculated surfaces known to date fall indeed into the three types described above. In the following sections we address in detail specific examples for each case. If the calculations lead to a stable intermediate of type (3) that can be reached via two transition states of type (4), i.e. if the weak coupling regime (G < 1=2) applies, stepwise transfer of the protons is possible, provided the intermediate state is thermally accessible. In that case the dynamics calculations can be carried out consecutively along the one-dimensional reaction coordinates x1 and x2 . If the temperature approaches zero, this mechanism will fade out. Transfer is still possible at T ¼ 0 but will require a degree of coordination between the motions of the two protons. Two pathways stand out: synchronous tunneling through the barrier of type (2) with energy ð1 þ GÞ2 and concerted but asynchronous tunneling through the minima (3) with energy 4G and transition states (4) with energy 2 =2 (all in units 2U0 ). The former pathway involves a tunneling distance (1 þp2G) pffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffi of 2 1 þ G along xp and the latter is longer by an amount of roughly 2 1 G along xm (both in units r=2). The same competition between these pathways, the one with the higher barrier and the one with the longer transfer distance, will govern transfer in the intermediate coupling region (1=2 < G < 1), characterized by very shallow minima of type (3) along xm or flat barrier tops of type (2). If the quantum-chemical calculations lead to a single strong maximum of type (2), the strong coupling regime (G > 1) applies and the dynamics are then governed by the synchronous motion of the two protons along a one-dimensional reaction coordinate xp . Chemically, the coupling regime can be altered by modification of the geometry of the transfer site. It is obvious that an increase in the separation between the protons by means of an increase in the parameter b in Fig. 29.1 will reduce the coupling. Alternatively, an increase in the parameter a will correspond to a weakening of the hydrogen bonding and a loss of XH X polarity. This may require the introduction of additional coupling terms such as those in the potential (29.5). For this potential, the expressions for the extrema in Table 29.1 will get additional terms proportional to aG. In particular, for the intermediate (3) we obtain 2 xm . 1 G þ 2aG;
U . 4Gð1 a=2Þ
(29.14)
903
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29 Multiple Proton Transfer: From Stepwise to Concerted
which implies that the intermediate exists if a”
3 ½ða 2RXH Þ=b2 > ðG 1Þ=2G 2
(29.15)
Thus even for strong coupling there may be an intermediate if the hydrogen bond is long enough. To verify these results for rate constants and tunneling splittings in real systems, we need to investigate the dynamics explicitly. As a preliminary to the proposed treatment of tunneling along two reaction coordinates, we review in the next section an approach that has been applied successfully to tunneling along a single reaction coordinate.
29.3 Approaches to Proton Tunneling Dynamics
In general, proton transfer occurs via a combination of over-barrier and throughbarrier pathways. The rate constant of over-barrier transfer is usually calculated by standard transition state theory (TST) [22] by separating the reaction coordinate from the remaining degrees of freedom. If tunneling effects and the curvature of the reaction path are neglected, this leads to the expression kTST ðTÞ ¼ ðkB T=hÞ
Q z UA =kB T e QR
(29.16)
where UA is the energy of the transition state (adiabatic barrier height), and Q R and Q z are the partition functions for the reactant and the transition state, respectively. Various methods are available to calculate the rate constant of through-barrier transfer or tunneling. Most of our evaluations are based on the approximate instanton method (AIM) [3, 19], an adaptation of instanton theory to proton transfer in large molecular systems. Instanton theory [1, 23–26] is a semiclassical approach in which, below a certain temperature, the manifold of tunneling trajectories for a system with a Hamiltonian H is replaced by a single, least-action trajectory, the instanton or bounce path. This instanton represents a trajectory that is periodic in imaginary time s ¼ it in the inverted potential, namely the trajectory for which the Euclidian action, defined by Z SI ¼
b=2
b=2
Hds;
b ¼ 1=kB T
(29.17)
has an extremum. The instanton equations are defined by dSI ¼0 dfxg
(29.18)
29.3 Approaches to Proton Tunneling Dynamics
where fxg represents the system of coordinates. Their solutions are subject to the periodic boundary conditions fxðbÞg ¼ fxð0Þg. The instanton method defines the thermal rate constant for tunneling transfer in terms of the action SI ðTÞ (expressed hereafter in units ") along this extremal path: ktun ðTÞ ¼ AðTÞeSI ðTÞ
(29.19)
where the preexponential factor AðTÞ accounts for fluctuations about the path. AIM is designed to allow direct application of this methodology to proton transfer in multidimensional systems for which the structure and vibrational force field of the stationary configurations along the reaction path can be evaluated quantumchemically. For simplicity, we focus on symmetric systems. For background on the application of instanton theory to chemical processes we refer to Benderskii et al. [1]. To outline the method used in our calculations, we first consider transfer along a single reaction coordinate involving a potential energy barrier. For double proton transfer, this may refer to the case where the two protons transfer synchronously. To calculate SI ðTÞ, AIM [27–30] generates a full-dimensional potential energy surface in terms of the normal (mass-weighted) coordinates fx; yj g of the transition state configuration. The AIM Hamiltonian separates the tunneling mode x, taken to be the mode with imaginary frequency ix*, from the other (transverse) modes fyj g with frequencies fxj g. If there is a single tunneling coordinate, i.e. if x is one-dimensional, it has the form 1 1X 2 T ¼ x_ 2 þ y_ ; 2 2 j j X 1X 2 2 xj ðyj Dy2j Þ x2 Cs ðys Dys Þ U ¼ UC ðxÞ þ 2 j s X X Ca ðya – Dya Þ þ x 2 Dj ðy2j Dy2j Þ x H ¼ T þ U;
a
(29:20Þ
j
where the transition state corresponds to fx; yj g ¼ 0 and the þ and signs represent the minima of the reactant and the product state, respectively. The kinetic energy, which is diagonal in the stationary configurations, is taken to be diagonal throughout. The Hamiltonian (29.20) accounts for the mixing of the normal modes between the stationary points and can be shown [27] to reduce to the Hamiltonian of the transition state and the minima for x ¼ 0 and x ¼ –Dx, respectively. The subscripts s and a refer to transverse modes that are symmetric and antisymmetric, respectively, with respect to the dividing surface in the transition state, which is perpendicular to x. Their coupling terms with the tunneling mode x are taken to be linear in the transverse mode coordinates, except for a biquadratic term that accounts for the frequency differences between the reactant and the transition state. They are calculated from the displacements Dya;s between
905
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29 Multiple Proton Transfer: From Stepwise to Concerted
these states and, in the case of the biquadratic term, from the corresponding frequency shifts Xj xj : Ca ¼ x2a Dya =Dx;
Cs ¼ x2s Dys =Dx2 ;
Dj ¼ ðX2j x2j Þ=2Dx2
(29.21)
where the Xj denote the frequencies in the equilibrium configuration. The antisymmetric modes have the same symmetry as the tunneling mode and undergo reorganization between reactant and product during the proton transfer while the symmetric modes do not undergo such reorganization but can be displaced between the equilibrium configurations and the transition state. Modes that are not displaced between the reactant and the transition state are not coupled linearly in the harmonic approximation and can contribute only via the biquadratic term of Eq. (29.20). The one-dimensional potential along the tunneling coordinate, represented by UC ðxÞ in Eq. (29.20), is a “crude-adiabatic” potential evaluated with the heavy atoms fixed in the equilibrium configuration, i.e. with ya ¼ –Dya ; ys ¼ Dys ; it is equivalent to the potential along the linear reaction path. This symmetric doubleminimum potential has a maximum UC ð0Þ ” U0 at x ¼ 0, minima UC ð–DxÞ ¼ 0 at x ¼ –Dx, and a curvature in the minima given by the effective frequency X0 which accounts for the contribution of the normal modes of the minima to the reaction coordinate [27]. For the shape of the potential in the intermediate points we use an interpolation formula based on the calculated energies and curvatures near the stationary points. We have found that in many cases the simple quartic potential of the form UC ðxÞ ¼ U0 ½1 ðx=DxÞ2 2
(29.22)
used in the model potentials (29.1) and (29.2) is satisfactory. To calculate the parameters governing the Hamiltonian, we use an approximation that amounts to separating the transverse modes into “high-frequency” (HF) modes, treated adiabatically, and “low-frequency” (LF) modes, treated in the sudden approximation. This separation is based on the value of the “zeta factor” [27] xa;s fa;s ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 =2x2 X2 Ca;s a;s
(29.23)
where X, the “scaling” frequency, is defined by X2 Dx 2 ¼ U0. Modes are treated as HF or LF depending on whether fa;s >> 1 or << 1. Modes for which fa;s ~ 1 require special treatment as discussed elsewhere [7]. Coupling to HF modes leads to an effective one-dimensional motion with renormalized potential UCeff ðxÞ and coordinate-dependent mass meff ðxÞ. Since each HF mode yi is assumed to follow the reaction coordinate x adiabatically, we have 2 ¶U=¶yi ¼ 0, so that yHF ¼ Cs x 2 =x2s and yHF s a ¼ Ca x=xa . Substitution in the Hamiltonian (29.20) provides a correction to the mass of the tunneling particle and thus modifies the kinetic energy operator:
29.3 Approaches to Proton Tunneling Dynamics
T eff ”
ðHFÞ 1 2 1X 2 1 y_ ¼ meff ðxÞ x_ 2 x_ þ 2 2 a;s a;s 2
(29.24)
Using Eq. (29.21), we obtain for the dimensionless renormalized mass meff ðxÞ ¼ 1 þ ðx=DxÞ2
ðHFÞ X
Dms þ
s
Dms ¼
2 ð2DyHF s =DxÞ ;
Dma ¼
ðHFÞ X
Dma a 2 ðDyHF a =DxÞ
(29.25)
Renormalization of the one-dimensional potential (29.22) yields a potential of the same shape but with a barrier height corrected by the standard vibrational-adiabatic correction for the HF modes only. The preexponential factor AðTÞ in the rate expression (29.19) consists of a longitudinal component Ak and a perpendicular component A? , representing the contributions of fluctuations that are, respectively, parallel and perpendicular to the instanton path. If in the one-dimensional potential UC ðxÞ the “long” tunneling action evaluated at E ¼ 0 for T ¼ 0 is replaced by the “short” action evaluated at the zero-point energy "X0 =2, we can use the approximation Ak . X0 =2p for the longitudinal component. The perpendicular component is treated in the adiabatic approximation, which yields A? . 1 if UC ðxÞ is replaced by its vibrationally adiabatic counterpart. Using these approximations, we obtain AAIM ðTÞ . X0 =2p;
UCeff ðxÞ ¼ U0;VA ½1 ðx=DxÞ2 2
(29.26)
where the effective one-dimensional potential retains the form (29.22) but includes vibrationally-adiabatic correction over all modes. To obtain an expression for the multidimensional instanton action, we generalize [29] the analytical solutions obtained [21, 31] for two- and three-dimensional Hamiltonians in the form ðLFÞ
SI ðTÞ ¼
X S0I ðTÞ þa da ðTÞ PðLFÞ 1 þ s ds ðTÞ a
(29.27)
where S0I ðTÞ is the corresponding instanton action for the one-dimensional Hamiltonian H0 ¼ 12 meff ðxÞx_ 2 þ UCeff ðxÞ. The da -terms of the form [3, 19] da ðTÞ ¼
ð2Ca DxÞ2 "xa tanh x3a 4kB T
(29.28)
lead to a Franck–Condon factor arising from the reorganization of antisymmetric LF modes, which act similarly to a thermal heat bath. Symmetric LF modes, represented by ds terms of the form [3, 19]
907
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29 Multiple Proton Transfer: From Stepwise to Concerted
ds ðTÞ ¼
X0 Cs Dx2 2 "xs coth xs 2U0 2kB T
(29.29)
effectively reduce the tunneling distance and thus enhance tunneling; the factor a < 1 in Eq. (29.27) is the square of this reduced distance (in dimensionless units) [29]. All parameters needed to generate the Hamiltonian (29.20) are obtained from the standard electronic structure and vibrational force field output of conventional quantum chemistry programs. If UC ðxÞ is approximated by a quartic potential of the form (29.22), these calculations need to be carried out only for the stationary configurations along the reaction path. The resulting output is fed directly as input into the DOIT program [30] to calculate the instanton action SI ðTÞ from Eqs. (29.27–29.29). This is a very efficient procedure since it does not require explicit knowledge of the instanton path. Once the instanton action is calculated, evaluation of rate constants and tunneling splittings is straightforward. For T £ T*, where T* ~ x*=2p, the total transfer rate constant is the sum of the tunneling and over-barrier rate constants kðTÞ ¼ ktun ðTÞ þ kTST ðTÞ;
ktun ðTÞ . kAIM ðTÞ ¼ ðX0 =2pÞeSI ðTÞ
(29.30)
where the over-barrier rate constant kTST ðTÞ, given by Eq. (29.16), and X0 is the effective frequency of the tunneling mode in the reactant state. For T ‡ 2T*, we ignore the tunneling contribution and in the intermediate temperature range we interpolate. The zero-point tunneling splitting is related to the low-temperature limit of the rate constant by D0 ¼ ð"X0 =pÞeSI ð0Þ=2
(29.31)
AIM can also be used to calculate tunneling splittings of vibrationally excited levels [3, 6]. This approach, as implemented in the computer program DOIT [19, 30], has been applied to a variety of tunneling potentials with a single imaginary frequency. It needs generalization for tunneling through barriers with more than one imaginary frequency or more than one maximum. Such a generalization is presented in the next section.
29.4 Tunneling Dynamics for Two Reaction Coordinates
Because we are dealing with double proton transfer, we need a more general Hamiltonian than Eq. (29.20). Following the approach introduced in the preceding section, we can construct such a Hamiltonian as the sum of two local Hamiltonians describing the transfer of each of the protons together with a proton– proton coupling:
29.4 Tunneling Dynamics for Two Reaction Coordinates
Hðx1 ; x2 Þ ¼ H1 ðx1 Þ þ H2 ðx2 Þ þ Kðx1 ; x2 Þ
(29.32)
where H1 ðx1 Þ and H2 ðx2 Þ, represent Hamiltonians of the form (29.20) with indices 1 and 2, respectively, added to the couplings Ca ; Cs ; and Dj , and Kðx1 ; x2 Þ represents the the proton–proton correlation, i.e. the coupling between the proton transfer modes x1 and x2 . The form of the coupling is discussed in Section 29.2. In practice, we use normal coordinates xp;m obtained by diagonalizing the total Hamiltonian Hðxp ; xm Þ. In the limiting cases where the resulting potential is governed by a single transition state, we can obtain the transfer rate constant in the same way as for single proton transfer. Thus for concerted double proton transfer Eqs. (29.30, 29.31) can be used directly to obtain the overall rate constant kðTÞ and/or the tunneling splitting. Similarly, it can be used to obtain the rate constant for a single step in a stepwise process if the temperature is high enough to make this process dominant; the total rate constant is obtained by combining the steps according to standard kinetic procedures. However, we need a more general approach when there is more than one reaction coordinate. This happens for weak and intermediate proton–proton coupling, when apart form the saddle point of second order along xp , the transfer potential has additional saddle point(s). For weak coupling, these are the two transition states that separate the stable intermediate from the global minima. At temperatures high enough to make the intermediate accessible, such a potential will give rise to thermally activated stepwise transfer via this intermediate. However, there will be additional contributions from tunneling transfer, and at low temperatures these contributions will become dominant. This may be transfer along the coordinate for synchronous transfer xp through a barrier of energy Uðxp ; xm Þ ¼ Uð0; 0Þ ¼ 2U0 ð1 þ GÞ2, but we should also consider the possibility of transfer along a longer two-dimensional pathway through the transition state whose barrier is lower by U0 =2 £ U0 ð1 2G2 Þ £ U0. Such a two-dimensional pathway will also be possible in the intermediate coupling region; then the stable intermediate will be replaced by a saddle point, lower by 0 £ 2U0 ð1 GÞ2 £ 2U0 than the maximum, thus eliminating the stepwise mechanism, but retaining tunneling through different paths. Only when the coupling becomes strong, so that these saddle points disappear and the second-order saddle point in the center turns into a first-order saddle point, does this ambiguity disappear, leaving synchronous tunneling as the only viable transfer mechanism, at least for the model of Section 29.2. In principle, the asynchronous mechanism may still play a role through coupling with skeletal modes that increase the tunneling distance. For practical reasons such modes are not included in the model; their effect on the relation between the two transfer mechanism deserves further study. For the time being we ignore these modes and use a Hamiltonian based on the potential (29.11) 1 2 2 4 Hðxm ; xp Þ ¼ T þ U ¼ ðx_ p2 þ x_ m Þ þ ðxp2 n2p Þ2 þ 6xm ðxp2 n2m Þ þ xm : 2
(29.33)
909
910
29 Multiple Proton Transfer: From Stepwise to Concerted
The instanton equations (29.18), which take the form dSI ¼ 0; dxp
dSI ¼0 dxm
(29.34)
are normally written as “equations of motion” in imaginary time in the inverted potential U ! U: x€p ¼
¶U ; ¶xp
x€m ¼
¶U ¶xm
(29.35)
to be solved with periodic boundary conditions xp;m ðbÞ ¼ xp;m ð0Þ. This leads to equations x€p ¼
¶U1D 2 þ 12xp xm ; ¶xp
2 x€m ¼ 12xm ðxp2 n2m þ xm =3Þ
(29.36)
where U1D is the one-dimensional (1D) double-minimum potential along the coordinate of synchronous motion, here represented by a quartic potential ðxp2 n2p Þ2 . The potential in Eq. (29.33) always allows such a solution in the form of a 1D instanton, since for xm ” 0, Eqs. (29.36) reduce to x€p ¼ ¶U1D =¶xp . Under certain conditions this 1D instanton becomes unstable, so that two-dimensional (2D) solutions of Eqs. (29.36) are required. Such solutions were obtained by Benderskii and coworkers [32–37] for a model surface of type (b) in Fig. 29.3. Here we are interested in the broader issue of establishing the dynamics features common to all three types of surfaces in Fig. 29.3, in order to relate the labels “stepwise” and “concerted” to the potential-energy surfaces obtained by quantum-chemical calculations for realistic systems. Solutions involving both coordinates exist in the weak and intermediate coupling regions as discussed in Section 29.2; specifically they exist if n2m > 0, i.e. G < 1. These solutions correspond to paths of lower energy but greater length than the 1D instanton path. First we consider the weak-coupling limit G < 1=2, where there is a stable intermediate. The high-temperature case where this intermediate is thermally accessible and supports stepwise transfer has been discussed in Section 29.2. Here we consider the low-temperature case where tunneling prevails and focus on the zero temperature limit for simplicity. To illustrate the interplay between barrier height and path length, we choose among the many possible 2D trajectories the one with lowest energy, i.e. the minimum barrier path (MBP). From the expression for Uðxp ; xm Þ in Eq. (29.33) and the extremum condition ¶Uðxp ; xm Þ=¶xm ¼ 0 in Eq. (29.12), it follows that the MBP is a parabola of the form 2 xm ¼ 3ðn2m xp2 Þ
(29.37)
depicted in Fig. 29.4. It starts on the xp axis at the “bifurcation point” jxp j ¼ nm and passes through the transition state (4) and the intermediate state (3), located,
29.4 Tunneling Dynamics for Two Reaction Coordinates
Figure 29.4 Competing tunneling paths on the two-dimensional surface of Fig. 29.3(a): the one-dimensional instanton (nm ; nm ) along xp , illustrated by a dashed line and one of a family of two-dimensional paths, here arbitrarily represented by the minimum barrier path (MBP), illustrated by a solid line. The two pathways have parts from MIN to –nm (not illustrated) in common.
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi respectively, at xp ¼ 1 2G=2; xm ¼ 1 þ 2G=2 and xp ¼ 0; xm ¼ 1 G, all characteristic points being indentified in Table 29.1. The tunneling probability at T ¼ 0 is proportional to exp½SI ð0Þ; to compare the contributions of the 1D and 2D paths to this probability, we calculate the respective actions after their bifurcation. Since at T ¼ 0 the energy E ¼ 0 is an integral of motion, the corresponding actions are given by [39, 40] Z S1D ðE ¼ 0Þ ¼ C
dxp
0
Z S2D ðE ¼ 0Þ ¼ C
nm
0
nm
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi U1D ðxp Þ;
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dxp UMBP ðxp Þmeff ðxp Þ
(29.38)
where the coordinates are in units r=2, the energies pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi in units 2U0 , and C is a constant in units ", dimensioned as C ¼ 4r 2U0 mH , mH being the hydrogen mass. For U1D ¼ ðxp2 n2p Þ2 the action along the 1D instanton is easily evaluated: S1D ðE ¼ 0Þ ¼ Cnm ðn2p n2m =3Þ
(29.39)
UMBP ðxp Þ is obtained by substituting Eq. (29.37) into the potential of Eq. (29.33):
911
912
29 Multiple Proton Transfer: From Stepwise to Concerted
UMBP ðxp Þ ¼ ðxp2 n2p Þ2 9ðxp2 n2m Þð2xp2 þ 2n2m 1Þ
(29.40)
The contribution of the xm coordinate is formally included as an effective mass meff ¼ 1 þ Dmðxp Þ, where the extra term Dmðxp Þ ¼
3xp2 n2m xp2
(29.41)
is due to the fact that xm from Eq. (29.37) modifies x_ p2 so as to yield a new term 2 . The resulting 2D action requires numerical evaluation. Here proportional to x_ m we limit ourselves to an analytical estimate based on the near-constancy of the potential along the MBP between the bifurcation point where U ¼ (4=9)(1 þ 2G)2 and the transition state where U ¼ ð1=2Þð1 þ 2GÞ2 (in units 2U0 ). We therefore divide the relevant section of the parabola (29.37) into two parts, each of which we approximate by a straight line. To the section from the bifurcation point jnm j to the transition state (4), we assign a constant energy ð1=2Þð1 þ 2GÞ2, and to that from (4) to the intermediate state (3), we assign an energy equal to the average of the energies of (3) and (4). Instead of integrating S2D along xp with an effective mass, we integrate along the MBP coordinate s; the result is Z
ffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð4Þ ð4Þ ds UMBP ðsÞ > f½xp nm 2 þ ðxm Þ2 gU ð4Þ MBP ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q ð3Þ ð4Þ ð4Þ þ f½xm xm 2 þ ðxp Þ2 g½U ð3Þ þ U ð4Þ =2
S2D ð0Þ ¼ C
(29.42)
where the coordinates and energies of the extrema (3) and (4), expressed in the coupling coupling constant G, are listed in Table 29.1. This allows a direct comparion of the mechanisms represented by Eqs. (29.39) and (29.42). As illustrated in Fig. 29.5, for the whole range of G values from 0 to 1, S2D ð0Þ is found to be substantially larger than S1D ð0Þ. In view of the fact that for relevant parameter values the constant C in Eq. (29.38) is at least 10, this implies that the contribution of the two-dimensional concerted but asynchronous mechanism to the transfer is a negligible fraction of that of the one-dimensional synchronous mechanism. The fact, implied by Eq. (29.42), that the calculated value of S2D ð0Þ is smaller than the actual value because of the linearization of the MBP, further strengthens this argument. In addition, it receives support from the hitherto neglected effect of promoting vibrations on the two mechanisms. In the presence of hydrogen bonding, the transition state for synchronous transfer will give rise to formation of two symmetric hydrogen bonds, leading to strong contraction, an effect that will be weaker for asynchronous transfer. These results single out the one-dimensional synchronous mechanism as dominant at low temperatures for model potential (29.11), regardless of the strength of the proton–proton correlation. It follows then that for systems with a stable intermediate the critical temperature where the mechanism changes from concerted to stepwise can be estimated by comparing the rate constant for synchronous dou-
29.4 Tunneling Dynamics for Two Reaction Coordinates
Figure 29.5 Instanton actions at T ¼ 0 along the one-dimensional instanton (nm ; nm ) (S1D ) and the MBP (S2D ) (solid lines, in units C), and their relation (dashed line) as function of the correlation parameter G. The vertical line divides the regions of weak (G < 1=2) and intermediate (1=2 < G < 1) coupling corresponding to surfaces (a) and (b) in Fig. 29.3, respectively.
ble proton tunneling, k2 ðTÞ, with twice that for the single proton step, k1 ðTÞexpðEi =kB TÞ, where Ei ð¼ 8GU0 Þ is the energy of the intermediate. A more rigorous analysis of the temperature dependence in the region of the critical temperature should involve 2D instantons. We note, however, that no such solutions have been obtained to date for surfaces of the type of Fig. 29.3(a). The model potential (29.11) can reproduce all the types of surfaces found to date and yields correct relations between the frequencies along the collective coordinates. Therefore the basic conclusions for the dynamics obtained above should remain valid. Since the potential is defined by three parameters and is, admittedly, simplified, the quantitative relations need further testing. As noted earlier, in practice the potential energy surface and the vibrational force field for any system of interest will be calculated quantum-chemically, which should lead to more accurate dynamics. In later sections, we discuss specific examples where this issue has been raised such as porphine, naphthazarin and dimeric formic acid, which together cover the range from weak via intermediate to strong coupling.
913
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29 Multiple Proton Transfer: From Stepwise to Concerted
29.5 Isotope Effects
Rate constants and tunneling splittings associated with proton transfer are sensitive to deuterium (and tritium) isotope effects resulting from the large difference in mass between the isotopes. Deuterium (and tritium) substitution thus provides a tool for studying these processes experimentally. The corresponding kinetic isotope effect (KIE) for a single proton transfer reaction is defined by gH=D ¼ kH ðTÞ=kD ðTÞ
(29.43)
An analogous expression applies to tritium substitution. If the reaction is obstructed by a potential-energy barrier, two modes of transfer may be distinguished, “classical” transfer over the barrier and quantum-mechanical tunneling through the barrier, the latter mode resulting from the small mass of the proton and its isotopes. For over-barrier transfer the rate constants can be obtained from standard TST leading to Eq. (29.16). To calculate the corresponding KIE, we can usually neglect rotational and translational partition functions and consider only vibrational partition functions of the form [22] Q¼
Y j
1 2 sinh ð"xj =2kB TÞ
(29.44)
where the product runs over all normal modes except the reaction coordinate for the transition state. If "xj >> kB T for all modes affected by the isotopic substitution, the KIE can be obtained from the familiar simplified formula kTST ðTÞ ¼ ðkB T=hÞeðUA DUÞ=kB T
(29.45)
where UA is the adiabatic barrier height and DU the correction for zero-point energy changes between the reactant and the transition states. Thus the corresponding KIE will be governed by the effect of isotopic substitution on the difference in zero-point energy between the initial state and the transition state. If the effect of this substitution on modes other than the reaction coordinate is neglected, the KIE for deuterium substitution of the transfering hydrogen, expressed in logarithmic form, reduces to H=D ln gTST
pffiffiffiffiffiffiffiffi "ðxH xD Þ "xH ð1 1=2Þ . . 2kB T 2kB T
(29.46)
where x ispthe frequency of the transfer mode in the initial well and xH : xD . pffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffi ffi H D 1=m : 1=m if we neglect the small difference between the atomic and the reduced mass ratio. Together with the same calculation for the tritium isotope effect, we obtain the well-known Swain–Schaad relation for through-barrier transfer [20, 38]
29.5 Isotope Effects H=T
ln gTST
H=D
ln gTST
pffiffiffiffiffiffiffiffi 1=3 pffiffiffiffiffiffiffiffi ¼ 1:44 . 1 1=2 1
(29.47)
or its alternative ln gH=T = ln gD=T ¼ 3:26. In practice, these Swain–Schaad exponents are usually calculated from the partition functions (29.44) rather than from approximate relations of the type (29.45, 29.46) but the result was found to be remarkably close to the approximation (29.47) [21]. For tunneling we use the AIM formalism developed in the preceding section. Combining Eqs. (29.19) and (29.27), we have for single proton transfer "
X S0I ðTÞ kAIM ðTÞ ¼ ðX0 =2pÞ exp da ðTÞ þa PðLFÞ 1 þ s ds ðTÞ a ðLFÞ
# (29.48)
To calculate the KIE, we neglect the weak isotope dependence of the da term and write the ds term in the simplified forms dsH;D . This yields pffiffiffi 0;H D H gH=D . 2 exp½S0;D I =ð1 þ ds Þ SI =ð1 þ ds Þ
(29.49)
H D H where normally dD s ‡ ds . If the coupling is weak or moderate and ds » ds ¼ ds , we can write 1=ð1 þ ds Þ . 1 ds , so that H=D
gH=D . g0
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi D H exp½ds S0;H I ð m =m 1Þ
(29.50)
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffi H=D 0;H D H where g0 ¼ 2 exp½SI0;D S0;H I . exp½SI ð m =m 1Þ represents the KIE in the absence of coupling. This confirms that coupling to promoting modes, which increases the rate constants, reduces the KIE, an effect that is always present and depends only on the frequency of the promoting mode and the strength of its coupling to the tunneling mode. In the absence of coupling, i.e. for one-dimensional tunneling, we obtain [21] instead of Eq. (29.47) H=T
ln gtun
H=D
ln gtun
pffiffiffi 31 . pffiffiffi ¼ 1:77 21
(29.51)
It follows that tunneling increases the Swain–Schaad exponent, contrary to what is usually assumed [38]. This increase is mitigated by coupling to promoting modes. It has been shown [21], that larger and larger contributions of these modes to the point where they are effectively taking over proton transfer leads to a limiting value of 1.44 for the exponent, i.e. the value originally derived for over-barrier transfer as given by Eq. (29.47). This means that we can combine Eqs. (29.47) and (29.51) by introducing a parameter rH that varies from 0, when over-barrier transfer dominates, to 1 for unassisted tunneling:
915
916
29 Multiple Proton Transfer: From Stepwise to Concerted
pffiffiffi pffiffiffi 2=ð 2 1Þ rH 3:414 rH ln gH=T . pffiffiffi pffiffiffi ¼ ln gH=D 3=ð 3 1Þ rH 2:366 rH
(29.52)
The resulting generalized Swain–Schaad exponent varies from 1.44 for rH ¼ 0 to 1.77 for rH ¼ 1. A more realistic upper limit that takes into account coupling to promoting modes will be 1.65 corresponding to rH ~ 0:75. Such generalized Swain–Schaad exponents can be used to estimate tunneling contributions to proton transfer [21]. The conclusion that tunneling increases the Swain–Schaad exponent runs opposite to that reported by Saunders [38], which was based on the (valid) argument that the tunneling contribution to the probability of transfer through a static onedimensional barrier decreases with the mass of the transferring particle. However, the model used to apply tunneling corrections to the rate constant for proton transfer in complex systems has serious deficiencies. It ignores the fact that in the one-dimensional model in which the reaction coordinate represents a hydrogenic mode, the energy spectrum is not a continuum starting at zero, but consists of discrete levels of which only one, namely the lowest at an energy "x0 =2 is significantly populated at most temperatures of interest. If treated quantum-mechanically such a model leads to the Swain–Schaad exponent 1.77 shown in Eq. (29.51) rather than a value < 1:44. The continuum of energy levels implicit in the model presupposes the presence of other degrees of freedom. However, these will interact with the reaction coordinate, implying that the reaction path is not the same for different hydrogen isotopes; therefore applying the tunneling corrections to an isotope-independent barrier, as done in the model, is not appropriate. Explicit introduction of additional modes, as in Eq. (29.52) or, more elaborately, in our earlier treatment [21] and that of Tautermann et al. [42], both applying multidimensional tunneling dynamics to high-level potential energy surfaces, yields exponents in the range 1:44 £ e1 £ 1:77. We therefore conclude that Saunders’ conclusion is an artifact resulting from the model used. To interpret rH in physical terms, we note that, for a barrier formed by the crossing of two equivalent harmonic potentials, the instanton action can be approximated by [21] SI ðTÞ ¼
2a20
r02 þ A2s ðTÞ
(29.53)
where r0 is the equilibrium transfer distance, a0 ¼ ð"=lH xH Þ1=4 is the zero-point amplitude of the proton, and As ðTÞ is the thermal amplitude of the promoting vibration(s). In this approximation rH can be defined as rH ¼ 2a20 =½2a20 þ A2s ðTÞ; a more accurate definition, based on the use of a quartic potential of the form (29.22) for the proton, is rH ¼
4a20
4a20 þ A2s ðTÞ
(29.54)
29.5 Isotope Effects
Thus rH measures the fraction of the transfer trajectory traveled by the protons rather than the atoms of the promoting modes. This fraction decreases with increasing temperature because excitation of the promoting mode increases the part traveled by them. At high temperature, we must include the temperature dependence of a0 , which will increase the over-barrier contribution to the transfer. If tunneling is strongly dominant in the temperature region of interest, the first of these effects should dominate, implying that the temperature dependence of rH should be proportional to that of the amplitude of the promoting mode(s): A20 ðTÞ ¼ A20 coth
"xs 2kB T
(29.55)
wherepxffiffiffiffiffiffiffiffiffiffiffiffiffiffi s is the frequency of the promoting mode with effective mass ls and A20 ¼ "=ls xs is the zero-point amplitude. The generalized Swain–Schaad exponent (29.52) is directly applicable to most two-proton transfers; obviously, this holds true for each step of a stepwise process, but it also applies to concerted processes in which the two proton isotopes are the same, since the effective mass and harmonic frequency of the relevant symmetric or antisymmetric XH-stretch modes are essentially the same as those of their onedimensional components. However, if the two proton isotopes are different, this argument no longer suffices because the normal mode that represents the frequency and effective mass of the transfer coordinate in the transition state correlates with two distinct normal modes in the equilibrium configuration. Hence there is no unambiguous Swain–Schaad type exponent relating HD to HH and DD transfer. However, we can relate the rate for stepwise HD transfer to the rates of HH and DD transfer through standard kinetics. In the case of a symmetric potential, we have kHD ¼ kDH and thus [2] gHH=DD ¼ gH=D ;
1 gHH=HD ¼ ð1 þ gH=D Þ; 2
gHD=DD ¼
2gH=D 1 þ gH=D
(29.56)
It follows that for gH=D >> 1 the Arrhenius curve for HD transfer will be much closer to the DD than to the HH curve. No simple rules can be given if the protons are not equivalent and face different barriers. In that case the relation between the KIEs depends on the relation between the rate of the proton step across the higher barrier and the deuteron step across the lower barrier [2]. To relate the rate of concerted HD transfer to the rates of HH and DD transfer, we use [2] a generalization of Eq. (29.49) ln gAB=CD »
S0;CD S0;AB I I 1 þ ds
(29.57)
where the capital superscripts are either H or D. Using the approximate but quite pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi is the action corresponding robust relation SI0;AB . S0I mA þ mB , where S0I ¼ S0;H I to a single-proton transfer and mH=D ¼ 1=2, one obtains
917
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29 Multiple Proton Transfer: From Stepwise to Concerted
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S0 ln gAB=CD » ð mC þ mD mA þ mB Þ I 1 þ ds
(29.58)
where the expression in parenthesis equals 0.32 for HH/HD, 0.27 for HD/DD and thus 0.59 for HH/DD. It follows that in the Arrhenius plot the HD curve is roughly halfway between the HH and DD curves but slightly closer to the latter. It follows also that for large KIEs and symmetric potentials, the spacing of the Arrhenius curves for HH, HD, and DD transfer can be an indication whether the transfer is concerted or stepwise, but that for small KIEs and asymmetric potentials the results are likely to be ambiguous.
29.6 Dimeric Formic Acid and Related Dimers
We begin our study of actual systems with an analysis of observed and calculated tunneling splittings in dimeric formic acid and related dimers. Dimeric formic acid, the simplest carboxylic acid dimer, is depicted in Fig. 29.6, top. It has been studied extensively, but only recently did Madeja and Havenith [4] succeed in observing level splittings characteristic of double proton tunneling. The observation was made by high-resolution infrared spectroscopy in a cold beam, the transition being between the zero-point level and a vibrationally excited level of the electronic ground state. The observed splitting of about 400 MHz (0.013 cm1 ) could be divided into two components. The authors tentatively assigned the larger component to the vibrationally excited level corresponding to a CO-stretch fundamental, but our calculations [6] revise this assignment. Based on symmetry considerations and backed by detailed calculations, we adopt the alternative assignment of Madeja and Havenith, leading to a zero-point splitting of 375 MHz and a splitting of 94 MHz for the CO-stretch fundamental. However, the precise magnitude of the splitting is immaterial in the following analysis. The observation of a tunneling splitting implies concerted although not necessarily synchronous transfer; the alternative possibility of transfer to an intermediate state with the same energy as the equilibrium state, corresponding to the complete absence of proton–proton correlation, can be excluded on elementary grounds. High-level calculations lead to a single transition state with an imaginary frequency of about half that of the symmetric CH-stretch vibration in the equilibrium configuration, consistent with synchronous transfer. The structure of the equilibrium configuration and transition state is illustrated in Fig. 29.6 (top). The two hydrogen bonds are almost linear; although relatively weak in the equilibrium configuration, they are strong and short in the transition state, as expected for symmetric hydrogen bonds. As a result, the transition state has a lower energy than the state corresponding to single proton transfer, which would correspond to a complex between the anion and the cation of formic acid. Earlier, Shida et al. [41] concluded, on the basis of MCSCF calculations, that in addition to the synchronous path, an asynchronous pathway appeared if the inter-
29.6 Dimeric Formic Acid and Related Dimers
Figure 29.6 Schematic representation of the synchronous double proton transfer process in the formic acid dimer (top) and benzoic acid dimer (bottom).
monomer distance was kept fixed at appropriate large values. In their calculation this bifurcation occurred at a distance slightly below the equilibrium separation. The opening of the asynchronous path reduced the calculated tunneling splitting by about 20%. A rough indication of the proton positions at the two equivalent transition states for asynchronous transfer is that if one proton had not moved significantly, the other would have overshot the midpoint by about 0.12 . Equation (29.15) indicates that such an asynchronous pathway will always appear for sufficiently large transfer distances in systems dominated by synchronous transfer. Shida et al. [41] have pointed out that such large distances may be reached during the O O vibration that modulates the tunneling distance. To probe this effect, we have repeated their calculations at the B3LYP/6-31+G(d) level, which yields a more accurate value for the tunneling splitting and compares well with high-level methods [7, 42]. It leads to a C C separation of 3.85 in the equilibrium configuration, which shrinks to 3.57 in the transition state, whose imaginary symmetric OH-stretch frequency amounts to 1322i cm1 and whose real antisymmetric OH-stretch frequency amounts to 1197 cm1 . If the transition state
919
920
29 Multiple Proton Transfer: From Stepwise to Concerted
calculation is repeated with the C C separation constrained, bifurcation characterized by a zero antisymmetric OH-stretch frequency appears at a separation of 3.79 , marginally smaller than the equilibrium separation, a result comparable to that of Shida et al. This effect, viz. weakening the coupling by restraining the optimization of the transition state, is represented by Eqs. (29.4, 29.5) in Section 29.2. In the present case it is brought about by coupling with promoting modes. However, at our level of calculation, the energy of the bifurcation point is found to be about 5.6 kcal mol–1 higher than that of the optimized transition state, so that the asynchronous path will have a negligible effect on the transfer dynamics, including the tunneling splitting. It seems likely that this conclusion, which is based on a method that includes electron correlation, and contradicts the results of Shida et al., based on a method without such correlation, can be generalized to all dimers held together by hydrogen bonding, but it may not apply to systems where the motion of the groups carrying the mobile protons is constrained. The methods used to calculate tunneling splittings have been applied also to the calculation of transfer rate constants as a function of temperature in the formic acid dimer and its DD and TT isotopomers in order to test the validity of the Swain–Schaad relation between HH, DD, and TT transfer [7, 42]. As expected, the conventional relation (29.47), derived for over-barrier transfer is inadequate for this system, but the generalized relation (29.52) yields good agreement over the entire temperature range for which calculations are available. The tunneling parameter rH is found to decrease with increasing temperature, in response to the increasing amplitude of the promoting mode and the increasing contribution of over-barrier transfer. It is instructive to compare the results for dimeric formic acid with calculations on structural analogs in which the O atoms are gradually replaced by NH groups. This changes the strength of the hydrogen bonds in the order OH–N > OH–O > NH–O > NH–N. The calculated equilibrium structures and transition states for four analogs of the formic acid dimer, calculated at the DFT-B3LYP/6-31G(d,p) level [43–46], are illustrated in Fig. 29.7. Comparison with Fig. 29.6 shows that the symmetric dimer, namely dimeric formamidine with a D2h transition state [43], shows the same pattern as the formic acid dimer, i.e. a transition state corresponding to synchronous transfer with tightened hydrogen bonding, despite the weakened hydrogen bonds. The higher barrier and longer transfer distance indicate that the rate of transfer will be much lower and the level splitting much smaller than in the formic acid dimer. Simultaneously, the proton–proton coupling parameter G is expected to be smaller than that of dimeric formic acid since the dipolar couplings will be weaker. However, the calculated potential energy surface indicates that it will still be strong enough to be in the strong coupling regime. The other dimers in Fig. 29.7 show asymmetry. If the proton transfer potential is asymmetric, there will be no synchronous transfer and at most accidental level splittings. In the formamide dimer [44] the two hydrogen bonds are the same but the donor and acceptor groups are different. The available calculations indicate that the structure of the equilibrium configuration is intermediate between the equilibrium configurations of dimeric formic acid and dimeric formamidine, as
29.6 Dimeric Formic Acid and Related Dimers
Figure 29.7 Stationary points representing the reactant (R), transition state (TS), product (P), and (where applicable) intermediate (Int) related to double proton transfer in analogs of the formic acid dimer: (a) formamidine dimer [43]; (b) formamide dimer [44]; (c) formamidine–formamide complex [45] and (d) formic acid–formamidine complex [46].
expected. However, the transition state belongs to the C2h rather than the D2h point group and the transfer is endothermic by about 10 kcal mol–1. No stable intermediate has been found; estimates of the barrier height vary widely. Concerted but asynchronous transfer is expected to be the dominant mechanism. Stepwise transfer is more likely to be favored when the two hydrogen bonds are different. This is the case in the mixed formamide–formamidine dimer [45], which has only Cs symmetry. In one of the hydrogen bonds the donor and acceptor groups are the same and in the other they are different. Calculations at the HF level yield a marginally stable zwitterionic intermediate; it disappears, however, at higher levels, where a single transition state appears with a barrier height of about 13 kcal mol–1 and an endothermicity that is smaller by only 1–2 kcal mol–1. In particular, it is found that the proton in the NH N hydrogen bond moves first, leading to a shortening of the NH O hydrogen bond, which allows the second proton to move. The reverse order is not observed, in keeping with the smaller proton affinity of formamide relative to formamidine. The probable mechanism for double proton transfer in this mixed dimer is thus concerted but highly asynchronous transfer along a single pathway. This mechanism may readily turn into stepwise transfer in a dielectric medium that can stabilize the intermediate zwitterion.
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29 Multiple Proton Transfer: From Stepwise to Concerted
An intermediate zwitterionic structure that corresponds to a minimum in the potential energy in the gas phase is found for the formic acid–formamidine complex [46], as illustrated in Fig. 29.7. Extrapolating back from this dimer via the formamide–formamidine dimer to the formamidine dimer, we observe that the replacement N!O in one monomer reduces the synchronous transfer to highly asynchronous transfer, so that it may be expected that a second replacement in the same molecule will lead to stepwise transfer. High-level calculations have partly confirmed this expectation. Although the equilibrium structure of this dimer has Cs symmetry, the double proton transfer potential is symmetric since the two hydrogen bonds are complementary, i.e. they turn into each other by proton transfer. Putting the two protons in the center of the hydrogen bonds, in an effort to construct a transition state for synchronous transfer of C2v symmetry, gives rise to a second-order saddle point. Moving along the symmetric ON-stretch coordinate leads to the equilibrium configuration and moving along the antisymmetric coordinate to the “stable” zwitterionic intermediate of C2v symmetry. The intermediate is very shallow, however, probably too shallow to support the dimer during a vibrational period. Hence this system, which deserves further investigation, seems to be on the border between weak and intermediate coupling. With one exception, these results are based solely on quantum-chemical calculations of the potential energy surface. Theoretical evaluation of the transfer dynamics has been attempted only for the formic acid dimer, for which two general level splittings have been observed and assigned to synchronous double proton tunneling in the ground state and a vibrational excited state, respectively.
29.7 Other Dimeric Systems
Experimental data relevant to double proton transfer are available for several other dimeric systems. Remmers et al. [5], who investigated the high-resolution ultraviolet spectrum of dimeric benzoic acid, shown in Fig. 29.6 (bottom), observed a splitting of 1107 MHz, which they assigned to double proton transfer in the ground state and/or the excited state. They left open the question of the relative contributions of the two states to the splitting. According to our analysis [7], it should be assigned to splitting of the zero-point level of the ground state rather than of the electronically excited state, the main reason being that the excitation is localized on one of the two monomers. The corresponding deformation of the symmetry of the dimer will tend to slow down proton transfer. This is supported by the observation that hydrogen bonding is weakened in the excited state. The larger splitting with respect to the formic acid dimer does not contradict this; on the contrary, it is in good agreement with the calculated hydrogen bond strengths in the two dimers. The ground-state assignment is supported by detailed calculations [7], which show that the coupling pattern closely resembles that of the formic acid dimer and leads to the conclusion that the transfer occurs by synchronous tunneling.
29.7 Other Dimeric Systems
Additional kinetic data are available for benzoic crystals [47, 48], in which the benzoic acid molecules are stacked as dimers. Since crystal forces reduce the intermolecular separation, the coupling causing the transfer is stronger in the crystal than in the gas-phase dimer. However, in the crystal no splitting can be observed since the protons move in an asymmetric potential. The asymmetry, which is much larger than this coupling, can be reduced at particular sites by doping the crystal with thioindigo; for dimers adjacent to the dopant the asymmetry assumes a value small enough to allow indirect observation of low-temperature tunneling splitting; the measured value extrapolates to about 8 GHz in the limit of zero asymmetry. The implied large value of the coupling has made it possible to measure the rate of proton transfer in neat crystals down to very low temperatures by NMR relaxometry. The observed low-temperature rate constant is in rough agreement with the extrapolated tunneling splitting, if the effect of doping on the adjacent dimer structure is taken into account [7]. These observations indicate that double proton transfer follows the same basic mechanism in the crystal as in the isolated dimer, although the asymmetry of the crystal potential will introduce a measure of asynchronicity in the tunneling. Recently these measurements were extended to crystals in which all or part of the benzoic acid molecules carry a mobile deuteron instead of a mobile proton. In this way it was possible to measure rate constants as a function of temperature not only for HH but also for HD and DD transfer [49–51]. The resulting Arrhenius plots, illustrated in Fig. 29.8,
Figure 29.8 Comparison of spin–lattice correlation rates measured by NMR relaxometry [51] with those calculated by AIM/DOIT [7] for solid benzoic acid isotopomers with mobile HH (top), HD (center), and DD (bottom) pairs. Measurements are depicted by symbols; the broken and dot-dash lines represent theoretical results for two limiting cases, the solid curve being their geometric mean [7].
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29 Multiple Proton Transfer: From Stepwise to Concerted
show strong curvature, the rate constants for all three isotopomers being constant below 20 K and showing classical activated behavior above 200 K, as expected for tunneling assisted by thermal excitation of promoting vibrations and, at higher temperatures, by over-barrier transfer. Correspondingly the ratio of DD/HH rate constants decreased from about 500 below 20 K to about 25 at room temperature. The HH, HD, and DD Arrhenius curves were evenly spaced, which, according to the analysis of Section 29.5, is consistent with concerted transfer. Observations analogous to those for carboxylic acid dimers have been reported for 2-pyridone2-hydroxypyridine (2PY2HP) [52, 53], illustrated in Fig. 29.9. This dimer, formed from two isomers, is asymmetric, but it has a symmetric double proton transfer potential since the transfer interchanges the isomers. In a collaborative effort, Pratt, Zwier, Leutwyler and their coworkers [52] measured and analyzed the high-resolution fluorescence-excitation spectrum of the S1 S0 origin and observed a level splitting of 527 MHz, which they assigned to double proton
Figure 29.9 Calculated structures of the equilibrium configuration and the transition state of the 2-pyridone 2-hydroxypyridine dimer in the ground state and the excited state [29]. Pertinent bond lengths are given in ; the numbers in parentheses refer to the equilibrium configuration of the excited state.
29.7 Other Dimeric Systems
transfer. Although the two protons are not equivalent, one being part of an OH O and the other of an N HN hydrogen bond, the observation of a splitting implies that the transfer is concerted. Evidently, it cannot be fully synchronous; however, the magnitude of the observed splitting, which is intermediate between the splittings observed for dimeric formic acid and dimeric benzoic acid, shows that this does not seriously interfere with the rate of transfer. The assignment leaves open the question whether the level splitting is mainly due to the ground state or the excited state. The conclusion that it is mainly due to the ground state [29] is based on arguments similar to those made for dimeric benzoic acid. The excitation is essentially localized on the 2PY component. That this tends to distort the dimer so as to trap the protons follows from the observation that hydrogen bonds are longer and thus weaker in the excited state than in the ground state. The lower symmetry of 2PY2HP compared to carboxylic acid dimers is reflected in the deuterium isotope effect on the tunneling splitting, since it implies that the splitting in 2PY-d1 2HP, where the isotopic substitutions is on N, will differ from that in 2PY2HP-d1 , where it is on O. This is confirmed by direct measurements, which give rise to splittings of £ 10 and 62 MHz, respectively, for these two isotopomers. This order of splittings is confirmed by high-level dynamics calculations, which yield splittings of 12 and 43 MHz, respectively [53]. It means that deuteration of the NH group in 2PY has a larger effect on the transfer dynamics than deuteration of the OH group in 2HP. This agrees with the notion that the NH N hydrogen bond is longer than the OH O hydrogen bond and thus makes a larger contribution to the transfer path and consequently to the KIE. On the basis of these arguments and calculations we propose that, as a general rule, the weaker link in a double proton transfer process can be recognized by its greater sensitivity to isotopic substitution. It is instructive to apply this rule to the dimer of 7-azaindole, illustrated in Fig. 29.10. In contrast to 2PY2HP, where the two monomers are different but the tunneling potential is symmetric, this dimer is formed from two identical monomers but exhibits an asymmetric tunneling potential, due to the different electronegativity of the two nitrogens in each monomer. The monomer exists in two tautomeric forms, depending on which nitrogen carries the hydrogen. The lower energy form in the ground state, i.e. the form with the NH group in the five-membered ring, becomes the higher-energy form in the excited state. By exciting the dimer in a cold beam and monitoring the fluorescence, one can follow the transformation of the higher-energy to the lower-energy tautomer in the excited state. In a careful study of HH, HD, and DD transfer, Sakota and Sekiya [54] showed convincingly that the transfer is concerted, contradicting earlier conclusions [55], and that HD transfer contains two components due to the fact that the coupling between the monomers is small (about 3.5 cm1 ) compared to the energy shift for NH!ND substitution (about 40 cm1 ), so that the excitation is effectively localized on one of the monomers in the mixed (i.e. d1 ) isotopomer, a situation similar to that encountered in dimeric benzoic acid and in 2PY2HP. Specifically, they found that H*D transfer is faster than HD* transfer, where the asterisk indicates the monomer on which the excitation is localized. By analogy to the 2PY2HP
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29 Multiple Proton Transfer: From Stepwise to Concerted
Figure 29.10 7-Azaindole and its dimer.
result, this implies that the NH* N hydrogen bond is weaker than the N HN bond in the higher-energy tautomer of the excited dimer. No theoretical study of the dynamics of these processes has been reported to date. The apparent prevalence of concerted transfer whenever there is hydrogen bonding, even if the two protons are inequivalent and/or replaced by a proton–deuteron pair, is striking. However, it has to be borne in mind that these are gas-phase experiments at low temperatures. The observed splittings do not exclude the possibility of a stable intermediate with an energy that makes it thermally inaccessible under these conditions. However, the conclusions of Section 29.4 as well as the available calculations for specific systems argue strongly against such a possibility.
29.8 Intramolecular Double Proton Transfer
Intramolecular proton transfer between keto and enol functions is well known. An example of intramolecular double proton transfer of this kind is observed in naphthazarin, illustrated in Fig. 29.2. Using an SCF approach, de la Vega et al. [15] calculated the corresponding two-dimensional potential energy surface. No stable intermediate was found, but moving from the second-order saddle point along the antisymmetric OH-stretch coordinate led to two first-order saddle points, from where motion along a path that involves both coordinates led back to the equilibrium configuration, as sketched in Fig. 29.3b. Although the authors considered this a stepwise process, it remains concerted although not synchronous. It involves a lower barrier than the synchronous process along the symmetric OH-stretch coordinate, but a longer pathway. To calculate the tunneling splitting, they approximated their potential analytically by a function with terms containing powers of xp;m of order four, including a biquadratic cross term, i.e. a term similar to the coupling term in our model potential (29.11). Both their analytical and our model potential depend on three parameters; in their case the distance between the minima, the energy of the maximum and the energy of the saddle point, found to be, respectively, 0.78 , 28.0 kcal mol–1 and 25.6 kcal mol–1. Using numerical diagonalization, the authors found the lowest vibrational states of this two-dimensional potential energy surface and evaluated the zero-point tunneling splitting. They found that the twodimensional pathway, representing asynchronous transfer along both xp and xm
29.8 Intramolecular Double Proton Transfer
contributed more to the splitting than the one-dimensional synchronous pathway along xp . This result contradicts our calculations based on model potential (29.11), which leads to a dominant contribution from the synchronous path. This difference can be traced back to the nature of the two potentials. Our potential (29.11) is derived from a model of two equivalent quartic potentials plus a coupling that is symmetric in the two local coordinates. If the potential of de la Vega et al. is transformed into local coordinates, it does not reduce to two equivalent potentials plus such a coupling. Hence it is not consistent with the symmetry of the system. As a result, it yields an inadequate force field in the equilibrium configuration, namely a frequency for the antisymmetric mode that is less than half that of the symmetric mode, instead of two frequencies of the same general magnitude, as appropriate in the present case where the localized coordinates x1;2 are weakly coupled. This renders their analytical potential inadequate for dynamics, and especially for evaluation of tunneling splittings, which depend crucially on the quality of the force field in the minimum. We note also that the use of adiabatic energies for the saddle points in the two-dimensional potential in Ref. [15] is incorrect; the crude-adiabatic energies corresponding to the “frozen” skeleton are the required parameters. As an example of double proton transfer in a molecule with little or no hydrogen bonding, we consider porphine [8–11], depicted in the insert of Fig. 29.11. In this molecule, belonging to the D2h point group, the two equivalent hydrogens in the inner ring are bound to two of the four equivalent nitrogens. In the reactant they are in one of the two trans positions, in the product they are in the other trans position. B3LYP/6-31G(p)-level calculations [11] indicate that the intermediate cis position has an energy that is higher by about 8.3 kcal mol–1, which can be reached via a transition state with an (adiabatic) energy of 16.7 kcal mol–1. The trans to trans (adiabatic) barrier for synchronous double proton transfer with an energy of 25.3 kcal mol–1 corresponds to a second-order saddle point. The angle between the NH bonds in the initial and final position is 90, which prevents effective hydrogen bonding. The structure of the molecule rules out deformations that reduce this angle significantly in the transition state. Hence the tightening of the hydrogen bonding in the transition states of the dimers discussed in Sections 29.6 and 29.7, which supports concerted transfer, is weak in porphine. Two sets of experimental data are available, one set measured by NMR spectroscopy in the range 200–300 K [8, 9] and another set measured by optical spectroscopy in the range 95–130 K [10]. Arrhenius plots of the data shown in Fig. 29.11 are slightly curved; at low temperature the slope approaches a constant value close to the calculated cis–trans energy difference of 8.3 kcal mol–1. The observation that double proton transfer remains thermally activated by roughly this amount down to low temperatures, immediately suggests that the process proceeds stepwise. The same conclusion follows from the observation that the HD Arrhenius curve is closer to the DD than the HH curve, in agreement with Eq. (29.56). Using the approach of Section 29.2, we can estimate the proton–proton coupling parameter G by associating the extrema of the calculated potential with those of the model potential. However, for this we require crude-adiabatic poten-
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29 Multiple Proton Transfer: From Stepwise to Concerted
Figure 29.11 Temperature dependence of the rate constant (in s1 ) of double proton transfer in porphine-d0 , -d1 , -d2 and -t2 evaluated for the stepwise mechanism. The symbols represent observed rate constants from Refs. [8–10] and the curves represent the results of a multidimensional AIM/DOIT calculation [11]. The insert shows the stepwise and concerted transfer mechanisms.
tials rather than the adiabatic potentials calculated quantum-chemically [11]. To obtain a rough order-of-magnitude estimate, we assume that the ratio of the crude-adiabatic barrier heights between the extrema (2) and (4) of Table 29.1 is smaller but of the order of that between the corresponding adiabatic barrier heights, and that the ratio of the crude-adiabatic to the adiabatic barrier heights of extremum (2) is about 3, as previously found for carboxylic acid dimers. Assuming further that the minimum (3) will not be much affected, we obtain from the energy ratio (3)/(2) the estimate G . 0:05, which roughly satisfies the ratio (4)/(2). This estimate clearly indicates weak coupling. Kinetic data are also available for porphine in which one or both inner protons are isotopically labeled [8–10]. The observed kinetic isotope effects are in good agreement with high-level dynamics calculations [11], which indicate stepwise transfer in the temperature regime where measurements are available. Although the kinetic data for HH, DD, and TT transfer do not cover a common range of temperatures, the availability of dynamics calculations that provide a good fit to the data allows extrapolations yielding sets of cis ! trans KIEs for a range of temperatures. As shown in Fig. 29.12, they lead to Swain–Schaad exponents in excellent agreement with Eq. (29.52) and show the gradual decrease with increasing temperature of the part of the transfer path located under the barrier.
29.8 Intramolecular Double Proton Transfer
Figure 29.12 Swain–Schaad-type exponents observed for porphine. The solid lines are derived from observed rate constants [8–10] extrapolated by high-level multidimensional dynamics calculations [11]. The broken lines are derived from multidimensional TST calculations without tunneling.
It is interesting to compare the results for porphine with those for the related molecule porphycene [12–14], depicted in Fig. 29.13. In porphycene the four nitrogen atoms form a rectangle with sides of about 2.65 and 2.84 calculated at the B3LYP/6-31G(d,p) level. The preferred proton exchange will be between the more closely spaced nitrogens. The longer NH bond (1.043 vs. 1.027 ) and the smaller N–H–N angle along the transfer path compared to porphine indicate substantial hydrogen bonding in porphycene. Hence one expects the double proton transfer to be considerably more rapid than in porphine. This is indeed observed; according to NMR measurements the transfer rate constant at 298 K in porphycene is larger by a factor of 3000. Since no low-temperature measurements are available and the observed activation energy in the range 228–355 K is about 6 kcal mol–1, it is not immediately clear whether the transfer is stepwise or concerted. The calculations [12, 14] indicate an energy difference between the cis and trans configurations of about 2.3 kcal mol–1, implying a weak proton–proton correlation. Attempts to fit the kinetic data to the calculated transfer potential have met with problems. The trans–cis barrier height of 4.7 kcal mol–1 is too low to fit the data. To obtain an acceptable fit, it is to be raised to about 11 kcal mol–1 with a cis
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29 Multiple Proton Transfer: From Stepwise to Concerted
Figure 29.13 Illustration of stepwise and concerted double-proton transfer in porphycene. Trans indicates the stable configuration, cis the intermediate corresponding to single proton transfer and SP(2) the saddle point of second order corresponding to concerted transfer.
energy of 3 kcal mol–1. If we assume concerted transfer, we can fit the data by a barrier corresponding to a second-order saddle point of about 14 kcal mol–1, whereas the calculated value is 6.6 kcal mol–1. These results suggest that porphycene is an intermediate case, where the mechanism combines aspects of stepwise transfer involving a very shallow intermediate with highly asynchronous concerted transfer. They also cast doubt on the ability of presently available DFT functionals to represent NH N hydrogen bonds.
29.8 Intramolecular Double Proton Transfer
Returning to systems without hydrogen bonding, we consider a group of molecules in which the hydrogen transfer occurs between carbon atoms, namely bridged ring compounds where the groups between which the two hydrogens are exchanged are of the general form illustrated in Fig. 29.14, the simplest example being exchange between (substituted) ethane and ethylene. In these compounds the ethane and ethylene analogs are oriented in a parallel fashion, their movements being restrained by stiff three-dimensional structures. Typical examples are the syn-sesquinorbornene disulfones of Fig. 29.14 studied by Paquette et al. [56, 57] and the compounds studied by Mackenzie et al. [58, 59]. The data available for these compounds are limited to temperatures near room temperature, the effective activation energies obtained from Arrhenius plots being in the range 24–30 kcal mol–1. Such high activation energies suggests either classical overbarrier transfer or stepwise tunneling involving a high-energy stable intermediate structure. The relatively large kinetic isotope effects (of order 10 at 373 K for HH compared to DD transfer) suggest the latter alternative. Since the barriers faced by the protons are not symmetric, the relation between the rates of HH, HD, and DD transfer cannot provide unequivocal answers. Also, these complex structures cannot be studied theoretically at a level high enough to settle this problem. However, the available calculations [57, 60] indicate that the observed rate constants and activation energies are incompatible with concerted transfer.
Figure 29.14 Temperature dependence of the rate constants of double proton transfer in syn-sesquinorbornene disulfone–d0 , -d1 , and -d2 , illustrated in the insert, evaluated for R1;2 =CH2 . The symbols represent observed rate constants [56, 57] and the solid lines the results of two-dimensional semi-empirical Golden Rule calculations [57].
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29 Multiple Proton Transfer: From Stepwise to Concerted
Qualitative arguments in favor of stepwise transfer are the absence of significant hydrogen bonding and the stiffness of the bridged structures. The transfer is between CH bonds whose polarity does not favor hydrogen bonding and thus assumes the character of neutral hydrogen transfer. The intermediate state produced by single hydrogen transfer will not be the ionic state typical of single proton transfer and hence will not create a significant dipole moment. Under these conditions the coupling parameter G will be very small. Moreover, the stiffness of the structure does not favor a transition state in which the two C H C bonds are significantly closer than in the equilibrium configuration while remaining aligned. Twisting appears the most likely deformation, which causes an asymmetric distortion of the active site that would favor single hydrogen transfer and thus stepwise transfer.
29.9 Proton Conduits
An OH or NH group carries a proton as well as a lone pair of electrons and can therefore form two connected hydrogen bonds through which protons can be conducted from a donor to an acceptor group by means of a relay mechanism. The resulting double proton transfer differs from most of the processes discussed in the previous sections in that it amounts to a net transport of charge. In biological systems, chains of OH groups, belonging to water molecules and amino acid residues, are known to transport protons over considerable distances. To investigate the mechanism of these processes, we first consider a double proton transfer reaction in the acetic acid–methanol complex [61, 62], illustrated in Fig. 29.15, for which the potential is almost symmetric. Although reactant and product are identical (except for HD transfer), the barrier is asymmetric because the two moving protons belong to different partners. To obtain transfer rate constants, Gerritzen and Limbach [61] carried out NMR measurements in tetrahydrofuran solution at 270–330 K. In Fig. 29.16 the measured rate constants are compared with the results of quantum dynamics calculations based on a high-level potential [62], which yield a single transition state and thus predict concerted transfer despite the relatively high temperature and the (weakly) polar medium. Because of the asymmetry of the barrier, the two protons move asynchronously; in the transition state they are closer to the methanol than to the acetic acid moiety. The asymmetry is clearly shown by the difference between the kHD ðTÞ and kDH ðTÞ values. Note that the kHD ðTÞ curve in Fig. 29.16 is closer to the kDD ðTÞ than the kHH ðTÞ curve, rather than being in the center. Proton conduits can also catalyze isomerization. A biologically interesting example is the isomerization of DNA bases such as guanine, as illustrated in Fig. 29.17. These molecules occur is several isomeric forms that differ in the position of one or more of the protons. Water or alcohol molecules can form an OH bridge connecting an occupied with an unoccupied position, which may lead to formation of an isomer. For the isomerization depicted in Fig. 29.17, a single water mol-
29.9 Proton Conduits
Figure 29.15 The two steps of complex formation and double proton exchange in the methanol–acetic acid complex [62].
Figure 29.16 Comparison of experimental [61] and theoretical [62] bimolecular rate constants of proton exchange in the methanol–acetic acid complex in tetrahydrofuran-d8 , represented by symbols and solid lines, respectively, for HH, HD and DD exchange. The dashed lines represent the rate constants obtained by transition state theory. The two (close) sets of data for the mixed isotope combinations HD and DH reflect the asymmetry of the barrier.
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Figure 29.17 Schematic representation of the tautomerization of guanine and its 1:1 and 1:2 complexes with water [16].
ecule can increase the rate of isomerization by up to 12 orders of magnitude [16]. A chain of two water molecules is also active but turns out to be a less effective catalyst. A noncanonical isomer can cause a GC!AT point mutation in the DNA chain; in the case of guanine, the isomer may replace adenine and pair with thymine rather than cytosine, thus forming, after a subsequent cell division, an AT base pair where a GC pair is required. An active hydroxyl group can catalyze such processes in two directions: it may produce noncanonical isomers, but it also may regenerate the canonical form once the unwanted isomer is produced. Hence it may play a role in point mutation as well as in enzymatic DNA repair [63]. To illustrate the relative efficiency of long and short proton conduits, we return to the 7-azaindole, molecule, whose dimer was briefly discussed in Section 29.7. As pointed out in Section 29.7, excitation of this molecule to the fluorescent state redistributes the charge between the two nitrogens. This redistribution renders the tautomeric form produced by the excitation unstable relative to the form in
29.9 Proton Conduits
which the nitrogen-bound proton has changed place; in other words, the redistribution is the driving force for the observed proton transfer. In the excited monomer this transfer is opposed by a high barrier and as a result is much too slow to compete with decay of the excited state, which has a lifetime of about 8 ns. (It is faster in the ground state [16] where the barrier is lower). However, the example treated in Section 29.7 shows that transfer can be catalyzed by dimerization [54]. In the dimer the excitation is essentially localized on one partner and the unexcited partner serves as an effective proton conduit. The same occurs in the monomer if water is present. Water molecules form hydrogen-bonded complexes with 7-azaindole, two of which are illustrated in Fig. 29.18 (top) [17, 64, 65]. The water molecules connect the NH group with the nonhydrogenated N atom, thereby facilitating proton exchange. It is well-known that tautomerization of 7-azaindole in aqueous solution is extremely rapid ( ‡ 109 s1 ) [66, 67]. To account for this effect of water, we calculated the rate of proton transfer through water chains connecting the two nitrogens [17]. The results show that a single water molecule does not form an effective proton conduit for neutralizing the effect of the excitation in a cold beam because the transfer is too slow to compete effectively with fluorescence decay. A chain of two water molecules is even less effective; in that case the transfer is still concerted but far from synchronous and the transition state shows a large charge separation, which makes the corresponding transfer subject to strong environmental effects. Although ineffective in
Figure 29.18 Calculated structures of the stationary points along the reaction coordinate for the excited state tautomerization in 7-azaindole complexes with one, two and five water molecules [17].
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29 Multiple Proton Transfer: From Stepwise to Concerted
a cold beam, the transfer rates are calculated to increase rapidly with increasing temperature and to increase further if the complexes are embedded in a dielectric continuum; nevertheless they still fall short of the values observed in aqueous solution. However, appropriately high values have been obtained [17] for complexes with five water molecules of the form illustrated in Fig. 29.18 (bottom). In this system an ionic intermediate state is formed through with the transfer occurs stepwise by a classical over-barrier process. Hence in the system excited 7-azaindole + water, we see a gradual change from concerted to stepwise transfer if more and more water molecules are added and if the temperature is increased. Short linear chains of water molecules tend to give give rise to concerted transfer, whereas branching or clustering of water chains seems to favor stepwise transfer. The apparent reason for this change of mechanism is the ability of the water cluster to stabilize an ionic structure. This flattens the barrier and ultimately generates a local minimum, which splits the barrier without reducing its width at the base. The ionic structure imposes a drastic rearrangement on the conducting water chain, which results in a large increase in the effective mass of the moving protons. This reduces the transfer rate at low temperatures but opens the possibility of proceeding stepwise via the intermediate minimum when the temperature increases. Such a transfer mechanism is just emerging in the 1:2 complex. The extreme form of this mechanism is proton transport in ice, which proceeds stepwise and classically, as indicated by the minimal isotope effect. These calculations illustrate two aspects of the role of hydrogen-bonding solvents in proton transfer processes. On the one hand they catalyze these processes by forming proton conduits between donor and acceptor atoms, and on the other they provide a dielectric medium that stabilizes ionic or highly polar intermediates. Representation of the solvent by a dielectric continuum cannot account for this dual role. To treat the transfer process adequately, it will be necessary to introduce a primary shell of discrete solvent molecules into the calculations. In the ground state of 7-azaindole the same proton transfer processes will occur but move in the opposite direction. Our calculations [16] indicate that the dependence of the transfer rate on the length of the water chain and on temperature is strikingly different from that in the excited state. The reduced polarity of the ground state prevents formation of an ionic structure in the 1:2 complex and keeps the protons moving more or less synchronously. As a result the transfer rates of the 1:1 and 1:2 complexes are calculated to be very similar. The corresponding deuterium isotope effects are calculated to be small, namely 6.6 and 2.6, respectively. Small isotope effects are typical for loose water chains, where the motions of the oxygen atoms contribute significantly to the transfer. A small isotope effect for proton transport through a water chain is also observed for catalytic conversion of CO2 to HCO 3 by carbonic anhydrase II [68, 69]. The rate-determining step in this process is the transfer of a proton from the H2 O ligand of a four-coordinated zinc ion to a histidine residue located at a distance of about 8 . The proton conduit is known to consists of water molecules located in a pocket that can contain several such molecules, which are freely exchanged with
29.9 Proton Conduits
embedding fluids. A minimum of two water molecules is sufficient to form a connecting chain, as indicated by a theoretical study of an active-site model of the enzyme with two water molecules forming the proton conduit in a pocket whose size is constrained to conform to available X-ray data [18]. The model is illustrated in Fig. 29.19; the structure and vibrational force field were calculated by a density functional method after extensive testing. A single transition state was found, corresponding to concerted triple proton transfer through an adiabatic barrier of about 6 kcal mol–1; the normal mode with imaginary frequency is illustrated in
Figure 29.19 The reactant (R), transition state (TS) and product (P) configurations for the rate-determining triple proton transfer step of the 58-atom model used to represent the active site of carbonic anhydrase II [18]. The numbers denote bond distances (in ) calculated at two different levels of theory. The arrows in the insert figure represent the tunneling mode and illustrate the degree of synchronicity of the transfer.
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29 Multiple Proton Transfer: From Stepwise to Concerted
the insert to Fig. 29.19. Tunneling rate constants were evaluated with AIM/DOIT and, on a more limited scale, with TST with semiclassical tunneling corrections. The results indicate that concerted transfer through this short water chain is fast and can serve as a feasible if unconventional model for proton transport in this enzymatic reaction. Tunneling rates are found to be faster than classical over-barrier rates by almost two orders of magnitude. Tunneling rate constants calculated for partial and total deuteration along the water chain closely match the observed KIEs in the range 1–4 at room temperature [18, 70], as shown in Fig. 29.20. KIEs calculated by TST for over-barrier transfer are larger because of the the cumulative effect of zero-point energy differences. By contrast, tunneling KIEs are small because of strong participation of the motion of heavier atoms, especially the oxygen atoms of the water chain and the zinc ligand. This behavior is common for chains of two or more water molecules. Such a proton conduit is a loose structure and can be easily deformed without substantial expenditure of energy. Both symmetric and antisymmetric modes participate in the deformation, the former helping and the latter hindering tunneling. The transfer in the chain is not only concerted but actually highly synchronous without any indication that an ionic intermediate is being formed. The KIE of partially deuterated chains does not depend strongly on the place of deuteration and the rate constant varies smoothly with the number of deuterium substituents.
Figure 29.20 Kinetic isotope effect in carbonic anhydrase II plotted as a function of the atomic fraction of deuterium in water. The dots represent experimental results taken from Ref. [70], the circles and squares are the results of quantum and classical calculations, respectively [18].
29.10 Transfer of More Than Two Protons
In this example the two water molecules together with the zinc-coordinated water molecule make up a chain of three waters. Given the size of the pocket, it is clear that many other connecting water bridges are possible. Cui and Karplus [71] found that the single transition state is maintained if a fourth water is added to the linear chain, but that an intermediate minimum appears when the chain is branched. No reliable calculation of the rate of proton transfer through these structures is available to date.
29.10 Transfer of More Than Two Protons
In the preceding section we encountered several examples of transfer of three or more protons along chains of water molecules. There is as yet no experimental evidence that any of these transfer reactions is concerted or stepwise. Calculations support the intuitive notion that the longer the chain the smaller will be the probability that the transfer is concerted. Strong coupling of the proton motions to oxygen atom displacements lead to the prediction of small KIEs, which limits the usefulnes of deuterium substitution as a diagnostic tool. To get a clear picture of the concertedness of the transfer, one needs systems in which the transfer can give rise to level splittings. Two systems of this kind are trimeric water and calix[4]arene. According to measurements of Pugliano and Saykally [72], the chiral water trimer, illustrated in Fig. 29.21 (top), occurs in two interconverting enantiomeric forms. Although this interpretation was not supported by Monte Carlo simulations [73], two recent multidimensional tunneling calculations [19, 74] confirm the interconversion by triple proton tunneling across a high barrier (about 26 kcal mol–1). The transfer is predicted to be concerted and to produce a zeropoint splitting in the range 1–10 MHz. This is a very small splitting that would be difficult to observe by presently available methods. The transfer rate is greatly enhanced by coupling to a symmetric breathing mode of about 730 cm1 ; the splitting of the fundamental of this mode is predicted to be 40 times as large as that of the zero-point level, which may put it within measureable range. Unfortunately, the breathing mode is not infrared active. Calix[4]arene is a bowl-shaped chiral molecule with four moving protons, as shown in Fig. 29.21 (bottom). Inside the bowl there are four hydroxy groups, which form a chiral ring of symmetry C4. Horsewill et al. [75, 76] used NMR relaxometry on crystalline powders to study proton exchange in calix[4]arene and p-tert-butyl calix[4]arene at low temperatures (30–80 and 15–21 K, respectively). They reported clear evidence for concerted quadruple proton transfer. Our AIM calculations for an isolated calix[4]arene molecule, based on a potential calculated with density functional theory at the B3LYP/cc-pVDZ level, are in agreement with this conclusion [77]. The calculated barrier height is about 17 kcal mol–1, a high value, as expected for a process involving rupture of four OH bonds, as illustrated in Fig. 29.21. Nevertheless, the predicted splitting amounts to almost 40 MHz due
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29 Multiple Proton Transfer: From Stepwise to Concerted
Figure 29.21 The two stereoisomers and the transition state corresponding to synchronous transfer of three and four protons in the water trimer (top) [19] and in calix[4]arene (bottom) [77], respectively.
to strong assistance of modes that modulate the O O distances. Unfortunately the measured splitting of the same general magnitude turned out to be an experimental artifact, so that there is no definite proof that the four protons move concertedly. It follows that thus far concerted multiple proton transfer has been demonstrated only for two protons.
29.11 Conclusion
The nonclassical dynamics of protons, which allows them to tunnel through barriers, also influences their collective behavior. Specifically, it gives them a propensity to transfer concertedly and even synchronously. The clearest evidence of concerted transfer is the observation of level splittings in high-resolution spectra. For the time being, these observations are limited to double proton transfer and single levels, mostly zero-point levels. The observed splittings are small, typically
29.11 Conclusion
£ 1 GHz (0.04 cm1 ). They require symmetric transfer potentials but not necessarily equivalent transfering particles. The experimental evidence for concerted proton transfer in rate processes is based mostly on the vanishing temperature dependence at low temperatures. Deuterium isotope effects observed at higher temperatures often lead to ambiguous results, because for over-barrier transfer they have a tendency to increase with increasing numbers of protons while for tunneling they have a tendency to decrease because of increasing coupling to transvers modes. Although the evidence for concerted transfer in rate processes is less firm than that obtained from level splittings, it is strongly supported by theory, in particular quantum-chemical calculations leading to single transition states. On the other hand, there is also convincing experimental evidence for rate processes in which protons move separately rather than collectively. Such stepwise transfers imply the existence of stable intermediates, which indeed have been found in theoretical calculations. In this contribution we have treated these two transfer mechanisms as limiting cases in a general picture of multiple proton transfer, represented by a model in which the degree of concertedness of the transfer is governed by specific parameters. The basic model concerns double proton transfer in a symmetric potential. The parameter controlling the concertedness is the proton–proton correlation represented by a term that is bilinear in the local proton coordinates. The model is combined with a previously developed approach to single proton transfer based on an approximate instanton method. This leads to the recognition of three coupling regimes governing the mechanism of nonclassical double proton transfer. Strong coupling between the hydrogen bonds along which the transfer takes place leads to a potential characterized by a single transition state, whose imaginary frequency is along the symmetric component of the two-dimensional reaction coordinate, the frequency along the antisymmetric component being real. A single mechanism is operative in this limit, namely concerted transfer and, if the potential is symmetric, synchronous transfer of the two protons, leading to level splittings. The transfer dynamics is identical to that of a single particle. The rate of transfer will be independent of temperature at low temperatures and its temperature dependence at moderate temperatures will be governed by thermal excitation of the skeletal modes coupled to tunneling. The rate will be subject to a deuterium isotope effect that tends to be weaker than that of single proton transfer reactions due to larger contributions of promoting modes. For symmetric potentials, the HD rate constant will be close to the geometric mean of the HH and DD rate constants. This limiting situation, represented by the potential of Fig. 29.3(c), is favored if the hydrogen bonds are strong, (anti)parallel, and closely spaced. The formic acid dimer is a typical example. Weakening of the coupling will lead to a point where the transition state that represents the barrier for synchronous double proton transfer turns into a secondorder saddle point; an intermediate also appears, which is a minimum along the antisymmetric collective coordinate but a saddle point along the symmetric one, as illustrated in Fig. 29.3(b). We then enter the intermediate coupling region where a single trajectory can no longer account for the transfer dynamics. In addi-
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29 Multiple Proton Transfer: From Stepwise to Concerted
tion to the one-dimensional synchronous path, there will be two-dimensional paths of concerted but asynchronous transfer that are longer but of lower energy. Hence, in addition to the synchronous mechanism that governs the strong-coupling regime, a two-dimensional concerted mechanism involving both reaction coordinates is possible. To compare the two concerted mechanisms, we have carried out simple model calculations, which suggest that the one-dimensional synchronous process will generally dominate at low temperature. This result requires further theoretical and experimental testing. Naphthazarin and porphycene may be suitable subjects for such an investigation. Further weakening of the coupling will turn the intermediate into a stable minimum, separated by transition states from the global minima, as illustrated in Fig. 29.3(a). This opens a third transfer mechanism consisting of two independent one-dimensional steps to and from the intermediate. Stepwise double proton transfer along this path requires enough thermal energy to reach the intermediate; its rate will tend to show a much stronger temperature dependence than that of the two concerted mechanisms. It will therefore be favored by high temperatures. At temperatures low enough to render the intermediate inaccessible, the two concerted mechanism operative for intermediate coupling will take over. It follows that under weak-coupling conditions three independent mechanisms contribute to the transfer. This limiting situation is favored if the hydrogen bonds are weak, not parallel, and far apart; porphine is a typical example. This classification scheme for multiple proton transfer remains incomplete. It needs to be extended to asymmetric transfer potentials, an aspect that has been briefly discussed only in the sections dealing with specific examples. Another aspect of symmetry breaking will arise when the effect of symmetric and antisysmmetric transverse vibrations is included. These vibrations should affect the symmetric and antisymmetric reaction coordinates differently, which will change the balance between the two concerted transfer mechanisms operative in the weak (Fig. 29.3(a)) and intermediate (Fig. 29.3(b)) coupling regions. Symmetric transverse modes tend to act as promoting modes for transfer along the symmetric reaction coordinate by shortening the effective tunneling distance, an effect illustrated by the corresponding hydrogen-bond contraction in the central maximum (2) of Table 29.1. This would favor synchronous transfer. On the other hand, antisymmetric transverse modes may favor the asynchronous transfer associated with the alternative lower-energy, longer-path mechanism since it breaks the instantaneous equivalence of the two protons. The degree of excitation of these transverse modes and thus the temperature will also play a part in these considerations. Obviously, this problem requires further study. The problem of how to distinguish these two concerted mechanism experimentally also remains unsolved. For the moment these unsolved problems do not seem to seriously hamper our ability to interpret the available data on multiple proton transfer. Most of these data concern concerted transfer under strong-coupling conditions where alternative mechanisms do not contribute. The systems identified as undergoing stepwise transfer under weak-coupling conditions have only been studied at tempera-
References
tures high enough to render the stepwise mechanism dominant. No system for which experimental data are available has been clearly identified as belonging to the intermediate-coupling regime. Finding such systems remains a challenge to both experimentalists and theorists.
Acknowledgment
A.F.-R. thanks the Ministerio de Educatin y Ciencia for a Ramon y Cajal Research Contract and for Project No. BQU2003-01639.
References 1 See, e.g., the review V. A. Benderskii,
D. E. Makarov, C. H. Wight, Adv. Chem. Phys. 88, 1 (1994), and the original literature cited therein. 2 Z. Smedarchina, W. Siebrand, A. Fernndez-Ramos, Kinetics isotope effects in multiple proton transfer in Isotope Effects in Chemistry and Biology, Marcel Dekker, New York, 2005. 3 W. Siebrand, Z. Smedarchina, M. Z. Zgierski, A. Fernndez-Ramos, Int. Rev. Phys. Chem. 18, 5 (1999). 4 F. Madeja, M. Havenith, J. Chem. Phys. 117, 7162 (2002). 5 K. Remmers, W. L. Meerts, I. Ozier, J. Chem. Phys. 112, 10890 (2000). 6 Z. Smedarchina, A. Fernndez-Ramos, W. Siebrand, Chem. Phys. Lett. 395, 339 (2004). 7 Z. Smedarchina, A. Fernndez-Ramos, W. Siebrand, J. Chem. Phys. 122, 134309 (2005). 8 J. Braun, M. Schlabach, B. Wehrle, M. Kocher, E. Vogel, H.-H. Limbach, J. Am. Chem. Soc. 116, 6593 (1994). 9 J. Braun, H.-H. Limbach, P.G. Williams, H. Morimoto, D. E. Wemmer, J. Am. Chem. Soc. 118, 7231 (1996). 10 T. J. Butenhof, C. B. Moore, J. Am. Chem. Soc. 110, 8336 (1988). 11 Z. Smedarchina, M. Z. Zgierski, W. Siebrand, P. M. Kozlowski, J. Chem. Phys. 109, 1014 (1998). 12 M. F. Shibl, M. Tashikawa, O. Khn, Phys. Chem. Chem. Phys. 7, 1368 (2005). 13 U. Langer, Ch. Hoelger, B. Wehrle, L. Latanowicz, E. Vogel, H.-H. Limbach, J. Phys. Org. Chem. 13, 23 (2000).
14 P. M. Kozlowski, M. Z. Zgierski,
J. Chem. Phys. 109, 5905 (1998). 15 J. R. de la Vega, J. H. Bush, J. H. Schau-
16
17
18
19
20
21 22
23 24 25 26 27
ble, K. L. Kunze, B. E. Haggart, J. Am. Chem. Soc. 104, 3295 (1982). Z. Smedarchina, W. Siebrand, A. Fernndez-Ramos, L. Gorb, J. Leszczynski, J. Chem. Phys. 112, 566 (2000). A. Fernndez-Ramos, Z. Smedarchina, W. Siebrand, M. Z. Zgierski, J. Chem. Phys. 114, 7518 (2001). Z. Smedarchina, W. Siebrand, A. Fernndez-Ramos, Q. Cui, J. Am. Chem. Soc. 125, 243 (2003). Z. Smedarchina, A. Fernndez-Ramos, W. Siebrand, J. Comp. Chem. 22, 787 (2001). C. G. Swain, E. C. Stivers, J. F. Reuwer, Jr., L. J. Schaad, J. Am. Chem. Soc. 80, 5885 (1958). Z. Smedarchina, W. Siebrand, Chem. Phys. Lett. 410, 370 (2005). See, e.g., the review D. G. Truhlar, B. C. Garrett, S. J. Klippenstein, J. Phys. Chem. 100 12771 (1996), and references therein. W. H. Miller, J. Chem. Phys. 62, 1899 (1975). C. G. Callan, S. Coleman, Phys. Rev. D 16, 1762 (1977). G. S. Langer, Ann. Phys. 54, 258 (1969). A. M. Polyakov, Nucl. Phys. 121, 429 (1977). Z. Smedarchina, W. Siebrand, M. Z. Zgierski, J. Chem. Phys. 103, 5326 (1995).
943
944
29 Multiple Proton Transfer: From Stepwise to Concerted 28 Z. Smedarchina, A. Fernndez-Ramos,
29
30
31
32
33
34
35
36
37
38 39 40 41 42
43 44 45 46
W. Siebrand, Chem. Phys. Lett. 395, 339 (2004). Z. Smedarchina, W. Siebrand, A. Fernndez-Ramos, E. MartnezNffl ez, Chem. Phys. Lett. 386, 396 (2004). Z. Smedarchina, A. Fernndez-Ramos, W. Siebrand, M. Z. Zgierski, DOIT 2.0, a computer program to calculate hydrogen tunneling rate constants and splittings. V. A. Benderskii, V. I. Goldanskii, D. E. Makarov, Chem. Phys. 154, 407 (1991). V. A. Benderskii, V. I. Goldanskii, D. E. Makarov, Chem. Phys. Lett. 186, 517 (1991). V. A. Benderskii, V. I. Goldanskii, D. E. Makarov, Chem. Phys. 159, 29 (1992). V. A. Benderskii, S. Yu. Grebenshchikov, E. V. Vetoshkin, G. V. Mil’nikov, D. E. Makarov, J. Phys. Chem. 98, 3300 (1994). V.A. Benderskii, S.Yu. Grebenshchikov, D.E. Makarov, E.V. Vetoshkin, Chem. Phys. 185, 101 (1994). V. A. Benderskii, S. Yu. Grebenshchikov, G. V. Mil’nikov, E. V. Vetoshkin, Chem. Phys. 188, 19 (1995); Chem. Phys. 194, 1 (1995); Chem. Phys. 198, 281 (1995). V. A. Benderskii, E. V. Vetoshkin, E. I. Kats, H. P. Trommsdorff, Phys. Rev. E 67, 26102 (2003). W. H. Saunders, Jr., J. Am. Chem. Soc. 107, 184 (1985). J. P. Sethna, Phys. Rev. B 24, 698 (1981). J. P. Sethna, Phys. Rev. B 25, 5050 (1982). N. Shida, P. F. Barbara, J. Alml f, J. Chem. Phys. 94, 3633 (1991). C. S. Tautermann, M. J. Loferer, A. F. Voegele, K. R. Liedl, J. Chem. Phys. 120, 11650 (2004). J.-H. Lim, E. K. Lee, Y. Kim, J. Phys. Chem. A 101, 2233 (1997). Y. Kim, S. Lim, H.-J. Kim, Y. Kim, J. Phys. Chem. A 103, 617 (1999). Y. Podolyan, L. Gorb, J. Leszczynski, J. Phys. Chem. A 106, 12103 (2002). Y. Kim, S. Lim, Y. Kim, J. Phys. Chem. A 103, 6632 (1999).
47 A. Oppenl nder, C. Rambaud,
48 49 50
51
52
53
54 55 56
57
58
59 60 61 62
63
64 65 66
H. P. Trommsdorff, J.-C. Vial, Phys. Rev. Lett. 63, 1432 (1989). C. Rambaud, H. P. Trommsdorff, Chem. Phys. Lett. 306, 124 (1999). A. Heuer, U. Haeberlen, J. Chem. Phys. 95, 4201 (1991). D. F. Brougham, A. J. Horsewill, R. I. Jenkinson, Chem. Phys. Lett. 272, 69 (1997). Q. Xue, A. J. Horsewill, M. R. Johnson, H. P. Trommsdorff, J. Chem. Phys. 120, 11107 (2004). D. R. Borst, J. R. Roscoli, D. W. Pratt, G. M. Florio, T. S. Zwier, A. Mller, S. Leutwyler, Chem. Phys. 283, 341 (2002). J. R. Roscoli, D. W. Pratt, Z. Smedarchina, W. Siebrand, A. FernndezRamos, J. Chem. Phys. 120, 11351 (2004). K. Sakota, H. Sekiya, J. Chem. Phys. A 109, 2722 (2005). A. Douhal, S. K. Kim, A. H. Zewail, Nature 378, 260 (1995). G. A. O’Doherty, R. D. Rogers, L. A. Paquette, J. Am. Chem. Soc. 116, 10883 (1994). K. N. Houk, Y. Li, M. A. McAllister, G. A. O’Doherty, L. A. Paquette, W. Siebrand, Z. Smedarchina, J. Am. Chem. Soc. 116, 10895 (1994). K. Mackenzie, E. C. Gravett, R. J. Gregory, J. A. K. Howard, J. Maher, Tetrahedron Lett. 30, 5005 (1989). K. Mackenzie, Recent Res. Devel. Org. Chem. 4, 295 (2000). Z. Smedarchina, W. Siebrand, J. Mol. Struct. 297, 207 (1993). D. Gerritzen, H.-H. Limbach, J. Am. Chem. Soc. 106, 869 (1984). A. Fernndez-Ramos, Z. Smedarchina, J. Rodrguez-Otero, J. Chem. Phys. 114, 1567 (2001). L. Gorb, Y. Podolyan, J. Leszczinski, W. Siebrand, A. Fernndez-Ramos, Z. Smedarchina, Biopolymers 61, 77 (2002). M. S. Gordon, J. Phys. Chem. 100, 3974 (1996). G. M. Chaban, M. S. Gordon, J. Phys. Chem. A 103, 185 (1999). D. McMorrow, T. J. Aartsma, Chem. Phys. Letters 125, 581 (1986).
References 67 R. S. Moog, M. Maroncelli, J. Phys. 68 69 70 71 72
Chem. 95, 10359 (1991). D. W. Christianson, C. A. Fierke, Acc. Chem. Res. 29, 331 (1996). D. N. Silverman, S. Lindskog, Acc. Chem. Res. 21, 30 (1988). K. S. Venkatassuban, D. N. Silverman, Biochemistry 19, 4984 (1980). Q. Cui, M. Karplus, J. Phys. Chem. B 107, 1071 (2003). N. Pugliano, R. J. Saykally, Science 257, 1938 (1992).
73 J. K. Gregory, D. C. Clary, J. Chem. Phys.
102, 7817 (1995). 74 K. R. Liedl, S. Sekusak, R. T. Kroemer,
B. M. Rode, J. Phys. Chem. A 101, 4707 (1997). 75 D. F. Brougham, R. Caciuffo, A. J. Horsewill, Nature 397, 241 (1999). 76 A. J. Horsewill, N. H. Jones, R. Caciuffo, Science 291, 100 (2001). 77 A. Fernndez-Ramos, Z. Smedarchina, F. Pichierri, Chem. Phys. Lett. 343, 627 (2001).
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II Biological Aspects Part I
Models for Biological Hydrogen Transfer
This section contains, in five chapters, treatments in model systems of the distinguishable classes of biological hydrogen-transfer reactions: proton transfer to and from carbon (Ch. 1 by Amyes and Richard), proton transfer among electronegative atoms as is typical in acid-base catalysis (Ch. 2 by Kirby), hydrogen-atom transfer (Ch. 3 by Scho¨neich), and hydride transfer (Ch. 4 by Schowen). Baltzer (Ch.5) then extends the important subject of acid-base catalysis from simple models toward the complexity of proteins by describing studies in designed peptides. Amyes and Richard’s treatment in Ch. 1 suggests that the correlation of C–H fission rates either in solution or in enzyme active sites with the thermodynamic acidity of the proton donor is not a simple matter. The Marcus-theory separation into intrinsic and thermodynamic barriers is rendered more complicated by the perhaps surprising observation that the intrinsic barrier rises as the acidity increases. This is consistent with the view that intrinsic barriers are small when the liberated electron pair is localized (as with electronegative atoms) and larger as the work of reorganization and delocalization becomes greater. Kirby’s presentation and analysis in Ch. 2 of the phenomenology of acid-base catalysis as a potential contributor to enzyme catalysis notes first the entropic cost of producing a potentially high-efficiency catalytic array from aqueous solution and the consequent utility of intramolecular reactions in exploring the preorganization strategy of proteins. The information to date is then found to leave a considerable gap between the efficiency of models and the efficiency of enzymes. Other points of note are the still incompletely understood superiority of intramolecular nucleophilic over intramolecular acid-base catalysis, and the fact that strong hydrogen bonds, if they play a catalytic role, must necessarily do so in the transition state and not in stable states. Scho¨neich’s Ch. 3 on hydrogen-atom transfers takes the reader through the comparative phenomenology of transfer of hydrogen atoms to the likely acceptors in the biological context (radicals centered on O, N, S, or C). A cautionary note is sounded on the dangers of uncritical extrapolation of model studies to the biological context. In Ch. 4, Schowen reviews on hydride-transfer models, principally Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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those related to nicotinamide and flavin cofactors, noting that these have indicated a major role for hydrogen-tunneling in the non-enzymic reactions. This thus indicates that the corresponding enzymes have not evolutionarily ‘‘invented’’ tunneling as a mechanism but rather have accelerated an existing tunneling pathway or diverted the system to a different, more rapid tunneling pathway. From these studies of relatively simple molecular species, Baltzer in Ch. 5 takes the subject of acidbase catalysis into the realm of designed peptides. The field is reviewed generally but proper emphasis is given peptides with the helix-loop-helix motif that dimerize into a four-helix bundle. These species are extraordinary in their susceptibility to imaginative introduction of catalytic functional groups.
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1
Proton Transfer to and from Carbon in Model Reactions Tina L. Amyes and John P. Richard 1.1
Introduction
Much of what is known about the mechanism for proton transfer to and from carbon in aqueous solution has come through experimental studies of model reactions. This work is, for several reasons, invaluable to biochemists interested in understanding the mechanism for proton transfer reactions at carbon in biological systems, virtually all of which are enzyme-catalyzed. First, model studies may be used to define the activation barrier for nonenzymatic proton transfer which must be lowered by the enzyme to obtain a catalytic rate acceleration. Second, the results of these studies help elucidate strategies which enzyme catalysts might follow to lower this barrier. Third, these results help to define the roles for various amino acid side-chains at an enzyme active site in the catalysis of proton transfer at carbon. This chapter will highlight recent model studies of proton transfer to and from carbon that we consider to be helpful in either defining the problems faced by enzyme catalysts of these reactions, or suggesting solutions to these problems.
1.2
Rate and Equilibrium Constants for Carbon Deprotonation in Water
The most fundamental experimental determinations in model studies of proton transfer at weakly basic carbon are of the rate and equilibrium constants for carbon deprotonation to form an unstable carbanion (Eq. (1.1)). These parameters define the kinetic and thermodynamic barriers to proton transfer (Eq. (1.2) for Fig. 1.1). They are of interest to enzymologists because they specify the difficulty of the problem that must be solved in the evolution of proteins which catalyze proton transfer with second-order rate constants k cat =K m of 10 6 –10 8 M1 s1 that are typically observed for enzymatic reactions [1, 2]. The barrier to thermodynamically unfavorable deprotonation of carbon acids (DGf y , Fig. 1.1) in water is equal to the sum of the thermodynamic barriers to proton transfer (DG ) and the barrier to downhill protonation of the carbanion in the reverse direction (DGr y , Eq. (1.2)). The thermoHydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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1 Proton Transfer to and from Carbon in Model Reactions
Figure 1.1. Free energy profile for deprotonation of a weak carbon acid (Eq. (1.1)) which shows that the barrier to thermodynamically unfavorable proton transfer
(DGf y ) is equal to the sum of the thermodynamic barriers to proton transfer (DG ) and the barrier to downhill protonation of the carbanion in the reverse direction (DGr y ).
dynamic barrier can be calculated directly from the equilibrium constant for ionization of the carbon acid in water. This barrier is the dominant term in Eq. (1.2) (DG g DGr y ) for strongly unfavorable ionization of weak carbon acids to form highly unstable carbanions. ð1:1Þ ð1:2Þ Acidity constants for ionization of weak carbon acids in water cannot be determined by direct measurement when the strongly basic carbanion is too unstable to exist in detectable concentrations in this acidic solvent. Substituting dimethylsulfoxide (DMSO) for water causes a large decrease in the solvent acidity because, in contrast with water, the aprotic cosolvent DMSO does not provide hydrogenbonding stabilization of hydroxide ion, the conjugate base of water. This allows the determination of the pK a s of a wide range of weak carbon acids in mixed DMSO/water solvents by direct measurement of the relative concentrations of the carbon acid and the carbanion at chemical equilibrium [3, 4]. The pK a s determined for weak carbon acids in this mixed solvent can be used to estimate pK a s in water,
1.2 Rate and Equilibrium Constants for Carbon Deprotonation in Water
subject to the uncertainty of the effect of the DMSO cosolvent on the carbon acid pK a [5]. The equilibrium constant for deprotonation of carbon acids is equal to the ratio of the rate constants for formation and reaction of the product carbanion (Scheme 1.1A–C). In recent years, kinetic methods have been used to provide solid values of the pK a s for ionization of a wide range of weak carbon acids. These experiments are, in principle, straightforward and require only the determination or estimate of two rate constants – one for the slow and thermodynamically unfavorable generation of the carbanion, and a second for fast downhill carbanion protonation. The observed first-order rate constant for carbanion formation may be controlled through the choice of the basic proton acceptor. Relatively strong carbon acids undergo detectable deprotonation by the weak base water in a pseudo-first-order reaction (Scheme 1.1A), but stronger general bases (Scheme 1.1B) or hydroxide ion (Scheme 1.1C) are required to give detectable deprotonation of weaker carbon acids in bimolecular reactions.
Scheme 1.1
1.2.1
Rate Constants for Carbanion Formation
Rate constants for deprotonation of carbon acids are determined under conditions where the carbanion is generated effectively irreversibly and then undergoes a fast reaction to form a detectable product. The most general fast reaction of a carbanion is ‘‘trapping’’ by a deuterium or tritium derived from solvent to give isotopically labeled product (Eq. (1.3)) [6, 7]. Tritium has the advantage of a high sensitivity for detection in hydron exchange. However, experiments to monitor tritium exchange reactions require quantitative separation of the tritium labeled solvent from the labeled carbon acid. This is difficult for volatile simple carbon acids such as ethyl acetate and acetonitrile when the solvent is water. In recent years high resolution proton NMR has been shown to be a simple and effective method for directly monitoring the incorporation of deuterium into weak carbon acids [8–20]. This analytical method has been used to determine rate constants for deprotonation of carbon
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1 Proton Transfer to and from Carbon in Model Reactions
acids with pK a s as high as 33.5 for proton transfer reactions at room temperature [17]. The pK a s of weaker carbon acids, which do not undergo detectable deprotonation at room temperature, may be determined by monitoring hydron transfer at a higher reaction temperature and making the appropriate temperature correction [21]. Studies of multistep chemical reactions that proceed through carbanion intermediates such as those shown by Eq. (1.4)–(1.6) have provided a rich and informative body of rate data for deprotonation of biologically important carbon acids in water. Carbon deprotonation to form a carbanion intermediate is effectively irreversible and rate determining for each of the reactions shown in Eq. (1.4)–(1.6). Eq. (1.4) is an example of an alkene-forming elimination reaction [22–24], where formation of the carbanion is effectively irreversible and is followed by rapid expulsion of a phosphate dianion or trianion leaving group [24]. In Eq. (1.5) and (1.6) the carbanion is trapped by an electrophilic carbonyl group in either an intramolecular aldol (Eq. (1.5)) [10, 25] or a bimolecular Claisen-type (Eq. (1.6)) [26] condensation reaction. Not shown is the classic diffusion-controlled trapping of a carbanion by a halogen, which has been used in the determination of the pK a of acetone [27, 28]. ð1:3Þ
ð1:4Þ
ð1:5Þ
ð1:6Þ
1.2 Rate and Equilibrium Constants for Carbon Deprotonation in Water
1.2.2
Rate Constants for Carbanion Protonation
Rate constants for thermodynamically favorable protonation of unstable carbanions are typically very large. These may be determined by direct methods. A description of these direct methods, the most important of which use laser flash photolysis in carbanion generation [29, 30], is outside the scope of this chapter. The indirect methods used to estimate rate constants for carbanion protonation will be described in greater detail, because they provide insight into the nature of the rate determining step for carbanion protonation in water. Carbanion protonation in water is a two-step reaction: (i) movement of a Brønsted acid into a reactive position, and (ii) proton transfer to carbon. The overall rate constant for carbanion protonation may be limited by either the rate constant for formation of the reactive complex, in which case the overall rate constant for proton transfer can be estimated by using a representative rate constant for the rate-determining transport step, or by the rate constant for proton transfer to carbon. The limiting rate constants for thermodynamically favorable protonation of carbanions, and the observations from experiments that provide evidence for these limiting reactions are different, depending upon the type of acid that protonates the carbanion. Protonation by Hydronium Ion The microscopic reverse of deprotonation of a carbon acid by water is protonation of the product carbanion by hydronium ion (Scheme 1.1A), with a limiting rate constant of ðk d ÞH A 10 10 M1 s1 for diffusional encounter of the carbanion and hydronium ion (Scheme 1.2A). A value of kH ¼ 7 10 9 M1 s1 has been determined by direct measurement for protonation of the enolate of acetone by hydronium ion, which is downhill by ca. 30 kcal mol1 (Table 13 of Ref. [30]). This 1.2.2.1
Scheme 1.2
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1 Proton Transfer to and from Carbon in Model Reactions
provides good justification for the use of a similar limiting rate constant for protonation of enolates of like thermodynamic stability. For example, a pK a of 18.0 (Scheme 1.1A) for the a-hydrogen of N,N,N trimethylammonium glycine methyl ester has been determined from the ratio of the experimentally determined rate constant k w ¼ 5 109 s1 for water-catalyzed deprotonation of the carbon acid and an estimated limiting rate constant of kH ¼ 5 10 9 M1 s1 for protonation of the enolate by hydronium ion [14]. Protonation by Buffer Acids A Brønsted coefficient of b ¼ 1:1 has been determined for deprotonation of ethyl acetate by 3-substituted quinuclidines to form the free enolate (Scheme 1.3) [11]. The microscopic reverse of deprotonation of a carbon acid by a buffer general base is protonation of the product carbanion by the conjugate acid of the Brønsted base (Scheme 1.1B). The limiting rate constant for exothermic proton transfer is k enc A 10 9 M1 s1 when encounter of the Brønsted acid and base is rate determining (Scheme 1.3) [31]. Now, the observed Brønsted coefficient of b > 1:1 for deprotonation of ethyl acetate shows that the base catalyst bears a net positive charge at the transition state for carbon deprotonation which is greater than the unit positive charge at the conjugate acid [11, 32]. This is consistent with reversible deprotonation of the carbon followed by rate determining separation of the cation–anion pair intermediate (k 0 d , Scheme 1.3). Protonation of the enolate of ethyl acetate by the Brønsted acid is rate determining for reaction in the microscopic reverse direction ðk enc A 10 9 M1 s1 , Scheme 1.3), with a ¼ 0:1 for formation of the encounter complex between the enolate ion and buffer acid (a þ b ¼ 1:0). 1.2.2.2
Scheme 1.3
The Brønsted parameters of b > 1:0 and a < 0 proton transfer at ethyl acetate (Scheme 1.3) show that the barrier to formation of encounter complexes between the enolate of ethyl acetate (k enc , Scheme 1.3) and the quinuclidinone cation catalyst increases with the acidity of the tertiary ammonium ion. This has been proposed to reflect the increasing strength of the hydrogen bond to water that is cleaved upon formation of the encounter complex [11, 32]. The small uncertainty in the barrier to desolvation of the Brønsted acid introduces a corresponding uncertainty into the value of the limiting rate constant for the encounter-limited reaction. The limits of kBH ¼ 2–5 10 9 M1 s1 for the encounter-limited reaction of the simple oxygen ester enolate with protonated quinuclidine (pKBH ¼ 11:5) were combined with kB ¼ 2:4 105 M1 s1 for deprotonation of ethyl acetate
1.2 Rate and Equilibrium Constants for Carbon Deprotonation in Water
by quinuclidine (Scheme 1.1B), to give pK a ¼ 25:6 G 0:5 for ionization of ethyl acetate as a carbon acid in aqueous solution [11]. Protonation by Water The microscopic reverse of deprotonation of a carbon acid by hydroxide ion is protonation of the product carbanion by water (Scheme 1.1C). The limiting rate constant for strongly exothermic carbanion protonation is k r A 10 11 s1 (Scheme 1.4) for a reaction in which rotation of water into a reactive position is the rate determining step [33–35]. The failure to observe a normal primary kinetic isotope effect on lyoxide-catalyzed hydron exchange between solvent and a carbon acid provides evidence that the rate determining step for exchange is solvent reorganization. For example, most of the 3-fold difference in the rate constants for hydroxide ion catalyzed exchange of H for D at CD3 CN (Scheme 1.4A) compared with deuteroxidecatalyzed exchange of D for H at CH3 CN (Scheme 1.4B) is due to the 2.4-fold greater basicity of HO compared with that of DO . There is only a small primary kinetic isotope effect on the hydron exchange reaction [13]. This provides strong evidence that hydron transfer to lyoxide ion is reversible and that reorganization of solvent (k r A 10 11 ) is largely rate determining for the lyoxide ion-catalyzed exchange reaction, so that kp > k r A 10 11 for protonation of the a-cyanomethyl carbanion (Scheme 1.4). A pK a of 29 for deprotonation of acetonitrile (CH3 CN) was calculated from the ratio of kHO ¼ 1:1 104 M1 s1 and k r ¼ kHOH A 10 11 (Scheme 1.1C) [13]. 1.2.2.3
Scheme 1.4
1.2.3
The Burden Borne by Enzyme Catalysts
The pK a s for ionization of several biologically important carbon acids are summarized in Scheme 1.5. The pK a s of 17 for pyruvate 2 [36] and 18 for dihydroxyacetone phosphate 3 [24] are close to the pK a of 19 for the parent ketone acetone 4 [37]. The a-protons of carboxylate anions are much less acidic than those of the
955
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1 Proton Transfer to and from Carbon in Model Reactions
Scheme 1.5
corresponding aldehyde. For example, a pK a of 23 has been determined for the benzylic a-proton of mandelic acid 7 [38], whose carbon deprotonation is catalyzed by mandelate racemase; and the pK a of the a-proton of 2-phosphoglycerate 8 must be at least as large as the pK a of 33.5 estimated for acetate anion [17]. The >21 unit difference in pK a A 13 for the b,g-unsaturated steroid 1 [39] and pK a A 34 for the a-proton of 2-phosphoglycerate 8 corresponds to a greater than 29 kcal mol1 difference in the thermodynamic barriers to deprotonation of these substrates that must be surmounted by the enzymes ketosteroid isomerase and enolase, respectively. By contrast, k cat =K m for enzymatic catalysis of deprotonation at carbon is not strongly dependent on intrinsic carbon acidity. For example, k cat =K m is close to the diffusion-controlled limit for both the ketosteroid-isomerase-catalyzed deprotonation of the ketone 1 (pK a A 13) [39] and the triosephosphate-isomerase-catalyzed deprotonation of the ketone 3 (pK a A 18) [40]. An extreme example is the small difference in the values of k cat =K m ¼ 3 10 8 and 1:4 10 6 M1 s1 for enzymecatalyzed isomerization of 1 [39] and the elimination reaction of 8 [41], respectively, both of which proceed by CaH bond cleavage. This corresponds to a ca. 3 kcal mol1 difference in the activation barriers for the enzyme-catalyzed reactions, but the corresponding difference in the activation barriers for nonenzymatic proton transfer in water will be similar to the >29 kcal mol1 difference in the thermodynamic barriers to these proton transfer reactions. Efficient catalysis of deprotonation of strongly acidic carbon that undergoes rela-
1.3 Substituent Effects on Equilibrium Constants for Deprotonation of Carbon
tively rapid deprotonation in water should be easier to achieve than catalysis of deprotonation of weakly acidic carbon acids. However it does not appear any easier to understand the mechanism for enzymatic catalysis of deprotonation of strong compared with weak carbon acids, perhaps because such explanations are not fully formulated. A simple test for quantitative explanations for enzyme catalysis of proton transfer is whether they provide a simple rationalization for the differences in the catalytic power of enzymes that catalyze deprotonation of carbon acids of widely different pK a with similar second-order rate constants k cat =K m .
1.3
Substituent Effects on Equilibrium Constants for Deprotonation of Carbon
The pK a s for simple alkanes have been estimated to be ca. 50 in water [42], and their deprotonation in this solvent has not been observed experimentally. The majority of enzyme-catalyzed proton transfer reactions are at a-carbonyl carbon and give as product enolates, which are strongly stabilized by delocalization of negative charge from carbon to the more electron-withdrawing oxygen (Eq. (1.7)). The acarbonyl substrates for enzyme-catalyzed proton transfer reactions span a wide range of acidity (Scheme 1.5). However, even the a-carbon of acetate anion (pK a ¼ 33:5) undergoes slow, but detectable, deuteroxide-ion catalyzed proton transfer with a half time of ca. 60 years for reaction at 25 C in the presence of 1.0 M KOD [17].
ð1:7Þ
Organic chemists and biochemists are comfortable referring to the product of deprotonation of a-carbonyl carbon as a carbanion, because most important organic reactions of this delocalized anion with electrophiles occur at carbon. However, the preponderance of negative charge at these alkenyl oxide anions lies on the more electronegative oxygen [43]. There is good evidence that the large activation barriers observed for thermodynamically favorable protonation of enolate anions and other resonance stabilized carbanions (DGr y , Fig. 1.1) are caused in some way by the requirement that movement of an electron pair from the enolate oxygen to carbon be coupled to CaH bond formation at this carbon (Section 1.4.3.2). The pK a s of simple carbon acids are also influenced by polar substituents. These substituent effects are significant, but are generally smaller than for the resonance effect of the carbonyl group which is mostly responsible for the 33 unit difference in the pK a s of ethane (pK a A 50) [42] and acetaldehyde (pK a ¼ 16:7) [44]. For example, the pK a for the a-carbonyl hydrogen of the amino acid glycine 9 decreases by 13 units upon protonation of the a-amino group 10 and methylation of the acarboxylate group 11 [14]. A notable exception is the large stabilizing polar interaction between localized positive and negative charge at adjacent carbon. For exam-
957
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1 Proton Transfer to and from Carbon in Model Reactions
ple the acidic hydrogen of the thiazolium group of thiamine (Eq. (1.8)), has a pK a of 18 [45] which is similar to that for the a-carbonyl hydrogen of a simple ketone.
ð1:8Þ
1.4
Substituent Effects on Rate Constants for Proton Transfer at Carbon 1.4.1
The Marcus Equation
The barrier to thermodynamically unfavorable deprotonation of carbon acids (DGf y , Fig. 1.1) in water is equal to the sum of the thermodynamic barrier to proton transfer (DG ) and the barrier to downhill protonation of the carbanion in the reverse direction (DGr y , Eq. (1.2)). The observation of significant activation barriers DGr y for strongly thermodynamically favorable protonation or resonance stabilized carbanions shows that there is some intrinsic difficulty to proton transfer. The Marcus equation defines this difficulty with greater rigor as the intrinsic barrier L, which is the activation barrier for a related but often hypothetical thermoneutral proton transfer reaction (Fig. 1.2B) [46]. DGH ¼ Lð1 þ DG =4LÞ 2
ð1:9Þ
The Marcus equation was first formulated to model the dependence of rate constants for electron transfer on the reaction driving force [47–49]. Marcus assumed in his treatment that the energy of the transition state for electron transfer can be calculated from the position of the intersection of parabolas that describe the reactant and product states (Fig. 1.2A). This equation may be generalized to proton transfer (Fig. 1.2A) [46, 50, 51], carbocation-nucleophile addition [52], bimolecular nucleophilic substitution [53, 54] and other reactions [55–57] by assuming that their reaction coordinate profiles may also be constructed from the intersection of
1.4 Substituent Effects on Rate Constants for Proton Transfer at Carbon
Figure 1.2. A, Reaction coordinate profiles for proton transfer at carbon constructed from the intersection of parabolas for the reactant and product states. B, The reaction coordinate profile for a reaction where DG ¼ 0 and DGy is equal to the Marcus intrinsic barrier L.
parabolas that describe the reactant and product states. This assumption is likely to be only approximately correct. Also, the profound differences between reaction coordinate profiles for the transfer of a light electron between two metal cations and for the transfer of the nearly 2000-times heavier proton between two heavy atoms are ignored by this simple model. More rigorous treatments of these differences would serve to emphasize the superficial nature of the similarities between electron and proton transfer reactions that allow for their common treatment by the Marcus equation. Many laboratories, including our own, have used the Marcus equation empirically as a relatively simple and convenient framework for describing the differences in the intrinsic difficulty for related reactions, after correction for differences in the reaction thermodynamic driving force. This has led to the determination of the Marcus intrinsic barriers for a variety of proton transfer reactions by experiment and through calculations [58–65]. This compilation of intrinsic reaction barriers represents an attempt to compress an essential feature of these kinetic barriers to a single experimental parameter. An examination of the substituent effects on these intrinsic barriers has provided useful insight into the transition state for organic reactions [66].
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1 Proton Transfer to and from Carbon in Model Reactions
1.4.2
Marcus Intrinsic Barriers for Proton Transfer at Carbon
There is only a small barrier for thermoneutral proton transfer between electronegative oxygen or nitrogen acids and bases [31]. These reactions proceed by encounter-controlled formation of a hydrogen-bonded complex between the acid and base (k d , Scheme 1.6), proton transfer across this complex (k p , Scheme 1.6), followed by diffusional separation to products (kd , Scheme 1.6) [31]. Much larger Marcus intrinsic barriers are observed for proton transfer to and from carbon [67]. There are at least two causes for this difference in intrinsic barriers for proton transfer between electronegative atoms and proton transfer at carbon.
Scheme 1.6
Hydrogen Bonding The first step in proton transfer between electronegative atoms is the formation of a hydrogen-bonded encounter complex between the proton donor and acceptor (Scheme 1.6A). The three-centered hydrogen bond is maintained during the proton transfer reaction, which proceeds through a symmetrical transition state in which there is approximately equal partial bonding of the proton to the donor and acceptor atom. Hydrogen cyanide is a simple and moderately strong carbon acid (pK a ¼ 9:4) for which there is little or no electron delocalization or changes in bond angles or bond lengths on ionization (Section 1.4.2.2.). The observation that the rate constant for thermoneutral deprotonation of HCN by oxygen anions is close to the diffusion-controlled limit (k p A 10 8 M1 s1 ) shows that there is only a small intrinsic barrier to these reactions [68]. By contrast, there is no detectable deprotonation of HCN in water by the thermoneutral reaction of a thiol anion or by CN . This corresponds to >200- and >1000-fold smaller rate constants, respectively, for thermoneutral deprotonation of HCN by carbon and sulfur bases (Scheme 1.6B) [68]. 1.4.2.1
1.4 Substituent Effects on Rate Constants for Proton Transfer at Carbon
Proton transfer between electronegative atoms may be thought of as the movement of a hydrogen across the potential energy surface for a hydrogen bond, where the relative energies of the symmetrical transition state for proton transfer in water and the asymmetric H-bond with hydrogen localized at a single atom is strongly dependent upon the medium [69–71]. The symmetrical hydrogen bond is almost always a local maximum for the transition state for proton transfer between electronegative atoms in water [72, 73]; and the symmetrical species changes from a local maximum to a local minimum for a single potential minimum hydrogen bond as the medium is changed to a vacuum for proton transfer in the gas phase [69–71]. The order of decreasing reactivity for thermoneutral deprotonation of HCN, O > S > C, parallels the decreasing hydrogen bonding ability of these atoms [74]. This trend suggests that the three-centered symmetrical transition state for proton transfer is strongest relative to the asymmetric hydrogen bond when the donor and acceptor are electronegative atoms such as O and N, and that the symmetric species becomes relatively more unstable with the change to less electronegative atoms such as C and S. Resonance Effects Figure 1.3 shows three distinct correlations on a plot of rate constants kHO (M1 s1 ) for carbon acid deprotonation by hydroxide anion against carbon acid acidity for deprotonation of a variety of carbon acids [20]. The upper correlation 1.4.2.2
Figure 1.3. Rate-equilibrium correlations of kHO (M1 s1 ) for deprotonation of carbon acids by hydroxide ion with the pK a of the carbon acid in water at 25 C. The values of kHO and pK a were statistically corrected for the number of acidic protons p at the carbon acid. (e) Correlation for neutral monocarbonyl carbon acids. (m) Correlation for cationic monocarbonyl carbon acids. (C) Data for cyanoalkanes which define a slope of 1.0. (^) Data for simple imidazolium cations
which define a slope of 1.0. (a) Data for the 3-cyanomethyl-4-methylthiazolium cation 1b. The Eigen/Marcus curve through the data for the imidazolium and 3-cyanomethyl-4methylthiazolium cations was constructed using an estimated Marcus intrinsic barrier of 5.0 kcal mol1 , as described in Ref. 20. Reprinted with permission from J. Am. Chem. Soc. 2004, 126, 4366–4374. Copyright (2004) American Chemical Society.
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1 Proton Transfer to and from Carbon in Model Reactions
Scheme 1.7
with a Brønsted slope of 1.0 is for deprotonation of cyanoalkanes (12–14), imidazolium cations 15–18, and the 3-cyanomethyl-4-methylthiazolium cations 19. These data have been fit to an Eigen-type mechanism (Scheme 1.7) for hydroxide ioncatalyzed (B ¼ HO , Scheme 1.7) exchange of hydrons between the carbon acid and solvent water (Scheme 1.7) [31], where k r (s1 ) (Scheme 1.4) is the rate constant for the dielectric relaxation of water [33–35]. This value for k r is assumed to be equal to the rate constant for reorganization of the surrounding aqueous solvation shell which leads to exchange of water labeled with the hydron derived from the carbon acid for the bulk solvent, as shown in Scheme 1.4 for the hydron exchange reactions of acetonitrile. The solid curve shows the calculated fit of the experimental data to the mechanism in Scheme 1.7 that is obtained using k d ¼ kHO ¼ 10 9:9 M1 s1 for the thermodynamically favorable diffusion-limited proton transfer between HCN (pK a ¼ 9:0) and hydroxide ion [68], k r ¼ 10 11 s1 , and a Marcus intrinsic barrier for the actual proton transfer step (kp ¼ 10 9 s1 ) of 5.0 kcal mol1 [20].
Eigen-type curvature is observed in Fig. 1.3 for reactions that undergo a change from a rate determining chemical step (k p , Scheme 1.7) to a rate determining transport step (k r ). Surprisingly, there is no evidence for curvature in plots of data for wholly chemically-limited reactions that is predicted by Marcus theory (see below). The figure shows that progressively smaller values of log kHO (M1 s1 ) for thermoneutral deprotonation of carbon acids of pK a ¼ 15:7 by hydroxide ion, and a systematic shift towards the right-hand side of the graph in the position of the downward break to slope of 1.0 are observed on moving from the top correlation line of Fig. 1.3 to the middle correlation line for hydroxide ion deprotonation of
1.4 Substituent Effects on Rate Constants for Proton Transfer at Carbon
cationic esters (e.g. 11) and ketones and then to the bottom correlation line for deprotonation of neutral carbonyl compounds. A variety of effects are manifested by the decreasing intrinsic reactivity and increasing Marcus intrinsic barrier L to proton transfer for these series of carbon acids [20]. 1. The small Marcus intrinsic barrier to proton transfer from C(2) of imidazolium and thiazolium cations is consistent with a high degree of localization of the lone pair at the in-plane sp 2 -orbital of the carbene/ylide conjugate base, similar to the localization of charge at electronegative atoms. The intrinsic barriers for these proton transfer reactions presumably are larger than for proton transfer at electronegative atoms, because of the relatively weak stabilization of the transition state by hydrogen bonding to carbon (see above). 2. A related, but more involved explanation has been offered to account for the small intrinsic barrier for deprotonation of a-cyano carbon compared with acarbonyl carbon [13]. 3. The Marcus intrinsic barriers for deprotonation of carbon acids to form enolates that are stabilized by resonance delocalization of negative charge from carbon to oxygen are larger than for deprotonation of carbon acids to form carbanions where the charge is localized mainly at carbon. 4. The difference in the Marcus intrinsic barriers for deprotonation of cationic (middle correlation) and neutral (bottom correlation) a-carbonyl carbon is consistent with a greater localization of negative charge at the a-carbon (right-hand resonance structure for a simple ester enolate, Scheme 1.8) of the formally neutral enolate zwitterions of cationic monocarbonyl carbon acids compared with the anionic enolates of monocarbonyl carbon acids. A simple explanation for this difference in resonance delocalization of charge is that it is due to the enhancement of polar interactions between opposing charges that occurs as negative charge is shifted from oxygen to the cation-bearing carbon of the enolate zwitterion [12, 14].
Scheme 1.8
5. The lower correlation on Fig. 1.3 for deprotonation of neutral a-carbonyl carbon is linear, with a slope of 0.4 for carbon acids of pK a < 30. By comparison, the simple Marcus equation (Eq. (1.9)) requires curvature for such rate equilibrium correlations and tangential slopes of >0.5 for thermodynamically unfavorable proton transfer [46, 50]. The absence of curvature and the reduced slope for this lower correlation are consistent with an increasing intrinsic carbon acid
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1 Proton Transfer to and from Carbon in Model Reactions
Table 1.1. Rate constants, equilibrium constants, and Marcus intrinsic reaction barriers for deprotonation of a-carbonyl carbon by hydroxide ion in water[a].
Carbon acid
Carbanion
log K eq
log kOH (MC1 sC1 )
L (kcal molC1 )
2.3
1.0
17.6
4.3
1.4
16.3
10.3
3.4
14.2
intrinsic barriers L were calculated using the rate and equilibrium constants summarized in Ref. [11] and Eq. (1.10).
a The
reactivity with decreasing carbon acidity, due to a decreasing Marcus intrinsic barrier for proton transfer [11]. The magnitude of this decrease is shown in Table 1.1 which reports intrinsic barriers L calculated using Eq. (1.10) [75] and representative individual rate and equilibrium data for the lower correlation from Fig. 1.3. 1 1:36 logðK w =K a Þ 17:44 L 1 log k p ¼ 1:36 4L
ð1:10Þ
Table 1.1 shows that there is a significant decrease in the Marcus intrinsic barrier L with decreasing acidity of a-carbonyl hydrogen that correlates well with the decreasing resonance stabilization of the product carbanion [11]. Many such correlations between intrinsic reaction barrier and resonance delocalization of charge at the product carbanion have been observed for proton transfer reactions at carbon [67, 76, 77]. The increase in the Marcus intrinsic barrier for deprotonation of carbon with increasing resonance stabilization of the carbanion product is observed because the fractional expression of the carbanion-stabilizing resonance substituent effect at the reaction transition state is smaller than predicted by the simple Marcus equation, which assumes that the intrinsic reaction barrier is independent of driv-
1.5 Small Molecule Catalysis of Proton Transfer at Carbon
ing force. This has been described by Jencks as an imbalance between the relatively small expression of resonance substituent effects at the reaction transition state (these effects cause the intrinsic reaction barrier to change), compared with the larger expression of polar substituent effects (these effects do not greatly affect the intrinsic reaction barrier) [78]. Bernasconi refers to the same phenomenon as nonperfect synchronization of polar and resonance substituent effects at the transition state [67, 76, 77]. Kresge has proposed that imbalances between the expression of polar and resonance substituent effects are observed at the transition state for deprotonation of carbon because [79]: (i) The fraction of the effect of polar electron-withdrawing substituents X on the equilibrium constant for proton transfer that is expressed at the reaction transition state is roughly proportional to the fractional buildup of negative charge at the reacting carbon (a), which in turn depends upon the fractional bonding between hydrogen and carbon at this transition state (1 a) (20). (ii) The fraction of the overall effect of resonance electron-withdrawing substituents Y on the equilibrium constant for proton transfer that is expressed at the transition state is less than expected for a transition state with fractional charge a, because the resonance interaction depends not only upon this fractional transition state charge, but is further reduced because delocalization of charge at the partly sp 3 -hybridized carbon of the transition state will be less effective than delocalization at the planar sp 2 -hybrized carbon for the product enolate.
It has been proposed that part or all of the intrinsic barrier for deprotonation of acarbonyl carbon is associated with the requirement for solvation of the negatively charged oxygen of the enolate anion [80]. However, the observation of small intrinsic barriers for deprotonation of oxygen acids by electronegative bases to form solvated anions [31] suggests that the requirement for a similar solvation of enolate anions should not make a large contribution to the intrinsic barrier for deprotonation of a-carbonyl carbon.
1.5
Small Molecule Catalysis of Proton Transfer at Carbon
Deprotonation of a-carbonyl carbon is catalyzed by small Brønsted bases, which react directly to abstract a proton from carbon (Scheme 1.9A); by small Brønsted
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1 Proton Transfer to and from Carbon in Model Reactions
Scheme 1.9
acids, which stabilize negative charge at the enolate oxygen by proton transfer (Scheme 1.9B); and by metal cations, which provide electrostatic stabilization of charge at the enolate oxygen (Scheme 1.9C). Finally, catalysis by the concerted reaction of a Brønsted base to abstract a proton from carbon and a Brønsted acid (Scheme 1.9D) or metal cation (Scheme 1.9E) electrophile to stabilize negative charge at oxygen is sometimes observed. 1.5.1
General Base Catalysis
Scheme 1.10 shows the relative importance of general base catalysis of deprotonation of several carbon acids, where the catalytic effectiveness is defined as the rela-
Scheme 1.10
1.5 Small Molecule Catalysis of Proton Transfer at Carbon
tive acceleration of the solvent reaction observed at 1 M buffer catalyst. Deprotonation of dihydroxyacetone phosphate (DHAP) by 1.0 M quinuclidinone buffer (pK a ¼ 7:5) at pH 7.0 and 25 C is 10 5 -times faster than deprotonation by hydroxide ion under the same conditions [24]. The greater reactivity of quinuclidinone compared with hydroxide ion toward deprotonation of DHAP is due to [81]: (i) hydroxide ion being an intrinsically unreactive base for its pK a and, (ii) the relatively small value of b ¼ 0:5 [24] for this proton transfer reaction, which causes the importance of general base catalysis to increase with decreasing pH and pK a of the buffer catalyst. The low intrinsic reactivity of hydroxide ion compared with other buffer bases toward deprotonation of a variety of carbon acids is known as the lyoxide ion anomaly [50, 82]. Good buffer catalysis is observed for deprotonation of ethyl acetate by substituted quinuclidinone due to the anomalously low reactivity of hydroxide ion. However, this catalysis is much weaker than for deprotonation of DHAP (Scheme 1.10) due to the larger value of b ¼ 1:09 for proton transfer [11]. There is only weak catalysis of deprotonation of the cationic amino acid ester 18 by quinuclidinol (pK a ¼ 10:0) [14]. Here the value of b ¼ 0:92 for proton transfer is large, and the intrinsic reactivity of hydroxide ion compared to tertiary amines toward deprotonation of cationic carbon acid is much greater than for deprotonation of neutral a-carbonyl carbon. The difference in the magnitude of the lyoxide ion anomaly for deprotonation of cationic (small anomaly) and neutral carbon acids (large anomaly) shows that this anomaly is partly electrostatic in origin [14]. There is no detectable buffer catalysis of exchange of deuterium for the a-methyl hydrogen of acetonitrile in D2 O (Scheme 1.10) [13]. This is because the ratedetermining step for the competing DO -catalyzed reaction is rotation of the D2 O into a reactive conformation with a rate constant k r A 10 11 s1 (Scheme 1.4) that is independent of the concentration of buffer bases [13]. The observation that buffer catalysis of exchange of deuterium for a-methyl hydrogen of the neutral carbon acid acetamide (Scheme 1.10) is just barely detectable provides evidence that this reaction also proceeds through a very reactive amide enolate, that is protonated by water with a rate constant that is approaching the value for a rotation limited reaction [17]. 1.5.2
Electrophilic Catalysis
Brønsted general acid catalysis of the deprotonation of acetone by water (Scheme 1.9B) can only be detected for strong buffer acids such as acetic acid (pK a ¼ 4:8) [83], that provide a strong thermodynamic driving force for protonation of the relatively weakly basic enolate ion (pK a ¼ 10:9 for enol acetone [37]) [84]. Again, general acid catalysis is weak, because of the high reactivity of hydronium ion in the competing solvent reaction. There is no obvious pattern in the metal ion requirements of enzymes that catalyze proton transfer at carbon. For example, mannose 6-phosphate isomerase [85] is a metalloenzyme while triosephosphate isomerase [86] and glucose 6-phosphate
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1 Proton Transfer to and from Carbon in Model Reactions
isomerase [87] are not. The observation that enzyme catalysts may use either metal cations or Brønsted acids to stabilize negative charge that develops at the enolate oxygen shows that both types of catalysis are viable, and raises questions about the imperatives for the observation of catalysis by one mechanism rather than another. In fact, there are only small differences between the second-order rate constant for nonenzymatic deprotonation of acetone by acetate anion and the third-order rate constants for catalysis of this reaction by acetic acid and Zn 2þ , so that the stabilities of the transition states for the acetate-ion-promoted reactions assisted by Zn 2þ , acetic acid and solvent water (55 M) are similar (Scheme 1.11) [19]. Scheme 1.11 shows that acetic acid and Zn 2þ , stabilize the transition state for proton transfer from acetone to acetate anion by 1.9 and 3.3 kcal mol1 , respectively, relative to a common standard state of 1 M water and 1 M electrophile.
Scheme 1.11
There is an increase in the importance of electrophilic catalysis by zinc cation relative to acetic acid for deprotonation of the a-carbonyl carbons of hydroxyacetone, a substrate which provides a second stabilizing chelate interaction between the hydroxy group at the substrate and the metal dication that is expressed at transition state for proton transfer [19]. For example, the third-order rate constants kT for the Zn 2þ -assisted acetate-ion-promoted deprotonation of the a-CH3 and a-CH2 OH groups of hydroxyacetone are 32-fold and 770-fold larger, respectively, than the corresponding second-order rate constants kAcO for proton transfer to acetate anion ‘‘assisted’’ by solvent water that is present at 55 M (Scheme 1.12). This shows that Zn 2þ stabilizes the transition state for proton transfer from the a-CH3
1.5 Small Molecule Catalysis of Proton Transfer at Carbon
Scheme 1.12
and a-CH2 OH groups of hydroxyacetone by 4.4 and 6.3 kcal mol1 , respectively, relative to a common standard state of 1 M water and 1 M Zn 2þ . A similar chelation of metal to enzyme-bound substrate may also contribute to enzyme catalysis of proton transfer at carbon. For example, X-ray crystallographic analysis of complexes between 3-keto-l-gulonate 6-phosphate decarboxylase and analogs of the 1,2-enediolate reaction intermediate provide evidence that the essential magnesium dication is stabilized by coordination to both the C-2 oxygen and the nonreacting C-3 hydroxy of the reaction intermediate [88]. In summary, catalysis of proton transfer at carbon in water by the small molecule reactions shown in Scheme 1.9 is generally weak. Small Brønsted acid and base buffer catalysts do not act to reduce the large thermodynamic barrier to endothermic proton transfer reactions (DG , Fig. 1.1), which constitutes most of the observed activation barrier (DGf y ). Buffer catalysis is the result of the lower Marcus intrinsic barrier for the buffer compared to the competing solvent-catalyzed reaction and catalysis is weak because the effect of these buffers on the intrinsic reaction barrier is small. The formation of a stable chelate between a metal cation and the product enolate anion may reduce the thermodynamic driving force for deprotonation at the a-carbonyl carbon compared with the solvent reaction. This results in effective metal cation catalysis when there is a second group to chelate the metal cation, such as the hydroxy group of hydroxyacetone [19]. The relatively weak catalysis by Zn 2þ observed in the absence of a second chelating group shows that this cation does not cause a large reduction in the intrinsic barrier for the competing solvent-catalyzed proton transfer reaction.
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1.6
Comments on Enzymatic Catalysis of Proton Transfer
Studies on proton transfer to and from carbon in model reactions have shown that the activation barrier to most enzyme-catalyzed reactions is composed mainly of the thermodynamic barrier to proton transfer (Fig. 1.1), so that in most cases this barrier for proton transfer at the enzyme active site will need to be reduced in order to observe efficient catalysis. A smaller part of the activation barrier to deprotonation of a-carbonyl carbon is due to the intrinsic difficulty of this reaction to form a resonance stabilized enolate. There is evidence that part of the intrinsic barrier to proton transfer at a-carbonyl carbon reflects the intrinsic instability of negative charge at the transition state of mixed sp 2 –sp 3 -hybridization at carbon [79]. Small buffer and metal ion catalysts do not cause a large reduction in this intrinsic reaction barrier. There is extensive evidence from site-directed mutagenesis and other studies of enzymes that catalyze proton transfer that acidic and basic amino side chains and, in some cases, metal cations, are required for the observation of efficient catalysis. However, catalysis of the deprotonation of a-carbonyl by small molecule analogs of these side chains, and by metal cations is generally weak. Relatively little attention has been directed towards understanding the mechanism for the ‘‘enhancement’’ of Brønsted acid/base and electrophilic catalysis for enzyme-catalyzed reactions [89]. An apparent enhancement of Brønsted acid base catalysis will result if there is a greater driving force for proton transfer to the catalytic base at the enzyme active site compared with solution. One mechanism to increase the thermodynamic driving force for deprotonation of a-carbonyl carbon at an enzyme-bound substrate compared to proton transfer in solution is to use an enzyme active site of low overall dielectric constant where there are several precisely oriented polar groups of opposite charge or dipole moment from the enolate anion to provide electrostatic stabilization of this anion. In addition, catalysis of deprotonation of cationic carbon acids will be strongly favored at a nonpolar enzyme active site by the strong stabilizing intramolecular electrostatic interaction at the product zwitterionic enolate anion [14, 18, 90]. There may also be a reduction in the intrinsic barrier for proton transfer at the enzyme active site compared to solution [80]. This possibility is intriguing; however, we are unable to offer a convincing mechanism for such a reduction of intrinsic reaction barrier.
Acknowledgment
We acknowledge the National Institutes of Health Grant GM 39754 for its generous support of the work from our laboratory described in this review.
References
References 1 R. Wolfenden, M. J. Snider Acc. 2 3
4 5
6
7 8
9 10
11 12 13 14
15
16
17
18
Chem. Res. 2001, 34, 938–945. S. L. Bearne, R. Wolfenden J. Am. Chem. Soc. 1995, 117, 9588–9589. W. S. Matthews, J. E. Bares, J. E. Bartmess, F. G. Bordwell, F. J. Cornforth, G. E. Drucker, Z. Margolin, R. J. McCallum, G. J. McCollum, N. R. Vanier J. Am. Chem. Soc. 1975, 97, 7006–7014. R. W. Taft, F. G. Bordwell Acc. Chem. Res. 1988, 21, 463–469. M. M. Kreevoy, E. H. Baughman J. Am. Chem. Soc. 1973, 95, 8178– 8179. T. Aroella, C. H. Arrowsmith, M. Hojatti, A. J. Kresge, M. F. Powell, Y. S. Tang, W. H. Wang J. Am. Chem. Soc. 1987, 109, 7198–7199. A. J. Kresge, M. F. Powell Int. J. Chem. Kinet. 1982, 14, 19–34. R. L. D’Ordine, B. J. Bahnson, P. J. Tonge, V. E. Anderson Biochemistry 1994, 33, 14734–14742. T. L. Amyes, J. P. Richard J. Am. Chem. Soc. 1992, 114, 10297–10302. R. W. Nagorski, T. Mizerski, J. P. Richard J. Am. Chem. Soc. 1995, 117, 4718–4719. T. L. Amyes, J. P. Richard J. Am. Chem. Soc. 1996, 118, 3129–3141. A. Rios, J. P. Richard J. Am. Chem. Soc. 1997, 119, 8375–8376. J. P. Richard, G. Williams, J. Gao J. Am. Chem. Soc. 1999, 121, 715–726. A. Rios, T. L. Amyes, J. P. Richard J. Am. Chem. Soc. 2000, 122, 9373– 9385. A. Rios, J. Crugeiras, T. L. Amyes, J. P. Richard J. Am. Chem. Soc. 2001, 123, 7949–7950. A. Rios, J. P. Richard, T. L. Amyes J. Am. Chem. Soc. 2002, 124, 8251– 8259. J. P. Richard, G. Williams, A. C. O’Donoghue, T. L. Amyes J. Am. Chem. Soc. 2002, 124, 2957–2968. G. Williams, E. P. Maziarz, T. L. Amyes, T. D. Wood, J. P. Richard Biochemistry 2003, 42, 8354–8361.
19 J. Crugeiras, J. P. Richard J. Am.
Chem. Soc. 2004, 126, 5164–5173. 20 T. L. Amyes, S. T. Diver, J. P.
21 22 23 24 25 26
27 28
29 30
31 32
33 34
35 36
37
38
Richard, F. M. Rivas, K. Toth J. Am. Chem. Soc. 2004, 126, 4366– 4374. A. Sievers, R. Wolfenden J. Am. Chem. Soc. 2002, 124, 13986–13987. R. C. Cavestri, L. R. Fedor J. Am. Chem. Soc. 1970, 92, 4610–4613. L. R. Fedor, W. R. Glave J. Am. Chem. Soc. 1971, 93, 985–989. J. P. Richard J. Am. Chem. Soc. 1984, 106, 4926–4936. J. P. Richard, R. W. Nagorski J. Am. Chem. Soc. 1999, 121, 4763–4770. K. Toth, T. L. Amyes, J. P. Richard, J. P. G. Malthouse, M. i. E. Ni’Beilliu J. Am. Chem. Soc. 2004, 126, 10538–10539. E. Tapuhi, W. P. Jencks J. Am. Chem. Soc. 1982, 104, 5758–5765. J. P. Guthrie, J. Cossar, A. Klym J. Am. Chem. Soc. 1984, 106, 1351– 1360. Y. Chiang, A. J. Kresge Science 1991, 253, 395–400. J. R. Keeffe, A. J. Kresge, in The Chemistry of Enols, Rappoport, Z. (Ed.), John Wiley and Sons, Chichester, 1990, pp. 399–480. M. Eigen Angew. Chem., Int. Ed. Engl. 1964, 3, 1–72. W. P. Jencks, M. T. Haber, D. Herschlag, K. L. Nazaretian J. Am. Chem. Soc. 1986, 108, 479–483. U. Kaatze J. Chem. Eng. Data 1989, 34, 371–374. U. Kaatze, R. Pottel, A. Schumacher J. Phys. Chem. 1992, 96, 6017–6020. K. Giese, U. Kaatze, R. Pottel J. Phys. Chem. 1970, 74, 3718–3725. Y. Chiang, A. J. Kresge, P. Pruszynski J. Am. Chem. Soc. 1992, 114, 3103–3107. Y. Chiang, A. J. Kresge, Y. S. Tang, J. Wirz J. Am. Chem. Soc. 1984, 106, 460–462. Y. Chiang, A. J. Kresge, V. V. Popik,
971
972
1 Proton Transfer to and from Carbon in Model Reactions
39
40 41
42
43 44
45 46 47 48 49 50 51 52 53 54 55 56 57 58
59
60
N. P. Schepp J. Am. Chem. Soc. 1997, 119, 10203–10212. D. C. Hawkinson, T. C. M. Eames, R. M. Pollack Biochemistry 1991, 30, 10849–10858. W. J. Albery, J. R. Knowles Biochemistry 1976, 15, 5631–5640. R. K. Poyner, W. W. Cleland, G. H. Reed Biochemistry 2001, 40, 8009– 8017. W. L. Jorgensen, J. M. Briggs, J. Gao J. Am. Chem. Soc. 1987, 109, 6857– 6858. K. B. Wiberg, H. Castejon J. Org. Chem. 1995, 60, 6327–6334. Y. Chiang, M. Hojatti, J. R. Keeffe, A. J. Kresge, N. P. Schepp, J. Wirz J. Am. Chem. Soc. 1987, 109, 4000– 4009. M. W. Washabaugh, W. P. Jencks Biochemistry 1988, 27, 5044–5053. R. A. Marcus J. Phys. Chem. 1968, 72, 891–899. R. A. Marcus J. Chem. Phys. 1956, 24, 966–978. R. A. Marcus J. Chem. Phys. 1957, 26, 872–877. R. A. Marcus J. Chem. Phys. 1957, 26, 867–871. A. J. Kresge Chem. Soc. Rev. 1974, 2, 475–503. R. A. Marcus J. Am. Chem. Soc. 1969, 91, 7224–7225. J. P. Richard Tetrahedron 1995, 51, 1535–1573. W. J. Albery, M. M. Kreevoy Adv. Phys. Org. Chem. 1978, 16, 87–157. E. S. Lewis, D. D. Hu J. Am. Chem. Soc. 1984, 106, 3292–3296. J. P. Guthrie ChemPhysChem 2003, 4, 809–816. J. P. Guthrie J. Am. Chem. Soc. 1997, 119, 1151–1152. E. Grunwald J. Am. Chem. Soc. 1985, 107, 125–133. C. F. Bernasconi, P. J. Wenzel J. Am. Chem. Soc. 1994, 116, 5405– 5413. C. F. Bernasconi, P. J. Wenzel J. Am. Chem. Soc. 1996, 118, 10494– 10504. C. F. Bernasconi, P. J. Wenzel, J. R. Keeffe, S. Gronert J. Am. Chem. Soc. 1997, 119, 4008–4020.
61 C. F. Bernasconi, P. J. Wenzel J. Am.
Chem. Soc. 2001, 123, 7146–7153. 62 C. F. Bernasconi, P. J. Wenzel J. Am.
Chem. Soc. 2001, 123, 2430–2431. 63 C. F. Bernasconi, P. J. Wenzel J. Org.
Chem. 2001, 66, 968–979. 64 J. E. Van Verth, W. H. Saunders, Jr.
J. Org. Chem. 1997, 62, 5743–5747. 65 J. W. Bunting, J. P. Kanter J. Am.
Chem. Soc. 1993, 115, 11705–11715. 66 J. P. Richard, T. L. Amyes, M. M.
67 68 69 70 71 72 73 74
75 76 77 78 79 80 81 82 83
84 85
Toteva Acc. Chem. Res. 2001, 34, 981–988. C. F. Bernasconi Tetrahedron 1985, 41, 3219–3234. R. A. Bednar, W. P. Jencks J. Am. Chem. Soc. 1985, 107, 7117–7126. Y. Pan, M. A. McAllister J. Am. Chem. Soc. 1998, 120, 166–169. Y. Pan, M. A. McAllister J. Org. Chem. 1997, 62, 8171–8176. S. Scheiner, T. Kar J. Am. Chem. Soc. 1995, 114, 6970–6975. C. L. Perrin Science 1994, 266, 1665–1668. C. L. Perrin, J. B. Nielson J. Am. Chem. Soc. 1997, 119, 12734–12741. S. N. Vinogradov, R. H. Linnell Hydrogen Bonding, Van NostrandReinhold, New York, 1971, pp. 120–124. J. P. Guthrie J. Am. Chem. Soc. 1991, 113, 7249–7255. C. F. Bernasconi Acc. Chem. Res. 1987, 20, 301–308. C. F. Bernasconi Adv. Phys. Org. Chem. 1992, 27, 119–238. D. A. Jencks, W. P. Jencks J. Am. Chem. Soc. 1977, 99, 7948–7960. A. J. Kresge Can. J. Chem. 1974, 52, 1897–1903. J. A. Gerlt, P. G. Gassman J. Am. Chem. Soc. 1993, 115, 11552–11568. W. P. Jencks Acc. Chem. Res. 1976, 9, 425–432. M. W. Washabaugh, W. P. Jencks J. Am. Chem. Soc. 1989, 111, 683–692. A. F. Hegarty, J. P. Dowling, S. J. Eustace, M. McGarraghy J. Am. Chem. Soc. 1998, 120, 2290–2296. W. P. Jencks J. Am. Chem. Soc. 1972, 94, 4731–4732. R. W. Gracy, E. A. Noltmann J. Biol. Chem. 1968, 243, 4109–4116.
References 86 K. A. Komives, L. C. Chang, E. Lolis,
88 E. L. Wise, W. S. Yew, J. A. Gerlt, I.
R. F. Tilton, G. A. Petsko, J. R. Knowles Biochemistry 1991, 30, 3011–3019. 87 C. J. Jeffrey, R. Hardre´, L. Salmon Biochemistry 2001, 40, 1560– 1564.
Rayment Biochemistry 2003, 42, 12133–12142. 89 J. P. Richard Biochemistry 1998, 37, 4305–4309. 90 J. P. Richard, T. L. Amyes Bioorg. Chem. 2004, 32, 354–366.
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General Acid–Base Catalysis in Model Systems Anthony J. Kirby 2.1
Introduction
Proton transfer is the most common reaction in living systems, in which reactions have to be strictly controlled, and most are catalyzed by enzymes. The great majority of enzyme catalyzed reactions are ionic, involving heterolytic bond making and breaking, and thus the creation or neutralization of charge. Under conditions of constant pH this requires the transfer of protons (Eq. (2.1)).
ð2:1Þ
General acid and general base catalysis are terms commonly used to describe two different characteristics of reactions, the (observable) form of the rate law or a (hypothetical) reaction mechanism proposed to account for it. It is important to be aware of (and for authors to make clear) which is meant in a particular case. General acid–base catalysis provides mechanisms for bringing about the necessary proton transfers without involving hydrogen or hydroxide ions, which are present in water at concentrations of only about 107 M under physiological conditions. At pHs near neutrality relatively weak acids and bases can compete with lyonium or lyate species because they can be present in much higher concentrations. 2.1.1
Kinetics
The basics of general acid and general base catalysis are described clearly and in detail in Chapter 8 of Maskill [1]. Acid–base catalysis is termed specific if the rate of the reaction concerned depends only on the acidity (pH, etc.) of the medium. This is the case if the reaction involves the conjugate acid or base of the reactant preformed in a rapid equilibrium process – normal behavior if the reactant is weakly basic or acidic. The conjugate acid or base is then, by definition, a strong Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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acid or base, and the reverse proton transfer to solvent is thus rapid, probably diffusion-controlled – and certainly faster than a competing forward reaction involving the making or breaking of covalent bonds. This forward reaction of the conjugate acid or base of the reactant is therefore rate determining, and the rate expression – for example for the hydrolysis of an unreactive ester (Scheme 2.1) – contains only a single term in (lyonium) acid concentration: d½1:1=dt ¼ kH ½1:1½H3 Oþ
Scheme 2.1
General acid–base catalysis is defined experimentally by the appearance in the rate law of acids and/or bases other than lyonium or lyate ions. For example, the hydrolysis of enol ethers 1.2 (Scheme 2.2) is general acid-catalyzed. In strong acid the rate expression will be the same as in Scheme 2.1, but near neutral pH the rate is found to depend also on the concentration of the buffer ðHA þ A Þ used to maintain the pH. Measurements at different buffer ratios show that the catalytic species is the acid HA. (If more than one acid is present there will be an additional term kHAi ½HAi ½1:2 for each.) d½1:2=dt ¼ kH ½1:2½H3 Oþ þ kHA ½1:2½HA
Scheme 2.2
If in these experiments the measurements at different buffer ratios showed that the catalytic species was the conjugate base A the reaction would be kinetically general base catalyzed. In which case HA and A would probably subsequently be referred to as BHþ and B. Thus the enolisation of ketones is general base catalysed (Scheme 2.3). d½1:3=dt ¼ kH ½1:3½HO þ kBi ½1:3½Bi
2.1 Introduction
Scheme 2.3
The rate constants kHA and kB depend on the strength of the acid or base, and for a given reaction are correlated by the Bro¨nsted equation: conventionally written for general acid and general base catalyzed reactions, respectively: log kHA ¼ a log KHA þ constant ¼ apKHA þ constant log kB ¼ b log KB þ constant ¼ b pKB þ constant The pK a s used are those of the conjugate acids, HA and BHþ . 2.1.2
Mechanism
Enzymes have evolved highly efficient mechanisms for catalysis under physiological conditions. Such mechanisms must avoid high energy intermediates, with their associated high energy barriers. So potential high energy species – such as the ions Xþ and Y in Eq. (2.1), above, need to be neutralised as part of the reaction. This is accomplished in water by the very general mechanism outlined in Scheme 2.4 (the bond that breaks may be either a s- or p-bond).
Scheme 2.4
Here a water molecule 2 acts as a nucleophile, generating the potentially strongly acidic H2 Oþ aX; but in a suitable buffered solution this can be neutralised, as part of the reaction, by a series of rapid proton transfers. Variants of this general mechanism account for almost all solvolyses in protic solvents giving, for sufficiently reactive systems, reactions which can be observed and studied in mechanistic detail.
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The mechanism of Scheme 2.4 is generalised further in Scheme 2.5. Water molecule 1 (Scheme 2.4), which removes the proton from the incipient H2 Oþ aX, acts formally as a general base. Water molecule 3 (Scheme 2.4) acts as a general acid, transferring a proton to the potential strong base Y. (Y ¼ C is a special case because the proton is transferred directly to an X–Y bonding orbital rather than to a lone pair on Y. See Section 2.4, below.)
Scheme 2.5
The mechanism of Scheme 2.5 is a general solution to the problem of avoiding high energy intermediates, and offers the prospect of seriously low activation energies: because a wide range of weak acids and bases are nevertheless much stronger acids, bases and nucleophiles than water. It is not however observed in solution under normal conditions because it requires the (entropically) prohibitively unfavorable encounter of four separate molecules – general acid, general base, nucleophile and substrate. Most observed reactions involve successful bimolecular encounters, and there is an entropic price to pay for the specific involvement even of solvent molecules. However, the mechanism of Scheme 2.5 might have been designed for an enzyme reaction (rather than, presumably, vice versa), since in the active site all the components bar the substrate (the molecule X–Y) come preassembled. Scheme 2.5 does indeed describe the mechanisms of many enzyme reactions, of which the serine proteases are perhaps the most familiar [2]. (Concerted) steps 1 and 2 of Scheme 2.5 define the ‘‘classical’’ general base catalysis mechanism, and step 3 the ‘‘classical’’ general acid catalysis mechanism. When step 3 is rate determining the ‘‘general acid’’ HA is present in the rate determining transition state, and thus appears in the observed rate law. The same applies to the ‘‘general base’’ B, when (concerted) steps 1 and 2 are rate determining. Thus the defining element of general acid–base catalysis is a rate determining step involving proton transfer. Proton transfers between electronegative centers, especially O and N, are known to be so fast in the thermodynamically favorable direction that they are diffusion-controlled, so are likely to be rate determining only if they involve species – particularly high energy intermediates – that are present in only very low concentration. For example, the very fast hydrolysis of dialkyl maleamic acids 1 (half-life < 1 s at 15 C) is general acid catalysed Scheme 2.6) [3]. The rate determining step was identified as the proton transfer that converts the tetrahedral intermediate T 0 to the zwitterion TG (and thus the amine to a viable leaving
2.1 Introduction
Scheme 2.6
group), and the reaction behaves, as expected, as a diffusion-controlled reaction. A similar, more recent, example is the general acid catalyzed cyclization of 1amino-8-trifluoroacetylaminonaphthalene [4]. In ‘‘classical’’ general-acid–base catalysis (Scheme 2.5) the proton transfer step is slow because it is concerted with the formation or cleavage of a bond between heavy (non-hydrogen) atoms. This broad generalisation includes the familiar general base catalyzed enolisation and related processes involving proton transfer to and from carbon. Such reactions are often considered to be ‘‘intrinsically’’ slow, but this is not fundamentally because of the involvement of a CaH bond as such, but because a carbanion is generally formed only in situations where the negative charge can be delocalised on to a more electronegative center (see, for example, Scheme 2.3): as before, the proton transfer step is relatively slow because it is concerted with the formation of a bond between heavy (non-hydrogen) atoms, which requires geometrical changes. Where no such geometrical changes are involved – for example in the ionization of HaCN or the C(2)aH bond of the thiazolium system, the proton transfers are (more or less) normal diffusion-controlled processes [5, 6]. Detailed mechanisms for proton transfers from carbon do of course show significant differences from those between two electronegative centers. These include the shape and height of the energy barrier to the reaction, and the absence of significant hydrogen bonding between CaH and solvent or general base in protic solvents. For these reasons they are discussed separately, in Section 2.4 below. 2.1.3
Kinetic Equivalence
The simple examples quoted so far might suggest that the observation of general acid or general base kinetics is prima facie evidence for the mechanisms of the same name. This is not the case, for the usual reasons of (i) kinetic equivalence (the proton is a uniquely mobile species), and (ii) the absence of direct evidence from the rate law of the involvement of the solvent (for example, water molecule 2 in Scheme 2.5). Thus (i) the kinetically observed general acid catalysis of ketone enolisation is explained not by the general acid catalysis mechanism a (Scheme 2.7) but by the kinetically equivalent specific acid–general base catalysis mecha-
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Scheme 2.7
nism b (which requires only bimolecular encounters). Similarly, general base catalysis of the breakdown of acetaldehyde hemiacetals is accounted for by general acid catalysis of the reaction of the hemiacetal anion [7]. Finally (ii), a common mechanistic problem is to distinguish between nucleophilic and general base catalysis in cases where the products are the same. A strong base is generally a good nucleophile (depending on the electrophilic center concerned), and the rate expressions will be identical for the two mechanisms. A classical example is catalysis of the hydrolysis of substituted acetate esters by acetate anion (Scheme 2.8): acetate acts as a nucleophile for esters with very good leaving groups like 2,4-dinitrophenolate, but as a general base for poor leaving groups like phenolate. For leaving groups of intermediate basicity, such as pnitrophenolate, both mechanisms are observed.
Scheme 2.8
The partitioning of the tetrahedral intermediate T of the nucleophilic mechanism is the key: acetate is eliminated preferentially, to regenerate the starting ester, if the leaving group is poor; but the elimination of better aryloxide leaving groups, to generate acetic anhydride (as a second intermediate, which can be trapped) be-
2.2 Structural Requirements and Mechanism
comes increasingly competitive. Acetate acting as a nucleophile can displace a phenolate of pK a some 3 units higher: the general base catalysis mechanism delivers hydroxide, effectively irreversibly, but is at an entropic disadvantage. Other things being equal, nucleophilic catalysis wins, and careful experimental design may be necessary to isolate general base catalysis. (A simple example is the work of Butler and Gold [8] on the hydrolysis of acetic anhydride: catalysis by acetate anion can only be due to general base catalysis because the nucleophilic mechanism simply regenerates acetic anhydride.)
2.2
Structural Requirements and Mechanism
The central reaction in the general mechanism of Scheme 2.5 involves two proton transfers (1 and 3 in Scheme 2.9), supporting the transfer of the group X to the nucleophile Nu. (Note that in the reverse reaction the original general base becomes the general acid, and vice versa: general acid catalysis is the microscopic reverse of general base catalysis, and establishing a mechanistic pathway for one identifies it also for the other.) In the transition complex TC (Scheme 2.9) both protons are involved in hydrogen bonds: typical proton transfers between electronegative centers take place within hydrogen bonds.
Scheme 2.9
Jencks’ ‘‘libido rule’’ [9, 10] attempts to identify situations in which proton transfer can be expected to be concerted with the making or breaking of covalent bonds: ‘‘Concerted general acid–base catalysis of complex reactions in aqueous solution can occur only (a) at sites that undergo a large change in pK a in the course of the reaction, and (b) when this change in pK converts an unfavorable to a favorable proton transfer with respect to the catalyst; i.e., the pK of the catalyst is intermediate between the initial and final pK a values of the substrate site.’’ [9].
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2.2.1
General Acid Catalysis
These conditions are, in broad terms, necessary but not sufficient. Thus general acids with pK a s of 7 G 4, of potential interest in biological systems, are well qualified to assist in the cleavage of bonds to oxygen: since the pK a s of ester oxygens are negative but those of their alcohol cleavage products typically >14. For example, general acid catalysis is readily observed in the hydrolysis of orthoesters, and indeed of most systems with three (or more) O, N or S atoms attached to a central carbon atom: including the tetrahedral intermediates involved in the acyl transfer reactions of esters and amides. However, the hydrolysis of acetals is typically specific acid catalyzed, and general acid catalysis is observed only for special cases. The two mechanisms are always in competition, but specific acid catalysis involves at least one, and most often two, intermediates of relatively high energy, the conjugate acid and the oxocarbocation (Scheme 2.10).
Scheme 2.10
If either intermediate is too unstable general acid catalysis is observed. In the case of orthoesters (Scheme 2.10) the electronic effect of the third OR group stabilizes the oxocarbocation and makes the oxygen centers less basic: so that CaO cleavage occurs before proton transfer is complete (Scheme 2.10, HA ¼ H3 Oþ or a general acid) [11, 12]. Aryl but not alkyl tetrahydropyranyl acetals show general acid catalysis, for the same reason [13]; but aryl methyl acetals do not, because the methoxymethyl carbenium ion is not sufficiently stable. (This situation can lead to ‘‘enforced’’ general acid catalysis, when the specific acid catalyzed reaction requires nucleophilic assistance: if the nucleophile is the conjugate base of the general acid this will be observed as general acid catalysis.) At the other extreme, sufficient stabilization of the carbenium ion can have the same effect, as shown by the observation of general acid catalysis of tropolone diethyl acetal 2.1 (Scheme 2.10) [14]. And even
2.2 Structural Requirements and Mechanism
steric effects can shift the balance, as revealed by the appearance of general acid catalysis in the hydrolysis of benzaldehyde acetals derived from tertiary alcohols [15, 16]. The reverse of reactions of this sort, the general base catalyzed neutralization of carbenium ions by alcohols and water has been studied in some detail by Jencks and Richard [17]. Catalysis is seen only with the more stable substituted 1-phenylethyl carbocations, is most important for the reactions with weakly basic alcohols and disappears when diffusion processes begin to compete. Thus the reaction of CF3 CH2 OH with the 4-dimethylamino compound has a Bro¨nsted b of 0.33, but the low b of 0.08 for the trifluorethanolysis of the 4-methoxy compound is consistent with a transition state with no more than hydrogen-bonding between the general base and the nucleophilic alcohol, which is itself only weakly involved in bonding in the very early transition state for this reaction. This behavior marks the borderline with specific acid catalysis of the hydrolysis reaction of the trifluorethyl ether: and probably also that of the corresponding fluoride [18]. HF has a pK a in the region of 3, depending on the solvent, so proton transfer to fluoride is not favorable from a general acid with pK a > 3, and none is observed by cyanoacetic acid (pK a ¼ 2:2) [18]. General acid catalysis of the hydrolysis of a-glucosyl fluoride by phosphate and phosphonate monoanions is characterized by a low Bro¨nsted b-value of 0.15 [19], and is presumed to reflect a hydrogen-bonding or solvationlevel interaction of the incipient fluoride anion. 2.2.2
Classical General Base Catalysis
General base catalysis is readily observed for the hydrolysis of acyl-activated esters with poor leaving groups, such as ethyl dichloroacetate. It can also be observed in the hydrolysis of typical carboxylate derivatives by using formates. Stefanidis and Jencks studied a series of formate esters, with alcohol leaving groups with pK a s between 12.4 and 16 [20]. In this paper the mechanism is analyzed in detail, in the light of a comprehensive series of structure–reactivity correlations. Solvent deuterium isotope effects of 3.6–5.3 for the water reaction and 2.5–2.8 for the acetate catalyzed process, and Bro¨nsted b-values of 0.36–0.58 for the reaction catalyzed by a series of substituted acetate anions are all consistent with the classical mechanism (steps 1 and 2 of Scheme 2.5). In the hydrolysis of aryl formates both nucleophilic and general base catalysis by acetate are observed, the balance depending on the leaving group. For general base catalysis of the hydrolysis of more reactive esters both the Bro¨nsted b and the solvent deuterium isotope effect fall, as the transition state changes in the direction of hydrogen-bonding catalysis [20]. The same change, from classical general base to nucleophilic catalysis by selected nucleophilic bases, has been observed and studied recently for the hydrolysis of activated amides (an example is 1-benzoyl-3-phenyl-1,2,4-triazole 2.2, Scheme 2.11) [21], and is observed also for esters of various oxyacids of phosphorus. The changeover to general base catalysis of the hydrolysis of aryl dialkyl phosphates 2.3 parallels that of the corresponding aryl carboxylates [22]. Thus kH2O =D2O for ca-
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2 General Acid–Base Catalysis in Model Systems
Scheme 2.11
talysis of the hydrolysis of the 2,4-dinitrophenyl triester by 2,6-lutidine 2.4, for which nucleophilic catalysis is expected to be minimised for steric reasons, is 1.95, consistent with general base catalysis. Catalysis by pyridine, an unhindered nucleophile, is characterized by values of kH2O =D2O ranging from 1.14 to 1.73, as the pK a of the leaving group is increased, consistent with increasing amounts of general base catalysis: which accounts for some 50% of the reaction for the 4-nitrophenyl ester 2.3. A recent proton inventory study of the methanolysis of the three triesters (MeO)0-2 PO(OAr)3-1 is consistent with the classical one-proton catalytic bridge model [23]; though the solvent deuterium isotope effects are low (in the region of 1.7) and the distinction from a ‘‘generalized solvation effect’’ is less than clear cut. It is no coincidence that all the examples described so far involve proton transfer from general acids or bases to or from oxygen. Compared with the OH group a primary or secondary amine is already a strong nucleophile: and thiols RSH, with pK a s in the region of 9, are available as the strongly nucleophilic anions in significant amounts near neutrality. And sulfide sulfur is less basic, so less susceptible to general acid catalysis. 2.2.3
General Base Catalysis of Cyclization Reactions Nucleophilic Substitution General base catalysis in simple systems is typically a default mechanism, observed in the absence of strong acid or base, or nucleophilic alternatives. It is a relatively inefficient and often slow process, readily observed only with specially designed or activated substrates. The simplest way of increasing reactivity without using ‘‘unnatural’’ activated functional groups is to make reactions intramolecular. Systems where the general base catalysis is itself intramolecular are discussed below, in Section 2.3.5: we discuss here systems where the nucleophilic reaction it supports is intramolecular – that is, a cyclization reaction. General base catalysis of the SN 2 reaction is not generally observed, for various reasons. Amine nucleophiles do not need it, and hydroxy groups are very weakly nucleophilic towards soft, polarisable centers like sp 3 -carbon. The only wellauthenticated example of an intermolecular general base catalyzed nucleophilic displacement at sp 3 -hybridized carbon is the trifluoroethanolysis of the benzylsul2.2.3.1
2.2 Structural Requirements and Mechanism
fonium cation 2.5 [24]. This is evidently a very special substrate (the exception that proves the rule?): because the reaction of the corresponding benzyl bromide does not show catalysis, nor do the hydrolysis or ethanolysis of 2.5. The Bro¨nsted b for catalysis by substituted acetate anions is 0.26, consistent with the classical general base catalysis mechanism shown, but there is no significant solvent deuterium isotope effect, suggesting a mechanism near the minimalist, hydrogen bonding end of the spectrum. (By contrast, general base catalysis, by amines as well as oxyanions, is readily observed for the SN (Si)-type solvolysis reactions of alkoxy and aryloxysilanes (see Dietze [25] for leading references)). General base catalysis of SN 2-type reactions of ordinary aliphatic alcohols by oxyanions is observed in the cyclization of 4-chlorobutanol [26], and of the sulfonium cation 2.6 [27] (Scheme 2.12) at 50 C and 40 C, respectively. (Amine buffers prefer to demethylate 2.6.) In all cases (including the reaction of 2.5 discussed above) catalysis by oxyanions shows a low solvent deuterium isotope effect and a Bro¨nsted coefficient b of 0.26 G 0.1. This reaction may be something of a curiosity, but there is little doubt that it has been properly identified.
Scheme 2.12
Ribonuclease Models The most interesting, and certainly the best studied general base catalyzed cyclization reaction is the cleavage of RNA and of related model ribonucleotides (Scheme 2.13). Work on this topic designed to shed light on the mechanism of action of 2.2.3.2
Scheme 2.13
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ribonucleases is extensive enough to deserve a review of its own, and several are available [28, 29]. (Of much current interest is the same reaction catalyzed by ribozymes. The mechanisms involved are highly intriguing because the catalysts are themselves RNA molecules, so ill-equipped to support efficient general acid–base catalysis. For recent references to relevant mechanistic work see Kuzmin et al. [30].) The common nucleophile in ribonuclease enzymes, and thus in relevant models, is the 2 0 -OH group of the central nucleotide. The work of the Williams group [31] confirmed the mechanism of hydrolysis of uridyl esters (Scheme 2.14, base ¼ U) with good, substituted-phenol leaving groups as a relatively simple process, described by the simple general base catalysis mechanism (Bro¨nsted b ¼ 0:67), with 2:10 Ð 2:11 as the rate determining step (Scheme 2.14), followed by rapid breakdown of the presumed phosphorane (pentacovalent addition) intermediate dianion 2.11 to the reactive cyclic ester 2.8 (Scheme 2.13). Recent evidence for a non-linear Bro¨nsted (leaving group) plot for the alkaline hydrolysis of an extended (to include alcohol leaving groups R ¼ alkyl, base ¼ U) series of the same esters 2.7, is consistent with a transient intermediate, which rapidly breaks down to reactant and cyclic ester 2.8. This can only reasonably be the phosphorane 2.11.
Scheme 2.14
At or near neutral pH, when the leaving group is an alcohol (or a nucleoside or nucleotide) OH, the situation is more complicated. Apart from the protonation state of the initial reactant (relevant because of the extraordinarily low reactivity of phosphodiester anions [32]) the phosphorane 2.11 stands at a mechanistic crossroads (Scheme 2.14). The phosphorane dianion is certainly very short-lived and strongly basic, and can be protonated on any one of the five PaO oxygens. Protonation of O(2 0 ) by BHþ , which certainly starts in the correct position, will regenerate starting material. Alternatively BHþ , or another general acid, could neutralise one of the diastereotopic oxyanions. This opens the way to pseudorotation at the phosphorus center, which makes the 3 0 -oxygen a potential leaving group: subsequent general acid catalysis of PaO(3 0 ) cleavage (dashed arrow in 2.12) leads to isomerization to the 2 0 -phosphodiester [33]. Finally – the route used by ribonuclease enzymes – general acid catalyzed cleavage of the exocyclic PaOR bond gives the cyclic ester 2.8.
2.3 Intramolecular Reactions
All these processes compete with each other in well-designed model systems, and to establish detailed mechanisms relevant to the situation in natural RNA requires at least oligonucleotide substrates. For example, Beckmann et al. [34] studied the hydrolysis of the bond to the single ribonucleotide in TTUTT (thymidyl-thymidyl-uridyl-thymidyl-thymidine) catalyzed by imidazole buffers, and the Lo¨nnberg group have examined reactivity within longer sequences [35].
2.3
Intramolecular Reactions
There is an enormous gap between the rates of model reactions (which generally have to be studied using activated substrates like p-nitrophenyl esters) and those of the same reactions, of natural, unactivated substrates, going on in enzyme active sites. We can go a long way towards bridging this gap by studying intramolecular reactions. 2.3.1
Introduction
Groups held in close proximity on the same molecule can react with each other – depending on the geometry – much faster than the same groups on separate molecules. This is one of the fundamental reasons why enzyme reactions – between groups held in close proximity in the enzyme–substrate complex – can be so fast. Intramolecular reactions are faster because DS z – the entropy of activation (the probability of the reactant groups meeting) – is high: and fastest when the reaction is a cyclisation (corresponding to intramolecular nucleophilic catalysis), which may be particularly favorable enthalpically. The simple measure of efficiency is the effective molarity (EM), the (often hypothetical) concentration of the neighboring group needed to make the corresponding intermolecular process go at the same rate [36]. It is simply measured, as the ratio of the first order rate constant of the intramolecular reaction and the second order rate constant for the (as far as possible identical) intermolecular process. In some convenient cases both reactions can be observed simultaneously, (Scheme 2.15) [37], and EM ¼ k1 =k2 measured di-
Scheme 2.15
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rectly. More often, and always for EM > about 10, the ‘‘corresponding’’ intermolecular reaction is too slow to be measured under the same conditions (or at all), and extrapolations or estimates are needed. Analysis of the large number of effective molarities available in the literature leads to an important generalisation. For simple cyclisation reactions EMs up to 10 9 M are possible, even in conformationally flexible systems (and can be pushed as high as 10 13 M by building in ground state strain that is relieved in the transition state, as in the case of the cyclisation of the maleamic acids in Scheme 2.6, above): so the proximity effect could go a long way to explaining the high rates of enzyme reactions (which may involve accelerations of the order of 10 17a20 ). But for intramolecular general acid and general base catalysed reactions, like the aspirin hydrolysis of Scheme 2.15, EMs are typically much lower, usually <10 M [36]. This poses a real problem for attempts to explain the efficiency of enzyme catalysis, since proton transfer is the reaction most often involved in enzyme reactions. 2.3.2
Efficient Intramolecular General Acid–Base Catalysis
A major goal of recent work has been the development of systems showing more efficient intramolecular general acid and general base catalysis. The starting point was the unique known exception to the discouraging generalisation above. Various derivatives of salicylic acid are hydrolyzed with efficient intramolecular general acid catalysis by the COOH group. In the case of acetals, general acid catalysis was first identified as an intramolecular reaction, after it was suggested to contribute to the mechanism of action of lysozyme. Capon [38] showed that the glucoside 3.1 (Scheme 2.16), with the carboxyl group protonated, is hydrolyzed significantly faster than expected for an aryl glycoside; and detailed physical organic studies with the more reactive system 3.2 confirmed the mechanism shown (3.2, Scheme
Scheme 2.16
2.3 Intramolecular Reactions
2.16) in detail [39]. General acid catalysis is easily observed because it is highly efficient in salicylic acid derivatives [40]: and Buffet and Lamaty estimated an EM > 10 4 M for the reaction of 3.3 [41]. (Possible because there is measurable intermolecular general acid catalysis of the hydrolysis of aryl alkyl acetals of benzaldehyde.) Detailed studies with several systems derived from salicylic acid suggest that the key to the highly efficient catalysis is the strong intramolecular hydrogen bond in the salicylate anion produced (Scheme 2.16). This is known to raise the pK a of the phenolic OH group, to 12.95 at 25 C in water [42], so is worth some 4–5 kcal mol1 : even though the pK a s of the two groups concerned are not closely matched. New systems designed to test this conclusion confirm the central importance of the intramolecular hydrogen bond. Note that the proton transfer in mechanism 3.2 follows Jencks’ libido rule, evolving from strongly unfavorable in the reactant to strongly favorable in the product: so the hydrogen bond could be close to its strongest in the transition state. Strong intramolecular hydrogen bonds are not common in water because neighboring H-bond acceptor and donor groups are generally solvated separately, but a number of applicable cases are known involving phenol and COOH groups. The most reactive system with this combination of functional groups is the benzisoxazole 3.4 ðX ¼ NÞ (Scheme 2.17). The two acetals 3.4 (X ¼ N and CH) support a closer-to-linear, and therefore stronger, hydrogen bond between carboxyl and leaving group: which are not conjugated with each other – a factor which might have made the salicylate system a special case – because they are in separate rings.
Scheme 2.17
The benzisoxazole 3.4 ðX ¼ NÞ is hydrolyzed with a half-life of 31 s at 39 C, compared with 8 min for the salicylate derivative 3.2. Hydrolysis is faster, at least in part, because of the strength of the general acid (pK a 1.55 compared with 3.77). The benzofuran 3.4 ðX ¼ CHÞ, with pK a (3.84) close to that of the salicylate derivative 3.2, has a half-life of 3.3 min. If we assume that the small difference in geometries of the two systems 3.4 is not a factor, this is evidence that the efficiency of catalysis depends on the strength of the general acid. This may seem self-evident, but earlier structure–activity studies on substituted salicylic acid systems [39] indicated that though the rate of hydrolysis depends strongly on the pK a of the leaving group, it depends not at all on that of the catalytic COOH general acid. The point is
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Figure 2.1. pH rate profiles for the intramolecular general acid catalyzed hydrolysis of a typical substrate, for example an acetal (with no other ionizing group). Curve A describes the specific acid catalyzed reaction: at sufficiently high pH reaction becomes pHindependent and a spontaneous, ‘‘water-
catalyzed’’ process is observed. Curves B and C show the effect on the rate of adding a catalytic group (for example COOH) ionizing with pK a s of 2.22 and 6.22, respectively, if the efficiency of catalysis is independent of the pK a .
an important one: if the efficiency of a general acid is independent of its pK a its rate advantage over specific acid-catalysed hydrolysis, or the spontaneous hydrolysis reaction, increases rapidly with pH – up to its pK a (Fig. 2.1). Since systems 3.4 are hydrolyzed faster, by up to an order of magnitude, than similar derivatives of salicylic acid, EMs of up to 10 5 may be estimated. However, it is not generally possible to measure EMs systematically because the necessary ‘‘control’’ – the corresponding intermolecular reaction – is often too slow to be observed above background. The most relevant measure of catalytic efficiency, for comparison with similar reactions in enzyme active sites (where pH is not simply meaningful) is the ratio of the rates of the pH-independent reactions (Fig. 2.1) in the presence and absence of the catalytic group. We use this parameter in the discussion which follows. Quite different systems, having in common with the salicylate and related systems only a strong intramolecular hydrogen bond, are obtained from 8dimethylamino-1-naphthol 3.5, related to proton sponge 3.6 (Scheme 2.18). (The pK a of the dimethylammonium group of the parent compound 3.5 is normal [43] – as is generally the case for compounds in this series with an exchangeable proton other than the one involved in the intramolecular hydrogen bond.)
2.3 Intramolecular Reactions
Scheme 2.18
The methoxymethyl acetal group of 3.5 is hydrolyzed with efficient catalysis by the neighboring dimethylammonium group (Scheme 2.19). The half-life is 50 min at 65 C: not obviously fast, but rapid for a methoxymethyl acetal, and corresponding to a rate acceleration of 1900 compared with the expected spontaneous hydrolysis rate for a simple naphthol acetal [44]. Catalytic efficiency is reduced compared with the carboxylic acids discussed above, for two important reasons: (i) The general acid is significantly weaker, by some 3 pK a units; and (ii) the observed pK a (7.4) is evidence for a rather strong intramolecular hydrogen bond, which stabilizes the reactant 3.7. However, an important consequence of this high pK a is that the spontaneous hydrolysis reaction extends almost to pH 7 (cf. the pHindependent region of curve C of Fig. 2.1).
Scheme 2.19
The acetal cleavage mechanisms sketched out in Schemes 2.15–2.19 have been written – for simplicity – as leading to oxocarbocations. This is likely to be the case for acetals derived from benzaldehyde or tetrahydropyran, but nucleophilic participation by the solvent is undoubtedly involved in the reactions of methoxymethyl acetals, and most likely in those of most glycosides. This aspect is discussed in more detail in Section 2.3.3 below. Aliphatic Systems The systems discussed so far have in common a good, phenolic, leaving group. This is convenient for two reasons: (i) intrinsically unreactive systems react faster with good leaving groups, and (ii) a (changing) aromatic chromophore makes possible continuous monitoring of reactions. An important disadvantage is that natural substrates for known hydrolytic enzymes are almost invariably non-aromatic, 2.3.2.1
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with aliphatic alcohols or sugars as typical leaving groups. So model systems derived from alcohols are of special interest. To date they have not been very revealing. Intramolecular general acid catalysis in aliphatic systems (examples almost always involve the COOH group) is rarely observed, and then rarely convincingly established [40]. Thus the benzaldehyde acetal 3.8 ðR ¼ HÞ, expected to be a good candidate, showed none [45], though the enol acetal 3.9 – with similar geometry but a better leaving group (an enol has a pK a similar to that of a phenol) – is actually slightly more reactive than the salicylic acid derivative 3.2 (Scheme 2.20). (Unpublished work with R. Osborne, cited in Ref. [44]). When the benzaldehyde acetal 3.8 ðR ¼ COOHÞ is deactivated by electron-withdrawing substituents in the aromatic ring some general acid catalysis is observed in 50% aqueous dioxan. A bellshaped pH–rate profile for hydrolysis between pH 3 and 7 implicates also the second carboxy group in its ionized COO form [45].
Scheme 2.20
Brown and Kirby [46] found relatively efficient intramolecular general acid catalysis for the hydrolysis of the three acetals 3.10, 3.11 and 3.12 (Scheme 2.21). Acetals of benzaldehyde were used to ensure measurable rates of reaction for the much less reactive aliphatic systems. They offered the further advantage that EMs could be estimated, since intermolecular general acid catalysis can be observed for dialkyl acetals of benzaldehyde.
Scheme 2.21
Systems 3.10 and 3.11 are based on the geometries of the salicylic acid and 8dimethylamino-1-naphthol derivatives, known to show efficient intramolecular
2.3 Intramolecular Reactions
general acid catalysis, and all three systems support strong intramolecular hydrogen bonds. Estimated EMs are 3000, 1000 and 10 4 for 3.10, 3.11 and 3.12, respectively. Hydrolysis was considered to involve the classical intramolecular general acid catalysis mechanism indicated by the arrows in the scheme: in particular, kinetic solvent deuterium isotope effects kH2O =kD2O of up to 2.2 were observed. System 3.10 based on salicylate has a half-life of <1 s at 25 C, while 3.12 is some 10 7 times less reactive. General conclusions should not be drawn from such a small sample, but these results suggest strongly that the development of a strong intramolecular hydrogen bond in the transition state supports efficient intramolecular general acid catalysis of the hydrolysis of acetals derived from alcohols as well as from phenols. In this context it is worth noting that acetal 3.11, which shows the lowest EM, is stabilized (like its aromatic ‘‘parent’’ 3.7, discussed above) by intramolecular hydrogen bonding in the ground state; as shown by its pK a of 6.93, (raised by over 2–3 pK a units compared with a simple naphthylamine). The most efficient system of this sort – and the only one to show intramolecular general acid catalysis of the hydrolysis of a methoxymethyl acetal derived from an aliphatic alcohol – is compound 3.13, based on the most reactive aromatic system 3.4. Compound 3.13 (Scheme 2.22) is hydrolyzed with a half-life of 3.5 h in water at 39 C, some 10 10 times faster than expected for the spontaneous hydrolysis of a methoxymethyl acetal of a tertiary alcohol, corresponding to a transition state stabilization of 14 kcal (58 kJ) mol1 [47], and at the rate expected for the methoxymethyl derivative of an alcohol of pK a about 4. Perhaps significantly, this is almost equal to the pK a (4.18) of the catalytic COOH group of 3.13. (Which also confirms that there is no significant intramolecular hydrogen bonding in the reactant.)
Scheme 2.22
2.3.3
Intramolecular General Acid Catalysis of Nucleophilic Catalysis
As discussed above (Section 2.2.2) the hydrolysis reactions of glycosides and methoxymethyl acetals involve nucleophilic participation by water. If water can act as a nucleophile in these systems then reactions with other, better nucleophiles are to be expected. (The model, and the inspiration for most work in this area is the enzyme lysozyme: which – like retaining glycosidases in general – uses two carboxyl groups, one acting as a nucleophile, the other as a general acid, to accomplish (exo-
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cyclic) CaO cleavage at the highly unreactive glycosidic center [48].) Much model work, designed to reproduce the two-carboxyl mechanism, has merely underlined how efficient are the enzymes concerned: however, the separate parts of the mechanism can be reproduced fairly convincingly: putting them together remains a challenge. Nucleophiles attack suitable reactive acetals – with good leaving groups – in wellcharacterized SN 2 reactions [49, 50]. The methylene center of methoxymethyl acetals is typical, and the reaction easily observed because it is sterically receptive towards nucleophilic attack (3.15 in Scheme 2.23, Ar ¼ 2,4-dinitrophenyl) [49]. The reaction is highly sensitive to (the pK a of ) the leaving group, but shows very low sensitivity to the nucleophile, with b nuc ¼ 0.1–0.2. This behavior is consistent with a transition state with weak bonding to both nucleophile and leaving group, and thus a substantial build-up of positive charge at the reaction center. The adeuterium isotope effect of 1.1–1.2 confirms this picture of an SN 1-like transition structure (3.16 in Scheme 2.23).
Scheme 2.23
This picture is general for reactions of methoxymethyl acetals and glycosides with any nucleophile, including solvent water. Estimates of the lifetimes of the free oxocarbocations that would be involved in unimolecular processes suggest that they would be too short, or at best borderline, for them to exist in water: and definitely too short in the presence of a better nucleophile than water. (For a succinct review of this topic see Davies et al. [48].) The good leaving groups of such systems are designed to model the behavior of the partially protonated alcohol or phenol leaving groups of acetals reacting with general acid catalysis. Recent results show that the extrapolation is not a simple one: reactivity depends, unexpectedly, on the charge type of the general acid. An obvious starting point was to look for general acid catalysis of the attack of nucleophiles on a methyoxymethyl acetal known to be subject to efficient carboxyl-catalyzed hydrolysis. Participation by nucleophiles other than water in the hydrolysis of the salicylic acid derivative 3.17 could not be convincingly distinguished from specific salt effects (the range of nucleophiles is limited by the requirement that the COOH group (pK a 3.77) be protonated) [49]. On the other hand there is clear involvement of nucleophiles, including carboxylate anions, in the reaction of the dimethylammonium system 3.18 [44] (Scheme 2.24). The difference is presumably simply quantitative.
2.3 Intramolecular Reactions
Scheme 2.24
An apparently qualitative difference between reactions catalysed by the COOH and Me2 NHþ groups is observed in the hydrolyses of the phosphate monoesters of salicylic acid and 8-dimethylammonium naphthol. The hydrolysis of the diethyl triester 3.19 (Scheme 2.25) shows efficient intramolecular general acid catalysis of the departure of the naphthol leaving group, assisting, if not concerted with, the attack of nucleophiles. (The reaction is thought to involve the pentacovalent addition intermediate 3.20: in which case the second step would be rate determining, since the naphthol is a poorer leaving group than the nucleophilic carboxylate.)
Scheme 2.25
On the other hand, phosphorane intermediates are not expected to be involved in the hydrolysis of phosphate monoesters, so the effective observed catalysis by the carboxyl group of salicyl phosphate 3.21 [51] (Scheme 2.26) is presumed to be concerted with nucleophilic attack. (The hydrolysis reaction involves the less abundant tautomer 3.22 of the dianion 3.21, and the acceleration is >10 9 -fold relative to the expected rate for the pH-independent hydrolysis of the phosphate monoester dianion of a phenol of pK a 8.52.) However, this system differs from the methoxymethyl acetals discussed above, in that there is a clear distinction between neutral nucleophiles, which react through an extended transition structure similar to 3.16 in Scheme 2.23, and anions, which do not react at a significant rate, presumably because of electrostatic repulsion. This distinction is well-established for the dianions of phosphate monoesters with good leaving groups ( p-nitrophenyl [52] and
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Scheme 2.26
2,4-dinitrophenyl phosphate [53]); and evidently holds also for the reactive tautomer 3.22 of salicyl phosphate (Scheme 2.26). Structure–activity relationships for the reactions of substituted derivatives of 3.21 are consistent with the extended transition state 3.23 ðNu ¼ H2 OÞ, with the bond to the leaving group largely broken but proton transfer scarcely begun; that is, with the COOH group close to fully protonated, as in the minor tautomer 3.22. The suggested explanation [51] was that the COOH group is initially rotated out of plane (the observed pK a of 3.76 refers, of course, to the major tautomer 3.21, and is consistent with the expected absence of significant intramolecular hydrogen bonding). For the reactive form 3.22 (Scheme 2.26) k1 – a probably intramolecular, thermodynamically favorable proton transfer – is expected to be faster than the rotation of the COOH group into plane, so that the proton transfer step is unlikely to be cleanly rate determining. (There is no significant solvent deuterium isotope effect on the reaction of the dianion.) Water is expected to be (weakly) involved as a nucleophile in the hydrolysis reaction (Scheme 2.26, 3.23, Nu ¼ H2 O), and reactions with substituted pyridines are catalyzed by the same mechanism (with accelerations of the order of 10 8 ). A Bro¨nsted b nuc ¼ 0:2 confirms the weak involvement of the nucleophile. At first sight the hydrolysis of the phosphate monoester of 8-dimethylammonium naphthyl-1-phosphate 3.24 (Scheme 2.27) looks very similar. However, significant differences have emerged [54]. Most surprising is that in the case of 3.24 there is no discrimination against anionic nucleophiles. Points for oxyanions, fluoride and amine nucleophiles are correlated by the same Bro¨nsted plot, with a slope corresponding to b nuc of 0.2. A second significant difference is that there is a strong intramolecular hydrogen bond in the reactant 3.24, as indicated by a major shift in the pK a of the dimethylammonium group to 9.3, compared with an expected, unperturbed value in the region of 4.6 (as observed for the diethyl triester 3.19).
2.3 Intramolecular Reactions
Scheme 2.27
It is reasonable to presume that these differences are connected. A strong intramolecular hydrogen bond to the leaving group oxygen will polarize the PaO bond involved. Polarization of this PaO bond will be supported by increased nO –s PaO interactions (curved arrows in 3.24: which always play a part in the cleavage of systems XaPO3 ¼ ). These will reduce the negative charge on, and thus the basicity of, the PaO centers. The second pK a of the phosphate group is reduced accordingly, to 3.94 from the expected value of about 6. It is presumed that this reduction in the negative charge on the three PaO centers is sufficient to reduce the electrostatic repulsion to an attacking anionic nucleophile to the levels found for a diester monoanion, or a phosphoramidate, R3 Nþ aPO3 ¼ , both of which are subject to attack by anionic nucleophiles [54]. Since biological phosphate transfer is often to oxyanions, it is of considerable interest that model reactions are facilitated selectively by cationic (NHþ ) general acids: not least because NHþ centers other than the active general acid are generally present in the enzyme active sites involved. Two model systems illustrate the potential of such effects. In 3.25 [55] (Scheme 2.28) a highly efficient nucleophilic reaction ðEM > 10 10 Þ supports the general acid catalyzed displacement of methoxide as methanol. Primary ammonium cations are well-behaved catalysts, following the Bro¨nsted relationship with a ¼ 0:33. Points for neutral, and especially negatively charged, general acids show negative deviations from this line, but diammonium dications show significant positive deviations. The observed rate enhancements depend systematically on the distance between the NHþ centers, reaching 100-fold for tetramethylethylenediammonium dication. A second stabilizing interaction (circled in 3.27 in Scheme 2.28) at the PO2 ¼ center of the phosphorane (3.26, thought to be of borderline stability) is suggested: which could be electrostatic, or involve hydrogen bonding, or both. (An Me3 Nþ group has only a small effect.) In the second model system 3.28 [56], a proton inventory study indicates that the guanidinium group is involved in hydrolysis as a general acid, rather than simply affording electrostatic stabilization of the phosphorane dianion. The nucleophilic part of the reaction, the cyclization of the 2-hydroxypropyl phosphate, is much less efficient than for 3.25, and the leaving group is a phenol: so the rate determining step will be the formation of the phosphorane, as shown (3.28, Scheme 2.28).
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Scheme 2.28
The pK a of the phosphorane is expected to be higher even than that (ca. 13) of the very weakly acidic guanidinium group, and the proton inventory (in water, pH 10.4 at 50 C; B ¼ N-methyl piperidine) is consistent with two protons in flight in the rate determining step shown. The rate enhancement attributed to assistance by the guanidinium group is 42 [56]: impressive for this flexible system in solvent water, and comparable with the best systems designed to show general acid catalysis of intramolecular nucleophilic catalysis discussed in the following section. (A substantial series of potential intermolecular catalysts for the hydrolysis of RNA based on guanidinium and amidinium groups has been examined by the Go¨bel group [57, 58].) 2.3.4
Intramolecular General Acid Catalysis of Intramolecular Nucleophilic Catalysis
The logical next step in the construction of intramolecular model reactions based on Scheme 2.5 is to make both nucleophilic and general acid catalysis components intramolecular. This will allow the identification of potential synergy between the two processes when both are optimised. For example, both nucleophilic catalysis and general acid catalysis are generally observed only for acetals with good leaving groups, and both have the effect of turning poorer into better leaving groups. So it is, in principle, possible that an otherwise abortive nucleophilic displacement might be ‘‘rescued’’ by protonation of the under-achieving leaving group by an efficient intramolecular general acid: and vice versa. Most model systems of this sort have tried to mimic the lysozyme mechanism. Anderson and Fife [59] showed many years ago that benzaldehyde disalicyl acetal 3.29 (Scheme 2.29) is hydrolyzed over 10 9 times faster than its dimethyl ester: but that the contribution of the second, carboxylate group (the potential nucleophile) is
2.3 Intramolecular Reactions
Scheme 2.29
small. The same is true, perhaps for somewhat different reasons, for the rapid hydrolysis of disalicyl phosphate 3.30 (10 10 times faster than that of diphenyl phosphate): where it is the contribution of the COOH group (the potential general acid) that is small [60]. A less reactive acetal, which nevertheless shows a better balance between the contributions from the two mechanisms, is 3.31, based on system 3.13 (above, Scheme 2.22), which supports the most efficient intramolecular general acid catalysis (Scheme 2.29). The nucleophilic contribution is less than optimally efficient because it involves the formation of a 7-membered ring, and in this case contributes about 100-fold to the total 10 5 -fold acceleration [61]. In all these cases bellshaped pH–rate profiles are observed, as expected for reactions involving both COOH and CO2 groups. But in none of them is there any evidence for synergy between the two mechanisms. (A result consistent, if nothing else, with the broad generalization that catalysis occurs where it is most needed.) 2.3.5
Intramolecular General Base Catalysis
There are no reports of intramolecular general base catalysis of efficiency comparable with those discussed for general acid catalysis in Sections 2.3.2 and 2.3.3 above. Such levels of efficiency must, in principle, be attainable, but there are genuine practical problems. Most significant is the dominance of intramolecular nucleophilic reactions when a general base is brought close to a neighboring electrophilic center. For example, the hydrolysis of aspirin (Scheme 2.15) shows intramolecular general base catalysis only because the much (ca. 10 6 -fold) faster nucleophilic mechanism is thermodynamically prohibited [37]. Thus structure–activity studies are only possible in systems, such as the malonate half-esters 3.32 (Scheme 2.30) where the nucleophilic mechanism is specifically disabled (in this case because the formation of a 4-membered ring containing two sp 2 -hybridized carbons would be involved). In this system 3.32 the angle of approach a could be varied over a broad range by varying the substituents R [62]. EMs remained <100 over the whole
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Scheme 2.30
series. Also, where intramolecular general base catalysis was coupled to a cyclization reaction, as in 3.33 (Scheme 2.30) the rate enhancements were precisely additive [63]. The most interesting result in this context is a reaction showing ‘‘Unusually Rapid Intramolecular General-Base Catalysis’’ of the reversible cleavage of a CaH bond [64]. The details are discussed below in Section 2.4.2.
2.4
Proton Transfers to and from Carbon
When Y in the general mechanism of Scheme 2.5 is a carbon center, proton transfer from a general acid generates a CaH bond without the possibility of initial hydrogen bond formation. The new bonding interaction involving the proton is to an X–Y bonding orbital (rather than to a lone pair on Y): a process that requires either a strong acid or – for a (relatively weak) general acid – a high energy bonding orbital. Typically this is the p-orbital of an enol or enolate (or an enamine). However, it can be a s-bonding orbital in special cases. An example is the general acid catalyzed ring-opening of the 1-phenylcyclopropanolate anion 4.1: here catalysis by tertiary ammonium cations follows a Bro¨nsted correlation, with a ¼ 0:25, and the primary deuterium isotope effect kH =kD is 1.9: consistent with an early transition state with proton transfer not far advanced, as would be expected for a reaction involving a developing primary carbanion [65]. (The inverted stereochemistry observed in related reactions suggests that the proton is transferred to the tail of the sCaC bonding orbital, as shown (4.1) in Scheme 2.31)
Scheme 2.31
2.4 Proton Transfers to and from Carbon
Closely related (from the point of view of the general acid) are a series of cyclization reactions in which a carbanion is partially or completely generated in water by the addition of a nucleophile to an alkene or alkyne. The extraordinarily rapid cyclization of the phenolate 4.2 (half-life 50 s at 39 C, corresponding to an EM of ca. 10 11 ) is described as a preassociation-concerted process (Scheme 2.31) [66]. Catalysis by alkylammonium cations follows the Bro¨nsted equation with a ¼ 0:06, and kH2O =kD2O ¼ 1:6, consistent again with the late intervention of the general acid before the incipient primary carbanion reverts to reactant. A (vinyl) carbanion is a full intermediate in the cyclization of the alkyne 4.3 (Scheme 2.32, R ¼ H, half-life 40 s at 39 C). Cyclization is rate determining and the reaction is not buffer catalyzed) [67]. (The 10 4 -fold greater electrophilic reactivity of the alkyne means that the steric acceleration provided by the orthomethyl groups in 4.2 is not needed in 4.3.) The solvent deuterium isotope effect kH2O =kD2O on the proton transfer step (derived from the product isotope effect) is 1.6. However, general acid catalysis is observed for the (1375 times slower) cyclization of the C–methyl compound 4.3 (R ¼ CH3 , Scheme 2.32): evidently methylation destabilizes the vinyl carbanion to the point where it no longer has a significant lifetime in water, and the preassociation-concerted mechanism is enforced once more [67].
Scheme 2.32
More familiar is proton transfer to the pCaC bonding orbital of an enol or enolate. As discussed in Section 2.1, above, the same rate determining step (proton transfer to the general base, Scheme 2.7) accounts for both general base and general acid catalysed ketonisation reactions of enols. The recent work of the Kresge and Richard groups has extended our knowledge of these reactions to the highly reactive enols and enolates obtained from carboxylic acid derivatives such as esters and amides, and even carboxylate anions. The same mechanisms persist in these extreme cases: thus the ketonization of the enol 4.4 derived from mandelamide is specific base-general acid catalyzed by acetic acid, phosphate and TRIS, and general acid catalyzed by the ammonium ion, all by the mechanism shown (Scheme 2.33): a good Bro¨nsted correlation gives a ¼ 0:33 [68]. But eventually proton transfer to such reactive enolates becomes so fast that encounter, or reorganization of solvent water, becomes rate determining [69].
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2 General Acid–Base Catalysis in Model Systems
Scheme 2.33
Not surprisingly the dienolate dianion from a carboxylic acid can also be generated by a cyclization reaction of the sort described in Scheme 2.31. Intramolecular Michael addition of the phenolate 4.5 (half-life 60 s at 39 C) [70] gives the dianion 4.6 as a full intermediate, now stable enough with respect to reversion to reactant that its protonation is rate determining, catalysis by protonated amines following a Bro¨nsted correlation with a ¼ 0:2. The proton transfer step 4.6 behaves remarkably differently depending on the type of general acid involved. Protonation by solvent water gives stereospecific anti addition, and shows a solvent isotope effect kH2O =kD2O of 5.1. But catalysis by the quinuclidinium cation gives syn addition, and kH2O =kD2O ¼ 1:34 G 0:05. These results are not fully understood, but suggest a shorter lifetime for the dianion in the presence of the cationic general acid. This is one more example of an increasing number of systems showing apparent electrostatic contributions to general acid catalysis. 2.4.1
Intramolecular General Acid Catalysis
Since the general acid catalyzed enolization of carbonyl compounds actually involves the specific acid–general base catalysis mechanism (Section 2.1.3, above), this would appear to be the wrong reaction to use in a search for intramolecular general acid catalysis. The ketonization of enols, on the other hand, is an example of a well-known range of reactions in which a general acid protonates a reactive psystem. More convenient substrates are the stable enol ethers [71], and several systems have been shown to be subject to general acid catalysis by neighbouring carboxyl groups [34, 72–74]. Of these two show interestingly high catalytic efficiency. Compound 4.7 is modelled on the salicylic acid system, and designed so that the proton transferred from the general acid is involved, as the new CaH bond develops, in an intramolecular hydrogen bond with the carboxylate anion. The geometry is closely similar to that of the salicylate monoanion, known to form a strong intramolecular hydrogen bond (Scheme 2.16, above): and the HaCaCbOþ Me group is certainly strongly acidic (estimated pK a between 2 and 5) so the libido rule is obeyed. The estimated effective molarities for the two geometrical isomers of 4.7
2.4 Proton Transfers to and from Carbon
are about 300 for 4.7E and 2200 for 4.7Z. (Catalysis as efficient as this swamps any intermolecular catalysis by buffer general acids, so the comparison is with general acid catalysis of the hydrolysis of the two methyl esters.) Deuterium isotope effects kH2O =kD2O are 3.0 for the reactions of both isomers [73]. Catalysis by the dimethylammonium group of the hydrolysis of the two enol ethers 4.10E and 4.10Z (Scheme 2.35) is more efficient still: hydrolysis is faster, with half-lives of the order of 10 s at 39 C even though the general acids ðpKa ¼ 4:0Þ are slightly weaker. The estimated EM for general acid catalysis by the dimethylammonium group of the reaction of 4.10E is >60 000 [74]. The mechanism is similar to that of Scheme 2.34, though there are evident differences of detail. In particular, the solvent deuterium isotope effects of 1.86 and 1.76 observed for the reactions of 4.10E and 4.10Z, respectively, are the lowest observed for enol ether hydrolysis, and significantly lower than those for compounds 4.7 described above (Scheme 2.34).
Scheme 2.34
Scheme 2.35
It is suggested that this reflects a mechanism in which the proton transfer (4.10) is not exclusively rate determining. If a single step is cleanly rate determining for the overall reaction it is likely to be the one (4.11) in which the intramolecular hydrogen bond opens. Equilibrium constants for the opening of strong intramolecular NaH N and OaH N hydrogen bonds in similar situations are of the order of l05 , with correspondingly low rate constants [75, 76]. The rate of the
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2 General Acid–Base Catalysis in Model Systems
thermodynamically favorable proton jump by which 4.11 reverts to enol ether seems certain to be faster. The effective molarity of the general acid, already much higher than other known values for intramolecular general acid catalyzed reactions, is thus likely to be higher than the initial estimate of 60 000 [74]. 2.4.2
Intramolecular General Base Catalysis
As discussed in Section 2.3.5 above, there are no reports of efficient intramolecular general base catalysis of efficiency comparable with those discussed above for general acid catalysis in Sections 2.3.2 and 2.3.3. This generalization applies also to reactions involving proton transfer to and from carbon. For example, early work by Bell and his coworkers [77, 78] found only inefficient catalysis (EMs < 10 [36]) of the enolisation of acetophenone derivatives with ortho COOH or OH substituents. A more detailed study of similar systems by the Anslyn group [79] confirms that the ortho OH group in 4.13, a potential general acid well placed to support a relatively strong intramolecular hydrogen bond, is responsible for only small (10–100fold) rate accelerations (Scheme 2.36, B ¼ imidazole). (Note that the adjacent phenol and enol of 4.14 will have similar pK a s.) The system is set up for an early proton transfer, and the authors suggest non-perfect synchronization as an explanation for the weak intramolecular catalysis. They also make the interesting suggestion that proton transfer transfer to the pCaO bonding orbital (a geometry not seen in hydrogen bonding interactions in typical crystal structures [80]) may be a more efficient way to activate the carbonyl group.
Scheme 2.36
In the light of the successful identification of efficient intramolecular general acid catalysis in the 8-dimethylaminonaphthol system (Scheme 2.35), this system would appear to offer the best chance of observing efficient intramolecular general base catalysis, by setting up the microscopic reverse process involving the same functional groups in the same geometry. The chosen system, conveniently also a plausible model for the mandelate racemase reaction (in which amine general bases remove a CaH proton from the position alpha to the mandelate carboxyl group [81]), were esters 4.15 (Scheme 2.37). The enolate 4.16, and thus the transition state leading to it, reproduces in detail the geometry of the enol ether 4.17,
2.4 Proton Transfers to and from Carbon
Scheme 2.37
shown to support very efficient proton transfer to the pCaC bonding orbital (see Scheme 2.35, above). When esters 4.15 were incubated as the free bases in D2 O, standard conditions for detecting small amounts of enolization by the exchange of solvent deuterium into the a-positions of esters [82], no trace of exchange was observed, even after many days under vigorous conditions [83]. A working explanation is that the enolate intermediate 4.16, specifically designed to support a strong intramolecular hydrogen bond between the NHþ group and the high energy pCaC orbital of the enolate, reverts to reactant ester (k1 in Scheme 2.37) much faster than the cyclic H-bond opens – a necessary preliminary to exchange with solvent deuterium. Proton transfers within such intramolecular hydrogen bonds have been shown in related systems to be much faster than ring opening [84], and it has already been suggested that ring-opening is at least partially rate determining in the efficient general acid catalyzed hydrolysis of the enol ether 4.10 (Scheme 2.35, above), a proton transfer with the same geometrical requirements (4.17). In this situation the report mentioned above (Section 2.3.5) of the reversible cleavage of a CaH bond 4.18 (Scheme 2.38) showing ‘‘unusually rapid’’ intramolec-
Scheme 2.38
1005
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2 General Acid–Base Catalysis in Model Systems
ular general base catalysis [64] is of particular interest. The authors conclude that intramolecular site-exchange of the proton proceeds at least 10 4 –10 5 times faster than the intermolecular reaction, so has an EM comparable with the best observed values for intramolecular general acid catalysis. Considerable extrapolations are involved, and the rates were measured by NMR line broadening, in toluene-d8 or CDCl3 (so the conditions differ from those for all the reactions discussed above): and the work has not been followed up. (Rapid deuterium exchange should be observed, for example, in the ND2 compound.) But this reaction suggests, as a minimum, an alternative starting point for work on efficiency in such systems. 2.4.3
Simple Enzyme Models
The model systems discussed so far in this chapter have been designed and studied specifically to investigate mechanisms of bond making and breaking. Any serious enzyme model must also incorporate a substrate binding step, and much effort has gone into this area in recent years. Not surprisingly, in the light of the evidence from small molecule systems discussed in Section 2.3, above, efficient general acid–base catalysis has not been observed in systems designed to bind specific substrates, and the synthetic effort involved in adding properly positioned catalytic functionality to such systems is a serious deterrent [85]. One model reaction that has proved a popular and appropriate probe for general base catalysis by potential binders of hydrophobic substrates is the Kemp elimination, the simple, single transition state ring-opening elimination of benzisoxazoles 4.19 (Scheme 2.39).
Scheme 2.39
The reaction is a well-characterized E2-type process involving the general base catalyzed removal of the 3-proton (kH =kD 4–6, depending on the ring substituents) [86], which is extraordinarily sensitive to the medium when the general base is an acetate anion; though much less so for catalysis by amine general bases. It is catalyzed apparently efficiently by catalytic antibodies raised against carefully designed haptens [87], but it is not a simple matter to distinguish medium effects from the contributions of general base catalysis by binding site carboxylate groups. The finding that serum albumens, non-specific binders of hydrophobic substrates, catalyze the reaction almost as efficiently using local lysine amino groups as general bases
2.5 Hydrogen Bonding, Mechanism and Reactivity
[88], suggests that the observed accelerations result from a combination of medium effects and functional group catalysis; and that general base catalysis is efficient but not extraordinarily so [89]. The Kemp elimination has also been shown to be catalyzed by polyethylenimine modified to bind hydrophobic substrates [90], by micelles and vesicles [91], and by various more or less specific binders with general bases attached [91–93]. The general conclusion remains the same.
2.5
Hydrogen Bonding, Mechanism and Reactivity
Recent thinking on general acid–base catalysis has been dominated by discussions of the contribution of ‘‘short, strong’’ or ‘‘low-barrier’’ hydrogen bonds, and – for proton transfers to and from carbon – the possible contribution of tunneling. Tunneling is discussed in detail by other contributors to this Handbook, but decisive results with model systems have been conspicuous by their absence. The hydrogen bond, on the other hand, is of central importance to any proton transfer reaction, and all but ubiquitous in discussions of the topic. It figures, explicitly or implicitly, in all the mechanistic schemes above, and has been suggested to make key contributions to the high efficiency of enzyme catalysis. The experimental evidence is clear, up to a point. Proton transfers between electronegative centers involve the transient formation of hydrogen bonds, along which the proton is transferred. The same mechanism applies to proton transfer to carbon, but only in special, overlapping, cases: if the carbanion concerned lives long enough for solvent equilibration, and if the CaH bond is strongly acidic. Weakly acidic CaH, and probably also p-bonding orbitals, are not expected to make significant hydrogen bonds to solvent or to general bases in solution in protic solvents (though examples are well established in the solid state [94], and are of potential importance in non-polar solvents and enzyme active sites). Strong hydrogen bonding in protic solvents is observed only between groups held or brought together in close and appropriate proximity: it is generally thermodynamically preferable for strong hydrogen bonding groups to be solvated separately. General acid–base catalysis is typically inefficient, compared with nucleophilic catalysis, and this is particularly well documented for intramolecular reactions, as discussed above (Section 2.3.1). The reasons for this disparity have been discussed in terms of broad generalizations, citing most often the ‘‘looseness,’’ and thus relatively low entropy, of the transition state for a general acid–base catalyzed reaction compared with a cyclization process in which ring formation is complete apart from one partial covalent bond. (Compare, for example, the observed general base catalyzed hydrolysis 5.1 and the abortive but 10 6 times faster nucleophilic reaction 5.2 (Scheme 2.40) reactions of aspirin (Section 2.3.5, above) [36].) However, it is not immediately obvious why, for example, the transition state for intramolecular general base catalyzed enolization 5.3 (EM 56 M [36]) should be significantly looser than 5.2. Though it seems clear that the presence of the proton in the cyclic transition structure is the key. (The entropy of activation is not: no third molecule is in-
1007
1008
2 General Acid–Base Catalysis in Model Systems
Scheme 2.40
volved in 5.3, and favorable TDS z values are typically far too small to explain the high effective molarities of nucleophilic reactions.) Pascal [95] has argued that, because proton transfer goes by way of a hydrogenbond, this already makes an intermolecular reaction effectively intramolecular: thus explaining the generally low efficiency of intramolecular general acid–base catalysis. This would be true if – and only if – the H-bonded complex were the major species in solution: it is not. A polar substrate in water is hydrogen-bonded predominantly to the solvent not to the general acid or base, so that the state of the reactant – on which free energy estimates must be based – retains the degrees of freedom which are lost in the transition state and the complex leading to it. (A corollary is that intramolecular proton transfers involving CaH bonds should not suffer from this disadvantage, but there is no evidence from the new generation of systems showing efficient general acid catalysis (Section 2.3.2, above) that proton transfer to carbon is specifically favored.) The low efficiency of intramolecular general acid–base catalysis, compared with intramolecular nucleophilic catalysis, is general but not universal. The exceptions, systems showing general acid catalysis with EMs > 1000, have in common a strong intramolecular hydrogen bond. So the simple (though not especially informative!) generalisation is that the efficiency of catalysis depends on the free energy of formation of the cyclic transition state. For nucleophilic catalysis this is known to mirror the equilibrium free energy change for the overall cyclization reaction [36]; so the effect on efficiency must be primarily thermodynamic rather than kinetic. A specifically kinetic effect may derive from the nature of the transition state. For a cyclization reaction the transition state is a ring with one partial covalent bond (for example, 5.2). This may be formed almost completely, as in some lactonisations; moderately, as in SN 2-type processes; or to a very minor extent, as perhaps in the hard-to-detect cyclisation reactions of acetals (see 3.29, above). Observed EMs for cyclization reactions fall in this order [36]. For a general base catalyzed reaction, by contrast, there is no formal equilibrium free energy of cyclization, because the product is not a ring: rather – at best – a cycle interrupted by an intramolecular hydrogen bond, set up for the reverse, intramolecular general acid catalyzed reaction (5.5, Scheme 2.41). In this situation it is clear that stronger
2.5 Hydrogen Bonding, Mechanism and Reactivity
Scheme 2.41
hydrogen-bonding can make ring formation more thermodynamically favorable, and thus stronger in the transition state than in either reactant or product, for example because the pK a s of the groups concerned can be better matched. The systems described above (Section 2.3.2) showing highly efficient intramolecular general acid catalysis are more or less rigid, and movement of the heavy atoms directly concerned in the proton transfer process minimal. (The Principle of Least Motion may apply [96].) Schowen et al. [97] have argued convincingly that the proton ‘‘in general catalysis bridges between oxygen, nitrogen and sulfur’’ will be in a stable potential, with the bond order conserved at unity, and will shift towards a residue that becomes more basic: that is, in the direction indicated by the curved arrows used in the schemes. In this picture the reaction coordinate is defined exclusively by the motions of the heavy atoms involved, uncoupled from the bridging proton, which is in a stable potential at the transition state (for example, 3.7 in Scheme 2.42). This would explain why the deuterium kinetic isotope effects for these reactions are particularly low. For the highly efficient general acid catalyzed reactions of Schemes 2.16–2.19 (Section 2.3.2, above) kH =kD ¼ 1:5 G 0:2. This compares with higher – but still low – values in the region of 2–3 for more typical general acid–base catalyzed reactions.
Scheme 2.42
There has been intensive recent discussion, summarized elsewhere in this Handbook, about the potential contribution of strong hydrogen bonding to the catalytic efficiency of enzymes. A key question is conveniently summarized by
1009
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2 General Acid–Base Catalysis in Model Systems
Chen et al. [98] ‘‘Is it possible that some hydrogen bonds . . . in the active sites of enzymes have energies in the range 10–20 kcal mol1 ?’’ (Guthrie suggested that the maximum reasonable value is 10 kcal mol1 [99].) The accumulating evidence from model systems suggests that the answer is positive, at least for transition state hydrogen bonds. (Note that hydrogen bonds in a product complex offer no rate advantage, and in a reactant complex are disadvantageous.) The rate enhancement from intramolecular general acid catalysis by the carboxyl group of 3.13 (Scheme 2.22), a system designed for optimal hydrogen bonding in the product, is worth 14 kcal mol1 , in water at 39 C [47]. In this system there is little or no intramolecular hydrogen bonding in the reactant. Systems like 3.7 (Sections 2.3.2 and 2.3.3) are less efficient in part because significant intramolecular hydrogen bonding stabilizes the reactant when the leaving group oxygen is sufficiently basic. All these rather subtle requirements are a challenge to the ingenuity of the designer of simple model systems: and a reminder of the extraordinary flexibility that is built in to enzymes, many of which have evolved to catalyze so efficiently complex and intrinsically slow reactions which may have many separate steps, with different geometrical requirements, in a single active site.
References 1 H. Maskill, The Physical Basis Of
2
3
4
5 6
7 8 9 10 11
Organic Chemistry, Oxford University Press, Oxford, New York, 1985. C. W. Wharton, in Comprehensive Biological Catalysis, Sinnott, M. L. (Ed.), Academic Press, London and San Diego, 1998, pp. 345–379. M. F. Aldersley, A. J. Kirby, P. W. Lancaster, R. S. McDonald, C. R. Smith, J. Chem. Soc., Perkin Trans 2 (1974) 1487–1495. A. S. Baynham, F. Hibbert, M. A. Malana, J. Chem. Soc., Perkin Trans. 2 (1993) 1711–1715. R. A. Bednar, W. P. Jencks, J. Am. Chem. Soc. 107 (1985) 7117–7126. M. W. Washabaugh, J. T. Stivers, K. A. Hickey, J. Am. Chem. Soc. 116 (1994) 7094–7097. C. A. Coleman, C. J. Murray, J. Am. Chem. Soc. 113 (1991) 1677–1684. A. R. Butler, V. Gold, J. Chem. Soc. (1961) 2305–2310. W. P. Jencks, J. Am. Chem. Soc. 94 (1972) 4731–4732. W. P. Jencks, Chem. Rev. 72 (1972) 705–718. E. H. Cordes, H. G. Bull, Chem. Rev. 74 (1974) 581–603.
12 E. H. Cordes, H. G. Bull, in
13 14 15
16
17 18 19 20 21
22
Transition States of Biolochemical Processes, R. D. Gandour, R. L. Schowen (Eds.), 1978, pp. 429–465. T. H. Fife, L. H. Brod, J. Am. Chem. Soc. 92 (1970) 1681–1684. E. Anderson, T. H. Fife, J. Am. Chem. Soc. 91 (1969) 7163–7166. A. T. N. Belarmino, S. Froehner, D. Zanette, J. P. S. Farah, C. A. Bunton, L. S. Romsted, J. Org. Chem. 68 (2003) 706–717. J. L. Jensen, L. R. Herold, P. A. Lenz, S. Trusty, V. Sergi, K. Bell, P. Rogers, J. Am. Chem. Soc. 101 (1979) 4672–4677. J. P. Richard, W. P. Jencks, J. Am. Chem. Soc. 106 (1984) 1396–1401. M. M. Toteva, J. P. Richard, J. Am. Chem. Soc. 124 (2002) 9798–9805. N. S. Banait, W. P. Jencks, J. Am. Chem. Soc. 113 (1991) 7958–7963. D. Stefanidis, W. P. Jencks, J. Am. Chem. Soc. 115 (1993) 6045–6050. N. J. Buurma, M. J. Blandamer, J. Engberts, J. Phys. Org. Chem. 16 (2003) 438–449. S. A. Khan, A. J. Kirby, J. Chem. Soc. B (1970) 1172–1182.
References 23 C. D. Bryan, K. B. Schowen, R. L.
24 25 26 27 28
29
30
31
32 33
34
35
36 37 38
39
40
41 42
Schowen, Can. J. Chem. 74 (1996) 931–938. P. E. Dietze, W. P. Jencks, J. Am. Chem. Soc. 111 (1989) 340–344. P. E. Dietze, Y. Y. Xu, J. Org. Chem. 59 (1994) 5010–5016. T. H. Cromartie, C. G. Swain, J. Am. Chem. Soc. 97 (1975) 232–233. J. O. Knipe, J. A. Coward, J. Am. Chem. Soc. 101 (1979) 4339–4348. D. M. Perreault, E. V. Anslyn, Angew. Chem., Intl. Ed. Engl. 36 (1997) 432–450. M. Oivanen, S. Kuusela, H. Lonnberg, Chem. Rev. 98 (1998) 961–990. Y. I. Kuzmin, C. P. Da Costa, M. J. Fedor, J. Mol. Biol. 340 (2004) 233–251. A. M. Davis, A. D. Hall, A. Williams, J. Am. Chem. Soc. 110 (1988) 5105– 5108. N. H. Williams, Biochim. Biophys. Acta 1697 (2004) 279–287. E. Maki, M. Oivanen, P. Poijarvi, H. Lonnberg, J. Chem. Soc., Perkin Trans. 2 (1999) 2493–2499. C. Beckmann, A. J. Kirby, S. Kuusela, D. C. Tickle, J. Chem. Soc., Perkin Trans. 2 (1998) 573–581. S. Mikkola, M. Kosonen, H. Lonnberg, Curr. Org. Chem. 6 (2002) 523–538. A. J. Kirby, Adv. Phys. Org. Chem. 17 (1980) 183–278. A. R. Fersht, A. J. Kirby, J. Am. Chem. Soc. 89 (1967) 4857–4863. B. Capon, M. C. Smith, E. Anderson, R. H. Dahm, G. H. Sankey, J. Chem. Soc., B (1969) 1038–1047. G.-A. Craze and A. J. Kirby, J. Chem. Soc., Perkin Trans. 2 (1974) 61–66. A. J. Kirby, A. R. Fersht, in Advances in Bioorganic Mechanisms, Vol. 1, Kaiser, E. T., Kezdy, F. J. (Eds.), Wiley, New York 1971, pp. 1–82. C. Buffet, G. Lamaty, Rec. Trav. Chim. 95 (1976) 1–30. J. Hermans, S. J. Leach, H. A. Scheraga, J. Am. Chem. Soc. 85 (1963) 1390–1395.
43 F. H. Hibbert, personal
communication. 44 A. J. Kirby, J. M. Percy, J. Chem. Soc.,
Perkin Trans. 2 (1989) 907–912. 45 T. H. Fife, T. J. Przystas, J. Am.
Chem. Soc. 101 (1979) 1202–1210. 46 C. J. Brown, A. J. Kirby, J. Chem.
Soc., Perkin Trans. 2 (1997) 1081–1093. 47 E. Hartwell, D. R. W. Hodgson, A. J.
48
49
50 51 52 53 54
55
56
57
58
59 60 61 62 63 64
Kirby, J. Am. Chem. Soc. 122 (2000) 9326–9327. G. Davies, M. L. Sinnott, S. G. Withers, in Comprehensive Biological Catalysis, Sinnott, M. L. (Ed.), Academic Press, London and San Diego, 1998, pp. 119–207. G.-A. Craze, A. J. Kirby, R. Osborne, J. Chem. Soc., Perkin Trans. 2 (1978) 357–368. B. L. Knier, W. P. Jencks, J. Am. Chem. Soc. 102 (1980) 6789–6798. R. H. Bromilow, A. J. Kirby, J. Chem. Soc., B (1972) 149. A. J. Kirby, W. P. Jencks, J. Am. Chem. Soc. 87 (1965) 3209. A. J. Kirby, A. G. Varvoglis, J. Chem. Soc., B (1968) 135. A. J. Kirby, M. F. Lima, D. da Silva, F. Nome, J. Am. Chem. Soc. 126 (2004) 1350–1351. K. N. Dalby, A. J. Kirby, F. Hollfelder, J. Chem. Soc., Perkin Trans. 2 (1993) 1269. A. M. Piatek, M. Gray, E. V. Anslyn, J. Am. Chem. Soc. 126 (2004) 9878– 9879. M.-S. Muche, M. W. Go¨bel, Angew. Chem., Intl. Ed. Engl. 35 (1996) 2126– 2129. S. Pitsch, S. Scheffer, M. Hey, A. Strick, M. W. Go¨bel, Helv. Chim Acta 86 (2003) 3740–3752. E. Anderson, T. H. Fife, J. Am. Chem. Soc. 95 (1973) 6437–6441. K. W. Y. Abell, A. J. Kirby, J. Chem. Soc., Perkin Trans. 2 (1983) 1171–1174. K. E. S. Dean, A. J. Kirby, J. Chem. Soc., Perkin Trans. 2 (2002) 428–432. A. J. Kirby, G. J. Lloyd, J. Chem. Soc., Perkin Trans. 2 (1976) 1753–1761. A. J. Kirby, G. J. Lloyd, J. Chem. Soc., Perkin Trans. 2 (1974) 637–642. F. M. Menger, K. Gabrielson, J. Am. Chem. Soc. 114 (1992) 3574–3575.
1011
1012
2 General Acid–Base Catalysis in Model Systems 65 A. Thibblin, W. P. Jencks, J. Am. 66
67
68
69
70 71 72
73 74 75 76 77
78 79
80
81 82
Chem. Soc. 101 (1979) 4963–4973. C. M. Evans, A. J. Kirby, J. Chem. Soc., Perkin Trans. 2. (1984) 1259– 1268. C. M. Evans, A. J. Kirby, J. Chem. Soc., Perkin Trans. 2 (1984) 1269– 1275. Y. Chiang, H. X. Guo, A. J. Kresge, J. P. Richard, K. Toth, J. Am. Chem. Soc. 125 (2003) 187–194. J. P. Richard, G. Williams, A. C. O’Donoghue, T. L. Amyes, J. Am. Chem. Soc. 124 (2002) 2957–2968. T. L. Amyes, A. J. Kirby, J. Am. Chem. Soc. 110 (1988) 6505–6514. A. J. Kresge, Accts. Chem. Res. 20 (1987) 364–370. A. J. Kirby, N. H. Williams, J. Chem. Soc., Chem. Commun. (1991) 1644–5. A. J. Kirby, N. H. Williams, J. Chem. Soc., Perkin Trans. 2 (1994) 643–648. A. J. Kirby, F. O’Carroll, J. Chem. Soc., Perkin Trans. 2 (1994) 649–655. F. Hibbert, J. Chem. Soc., Perkin Trans. 2 (1974) 1862–1866. A. Awwal, F. Hibbert, J. Chem. Soc., Perkin Trans. 2 (1977) 152–156. R. P. Bell, D. W. Earls, J. B. Henshall, J. Chem. Soc., Perkin Trans. 2 (1976) 39–44. R. P. Bell and D. W. Earls, J. Chem. Soc., Perkin Trans. 2 (1976) 45–46. Z. L. Zhong, T. S. Snowden, M. D. Best, E. V. Anslyn, J. Am. Chem. Soc. 126 (2004) 3488–3495. A. J. Kirby, The Anomeric Effect and Related Stereoelectronic Effects at Oxygen. Springer-Verlag, Berlin and Heidelberg, 1983, pp. 43–44. S. L. Bearne, R. Wolfenden, Biochemistry 36 (1997) 1646–1656. T. L. Amyes, J. P. Richard, J. Am. Chem. Soc. 118 (1996) 3129–3141.
83 F. Hollfelder, Thesis, Cambridge,
1997. 84 F. Hibbert, Acc. Chem. Res. 17 (1984)
115–120. 85 A. J. Kirby, Angew. Chem., Intl. Ed.
Engl. 35 (1996) 707–724. 86 M. L. Casey, D. S. Kemp, K. G. Paul,
87
88
89
90
91 92 93
94 95 96 97
98
99
D. D. Cox, J. Org. Chem. 38 (1973) 2294–2301. S. N. Thorn, R. G. Daniels, M. T. M. Auditor, D. Hilvert, Nature (London) 373 (1995) 228–230. F. Hollfelder, A. J. Kirby, D. S. Tawfik, Nature (London) 383 (1996) 60–63. F. Hollfelder, A. J. Kirby, D. S. Tawfik, K. Kikuchi, D. Hilvert, J. Am. Chem. Soc. 124 (2000) 1022– 1029. F. Hollfelder, A. J. Kirby, D. S. Tawfik, J. Am. Chem. Soc. 119 (1997) 9578–9579. J. E. Klijn, J. Engberts, Org. Biomol. Chem. (2004) 1789–1799. X. C. Liu, K. Mosbach, Macromol. Rapid Commun. 19 (1998) 671–674. P. G. McCracken, C. G. Ferguson, D. Vizitiu, C. S. Walkinshaw, Y. Wang, G. R. J. Thatcher, J. Chem. Soc., Perkin Trans. 2 (1999) 911–912. T. Steiner, Angew. Chem., Intl. Ed. Engl. 41 (2002) 48–76. R. Pascal, J. Phys. Org. Chem. 15 (2002) 566–569. M. L. Sinnott, Adv. Phys. Org. Chem. 24 (1988) 113–204. K. B. Schowen, H. H. Limbach, G. S. Denisov, R. L. Schowen, Biochim. Biophys. Acta-Bioenergetics 1458 (2000) 43–62. J. G. Chen, M. A. McAllister, J. K. Lee, K. N. Houk, J. Org. Chem. 63 (1998) 4611–4619. J. P. Guthrie, Chem. Biol. 3 (1996) 163–170.
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Hydrogen Atom Transfer in Model Reactions Christian Scho¨neich 3.1
Introduction
Hydrogen transfer reactions are of fundamental importance in synthetic [1], environmental [2] and biological [3] processes. This chapter focuses on the experimental and theoretical treatment of model reactions designed to understand the mechanistic details of and the parameters controlling hydrogen transfer processes. Specific emphasis is placed on hydrogen transfer reactions of oxygen-, nitrogenand sulfur-centered radicals relevant to oxidation mechanisms of amino acids, peptides and proteins. After much progress in deciphering the human genome, it was realized that insights into pathologic processes would require the analysis of the protein complement, the ‘‘proteome’’. Such analysis must include posttranslational protein modifications, and a thorough knowledge of the nature, abundance and location of oxidative post-translational modifications, such as are prevalent in many disease states and biological aging, requires a mechanistic and structural understanding of the reactions leading to the accumulation of specific oxidation products. The hydrogen transfer reactions described in this chapter comprise a subset of the reactions leading to the ultimate formation of oxidized proteins in vivo.
3.2
Oxygen-centered Radicals
Oxygen-centered radicals represent the most abundant class of radicals in biological systems. Several recent reviews have dealt with the reactions of oxygen-centered amino acid, peptide and protein radicals [4, 5]. Therefore, we will only give a brief review of the reactions of common oxygen-centered radicals, and especially those of amino acids and peptides, before focusing on some selected mechanistic aspects of biologically relevant hydrogen transfer reactions of specific oxygen-centered radicals. The smallest, but most reactive, oxygen-centered radical is the hydroxyl radical Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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3 Hydrogen Atom Transfer in Model Reactions
(HO ). The HO radical reacts efficiently with most amino acid and peptide CaH bonds [6], where k1 A 2 10 7 –2 10 9 M1 s1 for free amino amino acids and small peptides at pH ca. 7 [7].
HO þ PaH ! H2 O þ P
ð3:1Þ
The product carbon-centered radicals add molecular oxygen in a diffusioncontrolled process (k2 A 2 10 9 M1 s1 [8]). Pulse radiolysis studies on the reactions of peroxyl radicals from cyclic model dipeptides (diketopiperazines) have demonstrated a base-catalyzed elimination of superoxide [8]. In proteins, the resultant peroxyl radicals can abstract additional hydrogen atoms (Reaction (3.3)), initiating chain reactions, which ultimately lead to the accumulation of protein-bound hydroperoxides [9–11].
P þ O2 ! PaOaO
ð3:2Þ
0
PaOaO þ P aH ! PaOaOaH þ P
0
ð3:3Þ
Evidence for these pathways in vivo, and the initial involvement of HO radicals, has been presented [12]. An important feature of these protein-bound hydroperoxides is their sensitivity to reductive cleavage by transition metals, generating highly reactive alkoxyl radicals (Reaction (3.4)) [13].
PaOaOaH þ M nþ ! PaO þ HO þ Mðnþ1Þþ
ð3:4Þ
Recent theoretical studies have dealt with the potential structures of amino acid and protein peroxyl radicals and hydroperoxides at the a C position, i.e. A a CaOaO , A a CaOaOaH, P a CaOaO and P a CaOaOaH, respectively [14]. The amino acid hydroperoxides are stabilized through hydrogen bonding to the acyl oxygen, whereas the protein hydroperoxides show a hydrogen bond to the acyl oxygen of the i 1 residue. No hydrogen bonding is apparent for the amino acid peroxyl radicals, but for the protein peroxyl radicals hydrogen bonding to the amide group of the i þ 1 residue appears likely. The amino acid or peptide alkoxyl radicals formed in Reaction (3.4) eventually undergo an a–b fragmentation [15, 16], a 1,2-H-shift (vide infra), or react via hydrogen- or electron transfer [17]. The latter processes will ultimately generate hydroxy amino acids, which have been observed in vivo as a consequence of oxidative stress [12]. However, not all endogenous antioxidants will react efficiently with these alkoxyl radicals. For example, pulse radiolysis experiments in aqueous solution revealed a surprisingly low reactivity of model tert-butoxyl radicals ( tert BuO ) with glutathione (GSH), where k < 4 10 7 M1 s1 , while hydrogen abstraction from other antioxidants proceeded ca. two orders of magnitude faster, i.e., k ¼ 1:6 10 9 M1 s1 and 1:1 10 9 M1 s1 for the reaction of tert BuO with ascorbate and the water-soluble vitamin E analog trolox C, respectively [17]. Even the reaction of tert BuO radicals with polyunsaturated fatty acids occurred faster than
3.2 Oxygen-centered Radicals
that with GSH, where k ¼ 1:3; 1:6 and 1:8 10 8 M1 s1 for linoleate, linolenate and arachidonate, respectively [17]. For the a–b fragmentation of amino acid and protein a C-alkoxyl radicals, theoretical data [14] predict a clear preference for scission of the a CaCO bond, based on the free energies of activation. Such fragmentation has been observed experimentally in aqueous solution [15]. However, experiments with model alkoxyl radicals have shown that the nature of the solvent has a significant influence on both the a–b fragmentation [18] and the 1,2-H-shift [19]. Especially for proteins, that means that alkoxyl radicals could react differently depending on whether they are located in hydrophilic or hydrophobic protein regions. Recent studies on the 1,2-H-shift in benzyloxyl radicals suggest that this reaction is catalyzed by nucleophilic solvents, which contain hydroxy groups, such as water (Reaction (3.5)) and alcohols [19]. The mechanism of catalysis was suggested to involve two hydrogen-bonds, one between the benzylic hydrogen and the solvent oxygen and one between the exchangeable solvent proton and the alkoxyl radical oxygen.
PhCH2 O þ H2 O ! PhC HOH þ H2 O
ð3:5Þ
Pulse radiolysis studies on the 1,2-H-shift in ethyloxyl radicals in water indicate a kinetic isotope effect of kH =kD A 50 (for the intramolecular reaction of CH3 CH2 O vs. CD3 CD2 O ), indicating the potential participation of tunneling [20]. The latter observation suggests that the mechanism of the 1,2-H-shift is actually more complex than anticipated. Of particular interest in biology are redox processes of the amino acid tyrosine
ð3:6Þ
(Equilibrium (3.6)), where hydrogen transfer (or proton-coupled electron transfer, PCET) generates an aromatic alkoxyl (tyrosyl) radical. In a series of recent publications ([21] and references therein), Ingold and coworkers have pointed out the importance of hydrogen bonding for the rate constants of such hydrogen transfer reactions. This is summarized in Scheme 3.1, where hydrogen transfer to an attacking radical Y requires dissociation of any hydrogen bond between the hydrogen donor XH and the solvent S. A single empirical equation (I) was developed [21], which allows the prediction of rate constants k S for hydrogen transfer between the hydrogen donor XH and any radical Y in any solvent S based on the following parameters: (i) the rate constant k 0 of hydrogen transfer from XH in a reference solvent (a saturated hydrocarbon with no hydrogen bond acceptor properties), (ii) a parameter a2 H, which
1015
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3 Hydrogen Atom Transfer in Model Reactions
Scheme 3.1. Hydrogen bonding between substrate and solvent affects the efficiency of hydrogen transfer reaction to an attacking radical.
describes the ability of XH to act as a hydrogen bond donor, and (iii) a parameter b 2 H , which describes the ability of the solvent to act as a hydrogen bond acceptor. logðk S =M1 s1 Þ ¼ logðk 0 =M1 s1 Þ 8:3a2 H b 2 H
ðIÞ
It is important to note that Scheme 3.1 and Eq. (I) are valid for hydrogen transfer and, possibly, proton transfer processes [21]. However, it must be realized that while hydrogen bonding between the phenolic hydroxy group and a hydrogen acceptor may prevent hydrogen transfer, electron transfer processes can still proceed. Evidence is mounting that, especially in b-sheet structures, proteins form a CaH ObC hydrogen bonds [22, 23]. These bonds display association enthalpies of DH 298 A 3:0 G 0:5 kcal mol1 [22, 23], supported by theoretical and NMR spectroscopic data. It remains to be shown experimentally whether the formation of such a CaH ObC hydrogen bonds in peptides and proteins may affect hydrogen transfer kinetics of the a CaH bond (vide infra). Tyrosyl radicals are important intermediates utilized by enzymes, such as, for example, the ribonucleotide reductase class I (RNR1) [3, 24–27] or prostaglandin H synthase [28–30]. In RNR1, a tyrosyl radical ultimately oxidizes a Cys residue to produce a Cys thiyl (cysteinyl) radical, which subsequently attacks the C3 0 CaH bond of a ribonucleotide substrate [3, 24–27] (vide infra). Prostaglandin H synthase utilizes a tyrosyl radical at position Tyr 385 to abstract a hydrogen atom from arachidonic acid to yield a pentadienyl radical in the first step of the cyclooxygenase reaction [28–30]. Multiple additional inter- and intramolecular reactions may occur in proteins when tyrosyl radicals are produced in an uncontrolled manner during conditions of oxidative stress. The results of Foti et al. [31] suggest that tyrosyl radicals could actually be significantly more reactive than peroxyl radicals, at least in a nonaqueous environment. In other words, protein tyrosyl radicals could be efficient initiators of chain processes leading to protein hydroperoxides (vide supra). The hydrogen transfer reactivities of phenoxyl and peroxyl radicals towards a series of reductants were analyzed by laser flash photolysis experiments in organic solvents [31]. Generally, the phenoxyl radicals reacted ca. 100-fold faster than the peroxyl radicals. In benzene, the rate constant for the hydrogen transfer reaction be-
3.3 Nitrogen-dentered Radicals
tween the phenoxyl radical and a-tocopherol (vitamin E), k ¼ 1:1 10 9 M1 s1 , indicates a diffusion-controlled process. The large differences between the rate constants for phenoxyl and peroxyl radicals were rationalized in terms of hydrogenbonded complexes and transition state structures. It was suggested that peroxyl radicals form tightly associated hydrogen-bonded complexes, which are, however, incorrectly oriented for a hydrogen transfer reaction. In contrast, the phenoxyl radical associates weakly with the substrate phenol, enabling successful hydrogen transfer.
3.3
Nitrogen-dentered Radicals 3.3.1
Generation of Aminyl and Amidyl Radicals
Aminyl and amidyl radicals are conveniently generated from the homolytic or reductive cleavage of chloramines and chloramides [32–39]. The latter form under inflammatory conditions when amino acids and/or peptides are exposed, for example, to hypochlorous acid (HOCl). In vivo, the reduction of chloramines and chloramides may proceed through the action of superoxide, eventually catalyzed by redox-active transition metals, M nþ , where M may be Fe and/or Cu (Reactions (3.7) and (3.8)) [38, 39]. Nitrogen-centered protein radicals were detected by EPRspin trapping after the exposure of isolated proteins and plasma as well as red blood cells to HOCl (and HOBr) [32–35]. RaNHaCl þ M nþ ! RaNH þ Mðnþ1Þþ þ Cl
ð3:7Þ
R 0 aCOaNðClÞR þ M nþ ! R 0 aCOaNR þ Mðnþ1Þþ þ Cl
ð3:8Þ
Aminyl radicals have also been detected indirectly during the reaction of hydroxyl radicals (HO ) or their conjugated base ( O ) with the free amino group of amino acids (Reactions (3.9) and (3.10)) [40–43], and identified by time-resolved EPR experiments [44]. Similar reactions may be expected for peptides. While Reactions (3.9) and (3.10) show a net hydrogen transfer, they likely proceed via a stepwise electron-transfer and proton-transfer (Reaction (3.11)), a reaction commonly referred to as proton-coupled electron transfer (PCET). Proton transfer from the aminium radical cation to the base (OH ) will likely occur within the solvent cage.
ð3:9Þ
ð3:10Þ
HO þ RaNH2 ! H2 O þ RaNH
O þ RaNH2 ! HO þ RaNH
HO þ RaNH2 ½HO
þ
H2 NaR ! H2 O þ RaNH
ð3:11Þ
Aminyl and amidyl radicals are electrophilic, oxidizing radicals (cf. the oxidation of hydroquinone by aminyl radicals from Gly at pH 11; k ¼ 7:4 10 7 M1 s1 [40]).
1017
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3 Hydrogen Atom Transfer in Model Reactions
Moreover, they involve several fragmentation reactions, hydrogen transfer and protonation equilibria of potential biological significance (vide infra).
(3.12)
3.3.2
Reactions of Aminyl and Amidyl Radicals
Specifically intramolecular hydrogen transfer reactions of aminyl and amidyl radicals have been described, e.g., the 1,5-H-shift in the Hoffmann–Lo¨ffler–Freytag reaction, involving protonated aminyl radicals (aminium radical cations; reviewed in Ref. [45]). Amidyl radicals do not require protonation for hydrogen transfer. Representative kinetic data were obtained by laser flash photolysis for the intramolecular hydrogen transfer (1,5-H-shift) in the N-(6,6-diphenyl-5-hexenyl)acetamidyl radical 1 (Reaction (3.12); k12 ¼ 5:5 10 6 s1 [46]). Here, hydrogen transfer is facilitated by formation of the highly conjugated product radical. In addition, the intermolecular reaction of amidyl radicals with thiophenol (PhSH) proceeds with k ¼ 9 10 7 M1 s1 [46]. Davies and coworkers examined the reactivities of amidyl radicals derived from glucosamines, where evidence for both 1,5- and 1,2-H-shift processes was obtained (Scheme 3.2, Reactions (3.13) and (3.14)) [38, 39]. In aminyl radicals from amino acids and amidyl radicals from peptides, such a 1,2-H-shift (Reaction (3.15)) was considered feasible based on (i) the analogy to the well-known, solvent-assisted 1,2-H-shift within alkoxy radicals [19] and (ii) the exothermicity based on the homolytic bond dissociation energies (BDEs) of the NaH (406 kJ mol1 ) and the a CaH bond (363 kJ mol1 ) (representative values for the Gly anion [47]). However, both pulse radiolysis and g-radiolysis experiments concluded that the 1,2-H-shift in aminyl and amidyl radicals derived from amino acids and peptides must be rather slow (k15 A 1:2 10 3 s1 ) [37, 40].
HNaCH2 aCO2 ! H2 NaC HaCO2
ð3:15Þ
Some evidence for a reverse 1,2-H-shift was also obtained. In their studies on the radical-induced decarboxylation of Gly anion, Bonifacˇic´ et al. observed a protoncatalyzed decarboxylation of H2 NaC HaCO2 , which may proceed via Reactions (3.16)–(3.18) [40, 41].
H2 NaC HaCO2 ! þ H3 NaC HaCO2 þ
ð3:16Þ
H3 NaC HaCO2 ! þ H2 NaCH2 aCO2
þ
þ
H2 NaCH2 aCO2 ! H þ H2 NaCH2 þ CO2
ð3:17Þ ð3:18Þ
3.4 Sulfur-centered Radicals
Scheme 3.2.
1,2- and 1,5-H-shift in amidyl radicals of glucosamine moieties.
The latter mechanism would also serve to explain the decarboxylation via the reaction of Gly anion with methyl radicals, CH3 , and isopropyl radicals, (CH3 )2 C OH, namely via initial hydrogen abstraction by the carbon-centered radicals at the weak Gly anion a CaH bond, followed by Reactions (3.16)–(3.18).
3.4
Sulfur-centered Radicals
This section will mainly focus on two biologically relevant sulfur-centered radical species, thiyl radicals (RS ) and sulfide radical cations (R2 S þ ).
1019
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3 Hydrogen Atom Transfer in Model Reactions
3.4.1
Thiols and Thiyl Radicals Hydrogen Transfer from Thiols Thiols play an important role in the maintenance of the cellular redox state, the structural and functional integrity of proteins, and redox signaling. Moreover, specific enzymes utilize the one-electron oxidation products of thiols, thiyl radicals, for substrate turnover, e.g. the ribonucleotide reductases [3, 24–27], pyruvate formate lyase [3, 48–50], and benzylsuccinate synthase [51, 52]. Radiation chemical experiments have documented the potency of endogenous and exogenous thiols to protect cells against ionizing radiation [53–55]. Part of this protection is due to the direct reaction of primary and secondary radicals with thiols (the ‘‘repair reaction’’) according to the general reactions (3.19) and (3.20). 3.4.1.1
X þ RSH ! XH þ RS
X þ RS ! X þ RS
ð3:19Þ
ð3:20Þ
The repair of carbohydrate radicals within polynucleotides can proceed with remarkable stereoselectivity, as demonstrated for hydrogen transfer from both 2-mercaptoethanol and dithiothreitol to deoxyuridin-1 0 -yl radials within singleand double-stranded oligonucleotides (Scheme 3.3, Reactions (3.21a) and (3.21b)) [56]. Reactions (3.21a) and (3.21b) yield a ca. 4-fold excess of b- over a-doxyuridine in single-stranded oligonucleotides, which increases to a ca. (7–8)-fold excess for double-stranded oligonucleotides. To date, numerous reports have identified thiyl radical formation in vitro and in vivo as a consequence of enzyme turnover [3, 24– 27, 48–52, 57], oxidative stress [58] and drug metabolism [59]. Among the biologically relevant species generating thiyl radicals during conditions of oxidative stress are the nitrogen monoxide (NO ) metabolites nitrogen dioxide ( NO2 ) [60] and peroxynitrite/peroxynitrous acid (ONOO/ONOOH) [58, 61, 62], the oxygencentered hydroxyl (HO ) [53], alkoxyl (RO ) [17], peroxyl (ROO ) [63] and phenoxyl (ArO ) [64] radicals, and carbon-centered radicals [53]. The hydrogen transfer reaction between carbon-centered radicals and thiols has been especially the focus of intense theoretical and mechanistic investigation. Central to these studies is the controversy about the structure of the transition state, affecting the heights of the activation barriers. Zavitsas and coworkers utilize the four canonical structures I–IV, given below, to describe the transition state [65–67].
X"#H Y"ðIÞ "X H#"YðIIÞ X" H# Y"ðIIIÞ ½X H Y ðIVÞ Structure III represents an antibonding, triplet repulsion between the atoms or groups transferring the hydrogen atom (here, a carbon-centered and a thiyl radical), which has a significant influence on the activation barrier. They conclude that polar transition state structures are not necessary to rationalize experimental re-
3.4 Sulfur-centered Radicals
Scheme 3.3.
Reactions of deoxyuridin-1 0 -yl radials with thiols.
sults (and may even lead to predictions of reactivity which strongly deviate from experimental results). In contrast, Roberts and coworkers have devised the concept of ‘‘polarity reversal catalysis’’ (PRC), where polar transition states are dominant features explaining the catalytic affect of thiols and thiyl radicals on hydrogen transfer reactions between carbon-centered radicals and several hydrogen donors [68–70]. Theoretical support for polar transition states in the hydrogen transfer from thiols to carbon-centered radicals comes from recent work of Beare and Coote [71], who provide strong evidence for the involvement of Structures V and VI, given below.
Cþ H S ðVÞ C H Sþ ðVIÞ Reid and coworkers experimentally re-determined the rate constants for hydrogen transfer between a model thiol, 1,4-dithiothreitol, and several carbon-centered rad-
1021
1022
3 Hydrogen Atom Transfer in Model Reactions
icals [72]. The substrate 1,4-dithiothreitol (structure 2) represents an elegant model system for the direct time-resolved measurement of absolute rate constants for hydrogen transfer according to Reactions (3.22) and (3.23). Here, the product thiyl radical 3 undergoes spontaneous cyclization and deprotonation (pK a; 2 ¼ 5:2) to the radical anion 4, which has a strong UV absorption with l max ¼ 390 nm. In this sequence, concentrations can be adjusted such that Reaction (3.22) is rate-determining. The reactivity of carbon-centered radicals with 1,4-dithiothreitol increased in the following order: CH2 CðCH3 Þ2 OH < CH3 < CH2 OH < CHðCH3 ÞOH < C(CH3 )2 OH. Among these radicals, Reaction (3.24) generates the product with the lowest CaH bond energy (isopropanol), but, nevertheless, shows the highest rate constant for hydrogen transfer.
CðCH3 Þ2 OH þ RSH ! HaCðCH3 Þ2 OH þ RS
ð3:24Þ
Parallel theoretical studies (with CH3 SH instead of 1,4-dithiothreitol) gave clear evidence for polar transition state structures of the general type V, where, in the alcohol-derived radicals, the positive charge developing on the carbon forming the new CaH bond is stabilized by the a-OH substituent. Importantly, increasing charge separation in the transition state was observed within the series CH3 < CH2 OH < C(CH3 )2 OH, consistent with the introduction of additional a-substituents. These results are in agreement with the data of Beare and Coote [71]. The results of Reid et al. [72] are also discussed in terms of orbital interaction theory, where the isopropyl radical, C(CH3 )2 OH, is characterized by the highest SOMO energy, supporting interaction with the LUMO of CH3 SH, i.e. the s orbital of the HaS bond. Several enzymes utilize thiyl radicals for substrate conversion. In the ribonucleotide reductase (RNR) class III, pyruvate formate lyase and benzylsuccinate synthase, cysteine thiyl radicals are generated via hydrogen transfer from cysteine to glycine radicals (Reaction (3.25)) [3, 24–27, 48–52].
(3.25) The efficiency of Reaction (3.25) depends on the conformational properties of glycine and the product glycyl radical, respectively, within the protein. If the glycyl
3.4 Sulfur-centered Radicals
radical can adopt an ideal planar structure, hydrogen transfer from Cys is endothermic and the reverse reaction, i.e. hydrogen transfer from glycine to cysteinyl radicals (Reaction (3.25)), will prevail (vide infra). On the other hand, if the glycyl radical adopts a pyramidal structure, Reaction (3.25) would be exothermic. Here, the protein has the opportunity to fine-tune hydrogen transfer equilibria through conformational properties. Calculations have shown that the CaH homolytic bond dissociation energy (BDE) of glycine depends on the secondary strucure, in which the amino acid is located, i.e. BDE(Ca aH) ¼ 402; 404, and 361 kJ mol1 for Gly within an a-helix, parallel b-sheet and antiparallel b-sheet, respectively [73]. In contrast, BDE(Ca aH) ¼ 330–370 kJ mol1 for Gly within linear, relaxed peptide structures [73]. Hence, glycyl radicals within a-helical or parallel b-sheet conformation should especially rapidly abstract hydrogen from protein cysteine residues, which show SaH BDE values of the order of 370 kJ mol1 . In contrast, cysteinyl radicals may abstract hydrogen atoms from Gly located in antiparallel b-sheets or relaxed peptide conformations. In ribonucleotide reductase class II, thiyl radicals are generated via hydrogen transfer from Cys to the primary carbon-centered radical generated from 5 0 -deoxy5 0 -adenosylcobalamin [3]. In contrast, ribonucleotide reductase class I generates cysteinyl radicals via long-range electron and/or proton-coupled electron transfer involving an ultimate hydrogen transfer from Cys to a tyrosyl radical [3]. Hydrogen Abstraction by Thiyl Radicals The calculated bond energies (vide supra) provide one rationale for the propensity of thiyl radicals to abstract hydrogen atoms from a variety of biological substrates (Reaction (3.26)). Hence, with suitable substrates the ‘‘repair reaction’’ may actually proceed in the reverse direction [74]. 3.4.1.2
RS þ YH ! RSH þ Y
ð3:26Þ
In all three classes of ribonucleotide reductases, a cysteinyl radical (in the E. coli RNR1 sequence at position Cys 439 ) abstracts a hydrogen atom from the C3 0 position of the carbohydrate moiety of the ribonucleotide substrate [3]. Biomimetic model studies of this enzymatic process were designed, achieving intramolecular hydrogen transfer within a tetrahydrofurane-appended thiyl radical (Scheme 3.4; Reactions (3.27) and (3.28) [75, 76]. In kinetic NMR experiments, rate constants for the intermolecular hydrogen transfer from several carbohydrates to cysteinyl radicals were found to be of the order of k29 ¼ (1–3) 10 4 M1 s1 at 37 C [77]. These values agree with previous, pulse radiolytically determined rate constants for thiyl radical-mediated hydrogen abstraction from various model alcohols and ethers [74, 78, 79]. In contrast, the reverse reaction, hydrogen transfer from thiols to carbohydrate radicals, proceeds with k29 > 10 6 M1 s1 [80, 81], indicating that equilibrium (3.29) is normally located far to the left-hand side.
k29
RS þ ðCarbohydrateÞCaH ¼ RSH þ ðCarbohydrateÞC k29
ð3:29Þ
1023
1024
3 Hydrogen Atom Transfer in Model Reactions
Scheme 3.4. Biomimetic model reaction displaying a 1,5-Hshift in thiyl radicals containing a tetrahydrofuran substituent.
However, efficient water elimination [82] from the resulting carbohydrate C3 0 radical of the original ribonucleotide will shift equilibrium (3.29) to the right-hand side. Moreover, in RNR1, the activation barrier for hydrogen transfer to the cysteinyl radical may be lowered through hydrogen bonding of the C2 0 OH group to Glu 441 (model systems were calculated, in which the ribose moiety was replaced by ethylene glycol or cis-tetrahydrofurane-2,3-diol, and Glu 441 was replaced by formate, acetate and acetamide) [83].
ð3:30Þ
While equilibrium (3.29) for the uncatalyzed reaction of thiyl radicals with carbohydrates is located far to the left, the analogous equilibrium (3.30) with peptide and protein substrates may actually shift to the right-hand side. In equilibrium (3.30), the a C radical of the amino acid moiety is displayed in a planar conformation; in reality, this conformation may be approached in linear peptides by glycine (RbH) or cyclic peptide models, such as the diketopiperazines, but less likely by amino acid moieties different from glycine. Table 3.1 displays rate constants for the hydrogen abstraction by cysteamine thiyl radicals from several N-acetyl-amino acid amides and diketopiperazines [84]. These rate constants were obtained through competition kinetics in D2 O at pD 3.0–3.4, using isopropanol as a competitor. Several important features are noted: (i) the cyclic diketopiperazines show generally higher rate constants per a CaH bond compared to their linear analogs (cf., GlyA and N-Ac-Gly-NH2 ), (ii) the trend of calculated a CaH bond energies does not match the trend of experimental rate
3.4 Sulfur-centered Radicals Table 3.1. Rate constants for the reaction of cysteamine thiyl radicals with model peptides in D2 O, pD 3.0–3.4 at 37 C (adapted from Ref. [84]; abbreviations for the diketopiperazines: SarcA ¼ sarcosine anhydride, Gly ¼ glycine anhydride).
Substrate
k30 , 10 4 MC1 sC1
k30 per a CxH bond, 10 4 MC1 sC1
BDE of a CxH[a], kJ molC1
SarcA GlyA N-Ac-Gly-NH2 N-Ac-Ala-NH2 N-Ac-Asp-NH2 N-Ac-Gln-NH2 N-Ac-Pro-NH2
40 G 8 32 G 16 6.4 G 2.8 1.0 G 0.3 0.44 G 0.16 0.19 G 0.06 0.18 G 0.06
10 8.0 3.2 1.0 0.44 0.19 0.18
– 350 (340[b]) 350 345 332 334 358 (cis) 369 (trans)
a Ab
initio calculated values [85]; b experimental value [86].
constants, i.e. decreasing a CaH bond energies are paralleled by decreasing rate constants. This effect can be rationalized by steric constraints induced by the increasing bulkiness of the amino acid side chain, which prevents the generated peptide a C radical from approaching the ideal planar conformation for maximal captodative stabilization of the radical. Importantly, pulse radiolysis and steadystate radiolysis experiments failed to measure a rate-constant for the reaction of a C radicals from glycine anhydride with thiols, suggesting that for GlyA, k30 a 10 5 M1 s1 . Here k ¼ 10 5 M1 s1 reflects the lower limit of second order rate constants measurable by the pulse radiolysis technique, except for a few cases where very high substrate concentrations (>0.1 M) can be adjusted. Hence, K30 ð¼ k30 =k30 Þ b 3:0, indicating that equilibrium (3.30) for the diketopiperazines is located more on the right-hand side. This conclusion is well-supported by the deuterium NMR studies of Anderson and coworkers [87–89], who have exposed amino acids and peptides in D2 O to radiation chemically generated hydroxyl radicals, and monitored repair of the amino acid radicals by deuterated dithiothreitol. In all their experiments, Gly showed the lowest efficiency of deuterium incorporation, indicating that the reaction of glycyl radicals with dithiothreitol is of low efficiency. A low value for k30 is also in accord with similar findings for the reaction of thiyl radicals with polyunsaturated fatty acids, where hydrogen abstraction from bisallylic methylene groups occurs with k31 b 3 10 6 M1 s1 [90] (k31 depends on the number of bisallylic methylene groups within the fatty acid chain), generating a stable pentadienyl radical. No experimental evidence for the reverse reaction was obtained, i.e. k31 < 10 5 M1 s1 . Analogous pulse radiolysis experiments detected no measurable reaction of cyclohexadienyl radicals with thiols [81].
1025
1026
3 Hydrogen Atom Transfer in Model Reactions Table 3.2. Rate constants for the reaction of cysteamine thiyl radicals with selected amino acid substrates containing reactive side chains; in D2 O, pD 3.0–3.4 at 37 C (adapted from Ref. [91]).
Substrate
k32 , 10 4 MC1 sC1
kside chain , 10 4 MC1 sC1
AlaNH2 GlyNH2 HisNH2 MetNH2 PheNH2 SerNH2 ThrNH2 ValNH2
0.4 G 0.1 0.7 G 0.4 0.4 G 0.1 1.8 G 0.5 1.5 G 0.2 23 G 7 10 G 5 0.8 G 0.3
n.d. – n.d. 0.9 G 0.6 1.3 G 0.6 16 G 4 4.4 G 0.8 <0.3
ð3:31Þ
The kinetic NMR method permitted also the determination of rate constants k32 for hydrogen transfer to cysteamine thiyl radicals from selected amino acids containing reactive side chains [91]. A summary of these rate constants is given in Table 3.2. Here, the rate constant k32 represents the sum of the individual rate constants for hydrogen transfer from a CaH (k30 ) and from the side chain CaH bonds (ksc ), i.e., k32 ¼ k30 þ ksc .
ð3:32Þ
These rate constants were obtained with amino acid amides at pD 3.0–3.4. The low pD value ensures full protonation (deuteration) of the amino group while the use of the respective amides avoids any possible interference from zwitterion forma-
3.4 Sulfur-centered Radicals
tion, which could be a problem with the free amino acids. Full protonation of the amino group has a decelerating effect on hydrogen abstraction from a CaH due to the lack of possible captodative stabilization [92]. Hence, especially in the amino acid amides at low pD, hydrogen transfer from the amino acid side chains can compete with hydrogen transfer from a CaH. Noteworthy in Table 3.2 are the high rate constants k32 and ksc for SerNH2 , which are significantly larger than the comparable rate constants for ThrNH2 . These data are in clear contrast to rate constants for hydrogen transfer from ethanol (k ¼ 6 10 3 M1 s1 at 20 C) and isopropanol (k ¼ 2 10 4 M1 s1 at 20 C) [78, 79]. Moreover, these show the opposite trend with the higher value for the higher substituted substrate, consistent with a lower CaH BDE. At this point we can only speculate about a possible rationale for this observation, such as a potential stabilization of a polar transition state by the C-terminal amide (theoretical studies demonstrate that polar transition states play an important role in the hydrogen abstraction from amino acid moieties by thiyl radicals [93]). An analogous effect has been postulated by Easton and Merett for anchimeric assistance in the hydrogen abstraction from Phe derivatives [94].
Model calculations allow the predictions that, especially, the hydrogen transfer from a CaH to thiyl radicals may be of physiological significance. A detailed summary of these calculations is given elsewhere [91] and will not be repeated here. Important for these considerations is the fact that any of the carbon-centered amino acid/peptide radicals will react efficiently with molecular oxygen (k A 2 10 9 M1 s1 [8]). While thiyl radicals also react with oxygen, this reaction is reversible (k33 ¼ 2:2 10 9 M1 s1 ; k33 ¼ 6 10 5 s1 ) [95] and an efficient elimination of thiyl radicals from equilibrium (3.30) is only possible through the irreversible rearrangement of thiyl peroxyl radicals to sulfonyl radicals, where k34 A 2 10 3 s1 at 37 C [95]. To date no rate constants have been published for the intramolecular hydrogen transfer between amino acid moieties and cysteinyl radicals in peptides. Preliminary data exist for the reversible hydrogen transfer in radicals of the peptide Nacetyl-Cys-(Gly)6 , where glycyl radicals abstract the thiol hydrogen from Cys with k A 10 6 s1 and the reverse reaction occurs with k A 2 10 5 s1 [96]. The high reactivity of the glycyl radicals in this linear peptide (vs. the low reactivity of glycyl radicals in GlyA) may be rationalized by the propensity of polyGly peptides to adopt secondary structures such as helical and b-sheet conformations [97, 98] (possibly raising the a CaH BDE of the glycyl residues). A specific case of intramolecular hydrogen transfer was reported for thiyl radicals of the peptide glutathione [99, 100]. Here, thiyl radicals abstract the hydrogen atom from the Nterminal g-glutamyl residue, where the forming carbon-centered radical is stabilized captodatively by both a free amino group and a free carboxylate group.
1027
1028
3 Hydrogen Atom Transfer in Model Reactions
Besides peptides, proteins and polyunsaturated fatty acids, DNA and RNA represent a third large class of biomolecules sensitive to covalent modification under conditions of oxidative stress. Few studies have focused on the potential reaction of thiyl radicals with polynucleotides. The active site cysteinyl radical required for deoxynribonucleotide synthesis by the ribonucleotide synthases, and model studies with carbohydrates, have shown that DNA damage by thiyl radicals is, in principle, feasible. Obviously, thiyl radical reactions with DNA have to compete with thiyl radical reactions with endogenous antioxidants such as ascorbate and glutathione. However, charge repulsion excludes especially, negatively charged molecules [54, 55] (such as ascorbate and glutathione at physiological pH) from the immediate environment of the DNA strand. Hence, there will be a concentration gradient, where the concentration of these negatively charged antioxidant molecules close to the DNA strand may be lower than that in the ‘‘bulk solution’’. Jain et al. studied the degradation of DNA by glutathione and Cu(ii) under anaerobic conditions, suggesting the involvement of glutathione thiyl radicals [101]. Recently, evidence for a reaction of thiyl radicals with nucleobases has been provided. Carter et al. designed model experiments, which confirmed that thiyl radicals would add to pyrimidine bases [102]. Moreover, our own experiments provided rate constants for hydrogen abstraction at the C5aCH3 group of both thymine (Scheme 3.5; k35a ¼ 1:2 10 4 M1 s1 ) and thymidine-5 0 -monophosphate (k35b ¼ 0:9 10 4 M1 s1 ) [103]. These rate constants are comparable to that for hydrogen abstraction from toluenesulfonate (tosylate) (k ¼ 2:7 10 4 M1 s1 ) [103] and also to that
Scheme 3.5. Thiyl radicals react with the C5aCH3 group of thymine and thymidine-5 0 -monophosphate.
3.4 Sulfur-centered Radicals
for the reaction of thiyl radicals with the benzylic (ksc ¼ 1:3 10 4 M1 s1 ; see Table 3.2) [91].
b
C H bond in PheNH2
3.4.2
Sulfide Radical Cations
The one-electron oxidation of organic sulfides yields sulfide radicals cations (Reaction (3.36)) [104]. >S þ Ox ! >S
þ
þ Ox
ð3:36Þ
In general, sulfide radical cations would either deprotonate in the a-position to the sulfur, yielding a-(alkylthio)alkyl radicals, or engage in the one-electron oxidation of additional substrates. However, recent hypothesis and results have focused on a possible role of methionine sulfide radical cations in hydrogen abstraction reactions within the Alzheimer’s disease b-amyloid peptide (bAP) [73]. These mechanisms will be discussed here in some detail. bAP represents a 39–42 amino acid peptide, released from the amyloid precursor protein, with a pronounced tendency to form low and high molecular weight aggregates [105, 106]. The NMR structure of bAP recorded in aqueous micelles shows a helical conformation around Met 35 in the C-terminus [107]. This Met 35 residue appears to have a critical function as electron donor during the reduction of Cu(ii) [108], which complexes via three His residues to the N-terminal part of bAP [106]. Model calculations have pointed to the possible role of the helical conformation in stabilizing Met sulfide radical cations through three-electron bond formation with the carbonyl oxygen of the peptide bond C-terminal to Ile 31 [109]. In fact, substitution of Ile 31 by the helix-breaking Pro 31 lowers the propensity of bAP to reduce Cu(ii) [110]. A schematic representation of the three-electron bonded Met sulfide radical cation is given in structure 5 (Scheme 3.6). Theoretical studies by Rauk and coworkers [73] predict that such a sulfur– oxygen bonded radical cation complex can abstract a hydrogen atom from Gly, ultimately yielding a proton and reducing the Met sulfide radical cation back to Met (Scheme 3.6, Reactions (3.37) and (3.38)). Such a mechanism would combine the known redox activity of bAP with the generation of a carbon-centered radical at a specific site, which could serve as an origin for bAP cross-linking and formation of insoluble aggregates. This is an attractive hypothesis, and subsequent studies by Butterfield and coworkers showed that bAP containing the Gly 33 Val mutation was less neurotoxic [111]. When dissociated from the carbonyl complex (structure 5), the sulfide radical cation of Met would probably meet the conditions defined by Parker and coworkers [112], restricting hydrogen abstraction by radical cations to those species, where the odd electron is located in a nonbonding orbital. However, several facts and observations must be considered, which may limit the necessity or importance of Reactions (3.37) and (3.38) in bAP. First, the deprotonation of Met sulfide radical cations to a-(alkylthio)alkyl radicals generates carbon-centered radicals, even in the absence of any potential hydrogen transfer from Gly residues
1029
1030
3 Hydrogen Atom Transfer in Model Reactions
Scheme 3.6. The proposed hydrogen abstraction by (S8O) three-electron-bonded Met sulfide radical cation from Gly.
[113]. These a-(alkylthio)alkyl radicals could lead to covalent aggregation. Moreover, the addition of oxygen would yield peroxyl radicals, species, which have been identified by electron paramagnetic resonance (EPR) spectroscopy during the incubation of bAP in buffer. Second, pulse radiolysis experiments, in which Met sulfide radical cations were generated in linear, flexible N-Ac-(Gly)n Met(Gly)n model peptides (n ¼ 1 and 3) did not reveal any hydrogen transfer from either of the Gly residues to the sulfide radical cations [114]. In these peptides the Gly radical would have been easily detected on the basis of their strong absorbance around 320 nm. Hence, it must be concluded that the theoretically predicted hydrogen transfer from Gly to Met sulfide radical cations in bAP may be restricted to highly organized assemblies such as b-sheet structures. However, mechanistic studies suggest that redox reactions of bAP, involving Met oxidation, may occur predominantly in low molecular weight aggregates, which may not contain the b-sheet structure. Our recent results suggest an alternative potential pathway for the generation of a C radicals in Met-containing peptides [114], originating from sulfide radical cations and/or their intramolecular complexes with functionalities of the peptide bond. Pulse radiolysis experiments with model peptides provided the kinetics and yields for sulfur–oxygen three-electron bond formation between Met sulfide radical cations and peptide bond carbonyl groups. Supported by time-resolved UV and conductivity studies, a pH-dependent conversion of these sulfur–oxygen-bonded radical cations into sulfide–nitrogen-bonded radicals was observed, displayed in Scheme 3.7, Reactions (3.39)–(3.41) (control experiments with the model substrate N-acetylmethionineethyl ester confirmed that this mechanism can occur with the peptide bond N-terminal of the Met residue).
3.4 Sulfur-centered Radicals
Scheme 3.7. The pH-dependent rearrangement of (S8O) to (S8N) three-electron-bonded Met sulfide radical cation involving the amide bond N-terminal of the Met residue.
A fraction of these sulfur–nitrogen bonded radical complexes ultimately converted into a C radicals, identified through their characteristic absorbance with l max ¼ 350 nm. Scheme 3.8, Reactions (3.42)–(3.45), displays a tentative mechanism for the formation of these a C radicals, involving the formal 1,2-H-shift of
Scheme 3.8. Conversion of N-terminal (S8N) three-electron bonded Met sulfide radical cation into the a C. radical.
1031
1032
3 Hydrogen Atom Transfer in Model Reactions
an intermediary amidyl radical (analogous to the reactions described in the section on N-centered radicals; vide supra). Alternatively, amide radical protonation followed by a CaH deprotonation (Reactions (3.44) and (3.45)) of the intermediary nitrogen-centered radical cation would lead to the same product.
3.5
Conclusion
This article summarizes the mechanisms and kinetics of selected biologically relevant hydrogen transfer reactions of oxygen-, nitrogen- and sulfur-centered radicals. Special emphasis has been placed on hydrogen transfer reactions involving amino acids and peptides. Many of the rate constants known to date have been measured with small organic model compounds. These results provide a reasonable basis for an approximate extrapolation onto proteins. However, the higher order structure and molecular dynamics of proteins will affect both the mechanisms and kinetics of inter- and intramolecular hydrogen transfer reactions. Therefore, these reactions need to be monitored directly at some point. Hence, future research should focus on the design of experiments, instruments and software to support the direct kinetic measurements of hydrogen transfer reactions in proteins.
Acknowledgment
Support by the NIH (PO1AG12993) is gratefully acknowledged.
References 1 Radicals in Organic Synthesis,
2
3 4 5
6 7
P. Renaud, M. P. Sibi (Eds.), Vol. 1 and 2, Wiley-VCH, Weinheim, 2001. I. W. M. Smith, A. R. Ravishankara, J. Phys. Chem. A 2002, 106, 4798–4807. J. Stubbe, W. A. van der Donk, Chem. Rev. 1998, 98, 705–762. R. T. Dean, S. Fu, R. Stocker, M. J. Davies, Biochem. J. 1997, 324, 1–18. C. L. Hawkins, M. J. Davies, Biochim. Biophys. Acta 2001, 1504, 196–219. C. L. Hawkins, M. J. Davies, J. Chem. Soc., Perkin Trans. 2 1998, 2617–2622. G. V. Buxton, C. L. Greenstock, W. P. Helman, A. B. Ross, J. Phys. Chem. Ref. Data 1988, 17, 513–886.
8 O. J. Mieden, M. N. Schuchmann,
9 10 11 12
13 14 15
C. Von Sonntag, J. Phys. Chem. 1993, 97, 3783–3790. S. Gebicki, J. M. Gebicki, Biochem. J. 1993, 289, 743–749. J. Neuzˇil, J. M. Gebicki, R. Stocker, Biochem. J. 1993, 293, 601–606. S. Gieseg, S. Duggan, J. M. Gebicki, Biochem. J. 2000, 350, 215–218. S. Fu, R. Dean, M. Southan, R. Truscott, J. Biol. Chem. 1998, 273, 28603–28609. M. J. Davies, S. Fu, R. T. Dean, Biochem. J. 1995, 305, 643–649. M. L. Huang, A. Rauk, J. Phys. Org. Chem. 2004, 17, 777–786. M. J. Davies, Arch. Biochem. Biophys. 1996, 336, 163–172.
References 16 H. A. Headlam, A. Mortimer, C. J.
17
18
19
20
21
22
23
24 25
26 27
28 29
30
31
32 33 34 35
Easton, M. J. Davies, Chem. Res. Toxicol. 2000, 13, 1087–1095. M. Erben-Russ, C. Michel, W. Bors, M. Saran, J. Phys. Chem. 1987, 91, 2362–2365. D. V. Avila, C. E. Brown, K. U. Ingold, J. Lusztyk, J. Am. Chem. Soc. 1993, 115, 466–470. K. G. Konya, T. Paul, S. Lin, J. Lusztyk, K. U. Ingold, J. Am. Chem. Soc. 2000, 122, 7518–7527. M. Bonifacˇic´, D. A. Armstrong, I. Sˇtefanic´, K.-D. Asmus, J. Phys. Chem. B 2003, 107, 7268–7276. D. W. Snelgrove, J. Lusztyk, J. T. Banks, P. Mulder, K. U. Ingold, J. Am. Chem. Soc. 2001, 123, 469–477. R. Vargas, J. Garza, D. A. Dixon, B. P. Hay, J. Am. Chem. Soc. 2000, 122, 4750–4755. F. Cordier, M. Barfield, S. Grzesiek, J. Am. Chem. Soc. 2003, 125, 15750–15751. J. Stubbe, J. Ge, C. S. Yee, Trends Biochem. Sci. 2001, 26, 93–99. J. Stubbe, D. G. Nocera, C. S. Yee, M. C. Y. Chang, Chem. Rev. 2003, 103, 2167–2202. F. Himo, P. E. M. Siegbahn, Chem. Rev. 2003, 103, 2421–2456. L. Noodleman, T. Lovell, W.-G. Han, J. Li, F. Himo, Chem. Rev. 2004, 104, 459–508. A. Tsai, R. J. Kulmacz, G. Palmer, J. Biol. Chem. 1995, 270, 10503–10508. S. Peng, N. M. Okeley, A. Tsai, G. Wu, R. J. Kulmacz, W. A. van der Donk, J. Am. Chem. Soc. 2001, 123, 3609–3610. S. Peng, N. M. Okeley, A. Tsai, G. Wu, R. Kulmacz, W. A. van der Donk, J. Am. Chem. Soc. 2002, 124, 10785–10796. M. Foti, K. U. Ingold, J. Lusztyk, J. Am. Chem. Soc. 1994, 116, 9440– 9447. C. L. Hawkins, M. J. Davies, J. Chem. Soc., Perkin Trans. 2 1998, 1937–1945. C. L. Hawkins, M. J. Davies, Biochem. J. 1998, 332, 617–625. C. L. Hawkins, M. J. Davies, Biochem. J. 1999, 340, 539–548. C. L. Hawkins, B. E. Brown, M. J.
36
37
38
39
40
41
42
43
44
45
46
47
48 49
50 51
52
Davies, Arch. Biochem. Biophys. 2001, 395, 137–145. C. L. Hawkins, D. I. Pattison, M. J. Davies, Biochem. J. 2002, 365, 605–615. D. I. Pattison, M. J. Davies, K.-D. Asmus, J. Chem. Soc., Perkin Trans. 2 2002, 1461–1467. M. D. Rees, C. L. Hawkins, M. J. Davies, J. Am. Chem. Soc. 2003, 125, 13719–13733. M. D. Rees, C. L. Hawkins, M. J. Davies, Biochem. J. 2004, 381, 175–184. M. Bonifacˇic´, I. Sˇtefanic´, G. L. Hug, D. A. Armstrong, K.-D. Asmus, J. Am. Chem. Soc. 1998, 120, 9930–9940. M. Bonifacˇic´, D. A. Armstrong, I. Carmichael, K.-D. Asmus, J. Phys. Chem. B 2000, 104, 643–649. I. Sˇtefanic´, M. Bonifacˇic´, K.-D. Asmus, D. A. Armstrong, J. Phys. Chem. A 2001, 105, 8681–8690. D. A. Armstrong, K.-D. Asmus, M. Bonifacˇic´, J. Phys. Chem. A 2004, 108, 2238–2246. P. Wisniowski, I. Carmichael, R. W. Fessenden, G. L. Hug, J. Phys. Chem. A 2002, 106, 4573–4580. L. Feray, N. Kuznetsov, P. Renaud, in Radicals in Organic Synthesis, P. Renaud, M. P. Sibi (Eds.), Vol. 2, Wiley-VCH, Weinheim, 2001, pp. 246–278. J. H. Horner, O. M. Musa, A. Bouvier, M. Newcomb, J. Am. Chem. Soc. 1998, 120, 7738–7748. D. Yu, A. Rauk, D. A. Armstrong, J. Am. Chem. Soc. 1995, 117, 1789– 1796. F. Himo, L. A. Eriksson, J. Am. Chem. Soc. 1998, 120, 11449–11455. A. Becker, K. Fritz-Wolf, W. Kabsch, J. Knappe, S. Schultz, A. F. Volkner Wagner, Nature Struct. Biol. 1999, 6, 969–975. A. Becker, W. Kabsch, J. Biol. Chem. 2002, 277, 40036–40042. C. J. Krieger, W. Rooseboom, S. P. J. Albracht, A. M. Spormann, J. Biol. Chem. 2001, 276, 12924–12927. F. Himo, J. Phys. Chem. B 2002, 106, 7688–7692.
1033
1034
3 Hydrogen Atom Transfer in Model Reactions 53 C. von Sonntag, The Chemical Basis
54
55
56
57 58
59
60
61 62
63
64
65 66 67
68 69 70
71 72
of Radiation Biology, Taylor & Francis, London, 1987. S. Zheng, G. L. Newton, G. Gonick, R. C. Fahey, J. F. Ward, Radiat. Res. 1988, 114, 11–27. J. A. Aguilera, G. L. Newton, R. C. Fahey, J. F. Ward, Radiat. Res. 1992, 130, 194–204. J.-T. Hwang, M. M. Greenberg, J. Am. Chem. Soc. 1999, 121, 4311– 4315. C. Mottley, R. P. Mason, J. Biol. Chem. 2001, 276, 42677–42683. J. Vasquez-Vivar, A. M. Santos, V. B. Junqueira, O. Augusto, Biochem. J. 1996, 314, 869–876. I. Wilson, P. Wardman, G. M. Cohen, M. d’Arcy Doherty, Biochem. Pharmacol. 1986, 35, 21–22. E. Ford, M. N. Hughes, P. Wardman, Free Radical Biol. Med. 2002, 32, 1314–1323. R. M. Gatti, R. Radi, O. Augusto, FEBS Lett. 1994, 348, 287–290. X. Shi, Y. Rojanasakul, P. Gannett, K. Liu, Y. Mao, L. N. Daniel, N. Ahmed, U Saffiotti, J. Inorg. Biochem. 1994, 56, 77–86. K. Hildenbrand, D. SchulteFrohlinde, Int. J. Radiat. Biol. 1997, 71, 377–385. ¨ tz, in Sulfur-Centered W. A. Pru Reactive Intermediates in Chemistry and Biology, C. Chatgilialoglu, K.-D. Asmus (Eds.), NATO ASI Series A, Vol. 197, 1990, pp. 389–399. A. A. Zavitsas, J. A. Pinto, J. Am. Chem. Soc. 1972, 94, 7390–7396. A. A. Zavitsas, A. A. Melikian, J. Am. Chem. Soc. 1975, 97, 2757–2763. A. A. Zavitsas, C. Chatgilialoglu, J. Am. Chem. Soc. 1995, 117, 10645–10654. B. P. Roberts, Chem. Soc. Rev. 1999, 28, 25–35. Y. Cai, B. P. Roberts, J. Chem. Soc., Perkin Trans. 2, 2002, 1858–1868. H.-S. Dang, B. P. Roberts, D. A. Tocher, J. Chem. Soc., Perkin Trans. 1 2001, 2452–2461. K. D. Beare, M. L. Coote, J. Phys. Chem. A 2004, 108, 7211–7221. D. L. Reid, G. V. Shustov, D. A.
73
74
75 76
77 78
79
80
81
82 83 84 85
86
87 88
89
Armstrong, A. Rauk, M. N. Schuchmann, M. S. Akhlaq, C. von Sonntag, Phys. Chem. Chem. Phys. 2002, 4, 2965–2974. A. Rauk, D. A. Armstrong, D. P. Fairlie, J. Am. Chem. Soc. 2000, 122, 9761–9767. M. S. Akhlaq, H.-P. Schuchmann, C. Von Sonntag, Int. J. Radiat. Biol. 1987, 51, 91–102. M. J. Robins, G. J. Ewing, J. Am. Chem. Soc. 1999, 121, 5823–5824. Z. Guo, M. C. Samano, J. W. Krzykawski, S. F. Wnuk, G. J. Ewing, M. J. Robins, Tetrahedron 1999, 55, 5705–5718. D. Pogocki, Ch. Scho¨neich, Free Radical Biol. Med. 2001, 31, 98–107. Ch. Scho¨neich, M. Bonifacˇic´, K.-D. Asmus, Free Radical Res. Commun. 1989, 6, 393–394. Ch. Scho¨neich, K.-D. Asmus, M. Bonifacˇic´, J. Chem. Soc., Faraday Trans. 1995, 91, 1923–1930. M. Z. Baker, R. Badiello, M. Tamba, M. Quintiliani, G. Gorin, Int. J. Radiat. Biol. Relat. Stud. Phys. Chem. Med. 1982, 41, 595–602. C. von Sonntag, in Sulfur-Centered Reactive Intermediates in Chemistry and Biology, C. Chatgilialoglu, K.-D. Asmus (Eds.), NATO ASI Series A, Vol. 197, 1990, pp. 359–366. R. Lenz, B. Giese, J. Am. Chem. Soc. 1997, 119, 2784–2794. H. Zipse, Org. Biomol. Chem. 2003, 1, 692–699. T. Nauser, Ch. Scho¨neich, J. Am. Chem. Soc. 2003, 125, 2042–2043. A. Rauk, D. Yu, J. Taylor, G. V. Shustov, D. A. Block, D. A. Armstrong, Biochemisty 1999, 38, 9089–9096. M. Jonsson, D. D. M. Wayner, D. A. Armstrong, D. Yu, A. Rauk, J. Chem. Soc., Perkin Trans. 2 1998, 1967–1972. M. B. Goshe, V. E. Anderson, Radiat. Res. 1999, 151, 50–58. M. B. Goshe, Y. H. Chen, V. E. Anderson, Biochemistry 2000, 39, 1761–1770. B. N. Nukuna, M. B. Goshe, V. E. Anderson, J. Am. Chem. Soc. 2001, 123, 1208–1214.
References ¨ neich, U. Dillinger, F. 90 Ch. Scho
91
92
93
94 95
96 97 98
99
100
101
102
von Bruchhausen, K.-D. Asmus, Arch. Biochem. Biophys. 1992, 292, 456–467. T. Nauser, J. Pelling, Ch. Scho¨neich, Chem. Res. Toxicol. 2004, in press. C. J. Easton, in Radicals in Organic Synthesis, P. Renaud, M. P. Sibi (Eds.), Vol. 2, Wiley-VCH, Weinheim, 2001, pp. 505–525. D. L. Reid, D. A. Armstrong, A. Rauk, C. von Sonntag, Phys. Chem. Chem. Phys. 2003, 5, 3994– 3999. C. J. Easton, M. C. Merrett, J. Am. Chem. Soc. 1996, 118, 3035–3036. X. Zhang, N. Zhang, H.-P. Schuchmann, C. Von Sonntag, J. Phys. Chem. 1994, 98, 6541–6547. T. Nauser, G. Casi, W. H. Koppenol, Ch. Scho¨neich, unpublished results. T. E. Creighton, Proteins, W. H. Freeman, New York, 1993. R. Schweitzer-Stenner, F. Eker, Q. Huang, K. Griebenow, J. Am. Chem. Soc. 2001, 123, 9628–9633. L. Grierson, K. Hildenbrand, E. Bothe, Int. J. Radiat. Biol. 1992, 62, 265–277. R. Zhao, J. Lind, G. Mere´nyi, T. E. Eriksen, J. Chem. Soc., Perkin Trans. 2, 1997, 569–574. A. Jain, N. K. Alvi, J. H. Parish, S. M. Hadi, Mutat. Res. 1996, 357, 83–88. K. N. Carter, T. Taverner, C. H. Schiesser, M. M. Greenberg, J. Org. Chem. 2000, 65, 8375–8378.
¨ neich, Chem. 103 T. Nauser, Ch. Scho Res. Toxicol. 2003, 16, 1056–1061. ¨ neich, Arch. Biochem. 104 Ch. Scho Biophys. 2002, 397, 370–376. 105 A. I. Bush, W. H. Pettingell, G.
106
107
108
109 110
111
112
113 114
Multhaup, M. Paradis, J.-P. Vonsattel, J. F. Gusella, K. Beyreuther, C. L. Masters, R. E. Tanzi, Science 1994, 265, 1464–1467. C. C. Curtain, F. Ali, I. Volitakis, R. A. Cherny, R. S. Norton, K. Beyreuther, C. J. Barrow, C. L. Masters, A. I. Bush, K. J. Barnham, J. Biol. Chem. 2001, 276, 20466–20473. M. Coles, W. Bicknell, A. A. Watson, D. P. Fairlie, D. J. Craik, Biochemistry 1998, 34, 11064–11077. S. Varadarajan, J. Kanski, M. Aksenova, C. Lauderback, D. A. Butterfield, J. Am. Chem. Soc. 2001, 123, 5625–5631. D. Pogocki, Ch. Scho¨neich, Chem. Res. Toxicol. 2002, 15, 408–418. J. Kanski, M. Aksenova, Ch. Scho¨neich, D. A. Butterfield, Free Radical Biol. Med. 2002, 32, 1205–1211. J. Kanski, S. Varadarajan, M. Aksenova, D. A. Butterfield, Biochim. Biophys. Acta 2001, 1586, 190–198. K. L. Handoo, J.-P. Cheng, V. D. Parker, J. Chem. Soc., Perkin Trans. 2 2001, 1476–1480. K.-O. Hiller, K.-D. Asmus, Int. J. Radiat. Biol. 1981, 40, 597–604. Ch. Scho¨neich, D. Pogocki, G. L. Hug, K. Bobrowski, J. Am. Chem. Soc. 2003, 125, 13700–13713.
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Model Studies of Hydride-transfer Reactions Richard L. Schowen 4.1
Introduction [1]
Enzymes catalyze many oxidation–reduction reactions in which the equivalent of dihydrogen is added or removed from a substrate molecule. S þ H2 ðequivalent to 2Hþ þ 2e Þ > SH2
ð4:1Þ
As Eq. (4.1) emphasizes, dihydrogen is the equivalent of two protons and two electrons. If the reaction is conceived mechanistically as consisting of one proton and two electrons moving as a unit (the hydride ion, H: ) and the second proton being moved separately (or omitted entirely), then the process may with justice be called a hydride-transfer reaction. For example, in the case of the reduction of acetaldehyde to ethanol (as catalyzed by alcohol dehydrogenases) the following sequence of events, where Donor-H represents a hydride donor, is composed of a hydride-transfer mechanism for the step in Eq. (4.2a), a proton-transfer mechanism for the step in Eq. (4.2b), and a hydridetransfer/proton-transfer mechanism for the overall reaction formed by Eqs. (4.2a) and (4.2b): Donor-H þ CH3 CHO ! CH3 CH2 O þ Donorþ ðhydride transferÞ
ð4:2aÞ
CH3 CH2 O þ Hþ ! CH3 CH2 OH ðproton transferÞ
ð4:2bÞ
Other mechanistic variants decouple the transfers of one or both electrons from the transfer of the proton so that, for example, the reaction of Eq. (4.2a) might be accomplished by an initial proton transfer followed by a sequence of two oneelectron transfers or the transfer of an electron succeeded by the transfer of a hydrogen atom. These processes or combinations of steps within them may be called formal hydride-transfer reactions. This chapter is concerned with mechanistic observations on hydride-transfer processes in non-enzymic systems, but under conditions and with structures such that the observations are considered relevant to enzyme-catalyzed reactions. Even Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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4 Model Studies of Hydride-transfer Reactions
within this narrow compass, no effort at a comprehensive survey of the vast available literature has been made, but instead publications are described that are judged particularly relevant to current biochemical concerns. Their extensive lists of references should be consulted if comprehensive information is wanted. The terms ‘‘coenzyme’’ and ‘‘cofactor’’ are used as synonyms here, as seems to be the case in most textbooks (see Ref. [1] as an example). Duine (2004) has suggested specific distinctions among these and related terms but the distinctions appeared not to be crucial for the discussions in this chapter, which deals with nonenzymic reactions. 4.1.1
Nicotinamide Coenzymes: Basic Features
Nicotinamide coenzymes have large complex structures (Fig. 4.1) that divide conceptually into two parts, the nicotinamide nucleus and the dinucleotidederived part which may either be simple (NADþ/NADH) or phosporylated at the
Figure 4.1. The nicotinamide coenzymes, nicotinamide adenine dinucleotide (NADþ or NADPþ ) and dihydronicotinamide adenine dinucleotide (NADH or NADPH). The locations of C(4 0 ) and C(2 0 ) are indicated. The groups R and M are important only for binding
and orientation in complexes of the cofactor with enzymes and do not participate directly in the redox chemistry. The oxidized coenzymes bear an electrical charge one unit more positive than the reduced coenzymes and the interconversion is a formal hydride transfer.
4.1 Introduction
adenosine-2 0 -position (NADPþ/NADPH). The nicotinamide nucleus can exist either in the pyridinium form (oxidized form, with a net charge positive by one unit over the charge on phosphate ester moieties, NADþ/NADPþ ) or the 1,4dihydropyridine form (reduced form, with a net charge equal to the charge on the phosphate ester moieties, NADH/NADPH). The redox interconversion then is formally a hydride-transfer reaction. The remaining part of the structure does not undergo chemical reactions in the course of coenzyme action, and serves instead to bind the entire coenzyme in some specific orientation to the active site of the host redox enzymes. The two sets of nicotinamide coenzymes, NADþ/NADH and NADPþ/NADPH, differ from each other only in the structural region that is not a participant in the redox chemistry, so that a given model reaction can suffice to describe features of both. 4.1.2
Flavin Coenzymes: Basic Features
In a manner similar to the structures of the nicotinamide cofactors, the flavin cofactors FMN/FMNH2 and FAD/FADH2 also have structures that resolve into a chemically reactive unit, the flavin nucleus, and a large ancillary structure that has the function of binding the cofactor in a specific orientation to the host enzyme, as emerges from Fig. 4.2. Here again the flavin nucleus and thus the strictly chemical properties are common to the two coenzymes, which differ in the ancillary part of the structure. 4.1.3
Quinone Coenzymes: Basic Features
In relatively recent times, a number of biologically novel structures that function as cofactors in redox reactions, some of them as agents of hydride transfer, have been discovered to be present in enzyme or other protein structures. They are often covalently bound and are formed in post-translational reactions from the side-chains of normal, genetically encoded amino-acid residues. The structures are shown in Fig. 4.3, taken from Mure’s excellent review [2]. The important chemical functionality of these coenzymes is the quinone ring, an ortho-quinone in most cases, both a para-quinone and an ortho-quinone in TPQ. 4.1.4
Matters Not Treated in This Chapter
This chapter describes model studies of hydride transfer entirely with respect to nicotinamide coenzymes, flavin coenzymes and quinone coenzymes. Other coenzymes/cofactors may be alluded to but are not reviewed in detail. Some coenzymes involved either in hydride transfer or the transfer of other hydrogen species have been treated elsewhere in these volumes (thiamin diphosphate is treated by Hu¨bner et al., pyridoxal phosphate by Spies and Toney, folic acid by Benkovic
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Figure 4.2. The flavin coenzymes, flavine adenine dinucleotide/dihydroflavine adenine dinucleotide (FAD/FADH2 ), and flavin mononucleotide/dihydroflavin mononucleotide (FMN/FMN). The locations of N(5), N(10), and C(4a) are indicated. The groups Q are important only for binding and orientation in
complexes of the cofactor with enzymes and do not participate directly in the redox chemistry. The oxidized coenzymes bear an electrical charge equal to that of the reduced coenzymes and the interconversion is formally a dihydrogen-addition reaction, equivalent to the transfer of one hydride ion and one proton.
and Hammes-Schiffer, and cobalamin by Banerjee et al.) and articles on electron transfer and proton-coupled electron transfer may treat the role of metal ions, metal clusters, hemes, and related structures.
4.2
The Design of Suitable Model Reactions
The term, ‘‘model reactions,’’ can mean several things. Some studies that may be thought of as involving models focus on biomimetic reactions. This name is customarily applied to processes in which structures similar in some sense to those in-
4.2 The Design of Suitable Model Reactions
Figure 4.3. Structures of quinone cofactors. PQQ: pyrolloquinoline quinone; TPQ: 2,4,5-trihydroxyphenylalanine quinone; LTQ: lysine tyrosylquinone; TTQ: tryptophan tryptophyl quinone; CTQ: cysteine tryptophyl quinone. Taken with permission from Mure [2].
volved in biology are put to work in chemical or technological synthesis or analysis: for example, the use of NADH analogs as chemical reducing agents. There is a vast and valuable literature on this subject, which will be passed over here without comment. Sometimes, theoretical studies, such as the construction of potential surfaces for reactions important in biology, are referred to as ‘‘modeling’’ of the biological reactions. This sort of work will be brought in as needed. For our purposes, ‘‘model studies’’ or studies of ‘‘model reactions’’ will refer to investigations in which enzymes or other features of the biological environment are omitted so as to provide a system that is easier to construct and control than the true biological system and where the influences of biological agents such as enzymes are omitted. Often the structures most intimately involved are themselves decreased in complexity, as discussed below. The rates and mechanisms of the reactions thus simplified, which are the focus of model studies, then provide a kind of baseline information in which one hopes the biological influences have been removed, leaving only strictly chemical factors to determine the observed behavior. Comparison with the biological system can then illuminate what biological evolution has used from the basic chemical system, what it has invented, and what basic features it has enhanced or diminished.
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Previous writers have provided reviews of very high quality of parts or all of the studies reviewed here. Some of these are mentioned below at appropriate points. Here, two reviews by one of the great modern originators and practitioners of chemistry applied to biology, F.H. Westheimer, should be mentioned. His account [3] of the discoveries of enzyme mechanisms in the period 1947 to 1963 and an extraordinary critical review of model studies of nicotinamide (and to some extent flavin) coenzymes [4] are of great value and should be consulted by every reader of the present article. Earlier writers have also expressed useful views about proper characteristics of model reactions. In particular, Kosower, in a work that broke new ground in chemical biology ([5], pp. 276–277), suggested the difficulty of achieving the duplication of enzyme mechanisms with model compounds but noted that mechanistic parallels between enzyme and model reactions can nevertheless lead to informative results, culminating in what he denoted congruency between enzyme and model reactions, i.e., a very strong resemblance in terms of reactant structures and of the nature and sequential order of mechanistic events. 4.2.1
The Anchor Principle of Jencks
The structural complexity of coenzymes, in contrast to the chemical simplicity of the reactions they are involved in, has always given chemists pause for thought when they contemplate biology. Thus NADH serves as the carrier of a hydride ion (three elementary particles, with a mass slightly over 1 Da) yet has a total molecular weight around 664 Da. At first glance, this may seem quite extravagant of Nature, to which Newton [6] famously atttributed the opposite virtue (‘‘To this purpose the philosophers say that Nature does nothing in vain, and more is in vain when less will serve . . .’’). Something closer to the borohydride ion might seem to have been more advisable. It was William Jencks who put most clearly the idea that, for example, the effective delivery of three elementary particles to a specific atomic location at a high rate in the biological context can adhere entirely to the Newtonian principle of parsimony while requiring a substantial array of molecular superstructure. The concept is formulated this way in Jencks’s words [7]: Energy from the specific-binding interactions between an enzyme and a substrate or coenzyme is required to bring about the (highly improbable) positioning of reacting groups in the optimum manner and such binding requires both a high degree of three-dimensional structure and a large interaction area. Thus the binding interaction of the adenine-ribose-phosphate-phosphate-ribose moiety of NADþ [see Fig. 4.1] with a dehydrogenase provides the binding energy that anchors the coenzyme in the correct position, so that only an internal rotation of the CaN bond to the nicotinamide ring . . . need be frozen in order to bring the 4 position into the correct relationship for reduction to occur . . . Jencks also notes more generally: This anchoring effect immediately provides a qualitative rationale for the large sizes of enzymes, coenzymes, and some substrates. For model studies that target the chemical mechanistic features of the enzyme-
4.2 The Design of Suitable Model Reactions
catalyzed reactions, the anchor principle is of great practical value, for it allows the researcher to discard large and inconvenient fragments of the biologically active species, once these fragments have been shown to have an anchor function only. In such a case, a model compound need contain only the chemically significant features of the non-anchor portion of the natural species. One may then enjoy the convenience of structures that are smaller, easier to synthesize and modify, and cheaper. Figure 4.4 illustrates some of the ways in which these opportunities have been seized in model studies for the nicotinamide cofactors.
Figure 4.4. Illustrative examples of the liberty of design permitted the student of model reactions for the nicotinamide cofactors. From upper left, descriptions and references may be found in Bunting and Sindhuatmadja [8]; Bunting and Norris [9]; Bunting and Norris [9]; Bunting and Norris [9]; Ohnishi et al. [10];
Ohno et al. [11]; Lee et al. [12], Lee et al. [12]. It is easy to see the role of convenience in selection of compounds with chromophoric or solubility properties that lighten the burden of kinetics experiments or with substitution patterns that alleviate the pain of synthetic procedures.
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4.2.2
The Proximity Effect of Bruice
Two species near each other have a higher probability of colliding (the first prerequisite for reaction) than when they are not near each other: the idea that reaction of two species simultaneously bound to an enzyme active site might therefore react more rapidly with each other than when both are free in solution is thus a venerable idea in enzymology. It is an idea that has been fruitfully examined in non-enzymic intramolecular reactions. The fundamental development of the concept in quantitative terms owes much to Bruice and his coworkers. By the thorough study of intramolecular reactions in which the reacting groups were required by synthetic creativity to adopt specific distances and orientations, Bruice showed that the rate effects of appropriate relative locations were potentially many decades in magnitude and thus beyond doubt significant for an understanding of enzyme catalysis. Initially, Bruice and Benkovic [13] used the term ‘‘propinquity catalysis’’ to describe such accelerations. Later, others employed various terms for the same idea but today probably the most commonly used name is ‘‘proximity effect’’ and a deeply painstaking documentation and thorough analysis has been provided by Kirby [14]. As the power of computational science has grown, Bruice and his coworkers [15, 16] have further developed the concept by defining, through the use of experiential mechanistic information, specific molecular configurations in which the distances between reacting centers are less than a value slightly larger than a bond distance and the orientations of electronic orbitals are close to the final orientations appropriate for bond formation or fission. These configurations, which need not be, and generally are not, stationary points on the potential-energy surface, are called ‘‘near-attack conformations’’ or ‘‘NACs.’’ If the reacting-center separations and the orbital orientations are suitably chosen, then the NAC can be considered a structure especially likely to lead on to the transition state for the reaction. One carries out a molecular-dynamics simulation for the reactant-state assembly at a temperature of interest for a particular example, and counts the number of configurations attained within a specific time period that are within the chosen NAC limits. Very commonly, those species for which large numbers of NACs are observed are found experimentally to undergo reaction between the proximate centers more rapidly than is true for species with a smaller population of NACs. Such studies are capable of developing a reasonably reliable catalog of the distance and orientational requirements for a broad range of reactions and thus defining some of the requirements for enzymes to promote reactions by the adjustment of distances and orientation. The proper design of intramolecular reactions that simulate desired features of biological reactions is thus a major line of approach in using model reactions to investigate biochemical processes in general and hydride-transfer reactions in particular.
4.3 The Role of Model Reactions in Mechanistic Enzymology
4.2.3
Environmental Considerations
It has again been long realized that the chemical environments within enzymes can have an enormous range of properties, because of the diversity of the chemical structures of the natural amino-acid side chains in terms of polarity and lack thereof, electrostatic features, and the capacity to donate or accept hydrogen bonds, as well as the potential diversity of the secondary, tertiary and quaternary levels of protein structure in modulating these properties and producing others [17]. It is equally well-known that chemical reactions are very powerfully affected by the medium in which they occur [18]. It is one of the legitimate aims of model reactions to explore the ways in which environmental conditions within enzyme active sites may aid in controlling the rates and mechanisms of such processes as hydridetransfer reactions. Three main approaches have been taken in the general case of model reactions for all biochemical processes. On the one hand, model reactions have been studied in solvents with various characteristics that simulate particular features of a protein environment. In this approach, such macroscopic properties as dielectric constant or such microscopic properties as the propensities for donating and accepting hydrogen bonds are examined. Second, a more direct simulation of some of the properties of intact proteins has been attempted by the synthesis of small-peptide analogs with highly defined and thoroughly controlled structures. This approach to hydrogen-transfer reactions is described by Lars Baltzer in Chapter 5. Third, intramolecular reactions, particularly those within host–guest complexes have been exploited in the simulation of features of enzymic reactions, including environmental effects. Such studies have been reviewed recently from several viewpoints by Rebek [19–21].
4.3
The Role of Model Reactions in Mechanistic Enzymology 4.3.1
Kinetic Baselines for Estimations of Enzyme Catalytic Power
Enzymes are catalysts and the question of their quality as catalysts is irresistible to the chemist, although biologists may now and then regard the question as idle or eccentric. However, the magnitudes of enzymic catalytic acceleration factors certainly have a biological value, because the catalytic power of a modern enzyme represents the effect of molecular evolution in developing, from some primitive enzyme of low quality, the modern enzyme of today, which is often impressive in its catalytic power [22]. The catalytic power can be quantitatively measured, in principle, by a catalytic acceleration factor for any enzyme, which might logically be taken as the ratio of the rate of the enzyme-catalyzed reaction under chosen condi-
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4 Model Studies of Hydride-transfer Reactions
tions to the rate of the same reaction in the absence of the enzyme under the same conditions. By such a definition, one requires, for calculation of enzyme catalytic power, a knowledge of the kinetics – ideally the rate constants – for both the enzyme-catalyzed reaction and the non-enzymic reaction. The kinetic constants for the enzymic reaction, in this day of cloned enzymes and high-throughput kinetics, are frequently available at minimum investment, but the same may not be true for the non-enzymic reaction, particularly if the ratio of rates is large. Indeed it is frequently large, consistent with the idea that the basic biospheric strategy is to select intrinsically slow reactions as chemical components of physiological networks, then evolve powerfully catalytic enzymes, with the overall result that organismic chemistry exhibits a high ratio of signal (enzymic reaction) to noise (non-enzymic reaction). This means that determination of the kinetics of a non-enzymic reaction can present an experimental challenge of daunting proportions, a matter that has been addressed with great skill and determination by Wolfenden and his coworkers [23]. A much easier problem is posed by the fact that even the simplest enzymic reaction has two kinetic parameters (a second-order rate constant commonly denoted k cat =K M and a first-order rate constant known as k cat ; the notation may seem confusing to non-enzymologists but these two quantities are quite independent of each other) while the simplest non-enzymic reaction will have one rate constant (call it k unc and imagine it, for the sake of argument, to be a first-order rate constant). There are therefore two possible measures of catalytic power, [(k cat =K M )/ k unc ] and [k cat =k unc ], so which is correct? Radzicka and Wolfenden [24] elegantly show that both are correct and that they yield different and valuable information about the effects of the enzyme. The relevant equations have been gathered into Chart 4.1. The quantity [(k cat =K M )/k unc ], given the name catalytic proficiency, measures the equilibrium constant for binding of the transition state for the uncatalyzed reaction to the unoccupied active site of the enzyme (see Eq. (iv) in Chart 4.1), and thus the total stabilization of that transition state by the enzyme. The quantity [k cat =k unc ] is called the rate enhancement and measures (Eq. (v) of Chart 4.1) the equilibrium constant for expulsion of the reactant-state substrate molecule from the active site and its replacement in the active site by the transition state for the uncatalyzed reaction. The quantity there-
Chart 4.1.
Measures of enzyme catalytic power for a unireactant enzyme.
Catalytic Power of a Unireactant Enzyme with Unimolecular Non-enzymic Reaction K ¼ exp½ðDG k=K Þ=RT ¼ ðk cat =KM Þ=ðkB T=hÞ E þ S ! E:TSk=K ES ! E:TSk K ¼ exp½ðDG k Þ=RT ¼ ðk cat Þ=ðkB T=hÞ S ! TS unc K ¼ exp½ðDG unc Þ=RT ¼ ðk unc Þ=ðkB T=hÞ E þ TS unc ! E:TSk=K K ¼ ðk cat =KM Þ=ðk unc Þ ¼ catalytic proficiency ES þ TS unc ! E:TSk þ S K ¼ ðk cat Þ=ðk unc Þ ¼ rate enhancement
ðiÞ ðiiÞ ðiiiÞ ðivÞ ðvÞ
4.3 The Role of Model Reactions in Mechanistic Enzymology
fore gives the stabilization of the transition state for the uncatalyzed reaction by its binding to the enzyme diminished by the stabilization afforded the reactant substrate molecule by its binding to the enzyme. The rate enhancement is thus a measure of the net transition-state stabilization by the enzyme. The two quantities, catalytic proficiency (which has the dimensions M1 in the example above) and rate enhancement (which is dimensionless in the example above), give a valid account of two aspects of enzyme catalysis. The catalytic proficiency, as the equilibrium constant for transition-state binding to the free enzyme, measures quantitatively the affinity of the free enzyme for the transition state. The free-energy equivalent of the catalytic proficiency gives the total transition-state stabilization by the enzyme. The rate enhancement, as the equilibrium constant for the expulsion of a substrate molecule from the active site of the enzyme and its replacement by a transition-state molecule, quantitatively describes the relative affinity of the enzyme for the transition state compared to the reactant-state substrate. The free-energy equivalent of the rate enhancement gives the net transition-state stabilization (the excess of transition-state stabilization over reactant-state stabilization) by the enzyme. For more complex enzymic reactions, such as those that require more than two rate constants to describe the kinetics, and more complex non-enzymic reactions that also can require complex kinetic expressions, it is possible to define more than two measures of catalytic power. The questions involved are addressed in an appendix (see p. 1071) at the end of this chapter. 4.3.2
Mechanistic Baselines and Enzymic Catalysis
A reasonable ambition for model reactions is that their mechanisms ought to contain some clues about the mechanism of the enzyme-catalyzed reaction also. It has long been realized that it is fruitless simply to build the model-reaction mechanism into an enzyme active site. Such a procedure would entail the view that the factors present and at work in the model system render a complete account of the biological history of the enzyme. There is no reason to expect this to be so, and many reasons to think it would not be so. In the simplest sense, a given enzyme must occupy a niche in a metabolic network that may require its regulation and may influence its structure and mechanistic potentialities in ways that cannot be derived from non-enzymic studies. What the mechanistic baseline provided by a model reaction does do is to suggest where molecular evolution may have necessarily started, although it must be remembered that substrates and enzymes have co-evolved so that the chemical scope of a primitive substrate may not be that of a modern substrate. Furthermore, a model-reaction mechanism may indicate what processes it was necessary for an enzyme to avoid in order to open the way for a comparatively unfavorable reaction to be catalyzed. One of the most striking examples is provided by the recent studies of Kluger and his coworkers of the unexpected chemical properties of the cofactor thiamin diphosphate [25–29]. Although this work has nothing explicitly to do with
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hydride transfer, it constitutes a brilliant case of mechanistic deduction that gave rise to new ideas about thiamin-dependent enzymes. In the action of a-ketoacid decarboxylases, the cofactor thiamin diphosphate adds across the a-keto carbonyl group of the substrate, placing the thiazolium ring so as to delocalize the electron pair liberated by decarboxylation. In the normal course of the enzymic reaction, the delocalized species is protonated on the a-carbon center and the resulting alcohol then undergoes elimination of the thiazolium nucleus to regenerate the cofactor and form the product aldehyde. In the model reaction examined by Kluger and his coworkers, this pathway was dominated by a competing reaction in which the cofactor undergoes fragmentation and is destroyed. Thus the complex evolutionary problem solved in the molecular evolution of the thiamindependent decarboxylases involved acceleration of the decarboxylation reaction by a large factor (around 10 12 ) while preventing acceleration of the abortive, indeed self-sacrificial, fragmentation reaction that is chemically preferred. Without establishment of the non-enzymic mechanistic baseline, this fact might never have been known.
4.4
Models for Nicotinamide-mediated Hydrogen Transfer 4.4.1
Events in the Course of Formal Hydride Transfer
Since formal hydride transfer involves the transfer of one proton and two electrons, one can imagine various sequences and combinations by which this end can be achieved. Possible mechanisms can be classified according to the degree to which the transfers of the individual particles occur together in time or separately in time. In the limit that all three particles move precisely at the same time, the transferring entity amounts to a hydride ion and the process may accurately be described as a ‘‘true’’ hydride-transfer reaction. In the opposing limit, when each of three particles moves in a separate chemical reaction, the reaction must involve at least three separate steps and the process is said to be a stepwise transfer of electrons and proton. Sometimes an electron transfer is designated E and a proton transfer P so that the possible sequences are EEP, EPE, and PEE. Powell and Bruice [30] pointed out that for the simple identity reaction of Eq. (4.3):
ð4:3Þ
4.4 Models for Nicotinamide-mediated Hydrogen Transfer
in the light of the principle of microscopic reversibility or detailed balance and the necessary symmetry of the reaction, the only possible sequence of transfer steps is EPE: electron, proton, electron. All other sequences are different for forward and reverse reactions and therefore impossible. The two limiting mechanisms are presented in Fig. 4.5. In the most general sense, the problem is one of proton-coupled electron transfer, as described by Hammes-Schiffer and by Nocera in Volume 1, Chapters 16 and 17, respectively. The two limiting mechanisms described above are the cases of perfect coupling (concerted, one-step hydride transfer) and perfect uncoupling (EPE).
4.4.2
Electron-transfer Reactions and H-atom-transfer Reactions
Electron-transfer reactions and hydrogen-atom-transfer reactions are physically possible with NADH and its analogs. Much evidence indicates such a mechanistic versatility in redox reactions for this class of compounds. For example, Miller and Valentine [31] in 1988 showed that an extremely simple analog of NADH, 1-benzyl-1,4-dihydronicotinamide, underwent oxidation in propanol solvent by ferricinium ion in a three-step series of transfers (electron-protonelectron) to produce the analog of NADþ . The absence of an isotope effect for the transferring hydrogen indicates that its transfer does not occur in the rate-limiting step, while the lack of dependence of the rate on electrolyte concentration suggests the rate-limiting step to be electron transfer from the substrate to ferricinium ion with both reactants and transition state bearing a single positive charge. However, the reaction of both this model compound and NADH itself with quinone oxidants in water solution, as opposed to propanol solvent, occurred by one-step hydride transfer, the authors argued, because large isotope effects were observed and the reaction was 10 5a7 -fold faster than the electron-transfer rate estimated from Marcus theory. A simple interpretation is that powerful, obligate one-electron oxidants may elicit single-electron donation from NADH, but its reaction with two-electron acceptors is normally a single-step hydride transfer process. Almarsson et al. [32] found that the NADH-model compound 1-methyl-1,10dihydroacridan and its deuterated form underwent oxidation by Fe(CN)6 3 in aqueous solution by a sequence of: 1. A rapid, reversible one-electron transfer reaction to generate a radical cation. 2. A rate-limiting proton-transfer reaction to a general base with a Brønsted b of 0.2 and deuterium isotope effects of about 5–10, resulting in a neutral free radical. 3. A rapid one-electron transfer to a second molecule of ferricyanide ion. The sequence is shown in Eq. (4.4), an EPE process as described above.
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Figure 4.5. The limiting mechanisms of threestep hydride transfer and one-step hydride transfer, the former in the canonical order of Powell and Bruice [37], for the overall reduction by NAD(P)H of hydride-acceptor molecules. The operative distinctions are that (a) there are radical/radical-ion intermediates in the
multistep mechanism but not of course in the one-step mechanism; (b) the rate-determining step is necessarily the product determining step in a one-step mechanism, but if there are alternative products not shown here, then the two steps may differ in the multistep reaction.
4.4 Models for Nicotinamide-mediated Hydrogen Transfer
ð4:4Þ
The reaction thus conforms to the rough generalization already given, since ferricyanide ion is an obligate one-electron oxidant. Matsuo and Mayer [33], on the other hand, found that the same reactant in acetonitrile solution, upon treatment with Ru IV O 2þ , quickly generated the acridinium ion, as might have been anticipated for a simple hydride-transfer reaction, but in only 40–50% yield. Relatively slowly thereafter the acridinium compound and the remaining reactant were converted to the acridinium leuco-base (hydroxideion adduct). Matsuo and Mayer concluded that the process shown in Eq. (4.5) was occurring:
ð4:5Þ
First, hydrogen-atom abstraction occurred to generate the molecular pair shown in the box. This pair then underwent two competing reactions: electron transfer from
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4 Model Studies of Hydride-transfer Reactions
the acridine radical to ruthenium to produce the observed acridinium ion and Ru II OHþ , and hydroxyl-radical donation from Ru III OH 2þ to produce the leucobase shown at the bottom. Simultaneously the acridinium ion and Ru II OHþ formed along the electron-transfer route react by hydroxide-ion donation to the acridinium partner to produce the same final products. In further support of this scheme, the authors noted that reactant disappearance is accelerated about fivefold under aerobic conditions compared to anaerobic conditions, consistent with the initial hydrogen-atom transfer being to some degree reversible, with dioxygen then trapping away the acridine free radical under aerobic conditions. Matsuo and Mayer [33] note that the thermodynamic driving forces are not very different for hydrogen-atom and hydride transfers in this system, the faster hydrogen-atom-transfer then suggesting the intrinsic barrier may be lower for the atom-transfer reaction than for the hydride-transfer reaction. A contributing factor to such a difference could be transition-state stabilization in these specific hydrogen-atom-transfer reactions through a donor – acceptor polar effect that operates only in the transition state [34, 35: pp. 77–85]. The oxygen center of an oxoruthenium species, such as abstracts the hydrogen atom here, is electronegative and capable of bearing substantial negative charge, while the forming pyridinoid ring of the acridine partner is capable of easily stabilizing positive charge. Such a donor–acceptor pair tends to generate considerable charge dispersion in the favored direction in atom-abstraction transition states and the resulting transitionstate stabilization would lead to a reduced intrinsic barrier. 4.4.3
Hydride-transfer Mechanisms in Nicotinamide Models
Particularly in the 1970s, several lines of evidence were taken to suggest a major role for electron-transfer processes in model reactions for the action of nicotinamide cofactors. Bruice and his coworkers [30, 36–38] in 1982–1984 showed that subtle effects rendered these observations deceptive, and that in fact hydride transfer is the only mechanism at work in the aqueous-solution hydrogen-transfer models that had formed the earlier focus. Further relevant references and an extraordinary analysis are given in the review by Westheimer [4]. The main outlines are discussed below. A key line of evidence for a multistep mechanism, as opposed to the onestep hydride-transfer mechanism, had been derived from isotope effects measured in reduction of various substrates with monodeuterated analogs of NADH. One can compare the observed rate constants k HH and k HD , which in the case of negligible secondary isotope effects should obey the relationship k DH =k HH ¼ ð1 þ ½k D =k H Þ=2, allowing the calculation of the primary isotope effect k H =k D (if undeuterated, monodeuterated and dideuterated hydride donors are all used, both primary and secondary isotope effects can be obtained). In addition, for an oxidizing agent Acceptorþ one can determine the isotope ratio in the product Acceptor– H/Acceptor–D, called in these studies the product isotope effect YH =YD . For a simple one-step hydride-transfer mechanism, these two isotope effects
4.4 Models for Nicotinamide-mediated Hydrogen Transfer
should be identical. For an EPE mechanism, the value of k H =k D will reflect which step is more nearly rate-limiting and could vary from unity if one of the electrontransfer steps E is rate-limiting to large values if the proton-transfer step P is rate limiting. If the proton-transfer step is irreversible then, whether it is rate-limiting or not, its isotope effect will fix the value of YH =YD . Therefore if the two isotope effects are identical, no information about the nature of the mechanism is obtained. But if the two differ, and in particular if YH =YD (reflecting the true isotope effect on the hydrogen-transfer step) is larger than k H =k D (a weighted average of small isotope effects on electron transfer and the true effect for hydrogen transfer), then the one-step hydride-transfer mechanism is excluded. The reactions of various analogs of NADH with ketones and acridinium cations gave isotope effects on the rate constants for substrate reduction (k H =k D ) that were different in magnitude from the isotope effects measured by isotope abundances in products compared to reactants (YH =YD ). For example, YH =YD was found to be constant at around 6 in one series of reactions, while k H =k D varied with the structure of the hydride donor from about 3.3 to about 5.7. A hydride-transfer mechanism therefore appeared to be excluded. Early measurements were quickly shown to be in error as a result of the reversible formation in aqueous solution of hydrates of the dihydronicotinamide analogs and of adducts involving the hydride acceptors, but later studies were conducted in dried aprotic solvents and some made used of acridine-derived analogs of NADH that could not form hydrates or adducts. These later studies continued to exhibit discrepancies in the values of k H =k D and YH =YD . Reinvestigations of the matter and extended studies were reported by Powell, Wong, and Bruice [36], and by Powell and Bruice [30, 37, 38]. The discrepancies between k H =k D and YH =YD were shown to arise from isotope exchange reactions. For example, when the hydride acceptor N-methylacridinium cation MA(H)þ reacted with an NADH analog N(H,D) to form the reduced product MA(H,D), this material could react in a symmetrical hydride-transfer reaction with another molecule of the unreduced reactant MA(H)þ , still present in excess. Either of the product hydrogens of MA(H,D) could be transferred. If the H were transferred, as should occur more frequently, a molecule of MA(H,H) was fallaciously added to the apparent product mixture in place of the originally formed MA(H,D) and the deuterium was essentially permanently sequestered as MA(D)þ in a large excess of MA(H)þ . This process is facile and quantitatively accounts for the fallaciously large values of YH =YD that were previously measured. When a full account of all processes at work was constructed by Powell and Bruice [37, 38], there was no isotope-effect discrepancy remaining and all the available evidence favored a hydride-transfer mechanism for nicotinamide reactions. That remains the situation today, one-electron transfers or H-atom transfers arising only in the kinds of limiting circumstances described above. In a remarkable article published in 1991 [39], Bunting reviewed structure– reactivity studies relevant to the nature of the hydride-transfer process between materials that can be regarded as related to nicotinamide cofactors. Much of the article concerned the large quantity of work published from Bunting’s own laboratory,
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4 Model Studies of Hydride-transfer Reactions
and his interpretative section strikingly presages current thinking, particularly in the area of proton-coupled electron transfer, on the degrees of possible coupling among the motions of proton and electrons in a formal hydride-transfer reaction. Bunting’s suggestion was that it is fruitful to think in terms of what he denoted a ‘‘merged mechanism’’ with varying degrees of coupling arising under circumstances that depend on reactant properties and environmental considerations. 4.4.4
Transition-state Structure in Hydride Transfer: The Kreevoy Model
The Marcus formulation of the dependence of the free energy of activation DGz on the free energy of reaction DG has been enormously useful as a method of thinking about transition-state structure in solution reactions. Originally developed for electron-transfer reactions, it has been extended to proton-transfer and hydridetransfer reactions and thence to other group-transfer reactions. In an article on methyl-transfer reactions [40], Albery and Kreevoy described the consideration of variations in transition-state structure not just in terms of the parallel coordinate connecting reactants to products (along which Marcus theory accounts for the Hammond Postulate, the tendency of exergonic reactions to occur with reactantlike transition states and of endergonic reactions to occur with product-like transition states) but also along the perpendicular coordinate (see Fig. 4.6). In such maps as Fig. 4.6, sometimes called ‘‘maps of alternate routes,’’ the parallel coordinate represents a trajectory along which bond-order at the transferring H is maintained at unity, while other routes account for the possibility of either total bond orders at H greater than unity (tight transition states in the northwestern part of the map) or smaller than unity (loose transition states in the southeastern part of the map). Albery and Kreevoy [40] and later Kreevoy, Lee, and their coworkers [12, 41–43] put the concept of both reactant-product and tight-loose characteristics of transition states on a common quantitative basis (Chart 4.2). In the Albery–Kreevoy–Lee approach, as outlined in Chart 4.2, a hydride-transfer transition state can be described by the structure–reactivity sensitivity factor or Brønsted coefficient a ¼ d½lnðk i0 Þ=d½lnðK i0 Þ, where k i0 is the rate constant for one of a series of hydride-acceptors Ai þ reacting with a standard hydride donor A 0 H, and K i0 is the equilibrium constant for the transfer. The Brønsted coefficient in turn is a sum of two terms (Chart 4.2, Eqs. (vii)–(x)). The first term in Eqs. (x), w, describes transition-state variation along the reactant–product coordinate and is given by Eq. (viii) of Chart 4.2. This is the normal result of Marcus theory. In effect, RT½lnðK i0 Þ ¼ DGi0 can vary (for the circumstances we wish to address here) within the limits l to þl. Here l is the reorganization energy, or the work required to distort the reactant structure to a precise simulacrum of the product (and l=4 is the ‘‘intrinsic barrier’’ or reaction barrier in the absence of any thermodynamic driving force). If DGi0 ¼ þl, then the transition state will itself be a precise simulacrum of the product. If this limit is inserted into Eq. (viii) of Chart 4.2, then w ¼ 1 as expected for an exactly productlike transition-state structure. At the other limit of DGi0 ¼ l, the transition state
4.4 Models for Nicotinamide-mediated Hydrogen Transfer
Figure 4.6. A map of alternate routes for overall hydride transfer from NADH or an analog to an electrophile Eþ . The reactant structure is shown at bottom left (the ‘‘southwest’’ corner) and the product structure at upper right (the ‘‘northeast’’ corner). The bond order of the CaH decreases from one to zero along the abscissa and the bond order of the EaH bond increases from zero to one along the ordinate. Two hypothetical
intermediate structures are shown at the southeast corner (both bond orders about the hydride ion are zero) and at the northwest corner (the EaH bond has fully formed while the CaH bond remains fully intact). Any point in this map represents a possible transitionstate structure. Any trajectory that connects the reactant structure, one or more transition-state structure(s), and the product structure represents a possible reaction route.
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4 Model Studies of Hydride-transfer Reactions Chart 4.2. The transition-state descriptors for hydride-transfer reactions as developed by Kreevoy, Han Lee, and their coworkers [12, 40–43][a]
Reaction: A i þ þ HaA 0 ¼ Ai aH þ A 0 þ (i) Here the structure of Ai þ is varied while HaA 0 is a standard compound. Experimentally accessible: rate constants k i0 , k ii ; equilibrium constants K i0 Basic relationships: Thermodynamics: lnðK i0 Þ ¼ DGi0 =RT (ii) Transition-state theory: lnðk i0 Þ ¼ DGi0 z =RT þ lnðnÞ (iii) ‘‘ultrasimple’’ version: n ¼ kB T=h Marcus theory: DGi0 z ¼ W r þ ½l=4½1 þ ðDGi0 =lÞ 2 (iv) l ¼ ðl ii þ l 00 Þ=2 (v) From Eqs. (ii), (iii), and (iv): lnðk i0 Þ ¼ a þ b½lnðK i0 Þ þ c½lnðK i0 Þ 2 (vi) a ¼ lnðnÞ ðW r =RTÞ ðl=4RTÞ; n ¼ Gk nu b ¼ 1=2 c ¼ RT=4l Brønsted coefficient a ¼ d½lnðk i0 Þ=d½lnðK i0 Þ with i varied, 0 constant a ¼ ð1=2Þf1 ðRT=lÞ½lnðK i0 Þg þ ð1=2Þfd½lnðk ii Þ=d½lnðK i0 Þg½1 fðRT=lÞ½lnðK i0 Þg 2 (vii) Define: Fractional progress from reactant toward product: w ¼ ð1=2Þf1 ðRT=lÞ½lnðK i0 Þg (viii) (l as in Eq. (v) above) Compression from loose toward tight: (a) K i0 varied by changing structure of hydride acceptor: t ¼ 1 þ d½lnðk ii Þ=d½lnðK i0 Þ (ix-a) (b) K i0 varied by changing structure of hydride donor: t ¼ 1 d½lnðk ii Þ=d½lnðK i0 Þ (ix-b) From putting Eqs. (viii) and (ix) into Eq. (vii): Acceptor varied: a ¼ w þ ð1=2Þðt 1Þð1 fðRT=lÞ½lnðK i0 Þg 2 Þ (x-a) Donor varied: a ¼ w þ ð1=2Þð1 tÞð1 fðRT=lÞ½lnðK i0 Þg 2 Þ (x-b) and when fðRT=lÞ½lnðK i0 Þg 2 becomes negligible as lnðK i0 Þ approaches zero: a ¼ w G ð1=2Þðt 1Þ ¼ 1=2 G ð1=2Þðt 1Þ (xi)
assumption: Reactant-state work function W r and productstate work function W p are approximately equal.
a Additional
becomes a precise simulacrum of the reactant, and as expected w ¼ 0. Between these limits is the point at which reactants and products have equal energy (DGi0 ¼ 0) and Eq. (viii) then yields w ¼ 1=2, signifying a centrally-located or ‘‘symmetrical’’ transition state. The interpretations that have usually been given to the Brønsted coefficient a itself are thus assumed by the w-term in this formulation. The second term in Eqs. (x) for the Brønsted coefficient a contains a quantity ð1=2Þðt 1Þ or ð1=2Þð1 tÞ, depending on the site of structural variation, where t is defined by Eqs. (ix) and purports to describe the transition-state structure along
4.4 Models for Nicotinamide-mediated Hydrogen Transfer
a ‘‘tight–loose’’ coordinate. The quantities ð1=2Þðt 1Þ and ð1=2Þð1 tÞ are multiplied by a weighting factor ð1 fðRT=lÞ½lnðK i0 Þg 2 Þ. It should be noted that the weighting factor approaches zero as the equilibrium free-energy change approaches both of its upper and lower limits of Gl, which correspond to reactantlike and product-like structures of the transition state. Thus ‘‘tightness’’ and ‘‘looseness’’ play no role in the value of the Brønsted coefficient a in these limits. Instead the importance of these considerations enters only in the ‘‘symmetric’’ situation, where the weighting factor approaches its maximum value of unity, the term w approaches a value of 1/2 and, as shown in Chart 4.2 by Eq. (xi), the Brønsted coefficient a itself approaches a value of t=2 or ½1 ðt=2Þ, depending on the site at which structure is varied. A glance at the map of Fig. 4.4 suggests that it is logical that there should be no scope for transition states with reactant-like or product-like structures to develop ‘‘tight’’ or ‘‘loose’’ character, being confined in structure as they are to the southwest and northeast corners of the map. In contrast, there is maximal scope for such influences near the ‘‘symmetrical’’ point. The quantity t was originally suggested by Albery and Kreevoy [40] to correspond to the sum of the bond orders about the transferring entity, so that the terminally ‘‘loose’’ transition state ought to have t ¼ 0, the terminally ‘‘tight’’ transition state ought to have t ¼ 2, and that for a reaction in which bond-making and bond-breaking are exactly compensatory, the value should be t ¼ 1. As Eqs. (ix) in Chart 4.2 show, for these values to be achieved puts requirements on the value of the derivative d½lnðk ii Þ=d½lnðK i0 Þ, which would need to be equal to 1, for the terminally loose, þ1 for the terminally tight, and 0 for the fully compensatory transition state. That these requirements agree with expectations for the actual transition states is shown by arguments in Table 4.1, which summarizes the situation with respect to values under various circumstances of the variables w and t and of the Brønsted coefficient a. Kreevoy and his coworkers (and others such as Lee et al. [43] and Wu¨rthwein et al. [44]) have applied this formalism to various models for nicotinamide-mediated redox reactions. An immediate result was that the conclusions about transitionstate structure based only on the traditional interpretation of a, i.e., ascribing to it the properties of w, can lead to substantial error. For example, two systems with different but related structures considered by Lee et al. [42] generated a values of 0.67 (for one system in which structural variation was in the hydride donor) and 0.32 (for a different system in which structural variation was in the hydride acceptor). It is tempting, since the sum of these values is near unity, to imagine that the two systems have identical transition-state structures, with the hydride ion liberated to the extent of about 70% from the donor and attached to the acceptor to the extent of about 30% and the hydride atom itself therefore bearing little or no charge. However, these systems had been thoroughly studied from the viewpoint of Marcus theory and estimates were available to permit the values of w to be calculated from Eq. (viii) of Chart 4.2. The calculations yielded w ¼ 0:49 for variation of the hydride donor and w ¼ 0:48 for variation of the hydride acceptor, suggesting that in fact both transition states were centrally located and of ‘‘symmetrical’’ structure about the hydride moiety. Furthermore
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4 Model Studies of Hydride-transfer Reactions Table 4.1. Values of interest for the reaction-progress variable w, the compression variable t, the Brønsted coefficient a, and their significance.
Parameter
Value
Significance
w
0
Transition state is reactant-like along the reaction-progress coordinate; occurs when lnðKi0 Þ ¼ þl=RT, corresponding to DGi0 ¼ l, the limiting exergicity.
1/2
Transition state is central on the reaction-progress coordinate; occurs when Ki0 ¼ 1, corresponding to DGi0 ¼ 0. There is no driving force to influence the structure of the transition state.
1
Transition state is product-like along the reaction-progress coordinate; occurs when lnðKi0 Þ ¼ l=RT, corresponding to DGi0 ¼ þl, the limiting endergicity.
0
Transition state has no bonding to H which is therefore in a hydride-like (H: ) circumstance. The electron density available for bonding (2 electrons in a formal hydride-transfer reaction) is thus sequestered on H and shared neither by the donor moiety nor the acceptor moiety in the critical state for the identity reactions (rate constant k ii ). For the acceptor moiety, this corresponds to no change in electron density and for the donor moiety a decrease of unit electron density, as in the equilibrium (Ki0 ) reaction. Thus k ii and Ki0 respond equally to donor/acceptor structure ðd½lnðk ii Þ=d½lnðKi0 Þ ¼ þ1Þ and t ¼ 1 1 ¼ 0.
1
Transition state has unit total bond order to H, as is the case in both reactant and product states. The gain in bond order of the forming bond compensates exactly in the transition state for the loss in bond order of the breaking bond. The gain in electron density in the acceptor moiety for the identity reaction is exactly compensated by the loss in electron density from the donor moiety and k ii is independent of donor/acceptor structure ðd½lnðk ii Þ=d½lnðKi0 Þ ¼ 0). Thus t ¼ 1 0 ¼ 1.
2
In the transition state, the H is bound by a one-electron bond to each of the donor and acceptor moieties and bears the full positive charge so that the donor and acceptor moieties are electrically neutral. This corresponds in the identity reaction to no change in electron density for the donor moiety upon attaining the transition state, and a gain of unit electron density for the acceptor moiety. The net change is thus equal and opposite to that for the equilibrium (Ki0 ) reaction ðd½lnðk ii Þ=d½lnðKi0 Þ ¼ 1Þ, so that t ¼ 1 ð1Þ ¼ 2.
0
Traditionally taken to signify a reactant-like structure for the transition state, this value could result from such combinations as w ¼ 0, t ¼ 1 (transitional conclusion correct) or w ¼ 1=2, t ¼ 0 (traditional conclusion incorrect).
t
a
4.4 Models for Nicotinamide-mediated Hydrogen Transfer Table 4.1 (continued)
Parameter
Value
Significance
1/2
Traditionally taken to signify a central structure for the transition state, this value could result most simply only from w ¼ 1=2, t ¼ 1 (traditional conclusion correct). BUT see the text for more complex circumstances.
1
Traditionally taken to signify a product-like structure for the critical state, this value could result from such combinations as w ¼ 1=2, t ¼ 2 (transitional conclusion incorrect) or w ¼ 1, t ¼ 1 (traditional conclusion correct).
when Eqs. (x-a) and (x-b) of Chart 4.2 were used to calculate values of t from the quantity a w, values of t ¼ 0:64 (variation in the donor) and t ¼ 0:68 (variation in the acceptor) were obtained. Note that because of the difference between Eqs. (x-a) and (x-b), it is possible for these two reactions to have essentially identical values of w and of t and yet very different values of a. The suggestion of the complete analysis is then that the two reactions share a common transition-state structure with the hydride moiety about half-transferred (w around 1/2 in both cases) with less than conserved bond order (a loose transition state with t about 0.6 to 0.7, while a value near unity would have been expected for conserved bond order and values greater than one for a tight transition state). Since the question of tunneling arises in the next section, and the essential ubiquity of tunneling in nicotinamide reactions is a current theme in both model studies and enzymic studies, it is worthwhile to consider whether analyses of the sort just described are invalidated if the ‘‘ultrasimple’’ transition-state theory cannot describe the events in question. There seems to be no reason not to continue to use the framework of Chart 4.2 to investigate the nature of the states at or near the maximum of the activation barrier whether or not they require such sophisticated approaches as those described by Hynes, Hammes-Schiffer, Truhlar and Garrett, Warshel, Smedarchina, Klinman, Kohen, Scrutton, and Banerjee in these volumes. Although the results are currently cast in the language of transition-state structure, the measurements are rate-equilibrium comparisons that compare the effect of structure on the work required for barrier crossing (or penetration) with the work required for reaching the equilibrium products. The understanding that is generated by these comparisons, even if phrased in the language of simple transition-state theory as a convenience, should survive translation into the language of new ways of formulating rate-processes whenever that is desired. The treatment of isotope effects and their temperature dependences is more challenging, and such easy interconversions are not to be expected there. Indeed the general subject of how to reconcile findings from structure–reactivity/rate– equilibrium studies with the more complex theoretical treatments currently being introduced and applied needs much more careful study.
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4 Model Studies of Hydride-transfer Reactions
4.4.5
Quantum Tunneling in Model Nicotinamide-mediated Hydride Transfer
The articles in these volumes by Hynes, Hammes-Schiffer, Truhlar and Garrett, Warshel, Smedarchina, Klinman, Kohen, Scrutton, and Banerjee provide extensive evidence that enzymic hydride-transfer reactions very frequently, if not universally, proceed by a tunneling mechanism (see also the compilation by Romesberg and Schowen [45]). It is then of substantial interest to know whether tunneling also occurs in the non-enzymic reactions. If it does not, enzymes must in effect be creating de novo a tunneling mechanism to replace a slower non-tunneling mechanism, whereas if tunneling occurs also in model reactions, enzymes are simply accelerating an existing tunneling mechanism. Powell and Bruice ([38]) studied the temperature dependence of the isotope effects for the reaction shown in Eq. (4.6) (L ¼ H; D) from 2 C to 50 C in acetonitrile solution.
ð4:6Þ
Since two labels are present in the hydride donor, the isotope effects are a product of a primary isotope effect for the transferring hydrogen and a secondary isotope effect for the hydrogen that remains. The two effects were estimated in a related system, the secondary effect emerging as a few percent larger than unity, as expected because the hybridization state is changing from sp 3 to sp 2 and the freedom of motion of the non-transferring center is thus increased in the transition state. Rate constants for both isotopic reactions obey the Arrhenius relationship kLL ¼ A LL expðELL =RTÞ very well, the isotope effects k HH =k DD varying from about 6.2 at the lowest temperature to about 4.0 at the highest temperature. Most significantly, the difference in activation energies is far larger than the isotope effects would suggest, with EDD EHH ¼ 7:7 G 1:0 kJ mol1 . If this difference alone determined the value of the isotope effects, k HH =k DD would have been around 22 at 25 C instead of between 4 and 6, as is observed. The ratio ADD =AHH , which should be close to unity if the entire isotope effect arises from zero-point energy differences, was in fact 4:3 G 1:3. This combination, of an over-large isotopic activation-energy difference with a ratio of pre-exponential factors that is far from one with ADD greater than AHH , is one of the first-recognized indications of a role for tunneling in solution reactions, having been observed and interpreted by Bell and his collaborators in the 1950s and later [46]. Powell and Bruice made use of the most sophisticated theoretical treatment available at the time (the Bell approach implemented in a computer pro-
4.4 Models for Nicotinamide-mediated Hydrogen Transfer
gram of Kaldor and Saunders [47]) and estimated that around 70% to 80% of the reaction might be resulting from tunneling. Current approaches to the treatment of such results would probably lead to a different quantitative conclusion, but it remains clear that at least a considerable fraction of the overall hydride-transfer reaction is a result of tunneling. Indeed, as understanding deepens, it is becoming unclear whether this language of a division between parallel pathways of tunneling and over-the-barrier reaction will survive. Related studies by Lee et al. [12] produced isotope effects for the reduction of models for NADþ by a 1,3-dimethyl-2-phenylbenzimidazoline derivative labeled at the 2-position with either protium or deuterium. The isotope effects k H =k D varied from around 4 to about 6.3. It was possible by means of the Marcus formulation described in Chart 4.2 to ascribe the variations with structure to a combination of parallel effects (reactant-like vs. product-like, the parameter w) and perpendicular effects (tight vs. loose about the hydride center, the parameter t). The perpendicular effects corresponded very well to an expected linear dependence on the logarithm of the equilibrium constant and were the main source of structure-induced variation in the isotope effect. The smaller parallel effects produced a very good fit to the expected quadratic dependence. The authors point out that the failure to separate these effects is the probable reason for the considerable scatter seen in traditional plots of the phenomenological isotope effects against the free energy of reaction. The isotope effects were consistent with model calculations using variational transition-state theory with inclusion of large-curvature ground-state tunneling (see Chapter 27 by Truhlar and Garrett in Volume 1). The simplest conclusion is then that tunneling occurs both in enzymic hydridetransfer reactions and in related non-enzymic (model) reactions. It remains to be seen whether enzymic rate acceleration has evolved simply to make the existing tunneling reaction much more efficient or instead to create new tunneling mechanisms distinct from those observed in model systems. 4.4.6
Intramolecular Models for Nicotinamide-mediated Hydride Transfer
An early attempt to construct a close intramolecular model for enzymic hydride transfer was Overman’s [48] synthesis of the reactant shown in Eq. (4.7):
ð4:7Þ
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4 Model Studies of Hydride-transfer Reactions
The pyridinium ring simulates an NAD(P)þ cofactor and the transannular hydroxy function any of a variety of dehydrogenase substrates. Overman noted that spacefilling models ‘‘show that the hydroxy methine hydrogen and the pyridinium 4position are held tightly together and that conformations of the 14-membered ring do exist in which hydride addition could occur perpendicular to the plane of the pyridinium ring.’’ However, the transannular redox reaction proved impossible to observe. In aqueous solution at pH 12, a leuco-base was formed by hydroxideion addition at the 2-position of the ring. In hexamethylphosphoramide solvent with bases such as sodium hydride, lithium bis-(trimethylsilyl)amide or potassium tert-butoxide, no redox reaction occurred over 12 h at 30 C. The reasonable conclusion reached was that not only approximation of the reactants but other features not accessible to this model compound accounted for the rapid enzymic redox reaction. Fifteen years later, Meyers and Brown [49], now citing the rapidly accumulating and already large related literature, reported a highly stereospecific intramolecular model reaction, shown in Eq. (4.8).
ð4:8Þ
Here the side-chain is unrestricted but the required magnesium ion is thought to bind to both the carbonyl group to be reduced and the ring nitrogen center to bring the hydride-transfer distance into a range for reaction to occur. At essentially the same time, Kirby and Walwyn [50, 51] created a closely related model system for lactate dehydrogenase (Eq. (4.9)).
ð4:9Þ
It was then possible for Yang et al. [52] to make use of the results of Kirby and Walwyn to understand a significant mechanistic feature of the NADþ -dependent enzyme S-adenosylhomocysteine hydrolase. This enzyme possesses a molecule of NADþ , bound non-covalently but very tightly to the enzyme, that oxidizes the 2 0 -hydroxy group of the substrate Sadenosylhomocysteine in the first step of the mechanism. The resulting keto-group then activates the adjacent 4 0 -hydrogen for removal, allowing the elimination of
4.4 Models for Nicotinamide-mediated Hydrogen Transfer
homocysteine from the 5 0 -position followed by addition of water at the 5 0 -position. The NADH, formed in the first step of the mechanism, thereafter reduces the product of water addition, 3 0 -keto-adenosine, to generate adenosine in the last step of the mechanism. Throughout the events between these first and last steps, it is vital that the intermediates are not reduced – if this should happen, the subsequent normal reactions are impossible and the catalytic cycle is aborted. Yang et al., making use of kinetic studies of Porter and Boyd [53–55], were able to compare the rates of the normal reduction reactions of the enzyme, carried out during the catalytic cycle, with the rate of the abortive reduction reaction, which occurs rarely but for which the rate was carefully measured by Porter and Boyd. The free-energy barriers for the normal reductions were an average of 66 kJ mol1 in height, while that for the model reaction of Eq. (4.8) was 92 kJ mol1 in height (data for aqueous solution), showing that the enzyme during the catalytic cycle was accelerating the reduction by a factor of approximately 40 000 over the acceleration already present in the model reaction. The barrier height for the abortive reaction was 89 kJ mol1 , essentially equal to that for the model reaction (in fact the rate constant for the abortive reaction at 25 C was 2 103 s1 , while the rate constant for the model reaction at 39 C was 3 103 s1 ). Thus the enzyme prevents the abortive reduction from occurring by suspending, during the central part of the catalytic cycle, its acceleration of the redox reactions from a factor of about 40 000 over the effect of the model reaction to nil, so that the reaction is accelerated by only the approximation effect modeled in the reaction of Eq. (4.8). An examination of several crystal structures of the enzyme suggested that the enzyme may accomplish this suspension of catalytic power by means of a conformation change coupled to the initial and final redox reactions that begin and end the catalytic cycle. The enzyme before oxidation of the ligand appears to have a distance between C-4 0 of the cofactor and C-3 0 of the substrate (the distance over which the hydride would need to move if its transfer occurred with no change in the positions of cofactor and substrate) of about 3.2 A˚. After oxidation, this distance is increased to about 3.6 A˚ and two histidine residues (H55 and H301) move to buttress the cofactor in this more distant and thus less reactive position. All of these numbers have large errors but the apparent increase in the distances is present in four different structural comparisons, in agreement with the hypothesis that the first redox reaction, by means of a conformation change coupled to it, suspends part of the catalytic power of the enzyme for the redox reaction, and this catalytic power is then only restored when a reverse conformation change, coupled to the final redox reaction, occurs in concert with it. 4.4.7
Summary
Model reactions have been of major importance in the development of our current good understanding of the mechanisms of action of enzymes utilizing nicotinamide cofactors. The cofactors are now generally supposed to effect redox reactions by a hydride-transfer mechanism with structurally variable transition states, and to exhibit one-electron chemistry only in rarely encountered circumstances, e.g., reac-
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4 Model Studies of Hydride-transfer Reactions
tions with metal complexes that strongly favor such reactions. Quantum tunneling has been known for over 20 years to be important in nonenzymic redox chemistry of the cofactors. It has been learned over roughly the same period that the enzymic reactions accelerate the tunneling reaction powerfully by means that are the subject of vigorous investigation, much of the work discussed eleswhere in these volumes. In addition, molecular evolution, as reflected in enzymic mechanisms, has been found in some cases to employ chemical principles seen in model reactions, for example an enzyme can (for mechanistic purposes) powerfully reduce the rate of hydride transfer from NADH to an acceptor by lengthening the distance over which the hydride must travel.
4.5
Models for Flavin-mediated Hydride Transfer
Excellent reviews that make a fine starting point for the modern mechanistic history of flavin biochemistry are those of Hemmerich, Nagelschneider, and Veeder [56] and of Walsh [57, 58]. Palfrey and Massey [59] have provided a valuable account up to 1998. On specialized areas, an especially valuable review is that by Ghisla and Thorpe [60]. See also the brief remarks above in Section 4.1.3, including Fig. 4.2 illustrating the structures and numbering system. A general theme is the stability of the semiquinone form of the cofactors FMN and FAD, the free-radical species that results from one-electron redox reactions, as seen in Eq. (4.10):
ð4:10Þ
4.5.1
Differences between Flavin Reactions and Nicotinamide Reactions
The stability of the radical species FMNH and FADH is the source of the most dramatic distinctions between the nicotinamide cofactors and the flavins. This stability makes possible a number of reactions for flavins involving singleelectron transfers that are rendered essentially impossible by the high energy of the corresponding nicotinamide radical. The source of the relative stability of the
4.5 Models for Flavin-mediated Hydride Transfer
semiquinone form would logically be thought to arise from the more extensive delocalization of the unpaired electron, in comparison with the nicotinamide radical. This cannot be the whole story, however, because the mere substitution of N(5) by a CH group to form the 5-deaza derivative renders the cofactor incapable of oneelectron reactions (Blankenhorn [61]) or nearly so (Walsh [57]). The stability of the flavin radical, combined with the versatility of flavins, which also can engage in two-electron reactions, has evolutionarily led to a number of redox enzymes in which flavin-mediated reductions of dioxygen are fed by electrons transmitted from NADH to the flavin coenzyme by means of hydride-transfer events. This arrangement permits the very tight binding of the flavin unit to the enzyme, while its reducing power is restored by the loosely bound, freely circulating NADH. More generally, both FMN and FAD can be thought of as mediators between one-electron chemistry and two-electron chemistry in their interaction with the two-electron nicotinamide cofactors NADH and NADPH, on the one hand, and various one-electron reagents, on the other hand. 4.5.2
The Hydride-transfer Process in Model Systems
Classic work by Powell and Bruice (37) established the hydride-transfer nature of the interaction of flavins with nicotinamide cofactors. Among several lines of evidence, a very impressive experiment (Eq. (4.11)) involved the exposure in tertbutyl alcohol solvent at 30 C of various NADH analogs to the N,N-bridged flavin analog shown in Eq. (4.11a), which resulted in quick and complete reduction, and exposure to the radical cation shown in Eq. (4.11b), which gave no direct reduction product at all, although as explained below the observations required careful analysis.
ð4:11aÞ
ð4:11bÞ
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4 Model Studies of Hydride-transfer Reactions
Careful analysis was needed because the acridinium reactant of Eq. (4.11a) was present in the radical cation species of Eq. (4.11b) as a 5% impurity. The observed reaction was then the consumption of one equivalent of the dihydronicotinamide analog and formation of two equivalents of the product of one-electron reduction of the cation radical, just as if the nicotinamide analog were acting as a oneelectron reagent in two separate, sequential steps with overall liberation of a proton. The kinetics was more complex than this mechanism suggested, however. In addition, the relative rates of this reaction were essentially those observed for the reduction of the acridinium ion (Eq. (4.11a)) and addition of acridinium ion to the system of Eq. (4.11b) produced a linear increase in the rate. It was thus deduced that the events occurring were (i) direct delivery of a hydride ion from the NADH analog to the acridinium impurity to give the reduced product of Eq. (4.11a); (ii) a sequence of two one-electron transfers, each to a molecule of the radical cation, producing the reduced product of the radical cation, liberating a proton, and regenerating the catalytic acridinium ion. Finally it was reasoned that if the mechanism of Eq. (4.11a) involved an electron transfer or a hydrogen-atom transfer from the NADH analog to the acridinium species, then such processes should surely occur in the system of Eq. (4.11b). The fact that this did not occur, in spite of the electron transfer being thermodynamically favorable, demonstrated the extreme propensity of the NADH/flavin system for hydride-transfer reaction. The hydride transfer from reduced nicotinamides to N(5) of the flavin species (Eq. (4.12)) has been studied from other points of view in model systems, for example by Reichenbach-Klinke, Kruppa, and Ko¨nig [62], as shown in Fig. 4.7.
ð4:12Þ
Their aim was to explore the significance of the observation that all known structures of NADH-linked flavoproteins had a very similar, and thus – potentially – evolutionarily conserved, relationship between the NADH binding site and the flavin binding site such that the nicotinamide ring is forced by the enzyme to lie parallel to and about 3–4 A˚ distant from the central ring of the flavin coenzyme. Possibly this structural relationship has indeed been conserved by evolution because it confers especially favorable properties for the hyride-transfer process.
4.5 Models for Flavin-mediated Hydride Transfer
Figure 4.7. Structures used by ReichenbachKlinke et al. [62] as agents to reduce riboflavin tetraacetate as a model of the flavinnicotinamide redox interaction in flavoenzymes. The second-order rate constants shown are approximate values for the redox reaction at 50 mM concentrations of each reactant in aqueous solution at pH 7.4 and 25 C. The first-order rate constants for compounds with a Zn-center were obtained
from variation of the NADH-analog concentration from 50 mM to 0.5 mM, followed by analysis of the initial second-order rate constants on a model that assumed reversible complexation of the reactants followed by unimolecular reaction of the complex. Calculated disssociation constants for complexes ranged from 0.7 to 1.3 104 M, with an average value of 1.1 104 M.
To examine the point, Reichenbach-Klinke et al. [62] constructed the NADHanalogs illustrated in Fig. 4.7 and then measured the rate constants for their reduction of riboflavin tetraacetate, the flavin shown in Eq. (4.11) with Q ¼ CH2 (CHOAc)3 CH2 OAc). The hypothesis was that the NADH-analogs possessing a zinc binding site could complex the flavin at the Zn-center, most probably through coordination of the ionized imide function. Indeed all analogs equipped with the Zn-center exhibited saturation kinetics. When the NADH-analog concen-
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4 Model Studies of Hydride-transfer Reactions
tration was varied in the kinetic studies, the data were consistent with complex dissociation constants that for the various compounds had an average value of about 104 M and the first-order rate constants for unimolecular reaction within the complex that are shown in Fig. 4.7. These studies clearly show that a specific approximation of the reactants can lead to an acceleration of the reduction by a factor of some hundreds. That the nature of the approximation is specific is shown by the fact that only one of the analogs had such a large reduction rate, those with the binding site tethered at different distances or with tethers of different rigidity reacting some 10-fold more slowly. A preliminary theoretical exploration showed that the flavin complex of the most rapidly reacting NADH-analog was able to attain – with less strain energy than for any of the other analogs – a structure resembling the enzymic arrangement (nicotinamide parallel to and poised near the central ring of the flavin) with a 3.4 A˚ ring-toring distance. That the hydride-transfer step is under observation is shown by the isotope effect of the monodeuterated version of the same analog. The observed effect on the first-order rate constant is 1.3, which corresponds to 2k H =ðk H þ k D Þ or, neglecting secondary isotope effects, an isotope effect k H =k D of about 2. This is small but too large for a secondary effect and thus indicates the hydrogen transfer to be at least partially rate-limiting. Larger isotope effects consistent with tunneling have been observed in the enzymic equivalents of the reaction [63]. The result is therefore indicative of the importance in the enzymic reaction of an ‘‘axial’’ hydride transfer in which the hydride ion departing from the NADH approaches the flavin N(5) center perpendicular to the ring and thus the plane containing the unshared electron pair of N(5). This study is exemplary of what is becoming a common and vitally important type of model-reaction investigation. In contrast to the historical role of model reactions, which often elucidated the baseline chemistry of biomolecules with very little reliable information about the structure and functional properties of the relevant enzymes, current studies often begin with a sophisticated picture of the facts about the enzymic reaction and are designed to sort out which of the features derive from chemical rules and which from biological factors. The latter often have a basis in metabolic or regulatory imperatives that may not reflect realities in the chemistry of the reactions being effected.
4.6
Models for Quinone-mediated Reactions
There have been some extraordinarily effective contributions of model-reaction studies, particularly by Klinman and Mure [2], to the understanding of quinonecofactor chemistry, but there seem to have been no uses of this approach with respect to hydride-transfer reactions. Readers who wish to acquaint themselves with the current situation should consult Davidson’s volume of 1993 [64], Klinman and
4.6 Models for Quinone-mediated Reactions
Figure 4.8. Two proposed mechanisms for the reaction in bacterial alcohol dehydrogenases between the substrate alcohol and the cofactor PQQ. In the proton-transfer mechanism at the top, alcohol adds to the C(5) carbonyl group and an enzymic acid–base pair then effects an elimination reaction, leading to the aldehyde oxidation product and to the cofactor in its
reduced form. In the hydride-transfer mechanism at the bottom. The acid–base pair acts on the free alcohol to promote hydride transfer from the alcohol to the C(5) center. Again the oxidized alcohol is generated along with, in this case, a ketonic form of the reduced cofactor, which can readily enolize as shown. See the text and Refs. [69, 70].
Mu’s review of 1994 [65], Anthony’s review of 1998 [66], and the brief reviews of Duine [67], Klinman [68], and Mure [2]. A controversy currently abroad in the field seems a particularly likely candidate for investigations using model reactions. A number of bacterial alcohol dehydrogenases make use of free-standing PQQ (see Fig. 4.3 for the structure) as a cofactor. Figure 4.8 shows two possible mechanisms for a critical step in the mechanism: the question is whether the reaction follows a proton-transfer route or a hydride-transfer route [69, 70]. The question is essentially limited to the alcohol and sugar dehydrogenases, while the enzymes that catalyze amine oxidations tend
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Figure 4.9. Structural evidence favoring a hydride-transfer mechanism for the action of the PQQ cofactor in the soluble glucose dehydrogenase of Acinetobacter calcoaceticus (structure and concept of Oubrie et al. [71];
PDB file no. 1CQ1). The dashed red line indicates the 3.2 A˚ distance from C(1) of glucose to C(5) of PQQ and approximates the hydride-transfer trajectory (PQQH2 was the actual species present in the structure).
to make use of proton-abstraction mechanisms in the Schiff ’s base intermediates formed from cofactor and amine substrate [71]. In the proton-transfer mechanism, the alcohol is presumed to form a hemiacetal at the C(5) carbonyl group. Then an acid–base pair in the active site performs an elimination reaction, producing the aldehyde product and the reduced cofactor, PQQH2 . The hydride-transfer mechanism envisions the approximation of the scissile CaH bond of the alcohol to C(5) of the cofactor, followed by an acid–base catalyzed delivery of hydride ion to C(5), resulting in formation of the aldehyde product and the ketol form of PQQH2 , which can readily rearrange to the enediol form. The proton-transfer mechanism has been favored until recently, in particular up to the publication in 1999 by Oubrie et al. [72] of the structure of a PQQ-dependent bacterial glucose dehydrogenase, in which the active site contained a glucose molecule and a molecule of PQQH2 as a simulacrum of PQQ. As Fig. 4.9 shows, the two ligands are situated relative to each other in the active site, such that a short trajectory for hydride transfer from C(1) of the glucose substrate to C(5) of the cofactor can be identified (dashed red line in Fig. 4.9), the C(1)–C(5) distance being only 3.2 A˚. In addition, theoretical work from Zheng et al. [73], along with their rerefinement of an earlier structure of a methanol dehydrogenase (indicating a tetrahedral structure at C(5) in the bound PQQ cofactor) lent further support to this view. Certainly the situation is ideal, for example, for the design of intramolecular models that would permit the exploration of the hydrogen-transfer systematics under controlled conditions. A further advantage of the model system would be a posssible exploration of both proton-transfer and hydride-transfer mechanisms.
4.8 Appendix: The Use of Model Reactions to Estimate Enzyme Catalytic Power
4.7
Summary and Conclusions
1. Studies of model reactions for redox cofactors in general and for hydride-transfer reactions in particular have long formed a major part of the basis for mechanistic knowledge of the enzymic reactions. Model studies are likely to play at least as prominent a role in the future. Particularly as improved enzymological technology permits the dissection of ever finer points of enzyme mechanism, characterization of the scope and limitations of these factors through investigations of highly controlled systems should be more important than ever. 2. The field of model studies of hydride-transfer reactions involving analogs of nicotinamide cofactors is especially well-developed. The powerful preference for one-step hydride-transfer chemistry over multistep processes involving transfers of electrons, protons, and hydrogen atoms under most circumstances has been established very well by model studies. The important role of tunneling in model reactions shows that enzymes are accelerating, rather than originating, tunneling mechanisms in nicotinamide-dependent enzymic reactions. It is now a challenge to students of model reactions to construct analogs capable of evaluating the influence of coupled vibrations in promoting tunneling, as has been argued for various enzymic cases. Model reactions are continuing to expand our understanding of other aspects of nicotinamide-dependent enzyme reactions, including the stereochemistry and regiochemistry of hydride transfer. 3. Hydride-transfer reactions to N(5) of flavin cofactors are indicated by model studies to proceed by single-step hydride-transfer mechanisms, at least with nicotinamide donor/acceptors, and to favor the ‘‘axial’’ donation of hydride along a trajectory perpendicular to the ring plane of the flavin. The required parallel arrangement of the nicotinamide ring and flavin center-ring probably explains the conservation of this arrangement in the active sites of known enzymes that catalyze such hydride-transfer reactions. 4. Quinone cofactors are now thought, on the basis of some enzyme structural information, to prefer a hydride-transfer to a proton-transfer mechanism, at least with alcohol substrates. This distinction could benefit greatly from model studies.
4.8
Appendix: The Use of Model Reactions to Estimate Enzyme Catalytic Power
The examples in Chart 4.1 refer to a unimolecular non-enzymic (standard or model) reaction but there is no difficulty associated with extension of the basic insights of Radzicka and Wolfenden [24] to more general kinds of standard and enzymic reactions. For example, many NADþ -dependent dehydrogenases have a bimolecular standard reaction (NADþ þ Sred gives NADH þ Sox ) with a secondorder rate constant k2unc (dimensions M1 s1 ) and a ‘‘chemical mechanism’’ E þ NADþ gives ENAD, which binds Sred to give ENAD:Sred , which is then transformed to ENADH:Sox , which then releases Sox followed by release of NADH.
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The enzymic reaction has four rate constants k cat (s1 ), k cat =K mNAD (M1 s1 ), k cat =K mSred (M1 s1 ), and k cat =K iNAD K mSred (M2 s1 ) and thus four measures of catalytic power:
k cat =k2unc (M), which is the analog of rate enhancement. It is the equilibrium constant for the reaction ENAD:Sred þ Tunc ¼ E:Tk þ NADþ þ Sred
and measures the net enzymic stabilization of the transition state for k cat (Tk ) in the complex E:Tk over the enzymic stabilization of NADþ and Sred in the complex ENAD:Sred ; k cat =K mNAD k2unc (dimensionless), which is the equilibrium constant for the reaction E þ Tunc ¼ E:TNADbin þ Sred and measures the enzymic stabilization of the transition state for binding of NADþ (TNADbin ) diminished by the cost of liberating the elements of Sred from the transition state for the uncatalyzed reaction (Tunc ); k cat =K mSred k2unc (dimensionless), which is the equilibrium constant for the reaction ENAD þ Tunc ¼ E:Tk=K þ NADþ and measures the net enzymic stabilization of the transition state for reaction of ENAD with Sred (Tk=K ) over the enzymic stabilization of NADþ in the complex ENAD. k cat =K iNAD K mSred k2unc (M1 ), which is the equilibrium constant for the reaction E þ Tunc ¼ E:Tk=K and measures the total enzymic stabilization of the transition state Tk=K relative to the free transition state for the uncatalyzed (standard) reaction. The kinetic investigation of enzymic reactions and suitable non-enzymic standard reactions permits, as just described, the numerical calculation of measures of enzyme catalytic power. These measures are ratios of rate constants and they correspond to equilibrium constants for reactions of free enzyme or enzyme complexes with the transition state for the standard reaction to generate complexes of the enzyme with various transition states along the enzymic reaction pathway, sometimes with liberation of other ligands (see the examples above). The numerical values of the equilibrium constants can of course be converted to standard Gibbs free-energy changes through the relationship lnðKÞ ¼ DG =RT and it is frequently of interest to attempt interpretations of these free energies in terms of contributions of various individual interactions to the overall value. There
4.8 Appendix: The Use of Model Reactions to Estimate Enzyme Catalytic Power
are some points that need to be kept in mind when pursuing such attempts. A few of these are explored briefly here. Several of these matters and others have been treated with considerable effect by Miller and Wolfenden [74], Garcia-Viloca et al. [75], Benkovic and Hammes-Schiffer [76], and Sutcliffe and Scrutton [77]. Multiple transition states. Commonly for enzymic reactions there will not be a single rate-determining step with a single transition state for any of the kinetic parameters; instead several steps will contribute to determining the rate in various degrees, and the effective transition state for such a situation has been called a virtual transition state. Its properties, including its free energy, will be a weighted average of the properties of the contributing transition states, with those of highest free energy contributing the most (because they most nearly determine the rate). It is rare for sufficient information about any particular enzyme system to be available to permit the situation to be laid out in detail, but it is useful to keep in mind that measures of enzyme catalytic power generally deal with more than a single contributing enzymic transition state. In principle, this certainly may also be true of the standard or model reaction. Meaning of ‘‘transition-state stabilization.’’ When a reaction such as E þ T ¼ E:T has a large equilibrium constant and a correspondingly negative value of DG , thermodynamicists are accustomed to say, ‘‘E stabilizes T in the complex E:T relative to T in the free state.’’ For many of us, this kind of statement may generate a mental picture in which the stabilization is accomplished by the formation of attractive interactions between component structures of E and component structures of T in the complex E:T, the individual (negative) free energies of interaction in a simple case summing up to generate the overall value of DG . Reflection demonstrates of course that such a model is by no means required: indeed every interaction between components of E and T in the complex E:T may be strongly repulsive and make large positive contributions to DG . If E and T in the their free states, however, experience still more strongly repulsive interactions, and these are relieved upon complex formation, then the overall DG may still be quite negative. Failure to take this complication into account has led to some acrimonious interchanges on occasion, so it is necessary to note that ‘‘E stabilizes T in E:T’’ means only that the combination of E with T to form E:T produces a large equilibrium constant. Nothing is implied about the nature of the interactions that make this true, and indeed the investigation needed to clarify the nature of these interactions may be laborious and difficult. Novel kinetic formulations. The description given above of the calculation of measures of enzyme catalytic power relies initially on empirically determined rate constants for enzymic and non-enzymic reactions. The numerical results at the initial stage are therefore ‘‘theory-free’’ and may be used for many purposes with perfect confidence. The further interpretation in terms of equilibrium constants for transition-state binding to enzyme species, however, relies on the ‘‘ultrasimple’’ transition-state
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theory and there are increasing indications that this formulation may be oversimplified for the interpretation of data for hydride-transfer reactions (see Chapter 10 by Klinman, Chapter 12 by Kohen, and Chapter 19 by Banerjee). It is a not particularly demanding task to modify the language to correspond to the most modern forms of transition-state theory, and for those who use such descriptions to pursue the meaning of the empirical results, there is no great problem. For the use of other approaches, however, such as have been developed and applied in the context of ideas about vibrationally induced hydrogen tunneling, more careful analysis may be required to assign the origins of the observed measures of catalytic power.
References 1 Bugg, T. D. H. 2004 Introduction to
2
3
4
5 6
7
8
9
Enzyme and Coenzyme Chemistry, 2nd edn., Blackwell Publishing, Oxford UK. Mure, M. 2004 Acc. Chem. Res. 37, 131–139: Tyrosine-derived quinone cofactors. Westheimer, F. H. 1985 Adv. Phys. Org. Chem. 21, 1–36: The Discovery of the mechanisms of enzyme action, 1947–1963. Westheimer, F. H. 1987 in Coenzymes and Cofactors, Vol. II Part A, Pyridine Nucleotide Coenzymes, ed. D. Dolphine, R. Poulsen, and O. Abramovic´, Wiley, New York, pp. 253–322: Mechanism of action of the pyridine nucleotides. Kosower, E. M. 1962 Molecular Biochemistry, McGraw-Hill, New York. Newton, I. 1686 Rules of reasoning in philosophy, in Philosophiae Naturalis Principia Mathematica, reprinted in Newton’s Philosophy of Nature, ed. H. Thayer, Hafner, New York 1953. Jencks, W. P. 1975, Adv. Enzymol. 43, 219–410: Binding energy, specificity, and enzymic catalysis: the Circe effect, see particularly pp. 296–305. Bunting, J. W.; Sindhuatmaja, S. 1981 J. Org. Chem. 46, 4211–4219: Kinetics and mechanism of the reaction of 5-nitroisoquinolinium cations with 1,4-dihydronicotinamides. Bunting, J. W.; Norris, D. J. 1977 J. Am. Chem. Soc. 99, 1189–1196: Rates and equilibria for hydroxide
10
11
12
13
14
15
addition to quinolinium and isoquinolinium cations. Ohnishi, Y.; Kagami, M.; Ohno, A. 1975 J. Am. Chem. Soc. 97, 4766–4768: Reduction by a model of NAD(P)H. Effect of metal ion and stereochemistry on the reduction of a-keto esters by 1,4-dihydronicotinamide derivatives. Ohno, A.; Ishikawa, Y.; Yamazaki, N.; Okamura, M.; Kawai, Y. 1998 J. Am. Chem. Soc. 120, 1186–1192: NAD(P)þ-NAD(P)H Models. 88. Stereoselection without steric effect but controlled by electronic effect of a carbonyl group: Syn/Anti reactivity ratio, kinetic isotope effect, and an electron-transfer complex as a reaction intermediate. Lee, I.-S. H.; Jeoung, E. H.; Kreevoy, M. M. 2001 J. Am. Chem. Soc. 123, 7492–7496: Primary kinetic isotope effects on hydride transfer from 1,3dimethyl-2-phenylbenzimidazoline to NADþ analogues. Bruice, T. C.; Benkovic, S. J. 1966 Bioorganic Mechanisms, W.A. Benjamin, New York, Vol. I, pp. 119–211. Kirby, A. J. 1980 Adv. Phys. Org. Chem. 17, 183–278: Effective molarities for intramolecular reactions. Bruice, T. C.; Lightstone, F. C. 1999 Acc. Chem. Res. 32, 127–136. Ground state and transition state contributions to the rate of intramolecular and enzymic reactions.
References 16 Bruice, T. C. 2002 Acc. Chem. Res. 35,
17
18
19
20
21
22
23
24
25
26
27
28
139–148: A view at the millennium: the efficiency of enzymatic catalysis. Petsko, G. A.; Ringe, D. 2004 Protein Structure and Function, New Science Press, London. Reichardt, C. 2004 Solvents and Solvent Effects in Organic Chemistry, 3rd edn., Wiley-VCH, Weinheim. Purse, B. W.; Rebek, J., Jr. 2005 Proc. Natl. Acad. Sci. USA 102, 10777– 10782: Functional cavitands: Chemical reactivity in structured environments. Rebek, J., Jr. 2005 in NATO Science Series, Series I: Life and Behavioural Sciences, 364 (Structure, Dynamics and Function of Biological Macromolecules and Assemblies), pp. 91–105: Recognition, autocatalysis and amplification. Rebek, J., Jr. 2005 Angew. Chem., Int. Ed. Engl. 44, 2068–2078: Simultaneous encapsulation: molecules held at close range. Benner, S. A. 1989 Chem. Rev. 89, 789–806: Enzyme kinetics and molecular evolution. Wolfenden, R.; Snider, M. J. 2001 Acc. Chem. Res. 34(12), 938–945. The depth of chemical time and the power of enzymes as catalysts. Radzicka, A.; Wolfenden, R. V. 1995 Science 267, 90–93: A proficient enzyme. Hu, Q.; Kluger, R. 2002 J. Am. Chem. Soc. 124, 14858–14859: Reactivity of intermediates in benzoylformate decarboxylase: avoiding the path to destruction. Hu, Q.; Kluger, R. 2004 J. Am. Chem. Soc. 126, 68–69: Fragmentation of the conjugate base of 2-(1-hydroxybenzyl)thiamin: does benzoylformate decarboxylase prevent orbital overlap to avoid it? Hu, Q.; Kluger, R. 2005 J. Am. Chem. Soc. 127, 12242–12243: Making thiamin work faster: acid-promoted separation of carbon dioxide. Moore, I. F.; Kluger, R. 2000 Org. Lett. 2, 2035–2036.: Decomposition of 2-(1-hydroxybenzyl)thiamin. Ruling out stepwise cationic fragmentation.
29 Moore, I. F.; Kluger, R. 2002 J. Am.
30
31
32
33
34
35
36
37
38
Chem. Soc. 124, 1669–1673: Substituent effects in carbon-nitrogen cleavage of thiamin derivatives. Fragmentation pathways and enzymic avoidance of cofactor destruction. Powell, M. F.; Bruice, T. C. 1982 J. Am. Chem. Soc. 104, 5834–5836: Reinvestigation of NADH analog reactions in acetonitrile: Consequences of isotope scrambling on kinetic and product isotope effects. Miller, L. L.; Valentine, J. R. 1988 J. Am. Chem. Soc. 110, 3982–3989: On the electron-proton-electron mechanism for 1-benzyl-1,4dihydronicotinamide oxidations. ¨ .; Sinha, A.; Almarsson, O Gopinath, E.; Bruice, T. C. 1993 J. Am. Chem. Soc. 115, 7093–7102: Mechanism of one-electron oxidation of NAD(P)H and function of NADPH bound to catalase. Matsuo, T.; Mayer, J. M. 2005 Inorg. Chem. 44, 2150–2158: Oxidations of NADH analogues by cis[Ru IV (bpys)2 (py)O] 2þ occur by hydrogen-atom transfer rather than by hydride transfer. Roberts, B. R. 1999 Chem. Soc. Rev. 28, 25–35: Polarity-reversal catalysis of hydrogen-atom abstraction reactions: concepts and applications in organic chemistry. Huyser, E. S. 1970 Free-Radical Chain Reactions, Wiley Interscience, New York. Powell, M. F.; Wong, W. H.; Bruice, T. C. 1982 Proc. Natl. Acad. Sci. USA 79, 4604–4608: Concerning 1e transfer in reduction by dihydronicotinamde: Reaction of oxidized flavin and flavin radical with N-benzyl-1,4dihydronicotinamide. Powell, M. F.; Bruice, T. C. 1983 J. Am. Chem. Soc. 105, 1014–1021: Hydride vs. electron transfer in the redution of flavin and flavin radical by 1,4-dihydropyridines. Powell, M. F.; Bruice, T. C. 1983 J. Am. Chem. Soc. 105, 7139–7149: Effect of isotope scrambling and tunneling on the kinetic and product isotope effects for reduced
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39
40
41
42
43
44
45
46 47
48
49
nicotinamide adenine dinucleotide model hydride transfer reactions. Bunting, J. W. 1991 Bioorg. Chem. 19, 456–91: Merged mechanisms for hydride transfer from 1,4dihydronicotinamides. Albery, W. J.; Kreevoy, M. M. 1978 Adv. Phys. Org. Chem. 16, 87–157: Methyl transfer reactions. Lee, I.-S. H.; Jeoung, E. H.; Kreevoy, M. M. 1997 J. Am. Chem. Soc. 119, 2722–2728: Marcus theory of a parallel effect on a for hydride transfer reaction between NADþ analogs. Lee, I.-S. H.; Chow, K.-H.; Kreevoy, M. M. 2002 J. Am. Chem. Soc. 124, 7755–7761: The Tightness contribution to the Brønsted a for hydride transfer between NADþ analogues. Lee, I. S. H.; Ji, Y. R.; Jeoung, E. H. 2006 J. Phys. Chem. A 110, 3875–3881: Reinterpretation of the Bronsted a for redox reactions based on the effect of substituents on hydride transfer reaction rates between NADþ analogues. ¨rthwein, E.-U.; Lang, G.; Wu Schappele, L. H.; Mayr, H. 2002 J. Am. Chem. Soc. 124, 4084–4092: Rate-equilibrium relationships in hydride transfer reactions: The Role of intrinsic barriers. Romesberg, F. E.; Schowen, R. L. 2004, Adv. Phys. Org. Chem. 39, 27–77: Isotope effects and quantum tunneling in enzyme-catalyzed hydrogen transfer. Part I. The experimental basis. Bell, R. P. 1980 The Tunnel Effect in Chemistry, Chapman & Hall, London. Kaldor, S. B.; Saunders, W. H., Jr. 1979 J. Am. Chem. Soc. 101, 7594– 7599: Mechanisms of eleimination reactions 30. The contributions of tunneling and heavy-atom motions in the reaction coordinate to deuterium kinetic isotope effects in eliminations from 2-phenylethyl derivatives. Overman, L. E. 1972 J. Org. Chem. 37, 4214–4218: Dehydrogenase enzyme models: Approximation of an alcohol and a pyridinium ring. Meyers, A. I.; Brown, J. D. 1987 J. Am. Chem. Soc. 109, 3155–3156: The First nonenzymic stereospecific
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52
53
54
55
56
57
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intramolecular reduction by an NADH mimic containing a covalently bound carbonyl moiety. Kirby, A. J.; Walwyn, D. R. 1987 Tetrahedron Lett. 28, 2421–2424: Intramolecular hydride transfer from a 1,4-dihydropyridine to an a-ketoester in aqueous solution. A model for lactate dehydrogenase. Kirby, A. J.; Walwyn, D. R. 1987 Gazz. Chim. Ital. 117, 667–680: Effective molarities for intramolecular hydride transfer. Reduction by 1,4dihydropyridines of the neighbouring a-ketoester group. Yang, X.; Hu, Y.; Yin, D.; Turner, M. A.; Wang, M.; Borchardt, R. T.; Howell, P. L.; Kuczera, K.; Schowen, R. L. 2003 Biochemistry 42, 1900–1909: The catalytic strategy of Sadenosyl-L-homocysteine hydrolase: Transition-state stabilization and the avoidance of abortive reactions. Porter, D. J.; Boyd, F. L. 1991 J. Biol. Chem. 266, 21616–21625: Mechanism of bovine liver S-adenosylhomocysteine hydrolase. Steady-state and pre-steadystate kinetic analysis. Porter, D. J.; Boyd, F. L. 1992 J. Biol. Chem. 267, 3205–3213: Reduced S-adenosylhomocysteine hydrolase. Kinetics and thermodynamics for binding of 3 0 -ketoadenosine, adenosine, and adenine. Porter, D. J. 1993 J. Biol. Chem. 268, 66–73: S-adenosylhomocysteine hydrolase. Stereochemistry and kinetics of hydrogen transfer. Hemmerich, P.; Nagelschneider, G.; Veeger, C. FEBS Lett. 8, 69–83: Chemistry and molecular biology of flavins and flavoproteins. Walsh, C. 1978 Annu. Rev. Biochem. 47, 881–931: Chemical approaches to the study of enzymes catalyzing redox transformations. Walsh, C. 1980 Acc. Chem. Res. 13, 148–155: Flavin coenzymes: At the crossroads of biological redox chemistry. Palfey, B. A.; Massey, V. 1998 in Comprehensive Biological Catalysis, ed. M. Sinnott, Vol. III, pp. 83–154: Flavin-dependent enzymes.
References 60 Ghisla, S.; Thorpe, C. 2004 Eur. J.
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Biochem. 271, 494–508: Acyl-CoA dehydrogenases. A mechanistic overview. Blankenhorn, G. 1976 Eur. J. Biochem. 67, 67–80: Nicotinamidedependent one-electron and twoelectron (flavin) oxidoreduction: Thermodynamics, kinetics, and mechanism. Reichenbach-Klinke, R.; Kruppa, M.; Ko¨nig, B. 2002 J. Am. Chem. Soc. 124, 12999–13007: NADH Model systems functionalized with Zn(II)cyclen as flavin binding site – Structure dependence of the redox reaction within reversible aggregates. Basran, J.; Masgrau, L.; Sutcliffe, M. J.; Scrutton, N. S. 2006, in Isotope Effects in Chemistry and Biology, ed. Kohen, A.; Limbach, H.-H., pp. 671– 689: Solution and computational studies of kinetics isotope effects in flavoprotein and quinoprotein catalyzed substrate oxidations as probes of enzymic hydrogen tunneling and mechanism. Davidson, V. J. (ed.) 1993, Principles and Applications of Quinoproteins, Marcel Dekker, New York. Klinman, J. P.; Mu, D. 1994 Annu. Rev. Biochem. 63, 299–344: Quinoenzymes in biology. Anthony, C. 1998 in Comprehensive Biological Catalysis, ed. M. Sinnott, Vol. III, pp. 155–180: Quinoproteincatalysed reactions. Duine, J. A. 2000 Chem. Record, 74–83: Cofactor diversity in biological oxidations: Implications and applications. Klinman, J. P. 2001 Proc. Nat. Acad. Sci. USA 98, 14766–14768: How many ways to craft a cofactor? Kay, C. W. M.; Mennenga, B.; Go¨risch, H.; Bittl, R. 2006 Proc. Natl. Acad. Sci. USA 103, 5267–5272: Substrate binding in quinoprotein ethanol dehydrogenase from
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Pseudomonas aeruginosa studied by electron-nuclear double resonance. Kay, C. W. M.; Mennenga, B.; Go¨risch, H.; Bittl, R. 2006 J. Biol. Chem. 281, 1470–1476: Structure of the pyrroloquinoline quinone radical in quinoprotein ethanol dehydrogenase. Datta, S.; Mori, Y.; Takagi, K.; Kawaguchi, K.; Chen, Z.-W.; Okajima, T.; Kuroda, S.; Ikeda, T.; Kano, K.; Tanizawa, K., Mathews, F. S. 2001 Proc. Natl. Acad. Sci. USA 98, 14268–14273: Structure of a quinohemoprotein amine dehydrogenase with an uncommon redox cofactor and highly unusual crosslinking. Oubrie, A.; Rozeboom, H. J.; Kalk, K. H.; Olsthoorn, A. J. J.; Duine, J. A.; Dijkstra, D. W. 1999 EMBO J. 18, 5187–5194: Structure and mechanism of soluble quinoprotein glucose dehydrogenase. Zheng, Y.-J.; Xia, Z.-x.; Chen, Z.-w.; Mathews, F. S.; Bruice, T. C. 2001 Proc. Natl. Acad. Sci. USA 98, 432– 434: Catalytic mechanism of quinoprotein methanol dehydrogenase: A theoretical and x-ray crystallographic investigation. Miller, B. G., Wolfenden, R. 2002 Annu. Rev. Biochem. 71, 847–885: Catalytic proficiency: the unusual case of OMP decarboxylase. Garcia-Viloca, M.; Gao, J.; Karplus, M.; Truhlar, D. G. 2004 Science 303, 186–195: How enzymes work: analysis by modern rate theory and computer simulations. Benkovic, S. J.; Hammes-Schiffer, S. 2003 Science 301, 1196–1202: A perspective on enzyme catalysis. Sutcliffe, M. J.; Scrutton, N. S. 2002 Eur. J. Biochem. 269, 3096–3102: A new conceptual framework for enzyme catalysis: Hydrogen tunneling coupled to enzyme dynamics in flavoprotein and quinoprotein enzymes.
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Acid–Base Catalysis in Designed Peptides Lars Baltzer 5.1
Designed Polypeptide Catalysts
The purpose of rational design of folded and catalytically active polypeptides is to test critically our understanding of enzyme function and catalysis, and ultimately to provide new catalysts for biotechnical applications [1–3]. The rational design process is based on fundamental principles of organic reactivity implemented in the construction of active sites and any reaction for which the reaction mechanism is understood to a reasonable degree is a target for design. In a scaffold of sufficient complexity, functional groups capable of substrate binding, transition state stabilization, general-acid and general-base catalysis etc. can be introduced and combined to mimic the function of native enzymes or, even better, to catalyze reactions selected from the vast repertoire of chemical transformations developed by organic chemists. In folded polypeptide scaffolds catalytically active residues may be systematically varied and their properties tuned. It is, for example, possible to explore the effect of decreased or increased acidity of a catalytically active residue by introducing charged residues in close proximity to affect its pK a . It is also possible to explore the effects of charge–charge interactions between substrate and catalyst by variation of the number and position of charged amino acid residues. In the search for optimal active site constellations of amino acids, sequences are easily modified. Active sites in de novo designed polypeptides are, as a rule, built from surface exposed residues, even if the polypeptide is folded. The design from scratch of proteins or polypeptides that fold to form cavities is still in its infancy and systematic variations are, by necessity, difficult in complex structures because the structures may change with amino acid substitutions. Rate enhancements of three to four orders of magnitude have been reported several times in designed catalysts [4–9] but those of typical enzymes are unrealistic in solvent exposed catalytic sites. The number of functional groups that can interact with substrates, intermediates and transition states is limited and the many degrees of freedom of the active site residues reduce the catalytic efficiency for entropic reasons. However, incorporation of an active site developed in a surface catalyst into a constrained hydrophobic pocket Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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will affect ionization constants, the strengths of charge–charge interactions and the degrees of freedom of rotable bonds and it is possible, and even likely, that catalytic efficiencies will increase significantly for these reasons alone [10]. In the design process the access to an easily modified scaffold in which principles can be tested is more important than the actual rate enhancement. Surface catalysts serve the purpose of defining the roles of individual residues and what catalytic functions are needed. Following this ambition, polypeptide catalysts have been designed for e.g. ester hydrolysis [6, 7, 11, 12], transesterification [6], amidation [13], transamination [8], chemical ligation [5] and decarboxylation reactions [4, 14]. The reactions have been studied and mechanisms elucidated to various degrees and as a result considerable mechanistic understanding has been generated. Recently, computational approaches have been applied to the re-engineering of native proteins to introduce catalytic sites for monooxygenase [9] and triosephosphateisomerase [15] activities. The results are impressive and demonstrate that enzymatic activity may be introduced in folded proteins with no prior catalytic functions. Computational methods are now emerging as the most promising approach to de novo protein design and, in combination with mechanistically driven de novo design, may prove to be an efficient road to new enzymes. 5.1.1
Protein Design
The design of folded polypeptides and proteins has now reached a level where sequences of 100 residues or more can be designed from scratch and many welldefined proteins have been reported as well as folded but structurally not uniquely defined polypeptides [1–3, 16, 17]. For catalyst design a number of sequences may be taken from the literature and adapted to a catalytic problem since the synthesis of 40–50 residue sequences are, by todays standards, almost routine in a peptide chemistry laboratory. The choice of sequence may seem an enigmatic problem but most of the many helical bundle motifs that were reported ten years ago are likely to be adequate scaffolds for catalyst design, even though they do not have the properties of native proteins. They fold into several, but similar, conformers that are in rapid equilibrium and the advantage of using sequences that do not fold cooperatively is that they are very tolerant to modifications and that the introduction or deletion of charged residues will not significantly alter the balance between conformations. In contrast, a protein that folds cooperatively may undergo substantial conformational changes and may be difficult to redesign if residues that are critical for folding are replaced. The advantage of using folded proteins with well-defined tertiary structures is that crystal and NMR structures are available making it considerably easier to design active sites and to determine the relationships between structure and function. Helical folds have dominated in the pioneering development of de novo protein design [18] and have also been the most common in the design of new catalysts [4–9, 11–14], Fig. 5.1. The robustness of the motif has been a contributing factor
5.1 Designed Polypeptide Catalysts
Figure 5.1. Modelled structure of a 42-residue peptide folded into a helix–loop–helix motif and dimerized to form a four-helix bundle protein. Helices are amphiphilic with a hydrophobic and a polar face. Due to the robustness and ease of synthesis this has become a popular motif in de novo protein design.
to their popularity and so has the regularity of the folded structure that makes it highly suitable for active site engineering. The design principles have been elucidated in great detail [1–3]. A peptide with helix propensity is in an equilibrium between the folded and unfolded forms and the formation of a helix is favored by interactions that preferentially stabilize the folded state. Amino acids like alanine favor helix formation for steric reasons and every amino acid residue has a welldefined propensity for helix formation, high or low. Salt bridges between side chains of opposite charge may be introduced between residues four positions apart in the sequence to stabilize the helical conformations and charged residues are introduced at the helical ends to stabilize the macroscopic dipole resulting from helix formation. In addition, the amide protons and carbonyl oxygens in the first and last turn of the helix, for which no acceptors and donors of hydrogen bonding are available in the peptide backbone, may be stabilized by suitably selected side chain functional groups. Tertiary interactions are, however, the most important for structure formation of helical proteins in aqueous solution. Helical bundles are conveniently described in terms of the heptad repeat pattern ða; b; c; d; e; f ; gÞn , Fig. 5.2, according to which the a and d positions form one side of the folded helix, as do the b and e positions and the g and c positions. Helical bundles are formed from amphiphilic helices and the a and the d positions are
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Figure 5.2. Helical wheel representation of helical bundle proteins to illustrate principles of design. Helix–loop–helix dimers are predominantly antiparallel to neutralize helical dipole moments and can fold in two ways with consequences for which residues can form active sites. Hydrophobic residues in a and d positions form cores in the folded state and
drive folding. Residues in b and e positions control aggregation and organization of helical subunits. The three helices in a three-helix bundle may form a clockwise or an anticlockwise structure depending on the complementarity of the charged residues in b and e positions.
normally occupied by hydrophobic residues so that in the folded four helix bundle, for example, a core is formed from hydrophobic residues from four helices. The binding energy from these interactions is the main driving force for bundle formation. If the hydrophobic faces of the helices are shape complementary the polypeptides will fold to form well-defined tertiary structures, comparable to those of evolved proteins. If the shapes are not perfectly complementary the polypeptides may well fold anyway but not into a uniquely defined three-dimensional structure but into groups of similar conformations in rapid exchange. These structures are usually referred to as molten globules and are very useful as scaffolds for many
5.1 Designed Polypeptide Catalysts
purposes because, although the hydrophobic cores are slightly disordered, the overall fold is that of a helical bundle. In the antiparallel helix–loop–helix motif that has been used in several model catalysts, the b and e positions are occupied by charged residues and charge– charge interactions control the mode of dimerization. While charge–charge interactions are not sufficient to drive folding by themselves, charge repulsion between the residues in the b and e positions of each monomer subunit in a helix–loop– helix dimer is a powerful determinant of structure formation and can be used to completely inhibit dimerization. 5.1.2
Catalyst Design
The g and c positions that form one face of a four-helix bundle protein are preferentially used for active site engineering. The surface area of a folded helix–loop– helix hairpin is approximately 20 25 A˚ and roughly a dozen residues may be given catalytic functions. The distance between the a carbon atoms four residues apart in the sequence of a folded helix is 6.3 A˚, and the corresponding distance between residues three positions apart is 5.2 A˚. These distances appear to be well suited for e.g. acyl transfer between two residues, Fig. 5.3. While these distances are suitable for placing functional groups in positions to interact with different residues of substrates, intermediates and transition states, they cannot be fine tuned, as the helix is a structurally well-defined entity. The distance between the g and c positions in neighboring helices in a helix–loop–helix hairpin is roughly 10 A˚. Residues in neighboring helices may be positioned at the helix–helix interface in positions that makes the side chains of residues from one helix come into proximity with side chains of amino acids from the other helix and bind substrates, intermediates and transition states cooperatively. In contrast to distances between residues within a single helix the distances between residues in neighboring helices may be modulated. The available residues in g and c positions may not only be used to participate in bond making and bond breaking, but also to tune the properties of residues that
Figure 5.3. Intramolecular acyl transfer between residues four positions apart in the sequence in a helical conformation, the key step in the site-selective functionalization reaction [13].
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are part of the actual catalytic machinery. Positively charged arginine residues were shown to depress the pK a values of His residues by 0.5 units when one turn apart in the g and c positions of a helix [19]. The depressive effect was found to be approximately additive and two Arg residues in close proximity decreased the pK a of a His by roughly one pK a unit. Glu residues had the opposite effect. The ability to tune residue properties is an important asset in mechanistic investigations and it was shown to be possible to vary by rational design the pK a of a His in a solvent exposed position from 5.2 to 7.2 [6]. The random coil value of a His is 6.4 [20]. The residues in the f positions are also used to tune the properties of residues in the g and c positions. It has been suggested that buttressing effects of side chains in f positions are capable of forcing side chains in g and c positions into more reactive conformations [4]. The use of helical bundles in catalyst design expands the possibilites for fine tuning further. The binding energy of a helical bundle is predominantly provided by the hydrophobic residues in the a and d positions. The hydrophobic interactions are short range and proportional to the contact surface area of the hydrophobic side chains [21]. In 40 to 50 residue sequences with approximately 20 residues assigned to each helix, at least four a and d positions in each helix are occupied by hydrophobic amino acids, more than enough to make the sequence fold. The replacement of one or two of these residues by charged ones has large effects on the pK a values of the charged residues and thus on their reactivities but does not disrupt the fold of the bundle. The pK a of a lysine residue in a d position was measured to be 9.2, in comparison with 10.4, which is the random coil value [22]. The pK a of a His residue in a d position was 5.6, in comparison with 6.4 which is the random coil value [23]. Depending on the pH and type of reaction these changes can give rise to substantial effects on reactivity. Although residues formally in a and d positions according to the heptad repeat pattern are, in principle, buried in the hydrophobic core, they are very reactive and thus capable of participating in bond making and breaking in active sites. The modulation of pK a values has proven to be an important tool in mechanistic investigations of catalytic activity. The techniques commonly used for structural characterization of folded polypeptides are NMR and CD spectroscopy and analytical ultracentrifugation. NMR spectroscopy is informative at many levels, and simple one-dimensional 1 H NMR spectra provide very useful, qualitative information about substrates, intermediates and products under reaction conditions and about whether they bind to the macromolecular catalyst [12]. The sharp resonances of small molecules are easily observed in the presence of the broad peaks of biomacromolecules and the binding of a small molecule by a macromolecule is reflected in the increased line width of the small molecules upon binding. The chemical shift dispersion and linewidths in the 1 H NMR spectrum of the polypeptide catalyst provide qualitative information about whether it is well defined or unordered. The chemical shift dispersion and temperature dependence will reveal whether it is close to being well defined (well dispersed, slow on the NMR time scale) or poorly defined (poor dispersion, fast on the NMR time scale) [24]. High resolution solution structures may also be obtained, but only after considerably greater effort and in specialist laboratories.
5.1 Designed Polypeptide Catalysts
Highly repetitive peptide sequences, and sequences dominated by only a few amino acids are not easily studied by NMR spectroscopy since assignment of the NMR spectrum is difficult. A forward-looking aspect of the design process is therefore to vary the amino acid sequence as far as possible to enable one to carry out NMR spectroscopic analyses. The CD signature of a helical peptide, with minima at 208 and 222 nm, is a powerful source of information about solution structure and molecular interactions with molecules that affect the helical content. The dissociation behavior of a helix–loop–helix dimer is conveniently monitored by CD spectroscopy and provides critical information about what species dominates in solution under reaction conditions [6]. Information about the state of aggregation is obtained by analytical ultracentrifugation, which is especially interesting with regards to higher order aggregation. CD spectroscopy is, as a rule, not informative in this respect since helicity does not seem to increase when helical bundles aggregate further. 5.1.3
Designed Catalysts
Several designed polypeptide catalysts have been reported to date, together with reasonably complete reaction mechanistic analyses. These may serve as good introductions to rational catalyst design and are listed here for reference purposes. A helical 14-residue peptide, rich in lysine residues, was reported by Benner and coworkers in 1993 to catalyze the decarboxylation of oxaloacetate [4], Scheme 5.1. The catalytic efficiency was at least partially due to the depression of lysine pK a values caused by the presence of neighboring protonated lysines in the folded helix, and the resulting increased propensity for imine formation. Although the peptide was partially disordered there appeared to be a correlation between helical content and catalysis and specific acid catalysis was an important feature of the reaction mechanism. Follow up publications by Allemann in ordered polypeptide scaffolds showed enhanced activity [25].
Scheme 5.1
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Native chemical ligation, Scheme 5.2, is a two-step peptide ligation reaction in which a C-terminal thiol ester is reacted with the side chain of a N-terminal cysteine under release of the thiol leaving group, to form an intermediate that reacts further to form a peptide bond. The amino group replaces the cysteine side chain in an intramolecular rearrangement and forms the thermodynamically more stable product. Ghadiri et al. designed peptide templates on which the peptide fragments were assembled prior to reaction and catalysis was due mainly to proximity effects [5]. Selectivity was introduced by Chmielewski et al. and controlled by electrostatic interactions between catalyst and peptide [26]. Product inhibition was a problem.
Scheme 5.2
A 42-residue polypeptide that folded into a helix–loop–helix motif and dimerized to form a four-helix bundle was shown to catalyze the hydrolysis and transesterification reactions of active esters, Scheme 5.3 [6, 11, 12]. The solution structure and reaction mechanism were extensively studied, see Section 5.2, and the rate en-
Scheme 5.3
5.1 Designed Polypeptide Catalysts
hancement was shown to depend on cooperative nucleophilic and general-acid catalysis. A HisHþ -His pair was found to be the basic catalytic unit and supplementing charged residues in the catalyst enhanced the reactivity by factors that corresponded well to what was expected from transition state binding by salt bridge formation. Similar constructs were used to catalyze transformations of phosphate mono- and diesters, for example the cyclization of the RNA mimic uridine 3 0 -2,2,2trichloroethylphosphate with a leaving group pK a of 12.3, although the reaction mechanistic analyses were not as complete as for catalysis of ester hydrolysis (unpublished). The same scaffold was used to design catalysts for pyridoxal phosphatedependent deamination of aspartic acid to form oxaloacetate, one half of the transamination reaction [8], and oxaloacetate decarboxylation [14]. Catalysis was due to binding of pyridoxal phosphate in close proximity to His residues capable of rate limiting 1,3 proton transfer. A two-residue catalytic site containing one Arg and one Lys residue was found to be the most efficient decarboxylation agent, more efficient per residue than the Benner catalyst, most likely due to a combination of efficient imine formation, pK a depression and transition state stabilization. In order to bypass the problem of designing a pocket from scratch, Bolon and Mayo [27] introduced a catalytically active His residue in thioredoxin, a welldefined 108-residue protein for which much structural and functional information was available. The design was based on the well-known reaction mechanism of pnitrophenyl acetate hydrolysis and thioredoxin was redesigned by computation to accommodate a histidine with an acylated side chain to mimic transition state stabilization. The thioredoxin mutant was catalytically active and the reaction followed saturation kinetics with a kcat of 4:6 104 s1 and a KM of 170 mM. The catalytic efficiency, after correction for differential protonation and nucleophilicity, can be estimated to be a factor of 50 greater than that of 4-methylimidazole, due to nucleophilic catalysis and proximity effects, see Section 5.2.3. A four-helix bundle protein, S-824, reported by Wei and Hecht [7], selected from a focused binary patterned library showed catalytic activity towards p-nitrophenyl acetate. S-824 exhibited a larger catalytic efficiency than that of KO-42 at pH 5.1 (>2) and a larger kcat than that of PZD2 at pH 7 (>10) whereas kcat =KM at pH 7 was slightly smaller than that of PZD2. The pH profile was bell-shaped with a maximum at pH 8.5 and the reaction followed saturation kinetics. Since the catalyst has not yet been sufficiently characterized with regards to the identity of the catalytic machinery and the reaction mechanism it is not possible to make detailed comparisons with other catalysts, especially in the light of the fact that there are 12 histidines in the sequence. The pH profile suggests that acid–base catalysis is likely to play a role and the observation of the maximum rate at pH 8.5 suggests that His residues might function as nucleophiles and residues with pK a values of around 10 provide general-acid catalysis or transition state stabilization. A more detailed analysis should provide a better platform for further development of an enzyme-like catalyst. A rationally designed four-helix bundle diiron metalloprotein was shown by
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Kaplan and DeGrado [9] to catalyze the oxidation of aminophenol by a two-electron transfer pathway, Scheme 5.4. The catalyst has been extensively characterized with regards to structure and the designed protein provided not only an active site cavity but also a channel through which the active site could be reached. The reaction mechanism and reactive site residues were determined.
Scheme 5.4
The re-engineering of the ribose binding protein to introduce triose phosphate isomerase activity represents a major advance in enzyme design. Triose phosphate isomerase catalyzes the interconversion of dihydroxyacetone phosphate (DHAP) and glyceraldehyde 3-phosphate (GAP), Scheme 5.5. Computational design by Dwyer et al. [15] enabled not only the binding of substrate and product with micromolar affinities but also binding of the enediolate intermediate and the introduction of catalytically crucial Glu, His and Lys residues to catalyze the rate-limiting proton transfer reaction and to stabilize the intermediate. The catalyst NovoTim 1.2.4 catalyzed the DHAP to GAP transformation with a kcat =KM of 1 10 3 M1 s1 and the reverse reaction with a kcat =KM of 2:1 10 4 M1 s1 , only two and three orders of magnitude, respectively, lower than the rate constants measured for the wildtype enzyme. This achievement is remarkable, especially in view of the fact that triose phosphate isomerase is an enzyme operating at the diffusion controlled limit.
Scheme 5.5
5.2 Catalysis of Ester Hydrolysis
5.2
Catalysis of Ester Hydrolysis
One of the most studied chemical reactions is that of ester hydrolysis, Scheme 5.6. The well-defined tetrahedral intermediate in which partial negative charge develops and the well understood dependence of reactivity on leaving group pK a make it an obvious target for catalyst design. The acyl group and the leaving group may be optimized for binding and reactivity and the chromogenic properties may be adapted to simplify kinetic measurements. Furthermore, hydrolytic reactions are less prone to product inhibition than addition reactions and it is an important reaction in biology which makes it a target for drug development. From a mechanistic perspective, general-acid, general-base and nucleophilic catalysis, as well as transition state stabilization, may be considered for implementation in design and the success by which two or more of these principles can be incorporated cooperatively in a catalyst is a good measure of our understanding of the rational design principles. The hydrolysis of mono-p-nitrophenyl fumarate catalyzed by a designed 42-residue helix–loop–helix motif is one of the mechanistically best characterized polypeptide catalyzed systems. Since it exhibits cooperativity in catalysis it will be described here in some detail.
Scheme 5.6
5.2.1
Design of a Folded Polypeptide Catalyst for Ester Hydrolysis
The 42-residue sequence KO-42 was designed to fold into a helix–loop–helix motif and dimerize to form a four-helix bundle [6]. The design principles followed those
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of the previously described four-helix bundle SA-42 [28], and only five residues differed between the sequence of KO-42 and that of SA-42. These five residues were all in g and c positions on the surface of the folded motif and they were modified to introduce catalytic activity. Choosing from the common amino acids, histidine was the primary choice for catalysis of hydrolysis, because the imidazole side chain has a pK a of 6.4 in a random coil peptide and is capable of general-acid, general-base and nucleophilic catalysis at around neutral pH. Imidazole catalysis was elucidated in great detail previously by Bruice and Jencks [29, 30] and its reactions with active esters follow a two-step mechanism. In the first and rate-limiting step an acyl intermediate is formed under the release of the leaving group, and in the second step the acyl group reacts with the most potent nucleophile in solution to form the reaction product. If the hydroxide ion is the most efficient nucleophile the overall reaction is hydrolysis. If alcohols are the most efficient the overall reaction is transesterification, Scheme 5.3. Cooperativity in catalysis requires more than one catalytically active residue, but even more demandingly it requires the simultaneous catalytic activity by more than one residue in the rate-limiting step. The difficulty in predicting with high precision how to introduce two or more residues in positions and conformations where the probability is high for cooperative bond making and bond breaking in the transition state of the reaction suggests that a first generation catalyst should be designed with more than one possible combination of active site residues. KO42 was designed with six His residues in g and c positions on the surface of the helix–loop–helix motif in order for the catalyst to provide several alternative configurations for catalysis, Fig. 5.4, [6]. His-11, His-15, His-19, His-26, His-30 and His34 formed the catalytic surface of the folded polypeptide. Within each helix they represented a fixed i, i þ 4 pattern in which the structural relationship between
Figure 5.4. Schematic representation of the design of KO-42 with measured pK a values indicated next to the His residues. In solution under reaction conditions KO-42 is a dimer.
5.2 Catalysis of Ester Hydrolysis
each residue was well defined. A larger variation in inter-residue distances and orientations is represented by combinations of His residues in different helices. Every conceivable catalytically competent combination of His residues in a helix–loop– helix motif was represented in a single design using this approach. Not only were a large number of geometrical combinations represented but also a large number of pK a combinations. A protonated His will suppress the pK a of a neighboring His residue by electrostatic repulsion of the protonated and positively charged form of the flanking His. All in all, six ionizable residues represents 2 6 ¼ 64 states of protonation in a single molecule and each one will, in principle, have a different microscopic pK a value for each His residue. The combination of six His residues in a single polypeptide therefore represented a large chemical library with inter-residue distances, rotamer populations and pK a values as the variables. If no catalytic activity was found in this catalyst the likelihood of finding one based on the reactivity of His residues would be very small.
Scheme 5.7
The substrate designed and synthesized for initial kinetic investigations of catalysis was mono-p-nitrophenyl fumarate, Scheme 5.7, a rigid, negatively charged ester with an even more negatively charged transition state. This substrate was considered optimal for catalysis by a positively charged catalyst and due to the relatively low pK a of the p-nitrophenol leaving group it was expected to be susceptible to nucleophilic, general-acid or general-base catalysis, all of which could be executed by His residues. The negative charge of the acyl group of the ester should be able to bind to positively charged residues and, at a later stage, the fumarate group could be replaced by hydrophobic residues to probe whether substrate binding by hydrophobic forces could provide more efficient catalysis due to proximity effects. The use of activated esters in catalyst development has been questioned because the reaction mechanisms may not be applicable to less reactive substrates [31]. Nucleophilic catalysis depends critically on the relative magnitudes of the pK a values of the nucleophile and the leaving group and although a nucleophile with a pK a of 6.4 may provide efficient catalysis with p-nitrophenyl esters, it will not with alkyl esters. Nevertheless, the use of active esters in the early stages of catalyst design is necessary because, for very primitive catalysts, the reaction rates would otherwise be intolerably slow. 5.2.2
The HisHB-His Pair
The polypeptide KO-42 catalyzed the hydrolysis of mono-p-nitrophenyl fumarate with a second-order rate constant k2 of 0.1 M1 s1 , a rate enhancement of more
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than three orders of magnitude over that of the 4-methylimidazole catalyzed reaction (k2 of 8:8 105 M1 s1 ) in aqueous solution at pH 4.1 and 290 K [11]. In comparison with the uncatalyzed background reaction the rate enhancement was a factor of 43000 at pH 5.1. The pH profile was recorded and showed that catalysis depended on the unprotonated form of a residue with a pK a of around 5, suggesting histidine catalysis. The 1 H NMR spectrum of KO-42 was assigned and the apparent pK a value of each His residue was determined by titration of the nonexchangeable 2- and 4-protons of the imidazole ring. The apparent pK a values were found to be in the range 5.2 to 7.2, with His-34 exhibiting the lowest value. The kinetic solvent isotope effect, kH2O =kD2O was determined at pH 4.7 and found to be 2.0, a value that showed strong hydrogen bonding in the transition state, suggesting general-acid catalysis. The pH dependence and the kinetic solvent isotope effect taken together showed that there were two residues involved, one of which should be unprotonated and one of which provided strong hydrogen bonding in the transition state but not in the ground state. The unprotonated form of a His residue would be capable of nucleophilic as well as general-base catalysis, but the kinetic solvent isotope effect did not lend support to an interpretation of generalbase catalysis. Based on previous studies suggesting that imidazole catalyzes the hydrolysis of p-nitrophenyl acetate by a nucleophilic mechanism it was concluded that the unprotonated residue acted as a nucleophilic catalyst, Scheme 5.6. The number and the closely similar pK a values of His residues made it difficult to assign the catalytic activity to specific residues. In a series of polypeptides histidines were partially replaced by the residues used in the sequence of SA-42 to form a library of catalysts derived from KO-42 but with less complexity [12, 23]. Essentially, the catalytic site of KO-42 was divided into its components and analyzed. It was assumed that the sequence modifications had only minor effects on structure and that the rate constants of the resulting peptides could be directly compared. The peptide MN, closely related to KO-42 but with His-26, His-30 and His-34, reverted to the SA-42 residues Gln, Gln and Ala, catalyzed the reaction at pH 5.1 and 290 K with an efficiency that was less than 10% of that of the KO-42 catalyzed reaction. The peptide JN, in which His-11, His-15 and His-19 were reverted to Ala, Gln and Lys, exhibited a second-order rate constant that was 20% of that of KO42. The sum of the second-order rate constants of the MN and JN catalyzed reactions was therefore not equal to the second-order rate constant of KO-42, and there appeared to be cooperativity between residues in the two helices of the helix–loop– helix motif. However, the pK a values were affected and increased as a result of the modifications, which may account for at least part of the observed discrepancy. The complexity of the histidine site was further reduced and all combinations of two His residues four positions apart in the sequence were synthesized and analyzed. All were catalytically active with second-order rate constants in the range 0.008–0.055 M1 s1 , values that were higher than that of 4 methylimidazole, 0.00074 M1 s1 by a factor of 10–75. The largest second-order rate constant was found for the peptide JNII, Figure 5.5, in which His-30 and His-34 were the only His residues and, in general, the lower the pK a the larger the rate constant. The sum of the second-order rate constants for the hydrolysis reactions catalyzed by
5.2 Catalysis of Ester Hydrolysis
Figure 5.5. The 42-residue catalyst JNII has two His residues that catalyze the hydrolysis of mono-p-nitrophenyl fumarate by a combination of nucleophilic and general-acid catalysis. The pK a values are indicated and the relative rate
enhancement over that of the 4methylimidazole catalyzed reaction is the largest at a pH below that of both His residues.
peptides with two His residues corresponded well to the measured rate constants for the reactions catalyzed by peptides containing three His residues. Consequently, within a single helix, there was no cooperativity between three histidine groups, but clearly between two. It was concluded that the sites with two His residues were the basic catalytic units in the observed catalysis of ester hydrolysis. The pH dependence revealed that one of them should be unprotonated and the kinetic solvent isotope effect showed that one of them should be protonated. The basic catalytic unit was therefore the HisHþ -His pair [11]. 5.2.3
Reactivity According to the Bro¨nsted Equation
The reactivity of a nucleophile is described by the Bro¨nsted equation according to which log k2 ¼ A þ bpK a
ð5:1Þ
The Bro¨nsted coefficient b for imidazole catalysis of p-nitrophenyl acetate hydrolysis is 0.8 [29], and the second-order rate constants of all His residues can therefore be related to that of 4-methylimidazole to determine whether there are effects on reactivity beyond those of differential nucleophilicity and levels of protonation. The reactivity of His residues in the pH independent region may be estimated from rate constants, pH and pK a values. The second-order rate constant of the 4methylimidazole catalyzed hydrolysis of mono-p-nitrophenyl fumarate at pH 5.85 and 290 K is 1:02 102 M1 s1 . From this value and the pK a of 7.9, the secondorder rate constant of the unprotonated form of 4-methylimidazole was readily calculated to be 1.15 M1 s1 . From this value the second-order rate constants of each
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5 Acid–Base Catalysis in Designed Peptides
unprotonated His residue of KO-42 could be estimated using the Bro¨nsted equation, and that of His-34 (pK a 5.2) would be 0.008 M1 s1 , whereas that of His-26 (pK a 7.2) would be 0.32. The sum of the rate constants of all His residues in KO-42 is 0.75, very close to the second-order rate constant of the KO-42 catalyzed reaction at high pH, which is 0.74 M1 s1 . At a pH where all His residues are unprotonated KO-42 behaves catalytically merely as the sum of a number of independent imidazole groups. At a pH below the pK a of each histidine the situation is more complex. Here the more acidic His is the most efficient catalyst because log k2 is proportional only to 0:8 pK a , whereas the fraction of unprotonated and catalytically active residues is directly proportional to pK a . The more acidic catalyst is more efficient than one with a higher pK a by a factor of 10 0:2DpKa because the decrease in nucleophilicity of a residue with a lower pK a is outweighed by the increased availability of the catalytically active form. If nucleophilicity and the degree of protonation were the only factors involved, His-34 would be a better catalyst than 4-methylimidazole at pH 4.1 by a factor of 10 0:22:7 , or a factor of 3.5. The sum of second-order rate constants estimated for each His residue in KO-42 under these conditions would be 1 103 M1 s1 , a factor of 100 less than the experimentally determined value of 0.1 M1 s1 . The pH dependence of imidazole catalysis reveals that generalacid catalysed hydrolysis of ester hydrolysis by individual imidazolium ions at pH 4.1 is a very inefficient reaction and can be disregarded. The catalytic efficiency of KO-42 at low pH is therefore larger than the sum of that of each individual residue by a factor of 100, a factor that is most likely due to cooperativity between nucleophilic catalysis and general-acid catalysis. 5.2.4
Cooperative Nucleophilic and General-acid Catalysis in Ester Hydrolysis
The nature of the cooperativity was further characterized based on results from kinetic measurements. The two HisHþ -His pairs in helix II catalyzed the hydrolysis of mono-p-nitrophenyl fumarate at pH 5.1 and 290 K with second-order rate constants of 0.01 M1 s1 (JNI, His-26, His-30) and 0.055 M1 s1 (JNII, His-30, His34), respectively, and a rate constant ratio JNII/JNI of 5.5. The pK a values of both His residues in JNII are the same, so for the analysis it does not matter which residue is the nucleophile and which one is the acid. In JNI, however, the pK a values are 6.9 for His-26 and 5.6 for His-30. The rate constant ratio of 5.5 should therefore arise due to the difference in nucleophilicity or due to the difference in acidity, or if both residues in the pair can be both nucleophile and acid, from a mixture of the two. If His-30 functions as a general acid in JNI, then the rate constant ratio should arise from the difference in nucleophilicity between two nucleophiles with the pK a values 5.6 and 6.9. We can, however, calculate the reactivity difference as in Section 5.2.3 to find that 10 0:21:3 ¼ 1:8, one third of the observed ratio of 5.5. If, on the other hand, the rate constant ratio is due to a difference in general-acid catalysis by two residues with pK a values of 5.6 and 6.9, then the the Bro¨nsted equation for general-acid catalysis can be applied
5.2 Catalysis of Ester Hydrolysis
log k2 ¼ A apK a
ð5:2Þ
A value of the Bro¨nsted coefficient a for general-acid catalysis of 0.56 gives rise to a rate constant ratio of 5.5 for two acids with a difference in pK a of 1.3. If it is taken into consideration that an acid with a pK a of 5.6 is only 75% protonated at pH 5.1 then the second-order rate constant of the JNII catalyzed reaction is only 75% of its true value, and k2 for the HisHþ -His pair should be corrected to 0.073 M1 s1 . Even so a Bro¨nsted coefficient of 0.66 would account for the rate constant ratio. Both of these values fall within the range of Bro¨nsted coefficients typically observed for general-acid catalysis. An acid with a pK a of 6.9 is largely protonated at pH 5.1 and no corrections are required. From these considerations it is likely that the stereochemistry of the helix favors nucleophilic catalysis by the His residue with the highest number in the sequence and general-acid catalysis by the residue with the lowest number. 5.2.5
Why General-acid Catalysis?
It has been claimed that highly activated esters do not require catalysis for their hydrolysis and that p-nitrophenyl esters in general are degraded so rapidly that it is very difficult to find a catalyst efficient enough to make a difference [32]. This statement, however, is contradictory to the statement made by others that the hydrolysis of p-nitrophenyl esters is so easy to catalyze that catalysts for active esters are irrelevant for biologically significant esters [31]. The KO-42 catalyzed hydrolysis of mono-p-nitrophenyl fumarate, described in detail in Sections 5.2.2–5.2.4, was as efficient as that provided by six imidazoles with comparable pK a values, at a pH that in a broad sense is higher than or equal to the pK a of the corresponding acid of the p-nitrophenolate leaving group. At a pH lower than the pK a of p-nitrophenol the rate enhancement was two orders of magnitude larger than that of six imidazoles with comparable pK a values, and suggested by the experimental evidence to be due to general-acid catalysis. In comparing the high and low pH reactions it may be noted that they were measured under conditions where the released leaving group exists predominantly in its unprotonated and protonated forms, respectively. At low pH the leaving group therefore requires a proton, normally provided by the solvent water. A Hammet r value of 1.4 was determined by hydrolyzing a set of phenyl esters covering pK a values from 3.96 to 8.28 [33], and it was found that when comparing the r value for hydrolysis with that of ionization, which is 2.2, approximately half a negative charge was found to reside on the phenolate oxygen in the transition state of the reaction. A plausible explanation is therefore that general-acid catalysis may operate when the leaving group, after expulsion, exists predominantly in its protonated form. A complication with this interpretation is that at high pH the His residues of the catalyst are unprotonated and therefore incapable of proton donation. In order to determine whether the lack of general-acid catalysis at high pH was due to a lack of proton donors or whether it was due to the fact that the leaving
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5 Acid–Base Catalysis in Designed Peptides
group was not in need of a proton an even more activated ester was synthesized, 2,4-dinitrophenyl acetate, with a pK a of 3.96 [33]. The second-order rate constant of 7.2 M1 s1 for the JNII catalyzed reaction was determined at pH 5.1 and compared to that of 4-methylimidazole, 0.0081 M1 s1 . The rate constant ratio was almost three orders of magnitude. Estimating the catalytic efficiency of a hypothetical imidazole derivative with a pK a of 5.6, in the absence of differential protonation effects, as in Section 5.2.3, showed JNII to be a more efficient catalyst by a factor of 68, apparently due to very efficient nucleophilic catalysis. At pH 3.1 which is a value that is lower than that of the pK a of 2,4-dinitrophenol, the rate enhancement was 1800, the intrinsic catalytic efficiency was a factor of 140 and the kinetic solvent isotope effect 2.1. No kinetic solvent isotope effect was determined for JNII at pH 5.1, but a helix–loop–helix motif JNIIOR, that contained two His residues in the same positions as in JNII and differed by only two residues, gave rise to a kinetic solvent effect at pH 3.1 but not at pH 5.1. In these scaffolds at pH 5.1 protonated His residues were present to provide general-acid catalysis but none occurred. It was concluded that the leaving group state of ionization determines the need for general-acid catalysis in ester hydrolysis. Consequently, general-acid catalysis is efficient for the hydrolysis of active as well as inactive esters.
5.3
Limits of Activity in Surface Catalysis
While folded polypeptide catalysts are excellent vehicles for catalyst design and for mechanistic investigations of catalysis, they are limited with regards to the catalytic efficiency that can be expected. Experimentally, rate enhancements of the order of 10 3 –10 4 have been reported, but rate enhancements of the order of magnitude of even the slowest of enzymes have not been observed, with enzymatic efficiencies considered to be rate enhancements of not less than 10 6 over background [34]. The reasons for this are only understood at the hypothetical level since it is not easy to determine conclusively why a catalyst is not as fast as expected. Some aspects of catalysis may, however, be tested in detail in a folded polypeptide scaffold. The HisHþ -His pair has, for example, been systematically varied with regards to nucleophilicity and acidity, as described in Sections 5.2.3–5.2.5, to probe the intrinsic reactivity of the catalytic machinery. Tuning pK a values to optimal catalytic efficiencies at a given pH is an important aspect of enzyme catalysis. The use of active sites and pockets is also characteristic of enzymes, perhaps due to the reduced degrees of freedom and optimized positions of amino acid side chains involved in the making and breaking of bonds and to the strength of electrostatic interactions in a low dielectric medium. In a helix–loop–helix motif the relative positions of the HisHþ and the His can be varied but residues on the surface of folded polypeptides and proteins have many degrees of freedom and cannot be locked in fixed positions. Charge–charge interactions are weak but measurable. These aspects
5.3 Limits of Activity in Surface Catalysis
of catalysis were tested within the context of HisHþ -His-based catalysis of ester hydrolysis. 5.3.1
Optimal Organization of His Residues for Catalysis of Ester Hydrolysis
In the transition state of HisHþ -His-based catalysis of ester hydrolysis there is a partial bond between one of the nitrogen atoms of the imidazole ring and the carbonyl carbon of the ester and a hydrogen bond from the protonated imidazolium ring to one or both of the oxygen atoms of the carbonyl group of the substrate. The preferred conformation of each histidine side chain is determined by principles that are well understood and controlled by steric factors with anti, staggered conformations being energetically the most favorable, although gauche conformations are populated as well. In a folded helix the bonds between the a and b the carbons of amino acid side chains is not orthogonal to the helix axis but points slightly towards the N-terminal. Depending on the relative positions of the HisHþ and the His groups in the polypeptide scaffold bond formation between scaffold residues and substrate would be expected to be more or less energetically favorable, and rate enhancements correspondingly different. Several polypeptide sequences were designed and their activity towards model substrates determined [35]. Within each helix of the helix–loop–helix motif several combinations in which the two residues were four residues, or one helical turn, apart. In addition, a number of catalysts were designed in which the two His residues were in separate helices. Against this background of geometrical diversity it was expected that the kinetic results would provide some guidance as to what would be an optimal catalyst structure. No such guidance was found and all the catalysts studied provided rate constants that were in agreement with a model in which pK a values, and thus nucleophilicity and general-acid catalysis, were the dominant factors. It is likely that covalent bond formation between nucleophile and carbonyl group was near optimal and that proton donation from the imidazolium group was tolerant to a range of hydrogen bond distances and angles. Although residue side chains in polypeptides have preferred conformations they are free to rotate in solvent exposed sites since there are no contraints posed by neighboring groups. If there is only one catalytically active conformation then there is a cost in entropy associated with reaching the transition state of the reaction due to a reduction in the degrees of freedom. The side chain of a His residue has two rotatable carbon–carbon bonds and in an aliphatic substituent the entropy loss due to inhibition of rotation has been measured and estimated to be 0.9 kcal mol1 per bond [36]. Based on this estimate it is possible that as much as 3.6 kcal mol1 of the free energy of activation is due to the mobility of the His side chains in a surface exposed catalytic site, corresponding to almost three orders of magnitude in rate decrease, in comparison with that of a preorganized site. Although a further rate enhancement of three orders of magnitude in addition to the three due to cooperative nucleophilic general-acid catalysis would
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5 Acid–Base Catalysis in Designed Peptides
make an impressive catalyst, it does not bring it within range of native enzymes. Dynamics in the scaffold structure could contribute even more to the free entropy of activation and the relative positions of the catalytically active residues may not be optimal. 5.3.2
Substrate and Transition State Binding
Substrate binding is the hallmark of native enzymes and makes the chemical transformations in effect intramolecular. The hydrolysis of mono-p-nitrophenyl fumarate was investigated with regards to substrate binding and found to follow saturation kinetics with a kcat of 0.00017 s1 and a KM of 1 mM [12]. The interactions between substrate and catalyst were further probed by NMR spectroscopy and upon addition of the substrate under reaction conditions to a solution containing the catalyst the resonances of the hydrophobic residues of the folded polypeptide were shifted. Due to the spectral differences between substrate and product it could be established that the substrate and not the products interacted with the polypeptide. The reasons for the observed binding were probably that the hydrophobic p-nitrophenyl residue interacted with the hydrophobic core of the four-helix bundle while the fumarate group bound to the positively charged surface residues of the scaffold. The binding of the substrate by the catalyst does not prove that the binding is productive but only that a complex is formed at concentrations that are compatible with the observed dissociation constant. The binding site was not designed and the interactions of the substrate with hydrophobic core and positively charged residues may not have been specific. Further attempts to initiate specific binding of the substrate included the incorporation of arginine and lysine substituents in the neighbouring helix to interact with the negatively charged fumarate group and with the developing negative charge in the tetrahedral transition state, Figure 5.6, [12]. The number of methylene groups in the side chains of the flanking residues were varied in order to investigate whether the interactions could be optimized, again for the purpose of probing specificity. Rate enhancements were obtained upon introduction of flanking, positively charged residues close to the HisHþ -His pair to show that increased transition state binding could be introduced by rational design. The effects were significant but not larger than factors of 2–3, corresponding to A 0.5 kcal mol1 of binding energy, in agreement with what has been measured for a salt bridge in a helix [37]. Charge–charge interactions are inversely dependent on the dielectric of the solvent and would be stronger by a factor of ten or more in the dielectric of a hydrophobic pocket. Differential transition state binding by 5 kcal mol1 would result in an increase in rate constant by almost four orders of magnitude at room temperature. The transfer of the reactive site designed for ester hydrolysis into a hydrophobic environment would therefore be expected to enhance the catalytic efficiency considerably. On the surface of a folded polypeptide, practically in aqueous solution, the weakness of forces between residues is a major reason for the poor efficiency of the catalyst. Substrate and transition state binding is weak due to the high dielectric constant of the solvent water
5.3 Limits of Activity in Surface Catalysis
Figure 5.6. The incorporation of two His residues in one helix as well as one Arg and one Lys residue in the neighboring helix led to a catalyst capable of cooperative catalysis and transition state stabilization. The catalyst has enzyme-like properties but lacks catalytic efficiency in comparison with native enzymes.
and due to the complex solvation equilibria. Nevertheless, the active site can be expected to function better in the pocket of a protein and thus serves as a good model system for new biocatalysts. 5.3.3
His Catalysis in Re-engineered Proteins
On a naturally occurring scaffold with better defined structure it may not be straightforward to graft new catalytic sites because the effect on structure is difficult to predict. The introduction of a general acid or a general base is, however, a minor invasion that may be tolerated by the protein, and can be achieved by a single residue. From a mechanistic point of view such a modification may open new reaction pathways and allow us to test in a protein scaffold the structural requirements for general-acid and general-base catalysis. Human glutathione transferase is a detoxification enzyme that rids our bodies of hydrophobic compounds by catalyzing the conjugation of the non-endegenous molecule to the tripeptide glutathione, and secreting it. The active site is covered by a helix and two His mutations four residues apart in the helix, A216H and F220H, were selected to introduce the HisHþ -His pair [38]. S-benzoylglutathione was selected as substrate since its position in the active site was well defined and determined by crystallography. Although at a predictive level both His residues were within bond forming distance from the thiol ester, the reaction mechanism followed a different pathway and in the first step of the reaction the acyl group was transferred to a tyrosine residue to form an ester, and in the second step of the reaction His 216 catalyzed the hydrolysis of the tyrosyl ester, most likely by general-base catalysis. His-220 was too far away from the tyrosine side chain to be able to contribute by general-acid catalysis.
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5 Acid–Base Catalysis in Designed Peptides
The fact that His-216 was observed in the crystal structure of the mutant showed that its position was well defined with a distance that did not accommodate covalent bond formation to the carbonyl carbon of the ester. A water molecule would, however, nicely bridge the distance of 7 A˚ between the nitrogen and the carbon. The pH dependence showed that catalysis was due to a residue in its unprotonated form and by elimination it was concluded that general-base catalysis was the key to hydrolysis. The hydrolysis of S-benzoylglutathione did not take place in the wildtype enzyme where general-base catalysis did not operate, and the introduction of general-base catalysis opened a new reaction pathway. The rate enhancement in comparison with the wildtype enzyme cannot be calculated since the reaction does not take place in the absence of a catalytically active residue, it can only be concluded that it is very efficient. It may be that the distance of 7 A˚ between the imidazole nitrogen and carbonyl carbon is not optimal, but its well-defined orientation towards the ester group may be the reason for the catalytic efficiency.
5.4
Computational Catalyst Design
Early strategies in de novo protein design were influenced by respect for the difficulties in predicting structure from sequence and the idea that well behaved proteins could be built from combinations of stable secondary structure motifs. Much work was directed towards understanding the factors that controlled helix formation and helix stability, and subsequently also b-sheet formation and stability, although uncontrolled aggregation remained a long-standing problem in b-sheet design. Shape and charge complementarity were engineered into helices to control docking and drive folding, and an understanding of how to design well-behaved compact proteins emerged. The work by DeGrado pioneered the field of de novo protein design [3]. The design of pockets and cavities needed for sophisticated functions such as enzyme-like catalysis was, however, beyond this approach, although metal ion complexation was used in an effort to enable partial separation of secondary structure elements and form at least first generation clefts and hollows [39]. In this process the power of computation was appreciated but calculations of free energies of the possible conformers of a polypeptide in the search for global minima proved to be too demanding in terms of computer capacity. The redesign of proteins known to fold has been a considerably more successful approach, by reducing the computational problem using a simple but powerful assumption. Proteins known to fold are expected to fold in the same way, even if several amino acid side chains are replaced by others and by compounds that are not linked to the polypeptide scaffold. In simple terms the backbone of a selected protein is locked in its native conformation and a ‘‘hole’’ carved out by removing amino acid side chains in a part of the protein structure. After introducing a small organic molecule or transition state model into the hole by computation, the rest of the cavity is filled with amino acid side chains to form a compact structure. If a small molecule is introduced the result is a receptor for this molecule and if a tran-
5.4 Computational Catalyst Design
sition state analog is introduced the result is a catalyst capable of transition state stabilization. More sophisticated versions allow also the introduction of residues that enable acid–base catalysis etc. Computational methods following this strategy show great promise in the engineering of new enzymes. Some examples are described below. 5.4.1
Ester Hydrolysis
A site for His-dependent nucleophilic catalysis of p-nitrophenyl acetate hydrolysis was introduced into the thioredoxin protein scaffold by computational design. The acyl intermediate described in Section 5.2.1 formed at the side chain of a His residue was used as the starting point for design and after side chain rotamer library generation and analysis a His residue with an acylated side chain was introduced in the most favorable side chain conformation [27]. The surrounding protein residues were selected to stabilize the acyl intermediate and two resulting thioredoxin mutants were expressed and analyzed with regards to catalytic power. Wildtype thioredoxin is capable of His-mediated ester hydrolysis due to the presence of a surface exposed residue, but with a low efficiency, whereas catalysis by the mutant PZD2 followed saturation kinetics in aqueous solution at pH 6.95 with a kcat of 4:6 104 s1 and a KM of 170 mM. A comparison with the background reaction showed that kcat =k uncat for PZD2 was 180, and kcat =KM was 25 times larger than the second-order rate constant of the 4-methylimidazole catalyzed reaction. An analysis of the catalytic efficiency as conducted in Section 5.2.3 is difficult since the pK a of the catalytically active His residue of PZD2 was not reported. Under the assumption that it is 6.4, as in a random coil peptide, 4-methylimidazole, with a pK a of 7.9 is an intrinsically better catalyst than the His of PZD2 by a factor of two because the concentration of unprotonated and active His is larger than that of 4-methylimidazole by a factor of eight but the histidine is a weaker nucleophile by a factor of sixteen. The rate constant ratio ðkcat =KM Þ=k2 was reported as 25 but the ratio of catalytic efficiencies is better described as 50. The comparison with KO-42 at pH 6.95 is not interesting because at pH 6.95 KO-42 behaves as six unprotonated His residues and there is little general-acid catalysis in operation. At pH 4.1 the catalytic efficiency of the polypeptide catalyst, in comparison with that of 4methylimidazole, is slightly better than that of PZD2 at pH 6.95, due to the cooperativity between nucleophilic and general-acid catalysis. The catalytic activity of PZD2 was due to a combination of proximity effects and covalent catalysis by His but no attempt to incorporate a second catalytic mechanism was described. When this can be achieved considerably larger rate enhancements would be expected. 5.4.2
Triose Phosphate Isomerase Activity by Design
Although the ribose binding protein is not a peptide, the topic of this chapter, but a mature folded protein, it is discussed here because the simultaneous introduction
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5 Acid–Base Catalysis in Designed Peptides
of residues capable of acid–base catalysis in addition to substrate, intermediate and transition state binding represents a major advance in enzyme design. The key step in the dihydroxyacetone phosphate to glyceraldehyde 3-phosphate transformation is a 1,2 proton transfer between two carbon atoms. Efficient proton abstraction from a carbon acid with a pK a of A 18 and its subsequent delivery to a neighboring carbon atom requires a general base in a precisely organized position and would be expected to be difficult, for example, on the surface of a helical bundle. A Glu, a His and a Lys residue were introduced into the protein scaffold to abstract a proton, to provide a proton to the enediolate intermediate and to stabilize the negative charges in the active site. The precise organization of catalytically active residues demonstrated by Dwyer et al. [15] suggests that computational design may be used to engineer several new enzymes, primarily those that have simple reaction mechanisms. The rate enhancements were reported to be within two and three orders of magnitude, respectively, of the forward and reverse reactions of the native enzyme. The pH profiles for the forward and reverse reactions were bell-shaped with maxima between 7 and 8 and similar to those of the wild-type TIM. Singledouble- and triple-alanine mutations of the three putatively catalytic residues resulted in loss of enzymatic activity. While the individual role of each one of these residues has not been unequivocally established the bulk of the evidence is compatible with the design of the catalyst where Glu is the base and His and Lys are involved in hydrogen bonding and electrostatic stabilization of the developing charges in the transition state.
5.5
Enzyme Design
The description in this chapter of several designed catalysts with the capacity to enhance reaction rates of selected reactions by several orders of magnitude is intended to impress upon the reader that the understanding of how to implement catalytic sites into polypeptides and proteins is slowly emerging. Computational methods in particular have reached a level where the precise positioning of amino acid residues in protein and polypeptide scaffolds has become possible. In combination with an increased understanding of reaction mechanistic principles it may well prove to be the strategy for the future. The introduction of residues capable of general acid, general base and covalent catalysis has been demonstrated in several designs, as has the introduction of residues capable of transition state stabilisation and substrate binding. The rational design of new enzymes for practical purposes is slowly becoming reality.
References 1 L. Baltzer, H. Nilsson, J. Nilsson,
Chem. Rev. 101 (2001) 3153–3163.
2 L. Baltzer, J. Nilsson, Curr. Opin.
Biotechnol. 12 (2001) 355–360.
References 3 W. F. DeGrado, C. M. Summa,
4
5
6
7 8 9
10
11
12
13
14 15
16 17 18 19 20 21
22
V. Pavone, F. Nastri, A. Lombardi, Annu. Rev. Biochem. 68 (1999) 779–819. K. Johnsson, R. K. Allemann, H. Widmer, S. A. Benner, Nature. 365 (1993) 530–535. K. Severin, D. H. Lee, A. J. Kennan, R. M. Ghadiri, Nature. 389 (1997) 706–709. K. S. Broo, L. Brive, P. Ahlberg, L. Baltzer, J. Am. Chem. Soc. 119 (1997) 11362–11372. Y. N. Wei, M. H. Hecht, Protein Eng. Des. Sel. 17 (2004) 67–75. M. Allert, L. Baltzer, ChemBioChem. 4 (2003) 306–318. J. Kaplan, W. F. DeGrado, Proc. Natl. Acad. Sci. USA 101 (2004) 11566– 11570. F. Hollfelder, A. J. Kirby, D. S. Tawfik, J. Org. Chem. 66 (2001) 5866– 5874. K. S. Broo, H. Nilsson, J. Nilsson, A. Flodberg, L. Baltzer, J. Am. Chem. Soc. 120 (1998) 4063–4068. K. S. Broo, H. Nilsson, J. Nilsson, L. Baltzer, J. Am. Chem. Soc. 120 (1998) 10287–10295. K. Broo, L. Brive, A.-C. Lundh, P. Ahlberg, L. Baltzer, J. Am. Chem. Soc. 118 (1996) 8172–8173. M. Allert, L. Baltzer, Chem. Eur. J. 8 (2002) 2549–2560. M. A. Dwyer, L. L. Looger, H. W. Hellinga, Science, 304 (2004) 1967– 1972. R. B. Hill, W. F. DeGrado, J. Am. Chem. Soc. 120 (1998) 1138–1145. S. Olofsson, L. Baltzer, Folding Des. 1 (1996) 347–356. S. P. Ho, W. F. DeGrado, J. Am. Chem. Soc. 109 (1987) 6751–6758. K. S. Broo, L. Brive, R. S. Sott, L. Baltzer, Folding Des. 3 (1998) 303–312. C. Tanford, Adv. Protein Chem. 17 (1962) 69–165. A. Fersht, Structure and Mechanism in Protein Science: A Guide to Enzyme Catalysis and Protein Folding, W. H. Freeman, New York, 1999, Ch. 11. L. K. Andersson, G. T. Dolphin, L. Baltzer, ChemBioChem 3 (2002) 741– 751.
23 L. Baltzer, K. S. Broo, H. Nilsson,
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31 32
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J. Nilsson, Bioorg. Med. Chem. 7 (1999) 83–91. G. T. Dolphin, L. Brive, G. Johansson, L. Baltzer, J. Am. Chem. Soc. 118 (1996) 11297–11298. C. J. Weston, C. H. Cureton, M. J. Calvert, O. S. Smart, R. K. Allemann, ChemBioChem 5 (2004) 1075–1080. S. Yao, I. Ghosh, R. Zutshi, J. Chmielewski, Angew. Chem. Int. Ed. Engl. 37 (1998) 478–479. N. D. Bolon, S. L. Mayo, Proc. Natl. Acad. Sci. USA 98 (2001) 14274– 14279. S. Olofsson, G. Johansson, L. Baltzer, J. Chem. Soc., Perkin Trans 2. (1995) 2047–2056. T. C. Bruice, R. Lapinski, J. Am. Chem. Soc. 80 (1958) 2265–2272. D. G. Oakenfull, K. Salvesen, W. P. Jencks, J. Am. Chem. Soc. 93 (1971) 188–194. M. J. Corey, E. Corey, Proc. Natl. Acad. Sci. USA 93 (1996) 11428–11434. A. Fersht, Structure and Mechanism in Protein Science: A Guide to Enzyme Catalysis and Protein Folding, W. H. Freeman, New York, 1999, Ch. 2. J. Nilsson, L. Baltzer, Chem. Eur. J. 6 (2000) 2214–2220. A. Fersht, Structure and Mechanism in Protein Science: A Guide to Enzyme Catalysis and Protein Folding, W. H. Freeman, New York, 1999, Ch. 1. J. Nilsson, K. S. Broo, R. S. Sott, L. Baltzer, Can. J. Chem. 77 (1999) 990– 996. M. I. Page, W. P. Jencks, Proc. Natl. Acad. Sci. USA 68 (1971) 1678–83. Z. S. Shi, C. A. Olson, A. J. Bell, N. R. Kallenbach, Biopolymers 60 (2001) 366–380. S. Hederos, K. S. Broo, E. Jakobsson, G. J. Kleywegt, B. Mannervik, L. Baltzer, Proc. Natl. Acad. Sci. USA 101 (2004) 13161–13167. G. R. Dieckmann, D. K. McRorie, D. L. Tierney, L. M. Utschig, C. P. Singer, T. V. O’Halloran, J. E. Penner-Hahn, W. F. DeGrado, V. L. Pecoraro, J. Am. Chem. Soc. 119 (1997) 6195–6196.
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Part II
General Aspects of Biological Hydrogen Transfer Proton abstraction from carbon occupies a very substantial niche among enzyme catalyzed reactions, occurring for example in glucose oxidation and in the citric acid cycle. Initially, studies of the proteins within these pathways were focused on individual mechanistic features, whereas in recent years the focus has moved toward the establishment of general principles. Gerlt lays out the problems of rate acceleration by enzymes catalyzing proton loss from carbon: how to remove a proton from a site with an inherent pKa substantially higher than for any catalytic functional group within the active site? Marcus theory is introduced as a useful tool, in particular through its separation of the reaction barrier into driving force, DG o , and reorganization energy, l. Gerlt argues that even in the event of no contribution of l to the reaction barrier, the inherently uphill process of proton loss from carbon requires the stabilization of intermediates to obtain the observed enzymatic rate accelerations. The role of the enzyme in decreasing DG o could be approached by measuring the concentration of enzyme bound carbanion intermediates, but these species can be very difficult to detect and quantify. Additionally, few experimental data are available to compare the value of l in enzymatic deprotonations to their solution counterparts – a clear challenge for the future. Readers will want to compare Gerlt’s thesis of electrostatic/H-bonding stabilization of carbanion intermediates as a dominant factor in enzymes, with that of Herschlag and co-workers (Kraut DA, Sigala PA, Pybus B, Liu CW, Ringe D, Petsko GA, Herschlag D., PLoS Biol. 2006 Apr;4(4):e99. Epub 2006 Mar 28.), according to which the rate acceleration from electrostatic stabilization is at most 300-fold in the paradigmatic proton abstracting enzyme, ketosteroid isomerase. The chapter by Spies and Toney is focused on the enzymes that catalyze racemization and epimerization, largely by proton abstraction. Their discussion of alanine racemase is an elegant demonstration of experimental approaches that can demonstrate the formation of a carbanion intermediate when none can be observed directly. They show how kinetic isotope effects distinguish a step-wise from a concerted reaction, thereby implicating the elusive carbanionic intermediate. They suggest that maintaining a very low concentration for a carbanion may be beneficial, to minimize or prevent undesirable chemical side reactions. The chapter by Warshel and coworkers presents an excellent account of the use of the empirical valence bond approach (EVB) to calculate rates and their attendant properties for proton abstraction reactions. They emphaHydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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size the importance of fluctuations of the environment and the quantum nature of the hydrogen transfer, while pointing out the complexities that can arise when there is substantial mixing between reactant and product states as occurs in the transfer of the charged proton nucleus. In contrast to a focus on the role of DG o , Warshel has concluded (for many years) that a reduction in l is the dominant mechanism whereby enzymes catalyze proton transfer. In the concluding remarks, he and his coauthors address two issues that reappear in later chapters: the role of dynamical effects in enzyme reactions, and the extent to which tunneling effects may be different between enzymes and their solution counterparts. The reader should be aware that Warshel’s definition of dynamics is confined to the rate of barrier re-crossing, quite different from the use by some of the term dynamics to refer to protein motions and their possible coupling to the C–H activation step.
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6
Enzymatic Catalysis of Proton Transfer at Carbon Atoms John A. Gerlt 6.1
Introduction
Reactions in which protons are abstracted from carbon are ubiquitous in biochemistry. The proton that is abstracted is rendered ‘‘acidic’’ by its location either adjacent (a-proton) or vinylogously conjugated to a carbonyl or carboxylate group. With the ability to stabilize the resulting negative charge on the adjacent or conjugated carbonyl/carboxyl oxygen, the values of the pK a s of carbon acids range from 18 to 20 for aldehydes, ketones, and thioesters, 22 to 25 for carboxylic acids (presumably never encountered in enzymatic reactions at neutral pH), and 29 to 32 for carboxylate anions [1, 2]. Although depressed relative to the pK a of an alkane hydrogen, these values significantly exceed those of the pK a s of the conjugate acids of the active site bases to which the protons are transferred (<7), thereby explaining the intellectual interest in understanding the mechanisms of these reactions and the strategies that enzymes use to accelerate their rates relative to their nonenzymatic counterparts.
The glycolytic pathway includes three such reactions: glucose 6-phosphate isomerase (1,2-proton transfer), triose phosphate isomerase (1,2-proton transfer), and enolase (b-elimination/dehydration). The tricarboxylic acid cycle includes four: citrate synthase (Claisen condensation), aconitase (b-elimination/dehydration followed by b-addition/hydration), succinate dehydrogenase (hydride transfer initiated by aproton abstraction), and fumarase (b-elimination/dehydration). Many more reactions are found in diverse catabolic and anabolic pathways. Some enzyme-catalyzed proton abstraction reactions are facilitated by organic cofactors, e.g., pyridoxal phosphate-dependent enzymes such as amino acid racemases and transaminases and flavin cofactor-dependent enzymes such as acyl-C-A dehydrogenases; others, Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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6 Enzymatic Catalysis of Proton Transfer at Carbon Atoms
those that are the focus of this chapter, are either divalent metal-ion assisted or require no cofactor. Yet, despite the wide-spread occurrence of these reactions, the enzymological community has only recently recognized the structural and mechanistic strategies that enzymes employ to allow these reactions to occur at biologically acceptable rates. This chapter summarizes (i) the intellectual problem associated with understanding the rates of these reactions, i.e., the required reduction in the kinetic barrier for proton transfer from carbon to an active site general base so that kcat will not be limited by the rate of this overall reaction; (ii) the active site structural features that allow the necessary reduction in kinetic barrier; and (iii) specific enzymatic examples of how these strategies are employed.
6.2
The Kinetic Problems Associated with Proton Abstraction from Carbon
The high values of the pK a s of carbon acid substrates and the associated instability of enolate anion intermediates in nonenzymatic reactions first led to the expectation that these intermediates could not be rendered kinetically competent in enzymatic reactions [3]. As a result, the expectation was that these reactions must be concerted, thereby avoiding the problem of how an active site might provide sufficient, significant stabilization of the intermediates. However, the weight of the experimental evidence now is that enzymes that abstract protons from carbon acids are able to sufficiently stabilize enolate anion intermediates so that they can be kinetically competent. A convincing demonstration of a step-wise reaction involving a stabilized enediolate anion intermediate was provided by studies of mandelate racemase (MR). MR catalyzes a 1,1-proton transfer reaction in which the enantiomers of mandelate are equilibrated by a two-base mechanism [4]: Lys 166 is the (S)-specific base that mediates proton transfers to/from (S)-mandelate [5]; His 297, hydrogen bonded to Asp 270 in a His-Asp dyad, is the (R)-specific base [6]. The Asn mutant of His 297 (H297N) catalyzes exchange of the a-proton of (S)-mandelate with D2 O solvent, in the absence of racemization, at nearly the same rate the wild-type enzyme catalyzes racemization [6]. The only reasonable explanation is that Lys 166 retains its ability to abstract the a-proton of (S)-mandelate to generate a stabilized intermediate; following rotation of the Ce aNe bond, a solvent-derived deuteron can be delivered to the intermediate, resulting in exchange without racemization. In the reaction catalyzed by the wild-type enzyme, the enediolate intermediate would be competitively protonated on either face by Lys 166 and His 297, with the latter resulting in both incorporation of solvent hydrogen and racemization. Given the nearly equivalent rates of exchange catalyzed by H297N and racemization catalyzed by the wild-type enzyme, the inescapable conclusion is that an enolate anion intermediate is present on the reaction coordinate for the reactions catalyzed by both the mutant and wild-type enzymes. Now, enolate anions in which negative charge is localized on and, therefore, stabilized by the carbonyl/carboxyl oxygen are as-
6.2 The Kinetic Problems Associated with Proton Abstraction from Carbon Table 6.1. Examples of the rate accelerations for enzymecatalyzed proton abstraction from carbon acids.
Enzyme
Substrate
pK a
k non (sC1 )
k cat (sC1 )
Rate acceleration
triose phosphate isomerase
glyceraldehyde 3phosphate
18[a]
8 104 [b]
8300[c]
1:1 10 7
dihydroxyacetone phosphate
20[a]
6 107 [b]
600[c]
1 10 9
5-androstene-3,17dione
12.7[d]
1:7 107 [e]
3:8 10 4 [ f ]
2:2 10 11
4-androstene-3,17dione
16.1[d]
2:5 1012 [e]
– [g]
enoyl-CoA hydratase
3-hydroxybutyrylCoA
21[a]
3 107 [h]
600[i]
2 10 9
mandelate racemase
mandelate
29[j]
3 1013 [k]
650[l]
2:2 10 15
enolase
2-phosphoglycerate
32[m]
1:1 1014 [l]
80[n]
7:3 10 15
ketosteroid isomerase
a Ref.
[2]. b Ref. [78]. c Ref. [8]. d Ref. [79]. e Ref. [53]. f Ref. [9]. ¼ 2400, so this value is not available; Ref. [53]. h Ref. [65]. i Ref. eq [80]. j Ref. [1]. k Ref. [81]. l Ref. [10]. m Ref. [82]; assuming that the value of the pK a of 2-phosphoglycerate is the same as that of malate. n Ref. [83]. gK
sumed to be intermediates in all reactions involving abstraction of a proton from a carbon acid. Of course, this requires that those that study these reactions be able to provide a structural explanation for how the active sites stabilize the enolate anion intermediates so that they can be kinetically competent. As summarized in Table 6.1, the rate constants for nonenzymatic (k non ) and enzymatic (kcat ) proton abstraction have been measured directly for a number of carbon acids substrates, thereby allowing the rate accelerations to be quantitated. Despite the considerable range for the values of the pK a s and, therefore, of k non , the values of the kcat s fall in a narrow range. As a result, the rate accelerations vary over a large range and, in some cases, are very significant. As first espoused by Knowles and Albery, the limiting selective pressure on enzymatic function is the diffusion-controlled limit by which substrates bind and products dissociate [7]. In the case of triose phosphate isomerase [8], ketosteroid isomerase [9], mandelate racemase [10], and proline racemase [11], the energies of various transition states on the reactions coordinates have been quantitated, with the result that the free energies of the transition states for the proton transfer reactions to and from carbon are competitive with those for substrate association/ product dissociation. However, as discussed in later sections, the energies of the
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6 Enzymatic Catalysis of Proton Transfer at Carbon Atoms
enolate anion intermediates usually have not been quantitated but in some cases have been estimated by calculations. Irrespective of the identity of the substrate, the value of the pK a of its a-proton, and the rate acceleration, the necessary conclusion is that the active sites provide significant stabilization of the enolate anion intermediates as well as the transition states for proton transfer. 6.2.1
Marcus Formalism for Proton Transfer
Marcus formalism has been applied to understanding the strategies by which active sites stabilize the transition states for proton transfer to and from carbon [12, 13]. This is based on the usual assumption that the equation for an inverted parabola can be used to describe the dependence of the free energy, G, on the reaction coordinate, x, where x ¼ 0 for carbon acid substrate/general base and x ¼ 1 for the enolate anion intermediate/conjugate acid of the general base. G ¼ 4DGz int ðx 0:5Þ 2 þ DG o ðx 0:5Þ
ð6:1Þ
The equation employs two parameters, the thermodynamic barrier, DG o , and the intrinsic kinetic barrier, DGz int , to describe the dependence of G on the reaction coordinate. The value of DG o is determined by the difference in the values of the pK a s of the proton that is abstracted and of the conjugated acid of the active site general base to which it is transferred. The value of DGz int is an ‘‘extra’’ activation energy barrier associated with proton abstraction and is defined as the barrier that would remain if the proton transfer reaction were isoenergetic, i.e., the value of DG o were reduced to zero. According to Marcus formalism, the value of the activation energy barrier, DGz , is specified by the following equation: DGz ¼ DGz int ð1 þ DG o =4DGz int Þ 2
ð6:2Þ
Inspection of this equation reveals that a reduction in DGz from that associated with the nonenzymatic reaction (k non ) to that associated with the enzymatic reaction (kcat ) can be accomplished by reducing the value of DG o , DGz int , or both. If the structural strategies for achieving the rate accelerations associated with enzymatic proton abstraction from carbon are to be completely understood, the reduction in DGz must be partitioned into the individual contributions from DG o and DGz int so that these can be separately interpreted. From the previous equation, the amount of the contribution of DGz int to DGz depends on the value of DG o : if DG o is small, the contribution from DGz int will approach the value of DGz int ; if the value of DG o is large, the contribution from DGz int will approach zero. For example, if DGz int ¼ 12 kcal mol1 (a typical value for nonenzymatic proton abstraction from a carbon acid) and DG o ¼ 0 kcal mol1 (the substrate and intermediate states are isoenergetic), DGz ¼ 12 kcal mol1 , i.e., the ‘‘extra’’ activation energy as-
6.2 The Kinetic Problems Associated with Proton Abstraction from Carbon
sociated with DGz int is the ‘‘full’’ 12 kcal mol1 . However, if the value of DG o were increased to 10 kcal mol1 , DGz ¼ 17:5 kcal mol1 , i.e., the ‘‘extra’’ activation energy associated with DGz int is ‘‘only’’ 5.5 kcal mol1 . This dissection requires that the value of DG o be known, i.e., the concentration of the enolate anion intermediate must be quantitated. With this value and the measured value of DGz , the value of DGz int can be calculated. However, the values of DG o are usually unknown for enzyme-catalyzed reactions because the concentrations of the intermediates are too small to detect and quantitate, so the values of DGz int are also unknown. 6.2.2
DG o , the Thermodynamic Barrier
The factors underlying reductions in DG o are relatively easy to understand. As noted previously, the values of the pK a s of biochemically relevant carbon acids range from 18 to 20 for aldehydes, ketones, and thioesters to 29 to 32 for carboxylate anions [1, 2]. The values of the pK a s of the conjugate acids of the amino acid functional groups that participate as general bases are necessarily no larger than @7; otherwise, they would be protonated and unable to be kinetically competent as bases. Thus, the value of DG o is given by the following equation: DG o ¼ 2:303RTDpK a
ð6:3Þ
where DpK a is the difference between the pK a of the carbon acid and the conjugate acid of the active site base. If the value of DGz were determined only by DG o, the value of kcat would be specified by the equation kcat ¼ 6:2 10 12 10ðDGo=2:3RTÞ s1
ð6:4Þ
So, for example, in the case of the mandelate racemase-catalyzed reaction, for which the value of the pK a of mandelate anion is 29 [1] and the value of the pK a of Lys 166, the (S)-specific base, is 6 [6], the value of kcat would no larger than 6:2 1011 if the enolate anion intermediate were not stabilized in the active site; this value is @10 13 -fold less than the observed value for the kcat , 500 s1 . Recall that an enolate anion is necessarily on the reaction coordinate, so the value of DG o must be reduced for the enolate anion to be kinetically competent irrespective of whether DGz int can be reduced. Thus, the active site of mandelate racemase must decrease DG o from the value predicted from the values of the substrate carbon acid and the active site base in solution. The obvious strategy to accomplish this reduction is preferential stabilization of the enolate anion intermediate: relative to the carbon acid substrate, the increased negative charge on (or proton affinity of ) the carbonyl/carboxylate oxygen of the enolate anion intermediate provides a convenient handle for enhanced electrostatic or hydrogen bonding interactions with the active site.
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6 Enzymatic Catalysis of Proton Transfer at Carbon Atoms
6.2.3
DG ‡ int , the Intrinsic Kinetic Barrier
The interpretation of DGz int is not so straightforward, even disregarding the work term associated with bimolecular reactions that describes the energetic costs of bringing the reactants together. For convenience, the work terms for the nonenzymatic and enzymatic reactions are ignored if (i) the value of k non refers to that of an encounter complex of the carbon acid and base in the nonenzymatic reaction; and (ii) the value of kcat , the reactivity of the enzyme–substrate complex, is used to quantitate the rate of the enzymatic reaction. That the values of DGz int for nonenzymatic proton transfer from carbon acids (13 kcal mol1 ) are considerably greater than those for proton transfer between heteroatoms (a 3 kcal mol1 ) has been attributed to both the temporal requirements for reorganization of solvent that occurs as charge is localized on the carbonyl/carboxyl oxygen as well as for rehybridization of the tetrahedral carbon from which the proton is abstracted. Presumably, within the enzyme–substrate complex, the carbonyl/carboxyl oxygen will be prearranged relative to active site charges, dipoles, and hydrogen-bond donors and the a-carbon can be proximal to positive charge (associated with either an active site function group or resulting from protein structure, e.g., the N-terminal end of an a-helix). The author and others have proposed that this preorganization may provide a structural basis for a reduction in DGz int by enzyme active sites relative to the nonenzymatic reaction [12, 14]. However, this argument and the possible effects of active site structure on the value of DGz int remain controversial. Despite efforts, only limited success has been made in measuring the values of DG o and DGz int for enzyme-catalyzed proton abstraction reactions. Indeed, despite the importance of the reaction catalyzed by triose phosphate isomerase in our understanding of the conceptual strategies by which catalytic efficiency may evolve (uniform binding of substrate/intermediate/product, differential binding of bound species so that the conversion of bound substrate to an intermediate can be isoenergetic, and stabilization of transitions states for chemical steps so that diffusion-controlled and chemical steps can have competitive rates [7]), the concentration of the enediolate intermediate in this reaction has not been measured. Indeed, the intermediate has no useful UV/visible spectroscopic properties nor can it be chemically prepared and used as an alternate ‘‘substrate’’ for the enzymecatalyzed reaction. So, although the derived theory about evolution of enzymatic activity assumes that DG o for formation of the enolate intermediate is significantly reduced, thereby making the bound substrate, intermediate, and product nearly isoenergetic, the effects of the active site of triose phosphate isomerase on both DG o and DGz int are unknown. Similar situations exist for the ‘‘quantitative’’ reaction coordinates for both the Mg 2þ -dependent mandelate racemase- and metalindependent proline racemase-catalyzed reactions that also have provided considerable insight into understanding enzyme-catalyzed proton abstraction from carbon. Bearne and coworkers quantitated the reaction coordinate for mandelate racemase [10], and Knowles and Albery and coworkers also studied proline racemase [11],
6.2 The Kinetic Problems Associated with Proton Abstraction from Carbon
but in neither case could the concentration of the enolate anion intermediate be determined. Although not a subject of this chapter, Toney and coworkers have quantitated the reaction coordinate of a PLP-dependent l-alanine racemase [15]. Despite the expectation that the cofactor provides resonance stabilization of the carbanion/enolate anion (quinonoid) intermediate derived by abstraction of the a-proton, the spectroscopic and kinetic analyses for the wild type racemase at steady-state provided no evidence for the intermediate in the reaction catalyzed by the wild type enzyme. Indeed, Toney had previously demonstrated that a kinetically competent quinonoid intermediate accumulates in the impaired R219E mutant [16]; Arg 219 is hydrogenbonded to the pyridine nitrogen of the cofactor. For the wild type racemase, the derived transition state energies for conversion of the bound enantiomers of alanine, @12 kcal mol1 , could be explained by a value of DGz int that need not differ from that associated with nonenzymatic reactions if the quinonoid intermediate is present but at a concentration that is too low to be detected spectrophotometrically. However, in the case of the proton abstraction reactions catalyzed by ketosteroid isomerase, the concentration of the dienolate anion intermediate is known with some certainty [9]. The conjugated and unconjugated enone substrate/product are among the most acidic carbon acids found in enzymology (Table 6.1). The dienolate anion intermediate can be prepared chemically by treatment with NaOH and rapid neutralization with buffer (exploiting the slow protonation of the intermediate on carbon due to the large value of DGz int ), and the rates at which the neutralized intermediate partitions to substrate and product could be quantitated [17]. Analyses of the data revealed that, at pH 7, the value of DG o for formation of acetate-catalyzed formation of the intermediate is reduced from 10 kcal mol1 in solution to @0 kcal mol1 in the active site in the direction in proton abstraction from the more acidic nonconjugated enone substrate (pK a ¼ 12:7); in the reverse direction with the conjugated enone product (pK a ¼ 16:1), the intermediate is @5 kcal mol1 higher in energy (at equilibrium, the conjugated enone is favored). With these values and the measured rates of proton abstraction, the values of DGz int could be calculated and were found to be decreased by 3 kcal mol1 from the nonenzymatic reaction (from 13 kcal mol1 to 10 kcal mol1 ), so the kinetic barriers for the relatively slow proton transfer reactions are determined almost entirely by the value of DGz int . This provides persuasive evidence that, despite a preorganized active site structure in which stabilizing hydrogen-bonding Tyr and Asp residues are located proximal to the substrate carbonyl group, the value of DGz int is effectively unchanged. A similar conclusion can be reached for proton abstraction catalyzed by (S)mandelate dehydrogenase, a FMN-dependent reaction. In this active site, an active site His abstracts the a-proton, and the enolate anion is located proximal to oxidized isoalloxazine ring. A long wavelength charge-transfer complex is transiently formed, suggesting the accumulation of a ‘‘significant’’ amount of the intermediate [18]. Although the value of the extinction coefficient for the complex is uncertain, the rate of formation of the intermediate, 400 s1 , is consistent with a large, i.e., unperturbed, value for DGz int. This conclusion is consistent with observations
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6 Enzymatic Catalysis of Proton Transfer at Carbon Atoms
on acyl-CoA dehydrogenases that demonstrate the accumulation of charge-transfer complexes from substrate analogs that are enolizable but unable to reduce the cofactor by hydride transfer, e.g., 3-thiaoctanoyl-CoA [19]. In summary, insufficient data are available to decide whether enzymes that catalyze proton abstraction from carbon acids either need or are able to reduce the values of Gz int from those measured for nonenzymatic reactions. But the conclusion is inescapable: these enzymes must significantly stabilize the enolate anion intermediate if the observed values of kcat and the associated rate acceleration are to be understood.
6.3
Structural Strategies for Reduction of DG o
As noted previously, the vast majority of enzymes that catalyze proton abstraction from carbon acids must be able to reduce the value of DG o from that used to describe the nonenzymatic reaction. Focusing on reactions that do not involve organic cofactors, stabilization of the enolate anion intermediate is most reasonably accomplished either by hydrogen-bonding or electrostatic interactions with active site components. 6.3.1
Proposals for Understanding the Rates of Proton Transfer
In the early 1990s, considerable controversy emerged about the possible importance of hydrogen bonding in stabilizing anionic intermediates. The author and the late Gassman [12, 20] and, also, Cleland and Kreevoy [21] suggested that not all hydrogen bonds are ‘‘created equal’’ and that the strengths of these could increase sufficiently as a proton is abstracted from a carbon acid substrate to allow significant stabilization of an enolate anion intermediate. In an early application of site-directed mutagenesis to elucidate the structural bases of catalysis, Fersht and coworkers systematically examined the interactions of the acyladenylate intermediate with the active site of tyrosyl-tRNA synthetase [22]. From their results, that demonstrated that charged hydrogen bonds are somewhat stronger than neutral hydrogen bonds, the differential strengths of hydrogen bonds apparently could contribute only modestly to catalysis. Thus, suggestions to the contrary by the Gerlt– Gassman/Cleland–Kreevoy proposals were immediately met with resistance [23]. The Gerlt–Gassman/Cleland–Kreevoy proposals were virtually the same, although the semantics differed in ‘‘bonding’’ detail and, therefore, perceived emphasis. The structures of enzymes catalyzing proton abstraction from carbon acids without the participation of a divalent metal ion suggested the required presence of a hydrogen bond donor spatially proximal to the carbonyl/carboxylate acceptor oxygen of the substrate [1]. In an enzyme–substrate complex, the proton affinity (as assessed by value of the pK a ) of the carbonyl/carboxylate oxygen is low; in contrast, neutral His and Tyr are often the hydrogen bond donors, so their proton affinities
6.3 Structural Strategies for Reduction of DG o
are much greater. In fact, Knowles and coworkers had demonstrated that the neutral form of His 95 is the electrophile in the active site of triose phosphate isomerase and determined that the pK a of the imidazole proton is >14 [24, 25]. Both proposals also noted that proton abstraction from the carbon acid substrate results in an increased proton affinity for the carbonyl/carboxylate oxygen so that it can approach that of the hydrogen bond donor when the enolate anion was formed. In the extreme, the proton affinities of the enolate anion and active site donor could be the same, depending on the identities of the substrate and active site hydrogen bond donor. 6.3.2
Short Strong Hydrogen Bonds
A large body of experimental work in the physical chemistry community has addressed the properties of hydrogen bonds in which the proton affinities of the donor and acceptor are equal [26]. These exist in the crystalline state and in nonaqueous, but not aqueous, solutions. Their enthalpies of formation are measured and/or calculated to be 25 to 30 kcal mol1 , their lengths are as short as 2.29 A˚ in the [HOaHaOH] ion, and the hydrogen-bonded proton is located equidistant between the donor and acceptor. In contrast to asymmetric hydrogen bonds in which the hydrogen is located proximal to one heteroatom and must traverse an energy barrier to be transferred to another, these ‘‘low barrier’’ hydrogen bonds have covalent character with no energy barrier impeding the transfer of the proton from one heteroatom to another. Cleland–Kreevoy used the term ‘‘low barrier’’ to describe these hydrogen bonds; Gerlt–Gassman used the term ‘‘short, strong’’ to describe the properties of the hydrogen bond that would result as the developing negative charge resulting from abstraction of the a-proton is localized on the more electronegative oxygen. The existence and properties of a low-barrier hydrogen bond sometimes can be studied by measuring 1 H NMR chemical shift (d > 16 ppm) and isotope fractionation factor (F < 0:5) of the hydrogen-bonded proton [27, 28]. Although Cleland had previously pointed out the potential importance of ‘‘low barrier’’ hydrogen bonds in the interpretation of low deuterium fraction factors, the Gerlt–Gassman/Cleland–Kreevoy proposals focused on the largely unappreciated strengths (at least among biochemists) of ‘‘pK a -matched’’ hydrogen bonds in stabilizing enolate and other anionic intermediates in enzymatic reactions. Indeed, the proposals suggested that these hydrogen bonds could provide much, if not all, of the previously elusive energetic contribution required for sufficient stabilization of enolate anions so that they could be kinetically competent. 6.3.3
Electrostatic Stabilization of Enolate Anion Intermediates
The proposed importance of hydrogen bonds in providing significant differential stabilization of oxyanion intermediates was quickly challenged. Kluger and Guthrie
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6 Enzymatic Catalysis of Proton Transfer at Carbon Atoms
pointed out that electrostatic effects are likely to be significant in the apolar environment of enzyme active sites [23]: in media of low dielectric constant, the Coulombic stabilization provided by an ion-pair interaction between a dianionic intermediate and a divalent cation (as in the active site of mandelate racemase) could be as large as 18 kcal mol1 . So, for those enzymes in which a divalent metal is coordinated to a carbonyl/carboxylate oxygen of the substrate, e.g., mandelate racemase and enolase, enolate anion intermediates undoubtedly are significantly stabilized by ‘‘simple’’ electrostatic effect. But, not all enzymes that stabilize anionic intermediates require divalent metal ions, e.g., triose phosphate isomerase, ketosteroid isomerase, and enoyl-CoA hydratase, so another strategy must be used to stabilize the intermediates in such reactions. Perhaps, in some cases, this strategy may be electrostatic effects that are not associated with divalent metal ions. However as detailed in later sections of this chapter, the more prevalent strategy, as deduced from X-ray structures and supported by mutagenesis of the hydrogen bonding residues, is hydrogen bonding interactions with active site hydrogen bond donors. As discussed in the next sections, the magnitudes of these interactions are, in fact, sufficient to provide the necessary stabilization of the enolate anion intermediate so that it can be kinetically competent.
6.3.4
Experimental Measure of Differential Hydrogen Bond Strengths
Herschlag interpreted the Gerlt–Gassman/Cleland–Kreevoy proposals as invoking a ‘‘special stabilization’’ of an enolate anion intermediate when the proton affinities of the hydrogen bond donor and acceptor are matched (DpK a ¼ 0) [29]; however, the proposals did not specify a function that related hydrogen bond strength to DpK a but simply pointed out the enhanced strengths of hydrogen bonds involving pK a matched donors and acceptors relative to hydrogen bonds characterized by large values of DpK a . Herschlag determined this dependence by studying the dependence of intramolecular hydrogen bond strength (expressed as K HB ) on the DpK a between the neutral phenolic OH group (hydrogen bond donor) and the anionic carboxylate group (hydrogen bond acceptor) for a series of substituted salicylates [30]. The experiments were conducted in both water and dimethylsulfoxide, the latter assumed to mimic the environment of an active site. The difference, if any, in the values of the slopes of plots of log K HB versus DpK a (Brønsted b) in these solvents would describe the influence of the active site on the strengths of hydrogen bonds. Any enhanced effect (greater negative value of the Brønsted b) would produce a larger rate acceleration for the enzyme-catalyzed reaction if stabilization of an enolate anion intermediate by hydrogen bonding is an important feature of the reaction coordinate. The strengths of the intramolecular hydrogen bonds showed little dependence on the value of DpK a in aqueous solution: the Brønsted slope of a plot of log K HB versus DpK a is 0.05. However, in DMSO solution, the Brønsted slope is 0.73, describing a significant increase in hydrogen bond strength as the value of
6.3 Structural Strategies for Reduction of DG o
DpK a decreases. The difference in the values of the Brønsted bs, 0.68, predicts an enhancement of hydrogen bond strengths in active sites. In reactions involving the the enolization of carbon acid substrates, the pK a of the active site hydrogen bond donor is always much larger than the pK a of the conjugate acid of the substrate carbonyl group acceptor, i.e., DpK a g 0; however, the pK a of the hydrogen bond donor is usually similar to that of the conjugate acid of the enolate anion acceptor, i.e., DpK a @ 0. Thus, as the a-proton is abstracted, the DpK a between the hydrogen bond acceptor and donor decreases significantly. From Herschlag’s studies, the enhanced importance of hydrogen bonding in stabilizing an enolate anion intermediate in an active site, DDG o , is quantitated by the following equation DDG o ¼ 1:36 kcal mol1 ð0:73 0:05ÞDpK a ¼ 1:36 kcal mol1 ð0:68ÞDpK a
ð6:5Þ
where DpK a quantitates the effect of the increase in pK a of the conjugate acid of the carbonyl/enolate anion oxygen as the a-proton is abstracted. From this equation, the increase in the hydrogen bond strength available to stabilize an enolate anion intermediate is predicted to be substantial. For example, in the active site of enoyl-CoA hydratase, the thioester enolate anion intermediate is assumed to be stabilized by hydrogen bonding interactions with two peptide backbone NH groups in an oxyanion hole [31]. The pK a of a peptidic NH, the hydrogen bond donor, is @18; the pK a of the conjugate acid of the thioester oxygen of crotonyl-CoA, the hydrogen bond acceptor in the enzyme–substrate complex, is @2; and the pK a of the conjugate acid of the enolate anion resulting from abstraction of the a-proton by Glu 164, the acid site general base, is @10. Thus, assuming that the pK a of the peptidic NH is unchanged in the enzyme–substrate and enzyme–intermediate complexes, the 12 unit change in pK a of the acceptor is predicted to result in an 11 kcal mol1 increase in the strength of the hydrogen bond, even though the pKa s of the conjugate acid of the enolate anion intermediate and the active site hydrogen bond donor are not matched. In experimental support of this prediction, the value of kcat for the hydration reaction catalyzed by the G141P mutant of enoyl-CoA hydratase is decreased by 10 6 -fold, corresponding to destabilization of the transition state for proton abstraction 8.4 kcal mol1 [32]. Gly 141, located at the N-terminal end of an a-helix, provides one of two NH groups in an oxyanion hole occupied by the thioester carbonyl oxygen, so the G141P mutant lacks one of the NH groups. The second peptidic NH group is associated with a residue that is not appropriately located for a similar analysis. However, assuming that the peptidic NH groups provide independent stabilization of the enolate anion intermediate, hydrogen bonding interactions could provide as much as 17 kcal mol1 of stabilization, more than needed to account for the value of kcat . The important message in this analysis, which follows directly from Herschlag’s experimental studies, is that there is no need for any ‘‘special’’ stabilization associated with ‘‘matching’’ of the pK a s of the hydrogen donor and acceptor as the eno-
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6 Enzymatic Catalysis of Proton Transfer at Carbon Atoms
late anion is formed. A substantial increase in hydrogen bond strength is obtained simply from a marked increase in the affinity of the oxygen as the a-proton is abstracted and the enolate anion intermediate is formed. To realize this stabilization, the enzyme ‘‘simply’’ needs to bind the substrate so that the substrate carbonyl/ carboxyl group is hydrogen bonded to a weakly acidic donor, e.g., neutral His, neutral Tyr, or a peptide NH group. In fact, in those enzymes that do not require divalent cations, these hydrogen bond donors are (almost) always found in the active sites! So, the substance of the Gerlt–Gassman/Cleland–Kreevoy proposals appears correct, i.e., hydrogen bonding can provide much more stabilization of enolate anion intermediates under conditions of appropriate local dielectric environment than had been previously recognized by the bioorganic and biochemical communities.
6.4
Experimental Paradigms for Enzyme-catalyzed Proton Abstraction from Carbon
In recent years, several enzymes have been subjected to sufficient structural, mechanistic, and, in some cases, computational scrutiny so that the underlying principles by which these catalyze facile proton abstraction from carbon are reasonably well understood. This section highlights the current state of knowledge for four of these. 6.4.1
Triose Phosphate Isomerase
Triose phosphate isomerase (TIM), that catalyzes the cofactor-independent interconversion of dihydroxyacetone phosphate (DHAP) and d-glyceraldehyde 3-phosphate (G3P) in the glycolytic pathway, continues as a paradigm for understanding enzymatic strategies for proton abstraction from carbon as a result of the classical work of Knowles and workers who dissected the catalytic roles of active site residues [24, 33, 34] and, also, of Knowles and Albery and coworkers who quantitated the free energy profile for the reaction (with the exception of the energy/stability of the enediolate anion intermediate) [8]. However, as summarized in this section, some notable deficiencies remain in our understanding of the energetics of this seemingly simple reaction. The values of the pK a s of the dihydroxyacetone phosphate (DHAP) substrate and the glyceraldehyde 3-phosphate (G3P) product for the TIM-catalyzed reaction are estimated as 18 and 20, respectively [2]. Knowles established the importance of
6.4 Experimental Paradigms for Enzyme-catalyzed Proton Abstraction from Carbon
Glu 165 as the active site general base that abstracts a proton from carbon-1 of DHAP and delivers a proton to carbon-2 of G3P; the value of its pK a has been estimated as between 3.9 and 6.5 [35, 36]. The value of kcat using the less reactive DHAP as substrate is 750 s1 [8]. Given these values for the pK a s of Glu 165 and the DHAP substrate, the DGo for formation of the enediolate anion intermediate from DHAP must be reduced by at least 10 kcal mol1 in the active site of TIM for it to be kinetically competent (making the unlikely assumption that DGz int is reduced to zero). The value of the rate acceleration associated with the TIMcatalyzed reaction is @10 9 , confirming the importance of DGz int in understanding the enzyme-catalyzed reaction (Table 6.1). The equilibrium constant for the TIM-catalyzed reaction is 22 in the direction of DHAP for the reactive, nonhydrated forms of DHAP and G3P [8]; as a result, steady-state kinetics as well as the fates of substrate- and solvent-derived protons can be studied using either DHAP or G3P as substrate. In a series of landmark papers, Knowles and Albery quantitated the free energy profile for the reaction (Fig. 6.1) [37–42]. These studies utilized protiated, deuteriated, and tritiated forms of both DHAP and G3P in both unlabeled and tritiated water to follow the course of the transferred proton(s) during the course of the reaction. Several important conclusions were reached: (i) for protiated substrates, the transition state for binding/release of G3P is the highest point on the energy diagram; (ii) for tritiated
Figure 6.1. Reaction coordinate for the reaction catalyzed by TIM. The DHAP substrate is S, the enediolate intermediate is Z, and the G3P product is P. The dashed lines indicate uncertainties in the concentrations of
bound intermediate (EZ) and product (EP). The barrier labeled ‘‘enz’’ is that for the exchange of the conjugate acid of Glu 165 with solvent hydrogen.
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6 Enzymatic Catalysis of Proton Transfer at Carbon Atoms
substrates, the transition state for proton abstraction from DHAP is the highest point (the details of the reaction coordinates depend upon the identities of the substrate and solvent isotopes); (iii) the energies of bound DHAP and G3P are similar; and (iv) exchange of the substrate-derived proton with solvent hydrogen occurs in competition with intramolecular proton transfer from carbon-1 of DHAP and to carbon-2 of G3P. Unfortunately, the free energy(ies) of the enediolate/enediol intermediates could not be quantitated. The intramolecular 1,2-proton transfer catalyzed by TIM occurs in competition with exchange of the solvent-derived proton with solvent protons. Knowles and Albery reported that with [1R- 3 H]-DHAP as substrate, the formation of G3P is accompanied by @6% intramolecular transfer of the isotopic label [41]; realizing that the exchange of a triton from the conjugate acid of Glu 165 will be suppressed relative to exchange of a proton, the reaction of protiated DHAP is expected to occur with a lower level of intramolecular transfer. More recent experiments by Amyes and Richard using protiated DHAP and G3P in D2 O revealed 18% intramolecular proton transfer starting with DHAP and 49% intramolecular transfer starting with G3P [43, 44]. Again, assuming discrimination against solvent deuterium in the exchange reaction, lower levels of intramolecular proton transfer are expected in H2 O. Although none of these experiments allow quantitation of the exchange that would occur with protiated substrates in H2 O, they clearly demonstrate that a substrate-derived proton can be transferred, proving the formation of an enediolate intermediate rather than a hydride ion migration as in some other aldo–keto isomerization reactions. However, the challenge has been to provide a structural description of the mechanisms by which substrate-derived protons exchange with solvent-derived protons. On the basis of the early structures of TIM determined with bound analogs of the enediolate intermediate, e.g., phosphoglycolohydroxamate, His 95 was proposed to be an electrophilic catalyst, polarizing the carbonyl groups of DHAP/ G3P, thereby rendering the a-proton more acidic [45]. Lys 12 was also known to be proximal to the ketone oxygen of DHAP as well as the phosphate group. In accord with these structures, site-directed mutants of Glu 165, His 95, and Lys 12 were constructed and found to be markedly defective in catalysis [24, 33, 34]. A very high resolution X-ray structure of the complex with substrate DHAP is now available (Fig. 6.2) [46]. One carboxylate oxygen of Glu 165 is positioned in close proximity to the proton on carbon-1 as well as to carbon-2; the other carboxylate oxygen is proximal to the 1-OH group. The Ne H group of neutral His 95 participates in a bifurcated hydrogen bond to both the 2-ketone oxygen and the 1-hydroxyl oxygen of the bound DHAP. With this geometry, the carbonyl group is polarized but intramolecular hydrogen transfer from O1 to O2 is impeded; the potential for this transfer is important in understanding the energetics of the reaction coordinate. The electrophilic e-ammonium group of Lys 12 is hydrogen bonded to the 2-ketone oxygen, the bridging oxygen of the phosphate ester, and via an intervening water molecule to one of the nonesterified oxygens of the phosphate ester. On the basis of theses structures, three mechanisms have been proposed for the TIM-catalyzed reaction (Fig. 6.3):
6.4 Experimental Paradigms for Enzyme-catalyzed Proton Abstraction from Carbon
Figure 6.2.
The active site of TIM.
1. In the ‘‘classical’’ mechanism (path A in Fig. 6.3), Glu 165 abstracts the 1-proR proton from DHAP to generate an initial enediolate intermediate in which negative charge is localized on oxygen-2 and a proton is located on oxygen-1. The oxyanion is transiently stabilized by the Ne H group of neutral His 95, and a proton is transferred from His 95 to the enediolate intermediate to generate a neutral enediol and the conjugate base of His 95. The imidazolate anion so generated then accepts the proton from the 1-OH group to yield a second enediolate intermediate in which negative charge is localized on the 1-oxygen. (In the original formulation of the reaction coordinate, Knowles and Albery did not differentiate the tautomeric enediolate intermediates [8].) In competition with the intramolecular 1,2-proton transfer, the substrate-derived proton initially located on the carboxylate group of Glu 165 can exchange (by an unspecified mechanism) with a solvent-derived proton so that Glu 165 can deliver a fractional mixture of a substrate- and a solvent-derived proton to carbon-2 to generate G3P. The rate and extent of the exchange of the substrate-derived proton with a solventderived proton is of considerable interest. 2. In a variant of this mechanism (path B), the Ne H group of neutral His 95 stabilizes the enediolate anion in which negative charge is localized on oxygen-2 [24, 25]. Intramolecular proton transfer from the oxygen-1 to oxygen-2 then occurs without the involvement of His 95 as an acid/base catalyst, and the resulting tautomeric enediolate intermediate in which negative charge is localized on oxygen-2 is stabilized by the Ne H group of neutral His 95. A proton is delivered from Glu 165 to carbon-2 to generate G3P. During the course of this reaction, the substrate-derived proton initially located on Glu 165 can exchange with a solvent-derived proton, as is assumed in the classical mechanism. The difference between this mechanism and the previous mechanism is whether His 95 participates as an acid–base catalyst.
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6 Enzymatic Catalysis of Proton Transfer at Carbon Atoms
Figure 6.3.
Possible mechanisms for the reaction catalyzed by TIM.
6.4 Experimental Paradigms for Enzyme-catalyzed Proton Abstraction from Carbon
3. In the ‘‘criss-cross’’ mechanism (path C), Glu 165 abstracts a proton from carbon-1 of DHAP to generate an enediolate intermediate in which negative charge is localized on oxygen-2; this intermediate is stabilized by hydrogenbonding to the Ne H group of neutral His 95 [47–49]. The conjugate acid of Glu 165 then delivers the DHAP-derived proton to oxygen-2 to generate a neutral enediol intermediate. The deprotonated Glu 165 then abstracts the proton from the 1-OH group of the intermediate and delivers it to carbon-2, thereby generating G3P. In this mechanism, the proton delivered to carbon-2 of the G3P product is predicted to be derived exclusively from solvent; the proton abstracted from DHAP is predicted to be necessarily ‘‘lost’’ to solvent via its transfer to oxygen-2. Although this mechanism has been proposed to explain the behavior of the H95Q mutant [47, 48], the fact that the reaction catalyzed by wild-type TIM is accompanied by partial retention of the DHAP-derived proton in the G3P product requires the competing participation of one of the first two mechanisms in the reaction it catalyzes. In addition, the exchange of the solvent-derived proton with solvent required in the first two mechanisms may be explained by this mechanism. The energies of the enediolate/enediol intermediates relative to the bound DHAP/ G3P have not been evaluated experimentally: they do not accumulate sufficiently to allow spectroscopic detection. However, the proposals put forth by Albery and Knowles regarding the evolution of catalytic efficiency are based, in part, on the assumption that the various bound species, substrate, intermediates, and products, are isoenergetic on the reaction coordinate (‘‘differential binding’’ to achieve a reduction in DGo ) and that the transition states for the proton transfer reactions can be selectively stabilized (‘‘catalysis of elementary steps’’ to achieve a reduction in DGz int ) [7]. Without a measure of the stabilities of the enediol/enediolate intermediates relative to DHAP and G3P, the importance of reductions in DGo and/or DGz int cannot be dissected. Without the ability to measure experimentally the energies of the enediol/ enediolate intermediates produced by the various mechanisms, computational approaches may provide otherwise inaccessible insights. In recent studies reported by Friesner and coworkers [50], the starting coordinates were those obtained from the high resolution structure of the DHAP substrate complex (1.2 A˚) [46]. In earlier studies reported by Cui and Karplus [51, 52], the starting coordinates were those of the lower resolution structure of the complex with phosphoglycolohydroxamate, an analogue of the enediol/enediolate intermediates (1.9 A˚) [45]. Although these structures are similar, they differ in some potentially significant details, e.g., the location of the e-ammonium group of Lys 12 relative to the enediol/enediolate intermediate and its phosphate group. Both studies were in agreement that the mechanism in which intramolecular proton transfer from oxygen-1 to oxygen-2 occurs without the participation of either His 95 or Glu 165 is accompanied by a significant energy barrier that is incompatible with the measured kinetic parameters: the bifurcated hydrogen bond involving the Ne H group provides a steric and electrostatic barrier to this proton transfer.
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6 Enzymatic Catalysis of Proton Transfer at Carbon Atoms
Unfortunately, the computational studies differ in quantitative detail regarding the importance of the mechanisms that involve either Glu 165 or His 95 as the acid–base catalysts to catalyze interconversion of the tautomeric enediolate intermediates. Friesner and coworkers concluded that the transition state for proton abstraction from DHAP is the highest point on the energy diagram; after formation of the enediolate anion intermediate, the calculations predict that the barrier for the ‘‘criss-cross’’ mechanism catalyzed by Glu 165 is @3 kcal mol1 lower than that for ‘‘classical’’ mechanism involving catalysis of tautomerization of the enediolate intermediates by His 95, so the ‘‘criss-cross’’ mechanism is predicted to be the favored mechanism. In contrast, Cui and Karplus concluded that transition state energies for tautomerization of the enediolate anion intermediates via an enediol intermediate are isoenergetic for both the classical and criss-cross mechanisms. The extent of intramolecular proton transfer in the reaction catalyzed by wildtype TIM is low but measurable; however, quantitation of the potential competition between the classical and criss-cross mechanisms can be experimentally achieved only by ‘‘extrapolation’’ of the effect of isotopic substitutions to the all protium situation, i.e., the behavior of protiated substrates in H2 O. The observed low level of intramolecular transfer from DHAP to G3P can be explained by the Friesner calculations assuming that the disfavored intramolecular proton transfer from carbon-1 of DHAP to carbon-2 of G3P involves no, or inefficient, exchange of the DHAPderived proton with solvent hydrogen. The Karplus calculations better accommodate the intramolecular transfer of a proton via the classical mechanism, but a more extensive significant exchange of the conjugate acid of Glu 165 with solvent hydrogen would be required to explain the observed low levels of intramolecular proton transfer. Because the details of the process by which the conjugate acid of Glu 165 exchanges with solvent are unknown (presumably with a small ‘‘pool’’ of water molecules in the active site), the experimental observations do not allow the quantitative differences between the Friesner and Karplus calculations to be evaluated. As noted previously, experimental data are unavailable regarding the stabilities of the enediol/enediolate intermediates. However, quantitation of the relative stabilities of these relative to the bound DHAP and G3P is important in evaluating the Knowles and Albery proposal that the evolution of enzyme function requires that all of the bound species, including the reactive intermediates, be isoenergetic. In the classical mechanism in which His 95 catalyzes tautomerization, no enediol intermediate is present on the reaction coordinate; in the criss-cross mechanism, an enediol intermediate occurs. Karplus and Cui calculated that the enediol is essentially isoenergetic with the bound DHAP and G3P, as originally hypothesized by Knowles and Albery. In contrast, Friesner and coworkers predict that all three intermediates in the preferred criss-cross mechanism are higher in energy than bound DHAP and G3P: the enediolates derived from DHAP and G3P are predicted to be 11.4 kcal mol1 and 4.2 kcal mol1 less stable than DHAP and G3P, respectively; the enediol obtained via the preferred criss-cross mechanism is 9.2 kcal mol1 and 6.5 kcal mol1 less stable than DHAP and G3P, respectively. Thus, the latter calculations do not support the Knowles and Albery hypothesis.
6.4 Experimental Paradigms for Enzyme-catalyzed Proton Abstraction from Carbon
The different conclusions regarding the energies of the intermediates have an additional implication for the Knowles and Albery hypotheses, i.e., assessing the importance of ‘‘catalysis of elementary steps’’ to achieve a reduction in DGz int . If the enediol/enediolate intermediates are approximately isoenergetic with DHAP and G3P, as predicted by Karplus, the value of DGz int is not significantly reduced from the value (@12 kcal mol1 ) found in nonenzymatic reactions. However, if the intermediates are significantly more unstable than DHAP and G3P, the value of DGz int must be decreased to account for the observed rates of proton abstraction from DHAP and G3P. Thus, despite the apparent abundance of functional and structural information, important mechanistic issues remain to be resolved for a complete understanding of the strategy by which TIM catalyzes proton abstraction reactions. 6.4.2
Ketosteroid Isomerase
3-Oxo-D5 -ketosteroid isomerase (KSI), that catalyzes the cofactor-independent tautomeric interconversion of the a,b- and b,g-unsaturated 3-oxo-steroids via a dienolate anion intermediate, has received considerable recent mechanistic and structural scrutiny by Pollack and Mildvan and their coworkers. The reaction catalyzed by KSI is arguably ‘‘simpler’’ than that catalyzed by TIM: the value of the pK a of the unconjugated 5-androstene-3,17-dione is 12.7 whereas that of the conjugated 4-androstene-3,17-dione is 16.1 [53]; the value of the pK a of Asp 38 that mediates the intramolecular 1,2-proton transfer reaction is @4.7 [54]. As a result of the ‘‘low’’ values for the pK a of the substrate/product, the rate acceleration is ‘‘only’’ a factor of 10 7 (Table 6.1). As a result of the relatively low values for the pK a s of the substrate/product and its stability due to the absence of competing side reactions, the dienolate anion intermediate can be chemically prepared by treatment of substrate/product with strong base and, after rapid neutralization, can be supplied to KSI as a ‘‘substrate’’ to allow an evaluation of the kinetics of processing of the intermediate to substrate/ product [55]. Preparation of the enediolate intermediate in the TIM-catalyzed reaction is impossible because of its facile propensity to eliminate inorganic phosphate with the concomitant formation of methylglyoxal. The likely importance of strong hydrogen bonding in stabilizing the dienolate anion intermediate was prominent in the formulation of both the Gerlt–Gassman and Cleland–Kreevoy proposals, even prior to the availability of high resolution
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6 Enzymatic Catalysis of Proton Transfer at Carbon Atoms
Figure 6.4.
The active site of KSI.
structural information. When structures later became available, a high resolution NMR structure by Summers and Mildvan and coworkers [56] and high resolution crystal structures by Oh and coworkers [57–59], Asp 38 was located in a hydrophobic substrate binding cleft along with both Tyr 14, long known to be catalytically important, and Asp 99, whose presence but not identity had been suspected as a result of studies of the dependence of the kinetics constants on pH (Fig. 6.4). Tyr 14 and Asp 99, both potential hydrogen bond donors, were proximal to the suspected binding site for the 3-oxo group of the substrate/product; the remaining question was the geometry of the hydrogen bonding network involving these and the dienolate anion intermediate generated by proton abstraction from the substrate by Asp 38. Two hydrogen bonding geometries were proposed [56, 60]: (i) both Asp 99 and Tyr 14 would hydrogen bond to the 3-oxo group, thereby providing two ‘‘independent’’ hydrogen bonds to stabilize the anionic intermediate; and (ii) Asp 99 and Tyr 14 would form an interacting dyad, with only Tyr 14 directly involved in a hydrogen bond to the substrate/intermediate. Prior to the report of the high resolution crystal structure, Mildvan reported evidence in favor of the second geometry based on the downfield NMR spectra of wild type KSI and mutants of Tyr 14 and Asp 99
Figure 6.5.
Mechanism for the reaction catalyzed by KSI.
6.4 Experimental Paradigms for Enzyme-catalyzed Proton Abstraction from Carbon
[60]. However, the X-ray structure favored the first geometry, as did the observation that separate substitutions for both Tyr 14 and Asp 99 were accompanied by additive free energy effects on the values of the kinetic constants; as a result, each hydrogen bond was concluded to contribute one half, @5 kcal mol1 , of the total energy associated with the total rate acceleration [61]; the accepted mechanism is shown in Fig. 6.5. Although this dissection of the energetic importance of these hydrogen bonds allowed the conclusion that the intermediate is stabilized by strong hydrogen bonds rather than a single low barrier hydrogen bond, the important point is that the differential strengths of hydrogen bonds that can be achieved by large changes in the proton affinity of the carbon acid oxygen as it is transformed to an enolate anion intermediate are completely able to explain the rate acceleration for the KSI-catalyzed reaction. Prior to the formulation of the Gerlt– Gassman/Cleland–Kreevoy proposals and subsequent experimental confirmation by Herschlag, such changes in hydrogen bond strength were not expected in enzyme-catalyzed reactions. Experiments reported by Pollack and his coworkers allow the conclusion that the dienolate anion intermediate is approximately isoenergetic with the more unstable unconjugated enone substrate/product, as proposed by Knowles and Albery in their theory for understanding optimization of catalytic efficiency [9]. Thus, based on the value of the rate constant for proton abstraction from the unconjugated enone, 1:7 10 5 s1 , Pollack and coworkers calculated that the value of the Gz int for proton abstraction from carbon is 10 kcal mol1 , a modest reduction from that expected (@ 13 kcal mol1 ) for the nonenzymatic reaction. Various aspects of the reaction coordinate for the KSI-catalyzed reaction have been subjected to computational examination [62–64]. These are in accord with the experimental results, i.e., Tyr 14 and Asp 99 independently stabilize the dienolate anion intermediate via a hydrogen bond. Although the strengths of these hydrogen bonds each increase by @5 kcal mol1 as the anionic intermediate is formed, the hydrogen bonds are asymmetric with the protons associated with the donors. 6.4.3
Enoyl-CoA Hydratase (Crotonase)
Enoyl-CoA hydratase (ECH; commonly known as crotonase), that catalyzes the cofactor-independent hydration of conjugated enoyl-CoA esters in b-oxidation, has been the subject of considerable debate regarding the timing of bond-making reactions and, therefore, the importance of a thioester enolate anion on the reaction coordinate. The active site contains Glu 144 and Glu 164 as the only possible acid– base catalysts. In the nonphysiological dehydration direction, the value of the pK a
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6 Enzymatic Catalysis of Proton Transfer at Carbon Atoms
of the a-proton of the thioester is @21 [65]. The pH-dependence of the values of the kinetic constants allows the suggestion that the value of the pK a of one of the active site Glu residues is neutral and the other is unprotonated at physiological pH, with a value < 5 for the pK a of Glu 164 that is thought to abstract the a-proton in the direction of dehydration [66]. The rate acceleration is estimated as @10 9 (Table 6.1). Several high-resolution structures are available for ECH, with the structure of the complex with 4-(N,N-dimethylamino)cinnamoyl-CoA arguably providing the most valuable insights into the mechanism [67]: 4-(N,N-dimethylamino)cinnamoyl-CoA is a substrate for hydration, but conjugation of the enoyl ester with the substituted aromatic substituent shifts the direction of the hydration reaction from favoring the hydrated product by a factor of 7 to favoring the enoyl-CoA substrate by a factor of >1000. Importantly, this structure also contains a water molecule, the second substrate, apparently ‘‘poised’’ for nucleophilic attack on the conjugated thioester by both Glu 144 and Glu 164 (Fig. 6.6). Anderson and coworkers measured various substrate kinetic effects to deduce the timing of the CaH and CaO bond cleavage events in the ECH-catalyzed dehydration of 3-hydroxybutyrylpantetheine; the primary deuterium and oxygen-18 isotope effects were both significant, 1.60 and 1.053, respectively [68]. A further double isotope study examining the effect of solvent isotope substitution on the a-secondary deuterium isotope effect at carbon-3 for hydration of crotonylpantetheine revealed isotopic invariance, leading to the suggestion that incorporation of hydrogen at carbon-2 and the rehybridization at carbon-3 due to attack of the nucleophilic water occurred in the same transition state, i.e., the ECH-catalyzed reaction is concerted [69]. This interpretation is most simply explained by an E2 mechanism, in which Glu 144 functions as a general base to facilitate the attack of water (hydroxide) on carbon-3, and Glu 164 simultaneously delivers a solvent-derived hydrogen to carbon-2. However, as pointed out by Gerlt–Gassman in the formulation of their proposals [12], a concerted reaction would obviate the involvement of the thioester carbonyl group in facilitating the proton transfer events at carbon-2, suggesting an alternate explanation would be required to explain the measured isotope effects. The precise catalytic roles of Glu 144 and Glu 164 remained uncertain, despite the availability of crystal structures of necessarily nonproductive complexes [31]. These structures pointed to the expected proximity of Glu 164 to carbon-2 and led to the suggestion that it mediates proton transfers to/from carbon. Accordingly, Glu 144 was expected to facilitate attack of water on carbon-3. In addition, the interpretation of the dependence of the kinetic constants for reactions catalyzed by wild type ECH as well as the E144Q and E164Q mutants is uncertain: although ‘‘common sense’’ would require that one be anionic, i.e., a general base, and the other be neutral, i.e., a general acid, no self-consistent, unequivocal support for this expectation could be obtained. The complex with 4-(N,N-dimethylamino)cinnamoyl-CoA was solved at pH 7.3 by Bahnson, Anderson, and Petsko, conditions where ECH is active, at sufficiently high resolution (2.3 A˚) that the hydrogen bonding interactions of the substrate, nu-
6.4 Experimental Paradigms for Enzyme-catalyzed Proton Abstraction from Carbon
Figure 6.6.
The active site of ECH.
cleophilic water, and both active site Glu residues could be unambiguously interpreted [67]. The thioester carbonyl oxygen is located in an oxyanion hole formed by the peptide NH groups of Ala 98 and Gly 141. As expected, the oxygen of the water was proximal to carbon-3. Surprisingly, the hydrogen bonding interactions of both Glu residues required that both be anionic and participating as hydrogen bond acceptors from the nucleophilic water, with the more basic syn orbital of Glu 144 and the less basic anti orbital of Glu 164 participating in the hydrogen bonds. These unexpected details suggest a previously unrecognized E1cb mechanism for the hydration reaction (Fig. 6.7): Glu 144 is not an acid–base catalyst but orients the nucleophilic water molecule, and Glu 164 functions first as the general base that abstracts a proton from the water to catalyze rate-limiting addition to the bound enoyl-CoA with formation of a thioester enolate anion stabilized by hydrogen bonding interaction with the oxyanion hole. In the second, more rapid step, the conjugate acid of Glu 164 delivers the proton derived from the nucleophilic water to carbon-2. This mechanism is in accord with the results of the single and double kinetic isotope effect studies, summarized earlier, in which transfer of a
Figure 6.7.
Mechanism for the reaction catalyzed by ECH.
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6 Enzymatic Catalysis of Proton Transfer at Carbon Atoms
solvent-derived proton to Glu 164, rather than Glu 144, occurs in the same transition state as hydroxide attacks carbon-3. It also provides a rationale for the observation that neither the E144Q nor E164Q mutant can catalyze exchange of the a-proton from the thioester substrate as observed for wild type ECH – their positions in the active site are not independent by virtue of their interactions with the same water molecule. Other mechanisms are also consistent with this structure, including a cyclic four-membered transition state for a ‘‘concerted’’ reaction in which the bond forming reactions at carbons-2 and -3 are asynchronous, thereby allowing partial anionic charge to be localized on the carbonyl oxygen which it can be stabilized by the oxyanion hole. The catalytic importance of the oxyanion hole has been confirmed. Tonge and coworkers constructed and kinetically characterized the G141P mutant of ECH [32]: Gly 141 provides one of the two peptidic NH groups in the oxyanion hole and is located at the N-terminus of an a-helix. The value of kcat is reduced by a factor of 10 6 by the G141P substitution, providing persuasive evidence for the formation of a transiently stabilized thioester enolate anion intermediate; the reduction in kcat corresponds to the loss of @8 kcal mol1 of stabilization, which, based on Herschlag’ studies, is readily accommodated by the expected change in the pK a of the thioester carbonyl oxygen as the enolate anion is formed. No information is available concerning the concentration of the thioester enolate anion intermediate, by either experiment or computation, so the partitioning of the rate acceleration between reductions in DG o and DGz int is not possible. Further persuasive evidence in support of the expectation that the mechanism of the ECH-catalyzed reaction involves an E1cb mechanism with a stabilized thioester enolate anion intermediate is obtained from the membership of ECH in the mechanistically diverse enoyl-CoA hydratase superfamily [70]. Such superfamilies are derived from a common ancestor by divergent evolution; the members of these share a partial reaction, usually formation of a common intermediate, e.g., an enolate anion. The reactions catalyzed by members of the enoyl-CoA hydratase superfamily (almost) always utilize acyl esters of CoA as substrates; the reactions invariably can be rationalized with mechanisms that involve the formation of a thioester enolate anion intermediate, e.g., 1,3-proton transfer, 1,5-proton transfer, Dieckman and reverse Dieckman condensations, and b-decarboxylation. Although mechanisms with thioester enolate anion intermediates are plausible for each of these reactions, as in the ECH-catalyzed reaction, evidence for their existence on the reaction coordinate is circumstantial because the intermediates do not accumulate, thereby avoiding spectroscopic detection. However, 4-chlorobenzoyl-CoA dehalogenase is also a member of the enoyl-CoA hydratase superfamily. The mechanism of its reaction involves nucleophilic aromatic substitution in which an active site Asp adds to the 4-position of the benzoyl ring to necessarily form a Meisenheimer complex; this Meisenheimer complex is an analog of a thioester enolate anion. Although the Meisenheimer complex cannot be observed for displacement of chloride from 4-chlorobenzoyl-CoA due to the rate constants for formation and decomposition of the intermediate, the Meisen-
6.4 Experimental Paradigms for Enzyme-catalyzed Proton Abstraction from Carbon
heimer complex has been observed by Raman spectroscopy for displacement of fluoride from 4-fluorobenzoyl-CoA and nitrite from 4-nitrobenzoyl-CoA [71, 72]. The expectation is that the complex exists on the reaction coordinate for the reaction involving 4-chlorobenzoyl-CoA. By analogy, the reasonable assumption is that the structurally analogous thioester enolate anion is stabilized by the oxyanion hole in the reactions catalyzed by other members of the superfamily, including ECH. 6.4.4
Mandelate Racemase and Enolase
Both the 1,1-proton transfer reaction catalyzed by mandelate racemase (MR) and the dehydration catalyzed by enolase require Mg 2þ for activity. The values of the pK a s for mandelate and 2-phosphoglycerate, the substrates for the MR- and enolase-catalyzed reactions, are estimated as 29 and 32, respectively [1]. The values of the pK a s of the general basic Lys residues are @6 and @9 in MR [6] and enolase [73], respectively. Thus, formation of a dienolate anion intermediate is extremely endergonic, unless the active site can stabilize the intermediate which is the obvious function of the essential Mg 2þ . The rate accelerations for the MR- and enolase-catalyzed reactions are @10 15 as a direct result of the values of the pK a s of the a-protons (Table 6.1). The mechanisms of both reactions are reasonably well understood, so these serve as paradigms for understanding the mechanisms of divalent metal ionassisted proton abstraction from carbon acids. In the case of MR [4], a single Mg 2þ ion is located in the active site; one carboxylate oxygen of the substrate is coordinated to the Mg 2þ , and the second is hydrogen-bonded to the carboxylate of Glu 317. One face of the active site contains Lys 166 that is positioned to mediate proton transfers to/from (S)-mandelate; the opposite face contains His 297 hydrogen-bonded to Asp 270 (His-Asp dyad) that is positioned to mediate proton transfers to/from (R)-mandelate (Fig. 6.8). The simplest mechanism based on this structure is that the enediolate anion obtained by proton abstraction from a substrate enantiomer is transiently stabilized by enhanced electrostatic (Mg 2þ ) and hydrogen bonding (Glu 317) (Fig. 6.9). Then, the conjugate acid of the catalyst on the opposite face of the active site protonates the intermediate to form the product
1131
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6 Enzymatic Catalysis of Proton Transfer at Carbon Atoms
Figure 6.8.
The active site of MR.
enantiomer. The observation that the H297N mutant is inactive as a racemase but active as an (S)-mandelate ‘‘exchangease’’, i.e., in D2 O solvent hydrogen is incorporated without racemization, provides the most persuasive evidence for the transient formation of a stabilized enediolate anion intermediate on the reaction coordinate [6]. Bearne and coworkers have quantitated the reaction coordinate for the MRcatalyzed reaction, although, as might be expected, the concentration of the enediolate anion intermediate remains elusive [10]. The transition states for substrate binding/product dissociation are approximately isoenergetic.
Figure 6.9.
Mechanism for the reaction catalyzed MR.
6.4 Experimental Paradigms for Enzyme-catalyzed Proton Abstraction from Carbon
Figure 6.10.
The active site of enolase.
In the case of enolase, two Mg 2þ ions are located in the active site (Fig. 6.10) [74]. The carboxylate group of the substrate is a bidentate ligand of one Mg 2þ ; one carboxylate oxygen is also liganded to the second Mg 2þ ion (a m-oxo bridge ligand). One face of the active site contains Lys 345 that is positioned to abstract the a-proton from the 2-phosphoglycerate substrate to form a stabilized enediolate anion intermediate; the other face contains Glu 211 that is positioned to facilitate vinylogous departure of the 3-hydroxide leaving group from the intermediate by acid catalysis (Fig. 6.11). The coordination of the substrate carboxylate group to
Figure 6.11.
Mechanism for the reaction catalyzed by enolase.
1133
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6 Enzymatic Catalysis of Proton Transfer at Carbon Atoms
two Mg 2þ ions likely reflects the lower acidity of 2-PGA relative to the enantiomers of mandelate and the accompanying requirement for enhanced electrostatic stabilization of the intermediate. Yang and coworkers have reported computational studies of the enolasecatalyzed reaction that are in accord with this mechanism and address the interesting, and likely general, problem of how an active site with a pair of divalent metal ions can both stabilize the accumulated anionic charge of the enediolate intermediate formed by a-proton abstraction by electrostatic interactions and promote the vinylogous elimination of the electron-rich b-hydroxide group [75]. Their conclusion is that longer range interactions involving a large number of active site functional groups and water molecules differentially effect the energies of the transition states for formation and breakdown of the enediolate anion intermediate. Although many of these proposed interactions have not been investigated experimentally, it is intuitive that a single principle, e.g., stabilization of an enolate anion intermediate, cannot be the only feature associated with catalysis. Although not recognized until high-resolution structures were available for both, MR and enolase are homologous, i.e., members of the mechanistically diverse enolase superfamily [70, 76, 77]. The structures of both are composed of two domains: a ðb=aÞ7 b-barrel (a modified ðb=aÞ8 - or TIM-barrel) domain that provides the structural foundation for the ligands for the essential Mg 2þ ion(s) as well as the acid– base catalysts; and a capping domain formed from polypeptides segments at both the N- and C-terminal ends of the polypeptide. With these structures and the abundance of sequence data now in the databases, MR and enolase contain three carboxylates at conserved positions at the ends of the third, fourth, and fifth b-strands of the barrel-domain as well as positionally, but not chemically, conserved acid– base catalysts on opposite faces of the active site. The evidence is persuasive that the MR and enolase, as well as other members of the superfamily that can be identified in the sequence databases, are derived from a common ancestor by divergent evolution. Whatever the functional identity of the ancestor, the reaction undoubtedly involved Mg 2þ ion-assisted enolization of a carboxylate anion substrate.
6.5
Summary
A quantitative understanding of how enzymes catalyze rapid proton abstraction from weakly acidic carbon acids is necessarily achieved by dissecting the effect of active site structure on the values of DG o , the thermodynamic barrier, and DGz int , the intrinsic kinetic barrier for formation of the enolate anion intermediate. The structural strategies by which DG o for formation of the enolate anion is reduced sufficiently such that these can be kinetically competent are now understood. In divalent metal ion-independent reactions, e.g., TIM, KSI, and ECH, the intermediate is stabilized by enhanced hydrogen bonding interactions with weakly acidic hydrogen bond donors; in divalent metal-dependent reactions, e.g., MR and enolase, the intermediate is stabilized primarily by enhanced electrostatic interactions with
References
the directly coordinated metal ion. However, the influence of active site structure on DGz int for formation of the intermediate remains uncertain. Quantitation of the value of DGz int requires that the value DG o be known, but the concentrations of the intermediates usually cannot be measured, even in well-characterized reactions. Until that problem is solved, a complete understanding of catalytic strategies for proton abstraction from carbon acids remains elusive.
References 1 J. A. Gerlt, J. W. Kozarich, G. L.
2 3 4
5
6
7 8 9
10 11
12 13 14 15
16
Kenyon, P. G. Gassman, J. Am. Chem. Soc., 1991, 113, 9667–9669. J. P. Richard, T. L. Amyes, Curr. Opin. Chem. Biol., 2001, 5, 626–633. A. Thibblin, W. P. Jencks, J. Am. Chem. Soc., 1979, 101, 4963. G. L. Kenyon, J. A. Gerlt, G. A. Petsko, J. W. Kozarich, Acc. Chem. Res., 1995, 28, 178–186. J. A. Landro, J. A. Gerlt, J. W. Kozarich, C. W. Koo, V. J. Shah, G. L. Kenyon, D. J. Neidhart, S. Fujita, G. A. Petsko, Biochemistry, 1994, 33, 635–643. J. A. Landro, A. T. Kallarakal, S. C. Ransom, J. A. Gerlt, J. W. Kozarich, D. J. Neidhart, G. L. Kenyon, Biochemistry, 1991, 30, 9274–9281. W. J. Albery, J. R. Knowles, Biochemistry, 1976, 15, 5631–5640. W. J. Albery, J. R. Knowles, Biochemistry, 1976, 15, 5627–5631. D. C. Hawkinson, T. C. Eames, R. M. Pollack, Biochemistry, 1991, 30, 10849–10858. M. St Maurice, S. L. Bearne, Biochemistry, 2002, 41, 4048–58. J. G. Belasco, W. J. Albery, J. R. Knowles, Biochemistry, 1986, 25, 2552–2558. J. A. Gerlt, P. G. Gassman, J. Am. Chem. Soc., 1993, 115, 11552–11568. J. A. Gerlt, P. G. Gassman, Biochemistry, 1993, 32, 11943–11952. A. Warshel, J. Biol. Chem., 1998, 273, 27035–27038. M. A. Spies, J. J. Woodward, M. R. Watnik, M. D. Toney, J. Am. Chem. Soc., 2004, 126, 7464–7475. S. Sun, M. D. Toney, Biochemistry, 1999, 38, 4058–4065.
17 D. C. Hawkinson, T. C. Eames, R. M.
18 19
20 21 22
23 24
25 26
27 28
29 30
31
Pollack, Biochemistry, 1991, 30, 6956– 6964. A. R. Dewanti, B. Mitra, Biochemistry, 2003, 42, 12893–128901. S. M. Lau, R. K. Brantley, C. Thorpe, Biochemistry, 1988, 27, 5089– 5095. J. A. Gerlt, P. G. Gassman, J. Am. Chem. Soc., 1992, 114, 5928. W. W. Cleland, M. M. Kreevoy, Science, 1994, 264, 1887–1890. A. R. Fersht, J. P. Shi, J. KnillJones, D. M. Lowe, A. J. Wilkinson, D. M. Blow, P. Brick, P. Carter, M. M. Waye, G. Winter, Nature, 1985, 314, 235–238. J. P. Guthrie, R. Kluger, J. Am. Chem. Soc., 1993, 115, 11569–11572. E. A. Komives, L. C. Chang, E. Lolis, R. F. Tilton, G. A. Petsko, J. R. Knowles, Biochemistry, 1991, 30, 3011–3019. P. J. Lodi, J. R. Knowles, Biochemistry, 1991, 30, 6948–6956. J. A. Gerlt, M. M. Kreevoy, W. Cleland, P. A. Frey, Chem. Biol., 1997, 4, 259–267. P. A. Frey, S. A. Whitt, J. B. Tobin, Science, 1994, 264, 1927–1930. J. Lin, W. M. Westler, W. W. Cleland, J. L. Markley, P. A. Frey, Proc. Natl. Acad. Sci. USA, 1998, 95, 14664–14668. S. O. Shan, S. Loh, D. Herschlag, Science, 1996, 272, 97–101. S. O. Shan, D. Herschlag, Proc. Natl. Acad. Sci. USA, 1996, 93, 14474– 14479. C. K. Engel, T. R. Kiema, J. K. Hiltunen, R. K. Wierenga, J. Mol. Biol., 1998, 275, 847–859.
1135
1136
6 Enzymatic Catalysis of Proton Transfer at Carbon Atoms 32 A. F. Bell, J. Wu, Y. Feng, P. J.
33
34
35 36
37
38
39
40
41
42 43
44
45
46
47
48
49
50
Tonge, Biochemistry, 2001, 40, 1725– 1733. D. Straus, R. Raines, E. Kawashima, J. R. Knowles, W. Gilbert, Proc. Natl. Acad. Sci. USA, 1985, 82, 2272–2276. P. J. Lodi, L. C. Chang, J. R. Knowles, and E. A. Komives, Biochemistry, 1994, 33, 2809–14. B. Plaut and J. R. Knowles, Biochem J, 1972, 129, 311–20. S. De la Mare, A. F. Coulson, J. R. Knowles, J. D. Priddle, and R. E. Offord, Biochem J, 1972, 129, 321–31. L. M. Fisher, W. J. Albery, J. R. Knowles, Biochemistry, 1976, 15, 5621–5626. P. F. Leadlay, W. J. Albery, J. R. Knowles, Biochemistry, 1976, 15, 5617–5620. S. J. Fletcher, J. M. Herlihy, W. J. Albery, J. R. Knowles, Biochemistry, 1976, 15, 5612–5617. S. G. Maister, C. P. Pett, W. J. Albery, J. R. Knowles, Biochemistry, 1976, 15, 5607–5612. J. M. Herlihy, S. G. Maister, W. J. Albery, J. R. Knowles, Biochemistry, 1976, 15, 5601–5607. W. J. Albery, J. R. Knowles, Biochemistry, 1976, 15, 5588–5600. A. C. O’Donoghue, T. L. Amyes, J. P. Richard, Biochemistry, 2005, 44, 2622–2631. A. C. O’Donoghue, T. L. Amyes, J. P. Richard, Biochemistry, 2005, 44, 2610–2621. Z. Zhang, S. Sugio, E. A. Komives, K. D. Liu, J. R. Knowles, G. A. Petsko, D. Ringe, Biochemistry, 1994, 33, 2830–2837. G. Jogl, S. Rozovsky, A. E. McDermott, L. Tong, Proc. Natl. Acad. Sci. USA, 2003, 100, 50–55. E. B. Nickbarg, R. C. Davenport, G. A. Petsko, J. R. Knowles, Biochemistry, 1988, 27, 5948–5960. T. K. Harris, C. Abeygunawardana, A. S. Mildvan, Biochemistry, 1997, 36, 14661–14675. T. K. Harris, R. N. Cole, F. I. Comer, A. S. Mildvan, Biochemistry, 1998, 37, 16828–16838. V. Guallar, M. Jacobson, A.
51 52 53 54
55
56
57
58 59
60
61
62 63
64
65 66
67
68
McDermott, R. A. Friesner, J. Mol. Biol., 2004, 337, 227–239. Q. Cui, M. Karplus, J. Am. Chem. Soc., 2001, 123, 2284–2290. Q. Cui, M. Karplus, J. Am. Chem. Soc., 2002, 124, 3093–3124. B. Zeng, R. M. Pollack, J. Am. Chem. Soc., 1991, 113, 3838–3842. D. C. Hawkinson, R. M. Pollack, N. P. Ambulos, Jr., Biochemistry, 1994, 33, 12172–12183. B. F. Zeng, P. L. Bounds, R. F. Steiner, R. M. Pollack, Biochemistry, 1992, 31, 1521–1528. Z. R. Wu, S. Ebrahimian, M. E. Zawrotny, L. D. Thornburg, G. C. Perez-Alvarado, P. Brothers, R. M. Pollack, M. F. Summers, Science, 1997, 276, 415–418. S. W. Kim, S. S. Cha, H. S. Cho, J. S. Kim, N. C. Ha, M. J. Cho, S. Joo, K. K. Kim, K. Y. Choi, B. H. Oh, Biochemistry, 1997, 36, 14030–14036. H. S. Cho, G. Choi, K. Y. Choi, B. H. Oh, Biochemistry, 1998, 37, 8325–8330. H. S. Cho, N. C. Ha, G. Choi, H. J. Kim, D. Lee, K. S. Oh, K. S. Kim, W. Lee, K. Y. Choi, B. H. Oh, J. Biol. Chem., 1999, 274, 32863–32868. Q. Zhao, C. Abeygunawardana, A. G. Gittis, A. S. Mildvan, Biochemistry, 1997, 36, 14616–14626. L. D. Thornburg, F. Henot, D. P. Bash, D. C. Hawkinson, S. D. Bartel, R. M. Pollack, Biochemistry, 1998, 37, 10499–10506. I. Feierberg, J. Aqvist, Biochemistry, 2002, 41, 15728–15735. D. Mazumder, K. Kahn, T. C. Bruice, J. Am. Chem. Soc., 2003, 125, 7553–7561. K. S. Kim, K. S. Oh, J. Y. Lee, Proc. Nat. Acad. Sci. USA, 2000, 97, 6373–6378. T. L. Amyes, J. P. Richard, J. Am. Chem. Soc., 1992, 114, 10297–10302. H. A. Hofstein, Y. Feng, V. E. Anderson, P. J. Tonge, Biochemistry, 1999, 38, 9508–9516. B. J. Bahnson, V. E. Anderson, G. A. Petsko, Biochemistry, 2002, 41, 2621–2629. B. J. Bahnson, V. E. Anderson, Biochemistry, 1989, 28, 4173–4181.
References 69 B. J. Bahnson, V. E. Anderson, 70 71
72
73
74
75
Biochemistry, 1991, 30, 5894–5906. J. A. Gerlt, P. C. Babbitt, Annu. Rev. Biochem., 2001, 70, 209–246. J. Dong, P. R. Carey, Y. Wei, L. Luo, X. Lu, R. Q. Liu, D. DunawayMariano, Biochemistry, 2002, 41, 7453–7463. J. Dong, X. Lu, Y. Wei, L. Luo, D. Dunaway-Mariano, P. R. Carey, Biochemistry, 2003, 42, 9482–9490. P. A. Sims, T. M. Larsen, R. R. Poyner, W. W. Cleland, G. H. Reed, Biochemistry, 2003, 42, 8298– 8306. G. H. Reed, R. R. Poyner, T. M. Larsen, J. E. Wedekind, I. Rayment, Curr. Opin. Chem. Biol., 1996, 6, 736–743. H. Liu, Y. Zhang, W. Yang, J. Am. Chem. Soc., 2000, 122, 6560–6570.
76 P. C. Babbitt, M. S. Hasson, J. E.
77 78 79
80 81 82 83
Wedekind, D. R. Palmer, W. C. Barrett, G. H. Reed, I. Rayment, D. Ringe, G. L. Kenyon, J. A. Gerlt, Biochemistry, 1996, 35, 16489–164501. J. A. Gerlt, F. M. Raushel, Curr. Opin. Chem. Biol., 2003, 7, 252–264. A. Hall, J. R. Knowles, Biochemistry, 1975, 14, 4348–4353. R. M. Pollack, B. F. Zeng, J. P. G. Mack, S. Eldin, J. Am. Chem. Soc., 1989, 111, 6419–6423. L. F. Mao, C. Chu, H. Schulz, Biochemistry, 1994, 33, 3320–3326. S. L. Bearne, R. Wolfenden, Biochemistry, 1997, 36, 1646–1656. S. L. Bearne, R. Wolfenden, J. Am. Chem. Soc., 1995, 117, 9588–9589. R. R. Poyner, L. T. Laughlin, G. A. Sowa, G. H. Reed, Biochemistry, 1996, 35, 1692–1699.
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7
Multiple Hydrogen Transfers in Enzyme Action M. Ashley Spies and Michael D. Toney 7.1
Introduction
The focus of this chapter is on enzyme mechanisms that employ multiple hydrogen transfers, where both transfers are mechanistically central steps. The exchange of hydrons with solvent often presents both challenges and opportunities to the kinetic analysis of enzyme systems that undergo multiple hydrogen transfers. The 1,1-proton transfer mechanisms of epimerases and racemases are prototypes for exploring multiple hydrogen transfers, and will thus be the focus of this chapter. Although simple deprotonation/reprotonation of a carbon center is used in the majority of epimerases and racemases, there is variation in the specifics of how this is accomplished (e.g., cofactor-dependent or cofactor-independent, from an activated or unactivated substrate, one- or two-base mechanism, etc.).
7.2
Cofactor-Dependent with Activated Substrates
Many substrates for epimerases and racemases are considered to be ‘‘activated’’, in the sense that the reactive carbon is adjacent to a carbonyl or carboxylate group. In addition to the intrinsic substrate activation, enzymes frequently achieve epimerization or racemization with the aid of a cofactor (organic or inorganic). 7.2.1
Alanine Racemase
Perhaps the best characterized organic cofactor-dependent racemase is alanine racemase, which employs pyridoxal 5 0 -phosphate (PLP) (Table 7.1). d-alanine is necessary for the synthesis of the peptidoglycan layer of bacterial cell walls in Gram negative and positive bacteria [1]. Alanine racemase is thus a ubiquitous enzyme in bacteria and an excellent drug target [2]. Both its crystal structure and mechanism have been well investigated. PLP reacts with amino acids to produce Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
1140
7 Multiple Hydrogen Transfers in Enzyme Action Table 7.1.
Enzyme catalyzed racemization/epimerization.
Enzyme
Cofactor
Intermediates
Activated/ Unactivated substrate
alanine racemase; serine racemase; amino acid racemase of broad substrate specificity
PLP
cofactor-stabilized carbanion
activated
proline racemase; glutamate racemase; aspartate racemase; diaminopimelate (DAP) epimerase
none
carbanion
phenylalanine racemase; actinomycin synthetase II (ACMSII); d-l-(aaminoadipoyl)-l-cysteinyl-dvaline (ACV)
PAN
enzyme-bound thioester
mandelate racemase; Nacylaminoacid racemase
divalent metal (Mg 2þ , Mn 2þ , Co 2þ , Ni 2þ , Fe 2þ )
metal stabilizedenolate
d-ribulose-5-phosphate 3-epimerase
none
ene-diol
dTDP-l-rhamnose synthase (epimerase component)
none
two sequential enol intermediates
methylmalonyl-coenzyme-A epimerase
divalent metal ðCo 2þ > Mn 2þ > Ni 2þ Þ
metal-bound enolate
UDP-galactose-4-epimerase
NADH
keto-intermediate
UDP-N-acetylglucosamine2-epimerase
none
possible oxonium intermediate
l-ribulose 5-phosphate 4-epimerase
divalent metal ðMn 2þ > Ni 2þ > Ca 2þ > Zn 2þ Þ
glycoaldehyde phosphate þ metalbound enolate; retroaldol CaC bond cleavage
unactivated
an ‘‘external aldimine’’ intermediate (Fig. 7.1), which acidifies the Ca proton via resonance delocalization of negative charge in the resulting carbanionic intermediate [3]. Reprotonation of the carbanionic intermediate yields the antipodal aldimine. The deprotonation/reprotonation mechanism of alanine racemase is sup-
7.2 Cofactor-Dependent with Activated Substrates
Figure 7.1.
PLP external aldimine.
ported by the presence of solvent hydron at the Ca position of the racemized product [4]. A racemase (or epimerase) employing the deprotonation/reprotonation mechanism must be able to abstract a proton from one stereoisomer and reprotonate the other face of the ensuing carbanionic intermediate. This can either be accomplished by a ‘‘two-base’’ or ‘‘one-base’’ mechanism (Fig. 7.2). In the former, two bases flank Ca in the enzyme active site. In this case, the first base abstracts the Ca proton, while the conjugate acid of the second base donates a solvent-derived proton to Ca, generating the isomeric product. The reverse reaction is initiated by the second base abstracting the Ca proton, followed by the conjugate acid of the
Figure 7.2. A one-base versus a two-base mechanism for deprotonation/reprotonation with a planar carbanionic intermediate. In a one-base mechanism, either the catalytic base
or the substrate must reposition after the initial deprotonation, such that the opposite face of the substrate is reprotonated.
1141
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7 Multiple Hydrogen Transfers in Enzyme Action
first base donating a solvent-derived proton. Alternatively, a one-base mechanism (Fig. 7.2) can, in principle, be operative, with a single active site base abstracting the Ca proton, followed by rotation of either the intermediate or the base catalyst, and subsequent reprotonation (also referred to as the ‘‘swinging door’’ mechanism) [5]. A frequently investigated characteristic of epimerases and racemases is the degree to which they exchange solvent hydron at the Ca position (e.g., racemization of [ 1 H]-substrates in D2 O solutions). The pattern of isotopic incorporation in the product and substrate is often used to assign a two-base mechanism (or eliminate a one-base mechanism) [6–10]. A classic two-base mechanism is consistent with solvent-derived (i.e., isotopic) hydron incorporated into the product, and an absence of solvent-derived hydron in the remaining substrate pool at low conversions. However, in the intuitively unlikely, but theoretically possible, event that hydron exchange occurs between the two bases, ‘‘internal return’’ of the abstracted hydron into the Ca position of the product could occur. Although improbable, such a scenario would yield an ambiguous isotopic exchange pattern. In the classic interpretation of the one-base mechanism, deprotonation and reprotonation are thought to occur in identical environments, yielding identical isotopic incorporation patterns in the substrate and product [5]. A more realistic description of the one-base mechanism would involve base migration to the opposite face of the planar intermediate after deprotonation, such that reprotonation may occur in a distinctly different microenvironment, effectively giving a two-base mechanism as far as hydron exchange is concerned. In short, isotopic incorporation patterns are not sufficient for the absolute diagnosis of one- versus two-base mechanisms, but can be highly suggestive of one or the other. Alanine racemase has been found to have an asymmetry with regard to the rates of Ca proton exchange relative to racemization, with a smaller conversion/ exchange ratio in the d ! l than in the l ! d direction [11]. This is consistent with a two-base mechanism in which the two bases are in different environments. However, as noted above, this is also consistent with a one-base mechanism, in which the single base reacts from two distinct environments. Furthermore, polyprotic bases such as lysine will exchange with solvent hydron more rapidly than monoprotic bases, which also contributes to the conversion/exchange asymmetry. Asymmetry was also exhibited with regard to the substrate kinetic isotope effects (KIEs) [11, 12]. Note that this asymmetry does not apply to the magnitude of the kcat =KM values themselves, which must be equivalent according to the Haldane relationship (i.e., the equilibrium constant for any racemase is equal to one). Another measure of the asymmetric kinetic properties of the two bases in the alanine racemase mechanism is the qualitative behavior of the equilibrium ‘‘overshoots’’ observed. Overshoots are often observed in reaction progress curves run in deuterium oxide that are initiated with a single stereoisomer that is protiated at the Ca position (Fig. 7.3). The optical activity is monitored by polarimetry or circular dichroism (CD). At equilibrium, the signal is zero, since the product is a racemic mixture of d- and l-isomers. However, when there is a significant substrate-derived KIE on the reverse direction (product being fully deuterated in a two-base mecha-
7.2 Cofactor-Dependent with Activated Substrates
Figure 7.3. Racemization progress curves for protiated d- and l-alanine in a D2 O solution. The progress curve for the l isomer, but not the d isomer, shows an ‘‘overshoot’’ of the stereoisomeric equilibrium (i.e., CD ¼ 0). (Reproduced with permission, 8 2004 American Chemical Society.)
nism), the progress curve overshoots the initial point at which there is an equal concentration of stereocenters if the remaining substrate pool retains a substantial amount of protium at Ca. This is because the system is not at ‘‘isotopic’’ equilibrium (i.e., there is still protium-containing substrate, but all of the product is deuterated). This causes the reverse (deuterated) direction to be slower than the forward (protiated) direction, until all of the protium is washed out of the substrate, resulting in a transient excess accumulation of the deuterated product, i.e. an overshoot. The progress curve asymptotically returns to the zero point as the substrate protium is washed out, and both forward and reverse directions have an equivalent rate. The overshoot phenomenon was first characterized by Cardinale and Abels for proline racemase [13]. Progress curves for B. stearothermophilus alanine racemase catalyzed [ 1 H]-Ala racemization/washout in both directions are shown in Fig. 7.3 [14]. The l ! d direction exhibits a clear overshoot, while there is no detectable overshoot in the d ! l direction. This is in accordance with the smaller conversion/exchange ratio seen in the d ! l direction [11]. Several B. stearothermophilus alanine racemase crystal structures support the asymmetric two-base model [15–17]. The crystal structure of the alanine phosphonate external aldimine suggests that the Tyr265 hydroxyl group, from the adjacent monomer of a homodimer, is one of the catalytic bases (Fig. 7.4) [17]. The other base is thought to be Lys39, which forms the internal aldimine with the PLP cofactor [18]. These two residues are completely conserved in all known alanine racemases. Lys39 is proposed to abstract the Ca proton in the d ! l direction, while the Tyr265 would act as the base in the l ! d direction (Fig. 7.5) [12, 18– 20]. This agrees with both the asymmetry in the overshoots and in the isotopic
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7 Multiple Hydrogen Transfers in Enzyme Action
Figure 7.4. Active site of the B. stearothermophilus crystal structure with d-alanine phosphonate PLP-aldimine [17]. All distances are in A˚.
conversion/exchange ratios. Table 7.2 compares a number of different epimerases and racemases with regard to the identity of their two bases and the symmetry of their overshoots. Site-directed mutagenesis studies by Esaki and coworkers established that Lys39 acts as a base in the d ! l direction and an acid in the l ! d direction, while Tyr265 acts as a base in the l ! d direction and an acid in the d ! l direction
Figure 7.5. Racemization of l- to d-alanine by alanine racemase. (Reproduced with permission, 8 2004 American Chemical Society.)
7.2 Cofactor-Dependent with Activated Substrates Table 7.2.
Permutations of the two-base mechanism for racemization/epimerization.
Enzyme
Base 1
Base 2
Overshoots
mandelate racemase alanine racemase proline racemase; aspartate racemase glutamate racemase DAP-epimerase b N-acylamino acid racemase methylmalonyl CoA racemase c ribulose 5-phosphate 3-epimerase c
His Tyr Cys[a] Cys Cys Lys Glu Asp
Lys Lys Cys[a] Cys Cys Lys Glu Asp
asymmetric asymmetric symmetric symmetric yasymmetric ? ? ?
a Identical
cysteine residues from homodimer. b Double overshoot in the d,l ! l,l direction; single overshoot in l,l ! d,l direction. c Based on crystal structure.
[18–20]. The B. stearothermophilus K39A mutant had no detectible activity, but addition of methylamine restored approximately 0.1% of the wild-type activity [18]. Furthermore, the mutant exhibited an increase in the D ðVÞ substrate-derived KIE value (in the reaction rescued by methylamine) when [ 2 H]-D-Ala was used as substrate, but not when [ 2 H]-L-Ala was used, while only the l ! d direction yielded an increase in the D2O ðVÞ. The Y265A mutant had about 0.01% of the racemization activity of the wild-type [19]. Esaki and coworkers hypothesized that the identity of the base involved in racemization and transamination (a side reaction), in the l ! d direction, is the same. Accordingly, the Y265A mutant completely lacked transamination activity in the l ! d direction only. The apo-Y265A mutant also exhibited the ability to abstract stereospecifically tritium from the Risomer of 4 0 -[ 3 H]-PMP in the presence of pyruvate, in contrast to the apo-wildtype enzyme, which abstracts hydron nonspecifically from both (R)- and (S)-[ 3 H]PMP. The active site from the alanine phosphonate crystal structure (Fig. 7.4) shows the pyridine ring nitrogen of PLP hydrogen bonded to the highly conserved Arg219 [17]. This interaction with Arg219 prohibits protonation of the pyridine nitrogen, thereby preventing full utilization of the ‘‘electron sink’’ potential of the pyridine ring. This suggests that a fully stabilized quinonoid intermediate is not employed in the mechanism of alanine racemases. In fact, no quinonoid intermediate can be detected spectroscopically in the wild-type enzyme [14, 21]. However, replacement of Arg219 with a glutamate via site-directed mutagenesis resulted in a spectroscopically detectable quinonoid intermedate in the mutant enzyme, which suffered a drop in activity of three orders of magnitude [12]. The absence of a detectable quinonoid intermediate and the site-directed mutagenesis studies on Arg219 suggested that the alanine racemase mechanism might
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7 Multiple Hydrogen Transfers in Enzyme Action
Figure 7.6. Multiple hydrogen kinetic isotope effects used to diagnose a concerted versus stepwise mechanisms.
proceed via a concerted double proton transfer. Multiple kinetic isotope effects (MKIEs) are the method of choice for discerning stepwise versus concerted mechanisms [22]. For example, consider the free energy profile for a stepwise double proton transfer. There are two internal free energy barriers, one for abstraction of a substrate-derived proton and the other for donation of the solvent-derived proton. One may monitor, for example, a substrate KIE in one direction in the presence and absence of deuterated solvent. For systems exhibiting normal KIEs, the presence of isotope in the solvent will increase the energy barrier for Ca reprotonation, causing it to become more rate-determining. This results in a reduction in the observed substrate KIE (Fig. 7.6). Alternatively, a concerted mechanism has only a single internal barrier for both isotopically sensitive atom transfers (Fig. 7.6). Thus, introduction of deuterium at the solvent exchangeable position would either increase the expression of the substrate isotope effect if other steps are partially rate-determining, or result in no change if the isotopically sensitive step is fully rate-determining. The equations that describe the expression of MKIE values have been reviewed by O’Leary [22]. A method for obtaining very precise multiple hydrogen kinetic isotope effects was developed in order to determine whether alanine racemase catalyzes a concerted or a stepwise process [21]. The method employs an equilibrium perturbation-type
7.2 Cofactor-Dependent with Activated Substrates
analysis to deduce the substrate KIE in H2 O and in D2 O, thus enabling the MKIE to be determined. Cleland and coworkers first reported the equilibrium perturbation technique, which involves adding enzyme to an equilibrium mixture of substrate and product with only one of these being isotopically labeled [23]. Equilibrium perturbations are typically monitored with an optical spectroscopy. For normal isotope effects, the direction containing the heavy isotope will react more slowly than the opposite direction, producing a transient perturbation in the optical signal due to the transient accumulation of the slower reactant (i.e., the same phenomenon as the equilibrium overshoots described earlier). Cleland and coworkers derived the equations for extracting the D ðV=KÞ KIE values from the magnitude of the mole fraction of the perturbation [23]. However, the case for a twobase mechanism, as described for alanine racemase, is more complicated due to the irreversible loss of substrate hydron into the solvent pool. Bahnson and Andersen derived an expression for obtaining substrate KIE values from equilibrium perturbation-type deuteron washout traces, which was applied to the case of the crotonase-catalyzed dehydration of 3-hydroxybutyrylpantetheine [24]. The entire scheme for a deuterium washout equilibrium perturbation is described in Fig. 7.7A. The two reactants initially present are boxed. The starting substrates for the perturbation are [ 2 H]-D-Ala (lower manifold) and [ 1 H]-L-Ala (upper manifold). All hydrons on the upper manifold are considered to have the same identity as solvent. An equilibrium perturbation-type washout of the [ 2 H]-D-Ala in H2 O proceeds by abstraction of Ca deuteron by a protiated enzyme (lower manifold), followed by donation of a proton, to yield the protiated l-isomer. The enzyme rapidly and irreversibly exchanges the deuteron for proton, moving from the lower to the upper manifold. The contemporaneous racemization of the l-isomer on the upper manifold occurs more rapidly than the racemization from the lower manifold. This transient accumulation of the slower species (in this case d-isomer) produces the perturbation in the optical signal, from which D ðV=KÞ for the d ! l direction may be determined. The combination of stereoismers needed to obtain the D ðV=KÞ value for the d ! l direction with the solvent exchangeable site being deuterated is not immediately obvious. After considerable thought, it was determined that it is necessary to perform a perturbation starting with [ 1 H]-D-Ala and [ 2 H]-L-Ala in D2 O [21]. A complete protium washout in D2 O is described in Fig. 7.7B. The lower (washout) manifold is now faster than the upper (solvent) manifold, resulting in a transient accumulation of the [ 2 H]-L-Ala, instead of the isomer on the washout manifold. This yields a perturbation of the opposite direction (relative to the deuterium washout perturbation), with a magnitude that can be used to calculate D ðV=KÞD2O (Fig. 7.8). The D ðV=KÞH2O and D ðV=KÞD2O values allow one to determine if the double proton transfer takes place in a concerted or stepwise mechanism, as described above. There was a significant reduction in the D ðV=KÞD2O value, relative to the D ðV=KÞH2O value, which is only consistent with a stepwise mechanism. A recent global kinetic analysis of racemization progress curves for alanine racemase allowed the definition of the enzymatic free energy profile (Fig. 7.9) [14]. Nu-
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7 Multiple Hydrogen Transfers in Enzyme Action
Figure 7.7. Schematic representation of a Dhydron washout perturbation. The upper panel describes the washout of deuterated d-alanine in H2 O (equal starting concentrations of [ 2 H]d-alanine and [ 1 H]-l-alanine). Upon initiation of the perturbation, [ 2 H]-d-alanine–enzyme complex (lower manifold) and the [ 1 H]-lalanine–enzyme complex (upper manifold) dominate, with transient accumulation of the former, due to its slower racemization. Upon racemization of the [ 2 H]-d-alanine–enzyme complex, the deuteron is washed out into the solvent pool. At equilibrium only the upper manifold exists, in which forward and reverse racemization rates are equivalent. The
substrate-derived KIE is obtained from the difference in rates between the racemization of the [ 2 H]- and [ 1 H]-d-alanine–enzyme complexes. The same logic may be extrapolated to the washout of a proton in an all deuterated system. The lower panel describes the washout of a protiated d-alanine in D2 O (equal starting concentrations of [ 1 H]d-alaine and [ 2 H]-l-alanine). One may obtain a multiple kinetic isotope effect by comparing the magnitudes of the KIEs from the H2 O and D2 O perturbations (i.e., the effect of solvent on the substrate derived KIE). (Reproduced with permission, 8 2003 American Chemical Society.)
7.2 Cofactor-Dependent with Activated Substrates
Figure 7.8. Equilibrium perturbation-type washout experiments. The isotopic compositions of the reactants are indicated. At 25 C, H2 O solutions were pH 8.48 and D2 O
solutions were pD 8.90, which gives enzyme in the same ionic state. (Reproduced with permission, 8 2003 American Chemical Society.)
merical integration was used to simulate progress curves that correspond to the stepwise double proton transfer catalyzed by alanine racemase. Nonlinear regression was then used in global fits that reduced the mean square of the difference between the simulated and observed progress curves (Fig. 7.10). A series of global
Figure 7.9. Free energy profile obtained from global analysis of racemization progress curves at pH 8.9. Standard state is 5 mM alanine. The double arrow represents the region of uncertainty for the quinonoid intermediate,
which extends to a lower limit of approximately 4 kcal mol1 . All other ground and transition state energies have uncertainties of less than 0.06 kcal mol1 . (Reproduced with permission, 8 2004 American Chemical Society.)
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7 Multiple Hydrogen Transfers in Enzyme Action
Figure 7.10. Global fit of a stepwise double proton transfer model to racemization progress curves at pH 8.9. Dashed lines, experimental data; solid lines, fitted curves. Positive and negative CD signals correspond to l- and d-alanine, respectively. Alanine
concentrations range from 0.2 to 22 mM, yielding 17 progress curves, providing information about the enzyme in the unsaturated and saturated states. (Reproduced with permission, 8 2004 American Chemical Society.)
fits commenced from randomized sets of rate constants. The microscopic rate constants from the global fits were used to calculate the steady-state parameters, which were in good agreement with the experimental values. The free-energy profile was also consistent with viscosity variation studies, KIE values and overshoots. The two internal proton transfer steps are mostly rate-determining (88%) at the pH optimum (8.9). The asymmetry between the two internal barriers is expected, based on the larger substrate KIE and overshoot in the l ! d direction. Further underscoring this asymmetry, the microscopic rate constants from the global analysis were used to simulate overshoot progress curves (Fig. 7.11), which were consistent with the experimental overshoots [14]. Another interesting feature of the alanine racemase free energy profiles is the relatively high energy of the resonance-stabilized carbanionic intermediate. The precise energy of the intermediate could not be determined, due to the small contribution to the overall rate of the two rate constants leading away from it. However, the global analysis was able to show that it lies >4 kcal mol1 higher in energy than the flanking aldimine intermediates. The high energy of the carbanionic intermediate contributes to the poor catalytic efficiency of alanine racemase (having an efficiency factor, E f , of about 1 103 , where unity represents a ‘‘perfect’’ enzyme) [25]. Although catalytically inefficient, this high energy intermediate may prevent unwanted side reactions, and thus contribute to enhanced racemization fidelity.
7.2 Cofactor-Dependent with Activated Substrates
Simulated progress curves of protiated l- and dalanine in D2 O, using rate constants obtained from the global fits in Fig. 7.10, and the published substrate derived D ðV=KÞ values. An overshoot occurs in the l ! d direction only, as in the experimental overshoots shown in Fig. 7.3. Figure 7.11.
7.2.2
Broad Specificity Amino Acid Racemase
The ‘‘amino acid racemase of broad substrate specificity’’ is an alanine racemaselike enzyme that has, as the name implies, the ability to racemize a number of amino acids (Lys > Arg > Met > Leu > Ala > Ser), preferring positively charged side chains, and having no detectable activity with aromatic or negatively charged amino acids [26, 27]. It is a PLP-dependent homodimer, derived from a number of organisms: Pseudomonas putida (previously known as Pseudomonas striata, but reclassified to P. putida [28]; Pseudomonas taetrolens and Aeromonas caviae [29]. The P. putida genome sequence was recently published [30]. The P. putida racemase has 23% sequence identity with that from B. stearothermophilus (unpublished observation), retaining the two catalytic bases and the arginine that hydrogen bonds to the pyridine ring nitrogen. A salient difference between the broad substrate specificity racemase and most alanine racemases is the absence of a tyrosine (Tyr354, in the B. stearothermophilus), which partially controls access to the active site. In the broad substrate specificity racemase from P. putida, the enzyme has an alanine at this position. The importance of this residue to substrate specificity was further illustrated by site-directed mutagenesis studies on B. stearothermophilus, in which a
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7 Multiple Hydrogen Transfers in Enzyme Action
Y354A mutant was shown to have significantly enhanced serine racemase activity [31]. Although the sequence alignments suggest that these amino acid racemases employ a two-base mechanism, there are conflicting isotope incorporation data. Internal transfer of labeled Ca proton was detected in the d ! l direction of the P. putida enzyme, employing alanine as the substrate, which is difficult to reconcile with a two-base mechanism [9]. However, later studies measuring the rates of solvent incorporation into the substrate and product pools of each enantiomer of methionine showed an asymmetry, which is more difficult to explain with a one-base mechanism [32]. However, a one-base mechanism cannot entirely be eliminated, since the two faces of the carbanion may be exposed to significantly different protein environments. It may be that the mechanism changes between one and two bases as the structure of the substrate changes. One could imagine that a substrate that is not very tightly bound and thus able to rotate easily might default to a onebase mechanism while one that is tightly bound might be unable to rotate and require a two-base mechanism. 7.2.3
Serine Racemase
The presence of d-serine in mammalian brain tissue was first reported in 1989 [33, 34]. It has recently been established that d-serine is employed in the mammalian forebrain as a co-agonist for the N-methyl-d-asparate (NMDA) excitatory amino acid receptor [35, 36]. A PLP-dependent serine racemase has been cloned and purified from mammalian brain, and found to be a homodimer, which has a number of nonessential cofactors that enhance its activity, including Ca 2þ , Mg 2þ and ATP [37–40]. The mouse brain enzyme has also been shown to catalyze elimination from l-serine, to form pyruvate, with an activity comparable to that for racemization [41]. Interestingly, the first instance of this class of racemase was discovered by Esaki and coworkers in the silkworm, Bombyx mori [42]. d-serine concentration in the blood of B. mori larvae is thought to play a role in metamorphosis. 7.2.4
Mandelate Racemase
The mechanism of madelate racemase is very thoroughly characterized. The reaction catalyzed, stereoinversion of (S)- and (R)-mandelate, is shown in Fig. 7.12. The enzyme employs a metal cofactor (preferably Mg 2þ , but also accepting Mn 2þ , Co 2þ , Ni 2þ , and Fe 2þ ) [43, 44], as indicated in Table 7.1, and exhibits a high structural homology with the muconate lactonizing enzyme, which also employs a metal cofactor [45–47]. Both of these enzymes are members of an emerging class of enzymes, the ‘‘vicinal oxygen chelate’’ (VOC) superfamily, which includes methylmalonyl CoA epimerase and N-acylamino acid racemase (Table 7.1) [48–50]. The metal binding site of enzymes in the VOC superfamily is located at a conserved site within a TIM barrel, in which Mg 2þ and Mn 2þ are typically the preferred
7.2 Cofactor-Dependent with Activated Substrates
Mechanism for the stereoinversion of (S)- to (R)-mandelate catalyzed by mandelate racemase [10].
Figure 7.12.
metals. The crystal structure of the complex of the K166R mutant (Lys166 is one of the catalytic bases) madelate racemase with (R)-mandelate bound in the active site shows that the metal cofactor is bound to both an oxygen from the carboxylate and to the Ca hydroxyl (Fig. 7.13) [51]. Early studies on madelate racemase demonstrated that the substrate Ca proton fully exchanges with D2 O solvent during racemization, and that the proton abstrac-
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7 Multiple Hydrogen Transfers in Enzyme Action
Figure 7.13. Active site of the K166R mutant of mandelate racemase from the crystal structure of the Michaelis complex with (R)-mandelate. All distances are in A˚ [51].
tion is partially rate-determining, in both directions [8]. Also, linear free energy relationships were demonstrated by substitution of electron withdrawing substituents on the phenyl ring of the substrate [52]. These gave the expected result that stabilization of the Ca carbanion leads to a more efficient substrate. Further studies yielded an isotope exchange pattern for both directions that is consistent with a two-base mechanism [10]. The crystal structure indicated that the two likely bases flanking the Ca carbon are Lys166 and His297 (Fig. 7.13) [46, 51]. From the active site architecture, it is thought that Lys164 plays an important role in lowering the pKa (@4 units) of Lys166, such that it is present in the catalytically active basic form at physiological pH [53]. Similarly, the second catalytic base, His297 is hydrogen bonded to Asp270, which may act to increase its pKa . This asymmetry with respect to the catalytic bases in mandelate racemase is formally analogous to alanine racemase, and indeed the overshoots with mandelate racemase are highly asymmetric as with alanine racemase (Table 7.2) [10]. The ðSÞ ! ðRÞ direction exhibits a much smaller overshoot than the ðRÞ ! ðSÞ direction, and shows significant exchange of solvent deuteron into the substrate pool even when the extent of racemization is low. The ðRÞ ! ðSÞ direction shows much less exchange of deuterium into the substrate pool. 7.2.5
ATP-Dependent Racemases
Many peptide-based antibiotics contain d-amino acids. d-phenylalanine is a component of gramacidin S, and is produced by phenylalanine racemase, which is a
7.2 Cofactor-Dependent with Activated Substrates
member of a family of ATP-dependent racemases and epimerases that also require the 4 0 -phosphopantethein (PAN) cofactor for activity (Table 7.1) [54, 55]. Adenylation is used to activate the amino acid for transfer to the thiol group of PAN, yielding a thioester with an acidified Ca proton [56, 57]. The stereoinversion is catalyzed directly on the thioesterified substrate, producing an equilibrated mixture of the enantiomers. The overall reaction (Fig. 7.14) is referred to as a ‘‘thiol-template’’ mechanism [54]. The coupling to ATP produces an overall reaction that is irreversible. Interestingly, reactions initiated with ATP and a single stereoisomer result in
Figure 7.14. The thiol template mechanism for the stereoinversion of l- to d-phenylalanine catalyzed by phenylalanine racemase [54].
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7 Multiple Hydrogen Transfers in Enzyme Action
4:1 (d:l) mixtures of stereoisomers that are determined by the different rates of hydrolysis of the thioester intermediates [56, 57]. The thiol-template mechanism is utilized in other enzymes involved in production of peptide-based antibiotics. Actinomycin synthetase II (ACMSII) and d-l-(aaminoadipolyl)-l-cysteinyl-d-valine (ACV) synthetase catalyze the stereoinversion of valine residues within peptide-based antibiotics, and employ ATP and the PAN cofactor in a mechanism similar to that depicted in Fig. 7.14 [58, 59]. ACMSII catalyzes the stereoinversion of a valine within the tripeptide 4-MHA-l-Thr-d-Val (MHA, 4-methyl-3-hydroxyanthranilic acid), which is a precursor for the antibiotic actinomycin D. ACV synthetase catalyzes the stereoinversion of the valine within ACV, which is a precursor for penicillin and cephalosporin [60–63]. ACV synthetase has been shown to have much broader substrate specificity, also accepting non-natural substrates [64, 65]. A number of epimerases act at carbon centers that are a to thioester linkages with coenzyme-A (CoA). These enzymes are similar to mandelate racemase, in that they employ a metal cofactor (Table 7.1), which is thought to stabilize an enolate intermediate. They also belong to the VOC superfamily of enzymes, whose members all involve proton abstraction, proton transfer and metal cofactors that stabilize anionic intermediates [48–50]. 7.2.6
Methylmalonyl-CoA Epimerase
In animals, the breakdown of lipids involves conversion of propionyl-CoA to succinyl-CoA. Methylmalonyl-CoA is a metabolic intermediate in this process. In vivo, it is necessary to convert the 2-(S)-form of methylmalonyl-CoA to the 2-(R)form, for reaction with methylmalonyl-CoA mutase. This reaction is catalyzed by methylmalonyl-CoA epimerase (MMCE) [4, 66–68]. Methylmalonate is also employed in polyketide antibiotic biosynthesis, in the form of methylmalonate units, although less is known about the stereochemical requirements of these processes [69, 70]. MMCE is found in both animals and bacteria [67, 71]. The best characterized MMCE is from Propionibacterium shermanii, whose crystal structure with the Co 2þ cofactor has been published [72, 73]. Modeling of the 2-methylmalonate substrate into the active site of the crystal structure shows that the Ca of the 2-(R)-epimer is @3 A˚ from Glu48, while the 2-(S)-epimer is @3 A˚ from Glu141. It is possible that these two residues are the catalytic bases employed in the stereoinversion. Early studies using 2-(R)-[ 3 H]-methylmalonlyl-CoA as the substrate showed total washout of the label in the product [74, 75]. A similar experiment using unlabeled 2(R)-epimer in tritiated water showed no return of label into the substrate pool. This provides strong evidence for, but not definitive proof of, a two-base mechanism. In the event that a similar result is obtained for the 2ðSÞ ! 2ðRÞ direction, a one-base mechanism would be highly unlikely. The lack of internal return of substrate-derived hydron, in both directions, can only be explained by rapid exchange of the abstracted hydron with environmental solvent. However, rapid
7.4 Cofactor-Independent with Activated Substrates
exchange of hydron is not consistent with the observation that there is no incorporation of solvent hydron into the substrate pool.
7.3
Cofactor-Dependent with Unactivated Substrates
Some epimerases act on substrates that are not activated (i.e., carbon centers not adjacent to carbonyls or carboxylates). This may be achieved by creating a transiently activated species, which is the actual target for stereoinversion. This is the strategy used by a number of NADH/NADþ -dependent sugar epimerases. These may be further subdivided into enzymes that transiently oxidize the hydroxyl on the carbon adjacent to the stereogenic center, and those enzymes that transiently oxidize the stereogenic center itself. In the former case, the stereogenic center is activated for a 1,1-proton transfer, which precedes reduction of the keto-intemediate, to yield the epimeric product. In the latter case, a 1,1-hydride transfer directly results in epimerization about the stereogenic center. Figure 7.15 illustrates these two pathways. UDP-galactose 4-epimerase utilizes the 1,1-hydride transfer route for sugar epimerization, yielding a 4-hexose intermediate [76]. The ketohexose intermediate is produced by hydride transfer from C-4 to the B-face of the nicotinamide ring. The ketohexose then moves such that the opposite face of the keto group is reduced by NADH, yielding the antipodal enantiomer (Fig. 7.15). This is formally analogous to Henderson and Johnston’s ‘‘swinging door’’ one-base mechanism for 1,1 proton transfer [5], which has yet to be definitively demonstrated in a racemase. Another group of sugar epimerases, which uses a metal cofactor instead of NADH/NADþ , takes an entirely different approach to epimerization. l-ribulose 5phosphate 4-epimerase, which is involved in the bacterial metabolism of arabinose, performs a retro-aldol cleavage of a CaC bond to yield a metal-stabilized enolate of dihydroxyacetone and glycoaldehyde phosphate, similar to the reaction catalyzed by class II aldolases [77–79]. The glycoaldehyde phosphate is thought to rotate, such that addition of the enolate generates the isomeric product.
7.4
Cofactor-Independent with Activated Substrates 7.4.1
Proline Racemase
Proline racemase is a member of a broad family of cofactor-independent epimerases and racemases, and has been very well characterized mechanistically. The proline racemase from Clostridium sticklandii was the first of the cofactor-independent racemases to be characterized [13, 80]. The enzyme participates in the catabolism of l-proline, producing d-proline as a substrate for d-proline oxidase [4]. Early
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7 Multiple Hydrogen Transfers in Enzyme Action
Figure 7.15. Two possible pathways for the stereoinversion of sugars by sugar epimerases utilizing the NADH/NADþ cofactor.
studies showed that both directions fully incorporate isotopic label in the product, with no label returning to the substrate pool [13]. This is strongly suggestive of a two-base mechanism with a planar carbanionic intermediate. Investigations on deuterium incorporation and primary KIE values led Cardinale and Ables to ob-
7.4 Cofactor-Independent with Activated Substrates
serve the first overshoot phenomenon (discussed above) [13]. The enzyme is a homodimer, in which the same cysteine from each monomer contributes to a single active site [80]. This is qualitatively different than the other cofactor-independent racemases (glutamate racemase and aspartate racemase) and epimerases (DAPepimerase), which are monomers with pseudo-symmetry (i.e., the Cys active site bases are not at identical positions in two different subunits). This symmetry of proline racemase catalytic bases leads to a symmetry in the overshoots (Table 7.2) and KIE values. Global amino acid sequence alignments indicate that proline racemase is in a distinctly different protein family than aspartate/glutamate racemase (unpublished observation using the Pfam database [81]). The enzyme exists in two different protonation states of the active site cysteines, each binding a different enantiomer. Conversion between enantiomers can be through the racemization path (upper manifold of Fig. 7.16) or through direct proton exchange with water (lower manifold of Fig. 7.16). Knowles and coworkers found that interconversion of enzyme protonation states was kinetically significant [82]. This was determined by measuring rates of tritiated proline washout as a function of the proline concentration. It was found that higher concentrations of proline promote slower washout of the Ca proton. Additional support for the rela-
Figure 7.16. Mechanism for the stereoinversion of l- to dproline catalyzed by proline racemase (upper manifold) and water catalyzed proton exchange of the free enzyme (lower manifold).
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7 Multiple Hydrogen Transfers in Enzyme Action
tively slow interconversion of the two protonation states was provided by conceptually similar experiments in which ‘‘oversaturation’’ by substrate was observed. Thus, product release is followed by relatively slow interconversion of the ‘‘substrate’’ and ‘‘product’’ protonation states, which Northrop has termed an ‘‘isomechanism’’ [83]. The free energy profile for proline racemase, including the energetic barriers for interconversion of the enzyme protonation states, was described in a series of papers by Knowles and coworkers in 1986 [82, 84–88]. A ‘‘tracer-perturbation’’ experiment was employed to estimate the energy barriers for the proton exchange [84]. This is performed by adding an excess of unlabeled l-proline to an equilibrated mixture of [ 14 C]-d,l-proline, promoting the formation of the enzymic form that binds d-proline. The enzyme-d-proline complex releases d-proline and either (i) undergoes proton exchange to convert to the form that binds l-proline, or (ii) binds labeled d-proline and converts it to l-proline. This experiment results in a net flux of label into the l-proline pool since the high concentration of unlabeled l-proline effectively competes against the conversion of labeled l-proline to labeled d-proline. It is the net flux of label into the l-proline pool that allowed Knowles and coworkers to estimate the rate constants for proton exchange between the two enzymic forms (@1 10 5 s1 ). Oversaturation, mentioned above, is another phenomenon resulting from the competition between solvent catalyzed conversion of enzymic forms and the conversion via substrate racemization [82]. A consequence of this competition is that the net rate of racemization decreases, under reversible conditions, as the concentration of a proline increases. The loss of productivity in the racemization manifold is due to the product form of the enzyme binding substrate, and the substrate form of the enzyme binding product (i.e., substrate inhibition). Knowles and coworkers also performed ‘‘competitive deuterium washouts’’ (i.e., an equilibrium perturbation-type washout experiments), using deuterated substrates in H2 O solutions, which yielded the D ðV=KÞ values for both directions [85]. Further confirmation of these KIE values was validated by a ‘‘double competitive deuterium washout’’ experiment, in which both substrates are Ca deuterated, which yielded a ratio of the two D ðV=KÞ values. The authors were also able to perform competitive deuterium washout experiments where direct proton exchange between free enzyme forms is rate-limiting (i.e., at high substrate concentration the lower manifold of Fig. 7.16 is dominant). This experiment indicated that interconversion of free enzyme forms is very similar to the racemization manifold, in that loss of proton from one form yields the other free enzyme form, with water acting as the catalyst, Fig. 7.16. Isotope discrimination studies were employed to deduce if the double proton transfer of proline racemase is concerted or stepwise [88]. Isotope discrimination is an alternative manifestation of the multiple kinetic isotope effect techniques previously discussed, wherein racemization is conducted in mixed isotopic solvents of H2 O and D2 O and the discrimination in the incorporation of solvent deuterium is measured. If the double proton transfer is stepwise, deuteration of the substrate
7.4 Cofactor-Independent with Activated Substrates
causes the solvent incorporation step to be less rate-determining, resulting in a decrease in the isotope effect (i.e., a decrease in discrimination). For a concerted mechanism, deuteration of the substrate position would not affect the solvent incorporation, resulting in no change in the isotope effect (i.e., no change in discrimination). In conjunction with other studies, the isotope discrimination studies led Knowles and coworkers to favor a stepwise mechanism in proline racemase. 7.4.2
Glutamate Racemase
d-Glutamate, like d-alanine, is a constituent of the peptidoglycan layer of bacterial cell walls [1, 2]. Glutamate racemase is a member of the cofactor-independent family of epimerases and racemases, with high sequence homology to aspartate racemase [89]. The enzyme belongs to the Aspartate/Glutamate Racemase superfamily, with an ATC-like fold, consisting of two similar domains, related by pseudo-dyad symmetry. The enzyme showed no dependence on PLP or metal cofactors, and was shown to be inactivated by thiol-specific and oxidizing reagents [89–92]. In E. coli and Aquifex pyrophilus the enzyme is thought to be a dimer with two active sites, while in Lactobacillus fermenti it is monomeric with a single active site [89, 91, 93]. The crystal structure for glutamate racemase from Aquifex pyrophilus has been determined with d-glutamine bound in the active site [93]. The authors hypothesized that the two catalytic bases are Cys70 and Cys178. However, the Ca of the dglutamine ligand is not positioned for proton abstraction or donation from either of these groups, being @7 A˚ away. The authors hypothesize, based on modeling studies, that the d-glutamine ligand is flipped 180 from the catalytic position assumed by the glutamate substrate. Each cysteine base is within about 4 A˚ of a carboxylate-containing residue (Cys70 is proximal to Asp7, Cys178 is proximal to Glu147) and the D7S and E147N mutants were found to have activity losses between 1 and 2 orders of magnitude relative to wild-type. The role of these acidic residues may be to increase the pKa of the two catalytic cysteines. Isotope incorporation studies show that racemization in D2 O results in Ca deuterium incorporation in the product, from both directions, which is suggestive of a two-base mechanism [94, 95]. The D ðV=KÞ values and overshoots have been determined for both directions [96]. There is significant symmetry in the overshoots (Table 7.2) and KIE values, as one would expect, based on the identity of the catalytic bases. Unlike proline racemase, there is a single active site per monomer. Mutant enzymes lacking either of the two conserved cysteines (Cys to Ala in E. coli, and Cys to Thr in L. fermenti enzyme) residues exhibit a complete loss of activity [96]. Furthermore, mutants lacking one of the catalytic cysteines can eliminate HCl from threo-b-chloroglutamate, with each mutant being specific for one of the stereoisomers [96]. This suggests that the residues are on opposing sides of Ca. Unlike proline racemase, no oversaturation phenomenon was observed, indicating that interconversion of protonation states is kinetically insignificant [95].
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7 Multiple Hydrogen Transfers in Enzyme Action
7.4.3
DAP Epimerase
In addition to d-alanine and d-glutamate, many bacterial cell walls also contain meso-diaminopimelate (DAP) [2]. DAP is produced by epimerization from l,lDAP to d,l-DAP by the cofactor independent diaminopimelate epimerase [97, 98]. The structure of this enzyme has been solved and two cysteines in the active site were proposed to be the acid–base catalysts [99]. The pattern of label incorporation from tritiated water is consistent with a two-base mechanism [97]. The enzyme has been shown to be stoichiometrically inhibited by the thiol alkylating agent aziDAP [97]. Interestingly, DAP epimerase has an equilibrium constant of 2 ðK eq ¼ ½d;l=½l;lÞ due to the statistically expected higher concentration of the [d,l] form at equilibrium between these species [100]. Although both catalytic bases are cysteines, the D ðV=KÞ values for both directions are apparently not identical: 4:3 G 0:7 for the l,l ! d,l direction, and 5:4 G 1:1 for the d,l ! l,l direction [100]. These D ðV=KÞ values have been ascribed to differences in the intrinsic KIE values for abstraction of the Ca protons for the respective directions. The D V values are significantly smaller than the D ðV=KÞ values. Koo and Blanchard suggest this to be the result of a kinetically significant interconversion of the two protonation states, as observed with proline racemase [100]. The D2O ðV=KÞ values for DAP-epimerase are inverse (l,l ! d,l ¼ 0:83 G 0:08, d,l ! l,l ¼ 0:73 G 0:09), which can be ascribed to the low fractionation factor of the thiol groups of the two catalytic bases. However, the D2O V values (l,l ! d,l ¼ 1:8 G 0:1, d,l ! l,l ¼ 1:5 G 0:1) are not inverse. Koo and Blanchard hypothesize that this may be due to a large SIE in the interconversion of the different protonation states of the enzyme. DAP-epimerase yields an unusual overshoot pattern: a normal overshoot is seen in the l,l ! d,l direction, but an unprecedented double-overshoot is seen in the d,l ! l,l direction [100]. A simulation (using the program DynaFit [101]) of the DAP-epimerase double overshoot, based on rate constant values used in simulations by Koo and Blanchard, is shown in Fig. 7.17A. Koo and Blanchard proposed that the double overshoot is due to the fact that two stereocenters undergo exchange, but only one is racemized. The full reaction scheme, as presented by Koo and Blanchard, is illustrated in Fig. 7.18. The d,l-substrate initially reacts faster than the l,l-substrate, and enters an isotopically sensitive branch point. One observes a classic overshoot in both directions due to the fact that the substratederived KIE for the reverse direction results in a transient accumulation of the product (the orthodox source of an overshoot). However, the additional overshoot in the d,l ! l,l direction was attributed to accumulation of [ 2 H]-d,[ 1 H]-l-DAP in the isotopically sensitive branch pathway, which results in a transient accumulation of the d,l-isomer, even though the reaction commenced with [ 1 H]-d,[ 1 H]-lisomer (i.e., in the opposite direction from an orthodox overshoot). Surprisingly, removal of the isotopically sensitive branch point, such that only the bold species in Fig. 7.18 are present, yields an effectively identical simulated double overshoot
7.4 Cofactor-Independent with Activated Substrates
Figure 7.17. A, Simulated double overshoot for DAP-epimerase using the program DynaFit [101] and the rate constant values from Koo and Blanchard [100]. B, Simplified simulated double overshoot, in which the isotopically sensitive branch pathway from Fig. 7.18 is removed.
(Fig. 7.17B). This indicates that the source of the double overshoot phenomenon is simpler than previously thought. Figure 7.19 shows the concentrations of the various isotopic species of DAP during the double overshoot simulation shown in Fig. 7.17B. The peaks of the two overshoots are indicated in Fig. 7.19, demonstrating
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7 Multiple Hydrogen Transfers in Enzyme Action
Figure 7.18. Kinetic scheme for DAP-epimerase, as described in Koo and Blanchard [100], used to generate the simulated overshoot in Fig. 7.17A. The species in bold type represent the simplified overshoot used to generate simulated overshoot in Fig. 7.17B.
that the source of the double overshoot is simply due to sequential transient accumulations of first lH lD and then dD lD , and a lag phase in the formation of lD lD . At the peak of the first overshoot there is an equal concentration of lH lD (positive optical signal) and dH lH /dD lD (no optical signal). The peak of the second overshoot occurs when there is an equal concentration of dD lD and lD lD /lH lD .
Figure 7.19. Concentrations of products, substrates and intermediates from the double overshoot of DAP-epimerase. The time points that correspond to the peaks of the two overshoots of the double overshoot are indicated.
7.5 Cofactor-Independent with Unactivated Substrates
7.4.4
Sugar Epimerases
There are a number of cofactor independent carbohydrate epimerases that act on activated substrates, such as keto-sugars and keto-sugar nucleotides, although there is a paucity of details about their mechanisms. d-ribulose-5-phosphate 3epimerase catalyzes the stereoinversion of substrate about the C-3 carbon to form d-xylulose 5-phosphate (as in Fig. 7.15) [102, 103]. Solvent hydron is completely incorporated into the product at the C-3 carbon, during epimerization in the dxylulose 5-phosphate to d-ribulose 5-phosphate direction [102]. This was taken as evidence for a two-base mechanism. The keto-sugar nucleotide dTDP-l-rhamnose is synthesized from dTDP-4-keto-6deoxy-d-glucose by dTDP-l-rhamnose synthase [104, 105]. The enzyme consists of two components, a cofactor independent epimerase and an NADH-dependent reductase. The epimerase component is inactive without the reductase component. The mechanism involves epimerization of two stereocenters flanking a carbonyl group, via sequential deprotonation/reprotonation, with two enol intermediates. Complete solvent isotope incorporation into both epimerized stereocenters was observed, and primary substrate-derived KIEs have been determined [104].
7.5
Cofactor-Independent with Unactivated Substrates
UDP-N-acetylglucosamine (UDP-GlcNAc) epimerase catalyzes a mechanistically exotic stereoinversion of UDP-GlcNAc to UDP-ManNAc, which is used in the synthesis of some bacterial cell walls [106, 107]. The epimerase has the unusual requirement for a small amount of substrate UDP-GlcNAc for activity (i.e., UDPManNAc and enzyme alone will not react). It is thought that UDP-GlcNAc may bind in a modulating site, separate from the active site [106]. The absence of an activated stereogenic center or a cofactor makes simple deprotonation/reprotonation prohibitively difficult. Solvent hydron incorporation in the target carbon of the product has been observed in both directions [108]. However, 18 O positional isotope exchange studies show evidence of CaO anomeric carbon cleavage during the reaction [109]. The 18 O label became distributed into both the anomeric position and into the pyrophosphate during catalysis, indicating CaO cleavage. This is consistent with a glycal mechanism, as proposed by Sala et al. (Fig. 7.20), in which trans-elimination of UDP yields a 2-acetamidoglucal enzyme-bound intermediate, followed by syn-addition of UDP to generate the isomeric product [109]. Thus, the enzyme avoids the energetically unfavorable E1cb reaction, and proceeds by either an oxonium intermediate E1 or a concerted E2 reaction. Limited kinetic isotope effect studies have been carried out. The value of 1.8 for D ðVÞ in the forward direction indicates that CaH bond cleavage is at least partially rate-determining [109]. The 2-acetamidoglucal intermediate generated by UDP-N-acetylglucosamine 2-
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7 Multiple Hydrogen Transfers in Enzyme Action
Figure 7.20. The glycal mechanism for the conversion of UDP-N-acetylglucosamine (UDP-GlcNAc) to UDP-Nacetylmannosamine (UDP-ManNAc) catalyzed by UDP-GlcNAc epimerase [109].
epimerase is thought to be more stable than the reactants or products. Thus, the enzyme has the unusual challenge of trying to prevent the release of a thermodynamically stable intermediate (relative to the free reactants and products), as opposed to protecting a higher energy intermediate from undesirable side reactions. This is precisely the opposite scenario faced by alanine racemase, which has a highly destabilized carbanionic intermediate, which may serve to enhance the fidelity of its racemization reaction.
7.6
Summary
The stereoinversion of carbon centers catalyzed by racemases and epimerases is an archetypal enzyme catalyzed reaction for studying multiple hydrogen transfers.
References
Epimerases and racemases may or may not employ enzyme cofactors (organic or inorganic) to activate the stereogenic center of the substrate. Common cofactorstabilized intermediates include resonance-stabilized carbanions and metalstabilized enolates. The substrate itself can be intrinsically activated if the stereogenic center is adjacent to a carbonyl or carboxylate group. A preponderance of racemases and epimerases act on activated substrates. A number of sugar and sugar nucleotide epimerases act on unactivated substrates. Double proton transfers may proceed, in principle, by either a one- or two-base mechanism. However, only two-base mechanisms have been observed for racemases.
References 1 Neidhart, F. C. (1999) Escherichia coli
2 3 4 5
6
7
8
9
10
11 12 13 14
15
and Salmonella, 2nd edn., Blackwell Publishing, London. Walsh, C. T. (1989) J. Biol. Chem. 264, 2393–2396. Dixon, J. E., Bruice, T. C. (1973) Biochemistry 12, 4762–4766. Adams, E. (1976) Adv. Enzymol. Relat. Areas. Mol. Biol. 44, 69–138. Henderson, L. L., Johnston, R. B. (1976) Biochem. Biophys. Res. Commun. 68, 793–798. Adams, E., Mukherjee, K. L., Dunathan, H. C. (1974) Arch. Biochem. Biophys. 165, 126–132. Ahmed, S. A., Esaki, N., Tanaka, H., Soda, K. (1986) Biochemistry 25, 385– 388. Kenyon, G. L., Hegeman, G. D. (1979) Adv. Enzymol. Relat. Areas. Mol. Biol. 50, 325–360. Shen, S. J., Floss, H. G., Kumagai, H., Yamaka, H., Esaki, N., Soda, K., Wasserman, S. A., Walsh, C. (1983) J. Chem. Soc., Chem. Commun. 82–83. Powers, V. M., Koo, C. W., Kenyon, G. L., Gerlt, J. A., Kozarich, J. W. (1991) Biochemistry 30, 9255–9263. Faraci, W. S., Walsh, C. T. (1988) Biochemistry 27, 3267–3276. Sun, S. X., Toney, M. D. (1999) Biochemistry 38, 4058–4065. Cardinale, G. J., Abeles, R. H. (1968) Biochemistry 7, 3970–3978. Spies, M. A., Woodward, J. J., Watnik, M. R., Toney, M. D. (2004) J. Am. Chem. Soc. 126, 7464–7475. Watanabe, A., Yoshimura, T.,
16 17
18
19
20
21 22 23
24 25 26
27 28
Mikami, B., Hayashi, H., Kagamiyama, H., Esaki, N. (2002) J. Biol. Chem. 277, 19166–19172. Morollo, A. A., Petsko, G. A., Ringe, D. (1999) Biochemistry 38, 3293–3301. Stamper, C. G. F., Morollo, A. A., Ringe, D. (1998) Biochemistry 37, 10438–10445. Watababe, A., Kurokawa, Y., Yoshimura, T., Kurihara, T., Soda, K., Esaki, N. (1999) J. Biol. Chem. 274, 4189–4194. Watanabe, A., Yoshimura, T., Mikami, B., Esaki, N. (1999) J. Biochem. 126, 781–786. Watanabe, A., Kurokawa, Y., Yoshimura, T., Esaki, N. (1999) J. Biochem. 125, 987–990. Spies, M. A., Toney, M. D. (2003) Biochemistry 42, 5099–5107. O’Leary, M. H. (1989) Annu. Rev. Biochem. 58, 377–401. Schimerlik, M. I., Rife, J. E., Cleland, W. W. (1975) Biochemistry 14, 5347–5354. Bahnson, B. J., Anderson, V. E. (1991) Biochemistry 30, 5894–5906. Albery, W. J., Knowles, J. R. (1976) Biochemistry 15, 5631–5640. Inagaki, K., Tanizawa, K., Tanaka, H., Soda, K. (1984) Progr. Clin. Biol. Res. 144A, 355–63. Soda, K., Osumi, T. (1969) Biochem. Biophys. Res. Commun. 35, 363–368. Buchanan, R. E., Gibbons, N. E. (1974) Bergey’s Manual of Determinative Bacteriology, 8th edn., The Williams and Wilkins Co., Baltimore.
1167
1168
7 Multiple Hydrogen Transfers in Enzyme Action 29 Inagaki, K., Tanizawa, K., Tanaka,
30
31
32
33
34 35
36
37
38
39
40
H., Soda, K. (1987) Agric. Biol. Chem. 51, 173–180. Nelson, K. E., Weinel, C., Paulsen, I. T., Dodson, R. J., Hilbert, H., Martins dos Santos, V. A., Fouts, D. E., Gill, S. R., Pop, M., Holmes, M., Brinkac, L., Beanan, M., DeBoy, R. T., Daugherty, S., Kolonay, J., Madupu, R., Nelson, W., White, O., Peterson, J., Khouri, H., Hance, I., Chris Lee, P., Holtzapple, E., Scanlan, D., Tran, K., Moazzez, A., Utterback, T., Rizzo, M., Lee, K., Kosack, D., Moestl, D., Wedler, H., Lauber, J., Stjepandic, D., Hoheisel, J., Straetz, M., Heim, S., Kiewitz, C., Eisen, J. A., Timmis, K. N., Dusterhoft, A., Tummler, B., Fraser, C. M. (2002) Environ. Microbiol. 4, 799–808. Patrick, W. M., Weisner, J., Blackburn, J. M. (2002) Chembiochem 3, 789–792. Reynolds, K., Martin, J., Shen, S. J., Esaki, N., Soda, K., Floss, H. G. (1991) J. Basic Microbiol. 31, 177–188. Nagata, Y., Konno, R., Yasumura, Y., Akino, T. (1989) Biochem. J. 257, 291–292. Nagata, Y., Akino, T., Ohno, K. (1989) Experientia 45, 330–332. Mothet, J. P., Parent, A. T., Wolosker, H., Brady, R. O., Jr., Linden, D. J., Ferris, C. D., Rogawski, M. A., Snyder, S. H. (2000) Proc. Natl. Acad. Sci. USA 97, 4926–4931. Schell, M. J., Molliver, M. E., Snyder, S. H. (1995) Proc. Natl. Acad. Sci. USA 92, 3948–3952. Cook, S. P., Galve-Roperh, I., Martinez del Pozo, A., RodriguezCrespo, I. (2002) J. Biol. Chem. 277, 27782–27792. De Miranda, J., Santoro, A., Engelender, S., Wolosker, H. (2000) Gene 256, 183–188. Wolosker, H., Sheth, K. N., Takahashi, M., Mothet, J. P., Brady, R. O., Jr., Ferris, C. D., Snyder, S. H. (1999) Proc. Natl. Acad. Sci. USA 96, 721–725. Wolosker, H., Blackshaw, S.,
41
42
43
44
45
46
47 48 49 50
51
52 53
54 55
56
57 58
Snyder, S. H. (1999) Proc. Natl. Acad. Sci. USA 96, 13409–13414. Strisovsky, K., Jiraskova, J., Barinka, C., Majer, P., Rojas, C., Slusher, B. S., Konvalinka, J. (2003) FEBS Lett. 535, 44–48. Uo, T., Yoshimura, T., Shimizu, S., Esaki, N. (1998) Biochem. Biophys. Res. Commun. 246, 31–34. Fee, J. A., Hegeman, G. D., Kenyon, G. L. (1974) Biochemistry 13, 2533– 2538. Fee, J. A., Hegeman, G. D., Kenyon, G. L. (1974) Biochemistry 13, 2528– 2532. Petsko, G. A., Kenyon, G. L., Gerlt, J. A., Ringe, D., Kozarich, J. W. (1993) Trends Biochem. Sci. 18, 372– 376. Neidhart, D. J., Howell, P. L., Petsko, G. A., Powers, V. M., Li, R. S., Kenyon, G. L., Gerlt, J. A. (1991) Biochemistry 30, 9264–9273. Hoffman, M. (1991) Science 251, 31–32. Armstrong, R. N. (2000) Biochemistry 39, 13625–13632. Babbitt, P. C., Gerlt, J. A. (1997) J. Biol. Chem. 272, 30591–30594. Bernat, B. A., Laughlin, L. T., Armstrong, R. N. (1999) Biochemistry 38, 7462–7469. Kallarakal, A. T., Mitra, B., Kozarich, J. W., Gerlt, J. A., Clifton, J. G., Petsko, G. A., Kenyon, G. L. (1995) Biochemistry 34, 2788–2797. Kenyon, G. L., Hegeman, G. D. (1970) Biochemistry 9, 4036–4043. Kenyon, G. L., Gerlt, J. A., Petsko, G. A., Kozarich, J. W. (1995) Acc. Chem. Res. 28, 178–186. Lipmann, F. (1973) Acc. Chem. Res. 6, 361–367. Gevers, W., Kleinkauf, H., Lipmann, F. (1968) Proc. Natl. Acad. Sci. USA 60, 269–276. Gevers, W., Kleinkauf, H., Lipmann, F. (1969) Proc. Natl. Acad. Sci. USA 63, 1335–1342. Yamada, M., Kurahashi, K. (1969) J. Biochem. (Tokyo) 66, 529–540. Stindl, A., Keller, U. (1994) Biochemistry 33, 9358–9364.
References 59 Stindl, A., Keller, U. (1993) J. Biol. 60
61
62
63
64 65
66
67 68
69
70
71
72
73
74 75 76
Chem. 268, 10612–10620. van Liempt, H., von Dohren, H., Kleinkauf, H. (1989) J. Biol. Chem. 264, 3680–3684. Banko, G., Demain, A. L., Wolfe, S. (1987) J. Am. Chem. Soc. 109, 2858– 2860. Baldwin, J. E., Bird, J. W., Field, R. A., O’Callaghan, N. M., Schofield, C. J., Willis, A. C. (1991) J. Antibiot. (Tokyo) 44, 241–248. Jensen, S. E., Westlake, D. W., Wolfe, S. (1983) Can. J. Microbiol. 29, 1526–1531. Zhang, J., Wolfe, S., Demain, A. L. (1992) Biochem. J. 283(3), 691–698. Baldwin, J. E., Shiau, C. Y., Byford, M. F., Schofield, C. J. (1994) Biochem. J. 301(2), 367–372. Mazumder, R., Sasakawa, T., Kaziro, Y., Ochoa, S. (1962) J. Biol. Chem. 237, 3065–3068. Leadlay, P. F. (1981) Biochem. J. 197, 413–419. Allen, S. H., Kellermeyer, R., Stjernholm, R., Jacobson, B., Wood, H. G. (1963) J. Biol. Chem. 238, 1637– 1642. Pfeifer, B. A., Admiraal, S. J., Gramajo, H., Cane, D. E., Khosla, C. (2001) Science 291, 1790–1792. Marsden, A. F., Caffrey, P., Aparicio, J. F., Loughran, M. S., Staunton, J., Leadlay, P. F. (1994) Science 263, 378–380. Stabler, S. P., Marcell, P. D., Allen, R. H. (1985) Arch. Biochem. Biophys. 241, 252–264. McCarthy, A. A., Baker, H. M., Shewry, S. C., Patchett, M. L., Baker, E. N. (2001) Structure (Camb) 9, 637–646. McCarthy, A. A., Baker, H. M., Shewry, S. C., Kagawa, T. F., Saafi, E., Patchett, M. L., Baker, E. N. (2001) Acta Crystallogr. Sect. D 57, 706–708. Fuller, J. Q., Leadlay, P. F. (1983) Biochem. J. 213, 643–650. Leadlay, P. F., Fuller, J. Q. (1983) Biochem. J. 213, 635–642. Frey, P. A. (1996) Faseb J. 10, 461–470.
77 Deupree, J., Wood, W. A. (1975)
Methods Enzymol. 41, 412–419. 78 Deupree, J. D., Wood, W. A. (1972)
J. Biol. Chem. 247, 3093–3097. 79 Salo, W. L., Fossitt, D. D., Bevill,
80 81
82
83 84
85
86
87
88
89 90
91
92
93
94
95
R. D., 3rd, Kirkwood, S., Wood, W. (1972) J. Biol. Chem. 247, 3098–3100. Rudnick, G., Abeles, R. H. (1975) Biochemistry 14, 4515–4522. Bateman, A., Birney, E., Cerruti, L., Durbin, R., Etwiller, L., Eddy, S. R., Griffiths-Jones, S., Howe, K. L., Marshall, M., Sonnhammer, E. L. (2002) Nucleic Acids Res. 30, 276–280. Fisher, L. M., Albery, W. J., Knowles, J. R. (1986) Biochemistry 25, 2529–2537. Northrop, D. B., Rebholz, K. L. (1994) Anal. Biochem. 216, 285–290. Fisher, L. M., Albery, W. J., Knowles, J. R. (1986) Biochemistry 25, 2538–2542. Fisher, L. M., Belasco, J. G., Bruice, T. W., Albery, W. J., Knowles, J. R. (1986) Biochemistry 25, 2543–2551. Belasco, J. G., Bruice, T. W., Fisher, L. M., Albery, W. J., Knowles, J. R. (1986) Biochemistry 25, 2564–2571. Belasco, J. G., Bruice, T. W., Albery, W. J., Knowles, J. R. (1986) Biochemistry 25, 2558–2564. Belasco, J. G., Albery, W. J., Knowles, J. R. (1986) Biochemistry 25, 2552–2558. Gallo, K. A., Knowles, J. R. (1993) Biochemistry 32, 3981–3990. Yagasaki, M., Iwata, K., Ishino, S., Azuma, M., Ozaki, A. (1995) Biosci. Biotechnol. Biochem. 59, 610–614. Nakajima, N., Tanizawa, K., Tanaka, H., Soda, K. (1986) Agric. Biol. Chem. 50, 2823–2830. Nakajima, N., Tanizawa, K., Tanaka, H., Soda, K. (1988) Agric. Biol. Chem. 52, 3099–3104. Hwang, K. Y., Cho, C. S., Kim, S. S., Sung, H. C., Yu, Y. G., Cho, Y. (1999) Nat. Struct. Biol. 6, 422–426. Choi, S. Y., Esaki, N., Ashiuchi, M., Yoshimura, T., Soda, K. (1994) Proc. Natl. Acad. Sci. USA 91, 10144–10147. Gallo, K. A., Tanner, M. E., Knowles, J. R. (1993) Biochemistry 32, 3991–3997.
1169
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97 98 99
100 101 102
Knowles, J. R. (1993) Biochemistry 32, 3998–4006. Wiseman, J. S., Nichols, J. S. (1984) J. Biol. Chem. 259, 8907–8914. Antia, M., Hoare, D. S., Work, E. (1957) Biochem. J. 65, 448–459. Cirilli, M., Zheng, R., Scapin, G., Blanchard, J. S. (1998) Biochemistry 37, 16452–16458. Koo, C. W., Blanchard, J. S. (1999) Biochemistry 38, 4416–4422. Kuzmic, P. (1996) Anal. Biochem. 237, 260–273. Davis, L., Lee, N., Glaser, L. (1972) J. Biol. Chem. 247, 5862–5866.
103 McDonough, M. W., Wood, W. A.
(1961) J. Biol. Chem. 236, 1220–1224. 104 Melo, A., Glaser, L. (1968) J. Biol.
Chem. 243, 1475–1478. 105 Glaser, L., Zarkowsky, H., Ward, L.
(1972) Methods Enzymol. 28, 446–454. 106 Kawamura, T., Ishimoto, N., Ito, E.
(1979) J. Biol. Chem. 254, 8457–8465. 107 Kawamura, T., Kimura, M.,
Yamamori, S., Ito, E. (1978) J. Biol. Chem. 253, 3595–3601. 108 Salo, W. L. (1976) Biochim. Biophys. Acta 452, 625–628. 109 Sala, R. E., Morgan, P. M., Tanner, M. E. (1996) J. Am. Chem. Soc. 118, 3033–3034.
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Computer Simulations of Proton Transfer in Proteins and Solutions Sonja Braun-Sand, Mats H. M. Olsson, Janez Mavri, and Arieh Warshel 8.1
Introduction
Proton transfer (PT) reactions play a major role in many enzymatic and other biological processes. Thus it is important to quantify the nature of such reactions by reliable computer modeling approaches. This chapter will review the advances in the field and present a unified way of modeling and analyzing PT reactions in proteins and solutions. We will start by considering the current options for reliable simulations. We will focus on the empirical valence bond (EVB) approach that has been used in studies that paved the way for the modern microscopically based treatments of PT in solutions and proteins (e.g. Refs. [1, 2]). It will be argued that the EVB presents currently the most effective strategy for exploring and modeling different aspects of such processes, ranging from hydrogen bonding to PTs in enzymatic reactions and to proton translocations along a chain of donors and acceptors. We will demonstrate the effectiveness of the EVB in quantifying the trend in PT reactions and in analyzing linear free energy relationships (LFER). We will also clarify misunderstandings about the nature of LFER that involve PT reactions. The issue of proton translocations (PTR) along conduction chains will be discussed, considering some misconceptions about the role of proton wires and the orientations of the neutral water molecules. Finally we will address the role of dynamics and nuclear quantum mechanical effects in PT in enzyme catalysis.
8.2
Simulating PT Reactions by the EVB and other QM/MM Methods
The rates of proton transfer reaction in solutions and proteins are determined by the corresponding rate constants (e.g. Ref. [3]).
Corresponding author.
Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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8 Computer Simulations of Proton Transfer in Proteins and Solutions
k¼k
1 hjx_ jiTS =Dx z exp½DGz b 2
ð8:1Þ
Where k is the transmission factor, hjx_ jiTS is the average of the absolute value of the velocity along the reaction coordinate at the transition state (TS), and b ¼ 1=kB T (where kB is the Boltzmann constant and T the absolute temperature). The term DGz designates the multidimensional activation free energy that expresses the probability that the system will be in the TS region. The free energy reflects enthalpic and entropic contributions and also includes nonequilibrium solvation effects [4] and, as will be shown below, nuclear quantum mechanical effects. It is also useful to comment here on the common description of the rate constant as k ¼ A exp½DE z b
ð8:2Þ
This Arrhenius expression is of course useful for experimental analysis, but it may lead to unnecessary confusion about the factors that determine the rate constant. That is, as is now recognized by the chemical physics community [5–7], Eq. (8.1) provides an accurate description of the rate constant when all the dynamical effects are cast into the transmission factor and all the probabilistic effects are expressed by DGz. Of course, DGz includes the activation entropy while the use of Eq. (8.2) places this crucial effect in A and makes it hard to separate the dynamical and probabilistic factors. With the above background, we start the discussion of the evaluation of DGz , which in fact is the most important step. We would also like to emphasize that the ability to calculate DGz (and the corresponding free energy profiles) for enzyme reactions and the corresponding reference solution reaction is crucial for any attempt to obtain a quantitative understanding of enzyme reactions. The common prescription of obtaining potential surfaces for chemical reactions involves the use of quantum chemical computational approaches, and such approaches have become quite effective in treating small molecules in the gas phase (e.g. Ref. [8]). However, here we are interested in chemical reactions in very large systems, which cannot be explored at present by ab initio methods. Similarly, molecular mechanics simulations (e.g. Ref. [9]) that have been proven to be very effective in exploring protein configurational space cannot be used to describe bond breaking and bond making reactions in proteins or solutions. The generic solution to the above problem has been provided by the development of the hybrid quantum mechanics/molecular mechanics (QM/MM) approach [10]. This approach divides the simulation system (for example, the enzyme/substrate complex) into two regions. The inner region, region I, contains the reacting fragments which are represented quantum mechanically. The surrounding protein/solvent region, region II, is represented by a molecular mechanics force field. Molecular orbital (MO) QM/MM methods are now widely used in studies of complex systems in general, and enzymatic reactions in particular, and we can only mention several works (for example, Refs. [11–22]). Despite these advances,
8.2 Simulating PT Reactions by the EVB and other QM/MM Methods
we are not yet at the stage where one can use MO-QM/MM approaches in fully quantitative studies of enzyme catalysis. The major problem is associated with the fact that a quantitative evaluation of the potential surfaces for the reacting fragment should involve ab initio electronic structure calculations, and such calculations are too expensive to allow for the configurational averaging needed for proper free energy calculations. Specialized approaches can help one move toward ab initio QM/MM free energy calculations (see Ref. [23]), but even these approaches are still in a development stage. Fortunately, one can use approaches that are calibrated on the energetics of the reference solution reaction to obtain reliable results with semiempirical QM/MM studies, and the most effective and reliable way of doing this is the EVB method described below. During our search for reliable methods for studies of enzymatic reactions it became apparent that, in studies of chemical reactions, it is more physical to calibrate surfaces that reflect bond properties (that is, valence bond-based, VB, surfaces) than to calibrate surfaces that reflect atomic properties (for example, MO-based surfaces). Furthermore, it appears to be very advantageous to force the potential surfaces to reproduce the experimental results of the broken fragments at infinite separation in solution. This can be effectively accomplished with the VB picture. The resulting empirical valence bond (EVB) method has been discussed extensively elsewhere [3, 24], but its main features will be outlined below, because it provides the most direct microscopic connection to PT processes. The EVB is a QM/MM method that describes reactions by mixing resonance states (or more precisely diabatic states) that correspond to valence-bond (VB) structures, which describe the reactant, intermediate (or intermediates), and product states. The potential energies of these diabatic states are represented by classical MM force fields of the form: i i i þ Uintra ðR; QÞ þ USs ðR; Q; r; qÞ þ Uss ðr; qÞ ei ¼ agas
ð8:3Þ
Here R and Q represent the atomic coordinates and charges of the diabatic states, i and r and q are those of the surrounding protein and solvent. agas is the gas-phase energy of the i th diabatic state (where all the fragments are taken to be at infinite separation), Uintra ðR; QÞ is the intramolecular potential of the solute system (relative to its minimum); USs ðR; Q; r; qÞ represents the interaction between the solute (S) atoms and the surrounding (s) solvent and protein atoms. Uss ðr; qÞ represents the potential energy of the protein/solvent system (‘‘ss’’ designates surroundingsurrounding). The ei of Eq. (8.3) forms the diagonal elements of the EVB Hamiltonian (Hii ). The off-diagonal elements of the Hamiltonian, Hij , are represented typically by simple exponential functions of the distances between the reacting atoms. The Hij elements are assumed to be the same in the gas phase, in solutions and in proteins. Since one may wonder about this assumption we note the following; (i) the assumption of constant Hij is in fact the main reason for the empirical success of LFER approaches that correlate the changes of the diabatic energies with the activation barrier, and (ii) the validity of the assumption of a relatively small envi-
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8 Computer Simulations of Proton Transfer in Proteins and Solutions
ronmental effect on Hij has been established in recent constraint DFT studies [25], which follow the prescription proposed by Eqs. (17)–(18) of Ref. [26] and obtained a very small change in the ab initio effective Hij for SN 2 reaction in solution and in the gas phase. The ground state energy, Eg , is obtained by solving
HEVB Cg ¼ Eg Cg
ð8:4Þ
Here, Cg is the ground state eigenvector and Eg provides the EVB potential surface. For example, we can describe the reaction XH þ Y ! X þ HY þ
ð8:5Þ
by three resonance structures Ca ¼ ½X H Cb ¼ ½X
Cc ¼ ½X
Y fa
H Y þ fb Hþ
ð8:6Þ
Y fc
where the fs are the wave functions for the solvent and for the solute electrons, which are not included in the XH Y system. For simplicity, it is convenient to treat the high energy state, cc , by a perturbation treatment restricting ourselves to the two states ca and cb . The potential surface for the two-state VB model is obtained by solving the secular equation Haa E H S E ab
ab
Hba Sba E Hbb E
ð8:7Þ
where the matrix elements of H can be obtained by performing gas-phase ab initio calculations or represented by semiempirical analytical potential functions (fitted to the potential surface and charge distribution obtained from experimental information and/or ab initio calculations). The solvent can then be incorporated in the Hamiltonian of the system by using the expression 0 a þ USs þ Uss ea ¼ Haa ¼ Haa 0 b eb ¼ Hbb ¼ Hbb þ USs þ Uss
ð8:8Þ
where USs is the interaction between the solute (S) charges and the surrounding solvent (s), and Uss is the solvent–solvent interaction. The overlap integral, Sab , is usually absorbed into the semiempirical Hab and the solute-solvent interactions are described by analytical potential functions as discussed in Ref. [27]. The matrix elements for the isolated solute can be represented by
8.2 Simulating PT Reactions by the EVB and other QM/MM Methods ðaÞ
0 Haa ¼ ea0 ¼ DMðb1 Þ þ Unb þ
X1 mðaÞ
2
ðmÞ
Kb ðbm b0 Þ 2 þ
X 1 ðm 0 Þ K y ðym 0 y0 Þ 2 2 m 0 ðaÞ
ðbÞ
0 Hbb ¼ eb0 ¼ DMðb2 Þ þ Unb 332=r2 þ aðbÞ
þ
X1 mðbÞ
2
ðmÞ
Kb ðbm b0 Þ 2 þ
X 1 ðm 0 Þ K y ðym 0 y0 Þ 2 2 m 0 ðbÞ
ð8:9Þ
Hab ¼ A ab expfmðr2 r20 Þg where b1 , b3 and r2 are, respectively, the XaH, HaY, and XaY distances, DM is the value of the Morse potential for the indicated bond relative to its minimum value, the quadratic bonding terms describe all bonds in the solute system, which are connected to X or Y and the quadratic angle bonding term describes all angles defined by the given covalent bonding arrangement that includes the X, Y, or H atoms. Unb is the nonbonded interaction between nonbonded atoms in the a th resonance structure. These interaction terms are represented by either Aemr or 6-12 van der Waals potential functions. The parameter aðbÞ is the energy difference between ca and cb with the fragments at infinite separation in the gas phase. The off-diagonal term Hab can be evaluated by the three-state EVB approach of Ref. [28] and fitted to the two-state model. Note that the same two-state model can be fitted to gas-phase ab initio calculations. The EVB methodology provides a computationally inexpensive Born– Oppenheimer surface suitable for describing chemical reaction in an enzyme or in solution. Running such MD trajectories on the EVB surface of the reactant state can (in principle) provide the free energy function, Dg, that is needed to calculate the activation energy, Dg z . However, since trajectories on the reactant surface will reach the transition state only rarely, it is usually necessary to run a series of trajectories on potential surfaces that gradually drive the system from the reactant to the product state [3]. The EVB approach accomplishes this by changing the system adiabatically from one diabatic state to another. In the simple case of two diabatic states, this ‘‘mapping’’ potential, em , can be written as a linear combination of the reactant and product potentials, e1 and e2 : em ¼ ð1 hm Þe1 þ hm e2
ð0 a hm a 1Þ
ð8:10Þ
When hm is changed from 0 to 1 in n þ 1 fixed increments (hm ¼ 0=n; 1=n; 2=n; . . . ; n=nÞ, potentials with one or more of the intermediate values of hm will force the system to fluctuate near the TS. The free energy, DGm , associated with changing hm from 0 to m=n is evaluated by the well known free energy perturbation (FEP) procedure described elsewhere (see, for example, Ref. [3]). However, after obtaining DGm we still need to obtain the free energy that corresponds to the adiabatic ground state surface (the Eg of Eq. (8.4)) along the reaction coordinate, x. This free energy (referred to as a ‘‘free energy functional’’) is obtained by the FEP-umbrella sampling (FEP/US) method [3, 27], which can be written as
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8 Computer Simulations of Proton Transfer in Proteins and Solutions
Dgðx 0 Þ ¼ DGm b 1 lnhdðx x 0 Þ exp½bðEg ðxÞ em ðxÞÞiem
ð8:11Þ
where em is the mapping potential that keeps x in the region of x 0 . If the changes in em are sufficiently gradual, the free energy functionals, Dgðx 0 Þ, obtained with several values of m overlap over a range of x 0 , and patching together the full set of Dgðx 0 Þ gives the complete free energy curve for the reaction. In choosing the general reaction coordinate, x, we note that the regular geometrical coordinate, used in gas-phase studies, cannot provide a practical way to model the multidimensional reaction coordinate of reactions in solution and protein. In modeling such processes, it is crucial to capture the effect of the solvent polarization and probably the best way to describe this effect microscopically is to follow our early treatment [1, 3] and to use the electronic energy gap as the general reaction coordinate (x ¼ e2 e1 Þ. The FEP/US approach may also be used to obtain the free energy functional of the isolated diabatic states. For example, the diabatic free energy, Dg1 , of the reactant state can be calculated as Dg1 ðx 0 Þ ¼ DGm b 1 lnhdðx x 0 Þ exp½bðe1 ðxÞ em ðxÞÞiem
ð8:12Þ
The diabatic free energy profiles of the reactant and product states provide the microscopic equivalent of the Marcus’ parabolas [29, 30]. The EVB method satisfies some of the main requirements for reliable studies of enzymatic reactions. Among the obvious advantages of the EVB approach is the facilitation of proper configurational sampling and converging free energy calculations. This includes the inherent ability to evaluate nonequilibrium solvation effects [4]. Another important feature of the EVB method is the ability to capture correctly the linear relationship between activation free energies and reaction energies (LFER) observed in many important reactions (for example, Ref. [3]). Furthermore, the EVB benefits from the aforementioned ability to treat consistently and conveniently the solute–solvent coupling. This feature is essential not only in allowing one to properly model charge-separation reactions, but also in allowing a reliable and convenient calibration. Calibrating EVB surfaces using ab initio calculations was found to provide quite reliable potential surfaces. The seemingly simple appearance of the EVB method may have led to the initial impression that this is an oversimplified qualitative model, rather than a powerful quantitative approach. However, the model has been eventually widely adopted by other groups as a general model for studies of reactions in large molecules and in condensed phase (for example, Refs. [31–34]). Several very closely related versions have been put forward with basically the same ingredients as in the EVB method (see Refs. [35, 36]). It might also be useful to clarify that our EVB approach included calibration on ab initio surface from quite an early stage [27] so that this element is not a new development. Furthermore, although early works (e.g. Refs. [37, 38]) have some relationship to the EVB, they were merely combinations of VB and MM treatments and thus miss the crucial QM/MM coupling obtained by adding the MM description of each state in the diagonal EVB Hamiltonian (Eq.
8.3 Simulating the Fluctuations of the Environment and Nuclear Quantum Mechanical Effects
(8.12)). It is this coupling idea that made the EVB such a powerful way of modeling reactions in condensed phases. Since we will be dealing with proton transport processes, it might be useful to clarify that the EVB and the so-called MS-EVB [32, 39] (that was so effective in studies of proton transport in water) are more or less identical. More specifically, the so-called MS-EVB includes typically 6 EVB states in the solute quantum mechanical (QM) region and the location of this QM region changes if the proton moves. The QM region is surrounded by classical water molecules (the molecular mechanics (MM)), whose effect is sometimes included inconsistently by solvating the charges of the gas-phase QM region (this leads to inconsistent QM/MM coupling with the solute charges as explained in, for example, Refs. [4, 9]. More recently, the coupling was introduced consistently by adding the interaction with the MM water in the diagonal solute Hamiltonian. Now our EVB studies are performed repeatedly with multi-state treatment (for example, 5 states in Ref. [40]) and this has always been done with a consistent coupling to the MM region. Thus, the only difference that we can find between the two versions is that our EVB studies did not change the identity of the atoms in the QM region during simulations of individual chemical steps (this was done only while considering different steps). Such treatment provides the optimal strategy when one deals with processes in proteins that involve relatively high barriers, rather than with low barrier transport processes (so that the identity of the reacting region has not changed during the simulations). Also note that the MS-EVB simulations in proteins, where we have a limited number of quantum sites, do not have to change the QM region (for example, Ref. [41]) during the simulations. Thus we conclude that the EVB and MS-EVB are identical methods, although we appreciate the elegant treatment of changing the position of the QM region during simulations, which is a very useful advance in EVB treatments of processes with a very low activation barrier.
8.3
Simulating the Fluctuations of the Environment and Nuclear Quantum Mechanical Effects
The EVB provides an effective way to explore the effect of the fluctuations of the environment on PT reactions. That is, the electrostatic potential from the fluctuating polar environment interacts with the charge distribution of each resonance structure and thus the fluctuations of the environment are directly reflected in the time dependence of the EVB Hamiltonian. This point emerged from our early studies [1, 2, 4, 42] and is illustrated in Figs. 8.1 and 8.2. Figure 8.1 shows how the fluctuations of the field from the environment change the energy of the ionic state, and thus the potential for a PT at a given fixed environment. The same effect is illustrated in Fig. 8.2 where we consider the time-dependent energetics of the two EVB diabatic states approximately (the front and back panels) in the PT step in the reaction of lysozyme. The figure also describes the time dependence of the adiabatic ground state and the corresponding barrier (DE 0) for a PT process. As
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8 Computer Simulations of Proton Transfer in Proteins and Solutions
Figure 8.1. Energetics of the proton transfer between an acid (A) and a base (B) by valence bond resonance structures. The reaction is described in terms of a covalent resonance structure (AaH B) and an ionic resonance structure (A HaBþ ). The energies of the valence bond structures are as given in the text and depend on the coordinates of the reacting atoms, R, and the coordinates of the rest of
the system, r. Only the ionic resonance structure interacts strongly with the dipoles and charges of the surrounding solvent or protein cage. Thus, the energy of the ionic structure, e2 , changes strongly with fluctuation of the surrounding dipoles. The reaction potential surface, EðR; rÞ, obtained by mixing of the relevant resonance forms is also shown.
seen from the figure, the actual transfer would occur when the product state is stabilized and DE 0 is reduced. As pointed out in our early studies, the fluctuations of the energy gap between the back and front panels of Fig. 8.2 tells us when DE 0 will be reduced (the same point was adopted in Ref. [43], overlooking its origin). Furthermore, the fluctuations described in Fig. 8.1 can be used to evaluate dynamical effects by considering the autocorrelation of the time-dependent gap between the energies of the reactant and product states (see discussion in Ref. [44]). The fluctuations of the electrostatic energy gap can also provide an interesting insight into nuclear quantum mechanical (NQM) effects. That is, we can use an approach that is formally similar to our previous treatment of electron transfer (ET) reactions in polar solvents [1] where we considered ET between the solute vibronic channels (for example, Ref. [1]). Our starting point is the overall rate constant
kab ¼
X mm 0
X kam; bm 0 expfEam bg expfEam bg
ð8:13Þ
m
where b ¼ 1=ðkB TÞ (with kB the Boltzmann constant) and Eam is the energy of the m th vibronic level of state a. By Eq. (8.13) we assume that the reactant well vibrational states are populated according to the Boltzmann distribution. The individual vibronic rate constant, kam; bm 0 , is evaluated by monitoring the energy difference between Eam and Ebm as a function of the fluctuations of the rest of the molecule and therefore as a function of time. The time-dependent energy gap can be used to
8.3 Simulating the Fluctuations of the Environment and Nuclear Quantum Mechanical Effects
Figure 8.2. The time-dependent barrier for proton transfer from a carboxylic oxygen of Glu35 (OA ) to the glycosidic oxygen of the substrate (O4 ) in lysozyme. The solid lines represent the potential energies of the reactant state (O4 HaOA ), the product state (O4 HaOA þ ), and the TS, with the zero of the energy scale defined as the mean potential
energy of the reactant state. The energy of the TS is also shown. The energies were calculated during an MD trajectory on the reactant surface. The effective activation barrier (DE0) is determined mainly by fluctuations of the electrostatic energy of the product state, in which the EVB structure has a large dipole moment. (From Ref. [2] in part).
evaluate the probability of surface crossing between the two states by adopting a semiclassical trajectory approach [45] to rate processes in condensed phases [1, 46]. This approach can be best understood and formulated by considering Fig. 8.3 and asking what is the probability that a molecule in state am will cross to state bm 0 . Treating the fluctuation of the vibronic state classically, one finds that the time-dependent coefficient for being in state cbm 0 , while starting from state cam , is given by ðt C_ am; bm 0 ðtÞ ¼ ði=hÞHab Sm; m 0 exp ði=hÞ Debm 0 ; am dt 0
ð8:14Þ
where the Sm; m 0 is the Franck–Condon factor for transition from m to m 0 and Hab is the off-diagonal electronic matrix element of the EVB Hamiltonian. As illustrated in Fig. 8.2, the energy gap, De, is given by Debm 0 ; am ¼ ðeb ea Þ þ h
X r
! or ðmr0
mr Þ
ð8:15Þ
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8 Computer Simulations of Proton Transfer in Proteins and Solutions
Figure 8.3. A semiclassical vibronic treatment of proton transfer. This model, which is valid only for small H12 , treats the carbon–proton stretching vibration quantum mechanically and the rest of the system classically. In this way, we monitor the energy gap between the vibronic states e1 þ hoH =2ðn1 þ 1=2Þ and e2 þ hoH =ðn2 þ 1=2Þ for trajectories of the system with a fixed XaH bond length (see Ref.
[1] for a related treatment). The figure depicts the time dependence of e1 , e2 and e2 plus single and double excitations of the XaH bond and also provides the energy levels at two points on the trajectory. A semiclassical surface hopping treatment of the crossing probability between the vibronic states, due to the fluctuating energy gap, leads to Eq. (8.21) (see Ref. [42]).
where or and mr are the frequency and quantum number of the r th mode. The corresponding rate constant is given by [46] kam; bm 0 ¼ lim ð1=tjCbm 0 ; bm ðtÞjÞ t!y ðt X X 2 0 ¼ jHab =hj 2 Smm dt exp ioba tþi or ðmr0 mr Þt 0 þ ði=hÞ
ðt 0
2 dta0 uðta0 Þ t
ð8:16Þ
where u is the electronic energy gap relative to its average values, given by u ¼ eb ea hDeba ia
ð8:17Þ
8.3 Simulating the Fluctuations of the Environment and Nuclear Quantum Mechanical Effects
and h ia designates an average obtained over the fluctuations around the minimum of state a. The above rate constant can be treated using a cumulant expansion (see Ref. [46]) giving X
kam; bm 0 ¼ jHab =hj 2
ðy 2 Smm 0
y
exp½ði=hÞhDebm 0 ; am i þ gðtÞ dt
ð gðtÞ ¼ ði=hÞ 2 ðt t 0 ÞhDeð0ÞDeðt 0 Þia dt 0
ð8:18Þ
In the high temperature limit one obtains [42, 46] kam; bm 0 ¼ jHab Smm 0 =hj 2 ðph 2 =kB TlÞ 1=2 expfDg 0bg
ð8:19Þ
where l is the ‘‘solvent reorganization energy’’ defined by l ¼ hDeba ia DG0
ð8:20Þ
Basically, this expression reflects the probability of vibronic transition from the reactant well to the product well (as determined by the vibrational overlap integrals (the Smn 0 ) modulated by the chance that De will be zero. This chance is determined by the activation free energy, Dg 0, whose value can be approximated by the activation free energy, Dg 0, which can be approximated by " 0 Dgmm 0
A DG þ 0
X
h orðmr0
#2 mr Þ þ l
4l
ð8:21Þ
r
This relationship is only applicable if the system can be described by the linear response approximation (see Ref. [46]), but this does not require that the system will be harmonic. The above vibronic treatment is similar to the expression developed by Kuznetsov and Ulstrup [47]. However, the treatment that leads to Eq. (8.21), which was developed by Warshel and coworkers [1, 42, 46], is based on a more microscopic approach and leads to much more consistent treatment of Dg 0 (see also below) where we can use rigorously DG 0 rather than DE. Furthermore, our dispersed polaron (spin boson) treatment [46] of Eq. (8.18) and if needed Eq. (8.21) gives a clear connection between the spectral distribution of the solvent fluctuations and the low temperature limit of Eq. (8.18). It is also useful to note that Borgis and Hynes [48] and Antoniou and Schwartz [49] have used a similar treatment but considered only the lowest vibrational levels of the proton. Before considering the very serious limitation of the vibronic treatment, it is use0 ful to comment about Dgam; bm . That is, when the linear response approximation is not valid, we can obtain a more accurate estimate of Dg 0 using a free energy per-
1181
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8 Computer Simulations of Proton Transfer in Proteins and Solutions 0 0 turbation method. That is, Dgam; bm determines the probability that eam and ebm intersect by [46] 0 0 0 Dgmm 0 A kB T lnðnmm 0 =nmm 0 Þ
ð8:22Þ
where n0 mm 0 is the number of times the energy gap is between zero and DC and 0 0 nmm 0 is the number of times the energy gap is at the value De G DC that gives the largest value for nmm 0 and C is an energy bin width. This probability can be determined in a direct way using molecular dynamics by running trajectories on the reactant surface with fixed AaH bond distance and monitoring the energy gap ebm 0 eam and counting the times this gap is zero. However, a direct calculation of such surface intersection events might require an extremely long computer time. Instead we can use a free energy perturbation (FEP) approach, propagating trajectories over a mapping potential of the form of Eq. (10) eðhj Þ ¼ eam ð1 hj Þ þ ebm 0 hj
ð8:23Þ
where the change of h from zero to one moves the system from eam to ebm 0 . The vibronic free energy function can be determined in analogy to Eq. (8.12) by PðDe 0 Þam ¼ expfDgam ðDeam; bm 0 Þbg A expfDGðlj ÞbghdðDe De 0 Þ expfðeam ðDeÞ ej ðDeÞÞgbij
ð8:24Þ
Unfortunately, the use of the above vibronic treatment is valid only in the diabatic 2 is sufficiently small. Now, Hab in the case of PT processes is far limit when Hab Smn too large to allow for a diabatic treatment. Thus, the question is, what is the mag2 . Here we note that for 0 ! 0 transitions, Smn may be quite small nitude of Hab Smn since it is given by S00 ¼ expfD 2 =4g where D is the dimensionless origin shift for the proton transfer (DH A 6:5 ðDr=0:6Þðo=3000Þ 1=2 when Dr is given in A˚, o in cm1 , D in dimensionless units, and this expression is based on the fact that at 0.6 A˚, D is 6.5). However, Smn approaches unity for hot transitions. At any rate, if the largest contribution to the rate constant comes from S00 , we may use Eq. (8.16) as a guide. Here, however, we face another problem, that is, the magnitude of the parameters in Eq. (8.16) is far from obvious. First, if we consider a colinear PT and treat all the coordinates except the XaH stretching frequency, then we have to deal with a large intramolecular reorganization energy. Second, the effective frequency for the XaH stretch can be very different than the typical frequency of about 3000 cm1 once the X Y distance starts to be shorter than 3.2 A˚. In this range H12 starts to affect in a drastic way the ground state curvature (Fig. 8.4). Here one can use the idea introduced by Warshel and Chu [42] and modify the diabatic potential to make it close to the adiabatic potential. As long as the main contribution to the rate constant comes from the S00 term it is reasonable to represent this effect by using oðDÞ ¼ o0 ð1 ð4H12 =lH Þ 2 aÞ
ð8:25Þ
8.3 Simulating the Fluctuations of the Environment and Nuclear Quantum Mechanical Effects
Figure 8.4.
Dependence of adiabatic potential on the X Y distance.
where a is approximately 0.5. It may also be useful to try to account for the complications due to the fact that the intramolecular solute coordinate contributes to the apparent reorganization energy and are also coupled to the PT coordinate. A part of this problem can be reduced by integrating the vibronic rate constant over the ‘‘soft’’ coordinates, and in particular the X Y distance. This can be done by writing ð kab ¼ kab ðDÞ expfUðRðDÞbg dD
ð8:26Þ
The effectiveness of the above treatment will be examined in Section 8.7, but even if it can guide us with regards to the general trend it cannot be used in a phenomenological way to estimate actual molecular properties. Perhaps for this reason, microscopic estimates [50] of the parameters in Eq. (8.19) for the reaction catalyzed by lipoxygenase were found to be very different than those obtained by fitting Eq. (8.19) to the observed isotope effects [51–53]. The treatment of NQM effects can be accomplished on a much more quantitative level by including the adiabatic limit and modifying the centroid path integral approach [54–56]. The centroid path integral represents the unifying approach, which is valid both in the adiabatic and diabatic limits. This is done in a way that
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8 Computer Simulations of Proton Transfer in Proteins and Solutions
allows us to use classical trajectories as a convenient and effective reference for the corresponding centroid calculations. This QCP approach [57, 58] will be described briefly below. In the QCP approach, the nuclear quantum mechanical rate constant is expressed as kqm ¼ Fqm
kB T 0 expðDgqm Þ h
ð8:27Þ
where Fqm , kB , T, and h are, respectively, the transmission factor, Boltzmann’s constant, the temperature, Planck’s constant, and b ¼ 1=kB T. The quantum me0 chanical activation barrier, Dgqm , includes almost all the nuclear quantum mechanical effects, whereas only small effects come from the pre-exponential transmission factor in the case of systems with a significant activation barrier [31, 44]. 0 , can be evaluated by FeynThe quantum mechanical free energy barrier, Dgqm man’s path integral formulation [59], where each classical coordinate is replaced by a ring of quasiparticles that are subjected to the effective ‘‘quantum mechanical’’ potential
Uqm ¼
p X 1 1 MW 2 Dxk2 þ Uðxk Þ 2p p k¼1
ð8:28Þ
Here, Dxk ¼ xkþ1 xk (where x pþ1 ¼ x1 ), W ¼ p= hb, M is the mass of the particle, and U is the actual potential used in the classical simulation. The total quantum mechanical partition function can then be obtained by running classical trajectories of the quasiparticles with the potential Uqm . The probability of being at the transition state is in this way approximated by a probability distribution of the center of mass of the quasiparticles (the centroid) rather than the classical single point. Such calculations of centroid probabilities in the condensed phase reactions are very challenging since they may involve major convergence problems. The QCP approach offers an effective and rather simple way to evaluate this probability without significantly changing the simulation program. This is done by propagating classical trajectories on the classical potential surface of the reacting system and using the positions of the atom of the system to generate the centroid position for the quantum mechanical partition function. This treatment is based on the finding that the quantum mechanical partition function can be expressed as [57, 60] ** Zqm ðxÞ ¼ Zcl ðxÞ
(
exp ðb=pÞ
X k
)+ + Uðxk Þ UðxÞ
ð8:29Þ fp U
where x is the centroid position, h ifp designates an average over the free particle quantum mechanical distribution obtained with the implicit constraint that x coincides with the current position of the corresponding classical particle, and h iU
8.4 The EVB as a Basis for LFER of PT Reactions
designates an average over the classical potential U. It is worth stressing that path integral calculations involving computationally expensive quantum chemical evaluation of forces and energies would benefit much from the QCP scheme. In quantum chemical calculations involving quasiparticles, one cannot realize exclusions between quasiparticles and therefore computational effort is proportional to the number of the quasiparticles in the necklace. In the present approach the quantum connection can be performed a posteriori, using the stored trajectory. It would be interesting to apply this approach to a Car-Parinello path integral scheme and demonstrate almost negligible increases of the CPU time relative to the classical treatment of the nuclei [61]. Using Eq. (8.27) we can obtain the quantum mechanical free energy surface by evaluating the corresponding probability by the same combined free energy perturbation umbrella sampling approach that has been repeatedly applied in our classical simulations as well as in our quantum mechanical simulations, but now we use the double average of Eq. (8.15) rather than an average over a regular classical potential. The actual equations used in our free energy perturbation (FEP) umbrella sampling calculations are given elsewhere, but the main point of the QCP is that the quantum mechanical free energy function can be evaluated by a centroid approach, which is constrained to move on the classical potential. This provides stable and relatively fast converging results that have been shown to be quite accurate in studies of well-defined test potentials where the exact quantum mechanical results are known.
8.4
The EVB as a Basis for LFER of PT Reactions
The approach used to obtain the EVB free energy functionals (the Dgi of Eq. (8.12)) was originally developed in Ref. [1] in order to provide the microscopic equivalent of Marcus theory for electron transfer reactions [29]. This approach allows one to explore the validity of the Marcus formula on a microscopic molecular level [62]. While this point is now widely accepted by the ET community [44], the validity of the EVB as perhaps the most general tool in microscopic LFER studies of PT reactions is less appreciated. This issue will be addressed below. In order to explore the molecular basis of LFER, we have to consider a one-step chemical reaction and to describe this reaction in terms of two diabatic states, e1 and e2 , that correspond to the reactant and product states. In this case the ground state adiabatic surface is given by 1 Eg ¼ ½ðe1 þ e2 Þ 2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðe1 e2 Þ 2 þ 4H12
ð8:30Þ
With this well-defined adiabatic surface we can explore the correlation between Dg z and DG 0 . Now the EVB/umbrella sampling procedure (for example, Ref. [3]) allows one to obtain the rigorous profile of the free energy function, Dg, that corre-
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8 Computer Simulations of Proton Transfer in Proteins and Solutions
sponds to Eg and the free energy functions, Dg1 and Dg2 , that correspond to e1 and e2 , respectively (see Fig. 8.5). It is important to point out here that such profiles have been evaluated quantitatively in many EVB simulations of chemical reactions in solutions and proteins (for reviews see Refs. [24, 63]). The corresponding profiles provide the activation free energy, Dg z , for the given chemical step. The calculated activation barrier can then be converted (for example, see Ref. [3]) to the corresponding rate constant using transition state theory (TST): 0 =RTg k i!j G ðRT=hÞ expfDgi!j
ð8:31Þ
A more rigorous expression for k i!j can be obtained by multiplying the TST expression by a transmission factor that can be calculated easily by running downhill trajectories [3]. However, the corresponding correction which takes into account barrier recrossing is an order of unity for reactions in aqueous solutions and enzymes [4]. In many case it is useful to estimate Dg and Dg 0 by an approximated expression. Here we note that with the simple two-state model of Eq. (8.11) we can obtain a very useful approximation to the Dg curve. That is, using the aforementioned free energy EVB/umbrella sampling formulation, we obtain the Dg that corresponds to the Eg and the free energy functions, Dgi , that correspond to the ei surfaces. This leads to the approximated expression 1 DgðxÞ ¼ ½ðDg1 ðxÞ þ Dg2 ðxÞÞ 2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðxÞ ðDg1 ðxÞ Dg2 ðxÞÞ 2 þ 4H12
ð8:32Þ
This relationship can be verified in the case of small H12 by considering our ET studies [62], while for larger H12 one should use a perturbation treatment. Now we can exploit the fact that the Dgi curves can be approximated by parabolas of equal curvatures (this approximated relationship was found to be valid by many microscopic simulations (e.g. Ref. [24])). It is known empirically that for a series of chemical reactions those which are more exothermic typically proceed faster. This approximation can be expressed as ðiÞ
Dgi ðxÞ ¼ l
x xo ð jÞ
!2 ð8:33Þ
ðiÞ
xo xo
where l is the so-called ‘‘solvent reorganization energy’’ (which is illustrated in Fig. 8.3). Using Eqs. (8.32) and (8.33), one obtains the Hwang A˚qvist Warshel (HAW) equation [27, 64], which is given in the general case by ðiÞ
0 0 0 Dgi!j ¼ ðDGi!j þ l i!j Þ 2 =4l Hij ðx 0Þ þ Hij2 ðx0 Þ=ðDGi!j þ l i!j Þ þ Gij
ð8:34Þ
0 where DGi!j is the free energy of the reaction, and Hij is the off-diagonal term that mixes the two relevant states with the average value at the transition state, x 0, and
8.4 The EVB as a Basis for LFER of PT Reactions ðiÞ
at the reactant state, x0 . Gij is the NQM correction that reflects the effect of tunneling and zero point energy corrections in cases of light atom transfer reactions. G therefore includes all effects associated with the quantum mechanical nature of the nuclei motion. Repeated quantitative EVB studies of PT and other reactions in solutions and proteins (for example, Refs. [24, 65]) established the quantitative validity of Eq. (8.34). With this fact in mind we can take these equations as a quantitative correla0 0 and DGi!j . Basically, when the changes in DG 0 are small, we tion between Dgi!j 0 0 and DGi!j . This linear relationship, obtain a linear relationship between Dgi!j 0 of Eq. (8.34) with respect which can be obtained by simply differentiating the Dgi!j 0 , can be expressed in the form to DGi!j 0 0 DDgi!j ¼ yDDGi!j
ð8:35Þ
0 where y ¼ ðDGi!j þ lÞ=2l, and where the contribution from the last term of Eq. (8.34) is neglected. The linear correlation coefficient depends on the magnitude of DG 0 and l. At any rate, more details about this linear free energy relationship (LFER) or free energy relationship (FER), and its performance in studies of chemical and biochemical problems are given elsewhere [3, 24, 27, 66–68].
Figure 8.5. A schematic description of the relationship between the free energy difference DG0 and the activation free energy Dg z. The figure illustrates how a shift of Dg2 by DDG0 (that changes Dg2 to Dg2 0 and DG0 to DG0 þ DDG0 ) changes Dg z by a similar amount.
0 The main point of Eq. (8.36) and Fig. 8.3 is that the DGi!j , which determines the 0 , is correlated with the difference between the two minima of corresponding Dgi!j the Dg profile that correspond to states i and j, respectively.
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While our ability to reproduce the observed LFER might not look like a conceptual advance, the fact that the EVB provides a rigorous basis for FER in condensed phases leads to a different picture than what has been assumed in traditional LFER studies. That is, as is clear from the HAW relationship, it is essential to take into account the effect of Hij on LFER studies that involve actual chemical reactions (rather than ET reactions). In such cases, Hij is frequently very significant, and its neglect leads to an incorrect estimate of the relevant reorganization energy. This point has not been widely appreciated because of the fact that the correlation between Dg 0 and DG does not depend so critically on Hij . Thus, as long as one fits the experimentally observed relationship by phenomenological parameters, it is hard to realize that the relevant reorganization energies are underestimated in a drastic way. A case in point is provided by the systematic analyses of PT reactions in enzymes [24, 58], and of hydride transfer and SN 2 reactions [27, 66]. A specific example of a LFER analysis will be given in the next section. The use of the EVB and Eq. (8.34) in studies of reactions in solutions has been extended to studies of LFERs in enzymes. The successes of this approach have been demonstrated in several important systems. At present, we view these studies as the most quantitative LFER studies of enzymes. It is also useful to point out the successes of our approach in LFER studies of electron transport in proteins (for example, Ref. [69]). A recent study of Kiefer and Hynes [70] used an EVB formulation, with a dielectric continuum treatment of the solvent, in an attempt to derive a LFER for PT reactions. Although their derivation did not include the crucial effect of Hij , and overlooked our earlier works it is encouraging to see a further realization of the effectiveness of the EVB in providing a molecular basis to LFER treatments.
8.5
Demonstrating the Applicability of the Modified Marcus’ Equation
In order to illustrate our point about the difficulties associated with phenomenological LFER treatments of reactions in solutions and in enzymes, it is instructive to consider the studies of Human carbonic anhydrase III (which will be referred to here as CA III) [71]. Studies of this system [71, 72] demonstrated that the rate of PT in mutants of CA III is correlated with the pK a difference between the donor and acceptor. It was found that the observed LFER follows a Marcus’ type relationship. Although this study provided an excellent benchmark for studies of PT in proteins, it also raised the question about uniqueness of the parameters deduced from phenomenological LFER studies. This issue will be explored below. The catalytic reaction of CA III can be described in terms of two steps. The first is attack of a zinc-bound hydroxide on CO2 [73]. CO2 þ EZnþ2 ðOH Þ þ H2 O S HCO3 þ EZnþ2 ðH2 OÞ
ð8:36Þ
8.5 Demonstrating the Applicability of the Modified Marcus’ Equation
The reversal of this reaction is called the ‘‘dehydration step’’. The second step involves the regeneration of the OH by a series of PT steps [74, 75] kB
EZnþ2 ðH2 OÞ þ B T EZnþ2 ðHO Þ þ BHþ kB
ð8:37Þ
where KB ¼ kB =kB (in the notation of Ref. [71]), BHþ can be water, buffer in solution or the protonated form of Lys64 (other CAs have His in position 64). Previous experimental studies [71] have established a LFER that was fitted to the Marcus’ equation using Dg z ¼ w r þ f1 þ DG 0 =4DGz0 g 2 DGz0
ð8:38Þ
0 ¼ w r þ DG 0 w p, where where the observed reaction free energy is given by DGobs r w is the reversible work of bringing the reactants to their reacting configuration and w p is the corresponding work for the reverse reaction. DG 0 is the free energy of the reaction when the donor and acceptor are at their optimal distance. DGz0 is the so-called intrinsic activation barrier, which is actually 14 of the corresponding reorganization energy, l. Here we use Dg z rather than DGz for the activation barrier, following the consideration of Ref. [3]. Equation (8.38) can also be written in the well-known form
Dg z ¼ w r þ ðDG 0 þ lÞ 2 =4l
ð8:39Þ
The phenomenological fitting processes yielded l ¼ 5:6 kcal mol1 and w r G 10:0 kcal mol1 . The estimated value of l appears to be in conflict with the value deduced from microscopic computer simulation studies (l G 80 kcal mol1 in Ref. [64]). Furthermore, the large value of w r is hard to rationalize, since the reaction involves a proton transfer between a relatively fixed donor and acceptor (residue 64 and the zinc bound hydroxide). The very small value of l obtained by fitting Eq. (8.20) to experiment is not exclusive to CA III. Similarly, small values were obtained in analysis of other enzymes and are drastically different than the values obtained by actual microscopic computer simulations (note in this respect that l cannot be measured directly). As pointed out before [58, 76, 77], the above discrepancies reflect the following problems. First, the reaction under study may involve more than two intersecting parabolas and thus cannot be described by Eq. (8.20). Second, although Eq. (8.20) gives a proper description for electron transfer (ET) reactions where the mixing between the reactant and product state (H12 ) is small, it cannot be used to describe proton transfer or other bond breaking reactions, where H12 is large. In such cases one should use the HAW equation, Eq. (8.34) [27, 64]. In order to obtain a proper molecular description of LFERs, it is essential to represent each reactant, product or intermediate by a parabolic free energy function [3]. In the case of CA III, we describe the proton transfer from residue 64 (Lys or His) to the zinc bound hydroxyl via a bridging water molecule (and alternatively two water molecules), by considering the three states
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c1 ¼ BHþ ðH2 OÞb ðOH Þa Znþ2 c2 ¼ BðH3 Oþ Þb ðOH Þa Znþ2
ð8:40Þ
c3 ¼ BðH2 OÞb ðH2 OÞa Znþ2 where we denote by B the base at residue 64, and where c1 and c3 correspond, respectively, to the right and left sides of Eq. (8.37). The relative free energy of these states can be estimated from the corresponding pK a s, where the pK a s of (H2 O)a and B are known from different mutations [71], while the pK a of (H2 O)b can be calculated by the PDLD/S-LRA approach [78]. Note that our three-state system can be easily extended to include one more water molecule and one more state. The result of a HAW LFER analysis of the CA III system is illustrated in Fig. 8.6 and the overall dependence of DDg 0 on DG13 is presented in Fig. 8.7 (for more details see Ref. [77]). As seen from the figures our model reproduced the observed trend. However, the origin of the trend is very different than that deduced from the two-state Marcus’ equation. That is, the flattening of the LFER at DpK a > 0, which would be considered in a phenomenological analysis of a two-state model as the beginning of the Marcus’ inverted region (where DG0 ¼ l), is due to the behavior of the three-state system (see Ref. [79]). The extraction of l from fitting Eq. (8.38) to the observed LFER requires that l ¼ DG 0 so that DG 0 < 0 at the point where the LFER becomes flat. This means that we must have data from regions where DG 0 < 0. However, at least for the z 0 is rate limiting, DG12 cannot be negative, and the observation of cases when Dg12 the beginning of a flat LFER is actually due to other factors. It is also important to realize that l out cannot become too small and never approach zero, which is the continuum limit for a completely nonpolar environment (see discussion in Ref. [80]). The reason is quite simple; the protein cannot use a nonpolar environment, since this will decrease drastically the pK a of (H3 Oþ )b . Instead, proteins use polar environments with partially fixed dipoles. However, no protein can keep its dipoles completely fixed (the protein is flexible) and thus gives a non-negligible l out . Of course, this reorganization energy is still smaller than the corresponding value for proton transfer in solutions, but it never approaches the low value obtained from fitting in a two-state Marcus’ formula [81]. As long as we obtain the value of Hij from fitting to observed LFERs, it is possible to argue that both Eqs. (8.39) and (8.34) reflect a phenomenological fitting with _____________________________________________________________________G Figure 8.6. Analysis of the energetics of PT in the i, ii, and iii mutants of CA III for the case where the transfer of a proton from residue 64 to the zinc-bound hydroxide involves two water molecules. The figure describes the three states of Eq. (8.40) and considers their change in each of the indicated mutants (relative to the native enzyme), and displays the changes
in the diabatic potential surfaces and the corresponding changes in the adiabatic activation barriers. The figure also gives the changes in the diabatic activation energies. The final activation barrier is taken in each case as the highest adiabatic barriers (taken from Ref. [79]).
8.5 Demonstrating the Applicability of the Modified Marcus’ Equation
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a free parameter (o and l in the case of Eq. (8.39), and Hij in the case of Eq. (8.34)). The difference, however, is that Eq. (8.34) and the use of three free energy functionals reflects much more realistic physics. This is evident, for example, from the fact that with Eq. (8.34) we do not obtain an unrealistically large w r . Note in this 0 in Eq. (8.23) might look like w in the phenomenological fitting respect that DG12 to the Marcus’ equation. It is also important to emphasize at this point that the present treatment is not a phenomenological treatment with many free parameters, as might be concluded by those who are unfamiliar with molecular simulations. That is, our approach is based on realistic molecular parameters obtained while starting from the X-ray structure of the protein and reproducing the relevant pK a s and reorganization energy. Reproducing the observed LFER by such an approach without adjusting the key parameters is fundamentally different than an approach that takes the observed LFER and adjusts free parameters in a given model to reproduce it. In such a case, one can reproduce experimental data by almost any model.
Figure 8.7. Calculated and observed FER for CA III. The different systems are marked according to the notation of Ref. [79]. The term DpKa corresponds to the pKa difference between the zinc-bound water and the pKa of the given donor group (DpKa ¼ DG13 =2:3RT ).
Finally, we would like to address the validity of the general use of the HAW Equation (Eq. (8.34)) and the multistate procedure used for studies of the proton transport (PTR) in CA. The use of Eq. (8.34) for subsequent PT steps might look to some as an ad hoc approach, considering the assumption that PTR processes involve the Grotthuss mechanism, which is not sensitive to the DGij0 values for the sequential transfer process. However, the assumption that the Grotthuss mechanism is a key factor underwent recently a major paradigm shift, where those who supported this idea started to attribute major importance to the electrostatic barrier
8.5 Demonstrating the Applicability of the Modified Marcus’ Equation
[82], in agreement with our view [83, 84]. Further support to this point is given below. In order to further explore the validity of the stepwise modified Marcus’ model, we developed recently [85] a simplified EVB model which represents the given conduction chain by an explicit EVB, while representing the rest of the environment (protein and solvent) implicitly. This is done by using the same type of solute surface as in Eq. (8.8), while omitting the explicit solute–solvent and solvent–solvent terms (the USs and Uss terms) and replacing them by implicit terms using: ei ¼ ei0 þ ðh oQ =2ÞbðQ i; kðiÞ þ dÞ 2 þ ðQ i; k 0 ðiÞ dÞ 2 c þ DðiÞ E tot ¼ E g þ
X ðh oQ =2ÞbðQ i;2 kðiÞ þ BðQ i; kðiÞ Q i; k 0 ðiÞ Þ 2 Þc
ð8:41aÞ ð8:41bÞ
i
Where the Qs are the solvent coordinates that are given by the electrostatic component of the energy gap ððh oQ dQ ÞQ ij ¼ ejel eiel Þ, d is the dimensionless origin shift of the solvent coordinate, oQ is the effective vibrational frequency of the solvent, and E g is the lowest eigenvalue of Eq. (8.7), and the B term represents the coupling between the solvent coordinates. Here E g reflects the effect of the ei of Eq. (8.41a) and the other term in Eq. (8.41b) reflect the cost in solvent energy associated with moving the solvent coordinates from their equilibrium positions. Equation (8.41) is written for the case of a chain of water molecules, so that we assign one solvent coordinate to each pair of oxygens. In this case, the index i corresponds to a proton on the ith oxygen inside the chain, while k 0 ðiÞ and kðiÞ correspond to the oxygens before and after i, respectively. When i is the first oxygen, there is no Q i; k 0 . The free energy, g g , associated with the energy surface, E g , (here the free energy accounts for the average over the coordinates of the active space) is treated as the effective free energy surface that includes implicitly the rest of the system. That is, we use gðrÞeff ¼ g g ðrÞ
ð8:42Þ
where r are the coordinates of the active space. In doing so, we note that in this simplified expression we treat the environment implicitly by adjusting the DðiÞ s to DðiÞ while imposing the requirement ðDGi!j Þeff ¼ ðDGi!j Þcomplete z z ðDgi!j Þeff ¼ ðDgi!j Þcomplete
ð8:43Þ
where ð Þeff represents the quantity obtained with the effective EVB potential and ð Þcomplete designates the results obtained when the EVB of the entire system is included explicitly. For convenience we usually determine ðDGi!j Þcomplete (and the corresponding DðiÞ values of the effective model) by the semimacroscopic electrostatic calculations outlined below. The simplified system has therefore identical free energy of activation and identical reaction free energy as the full system, and it allows for much longer simulations.
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With the effective potential defined above it is possible to examine the time dependence of PTR processes by Langevin dynamics (LD) simulations (considering the fluctuation of the missing parts of the system by using an effective friction), and such simulations were used to study the PTR in CA. The simulation established that the rate of the PTR process is determined by the energetics of the proton along the conduction chain, once the energy of the proton in two successive sites is significantly higher than the energy of the proton in the bulk water. The model was also applied to PTR in the K64H-F198D mutant of CA III and reproduced the observed rate constant. Typical simulations for the case where the energy of the proton on His64 is raised by 1.2 kcal mol1 , in order to accelerate the calculations, are described in Fig. 8.8. The calculated average time for PTR from His64 to the Zn-bound hydroxide is about 5 106 s. Correcting this result for the energy shift and the effect of using overdamped rather than underdamped Brownian dynamics (BD) simulation gives a result that is close to the observed kB (kB ¼ 3 106 s). The simulation provides an additional major support for the use of the HAW model.
8.6
General Aspects of Enzymes that Catalyze PT Reactions
Computer simulation studies have been used since 1976 to explore the origin of the catalytic power of different enzymes (for a recent review see Ref. [9]). Basically, the EVB studies, as well as the consistent QM/MM calculations identified electrostatic transition state stabilization (TSS) as the key catalytic factor (a discussion of
Figure 8.8. The time dependence of the probability amplitude of the transferred proton for a LD trajectory for a PTR that starts at His64 and ends at OH in the overdamped version of model S/A of the K64H-F198D
mutant of CA III. The calculations were accelerated by considering a case where the minimum at site d is raised by 1.2 kcal mol1 (taken from Ref. [85]).
8.7 Dynamics, Tunneling and Related Nuclear Quantum Mechanical Effects
inconsistent analyses has been given elsewhere [9, 63]. In many cases, it was found that enzymes catalyze PT steps by reducing the pK a differences between the donor and acceptor [86]. However, in other cases (for example, the reaction of serine proteases [87]) the catalytic effect is exerted at the highest transition state, which is not a PT step, and the PT step is not catalyzed. As far as the present work is concerned, it is interesting to note that when a PT or hydride transfer step is catalyzed (for example, Refs. [3, 4, 88]) it is always accomplished by electrostatic stabilization of the corresponding change in charge distribution. This is done by the preorganized polar environment of the protein, which reduces the reorganization energy during the PT step (see discussion in Ref. [89]). In considering the catalytic effect in PT processes, it is important to avoid common confusion associated with the so-called low barrier hydrogen bond (LBHB) proposal (for example, Ref. [90]). The LBHB proposal assumes that hydrogen bonding to the TS involves covalent interactions with special catalytic power. EVB considerations have shown that this assumption is incorrect since covalent interactions lead to delocalized charge distribution, which is less stable than localized charge in the protein polar environment (see for example Ref. [91]). In the polar environment the existence of a localized charge is more favorable than a delocalized charge. Since the latter case corresponds to the LBHB that corresponds to the transition state, the LBHBs in this sense are anticatalytic rather than catalytic. Unfortunately, in addition to the clear inconsistency of the LBHB proposal, it was also invoked in discussing PT steps. Now the transition states of PT steps do involve covalent delocalized TSs, but this has nothing to do with the LBHB proposal or with catalysis, since the same delocalization is involved in the reference reaction in aqueous solution. Regardless of the exact nature of the PT step and the corresponding catalytic effect, we feel that our approach offers an extremely robust way of examining the role of the enzyme in these steps. All that is needed is to compare the energetics as to ‘‘reactant’’ and ‘‘product’’ states in the enzyme and in solution. This reduces to a simple electrostatic problem that can be addressed by the EVB/FEP calculations.
8.7
Dynamics, Tunneling and Related Nuclear Quantum Mechanical Effects
Recent studies (see Ref. [92] and references in Ref. [4]) have suggested that vibrationally enhanced tunneling (VET) of PT, hydride transfer, and hydrogen transfer reactions plays a major role in enzyme catalysis. According to this interesting proposal, nature created by evolution protein vibrational modes that are strongly coupled to the hydrogen atom motion. Some workers (for example, Ref. [93]) assumed that there exists here an entirely new phenomenon that makes TST inapplicable to enzymatic reactions. However, the VET effect is not new and is common to many chemical reactions in solution [1, 48, 94]. Moreover, the VET is strongly related to TST. That is, when the solvent fluctuates and changes the energy gap (see Refs. [1, 2]) the light atom sees a fluctuating barrier that allows, in some cases, for a larger rate of tunneling. As shown in Ref. [2], these fluctuations are taken into
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account in the statistical factor of the classical TST and the same is true when quantum effects are taken into account. Thus, the recent realization that the solvent coordinates should be considered in tunneling studies is not new, nor does it mean that this effect is important in catalysis. Warshel and Chu [42] and Hwang et al. [60] were the first to calculate the contribution of tunneling and other nuclear quantum effects to PT in solution and enzyme catalysis, respectively. Since then, and in particular in the past few years, there has been a significant increase in simulations of quantum mechanicalnuclear effects in enzyme and in solution reactions [16]. The approaches used range from the quantized classical path (QCP) (for example, Refs. [4, 58, 95]), the centroid path integral approach [54, 55], and variational transition state theory [96], to the molecular dynamics with quantum transition (MDQT) surface hopping method [31] and density matrix evolution [97–99]. Most studies of enzymatic reactions did not yet examine the reference water reaction, and thus could only evaluate the quantum mechanical contribution to the enzyme rate constant, rather than the corresponding catalytic effect. However, studies that explored the actual catalytic contributions (for example, Refs. [4, 58, 95]) concluded that the quantum mechanical contributions are similar for the reaction in the enzyme and in solution, and thus, do not contribute to catalysis. Interestingly, the MDQT approach of Hammes-Schiffer and coworkers [31] allowed them to explore the quantum mechanical transmission factor. It was found that even with quantum mechanical considerations, the transmission factor is not so different from unity, and thus, we do not have a large dynamical correction to the TST rate constant. It is important to clarify here that the description of PT processes by curve crossing formulations is not a new approach nor does it provide new dynamical insight. That is, the view of PT in solutions and proteins as a curve crossing process has been formulated in early realistic simulation studies [1, 2, 42] with and without quantum corrections and the phenomenological formulation of such models has already been introduced even earlier by Kuznetsov and others [47]. Furthermore, the fact that the fluctuations of the environment in enzymes and solution modulate the activation barriers of PT reactions has been demonstrated in realistic microscopic simulations of Warshel and coworkers [1, 2]. However, as clarified in these works, the time dependence of these fluctuations does not provide a useful way to determine the rate constant. That is, the electrostatic fluctuations of the environment are determined by the corresponding Boltzmann probability and do not represent a dynamical effect. In other words, the rate constant is determined by the inverse of the time it takes the system to produce a reactive trajectory, multiplied by the time it takes such trajectories to move to the TS. The time needed for generation of a reactive trajectory is determined by the corresponding Boltzmann probability, and the actual time it takes the reactive trajectory to reach the transition state (of the order of picoseconds), is more or less constant in different systems. It is also important to clarify that the solvent reorganization energy, which determines the amplitude of the solvent fluctuations, is not a ‘‘static dynamical effect’’ (as proposed by some) but a unique measure of the free energy associated with the
8.7 Dynamics, Tunneling and Related Nuclear Quantum Mechanical Effects
reorganization of the solvent from its reactant to its product configuration (see Ref. [62] for a more rigorous definition). In fact, the reorganization energy, l, and the reaction energy, DG, determine the activation free energy (DGz ) and the corresponding Boltzmann probability of reaching the transition state (see discussion in Refs. [2, 4]). Now, since the DGz is a probability factor it can be determined by Monte Carlo simulations without any dynamical considerations. Furthermore, since the transmission factor (k in Eq. (8.1)) is the only rigorous dynamical part of the rate constant and since k is close to unity in enzymes and solutions, see e.g. Ref. [4], the corresponding rate constants do not show significant dynamical effects. Furthermore, attempts to define dynamical catalytic effect in a different way and to include in such factor nonequilibrium solvation effects [100] have been shown to be very problematic (e.g. Ref. [4]). Similarly, we have shown that the reasonable definition of dynamical effects by the existence of special vibrations that lead coherently to the TS does correspond to the actual simulation in enzyme and solution. Before concluding this section, we find it useful to discuss the specific case of lipoxygenase, which has been brought recently [101] as an example of the role of NQM in catalysis. The catalytic reaction of lipoxygenase involves a very large isotope effect (@80) and thus it is tempting to suggest that the enzyme catalyzes this reaction by enhancing the tunneling effect. This proposal [53] has been examined by several theoretical approaches ranging from phenomenological models [31, 53, 102] to continuum representations of the protein [103] and to complete microscopic treatment of the system using the QCP approach [50]. The phenomenological studies were able to fit the observed kinetics with an unrealistically large reorganization energy (l A 20 kcal mol1 ) using the vibronic formulation of Eq. (8.16), while the microscopic reorganization energy was actually found to be around 2 kcal mol1 [50]. The unrealistic phenomenological parameters may reflect several major problems, including the fact that the vibronic formula is invalid in the adiabatic limit and the other problems discussed in Section 8.3. Some of these fundamental problems can be reduced by modifying the diabatic potential to reflect the enormous effect of H12 (which is not considered in any of the vibronic treatments except in that of Warshel and Chu [42]). This type of treatment, which leads to Eq. (8.25) has been used recently [104] in a very qualitative examination of the KIE in lipoxygenase that compares the vibronic and the much more rigorous QCP simulations that will be considered below. Hammes-Schiffer and coworkers [103] have progressed beyond the phenomenological vibronic treatment by using much more realistic potentials and a semimicroscopic treatment. However, the protein effect was modeled macroscopically with an arbitrarily low dielectric constant. Such a treatment makes it hard to explore the actual role of the protein. Thus, at present, the only study that actually examines the microscopic origin of the observed isotope effect by taking into account the entire protein, and more importantly the nature of the catalytic effect, is the study of Olsson et al. [50]. Here it was found that the QCP simulation reproduces the observed isotope effect and the corresponding reduction in activation free energy. Most significantly, the simulations show that the same NQM effect oc-
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curs in the enzyme and solution and that the reorganization energy in the protein and solution is extremely small (l out A 2 kcal mol1 ) since we are dealing with a hydrogen transfer (rather than PT) reaction. In view of the similarity between the NQM in the enzyme and solution, it seems that the catalysis does not involve optimization of NQM effects. At this point one might wonder about our assertion that the reaction in solution and in the protein have similar quantum corrections since a reaction with a model compound that is assumed to be related to lipoxygenase show only an isotope effect of 6. Here, we can only bring out the following points: (i) we are quite convinced that the effect of the protein and the solution on the H atom transfer reaction is quite small, (ii), our studies have shown that the isotope effect depends strongly on the donor acceptor distance (see also above) and it is possible that the average distance is longer in the protein than in water, (iii), it is not clear that the model reaction in water reflects only the H-transfer step. Finally, our main point is that if the quantum corrections are smaller in water than in the protein (and the reaction is the same), we must have a larger donor–acceptor distance in the protein and thus a negative catalytic effect (the barrier is higher at a longer distance). In other words we do not see any simple way for the NQM effects to catalyze this reaction. To conclude this section, it is useful to point out an interesting conclusion that emerged from the use of Eqs. (8.25) and (8.27). That is, using the above equations we found that the degree of tunneling (or at least the magnitude of the isotope effect) decreases, rather than increases, when the donor–acceptor distance is reduced. This reflects the reduction in the effective diabatic XaH stretching frequency. This means that the common idea that enzymes can catalyze H transfer or PT reactions by compressing the donor and acceptor complexes [101] is very problematic. Such a compression will in fact reduce the tunneling contributions, 2 2 ÞD =ðS00 ÞH , whose value since the largest contribution to the KIH comes from ðS00 decreases drastically when DH and oH decrease. Furthermore, as we have shown repeatedly, enzymes are flexible and unlikely to be able to change drastically the reaction surface [3, 105]. Thus it is quite likely that the main difference between reactions with large tunneling and small tunneling corrections is the intrinsic shape of the potential surface rather than the effect of the environment on this surface. It is thus possible that radical reactions involve steep potential surfaces with relatively small H12 , while other reactions involve large H12 and shallow surfaces with small effective oH .
8.8
Concluding Remarks
This work addressed the issue of proton transfer, focusing on clear microscopically based concepts and the power of computer simulation approaches. It was shown that when such concepts as reorganization energy and Marcus’ parabolas are formulated in a consistent microscopic way, they could be used to explore the nature
Abbreviations
of PT and PTR in proteins. It was also clarified that phenomenological applications of the Marcus’ formula or related expressions can lead to problematic conclusions. The use of the EVB approach is shown to provide a powerful quantitative bridge between the classical concepts of physical organic chemistry and the actual energetics of enzymatic reactions. This approach provides quantitative LFERs for PT in enzymes and solution, and allows us to quantify catalytic effects and to define them in terms of the relevant reorganization energies, reaction free energies, and the preorganization of enzyme active sites. Our studies have demonstrated that dynamical effects do not play an important role in enzyme catalysis. We also show that NQM effects do not contribute significantly since similar effects occur in the reference solution reactions. Nevertheless, one should be able to calculate NQM effects and to treat dynamical effects in order to reproduce the actual rate constant in enzymes and to analyze and discriminate between different catalytic proposals. The ability to address such problems has been provided by our approaches. In summary, the approaches and concepts outlined in this work provide a powerful way to address different aspects of PT in proteins. Using the EVB and related approaches should allow one to resolve most of the open questions about PT and PTR in proteins. It also allows one to obtain a reliable structure function correlation in specific cases, and thus to convert qualitative concepts about proton transfer in biology to quantitative microscopic concepts.
Acknowledgements
This work was supported by NIH grants GM-24492 and GM-40283. One of us (JM) thanks the J. William Fulbright Scholarship Board for the award of a research scholarship. We also gratefully acknowledge the University of Southern California’s High Performance Computing and Communications Center for computer time.
Abbreviations
a DGz Dg1 l o BD Cg Ea Eg EVB F or k
Gas-phase shift Reaction free energy barrier Free energy function Reorganization energy Frequency Brownian dynamics Ground state eigenvector Activation energy Ground state adiabatic energy surface Empirical valence bond Transmission factor
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8 Computer Simulations of Proton Transfer in Proteins and Solutions
FEP/US HEVB K kB LBHB LD LFER MDQT MM NQM PT PTR QCP QM R R r Smn S T TS TST VB VET x Z
Free energy perturbation/umbrella sampling EVB Hamiltonian Rate constant Boltzmann’s constant Low barrier hydrogen bond Langevin dynamics Linear free energy relationships Molecular dynamics with quantum transition Molecular mechanics Nuclear quantum mechanical Proton transfer Proton translocations Quantum classical path Quantum mechanics Gas constant, same as kB , but usually in different units Solute coordinate Solvent coordinate Franck–Condon factor for transition from state m to state n Overlap matrix element Temperature Transition state Transition state theory Valence bond Vibrationally enhanced tunneling Reaction coordinate, energy gap Partitionfunction
References 1 Warshel, A., Dynamics of Reactions
2
3
4
5
in Polar Solvents. Semiclassical Trajectory Studies of Electron-Transfer and Proton-Transfer Reactions, J. Phys. Chem. 1982, 86, 2218–2224. Warshel, A., Dynamics of Enzymatic Reactions, Proc. Natl. Acad. Sci. USA 1984, 81, 444–448. Warshel, A., Computer Modeling of Chemical Reactions in Enzymes and Solutions, John Wiley & Sons, New York, 1991. Villa, J., Warshel, A., Energetics and Dynamics of Enzymatic Reactions, J. Phys. Chem. B 2001, 105, 7887–7907. Keck, J. C., Variational Theory of Reaction Rates, Adv. Chem. Phys. 1966, 13, 85–121.
6 Bennett, C. H., Molecular dynamics
and transition state theory: the simulation of infrequent events, in Algorithms for Chemical Computations, Christofferson, R. E. (Ed.), American Chemical Society, Washington, D. C., 1977, pp. 63–97. 7 Grimmelmann, E. K., Tully, J. C., Helfand, E., Molecular Dynamics of Infrequent Events: Thermal Desorption of Xenon from a Platinum Surface, J. Chem. Phys. 1981, 74, 5300–5310. 8 Pople, J. A., Quantum chemical models (Nobel lecture), Angew. Chem. Int. Ed. Engl. 1999, 38, 1894–1902. 9 Shurki, A., Warshel, A., Structure/ Function Correlations of Protreins
References
10
11
12
13
14
15
16
17
18
using MM, QM/MM and Related Approaches; Methods, Concepts, Pitfalls and Current Progress, Adv. Protein Chem. 2003, 66, 249–312. Warshel, A., Levitt, M., Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme, J. Mol. Biol. 1976, 103, 227–249. The´ry, V., Rinaldi, D., Rivail, J.-L., Maigret, B., Ferenczy, G. G., Quantum Mechanical Computations on Very Large Molecular Systems: The Local Self-Consistent Field Method, J. Comput. Chem. 1994, 15, 269–282. Zhang, Y., Liu, H., Yang, W., Free energy calculation on enzyme reactions with an efficient iterative procedure to determine minimum energy paths on a combined ab initio QM/MM potential energy surface, J. Chem. Phys. 2000, 112, (8), 3483–3492. Gao, J., Hybrid quantum and molecular mechanical simulations: an alternative avenue to solvent effects in organic chemistry, Acc. Chem. Res. 1996, 29, 298–305. Bakowies, D., Thiel, W., Hybrid Models for Combined Quantum Mechanical and Molecular Approaches, J. Phys. Chem 1996, 100, 10580–10594. Field, M. J., Bash, P. A., Karplus, M., A Combined Quantum Mechanical and Molecular Mechanical Potential for Molecular Dynamics Simulations, J. Comput. Chem. 1990, 11, 700–733. Friesner, R., Beachy, M. D., Quantum Mechanical Calculations on Biological Systems, Curr. Opin. Struct. Biol. 1998, 8, 257–262. Monard, G., Merz, K. M., Combined Quantum Mechanical/Molecular Mechanical Methodologies Applied to Biomolecular Systems, Acc. Chem. Res. 1999, 32, 904–911. Garcia-Viloca, M., GonzalezLafont, A., Lluch, J. M., A QM/MM study of the Racemization of Vinylglycolate Catalysis by Mandelate Racemase Enzyme, J. Am. Chem. Soc 2001, 123, 709–721.
19 Marti´, S., Andre´s, J., Moliner, V.,
20
21
22
23
24
25
26
27
28
Silla, E., Tunon, I., Bertran, J., Transition structure selectivity in enzyme catalysis: a QM/MM study of chorismate mutase, Theor. Chem. Acc. 2001, 105, 207–212. Field, M., Stimulating Enzyme Reactions: Challenges and Perspectives. J. Comp. Chem. 2002, 23, 48–58. Mulholland, A. J., Lyne, P. D., Karplus, M., Ab Initio QM/MM Study of the Citrate Synthase Mechanism. A Low-Barrier Hydrogen Bond is not Involved, J. Am. Chem. Soc. 2000, 122, 534–535. Cui, Q., Elstner, M., Kaxiras, E., Frauenheim, T., Karplus, M., A QM/ MM Implementation of the SelfConsistent Charge Density Functional Tight Binding (SCC-DFTB) Method, J. Phys. Chem. B 2001, 105, 569–585. Strajbl, M., Hong, G., Warshel, A., Ab-initio QM/MM Simulation with Proper Sampling: ‘‘First Principle’’ Calculations of the Free Energy of the Auto-dissociation of Water in Aqueous Solution, J. Phys. Chem. B 2002, 106, 13333–13343. Aqvist, J., Warshel, A., Simulation of Enzyme Reactions Using Valence Bond Force Fields and Other Hybrid Quantum/Classical Approaches, Chem. Rev. 1993, 93, 2523–2544. Hong, G., Rosta, E., Warshel, A., Using the Constrained DFT Approach in Generating Diabatic Surfaces and Off Diagonal Empirical Valence Bond Terms for Modeling Reactions in Condensed Phase, J. Chem. Phys. In press. Wesolowski, T., Muller, R. P., Warshel, A., Ab Initio Frozen Density Functional Calculations of Proton Transfer Reactions in Solution, J. Phys. Chem. 1996, 100, 15444–15449. Hwang, J.-K., King, G., Creighton, S., Warshel, A., Simulation of Free Energy Relationships and Dynamics of SN 2 Reactions in Aqueous Solution, J. Am. Chem. Soc. 1988, 110, (16), 5297–5311. Warshel, A., Weiss, R. M., An Empirical Valence Bond Approach for Comparing Reactions in Solutions and
1201
1202
8 Computer Simulations of Proton Transfer in Proteins and Solutions
29
30
31
32
33
34
35
36
37
38
in Enzymes, J. Am. Chem. Soc. 1980, 102, (20), 6218–6226. Marcus, R. A., Chemical and electrochemical electron transfer theory, Annu. Rev. Phys. Chem. 1964, 15, 155–196. Marcus, R. A., Electron-transfer reactions in chemistry – theory and experiment (Nobel lecture), Angew. Chem. Int. Ed. Engl. 1993, 32, 1111–1121. Billeter, S. R., Webb, S. P., Agarwal, P. K., Iordanov, T., Hammes-Schiffer, S., Hydride Transfer in Liver Alcohol Dehydrogenase: Quantum Dynamics, Kinetic Isotope Effects, and Role of Enzyme Motion, J. Am Chem. Soc. 2001, 123, 11262–11272. Vuilleumier, R., Borgis, D., An Extended Empirical Valence Bond Model for Describing Proton Transfer in Hþ (H2 O)n Clusters and Liquid Water, Chem. Phys. Lett. 1998, 284, 71–77. Smondyrev, A. M., Voth, G. A., Molecular dynamics simulation of proton transport near the surface of a phospholipid membrane, Biophys. J. 2002, 82, (3), 1460–1468. Billeter, S. R., Webb, S. P., Iordanov, T., Agarwal, P. K., Hammes-Schiffer, S., Hybrid approach for including electronic and nuclear quantum effects in molecular dynamics simulations of hydrogen transfer reactions in enzymes, J. Chem. Phys. 2001, 114, 6925–6936. Florian, J., Comment on Molecular Mechanics for Chemical Reactions, J. Phys. Chem. A 2002, 106(19), 5046–5047. Truhlar, D. G., Reply to Comment on Molecular Mechanics for Chemical Reactions, J. Phys. Chem. A 2002, 106(19), 5048–5050. Warshel, A., Bromberg, A., Oxidation of 4a,4b-Dihydrophenanthrenes. III. A Theoretical Study of the Large Kinetic Isotope Effects of Deuterium in the Initiation Step of the Thermal Reaction With Oxygen, J. Chem. Phys. 1970, 52, 1262. Raff, L. M., Theoretical investigations
39
40
41
42
43
44
45
46
47
48
of the reaction dynamics of polyatomic systems: Chemistry of the hot atom (T* þ CH4) and (T* þ CD4), J. Chem. Phys. 1974, 60, (6), 2220. Schmitt, U. W., Voth, G. A., Multistate Empirical Valence Bond Model for Proton Transport in Water, J. Phys. Chem. B 1998, 102, 5547– 5551. Warshel, A., Russell, S., Theoretical Correlation of Structure and Energetics in the Catalytic Reaction of Trypsin, J. Am. Chem. Soc. 1986, 108, 6569–6579. Cuma, M., Schmitt, U. W., Voth, G. A., A multi-state empirical valence bond model for weak acid dissociation in aqueous solution, J. Phys. Chem. A 2001, 105, (12), 2814–2823. Warshel, A., Chu, Z. T., Quantum Corrections for Rate Constants of Diabatic and Adiabatic Reactions in Solutions, J. Chem. Phys. 1990, 93, 4003. Geissler, P. L., Dellago, C., Chandler, D., Hutter, J., Parrinello, M., Autoionization in liquid water, Science 2001, 291, (5511), 2121–2124. Warshel, A., Parson, W. W., Dynamics of biochemical and biophysical reactions: insight from computer simluations, Q. Rev. Biophys. 2001, 34, 563–670. Tully, J. C., Preston, R. M., Trajectory surface hopping approach to nonadiabatic molecular collisions: the reaction of Hþ with D2 , J. Chem. Phys. 1971, 55, 562–572. Warshel, A., Hwang, J.-K., Simulation of the Dynamics of Electron Transfer Reactions in Polar Solvents: Semiclassical Trajectories and Dispersed Polaron Approaches, J. Chem. Phys. 1986, 84, 4938–4957. Kuznetsov, A. M., Ulstrup, J., Proton and hydrogen atom tunnelling in hydrolytic and redox enzyme catalysis, Can. J. Chem.-Rev. Can. Chim. 1999, 77, (5–6), 1085–1096. Borgis, D., Hynes, J. T., Moleculardynamics simulation for a model nonadiabatic proton transfer reaction in solution, J. Chem. Phys. 1991, 94, 3619–3628.
References 49 Antoniou, D., Schwartz, S. D.,
50
51
52
53
54
55
56
57
58
Large kinetic isotope effects in enzymatic proton transfer and the role of substrate oscillations, Proc. Natl. Acad. Sci. USA 1997, 94, 12360– 12365. Olsson, M. H. M., Siegbahn, P. E. M., Warshel, A., Simulations of the large kinetic isotope effect and the temperature dependence of the hydrogen atom transfer in lipoxygenase, J. Am. Chem. Soc. 2004, 126, (9), 2820–2828. Smedarchina, Z., Siebrand, W., Ferna´ndez-Ramos, A., Cui, Q., Kinetic Isotope Effects for Concerted Multiple Proton Transfer: A Direct Dynamics Study of an Active-Site Model of Carbonic Anhydrase II, J. Am. Chem. Soc 2003, 125, (1), 243–251. Lehnert, N., Solomon, E. I., Densityfunctional investigation on the mechanism of H-atom abstraction by lipoxygenase, J. Biol. Inorg. Chem. 2003, 8, (3), 294–305. Knapp, M. J., Rickert, K., Klinman, J. P., Temperature-dependent isotope effects in soybean lipoxygenase-1: Correlating hydrogen tunneling with protein dynamics, J. Am. Chem. Soc. 2002, 124, (15), 3865–3874. Gillan, M. J., Quantum-Classical Crossover of the Transition Rate in the Damped Double Well, J. Phys. C. Solid State Phys. 1987, 20, 3621–3641. Voth, G. A., Path-integral centroid methods in quantum statistical mechanics and dynamics, Adv. Chem. Phys. 1996, 93, 135–218. Voth, G. A., Chandler, D., Miller, W. H., Rigorous Formulation of Quantum Transition State Theory and Its Dynamical Corrections, J. Chem Phys. 1989, 91, 7749. Hwang, J.-K., Warshel, A., A Quantized Classical Path Approach for Calculations of Quantum Mechanical Rate Constants, J. Phys. Chem. 1993, 97, 10053–10058. Hwang, J.-K., Warshel, A., How Important are Quantum Mechanical Nuclear Motions in Enzyme Catalysis? J. Am. Chem. Soc. 1996, 118, 11745–11751.
59 Feynman, R. P., Statistical Mechanics,
Benjamin, New York, 1972. 60 Hwang, J.-K., Chu, Z. T., Yadav, A.,
61
62
63
64
65
66
67
68
69
Warshel, A., Simulations of Quantum Mechanical Corrections for Rate Constants of Hydride-Transfer Reactions in Enzymes and Solutions, J. Phys. Chem. 1991, 95, 8445–8448. Tuckerman, M. E., Marx, D., Heavyatom skeleton quantization and proton tunneling in ‘‘intermediate-barrier’’ hydrogen bonds, Phys. Rev. Lett. 2001, 86, (21), 4946–4949. King, G., Warshel, A., Investigation of the Free Energy Functions for Electron Transfer Reactions, J. Chem. Phys. 1990, 93, 8682–8692. Warshel, A., Computer Simulations of Enzyme Catalysis: Methods, Progress, and Insights, Annu. Rev. Biophys. Biomol. Struct. 2003, 32, 425–443. Warshel, A., Hwang, J. K., A˚qvist, J., Computer Simulations of Enzymatic Reactions: Examination of Linear Free-Energy Relationships and Quantum-Mechanical Corrections in the Initial Proton-transfer Step of Carbonic Anhydrase, Faraday Discuss. 1992, 93, 225. Warshel, A., Simulating the Energetics and Dynamics of Enzymatic Reactions, Pontificiae Academiae Scientiarum Scripta Varia, 1984, Vol. 55. Kong, Y., Warshel, A., Linear Free Energy Relationships with Quantum Mechanical Corrections: Classical and Quantum Mechanical Rate Constants for Hydride Transfer Between NADþ Analogues in Solutions, J. Am. Chem. Soc. 1995, 117, 6234–6242. Schweins, T., Warshel, A., Mechanistic Analysis of the Observed Linear Free Energy Relationships in p21 ras and Related Systems, Biochemistry 1996, 35, 14232–14243. Warshel, A., Schweins, T., Fothergill, M., Linear Free Energy Relationships in Enzymes. Theoretical Analysis of the Reaction of TyrosyltRNA Synthetase, J. Am. Chem. Soc. 1994, 116, 8437–8442. Warshel, A., Chu, Z. T., Parson, W. W., Dispersed Polaron Simulations
1203
1204
8 Computer Simulations of Proton Transfer in Proteins and Solutions
70
71
72
73
74
75
76
77
78
79
of Electron Transfer in Photosynthetic Reaction Centers, Science 1989, 246, 112–116. Kiefer, P. M., Hynes, J. T., Nonlinear free energy relations for adiabatic proton transfer reactions in a polar environment. I. Fixed proton donoracceptor separation, J. Phys. Chem. A 2002, 106, (9), 1834–1849. Silverman, D. N., Tu, C., Chen, X., Tanhauser, S. M., Kresge, A. J., Laipis, P. J., Rate-Equilibria Relationships in Intramolecular Proton Transfer in Human Carbonic Anhydrase III, Biochemistry 1993, 34, 10757–10762. Silverman, D. N., Marcus Rate Theory Applied to Enzymatic Proton Transfer, Biochem. Biophys. Acta. 2000, 1458, (1), 88–103. A˚qvist, J., Fothergill, M., Warshel, A., Computer Simulation of the CO2/ HCO 3 Interconversion Step in Human Carbonic Anhydrase I, J. Am. Chem. Soc. 1993, 115, 631–635. Silverman, D. N., Lindskog, S., The Catalytic Mechanism of Carbonic Anhydrase: Implications of a RateLimiting Protolysis of Water, Acc. Chem. Res. 1988, 21, 30–36. A˚qvist, J., Warshel, A., Computer Simulation of the Initial Proton Transfer Step in Human Carbonic Anhydrase I, J. Mol. Biol. 1992, 224, 7–14. Schweins, T., Geyer, M., Scheffzek, K., Warshel, A., Kalbitzer, H. R., Wittinghofer, A., Substrate-assisted Catalysis as a Mechanism for GTP Hydrolysis of p21 ras and Other GTPbinding Proteins, Nature Struct. Biol. 1995, 2, (1), 36–44. Warshel, A., Russell, S. T., Calculations of Electrostatic Interactions in Biological Systems and in Solutions, Q. Rev. Biophys. 1984, 17, 283–421. Schutz, C. N., Warshel, A., What are the dielectric ‘‘constants’’ of proteins and how to validate electrostatic models, Proteins: Struc., Func., and Gen. 2001, 44, 400–417. Schutz, C. N., Warshel, A., Analyzing Free Energy Relationships for Proton Translocations in Enzymes;
80
81
82
83
84
85
86
87
88
89
Carbonic Anhydrase Revisted, J. Phys. Chem. B 2004, 108, (6), 2066–2075. Muegge, I., Qi, P. X., Wand, A. J., Chu, Z. T., Warshel, A., The Reorganization Energy of Cytochrome c Revisited, J. Phys. Chem. B 1997, 101, 825–836. Gerlt, J. A., Gassman, P. G., An Explanation for Rapid EnzymeCatalyzed Proton Abstraction from Carbon Acids: Importance of Late Transition States in Concerted Mechanisms, J. Am. Chem. Soc. 1993, 115, 11552–11568. Yarnell, A., Blockade in the Cell’s Waterway, Chem. Eng. News 2004, 82, (4), 42–44. Warshel, A., Conversion of Light Energy to Electrostatic Energy in the Proton Pump of Halobacterium halobium, Photochem. Photobiol. 1979, 30, 285–290. Burykin, A., Warshel, A., What Really Prevents Proton Transport Through Aquaporin? Charge SelfEnergy versus Proton Wire Proposals, Biophys. J. 2003, 85, 3696–3706. Braun-Sand, S., Strajbl, M., Warshel, A., Studies of Proton Translocations in Biological Systems: Simulating Proton Transport in Carbonic Anhydrase by EVB Based Models, Biophys. J. 2004, 87, 2221–2239. Warshel, A., Calculations of Enzymic Reactions: Calculations of pK a , Proton Transfer Reactions, and General Acid Catalysis Reactions in Enzymes, Biochemistry 1981, 20, 3167–3177. Warshel, A., Sussman, F., Hwang, J.-K., Evaluation of Catalytic Free Energies in Genetically Modified Proteins, J. Mol. Biol. 1988, 201, 139–159. A˚qvist, J., Warshel, A., Free Energy Relationships in MetalloenzymeCatalyzed Reactions. Calculations of the Effects of Metal Ion Substitutions in Staphylococcal Nuclease, J. Am. Chem. Soc. 1990, 112, 2860–2868. Warshel, A., Electrostatic Origin of the Catalytic Power of Enzymes and the Role of Preorganized Active Sites, J. Biol. Chem. 1998, 273, 27035–27038.
References 90 Frey, P. A., Whitt, S. A., Tobin, J. B.,
91
92
93
94 95
96
97
98
A Low-Barrier Hydrogen Bond in the Catalytic Triad of Serine Proteases, Science 1994, 264, 1927–1930. Schutz, C. N., Warshel, A., The low barrier hydrogen bond (LBHB) proposal revisited: The case of the Asp.His pair in serine proteases, Proteins 2004, 55, (3), 711–723. Kohen, A., Klinman, J. P., Hydrogen tunneling in biology, Chem. Biol. 1999, 6, R191–R198. Sutcliffe, M. J., Scrutton, N. S., Enzyme catalysis: over-the-barrier or through-the-barrier? Trends Biochem. Sci. 2000, 25, 405–408. German, E. K., J. Chem. Soc., Faraday Trans. 1 1981, 77, 397–412. Feierberg, I., Luzhkov, V., A˚qvist, J., Computer simulation of primary kinetic isotope effects in the proposed rate limiting step of the glyoxalase I catalyzed reaction, J. Biol. Chem. 2000, 275, 22657–22662. Alhambra, C., Corchado, J. C., Sanchez, M. L., Gao, J., Truhlar, D. G., Quantum Dynamics of Hydride Transfer in Enzyme Catalysis, J. Am. Chem. Soc. 2000, 122, (34), 8197–8203. Berendsen, H. J. C., Mavri, J., Quantum Simulation of Reaction Dynamics by Density-Matrix Evolution, J. Phys. Chem. 1993, 97, (51), 13464–13468. Mavri, J., Grdadolnik, J., Proton transfer dynamics in acetylacetone: A mixed quantum-classical simulation of
99
100
101
102
103
104
105
vibrational spectra, J. Phys. Chem. A 2001, 105, (10), 2045–2051. Lensink, M. F., Mavri, J., Berendsen, H. J. C., Simulation of slow reaction with quantum character: Neutral hydrolysis of carboxylic ester, J. Comput. Chem. 1999, 20, (8), 886–895. Neria, E., Karplus, M., Molecular Dynamics of an Enzyme Reaction: Proton Transfer in TIM, Chem. Phys. Lett. 1997, 267, 23–30. Ball, P., Enzymes – By chance, or by design? Nature 2004, 431, (7007), 396–397. Kosloff, D., Kosloff, R., A Fourier Method Solution for the TimeDependent Schrodinger-Equation as a Tool in Molecular-Dynamics, J. Comput. Phys. 1983, 52, (1), 35–53. Hatcher, E., Soudackov, A. V., Hammes-Schiffer, S., Proton-coupled electron transfer in soybean lipoxygenase, J. Am. Chem. Soc. 2004, 126, (18), 5763–5775. Olsson, M. H. M., Mavri, J., Warshel, A., Transition State Theory can be Used in Studies of Enzyme Catalysis: Lessons from Simulations of Tunneling and Dynamical Effects in Lipoxygenase and Other Systems, Phil. Trans. R. Soc. B. 2006, 361, 1417–1432. Shurki, A., Sˇtrajbl, M., Villa, J., Warshel, A., How Much Do Enzymes Really Gain by Restraining Their Reacting Fragments? J. Am. Chem. Soc. 2002, 124, 4097–4107.
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Part III
Quantum Tunneling and Protein Dynamics This section deals with the timely subject of the role of quantum mechanical tunneling in enzyme reactions and the way in which this tunneling is linked to protein structure and dynamics. The contributions come primarily from experimentalists, though a stimulating theoretical chapter by Schwartz introduces this section. Schwartz has used a Quantum Kramers approach to model H- transfer in the condensed phase, leading to a formalism for motions within the environment that can be coupled to the H-transfer coordinate in either an anti-symmetric or symmetric manner. The former is similar to the l parameter in Marcus theory, whereas the latter describes the change in the distance between the reactants, referred to as a promoting vibration(s). Promoting vibrations occur on a very fast time scale and are considered to be ‘‘directly’’ coupled to the reaction coordinate (contrasting with statistical views of protein motions that impact the probability of H-transfer in condensed phases). Schwartz has developed an algorithm to define promoting modes within a protein, applying these methods to both alcohol and lactate dehydrogenases. Recent studies suggest that analyses linking protein motions to the chemical step can be performed also for enzyme catalyzed cleavage of heavy atoms (Antoniou et al. (2006) Chem. Rev. 106, 3170–3187). The chapters by Klinman and co-workers, Kohen, and Scrutton and co-workers all address the growing evidence for H-tunneling in enzyme reactions and the facilitating role of the protein environment. All three chapters lay out methodologies available for detecting tunneling, and their strengths and weaknesses. The range of enzyme reactions that have now been implicated to have tunneling components is quite impressive. The importance of full tunneling models, instead of tunneling correction models, is emphasized, as new data emerge that cannot be easily rationalized by tunneling corrections. The chapter by Huskey focuses on the Swain-Schaad relationship as a basis for detecting tunneling. This is a thoughtful treatise, indicating that single site isotope substitutions are not likely to show deviations indicative of tunneling. By contrast, multi-site substitutions have the potential to be very informative in this regard, especially in the case of secondary isotope effect measurements. Knapp et al., Kohen, Scrutton and Huskey all emphasize the critical importance of isolating single rate-limiting hydrogen-transfer steps for the successful diagnosis of tunneling. The measurement of protein dynamics and its link to catalysis, is a challenging area, normally approached by NMR and/or H/D exchange methodologies. Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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The chapter by Ahn and co-workers provides a thorough summary of the methods available for the measurement of hydrogen exchange in proteins, which include NMR, mass spectrometry and FT-IR. These methods differ in their spatial resolution, the mass spectrometric approach offering a compromise between moderate resolution and general applicability. This chapter also outlines the full range of questions that can be addressed via H/D exchange including an assessment of the link between protein motions and the hydrogen transfer step. In the final chapter of this section, Callender and Deng describe the application of electronic and vibrational spectroscopy to illuminate the impact of the enzyme active site on the properties and activation of the bound substrates. Temperature jump experiments with lactate dehydrogenase indicate the multi-step nature of substrate binding and show how some protein ‘‘melting’’ may be essential during the formation of the catalytic complex.
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The Quantum Kramers Approach to Enzymatic Hydrogen Transfer – Protein Dynamics as it Couples to Catalysis Steven D. Schwartz 9.1
Introduction
Though all life forms are dependent on the catalytic effect of enzymes, detailed understanding of the microscopic mechanism of their action has lagged. This is largely due to the great complexity of enzyme catalyzed chemical reactions. Certainly a large portion of the catalytic effect in enzyme catalyzed reactions comes from the lowering of the free energy barrier to reaction. This preferential binding of the enzyme to the transition state is a concept credited to Pauling [1], and is the origin of the extraordinary potency of transition state inhibitors [2]. This viewpoint is, however, a statistical view of the catalytic process, not a dynamic understanding of how atoms or groups of atoms promote the catalytic event in microscopic detail. One would wish for such a detailed understanding. Work in our group over the past few years has focused on providing a formulation which allows such analysis [3]. Chemical reactions involve the making and breaking of chemical bonds, and so are inherently quantum mechanical in nature. At the very least, a quantum mechanical method is needed to generate a potential energy surface for the reaction of interest. In addition, many of the atom transfer reactions in the chemical step of certain enzymes, inherently involve quantum dynamics – that is if one uses classical mechanics to study their dynamics, the wrong answer will be obtained. One would thus like a fully quantum theory for the study of rate processes in enzymes, but the systems are far too complex for exact solution. We developed our approach, the Quantum Kramers theory to study chemical reactions in condensed phases and then applied it to enzymatic reactions. In fact, it is not an understatement to say that our current work detailing the importance of protein dynamics in the catalytic process of enzymes is in fact due to the failure of our simple theory of condensed phase chemical reactions to be applicable to some enzymatic reactions. The correction of the simple theory resulted in the inclusion of basically different chemical physics than that contained in our earlier work. This chapter will outline the development of our theory and then describe applications of the methodology and further work we have undertaken to understand the importance of protein dynamics in enzymatically catalyzed reactions. Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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9 The Quantum Kramers Approach to Enzymatic Hydrogen Transfer
The structure of this chapter is as follows: Section 9.2 describes the theoretical development of the basic Quantum Kramers methodology [4]. In Section 9.3.1 we proceed to understand the nature of the ‘‘promoting vibration,’’ why this physical feature is not present in the basic Quantum Kramers methods and how it can be incorporated. Section 9.3.2 describes why the symmetry of the coupling of promoting vibrations results in the phenomenon known as corner cutting and why, in turn, this masks kinetic isotope effects. In Section 9.4 we begin our study of specific enzyme systems, concentrating first on alcohol dehydrogenases. In Section 9.5 we study lactate dehydrogenase and both identify a unique kinetic control mechanism that may be present in two highly similar human isoforms of the enzyme, and apply a new technique known as Transition Path Sampling [5]. Developed by David Chandler and coworkers, this approach allows the study of an enzymatic reaction in microscopic detail. The atomic motions necessary for chemical reaction to occur are specified. Section 9.6 presents a general expansion of the Quantum Kramers approach to the study of coupled electron proton transfer reactions. A brief Section 9.7 provides preliminary results of a coupled protein motion in a reaction not involving hydrogen transfer, but in which protein motion polarizes bonds and allows leaving group departure. Finally Section 9.8 concludes with discussion of future direction for this area of work.
9.2
The Derivation of the Quantum Kramers Method
It is known that for a purely classical system [6], an accurate approximation of the dynamics of a tagged degree of freedom (for example a reaction coordinate) in a condensed phase can be obtained through the use of a generalized Langevin equation. The generalized Langevin equation is given by Newtonian dynamics plus the effects of the environment in the form of a memory friction and a random force [7]. m€s ¼
qVðsÞ þ qs
ðt
dt 0 gðt t 0 Þ_s þ FðtÞ
ð9:1Þ
0
Here the first two terms just give ma ¼ Force as mass times the second time derivative of the friction equal to the F as the negative derivative of potential. g is the memory friction, and FðtÞ is the random force. Thus the complex dynamics of all degrees of freedom other than the reaction coordinate are included in a statistical treatment, and the reaction coordinate plus environment are modeled as a modified one-dimensional system. What allows realistic simulation of complex systems is that the statistics of the environment can in fact be calculated from a formal prescription. This prescription is given by the Fluctuation–Dissipation theorem, which yields the relation between the friction and the random force. In particular, this theory shows how to calculate the memory friction from a relatively short-time classical simulation of the reaction coordinate. The Quantum Kramers approach,
9.2 The Derivation of the Quantum Kramers Method
in turn, is dependent on an observation of Zwanzig [8], that if an interaction potential for a condensed phase system satisfies a fairly broad set of mathematical criteria, the dynamics of the reaction coordinate as described by the generalized Langevin equation can be rigorously equated to a microscopic Hamiltonian in which the reaction coordinate is coupled to an infinite set of Harmonic Oscillators via simple bilinear coupling: X Pk 2 1 Ps 2 ck s 2 2 þ Vo þ þ mk ok qk H¼ mk ok 2 2m s 2mk 2 k
ð9:2Þ
The first two terms in this Hamiltonian represent the kinetic and potential energy of the reaction coordinate, and the last set of terms similarly represent the kinetic and potential energy for an environmental bath. Here s is some coordinate that measure progress of the reaction (for example in alcohol dehydrogenase where the chemical step is transfer of a hydride, s might be chosen to represent the relative position of the hydride from the alcohol to the NAD cofactor.) ck is the strength of the coupling of the environmental mode to the reaction coordinate, and mk and ok give the effective mass and frequency of the environmental bath mode. A discrete spectral density gives the distribution of bath modes in the harmonic environment: JðoÞ ¼
p X ck2 ½dðo ok Þ dðo þ ok Þ 2 k mk ok
ð9:3Þ
Here dðo ok Þ is the Dirac delta function, so the spectral density is simply a collection of spikes, located at the frequency positions of the environmental modes, convolved with the strength of the coupling of these modes to the reaction coordinate. Note that this infinite collection of oscillators is purely fictitious – they are chosen to reproduce the overall physical properties of the system, but do not necessarily represent specific physical motions of the atoms in the system. Now it would seem that we have not made a huge amount of progress – we began with a many-dimensional system (classical) and found out that it could be accurately approximated by a one-dimensional system in a frictional environment (the generalized Langevin equation.) We have now recreated a many-dimensional system (the Zwanzig Hamiltonian.) The reason we have done this is two-fold. First, there is no true quantum mechanical analog of friction, and so there really is no way to use the generalized Langevin approach for a quantum system, such as we would like to do for an enzyme. Second, the new quantum Hamiltonian given by Eq. (9.2) is very much simpler than the Hamiltonian for the full enzymatic system. Harmonic oscillators are the one type of problem that can easily be solved in quantum mechanics. Thus, the prescription is, given a potential for a reaction, we model the exact problem using a Zwanzig Hamiltonian, as in Eq. (9.2), with distribution of harmonic modes given by the spectral density in Eq. (9.3), and found through a simple classical computation of the frictional force on the reaction coordinate.
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9 The Quantum Kramers Approach to Enzymatic Hydrogen Transfer
Then using methods to compute quantum dynamics developed in our group [9], quantities such as rates or kinetic isotope effects may be found. These methods are an approximate but accurate way to compute the quantum mechanical evolution of any systems. The details are given in the literature [10], but in short, we write a general Hamiltonian as: _
_
_
_
H ¼ Ha þ Hb þ f ða; bÞ
ð9:4Þ
where ‘‘a’’ and ‘‘b’’ are shorthand for any number of degrees of freedom. f ða; bÞ is a coupling, usually only a function of coordinates, but this is not required. Our approach rests on the fact that because these three terms are operators, the exact evolution operator may not be expressed as a product: _
_
_
_
eiHt 0 eiHa t eiHb tþ f ða; bÞ
ð9:5Þ
but in fact equality may be achieved by application of an infinite order product of nth order commutators: _
_
_
_
eiHt ¼ eiHa t eiHb tþ f ða; bÞ e c1 e c2 e c3
ð9:6Þ
This is usually referred to as the Zassenhaus expansion or the Baker Campbell Hausdorf theorem [11]. As an aside a symmetrized version of this expansion terminated at the C1 term results in the Feit and Fleck [12] approximate propagator. We have shown [13] that an infinite order subset of these commutators, may be resummed exactly as an interaction propagator: UðtÞresum ¼ UðtÞHa UðtÞHb þf ða; bÞ U 1 ðtÞHa þf ða; bÞ UðtÞHa
ð9:7Þ
The first two terms are just the adiabatic approximation, and the second two terms the correction. For example, if we have a fast subsystem labeled by the ‘‘coordinate’’ a, and a slow subsystem labeled by b; then the approximate evolution operator to first order in commutators with respect to the slow subsystem bð½ f ða; bÞ; Hb Þ, and infinite order in the commutators of the ‘‘fast’’ Hamiltonian with the coupling: ð½ f ða; bÞ; Ha Þ is given by: eiðHa þHb þf ða; bÞÞt=h A eiHa t=h eiðHb þf ða; bÞÞt=h eþiðHa þf ða; bÞÞt=h eiHa t=h
ð9:8Þ
The advantage to this formulation is that higher dimensional evolution operators are replaced by a product of lower dimensional evolution operators. This is always a far easier computation. In addition, because products of evolution operators replace the full evolution operator, a variety of mathematical properties are retained, such as unitarity, and thus time reversal symmetry. What we have produced so far is an approximate Hamiltonian designed to study chemical reactions in complex condensed phases. We also have a mathematical method to evaluate quantum propagation using this Hamiltonian. We as yet have no practical method to compute observables such as rates. The flux correlation
9.3 Promoting Vibrations and the Dynamics of Hydrogen Transfer
function formalism of Miller, Schwartz, and Tromp [14] provides such a method. Combination of the quantum Kramers idea with the re-summed evolution operators results in a largely analytic formulation for the flux autocorrelation function for a chemical reaction in a condensed phase. After a lengthy but not complex computation the quantum Kramers flux autocorrelation function has been shown to be [15]: ðy Cf ¼
Cf0 B1 Zbath
0
dokf0 JðoÞB2 Zbath
ð9:9Þ
Here Cf0 is the gas phase (uncoupled) flux autocorrelation function, Zbath is the bath partition function, JðoÞ is the bath spectral density (computed as described above from a classical molecular dynamics computation), B1 and B2 are combinations of trigonometric functions of the frequency o and the inverse barrier frequency, and finally: kf0 ¼
1 jhs ¼ 0jeiHs tc =h js ¼ 0ij 2 4m s2
ð9:10Þ
i hb . As in other flux correlation function computations, tc is the complex time t 2 Thus, given the Quantum Kramers model for the reaction in the complex system, and the re-summed operator expansion as a practical way to evaluate the necessary evolution operators needed for the flux autocorrelation function, the quantum rate in the complex system is reduced to a simple combination of gas phase correlation functions with simple algebraic functions. This approach is able to model a variety of condensed phase chemical reactions with essentially experimental accuracy [16]. We did find, however, one specific experimental system for which this methodology was not able to reproduce experimental results, and that is proton transfer in benzoic acid crystals. In developing a physical understanding of this system, we first identified the concept of the promoting vibration.
9.3
Promoting Vibrations and the Dynamics of Hydrogen Transfer 9.3.1
Promoting Vibrations and The Symmetry of Coupling
The Hamiltonian of Eq. (9.2) couples the reaction coordinate to the environmental oscillator degrees of freedom by terms linear in both reaction coordinate and bath degree of freedom. This is derived in Zwanzig’s original approach by an expansion of the full potential in bath coordinates to second order. This innocuous approximation in fact conceals a fair amount of missing physics. We have shown [16a] that this collection of bilinearly coupled oscillators is in fact a microscopic version
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9 The Quantum Kramers Approach to Enzymatic Hydrogen Transfer
of the popular Marcus theory for charged particle transfer [17]. The bilinear coupling of the bath of oscillators is the simplest form of a class of couplings that may be termed antisymmetric because of the mathematical property of the functional form of the coupling on reflection about the origin. This property has deeper implications than the mathematical nature of the symmetry properties. Antisymmetric couplings, when coupled to a double well-like potential energy profile, are able to instantaneously change the level of well depths, but do nothing to the position of well minima. This modulation in the depth of minima is exactly what the environment is envisaged to do within the Marcus theory paradigm. As we have shown [16], the minima of the total potential in Eq. (9.2) will occur, for a twodimensional version of this potential, when the q degree of freedom is exactly cs , and the minimum of the potential energy equal and opposite in sign to mo 2 profile along the reaction coordinate is unaffected by this coupling. Within Marcus’ theory, which is a deep tunneling theory, transfer of the charged particle occurs at the value of the bath coordinates that cause the total potential to become symmetrized. Thus, if the bare reaction coordinate potential is symmetric, then the total potential is symmetrized at the position of the ‘‘bath plus coupling’’ minimum. When this configuration is achieved, the particle tunnels, and in fact the activation energy for the reaction is largely the energy to bring the bath into this favorable tunneling configuration. The question is if such motions and their mathematical representations encompass all important motions in the coupling of dynamic motions to a reaction coordinate. We became aware of an example in which there is another significant contributor to the chemical dynamics – benzoic acid crystals. There is a long history of the study of proton transfer in crystalline benzoic acid [18]. These experiments seemed to yield anomolous results when compared with quantum chemistry computations. That is, computations showed a reasonably high barrier while experiment showed a low activation energy. That is of course normally indicative of a significant contribution to the chemical reaction from quantum mechanical tunneling. In this system, however, kinetic isotope effects were quite modest (close to three) – classical in behavior. It became clear to us that we could not model such behavior using the mathematical formalism we had developed. The reason for this is apparent in Fig. 9.1. Motions of the carboxyl oxygens toward each other in each dimer that forms the crystal of benzoic acid modulate the potential for proton transfer through symmetric motions of the well bottoms toward each other. This environmental modulation both lowers and thins the barrier to proton transfer. This symmetric coupling of motion to the reaction coordinate requires modification of the Hamiltonian in Eq. (9.2): X Pk 2 1 Ps 2 ck s 2 2 þ Vo þ þ mk ok qk H¼ mk ok 2 2m s 2mk 2 k 2 PQ 2 1 Cs 2 2 þ MW Q þ 2M 2 MW 2
ð9:11Þ
9.3 Promoting Vibrations and the Dynamics of Hydrogen Transfer
Figure 9.1. A benzoic acid dimer showing how the symmetric motion of the oxygen atoms will affect the potential for hydrogen transfer.
We note that in this case, the oscillator that is symmetrically coupled, represented by the last term in Eq. (9.11), is in fact a physical oscillation of the environment. 9.3.2
Promoting Vibrations – Corner Cutting and the Masking of KIEs
We were able to develop a theory [19] of reactions mathematically represented by the Hamiltonian in Eq. (9.11), and using this method and experimentally available parameters for the benzoic acid proton transfer potential, we were able to reproduce experimental kinetics as long as we included a symmetrically coupled vibration [20]. The results are shown in Table 9.1. The two-dimensional activation energies refer to a two-dimensional system comprised of the reaction coordinate and a symmetrically coupled vibration. The reaction coordinate is also coupled to an infinite environment appropriate for a crystalline phase. Kinetic isotope effects in this system are modest, even though the vast majority of the proton transfer occurs via quantum tunneling. The end result of this study is that symmetrically coupled vibrations can significantly enhance rates of light particle transfer, and also significantly mask kinetic isotope signatures of tunneling. A physical origin for this masking of the kinetic isotope effect may be understood from a comparison of the two-dimensional problem comprised of a reaction coordinate coupled symmetrically and antisymmetrically to a vibration. As Fig. 9.2 shows, antisymmetric coupling causes the minima (the reactants and products) to lie on a line – the minimum energy path, which passes through the transition state. In contradistinction, symmetric coupling causes the reactants and products to be moved from the reac-
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9 The Quantum Kramers Approach to Enzymatic Hydrogen Transfer Table 9.1. Activation energies for H and D transfer in benzoic acid crystals at T ¼ 300 K. Three values are shown: the activation energies calculated using a one- and twodimensional Kramers problem and the experimental values. The energies are in kcal mol1 .
H D
E1d
E2d
Experiment
3.39 5.21
1.51 3.14
1.44 3.01
tion coordinate axis in such a fashion that a straight line connection of reactant and products would pass nowhere near the transition state. This, in turn, results in the gas phase physical chemistry phenomenon known as corner cutting [21]. Physically, the quantity to be minimized along any path from reactant to products is the action. This is an integral of the energy and so, loosely speaking, it is a prod-
Figure 9.2. The location of stable minima in two-dimensional systems. The figure represents how antisymmetrically and symmetrically coupled vibrations affect the position of stable minima – that is reactant and product. The x-axis, s, represents the reaction coordinate, and q the coupled vibration. The points labeled S and A are the positions of the well minima in the twodimensional system with symmetric and
antisymmetric coupling respectively. An antisymmetrically coupled vibration displaces these minima along a straight line, so that the shortest distance between the reactant and product wells passes through the transition state. In contradistinction, a symmetrically coupled vibration, allows for the possibility of ‘‘corner cutting’’ under the barrier. For example, a proton and a deuteron will follow different paths under the barrier.
9.4 Hydrogen Transfer and Promoting Vibrations – Alcohol Dehydrogenase
uct of distance and depth under the barrier that must be minimized to find an approximation to the tunneling path. The action also includes the mass of the particle being transferred and so, in the symmetric coupling case, a proton will actually follow a very different physical path from reactants to products in a reaction than will a deuteron.
9.4
Hydrogen Transfer and Promoting Vibrations – Alcohol Dehydrogenase
Finding that a promoting vibration, such as that present in benzoic acid crystals, can promote quantum tunneling while inhibiting indicators of tunneling such as kinetic isotope effects we were struck by similar experimental observations in certain enzymes in which the chemical step is thought to involve tunneling. Alcohol dehydrogenase is such an example. Klinman and coworkers have pioneered the study of tunneling in enzymatic reactions. Alcohol dehydrogenases are NADþ dependent enzymes that oxidize a wide variety of alcohols to the corresponding aldehydes. After successive binding of the alcohol and cofactor, the first step is generally accepted to be complexation of the alcohol to one of the two bound Zinc ions [22]. This complexation lowers the pK a of the alcohol proton and causes the formation of the alcoholate. The chemical step is then transfer of a hydride from the alkoxide to the NADþ cofactor. They [23] have found a remarkable effect on the kinetics of yeast alcohol dehydrogenase (a mesophile) and a related enzyme from Bacillus stereothermophilus, a thermophile. A variety of kinetic studies from this group have found that the mesophile [24] and many related dehydrogenases [25] show signs of significant contributions of quantum tunneling in the rate-determining step of hydride transfer. Their kinetic data seem to show that the thermophilic enzyme actually exhibits less signs of tunneling at lower temperatures. Data of Kohen and Klinman [26] also show, via isotope exchange experiments, that the thermophile is significantly less flexible at mesophilic temperatures, as in the Petsko group’s results [27] in studies of 3-isopropylmalate dehydrogenase from the thermophilic bacteria Thermus thermophilus. More detailed studies from the Klinman group analyze changes in dynamics, and seem to localize the largest correlations in changes in tunneling parameters with the substrate binding area of the protein rather than the cofactor side of the protein [28]. As we will discuss in detail below, the promoting vibration seems to originate on the cofactor side of the binding pocket, and so these most recent experimental data are currently difficult to understand. These data have been interpreted in terms of models similar to those we have described above, in which a specific type of protein motion strongly promotes quantum tunneling – thus, at lower temperatures, when the thermophile has this motion significantly reduced, the tunneling component of the reaction is hypothesized to decrease, even though one would normally expect tunneling to increase as temperature decreases. Hints as to the mechanism causing the odd kinetics are found in mutagenesis experiments. The active site geometry of HLADH is shown in Fig. 9.3. Two specific
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9 The Quantum Kramers Approach to Enzymatic Hydrogen Transfer
Figure 9.3. A schematic of the active site of horse liver alcohol dehydrogenase. The bound substrate (in this case benzyl alcohol) and the cofactor NAD are shown together with several residues in the active site.
mutations have been identified, Val203 ! Ala and Phe93 ! Trp, which significantly affect enzyme kinetics. Both residues are located at the active site – the valine impinges directly on the face of the NADþ cofactor distal to the substrate alcohol. Modification of this residue to the smaller alanine significantly lowers both the catalytic efficiency of the enzyme, as compared to the wild type, and also significantly lowers indicators of hydrogen tunneling [29]. Phe-93 is a residue in the alcohol-binding pocket. Replacement with the larger tryptophan makes it harder for the substrate to bind, but does not lower the indicators of tunneling [30]. Bruice’s recent molecular dynamics calculations [31] produce results consonant with the concept that mutation of the Valine changes protein dynamics, and it is this alteration, missing in the mutation at position 93, which in turn changes tunneling dynamics. (We note that recent experimental results from Klinman’s group [32] on mesophilic HLADH do not exhibit a decrease in tunneling as the temperature is raised. This indicates that the mesophile has a basically different coupling of the protein motion to reaction than the thermophile.) The low level of primary kinetic isotope effect in the benzoic acid crystal when
9.4 Hydrogen Transfer and Promoting Vibrations – Alcohol Dehydrogenase
tunneling is the dominant transfer mechanism suggested a similarity between the proton transfer mechanism in the organic acid crystal and that of hydrogen transfer in some enzymatic reactions. We note that there have been previous attempts to understand the anomalously low primary kinetic isotope effects in alcohol dehydrogenases in the presence of a large body of experimental evidence that quantum tunneling is involved in the hydride transfer. Of note, coupled motions of nearby atoms in enzymatic reactions have been shown to result in such anomalous kinetic isotope effects in numerical experiments [33], but these studies were classical kinetics with semiclassical tunneling added (the Bell correction [34]) and they could not be used to account for enzymatic reactions in a deep tunneling regime. With the suggestion of tunneling with a low kinetic isotope effect, we wish to investigate the dynamics of the enzyme to search for the possible presence of a promoting vibration. The quantity that naturally describes the way in which an environment interacts with a reaction coordinate in a complex condensed phase is the spectral density. In Eq. (9.3), the spectral density can be seen to give a distribution of the frequencies of the bilinearly coupled modes, convolved with the strength of their coupling to the reaction coordinate. The concept of the spectral density is, however, quite general and the spectral density may be measured or computed for realistic systems in which the coupling of the modes may well not be bilinear [35]. We have also shown [36] that the spectral density can be evaluated along a reaction coordinate. One only obtains a constant value for the spectral density when the coupling between the reaction coordinate and the environment is in fact bilinear. We have shown that a promoting vibration is created as a result of a symmetric coupling of a vibrational mode to the reaction coordinate. Analytic calculations demonstrated that such a mode should be manifest by a strong peak in the spectral density when it was evaluated at positions removed from the exact transition state position, in particular in the reactant or product wells. In cases in which there is no promoting vibration, while the spectral density may well change shape as a function of reaction coordinate position, there will be no formation of such strong peaks. Numerical experiments completed in our group have shown a delta function at the frequency position of the promoting vibration as the analytic theory predicted when we study a model problem in which a vibration is coupled symmetrically [37]. Our analysis began with the 2.1 A˚ crystal structure of Plapp and coworkers [38]. This crystal structure contains both NADþ and 2,3,4,5,6-pentafluorobenzyl alcohol complexed with the native horse liver enzyme (metal ions and both the substrate and cofactor.) The fluorinated alcohol does not react and go onto products because of the strong electron withdrawing tendencies of the fluorines on the phenyl ring, and so it is hypothesized that the crystal structure corresponds to a stable approximation of the Michaelis complex. We then replaced the fluorinated alcohol with the unfluorinated compound to obtain the reactive species as in Ref. [31]. This structure was used as input for the CHARMM program [39]. Both crystallographic waters [38] (there are 12 buried waters in each subunit) and environmental waters were included via the TIP3P potential [40]. The substrates were created from the MSI/CHARMM parameters. The NAD cofactor was modeled using the force field
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9 The Quantum Kramers Approach to Enzymatic Hydrogen Transfer
of Mackerell et al. [41]. The lengths of all bonds to hydrogen atoms were held fixed using the SHAKE algorithm. A time step of 1 fs was employed. The initial structure was minimized using a steepest descent algorithm for 1000 steps followed by an adapted basis Newton–Raphson minimization of 8000 steps. The dynamics protocol was heating for 5 ps followed by equilibration for 8 ps followed finally by data collection for the next 50 ps. Using CHARMM, we computed the force autocorrelation function on the reacting particle. The force is calculated in CHARMM as a derivative of the velocity. This is a numerical procedure, which can of course introduce error. We have recently found that spectral densities may also be calculated from the velocity autocorrelation function directly, and these spectral densities exhibit exactly the same diagnostics for the presence of a promoting vibration, as do those calculated from the force. In addition, the Fourier transform of the force autocorrelation function can be shown to be related to the Fourier transform of the velocity autocorrelation function times the square of the frequency. This square of the frequency tends to accentuate high frequencies. In a simple liquid this is not a problem because there are essentially no high frequency modes. In a bonded system, such as an enzyme, many high frequency modes remain manifest in autocorrelation functions, and it is advantageous to employ spectral densities calculated from Fourier transforms of the velocity function. Application of this methodology to this model of horse liver alcohol dehydrogenase yields the results shown in Fig. 9.4. In fact we do see strong numerical evidence for the presence of a promoting vibration – intense peaks in the spectral density for the reaction coordinate are greatly reduced at a point between the reactant and product wells. This is defined as a point of minimal coupling. As we have described, the restraint on the hydride does not impact the spectral density computation. This computation measures the forces on the reaction coordinate, not those
Figure 9.4. The spectral density of the hydride in the reactant well, product well, and at a point of minimal coupling for HLADH.
9.4 Hydrogen Transfer and Promoting Vibrations – Alcohol Dehydrogenase
Figure 9.5. The spectral density for the hydride in the reactant well for both wild type HLADH, and one in which we mutate (in the computer) Val203 ! Ala. The smaller size of the alanine results in a much smaller effective force on the reaction coordinate.
of the reaction coordinate itself [37]. We are also able to rationalize mutational experimental data. Figure 9.5 shows the results of a mutation of Val203 to a smaller Ala. We note that the intensity of the peak in the spectral density is reduced, indicative of a smaller force on the reaction coordinate. Recall that it is this mutant in which indicators of tunneling decrease. In Fig. 9.6 we show analogous results for a mutation of Phe93 to Trp. This mutation shows no experimental effect on tunneling (though it does affect the rate by lowering binding of substrate,) and in fact the two spectral densities are quite similar.
Figure 9.6. The spectral density for the hydride in the reactant well for both wild type HLADH, and one in which we mutate (in the computer) Phe93 ! Trp.
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9 The Quantum Kramers Approach to Enzymatic Hydrogen Transfer
These computational experiments were undertaken under the guidance of a large body of experimental literature on this enzyme. In some sense all we have done is rationalize the known experimental results. It is desirable to have a method to identify residues likely to be involved in the creation of a promoting vibration without prior experimental guidance. We have developed such an algorithm [42], and here we sketch the approach and the results found for the HLADH system. The method depends on computing the projection of motions of the center of mass of individual residues along the reaction coordinate axis (by this we mean the donor acceptor axis – we do not mean to imply that the actual set of atomic motions needed for the reaction are identified). A correlation function of this quantity with the donor acceptor motion is found. When Fourier transformed, strong peaks at the frequency location of an identified promoting vibration are indicative of the involvement of a residue in creation of the promoting vibration. The reader is referred to the reference above for mathematical and implementation details. Eight residues are found to be strongly correlated in their motion to that of the donor and acceptor. They are shown in Fig. 9.7. Some residues identified with this algorithm agree directly with experimental evidence. For example, Val203 has been identified by both Klinman [43], and Plapp [44] as being a residue that on mutagenesis changes kinetic parameters and signatures of tunneling. In addition, Val292 [45], has been found by Plapp et al. to be similarly implicated in tunneling for the hydride reaction coordinate. Phe93 is found by Klinman to not change the indicators of tunneling [46], and we find no evidence for coupling of the dynamics of this residue to the reaction coordinate. There are, however, some potential discrepancies – Plapp finds that Thr178 affects the kinetics. Our algorithm found no evidence of dynamic coupling of this residue to the reaction coordinate. It is possible that there is no contradiction here – clearly static effects such as binding geometries can alter kinetics – they just do it in a different way than the dynamic coupling of residues to the reaction coordinate. It is also important to note that these results fit with the general observations of the Bruice group who find general anticorrelated motions in the protein [47]. They see that one side of the protein generally seems to move towards the other side of the protein. Our results seem to find the dominant motion on the side of the cofactor, but in any case there is clearly a motion of the center of mass of this side of the protein towards the substrate binding side. Viewed from the center of mass of the entire protein, this would be seen as such an anticorrelated motion. An important question to ask is the extent to which the protein dynamics is actually involved in the catalytic process. If it only produces a tiny fraction of the catalytic effect, then it is of little interest. This is hard to measure experimentally, and difficult to predict accurately from theory. Because alcohol dehydrogenase is a highly studied enzyme, there are some experimental results which seem to indicate that the promoting vibration is a significant contributor to the catalytic effect. The mutagenesis experiments show that 2 residues alone, Val203 and Val292, when mutated to smaller residues contribute at least 3 orders of magnitude of catalytic effect individually. As stated, one cannot ‘‘turn off ’’ the promoting vibration. One can lower its effect by mutating the large residues which impact the NAD cofactor to smaller ones. In any case, it is clear that while the promoting vibration is
9.5 Promoting Vibrations and the Kinetic Control of Enzymes – Lactate Dehydrogenase
Figure 9.7. Residues found computationally to be important in the creation of a protein promoting vibration in HLADH.
not the only source of the catalytic effect, it is a major contributor. In the last section of this chapter where we examine a very different type of enzyme, purine nucleoside phosphorylase, and a very different type of promoting vibration, we will quantify how protein motion specifically lowers barrier height.
9.5
Promoting Vibrations and the Kinetic Control of Enzymes – Lactate Dehydrogenase
Lactate dehydrogenase (LDH) catalyzes the interconversion of the hydroxy-acid lactate and the keto-acid pyruvate with the coenzyme nicotinamide adenine dinucleotide [48]. This enzyme plays a fundamental role in respiration, and multiple isozymes have evolved to enable efficient production of substrate appropriate for the microenvironment [49]. Two main subunits, referred to as heart and muscle (skeletal), are combined in the functional enzyme as a tetramer to accommodate aero-
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9 The Quantum Kramers Approach to Enzymatic Hydrogen Transfer
bic and anaerobic environments. Subunit combinations range from pure heart (H4 ) to pure muscle (M4 ). The reaction catalyzed involves the transfer of a proton between an active site histidine (playing the role of the metal ion in alcohol dehydrogenase) and the C2 bound substrate oxygen, as well as hydride transfer between C4N of the cofactor, NAD(H), and C2 of the substrate. Remarkably, the domain structure, subunit association, and amino acid content of the human isozyme active sites are comparable. In fact the active sites have complete residue identity, with the overall subunits only differing by about 20%. What is astounding is that the kinetic properties of the two isozymes are quite different. The heart isoforms favors the production of pyruvate over lactate as the heart predominantly employs aerobic respiration. In contradistinction, muscles are quite comfortable under periods of stress undergoing anaerobic respiration, and so the muscle isoform favors lactate production. The question that remains is how two proteins that are so strikingly similar in composition can possibly have such different kinetic behavior. We were recently able to propose a solution based on variations in protein dynamics [50]. In addition we will describe a very recent application of the method known as Transition Path Sampling [5] to the actual reactive event in one isoform which shows in microscopic detail how the protein backbone is involved in promoting catalysis. The first step in the theoretical study of this problem is a molecular dynamics computation on the human proteins. Our methodology is described in detail elsewhere [51], but, in brief: the starting point for computations were crystal structures solved by Read et al. [52] for homo-tetrameric human heart, h-H4 LDH, and muscle, h-M4 LDH, isozymes in a ternary complex with NADH and oxamate at 2.1 A˚ and 2.3 A˚ resolution respectively. Numerical analysis of molecular dynamics computations followed our previously published approach [53]. While the chemical step of lactate dehydrogenase and alcohol dehydrogenase is quite similar – transfer of a hydride from or to an NAD cofactor, there have been no mutagenesis studies around the active site to implicate protein dynamics in the preferential formation of one product or another. The first step in the analysis is to search for the presence of a protein promoting vibration. A Fourier transform of the correlation function of the donor acceptor velocity in the two isoforms shows the relative motion that may be imposed on the reaction coordinate. The absence of strong peaks in a similar Fourier transform for the reaction coordinate at a point of minimal coupling – the putative transition state demonstrates, as we have shown, the presence of a symmetrically coupled protein promoting vibration. Such computations are shown in Fig. 9.8 as an example for the heart isoform. A similar set of data obtains for the muscle isoforms. Such figures demonstrate convincing numerical evidence that there is in fact a protein promoting vibration present in both isoforms of this enzyme. A strange result is found, however, when we examine the relative intensity of the peaks in the reaction coordinate figures for the 2 isoforms – Fig. 9.8 and 9.9. It seems that the strength of coupling of the promoting vibration in the heart isoform is larger when pyruvate is bound and, in the muscle isoform, the signal is more intense when lactate is bound. This would seem to favor the production of the opposite chemical species than that which is
9.5 Promoting Vibrations and the Kinetic Control of Enzymes – Lactate Dehydrogenase
Figure 9.8. The spectral density Gs ðoÞ for the reaction coordinate in the wild type human heart lactate dehydrogenase isoform. The solid line represents the configuration where lactate and NADþ are bound, the dotted line is when pyruvate and NADH are bound, the dashed line is the minimal coupling (MC) simulation with lactate and NADþ bound and the
(hydride–C2) and (hydride–C4N) distances restrained, and the dot-dash line is exemplary of the restrained hydride (RH) simulations to search for the point of minimal coupling. Distances are in A˚ and defined in the form (C2-A˚-Hydride-A˚-C4N). The power spectrum is reported in CHARMM units.
required for each tissue. The explanation is found in Fig. 9.10(a) and (b). These figures show time series of the donor–acceptor distance in both the heart and muscle isoforms respectively. Note for example that in the heart isoform the distance between the donor and acceptor when lactate is bound is on average 0.6 A˚ less than when pyruvate is bound. In contradistinction, in the muscle isoform, the donor acceptor distance is 0.6 A˚ less when pyruvate is bound. We recall that the in-
Figure 9.9.
Similar to Fig. 9.8, but for the human muscle isoforms.
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9 The Quantum Kramers Approach to Enzymatic Hydrogen Transfer
Figure 9.10. (a) Donor–acceptor distance for the wild type human heart lactate dehydrogenase isoform; this is the distance between the C2 carbon of substrate and carbon C4N of the nicotinamide ring of the cofactor. The solid line represents the configuration where lactate and NADþ are bound, and the dashed line is when pyruvate and NADH are bound. (b) Donor–acceptor
distance for the wild type human muscle lactate dehydrogenase isoform; this is the distance between the C2 carbon of the substrate and carbon C4N of the nicotinamide ring of the cofactor. The solid line represents the configuration where lactate and NADþ are bound, and the dashed line is when pyruvate and NADH are bound.
tensity of the promoting vibration is in fact the product of the strength of the coupling times the distance from the point of minimal coupling – the putative transition state. Thus the argument for these isoforms is that, for example, in the heart isoform when lactate is bound there is rapid conversion to pyruvate followed by relaxation of the protein structure by 0.6 A˚. This could be a mechanism for ‘‘locking in’’ the formed pyruvate. For this mechanism to be viable, there either needs to be
9.5 Promoting Vibrations and the Kinetic Control of Enzymes – Lactate Dehydrogenase
significant quantum tunneling in the hydride transfer step or significant dissipation to the protein medium as the hydride transfers. If there is tunneling, then clearly the longer distance for the ‘‘less preferred’’ substrate will significantly favor the other substrate. If there is no tunneling, but rather activated transfer across the barrier, the frictional dissipation could lower the probability of transfer across a longer distance. The foregoing analysis shows through classical mechanics that there is coupling of protein motion to progress along the reaction coordinate. It does not, however, actually chart the course of the chemical reaction as it is proceeding in the enzyme. The potential on which the analysis was done was a simple molecular mechanics potential, and this can certainly never make and break chemical bonds. In order to do this, some form of quantum chemistry must be invoked. One would like to develop a method to use a quantum chemically generated potential energy surface and follow the entire enzyme as the substrates moves from reactants to products. The difficulty with this goal is that there is not a single way for reactants to go to products. The simple one-dimensional view of a reaction coordinate with a free energy barrier to reaction is far too simplistic – the actual surface is highly complex with thousands of ‘‘hills and valleys.’’ A single reactive event will not elucidate the nature of the reaction. The difficulty is reaction is an extremely rare event – we note that most enzymes turn over about every millisecond while the actual passage from reactants to products takes picoseconds. Thus one cannot hope to generate a large set of reactive trajectories by simply running a large number of trajectories. This problem has been solved by transition path s ampling developed by Chandler and coworkers [5]. The method has been applied to small systems [54], and we here report on an unpublished first application of TPS to an enzymatically catalyzed chemical reaction. We again focus on LDH, in particular the heart isozyme. In order to follow the reaction, one must identify ‘‘order parameters’’, simple numerical features which identify whether the reaction is in the reactants or products region. We defined the pyruvate region to include all configurations where the bond length of the reactive proton and the reactive nitrogen of the active site histidine (NE2) was 1.3 A˚ or shorter and the bond length of the reactive hydride and the reactive carbon (NC4) of the NADH coenzyme was 1.3 A˚ or shorter. The lactate region was defined to include all configurations where the bond length of the reactive proton and the reactive substrate oxygen (O) was 1.3 A˚ or shorter and the bond length of the reactive hydride and reactive substrate carbon (C2) was 1.3 A˚ or shorter. The transition region was then comprised of all configurations where neither of the above combined bond lengths were satisfied. Order parameters are simply guideline to differentiate regions; 1.3 A˚ was found to be a viable discriminator. Quantum mechanical/molecular mechanical calculations were performed on a Silicon Graphics workstation using the CHARMM/MOPAC [55] interface with the CHARMM27, all hydrogen force field, and the AM1 semi-empirical method. The CHARMM27 force field includes specific parameters for NADþ/NADH. Oxamate (NH2 COCOO), an inhibitor of LDH, is an isosteric, isoelectronic mimic of pyruvate with similar binding kinetics. Changes to the PDB file included substitution of the oxamate nitrogen with carbon to create pyruvate and replacement of the
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active site neutral histidine with a protonated histidine to establish appropriate starting conditions with pyruvate and NADH in the active site. A total of 39 atoms were treated with the AM1 potential; 17 or 16 atoms of the NADH or NADþ nicotinamide ring, 13 or 12 atoms of the protonated or neutral histidine imidazole ring, and 9 or 11 atoms of the substrate pyruvate or lactate, respectively. The generalized hybrid orbital (GHO) [56] approach was used to treat the two covalent bonds which divide the quantum mechanical and molecular mechanical regions. The two GHO boundary atoms are the histidine Ca atom and the NC1 0 carbon atom of the NADþ/NADH adenine dinucleotide structure which covalently bonds to the nicotinamide ring. Protein structure (PSF) and coordinate (CRD) input files were created with CHARMM. Crystallographic waters were treated as TIP3P [57] residues. A single subunit of the enzyme was used in all QM/MM calculations. A TPS interface to CHARMm was created and a transition path ensemble was generated. In order to start an initial reactive trajectory is needed. This was generated by placing the hydride and proton at the midpoint of their respective donor–acceptor axis. The velocities of all atoms in the protein substrate complex obtained from a 300 K equilibration run were then used with the above coordinates to initiate simulations both forward and backward in time. Recall, for time reversible deterministic dynamics, inverting the sign of each xyz momentum and then integrating forward in time is equivalent to simulating a trajectory backwards in time. The hydride initial velocity was slightly altered to move along the donor–acceptor axis. This produced a 100 fs trajectory that began in the reactant well and finished in the product well. We initially attempted to generate a reactive trajectory using high temperature simulations, but were not successful. To demonstrate the power of TPS sampling, we first investigated what appeared to be a paradox in the computational literature on LDH. Some studies have found the hydride and proton transfer to be concerted while others found it to be sequential [58]. Our transition path sampling study showed that all paths (with different orders in the case of sequential) are possible. Subtle changes in enzyme motions shift the transfer order and timing. Figure 9.11 shows 100 fs of three reactive trajectories. For each graph, the x-axis is the distance in A˚ of the proton from the NE2 atom of the active site histidine while the y-axis is the distance in A˚ of the hydride from the NC4 atom of the coenzyme. The reaction direction, reading from left to right, is pyruvate to lactate (true for all figures unless mentioned otherwise). Part (a) shows all three trajectories plotted together for comparison. Parts (b)–(d) are the three trajectories plotted individually, where each dot represents a 1 fs time step. The time step in which the hydride–cofactor bond breaks, the proton– histidine bond breaks, the hydride–substrate bond forms and the proton–substrate bond forms are color labeled. Using the order parameter values discussed earlier, 1.3 A˚ for each bond distance involved with transferring atoms, the transfer order can be discerned. In the first trajectory, (trajectory 1 of (b)) the hydride–cofactor bond initially breaks, then the proton–histidine bond, and then the proton– substrate bond forms before the hydride bond. Trajectory 2 is very similar except the hydride–substrate bond forms before the proton–substrate bond. These two
9.5 Promoting Vibrations and the Kinetic Control of Enzymes – Lactate Dehydrogenase
Figure 9.11. Three reactive trajectories demonstrate unique pathways from reactants to products for the lactate dehydrogenase enzymatic reaction. The distance of the proton from the NE2 reactive atom of the active site histidine versus the distance of the hydride from the NC4 reactive atom of the coenzyme nicotinamide is plotted. (b) Reactive trajectory 1 where the hydride–coenzyme bond breaks first, then the proton–histidine bond, with the proton–substrate bond forming before the hydride–substrate bond. (c) Reactive trajectory 2 where again the hydride–coenzyme bond breaks first, but now the hydride–substrate bond forms before the proton–substrate bond. (b) and (c) are examples of a concerted
reaction. In (d) the hydride–coenzyme bond breaks and the hydride-substrate bond forms before the proton–histidine bond breaks. (d) is an example of a step-wise, sequential transfer. The enzyme lactate dehydrogenase was previously thought to be limited to one or the other mechanism. Application of the transition path sampling algorithm has demonstrated that either mechanism is possible. Each dot represents a 1 fs time step. Color coding indicates when the hydride coenzyme bond breaks, the proton–histidine bond breaks, the hydride–substrate bond forms, and the proton–substrate bond forms for the pyruvate to lactate reaction direction.
trajectories exemplify the notion of a concerted reaction, where the bond making and bond breaking events occur more or less simultaneously. For Trajectory 3, in (d), the hydride bond breaks and forms with the substrate before the proton– histidine bond even breaks. This trajectory exemplifies a stepwise or sequential mechanism of transfer. Apparently LDH has the capability of interconverting pyruvate and lactate by either mechanism proposed in the literature. Figure 9.12 plots four distances over a 7.3 ps reactive trajectory (extension of Tra-
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Figure 9.12. Enzyme-wide changes during transition from reactant to product. Exemplary critical distance shifts during the interconversion of pyruvate and lactate by lactate dehydrogenase. Reading the graph from left to right, the pyruvate to lactate reaction direction, the reaction occurs slightly after the minimum hydride donor–acceptor distance. Distances are plotted every 1 fs over a 7.3 ps
sampling period. (a) Hydride donor–acceptor distance, (b) the proton donor–acceptor distance, (c) the distance of residue Valine 31, located behind the coenzyme nicotinamide ring, from the active site; (d) the distance of residue Aspartate 194, located behind the substrate, from the active site. Although subtle, these enzyme shifts must occur to have a complete reaction.
jectory 1 forward and backward in time). Plots of specific amino acid distances from the active site, residue Valine 31 and residue Aspartate 194, demonstrate a general pattern of the protein structure proximal to the reaction event. Valine 31, whose distance is plotted in (c), is the first amino acid located directly behind the nicotinamide ring of NAD(H) while Aspartate 194 of (d) is located behind the substrate. The atom transfers begin slightly after the minimum hydride donor– acceptor distance. Valine 31 has been studied and associated with protein promoting vibrations (PPVs) in LDH, as well as, analogously in ADH. Valine 31 is thought to push the coenzyme nicotinamide ring closer to the substrate carbon involved with hydride transfer. It is popular to envision breathing motions in enzymes that drive the reacting species together. However, (c) and (d) show an alternative picture, at least on the picosecond time scale. For the pyruvate to lactate reaction direction all residues located behind the coenzyme compress towards the active site, while all residues located behind the substrate relax away from the active site. The motion is thus akin to a compressional wave, since the compression causes the re-
9.6 The Quantum Kramers Model and Proton Coupled Electron Transfer
laxation. The compression causes the hydride donor–acceptor distance to come sharply closer right before the atom transfers. In fact we have been able to show that nonreactive trajectories can be transformed into reactive ones by imposing this compressional motion on the dynamics. This demonstrates that the motion is both necessary and sufficient for the reaction to occur.
9.6
The Quantum Kramers Model and Proton Coupled Electron Transfer
The foregoing discussion shows how the Quantum Kramers method may be augmented to study complex systems, such as enzymes in which there is a promoting vibration which modulates chemical passage over a barrier. One class of enzymatic reactions for which this model as described will not work is proton coupled electron transfer reactions (PCET). These reactions are clearly of basic biological interest, and have attracted significant biochemical study recently. Two such enzymes are lipoxygenase, which has been studied by Klinman’s group [59], and trimethylamine dehydrogenase studied by Scrutton and coworkers [60]. An interesting difference between these reactions and those of alcohol dehydrogenase is the presence of rather large kinetic isotope effects. The amine dehydrogenases exhibit KIEs in the range 15 to 25 while soybean lipoxygenase has one of almost 100. The involvement of protein dynamics is suggested by unexpected temperature dependence of the KIEs. There have been previous model studies of these systems [61]. These studies, while including the effects of environment, did not address the question of the effect of a promoting vibration. These reactions are inherently electronically nonadiabatic, while the formulation we have thus far presented included evolution only on a single Born–Oppenheimer potential energy surface. We have developed a model system to allow the extension of the Quantum Kramers methodology to such systems, and we now describe that model. The starting point for the study is a simple model of the coupled process. This model is found from a generalization of the Hamiltonian in Eq. (9.2) to include the modulation of hydrogen transfer potential as a result of electron transfer. H¼
X Pk 2 1 Ps 2 ck s 2 þ VD jDihDj þ VA jAihAj þ þ mk ok 2 qk mk ok 2 2m s 2mk 2 k þ
PQ 2 1 D þ MW 2 Q 2 þ cQ ðs 2 so2 ÞQ þ sz þ Vc ðsÞsx 2 2M 2
ð9:12Þ
The modifications to the Hamiltonian used previously are: 1. There are two different bare potentials for hydrogen transfer VD and VA – the potentials are chosen by the state of the electron given by the projection operators jDihDj and jAihAj.
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2. The states jAi and jDi are the states of an electron degree of freedom approximated by a 2 state spin system. The rate of electron transfer from one state to the other (from the electron donor to acceptor) is given by Vc. While there are methods available to measure this parameter experimentally, it has not been done for any of the reactions of interest here. We set it to 0.45 eV and 4.5 eV to get a sense of range of effect. We note that the reaction coordinate is coupled to an infinite bath of harmonic oscillators, which represent the bulk protein, and to a protein promoting vibration. For each mathematical implementation, we here choose the zero of promoting vibration coupling to be in the well rather than at the barrier top, but this is arbitrary. We point out that we can tune this model to allow for both sequential and concerted hydrogen-electron transfer. Sequential transfer is found with a very high transfer rate, and concerted with a lower one. Our initial results are presented in Table 9.2. Introduction of the electronic degree of freedom significantly raises the KIE. In fact the results for 11 kcal mol1 are similar to those found by Scrutton et al. for amine dehydrogenase. Thus, the stronger the electronic coupling (given by Vc ), the lower the enhancement of the KIE. This is understood by the result that very strong electron coupling yields results asymptotic to sequential transfer – in other words, hydrogen transfer in the presence of a promoting vibration in the electron acceptor state alone. This clearly rationalizes the high KIE found in the coupled electron–hydrogen systems with the possibility of the presence of a promoting vibration. In addition, the natural log of the KIEs versus 1/T over the biochemically accessible range is essentially temperature independent – again in direct agreement with the amine dehydrogen-
Table 9.2. Kinetic isotope effects from exact quantum rate computations on the model of Eq. (9.12). In one case there is no protein promoting vibration, in the second case there is a promoting vibration coupled with a strength similar to that in our previous model studies. In each case there are two levels of electron coupling – essentially the rate of electron transfer between the two states. Moderate electron transfer enhances the kinetic isotope effect while strong electron coupling enhances it less. We have found that high coupling is asymptotic to sequential transfer.
No promoting vibration
Moderate promoting vibration
Kinetic isotope effect Barrier height (kcal mol1 ) 11 30
Vc ¼ 0:45 eV 56 1942
Vc ¼ 4:5 eV 65 1256
Vc ¼ 0:45 eV 38 1218
Vc ¼ 4:5 eV 24 685
9.8 Conclusions
Figure 9.13. hPNP-catalyzed phosphorolysis of the purine nucleoside. The guanine leaving group and phosphate nucleophile are well separated from the oxacarbenium ion, defining a very dissociative TS.
ase results. There is, however a clear activation energy found from plots of k versus 1/T – the primary evidence suggested by the Scrutton group for significant ‘‘extreme tunneling’’ in amine dehydrogenase.
9.7
Promoting Vibrations and Electronic Polarization
Before concluding, it is worth mentioning the recent discovery of a very different type of promoting vibration in an enzyme. We have also studied the enzyme purine nucleoside phosphorylase [62]. This enzyme catalyzes the reaction shown in Fig. 9.13. Crystal structures of strongly bound transition state mimics and later transition state analysis [63] showed the oxygen atoms aligned in a closely packed stack. We hypothesized that this stack polarizes the ribosidic bond, and allows leaving group expulsion. Further, it seemed reasonable to search for a protein vibration that would compress this stack, and further destabilize the bond to the leaving group. Using the methods we have described, we did find that the protein imposes a very different vibration than might be found in gas or solution phase substrates. We were also able to show via QM/MM calculations that this vibration in fact results in an average lowering of the chemical barrier to reaction of about 7 kcal mol1 – significant to the overall mechanism [64]. 9.8
Conclusions
This chapter has focused on the technology known as the Quantum Kramers methodology, and how it can be used to increase our knowledge of enzymatic catal-
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ysis. In fact, a central discovery from the application of this method, the promoting vibration, has come from recognition of when the method does not work. The simple formulation represented by the Hamiltonian of Eq. (9.2) cannot reproduce experimental data in some systems such as benzoic acid crystals and enzymes such as alcohol dehydrogenase. The augmentation of the model with a symmetrically coupled vibration not only permits reproduction of experimentally reasonable results, but, more importantly, also gives physical insight into a portion of the catalytic mechanism of the enzyme. All enzymes incorporate dynamics into their function – for example hinge motions that allow the binding of substrates. Here we refer to something very different. The fact that enzymes employ dynamics, should in no way be surprising – evolution knows nothing of quantum mechanics, classical mechanics, or vibrationally enhanced tunneling. Rates of reaction are optimized for living systems using all physical and chemical mechanisms available. It is also important to point out that such protein dynamics are far from the only contributor to the catalytic effect. In fact in an enzyme such as alcohol dehydrogenase, transfer of a proton from the alcohol to the coordinated zinc atom is critical to the possibility of the reaction. The specific modulation of the chemical barrier to reaction via backbone protein dynamics is now seen to be part of the chemical armamentarium employed by enzymes to catalyze reactions. Acknowledgment
The author gratefully acknowledges the support of the Office of Naval Research, The National Science Foundation, and the National Institutes of Health. References 1 L. Pauling, Nature of forces between
large molecules of biological interest, Nature 161, 707–709 (1948). 2 a) V. L. Schramm, ‘‘Enzymatic Transition State Analysis and Transition-State Analogues, Methods Enzymol. 308, 301–354 (1999); b) R. L. Schowen, Transition States of Biochemical Processes, Plenum Press, New York (1978). 3 D. Antoniou, S. D. Schwartz, Internal Enzyme Motions as a Source of Catalytic Activity: Rate Promoting Vibrations and Hydrogen Tunneling, J. Phys. Chem. B, 105, 5553–5558 (2001). 4 a) S. D. Schwartz, Quantum Activated Rates – An Evolution Operator Approach, J. Chem. Phys.,
105, 6871–6879 (1996); b) S. D. Schwartz, Quantum Reaction in a Condensed Phase – Turnover Behavior from New Adiabatic Factorizations and Corrections, J. Chem. Phys., 107, 2424–2429 (1997). 5 a) F. S. Csajka, D. Chandler, Transition pathways in many body systems: application to hydrogen bond breaking in water, J. Chem. Phys., 109, 1125–1133 (1998); b) P. G. Bolhuis, C. Dellago, D. Chandler, Sampling ensembles of deterministic pathways, Faraday Discuss., 110, 421–436 (1998); c) P. G. Bolhuis, C. Dellago, D. Chandler, Reaction coordinates of biomolecular isomerization, Proc. Natl. Acad. Sci. USA, 97, 5877–5882 (2000). 6 a) J. E. Straub, M. Borkovec, B. J.
References
7
8
9
10
Berne, Molecular Dynamics Study of an Isomerizing Diatomic in a Lennard-Jones Fluid, J. Chem. Phys., 89, 4833 (1988); b) B. J. Gertner, K. R. Wilson, J. T. Hynes, Nonequilibrium Solvation Effects on Reaction Rates for Model SN2 Reactions in Water, J. Chem. Phys., 90, 3537 (1988). E. Cortes, B. J. West, K. Lindenberg, On the Generalized Langevin Equation: Classical and Quantum Mechanical, J. Chem. Phys., 82, 2708– 2717 (1985). a) R. Zwanzig, The nonlinear Generalized Langevin Equation, J. Stat. Phys., 9, 215 (1973); b) R. Zwanzig, Nonequilibrium Statistical Mechanics, Oxford University Press, Oxford (2001). a) S. D. Schwartz, Accurate Quantum Mechanics From High Order Resumed Operator Expansions, J. Chem. Phys., 100, 8795–8801 (1994); b) S. D. Schwartz, Vibrational Energy Transfer from Resumed Evolution Operators, J. Chem. Phys., 101, 10436– 10441 (1994); c) D. Antoniou, S. D. Schwartz, Vibrational Energy Transfer in Linear Hydrocarbon Chains: New Quantum Results, J. Chem. Phys., 103, 7277–7286 (1995); d) S. D. Schwartz, The Interaction Representation and Non-Adiabatic Corrections to Adiabatic Evolution Operators, J. Chem. Phys., 104, 1394– 1398 (1996); e) D. Antoniou, S. D. Schwartz, Nonadiabatic Effects in a Method that Combines Classical and Quantum Mechanics, J. Chem. Phys., 104, 3526–3530 (1996); f ) S. D. Schwartz, The Interaction Representation and Non-Adiabatic Corrections to Adiabatic Evolution Operators II: Nonlinear Quantum Systems, J. Chem. Phys., 104, 7985–7987 (1996). a) S. D. Schwartz, Accurate Quantum Mechanics From High Order Resummed Operator Expansions, J. Chem. Phys., 100, 8795– 8801 (1994); b) S. D. Schwartz, Vibrational Energy Transfer from Resummed Evolution Operators, J. Chem. Phys., 101, 10436–10441 (1994); c) D. Antoniou, S. D. Schwartz, Vibrational Energy
11
12
13
14
15
16
Transfer in Linear Hydrocarbon Chains: New Quantum Results, J. Chem. Phys., 103, 7277–7286 (1995); d) S. D. Schwartz, The Interaction Representation and Non-Adiabatic Corrections to Adiabatic Evolution Operators, J. Chem. Phys., 104, 1394– 1398 (1996); e) D. Antoniou, S. D. Schwartz, Nonadiabatic Effects in a Method that Combines Classical and Quantum Mechanics, J. Chem. Phys., 104, 3526–3530 (1996); f ) S. D. Schwartz, The Interaction Representation and Non-Adiabatic Corrections to Adiabatic Evolution Operators II: Nonlinear Quantum Systems, J. Chem. Phys., 104, 7985– 7987 (1996). W. Magnus, On the Exponential Solution of Differential Equations for a Linear Operator, Commun. Pure Appl. Math., VII, 649 (1954). M. D. Feit, J. A. Fleck Jr., Solution of the Schrodinger Equation by a Spectral Method II: Vibrational Energy Levels of Triatomic Molecules, J. Chem. Phys., 78, 301 (1983). S. D. Schwartz, The Interaction Representation and Non-Adiabatic Corrections to Adiabatic Evolution Operators, J. Chem. Phys., 104, 1394– 1398 (1996). Wm. H. Miller, S. D. Schwartz, and J. W. Tromp, Quantum Mechanical Rate Constants for Bimolecular Reactions, J. Chem. Phys., 79, 4889– 4898 (1983). S. D. Schwartz, Quantum Activated Rates – An Evolution Operator Approach, J. Chem. Phys., 105, 6871– 6879 (1996). a) R. Karmacharya, D. Antoniou, S. D. Schwartz, Nonequilibrium solvation and the Quantum Kramers problem: proton transfer in aqueous glycine, J. Phys. Chem. B (Bill Miller festschrift), 105, 2563–2567 (2001); b) D. Antoniou, S. D. Schwartz, A Molecular Dynamics Quantum Kramers Study of Proton Transfer in Solution, J. Chem. Phys., 110, 465–472 (1999); c) D. Antoniou, S. D. Schwartz, Quantum Proton Transfer with Spatially Dependent Friction:
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20
21
Phenol-Amine in Methyl Chloride, J. Chem. Phys., 110, 7359–7364 (1999). a) R. A. Marcus, Chemical and electrochemical electron transfer theory, Annu. Rev. Phys. Chem., 15, 155–181 (1964); b) V. Babamov, R. A. Marcus, Dynamics of Hydrogen Atom and Proton Transfer reactions: Symmetric Case, J. Chem. Phys. 74, 1790 (1981). a) K. Fuke, K. Kaya, Dynamics of Double Proton Transfer Reactions in the Excited State Model of Hydrogen Bonded Base Pairs, J. Phys. Chem., 93, 614 (1989); b) D. F. Brougham, A. J. Horsewill, A. Ikram, R. M. Ibberson, P. J. McDonald, M. Pinter-Krainer, The Correlation Between Hydrogen Bond Tunneling Dynamics and the Structure of Benzoic Acid Dimers, J. Chem. Phys., 105, 979 (1996); c) B. H. Meier, F. Graf, R. R. Ernst, Structure and Dynamics of Intramolecular Hydrogen Bonds in Carboxylic Acid Dimers: A Solid State NMR Study, J. Chem. Phys., 76, 767 (1982); d) A. Stockli, B. H. Meier, R. Kreis, R. Meyer, R. R. Ernst, Hydrogen bond dynamics in isotopically substituted benzoic acid dimers, J. Chem. Phys., 93, 1502 (1990); e) M. Neumann, D. F. Brougham, C. J. McGloin, M. R. Johnson, A. J. Horsewill, H. P. Trommsdorff, Proton Tunneling in Benzoic Acid Crystals at Intermediate Temperatures: Nuclear Magnetic Resonance and Neutron Scattering Studies, J. Chem. Phys., 109, 7300 (1998). D. Antoniou, S. D. Schwartz, Activated Chemistry in the Presence of a Strongly Symmetrically Coupled Vibration, J. Chem. Phys., 108, 3620– 3625 (1998). D. Antoniou, S. D. Schwartz, Proton Transfer in Benzoic Acid Crystals: Another Look Using Quantum Operator Theory, J. Chem. Phys., 109, 2287–2293 (1998). a) V. A. Benderskii, S. Yu. Grebenshchikov, G. V. Mil’nikov, Tunneling Splittings in Model 2Dpotentials. II: VðX; YÞ ¼
lðX 2 Xo2 Þ 2 CX 2 ðY Yo Þ þ Yo þ CXo2 =W 2 Þ 2 C 2 Xo4 =2W 2 ; Chem. Phys. 194, 1 (1995); b) V. A. Benderskii, S. Yu. Grebenshchikov, G. V. Mil’nikov, Tunneling Splittings in Model 2D potentials. III: VðX; YÞ ¼ lðX 2 Xo2 Þ 2 CXY þ 12 kY 2 þ C 2 =2kX 2 Generalization to N-Dimensional Case, Chem. Phys. 198, 281 (1995); c) V. A. Benderskii, V. I. Goldanskii, D. E. Makarov, Low-temperature Chemical Reactions. Effect of Symmetrically Coupled Vibrations in Collinear Exchange Reactions, Chem. Phys. 154, 407 (1991). P. K. Agarwal, S. P. Webb, S. Hammes-Schiffer, Computational studies of the mechanism for proton and hydride transfer in liver alcohol dehydrogenase, J. Am. Chem. Soc., 122, 4803–4812 (2000). A. Kohen, R. Cannio, S. Bartolucci, J. P. Klinman, Enzyme dynamics and hydrogen tunneling in a thermophilic alcohol dehydrogenase, Nature 399, 496–499 (1999). Y. Cha, C. J. Murray, J. P. Klinman, Hydrogen Tunneling in Enzyme Reactions, Science 243, 1325 (1989). a) K. L. Grant, J. P. Klinman, Evidence that both Protium and Deuterium Undergo Significant Tunneling in the Reaction Catalyzed by Bovine Serum Amine Oxidase, Biochemistry 28, 6597 (1989); b) A. Kohen, J. P. Klinman, Enzyme Catalysis: Beyond Classical Paradigms, Acc. Chem. Res. 31, 397 (1998); c) B. J. Bahnson, J. P. Klinman, Hydrogen Tunneling in Enzyme Catalysis, Methods Enzymol., 249, 373 (1995); d) J. Rucker, Y. Cha, T. Jonsson, K. L. Grant, J. P. Klinman, Role of Internal Thermodynamics in Determining Hydrogen Tunneling in Enzyme-Catalyzed Hydrogen Transfer Reactions, Biochemistry, 31, 11489 (1992). A. Kohen, J. P. Klinman, Protein Flexibility Correlates with Degree of Hydrogen Tunneling in Thermophilic and Mesophilic Alcohol Dehydrogenases, J. Am. Chem. Soc., 122, 10738–10739 (2000). 1 2 2 W ðY
22
23
24
25
26
References 27 P. Zavodsky, J. Kardos, A. Svingor,
28
29
30
31
32
33
34
35
36
G. A. Petsko, Adjustment of conformational flexibility is a key event in the thermal adaptation of proteins, Proc. Natl. Acad. Sci. U.S.A. 95, 7406–7411 (1998). Z.-X. Liang, T. Lee, K. A. Resing, N. G. Ahn, J. P. Klinman, Thermalactivated protein mobility and its correlation with catalysis in thermophilic alcohol dehydrogenase, Proc. Natl. Acad. Sci. U.S.A., 101, 9556– 9561 (2004). B. J. Bahnson, T. D. Colby, J. K. Chin, B. M. Goldstein, J. P. Klinman, A link between protein structure and enzyme catalyzed hydrogen tunneling, Proc. Natl. Acad. Sci. U.S.A. 94, 12797–12802 (1997). B. J. Bahnson, D-H. Park, K. Kim, B. V. Plapp, J. P. Klinman, Unmasking of hydrogen tunneling in the horse liver alcohol dehydrogenase reaction by site-directed mutagenesis, Biochemistry 32, 5503–5507 (1993). J. Luo, K. Kahn, T. C. Bruice, The linear dependence of logðkcat =Km Þ for reduction of NADþ by PhCH2 OH on the distance between reactants when catalyzed by horse liver alcohol dehydrogenase and 203 single point mutants, Bioorg. Chem. 27, 289–296 (1999). S-C. Tsai, J. P. Klinman, Probes of Hydrogen tunneling with horse liver alcohol dehydrogenase at subzero temperatures, Biochemistry, 40, 2303– 2311 (1999). P. Huskey, R. Schowen, Reaction coordinate tunneling in hydridetransfer reactions, J. Am. Chem. Soc. 105, 5704–5706 (1983). R. P. Bell, The Tunnel Effect in Chemistry, Chapman & Hall, New York (1980). S. A. Passino, Y. Nagasawa, G. R. Fleming, Three Pulse Stimulated Photon Echo Experiments as a Probe of Polar Solvation Dynamics: Utility of Harmonic Bath Modes, J. Chem. Phys. 107, 6094 (1997). D. Antoniou, S. D. Schwartz, Quantum Proton Transfer with Spatially Dependent Friction: Phenol-
37
38
39
40
41
42
43
44
45
Amine in Methyl Chloride, J. Chem. Phys. 110, 7359–7364 (1999). S. Caratzoulas, S. D. Schwartz, A computational method to discover the existence of promoting vibrations for chemical reactions in condensed phases, J. Chem. Phys., 114, 2910– 2918 (2001). S. Ramaswamy, H. Elkund, B. V. Plapp, Structures of horse liver alcohol dehydrogenase complexed with NADþ and substituted benzyl alcohols, Biochemistry, 33, 5230–5237 (1994). B. R. Brooks, R. E. Bruccoleri, B. D. Olafson, D. J. States, S. Swaminathan, M. Karplus, CHARMM: A program for macromolecular energy, minimization, and dynamics calculations, J. Comput. Chem. 4, 187–217 (1983). W. L. Jorgensen, J. Chandrasekher, J. D. Madura, R. W. Impey, M. L. Klein, Comparison of .23 Simple Potential Functions for Simulating Liquid Water, J. Chem. Phys. 79, 926 (1983). J. J. Pavelites, J. Gao, P. A. Bash, D. Alexander, J. Mackerell, A molecular mechanics force field for NADþ NADH, and the pyrophosphate groups of nucleotides, J. Comput. Chem. 18, 221–239 (1997). J. S. Mincer, S. D. Schwartz, A computational method to identify residues important in creating a protein promoting-vibration in enzymes, J. Phys. Chem. B, 107, 366–371 (2003). B. J. Bahnson, T. D. Colby, J. K. Chin, B. M. Goldstein, J. P. Klinman, A Link between Protein Structure and Enzyme Catalyzed Hydrigen Tunneling, Proc. Natl. Acad. Sci. U.S.A., 94, 12797–12802 (1997). J. K. Rubach, B. V. Plapp, Amino Acid Residues in the Nicotinamide Binding site Contribute to Catalysis by Horse Liver Alcohol Dehydrogenase, Biochemistry, 42, 2907–2915 (2003). J. K. Rubach, S. Ramaswamy, B. V. Plapp, Contributions of Valine-292 in the Nicotinamide Binding Site of Liver Alcohol Dehydrogenase and Dynamics
1237
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46
47
48
49
50
51
52
53
54
to Catalysis, Biochemistry 40, 12686– 12694 (2001). a) B. J. Bahnson, D.-H. Park, K. Kim, B. V. Plapp, J. P. Klinman, Unmasking of hydrogen tunneling in the horse liver alcohol dehydrogenase reaction by site-directed mutagenesis, Biochemistry, 32, 5503–5507 (1993); b) J. K. Chin, J. P. Klinman, Probes of a Role for Remote Binding Interactions on Hydrogen Tunneling in the Horse Liver Alcohol Dehydrogenase Reaction, Biochemistry, 39, 1278–1284 (2000). J. Luo, T. C. Bruice, Anticorrelated motions as a driving force in enzyme catalysis: The dehydrogenase reaction, Proc. Natl. Acad. Sci. U.S.A., 101, 13152–13156 (2004). M. Gulotta, H. Deng, R. B. Dyer, R. H. Callender, Toward an Understanding of the Role of Dynamics on Enzymatic Catalysis in Lactate Dehydrogenase, Biochemistry, 41, 3353–3363 (2002). A. Meister, Advances in Enzymology and Related Areas of Molecular Biology, Vol. 37, John Wiley & Sons, New York (1973). J. E. Bassner, S. D. Schwartz, Donor acceptor distance and protein promoting vibration coupling as a mechanism for kinetic control in isozymes of Human Lactate Dehydrogenase, J. Phys. Chem. B., 108, 444– 451 (2004). J. E. Bassner, S. D. Schwartz, How Enzyme Dynamics Helps Catalyze a Chemical Reaction in Atomic Detail: A Transition Path Sampling Study, J. Am. Chem. Soc., submitted. J. A. Read, V. J. Winter, C. M. Eszes, R. B. Sessions, R. L. Brady, Structural basis for altered activity of M- and H-isozyme forms of human lactate dehydrogenase, Proteins: Struct., Funct., Genet., 43, 175–185 (2001). S. Caratzoulas, J. S. Mincer, S. D. Schwartz, Identification of a protein promoting vibration in the reaction catalyzed by Horse Liver Alcohol Dehydrogenase, J. Am. Chem. Soc., 124 (13), 3270–3276 (2002). C. Dellago, P. G. Bolhuis, D.
55 56
57
58
59
60
61
Chandler, Efficient transition path sampling: application to LennardJones cluster rearrangements, J. Chem. Phys., 108, 9236–9245 (1998). M. J. Field, A. Bash, M. Karplus, J. Comput. Chem., 11, 700–733 (1990). J. Gao, P. Amara, C. Alhambra, M. J. Field, J. Phys. Chem., 102, 4714–4721 (1998). W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, J. Chem. Phys., 79, 926– 935 (1983). a) J. Andres, V. Moliner, J. Krechl, E. Silla, Bioorg. Chem., 21, 260–274 (1993); b) A. J. Turner, V. Moliner, I. H. Williams, Phys. Chem. Chem. Phys., 1(6), 1323–1331 (1999); c) S. Ranganathan, J. E. Gready, J. Phys. Chem. B, 101, 5614–5618 (1997). a) M. J. Knapp, K. Rickert, J. P. Klinman, Temperature-Dependent Isotope Effects in Soybean Lipoxygenase-1: Correlating Hydrogen Tunneling with Protein Dynamics, J. Am. Chem. Soc. 124, 3865 (2002); b) M. J. Knapp, J. P. Klinman, Environmentally coupled hydrogen tunneling, Eur. J. Biochem. 269, 3113 (2002). a) J. Basran, M. Sutcliffe, N. Scrutton, Enzymatic H-Transfer Requires Vibration-Driven Extreme Tunneling, Biochemistry, 38, 3218 (1999); b) M. J. Sutcliffe, N. S. Scrutton, A new conceptual framework for enzyme catalysis, Eur. J. Biochem., 269, 3096 (2002). a) R. I. Cukier, Mechanism for Proton-Coupled Electron-Transfer Reactions, J. Phys. Chem. 98, 2377 (1994); b) X. Zhao, R. I. Cukier, Molecular Dynamics and Quantum Chemistry Study of a Proton-Coupled Electron Transfer Reaction, J. Phys. Chem. 99, 945 (1995); c) R. I. Cukier, Proton-Coupled Electron Transfer through an Asymmetric HydrogenBonded Interface, J. Phys. Chem. 99, 16101 (1995); d) R. I. Cukier, ProtonCoupled Electron Transfer Reactions: Evaluation of Rate Constants, J. Phys. Chem. 100, 15428 (1996); e) S. Shin, H. Metiu, Nonadiabatic effects on the charge transfer rate constant: A
References numerical study of a simple model system, J. Chem. Phys. 102, 9285 (1995); f ) S. Hammes-Schiffer, Theoretical perspectives on protoncoupled electron transfer reactions, Acc. Chem. Res. 34, 273–281 (2001); g) N. Iordanova, S. Hammes-Schiffer, Theoretical investigation of large kinetic isotope effects for protoncoupled electron transfer in ruthenium polypyridyl complexes, J. Am. Chem. Soc. 124, 4848–4856 (2002). 62 S. Nunez, D. Antoniou, V. L. Schramm, S. D. Schwartz, Promoting vibrations in human purine nucleoside phosphorylase: A molecular dynamics and hybrid
quantum mechanical/molecular mechanical study, J. Am. Chem. Soc., 126, 15720–15729 (2004). 63 A. Fedorov, W. Shi, G. Kicska, E. Fedorov, P. C. Tyler, R. H. Furneaux, J. C. Hanson, G. J. Gainsford, J. Z. Larese, V. L. Schramm, S. C. Almo, Biochemistry, 40, 853–860 (2001). 64 S. Nunez, D. Antoniou, V. L. Schramm, S. D. Schwartz, Electronic promoting motions in human purine nucleoside phosphorylase: a molecular dynamics and hybrid quantum mechanical/molecular mechanical study, J. Am. Chem. Soc., 126, 15720– 15729 (2004).
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Nuclear Tunneling in the Condensed Phase: Hydrogen Transfer in Enzyme Reactions Michael J. Knapp, Matthew Meyer, and Judith P. Klinman 10.1
Introduction
Hydrogen transfer is one of the most pervasive and fundamental processes that occur in biological systems. Examples include the prevalent role of acid–base catalysis in enzyme and ribozyme function, the activation of CaH bonds leading to structural transformations among a myriad of carbon-based metabolites, and the transfer of protons across membrane bilayers to generate gradients capable of driving substrate transport and ATP biosynthesis. Until quite recently, the kinetic and chemical properties of biological hydrogen transfer had been conceptualized in the same context as reactions involving heavier atoms, i.e., within the framework of transition state theory (TST). This treatment led to a generally accepted theory for the origin of rate discrimination among the isotopes of hydrogen (protium, deuterium and tritium), referred to as the kinetic isotope effect (KIE). Although model reactions were observed, from time to time, to display properties of the KIE that deviated significantly from predictions based on TST, these were often relegated to a ‘‘corner of oddities and possible artifacts.’’ Enzyme reactions offer unique advantages over simple model reactions in the study of fundamental chemical properties. In general, they are specific for a given substrate and, more importantly, lead to a single reaction product. Additionally, in reactions at carbons bearing two hydrogens (methylene centers), enzymes discriminate between the pro-R and pro-S hydrogens, allowing a clear distinction between the properties of the bond that is cleaved from the one that is left behind. It is, perhaps then, not very surprising that the growing evidence for quantum mechanical tunneling in H-transfer has come from the characterization of enzyme reactions. This chapter has been written largely for the reader who has little or no background in enzyme kinetics. We begin with a simple introduction to the nature of kinetic measurements in enzyme reactions, since many confusing statements have appeared in the literature regarding the definition of catalysis and rate limiting steps. This is followed by a description of the methodology that is currently availHydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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able for the detection of nonclassical hydrogen transfers, together with a discussion of some relevant theoretical treatments of H-transfer. In the final section, we focus on selected experimental examples from the Berkeley laboratory that illustrate the differing ways in which tunneling can be demonstrated, together with the implications of tunneling in enzyme catalyzed hydrogen transfers.
10.2
Enzyme Kinetics: Extracting Chemistry from Complexity
The dominant tool to study hydrogen tunneling in an enzyme reaction is the measurement of isotope effects on the chemical step of catalysis via steady-state kinetics experiments. However, steady-state kinetics are often complicated by the contribution of several microscopic steps to the macroscopically observed rates, making it difficult to study the chemical step. The following section introduces basic enzyme kinetics, with a discussion of the macroscopic rate constants kcat and kcat =KM and their interpretations. More detailed references on this matter are available [1, 2]. The first concern of the experimentalist is to be able to observe the intrinsic rate of chemistry, thereby allowing probes into the mechanism of hydrogen transfer. A minimal enzymatic reaction, in which the substrate, S, is converted into the product, P, is shown in Eq. (10.1). Under initial-rate conditions ð½P0 ¼ 0Þ, product release is a kinetically irreversible step ðk3 ½P0 ¼ 0Þ as shown. k1
k2
k1
k2
k3
E þ S Ð ES Ð EP ! E þ P
ð10:1Þ
The velocity of this reaction ðv ¼ d½P=dtÞ is a function of the bimolecular rate of substrate binding ðk1 Þ and the unimolecular rates of chemistry ðk2 ; k2 Þ and substrate and product release ðk1 ; k3 Þ. The steady-state velocity expression under initial rate conditions (Eq. (10.2)) demonstrates how each microscopic rate constant contributes to the macroscopic reaction rate and the dependence of the velocity upon substrate concentration. u¼
k1 k2 k3 ½ET 1 ðk2 k3 þ k1 k2 þ k1 k3 Þ þ k1 k2 þ k1 k2 þ k1 k3 ½S
ð10:2Þ
One useful limit is the velocity at saturating substrate ð½S ! yÞ, which, when normalized for the enzyme concentration, gives the macroscopic rate constant kcat . It can be seen (Eq. (10.3)) that kcat is independent of the rate of substrate binding, a situation that exists for more complex mechanisms as well. Consequently, kcat is a unimolecular rate constant obtained in the limit of infinite substrate concentration that reflects the rate of all steps after the formation of the ES complex.
10.2 Enzyme Kinetics: Extracting Chemistry from Complexity
When one of these unimolecular rates is much slower than the others, it is said to be rate-limiting on kcat ; these steps can include chemistry or product release. kcat ¼
u k2 k3 ¼ ½ET k2 þ k2 þ k3
ð10:3Þ
Another limiting regime is the velocity under conditions of limiting substrate ð½S ! 0Þ, which, when normalized for enzyme concentration, gives the macroscopic rate constant kcat =KM (Eq. (10.4)). kcat =KM ¼
u k1 k2 k3 ¼ ½ET ½S k1 k2 þ k1 k3 þ k2 k3
ð10:4Þ
It can be seen that kcat =KM reflects a bimolecular binding step, and other subsequent steps, including chemistry. If the chemical step is irreversible ðk2 ¼ 0Þ, kcat =KM simplifies to Eq. (10.5). kcat =KM ¼
u k1 k2 ¼ ½ET ½S k1 þ k2
ð10:5Þ
This demonstrates that kcat =KM reflects all steps from substrate binding up to and including the first irreversible step – whether this step is chemistry (Eq. (10.5)) or product release (Eq. (10.4)). When one of these steps is slow (e.g. substrate binding, chemistry, or product release), it is rate-limiting on kcat =KM . We emphasize that the chemical step can be experimentally probed, e.g. by isotope effects, through measurements of the macroscopic rate constant kcat =KM , despite suggestions to the contrary [3]. In summary, kcat and kcat =KM have some microscopic steps in common, the details of which depend upon the particular enzyme mechanism. Careful study of each macroscopic rate constant can reveal which microscopic step or steps are rate-limiting under specific conditions. Standard kinetic tools to determine whether substrate binding, chemistry, or product release is rate-limiting have been developed over the years [4, 5]. The most straightforward way to demonstrate that chemistry is fully rate-limiting in the steady state is to show that the single-turnover rate of reaction is identical to kcat . Other probes rely on perturbing the experimental conditions, such as site specific mutagenesis of the enzyme or alterations in pH, substrate structure, or viscosity, in a fashion that will affect only one microscopic step. An especially powerful kinetic tool uses substrates deuterated at an appropriate position in order to alter the rate of the chemical step to the exclusion of other steps. Observation of an H/D kinetic isotope effect on the macroscopic rate constants can indicate that chemistry is partially rate limiting. If a KIE is observed on kcat but not on kcat =KM this suggests that chemistry is at least partially rate limiting on kcat , while being not at all rate limiting on kcat =KM . Multiple probes can often reveal which steps limit the macroscopic rate constants obtained from steady-state kinetic measure-
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ments. For example, the use of slow substrates or site-directed mutants of the enzyme can alter relative microscopic rates such that isotope effects become fully expressed on one or both of the steady-state rate constants [5, 6]. Once the appropriate conditions have been found to isolate chemistry, isotopically labeled substrates can then be used to probe further for nuclear tunneling during the chemical step on the enzyme. There are three limiting kinetic relationships that affect which types of isotope effects can be used to study enzyme chemistry. The first case is when kcat is fully limited by chemistry, the second is when kcat =KM is limited by chemistry, and the third arises when multiple steps are partially rate limiting. It should be noted that circumstances may also arise where both kcat and kcat =K M reflect the chemical step. The simplest case conceptually is when kcat is fully rate limited by chemistry and, therefore, probes of chemistry (such as isotope effects) are revealed in kcat . This limit is realized in recombinant soybean lipoxygenase-1 (SLO) and its mutants, greatly facilitating the study of CaH cleavage in this enzyme [7–9]. The study of chemistry in this case simply requires that kcat can be faithfully measured as a function of external perturbation, such as temperature, pH, or substrate deuteration. It is essential to show substrate saturation ð½S g KM Þ under all conditions, however, and this requirement can present experimental limitations. The principal probe for tunneling in enzymes in this kinetic case is the magnitude and temperature dependence of noncompetitive kinetic isotope effects, D kcat ¼ kcatðHÞ =kcatðDÞ . The next simple case is when kcat =KM is fully rate limited by chemistry. This limit is realized in yeast alcohol dehydrogenase (YADH), providing a steady-state probe of chemistry in this enzyme [10]. The greatest difficulty here is measuring kcat =KM precisely, as the exact substrate concentration must be known and KM can vary with each enzyme preparation. The principal probe for tunneling in this kinetic case is the magnitude of isotope effects, e.g. D ðkcat =KM Þ ¼ ðkcat =KM ÞH =ðkcat =KM ÞD , which can be measured noncompetitively or competitively. The latter case bypasses the scatter in individual kcat =KM determinations, such that the relatively small secondary KIEs (section 10.3.1) can be precisely measured; these have proven to be a particularly powerful tool for demonstrating tunneling. Finally, many enzymes are kinetically complex, and have multiple steps that partially limit both kcat and kcat =KM . One approach is to use single-turnover studies to obtain the rate of the chemical step and the kinetic isotope effects by this noncompetitive technique. Several examples of single-turnover studies of enzymes that exhibit the characteristic of tunneling are in the literature [11, 12]. Alternatively, tools that allow microscopic rate constants to be calculated from observed rate constants can be applied. This approach has been documented for peptidylglycine-ahydroxylating monooxygenase [13], and more recently, for dihydrofolate reductase [14]. In conclusion, steady-state kinetics provide macroscopic rate constants describing enzyme catalysis. Through careful analysis of kinetic data, rate limiting steps on kcat and kcat =KM can be identified, as can optimal conditions to isolate kinetically the chemical step. Following kinetic isolation, the nature of the chemical steps, including tunneling effects, can be studied with fine detail.
10.3 Methodology for Detecting Nonclassical H-Transfers
10.3
Methodology for Detecting Nonclassical H-Transfers
Isotope effects are used to probe chemical processes, as isotopic substitution generally alters only the mass of the reacting groups without changing the electronic properties of the reactants. In this fashion, isotope effects can be used as subtle probes of mechanism in chemical transformations. This section will discuss how to use isotope effects to probe for tunneling effects on enzymes. The basic criteria for tunneling are experimental isotope effects that have properties that deviate from those predicted within the semi-classical transition state model, which includes only zero-point energy effects (we refer to this as the ‘‘bond stretch model’’). Many of the available methods evolved within this context, as described by Bell regarding tunneling corrections [15]. While the Bell model is oversimplified and will not apply to numerous enzyme systems, it has pedagogical value in explaining how certain isotope experiments can demonstrate tunneling. In many cases, multiple anomalous KIEs are required before one can really implicate tunneling as being a likely explanation of the observed KIEs. Detailed interpretation of isotope effects requires theoretical models for hydrogen transfer that incorporate quantum effects (see Section 10.4). 10.3.1
Bond Stretch KIE Model: Zero-point Energy Effects
Conventional theories for kinetic isotope effects (KIEs) start with transition-state theory [16]. Reaction rates within transition-state theory are formulated as the product of three terms (Eq. (10.6)), k TST ¼ knK z
ð10:6Þ
where K z is the equilibrium constant between the ground state and the transition state, n is the frequency of barrier crossing, and k is the transmission coefficient. It is conventionally assumed that isotopic substitution at hydrogen will not perturb the potential energy surface, leaving k and n largely unchanged but, by virtue of the altered vibrational energy levels, affecting K z . Reaction rates are often reported in terms of the empirical Arrhenius expression, (expressed in terms of Ea , the apparent activation energy, and A, the pre-exponential factor1); KIEs can, thus, be reported as simple rate ratios (KIE ¼ kH =kD ), or as parameter ratios (KIE ¼ AH =AD or DEa ¼ Ea ðDÞ Ea ðHÞ). In this semi-classical context, KIEs arise from the difference in vibrational, rotational, and translational degrees of freedom (quantized properties) in the ground state and in the transition state [16–18], with primary and secondary KIEs distinguished by the position of the isotopic comparison. 1) According to Eyring theory, the reaction
coordinate frequency is treated classically as an equilibrium process defined by K z, which leads to kn T= hn expðDGz =RTÞ where kB is
Bolztmann’s constant, n is the reaction coordinate frequency, DGz is the activation free energy and R is the gas constant. In this instance E a ¼ DH z þ RT.
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Primary Kinetic Isotope Effects Primary KIEs for H-transfers are observed when the rate of reaction is studied as a function of isotopic labels at the transferred position. The reaction coordinate for H-transfer is composed of many degrees of freedom, but in the simplest limit will be dominated by the loss of the X–H stretching mode, in that the reaction X–H þ B ! ½X–H–Bz ! X þ B–H converts the X–H stretch to a translation at the transition state. The loss of zero-point energy (ZPE) from this stretch will dominate primary KIEs in H-transfer reactions, due to the extremely large difference in ground-state ZPE for X–H vs. X–D. The resulting maximal primary kH =kD ratios for X–H versus X–D are 6.5, 7.0 and 7.9 when X is C, N, or O. These estimates arise from the ZPE differences which are 1.1, 1.2, and 1.3 kcal mol1 , respectively. It can be seen that the largest primary kH =kD ratio is around 8 at 25 C. This assumes that a stretching mode is lost in the transition state; smaller primary kH =kD ratios result if a bending mode is lost at the transition state, as the frequency is less for bonding modes leading to a smaller value for Ea ðDÞ Ea ðHÞ. Additionally, a reduced primary kH =kD ratio may arise from vibrational energy in modes perpendicular to the reaction coordinate [18]. The temperature dependence of primary kH =kD within the bond-stretch model arises from the zero-point energy differences of the X–H and X–D stretch. The magnitude of kH =kD is related to the difference in activation energy for X–H and X–D, as per Eq (10.7) [16], 10.3.1.1
kH AH Ea ðDÞ Ea ðHÞ DZPE A exp ¼ exp RT RT kD AD
ð10:7Þ
where, in the simplest case, DZPE is the ground-state zero-point energy difference for X–H and X–D ð1=2hnH 1=2hnD Þ. Note that similar equations can be written for any two isotopes (e.g. H and T or D and T). The bond-stretch model predicts that the KIE originates almost exclusively from vibrational energy effects, and predicts that DZPE is an upper limit to the activation energy difference. Although AH =AD is expected to be unity, experimental scenarios can be simulated that predict lower and upper limits of 0.7 and 1.2, respectively [19]. Compensatory motions in the transition state can lead to small deviations of AH =AD from unity, but it is generally accepted that this ratio will lie between 0.7 and 1.2 [19]. A traditional use of the primary kH =kD ratio is to infer the transition-state structure for a reaction. Large primary kH =kD ratios are predicted for symmetric transition-states; kH =kD ratios decrease for an early or a late transition state, as compensatory transition-state motions increase in these situations [18]. The simple bond-stretch model predicts a direct relationship between the symmetry of the transition-state structure and the magnitude of the observed primary kH =kD. As discussed below and in other sections, this view no longer holds in the context of significant hydrogen tunneling.
10.3 Methodology for Detecting Nonclassical H-Transfers
Secondary Kinetic Isotope Effects Secondary isotope effects can also arise from differences in vibrational frequencies between the ground state and the transition state. The isotope at a secondary position retains its vibrational modes in the transition state, and consequently experiences much smaller frequency changes than do primary positions. As with primary effects, secondary kH =kD ratios have been used to infer transition-state geometry [20, 21]. If the transition state resembles the reactants (an early TS), then there will be little change in vibrational frequencies between the ground state and transition state, leading to a small secondary kH =kD that approaches unity. Alternatively, if the transition state resembles the products (a late TS), there will be a large change in vibrational frequencies, leading to a relatively large secondary kH =kD effect that approaches the equilibrium KH =KD . In the absence of tunneling, secondary kH =kD ratios are expected to lie between unity and the equilibrium KH =KD value. The difference between primary and secondary kinetic effects can be elucidated by using the oxidation of benzyl alcohol by nicotinamide adenine dinucleotide (NADþ ) as an example (Scheme 10.1 (A)). This reaction is catalyzed by alcohol dehydrogenase (ADH), and has been extensively studied [10, 21–27]. In this reaction, the hydrogen at position L 1 is transferred from benzyl alcohol to NADþ , forming benzaldehyde and reduced nicotinamide (NADH), making L 1 the primary position. Conversely, L 2 is retained upon reaction, making this the secondary position. 10.3.1.2
Scheme 10.1
10.3.2
Methods to Measure Kinetic Isotope Effects Noncompetitive Kinetic Isotope Effects: kcat or k cat /KM Measuring isotope effects on enzyme chemistry requires a careful integration of enzymology and organic chemistry. Enzymology is crucial to ensure that kinetic 10.3.2.1
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10 Nuclear Tunneling in the Condensed Phase: Hydrogen Transfer in Enzyme Reactions
complexity has been resolved, and that the measured isotope effect is intrinsic to the chemical step, as discussed in Section 10.2. Organic chemistry is crucial to synthesizing substrates that are isotopically labeled in the correct position(s). Clever use of multiple and/or tracer isotopic labels can lead to detailed information on the reaction coordinate via analysis of the KIEs. The simplest way to measure an isotope effect is the noncompetitive technique, in which the rate ðkH Þ with fully protiated substrate ( 1 H labeled), is compared to the rate ðkD Þ at which deuterium labeled substrate ( 2 H labeled) reacts [28]. The label may be in the primary or a secondary position, yielding the primary or secondary KIE, respectively. Steady-state noncompetitive measurements yield the isotope effect on the rate constants kcat or kcat =KM, but suffer from the requirement of both high substrate purity and isotopic enrichment, and from a large uncertainty in the KIE (ca. 5–10%) due to propagated errors. Single-turnover experiments can yield noncompetitive KIEs on the chemical step, but also generally have large uncertainties. Nevertheless, noncompetitive measurements are the only way to obtain KIEs on kcat , which for certain enzymes may be the sole kinetic parameter that reflects the chemical step(s). Competitive Kinetic Isotope Effects: k cat /KM In the competitive technique, the enzyme reacts with a mixture of labeled and unlabeled substrate, yielding isotope effects on kcat =KM [29]. Competitive measurements, while limited to kcat =KM isotope effects, are substantially more precise than noncompetitive measurements. In addition, they allow the use of tracerlevel radioactive labels, permitting tritium isotope effects at the primary and secondary positions (kH =k T or kD =k T ) to be determined. General methods for determining competitive isotope effects have been published [17b]. One drawback is that multiple isotopic labels must often be used, leading to extensive synthetic efforts. Radioactive isotopes are commonly used for competitive KIE measurements in a double-label experiment, yielding kH =k T or kD =k T ratios on kcat =KM . This technique typically utilizes tracer-level radioactivity in the position of interest (primary or secondary) to monitor the transfer of radioactivity from reactant to product, and requires a remote label (e.g. 14 C) in order to measure the conversion of unlabelled substrate to product. As an example, [ring- 14 C(U)]benzyl alcohol and [1- 3 H]benzyl alcohol (Scheme 10.2) can be used to simultaneously measure the primary and asecondary kH =k T effects in the reaction catalyzed by alcohol dehydrogenase (ADH), as the tracer tritium is incorporated randomly into primary and a-secondary positions [6, 10]. In summary, competitive measurements yield the kinetic isotope effect on kcat =KM , and often rely upon tracer-level radioactivity, though recent developments also allow these values to be obtained using natural abundance NMR techniques [123]. Noncompetitive measurements can reveal the kinetic isotope effects on kcat or kcat =KM, but suffer from larger propagated errors. 10.3.2.2
10.3 Methodology for Detecting Nonclassical H-Transfers
Scheme 10.2.
The star ðÞ represents C-14.
10.3.3
Diagnostics for Nonclassical H-Transfer
The bond-stretch model provides an upper limit for kinetic isotope effects that arise solely from ground state zero-point energy effects. Observations that deviate from this model imply a nonclassical effect. Provided that potential artifacts are controlled, the observation of KIEs that disobey the bond-stretch predictions calls into question the basic theory. Theories for hydrogen transfer that treat hydrogen as a quantum mechanical particle have been presented [30–35]; however, most of these models are not fully developed with respect to KIE predictions. These models do agree with some of the basic conclusions taken from the bond-stretch model and the Bell correction, specifically that marked deviations of KIEs from predictions of the bond-stretch model occur when the quantum nature of hydrogen is pronounced. The basic criteria used to evaluate how closely a particular reaction obeys the bond-stretch KIE model and, by extension, a classical reaction model is presented below. In the subsequent sections of theory (Section 10.4) and experimental systems (Section 10.5), more detailed examples of nonclassical KIEs are presented. The Magnitude of Primary KIEs: kH /kD I 8 at Room Temperature The magnitude of primary kH =kD ratios is a crude yardstick for diagnosing nonclassical hydrogen transfer. These ratios are easily obtained from competitive or 10.3.3.1
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10 Nuclear Tunneling in the Condensed Phase: Hydrogen Transfer in Enzyme Reactions
noncompetitive measurements, with the principal difficulty being kinetic complexity (see Section 10.2). Measured kH =kD ratios that exceed the limit predicted by the bond-stretch model (ca. 8 at 25 C), as in several enzymatic reactions [36–40], suggest tunneling [15]. Reactions exhibiting normal kH =kD ratios may still have appreciable tunneling components, as coupled motion between primary and a-secondary positions will reduce the size of kH =kD [25], as can the contribution of heavy atom motion in controlling tunneling [30–35]. Therefore, hydrogen tunneling is likely to be far more prevalent than is commonly thought on the basis of reported kH =kD ratios, and is merely awaiting more refined models. The potential for quantum behavior by hydrogen isotopes has been recognized from the very earliest models, and was incorporated by Bell as a correction to transition-state theory [15]. In brief, light particles (H, D, and T) can tunnel through narrow portions of the reaction barrier, in particular near the very top (Fig. 10.1). This means that particles can react without attaining enough thermal energy to populate the transition state. The extent of tunneling behavior depends on the mass of the particle and the width of the barrier. The net effect is that lighter isotopes can tunnel lower down on the potential surface than heavier isotopes, leading to kH =kD or kH =k T ratios that exceed the bond-stretch predictions. An analysis of a tunneling correction from the experimental kH =kD relies upon a calculation of the transition-state structure to obtain the bond-stretch kH =kD , and the tunneling effect. Once the transition-state structure is calculated, the tunneling probability is primarily a function of the imaginary frequency ðn z Þ for the reaction coordinate. The truncated Bell correction is shown in Eq. (10.8). This correction
Figure 10.1. A cartoon of the Bell tunneling model, emphasizing that tunneling is more pronounced for lighter particles ðH > D > TÞ. Reactants have a probability of forming products, even when their energy is less than that of the transition state ðzÞ, via tunneling.
10.3 Methodology for Detecting Nonclassical H-Transfers
has been applied with notable success by Limbach et al. [41], and has often been used to account approximately for tunneling effects [25, 36]; a more complete description of the Bell model is given in Section 10.4. QL ¼
hn z =2kB T sinðhn z =2kB TÞ
ð10:8Þ
Q L is the ratio of rate that occurs by including tunneling to the rate that would have occurred solely by thermal activation, n z was defined above, and the other symbols have their usual meanings. It should be noted that, as a correction to transition-state theory, large Q L values (exceeding 2) are almost certainly physically unreasonable, and simply indicate that tunneling is very important to a reaction. This correction works fairly well for reactions that do not deviate appreciably from classical predictions. Explaining primary kH =kD ratios greater than 10 usually requires that Q H and Q D exceed 2, such that this basic approach becomes dubious. Many examples of primary kH =kD or kH =k T ratios are known that exceed the maximally predicted values of the bond-stretch model, some by a very large margin [37–40]. As compensatory motions in the transition state will only reduce the kH =kD ratio, these large KIEs suggest nuclear tunneling during the H-transfer. Very large kH =kD ratios are generally impossible to interpret within the Bell correction and require a full quantum model to explain their reactions. For example, large kH =kD ratios in the reactions catalyzed by the enzymes, methylamine dehydrogenase [42] and lipoxygenase [43], have recently been interpreted within environmentally-mediated tunneling models (cf. Sections 10.4 and 10.5). Provided that the intrinsic KIE on a single step is observed, a single temperature primary kH =kD ratio can suggest tunneling. It is important to control for artifacts that can inflate the KIE, such as multiplicative isotope effects (two concerted bond cleavages that exhibit ordinary KIEs), kinetic branching, or magnetic isotope effects. In general, corroborating data are needed to demonstrate conclusively that H-tunneling is important to the reaction. 10.3.3.2 Discrepant Predictions of Transition-state Structure and Inflated Secondary KIEs The magnitudes of primary and secondary KIEs have been used traditionally to infer transition-state structure [21]. Discrepancies between the transition-state structure predicted by these, as well as by other mechanistic probes, can suggest nonclassical behavior. This has been found in the alcohol dehydrogenase (ADH) reaction, where different transition-state structures were obtained from structure– reactivity correlations [44, 45] and the a-secondary KIEs [26, 27]. This discrepancy was later shown to be the result of hydrogen tunneling [10]. In the reactions catalyzed by dopamine b-monooxygenase (DbM) and peptidyl glycine a-hydroxylating monooxygenase (PHM), the magnitude of the primary KIE implied a symmetric transition state whereas a-secondary KIEs implied a product-like transition-state structure [46–48]. Once again, tunneling has been invoked to explain the observed discrepancies [13, 48].
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In fact, some of the earliest suggestions for tunneling came from the observation of an a-secondary kH =kD ratio that exceeded the maximally predicted value (secondary D k > D K eq ) [26, 49]. For the sake of the present discussion, discrepant predictors of transition-state structure serve to demonstrate that factors other than changes in vibrational modes are needed to account for the observed KIEs. Two factors that can inflate a-secondary KIEs are coupled motion in the transition state (a classical effect), and tunneling (a quantum mechanical effect), with an estimate of these separate effects requiring computational studies. The classical effect of coupled motion is to reduce the primary KIE by coupling the primary H translation with the a-secondary H bending modes, which has the effect of ‘leaking’ some of the primary KIE into the a-secondary KIE. This leads to an enhanced a-secondary KIE, as this position acquires some of the characteristics of the primary position. The extent to which coupled motion can inflate the a-secondary KIEs in the absence of tunneling has been discussed, and serves as a tunneling discriminator [25, 50–52]. It is the combined effect of coupled motion and tunneling that leads to the largest anomalies [25, 52]. In addition to the classical effects of coupled motion, tunneling further increases the a-secondary KIE while significantly increasing the primary KIE. In ADH, as well as several other enzymatic and chemical examples, both tunneling and coupled motion have been invoked to reproduce the experimentally observed primary and a-secondary KIEs [6, 10, 25, 26, 49, 53–55]. Multiple-position KIEs, when combined with computational modeling, can provide enough information to successfully model a reaction coordinate and demonstrate hydrogen tunneling, even when the primary kH =kD ratio is not enormous. More complete experimental evidence for tunneling can be obtained by demonstrating a breakdown in the exponential relationships (e.g. kH =k T versus kD =k T ) or by variable-temperature KIE measurements. 10.3.3.3 Exponential Breakdown: Rule of the Geometric Mean and Swain–Schaad Relationships The bond-stretch model of KIEs results in predictable relationships between kH , kD , and k T due to the ZPEs of X–H, X–D, X–T, as first noted by Swain et al. in 1958 [56]. These Swain–Schaad relationships are historically expressed with X–H as the reference state, kH =k T ¼ ðkH =kD Þ 1:44 . Using X–T as the reference state leads to a similar relationship in which the exponent, S, is 3.26: kH =k T ¼ ðkD =k T Þ 3:26 , and facilitates experimental determinations of exponential breakdown [10, 50]. In mixed-label experiments, the rule of the geometric mean (RGM) is an additional factor, causing R to be included in the observed exponent (see Eq. (10.10) below). The experimental KIE exponent, RS is evaluated by Eq. (10.9) as a composite of the Swain–Schaad (S) and RGM (R) exponents. RS is a good indicator of tunneling when it exceeds 3.3 by a large margin, with an extreme semi-classical upper-bound of ca. 5 [57].
RS kH kD ¼ kT H kT D
ð10:9Þ
10.3 Methodology for Detecting Nonclassical H-Transfers
Breakdown in the rule of the geometric mean (RGM) can contribute to inflation of the RS exponent. The RGM states that isotope effects are insensitive to remote labels [58]. For example, the magnitude of the secondary kH =kT ratio will be independent of the primary label (H or D) so long as the isotope effects arise solely from vibrational modes, which can be expressed as the following exponential relationship:
k2 H k2 T
1 H
¼
k2 H k2 T
1 D
R ð10:10Þ
where R is close to 1 [52]. The combined exponential relationship (RS) for secondary KIEs will breakdown if there is mechanical coupling between the primary and secondary positions when tunneling is important. Measuring exponential KIE relationships generally relies upon the use of tracerlabeled isotopically substituted substrates and, consequently, must be done by competitive methods. Two experiments must be performed, one of which measures kH =k T competitively, the other of which measures kD =k T competitively. It is then a simple matter to obtain the exponential relationship for both primary and secondary positions, where lnðkH =k T ÞH =lnðkD =k T ÞD ¼ RS. The primary exponential relationship comes from a comparison of the primary ðkH =k T Þ2 H to primary ðkD =k T Þ2 D isotope effects. It has been shown that primary exponents are not susceptible to large Swain–Schaad deviations, even in the event of fairly extensive tunneling [59]; furthermore, primary exponents are not susceptible to large RGM deviations [52], and consequently, the composite exponent RS should remain close to 3.3 in the absence of kinetic complexity. This is a useful control, as the magnitude of the primary exponent is reduced when chemistry is only partially rate limiting (i.e., it can be use to establish that H-transfer has been kinetically isolated) [60]. For a-secondary KIEs, the exponents turn out to be highly susceptible to RGM deviations when tunneling is important, and can inflate RS from 3.3 significantly. Huskey showed that the dominant contributor to such exponential deviations is RGM breakdown, and that this effect was only pronounced in the event of tunneling [51]. The mechanism for large RGM deviations in secondary exponential relationships can be described within the Bell model for tunnel corrections. Since the tunnel correction depends principally upon the mass of the transferred hydrogen, it will be different for a primary H, D, and T. When the primary label is heavy (e.g.primary D) the degree of tunneling is small, causing the perturbation of the a-secondary isotope effect (e.g. secondary kD =k T ) to also be small. When the primary label is light (e.g. primary H) tunneling is more extensive, and coupled motion can inflate the a-secondary isotope effect (e.g. secondary kH =k T ) significantly. In this manner, the secondary KIE depends upon the primary label. The RS exponential relationship has been successfully used to demonstrate tunneling in several dehydrogenase enzymes and related systems [10, 23, 24, 53, 55, 61]. This approach is quite powerful, and provides an elegant experimental demonstration of a breakdown in the semi-classical KIE model. Its limitation, however, is the requirement
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Figure 10.2. Temperature dependence of the rate of hydrogen transfer ðkL Þ, where L1 ¼ H, L2 ¼ D. Experimentally accessible temperatures are indicated by the vertical solid lines, and extrapolations to obtain AH and AD are indicated by dashed lines.
for coupled motion between the primary and a-secondary hydrogen positions, as well as the condition that the competitively measured kcat =KM KIE be fully limited by chemistry. Variable Temperature KIEs: AH /AD I I 1 or AH /AD H H1 Variable-temperature kinetic isotope effects are the most widely recognized diagnostic tools for nonclassical H-transfers [62]. The bond-stretch model of isotope effects predicts Arrhenius prefactor isotope effects that are very close to unity, AH =AD A 1, with the limits on AH =AD between 1.2 and 0.7 for relatively unusual force constants and mass effects [19]. KIEs on the Arrhenius prefactor that deviate from these limits indicate nonclassical H-transfer, provided that kinetic complexity has been resolved. Arrhenius prefactor ratios that are significantly less than unity ðAH =AD < 0:7Þ have been recognized as signatures of tunneling for quite some time, with the simple argument that the lighter isotope tunnels more than the heavier isotope. This leads to greater overall curvature in the Arrhenius plot for the lighter isotope. As shown in Fig. 10.2, kinetic measurements are generally restricted to a limited temperature range, such that extrapolation of tangents to the H and D lines within this range leads to an apparent ‘‘crossing’’ and values of AH =AD < 0:7. There are a growing number of AH =AD ratios that are much greater than unity (Table 10.1) that cannot be readily explained within a bond-stretch or tunnelcorrection view. One ad hoc explanation is that both isotopes tunnel appreciably, leading to the observed behavior. An alternative idea, that we advocate, is that the large majority of H-transfer reactions can be viewed as dominantly nonclassical, and should be treated within a quantum mechanical model for hydrogen transfer. In the nonadiabatic limit for hydrogen transfer, this leads to rate equations that are dominated by three contributors: environmental reorganization energy, Franck– Condon factors for hydrogen tunneling, and dynamic modulation of the tunneling 10.3.3.4
10.3 Methodology for Detecting Nonclassical H-Transfers Table 10.1.
Examples of enzymatic reactions where AH =AD g 1.
Enzyme
kH /kD
AH /AD
SLO[a] HtADH[b] PHM[c] MADH[d] TMADH[e] SADH[f ] AcCoA Desat[g] DHFR[h]
81 3.2 10 17 4.6 7.3 23 3.5
18 2.2 5.9 13 7.8 5.8 2.2 4.0
a Soybean
lipoxygenase, Ref [43]. b High temperature alcohol dehydrogenase, Ref [24]. c Peptidylglycine a-hydroxylating monooxygenase, Ref [13]. d Methylamine dehydrogenase, Ref [42]. e Trimethylamine dehydrogenase, Ref [11]. f Sarcosine dehydrogenase, Ref [12]. g Acyl CoA desaturase, Ref [40]. h Dihydrofolate reductase, Ref [14].
barrier [31–34]. These models, which are discussed in more depth in Section 10.4, provide for a range of AH =AD ratios that can either exceed or be much less than unity. The principal difficulty with the use of variable-temperature kH =kD measurements is the relatively small range of accessible temperatures (0–50 C) for most enzymes, though a few enzymes from extremophiles are active over a wider range [24]. This leads to a few limitations worth noting. One is that kinetic complexity, in which steps other than chemistry are partially rate limiting, can have varied effects on AH =AD ratios [61]. This is particularly troublesome when the amount of kinetic complexity varies across a temperature range. Another limitation is that propagation of experimental error into the AH =AD ratios, particularly from noncompetitive measurements, can make it difficult to diagnose tunneling [11, 13, 37, 42, 43, 63, 64]. Given that the slopes of Arrhenius plots can generally be determined with greater precision than the intercepts, it may be preferable to compare differences in energies or enthalpies of activation, DEa ¼ Ea ðDÞ Ea ðHÞ or DDH z ¼ DHðDÞ DHðHÞ, since changes in DEa correlate with changes in AH =AD . Competitive KIEs can reduce the uncertainty in prefactor isotope effects, and have been used to demonstrate tunneling in several enzymes [24, 36, 65]. As discussed above, the competitive, double-label, technique for measuring KIEs is inherently more precise than noncompetitive techniques, and can reduce the experimental uncertainty in the KIE on the Arrhenius prefactor and energy of activation. The use of tritium also provides multiple ratios AH =AT and AD =AT , which are helpful in resolving kinetic complexity [61]. It has been noted that a change in the rate-limiting step over the temperature range can lead to anomalous Arrhenius
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prefactor ratios [65], which could give a false indication of tunneling. However, the reactions of X–D and X–T are slower than the reaction of X–H, making the AD =AT ratio relatively unaffected by kinetic complexity and, consequently, a useful diagnostic for tunneling. In recent years, studies of the temperature dependence of isotope effects on kcat =KM that permit the calculation of the intrinsic primary isotope effect (the isotope effect on a single step that is free of potential complications arising from kinetic complexity) at each temperature have been carried out. In both instances the magnitude of AH =AD was found to lie very significantly above unity [13, 14].
10.4
Concepts and Theories Regarding Hydrogen Tunneling
Underlying the development of semi-classical KIEs [17] (referred to as the bondstretch model in Section 10.3) has been the assumption that the motion along the reaction coordinate itself behaves classically. In truth, the most accurate description of molecular events would be completely quantum mechanical. However, methods and computational power are only now evolving to the point where accurate quantum mechanical rates can be computed for reactions of interest in the condensed phase. The following sections discuss theoretical approaches that have been applied by this laboratory to explain our experimentally observed data. The past five years have been a period during which our conceptual understanding of tunneling in enzymatic systems has evolved away from one in which tunneling effects are treated as a small correction to the semi-classical KIE to one in which quantum mechanical effects are dominant and require full-tunneling models. Under these conditions, the dynamical behavior of heavy atoms surrounding the transferred hydrogen determine the magnitudes and the temperature dependence of KIEs. This section outlines the concept of tunneling and the evolution of the conceptual view of tunneling phenomena for systems studied within the Berkeley laboratory. 10.4.1
Conceptual View of Tunneling
The wave particle duality of matter, first proposed in 1923 by de Broglie, is intimately associated with the concept of tunneling through a classical energy barrier [66]. Spatial delocalization is one major consequence of wave-like behavior. The de Broglie wavelength, Eq. (10.11), is a means of demonstrating how mass affects the quantum nature of objects where h is Planck’s constant and p is momentum (equal to mass times velocity). Conceptually, the small wavelength ðlÞ limit corresponds to more classical or particle-like behavior, while the large wavelength limit corresponds to more quantum or wave-like behavior. The comparison of de Broglie wavelengths associated with several free particles of equivalent kinetic energy (ca. 5 kcal mol1 ) shows how this parameter changes substantially among the isotopes of
10.4 Concepts and Theories Regarding Hydrogen Tunneling
Figure 10.3. Plot of the squared overlap of ground state harmonic oscillator wavefunctions representative of CaH and CaD stretches (3000 cm1 and 2121 cm1 , respectively) separated by r in A˚. Inset shows
that overlap is greatly attenuated at larger separations and that the ratio of overlap for the light isotopomer to that for the heavy isotopomer increases markedly with increasing distances. CaH (a); CaD (- - -).
hydrogen: l ¼ 0:63; 0:45, and 0.36 A˚ for H, D, and T, respectively, in comparison to l ¼ 27 A˚ for the free electron as a frame of reference. l ¼ h=p
ð10:11Þ
Tunneling probability is proportional to the overlap between the hydrogen donor and acceptor wavefunctions, which can be understood from the wave picture of matter. Figure 10.3 illustrates the degree to which mass and distance can affect wavefunction overlap between a hydrogen donor and acceptor. Distance is most critical for determining the overlap of less dispersed wavefunctions, such that the overlap between two CaD stretching vibrational wavefunctions is more dependent on distance than the corresponding overlap between the two CaH stretching vibrational wavefunctions. This concept is central to understanding the role of dynamics in catalysis (cf. Eqs. (10.10)–(10.20) and Section 10.4.3). Another useful viewpoint for introducing tunneling is the classically forbidden transmission of a free particle through a barrier. According to this physical picture introduced in Bell’s excellent treatise [15], a potential energy barrier is bombarded from the left by a stream of free particles (A). The barrier reflects some of the particles to the left (C) and allows some of the particles to either penetrate or go over the barrier (B) (depending on the energy of the incident particle). Mathematically, the proportion of incident particles that penetrate or surmount the barrier as a function of energy (E) is expressed as the permeability of the barrier, GðEÞ in Eq. (10.12), where jAj 2 and jBj 2 are the fluxes for the incident and transmitted beams, respectively.
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GðEÞ ¼ jBj 2 =jAj 2
ð10:12Þ
The fundamental way in which a quantum physical picture differs from the classical picture is that classical permeability is Boolean in nature: either a particle has an energy equal to or greater than V, the barrier height, and is able to surmount the barrier, or the particle has an energy less than V and is reflected. By contrast, the quantum permeability ½GðEÞ is a smooth function of E for both light and heavy particles, though it varies more sharply for heavier particles making their behavior more classical. Analogous to the delocalization picture, the barrier penetration picture illustrates that tunneling is more favorable for particles of light mass. 10.4.2
Tunnel Corrections to Rates: Static Barriers
The most utilized treatment of tunneling thus far has been the one developed by Bell [67]. The rate for passage through a barrier, J in Eq. (10.13a), is an integration of the product of the probability ½PðEÞ for attaining energy E, Eq. (10.13b), and the probability ½GðEÞ of a particle of that energy being transmitted from the reactant state to the product state (multiplied by the incident particle flux from the reactant side, J0 ). ðy J ¼ J0
PðEÞGðEÞ dE
ð10:13aÞ
0
where b ¼ 1=kB T and kB is Boltzmann’s constant. The tunnel correction is derived from the ebE dE PðEÞ dE ¼ Ð y bE dE 0 e
ð10:13bÞ
ratio of the quantum rate (Eq. (10.14a)) to the rate predicted from classical mechanics (Eq. (10.14b)). GðEÞ can be obtained in an analytic form for a parabolic and other types of barrier. Appendix C of Ref. [15] gives two methods for the development of the tunnel correction for a parabolic barrier; although these expressions contain some typographical errors, they have been corrected by Northrop [68]. The full expression for the Bell tunnel correction, is given in Eq. (10.15a). The two parameters for input into Eq. (10.15a) are the barrier height, V, and the imaginary frequency, u0, which defines the curvature at the top of the parabolic barrier. These are entered into the equation in their reduced forms which give their magnitude relative to thermal energy (Eqs. (10.15b) and (10.15c)), where NA is Avogadro’s number. ðy Jq ¼ bJ0 0
GðEÞebE dE
ð10:14aÞ
10.4 Concepts and Theories Regarding Hydrogen Tunneling
ðy Jc ¼ bJ0
ebE dE ¼ J0 ebV
u t 2np exp a y X u t =2 ut Qt ¼ ð1Þ nþ1 þ u t 2np sinðu t =2Þ n¼1 ut u t ¼ bhu0
ð10:14bÞ
V
a ¼ bV=NA
ð10:15aÞ ð10:15bÞ ð10:15cÞ
As a matter of convenience, most practitioners use the truncated Bell correction, Eq. (10.8) in Section 10.3, which is the first term of Eq. (10.15a). However, this term inflates rapidly as a function of the reduced imaginary frequency. Inserting a reasonable barrier height of 20 kcal mol1 and a barrier frequency of 800i cm1 into Eq. (10.15a) yields the following parameters: kH =kD ¼ 12:6; Ea ðDÞ Ea ðHÞ ¼ 1:86 kcal mol1 and AH =AD ¼ 0:55; these quantities differ substantially from the semi-classical values of kH =kD G 7, Ea ðDÞ Ea ðHÞ G 1:1 kcal mol1 and AH =AD G 1. An additional indicator of tunneling that derives from a Bell treatment is inflation of the Swain–Schaad exponent. As discussed in Section 10.3, this can be further altered by breakdowns in the rule of geometric mean, leading to values for RS, Eq. (10.9), that show extensive deviations from semi-classical behavior. Importantly, as with the truncated Bell correction, Eq. (10.15a) has limited applicability as tunneling becomes appreciable. For example, increasing the value of uz to 1000i cm1 (298 K), produces Q t > 2, calling into question the physical relevance of its function as a ‘‘correction’’ as the contribution to the rate by tunneling exceeds 100%. A number of modern and quite sophisticated treatments of H-transfer in the condensed phase are not that dissimilar from the approach taken by Bell, in that they formulate the rate constant for H-transfer as a semi-classical term multiplied by a tunneling correction factor, e.g. Eqs. (10.16a) and (10.16b). kobs ¼ Qksc ¼ gðTÞve
ð10:16aÞ DGz =RT
ð10:16bÞ
According to Eq. (10.16b), the tunneling ‘‘correction’’ appears in the prefactor terms gðTÞ that has been written as the product of rðTÞ, the dynamical re-crossing of the barrier and kðTÞ the actual tunneling correction [69]. As pointed out in Ref. [69], rðTÞ is expected to decrease the rate somewhat while kðTÞ enhances the rate. We have already noted the difficulty in relying on the use of corrections to absolute rate theory to explain the anomalies in H-transfer when reactions deviate very significantly from semi-classical behavior. One recurring type of behavior that eludes treatment via tunnel corrections is the repeated observation of large isotope effects that show very small temperature dependences, leading to values for AH =AD g 1. The growing list of examples of the latter behavior in enzymatic hydrogen transfer reactions has been summarized in Table 10.1.
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10.4.3
Fluctuating Barriers: Reproducing Temperature Dependences
Recognizing the potential limitations of using a static barrier model to reproduce tunneling effects on KIEs, Bruno and Bialek attempted to model the effects of a full tunneling model with a fluctuating reaction barrier [32]. This attempt came in response to experimental data published by this laboratory on isotope effects in the oxidation of benzylamine catalyzed by bovine serum amine oxidase (BSAO) [36]. While Grant and Klinman attributed their measurements to a tunnel correction through a static barrier, Bruno and Bialek recognized two potentially conflicting observations: primary H/T and D/T isotope effects that seemed large enough (35 and 3, respectively) to be due to tunneling from ground-state vibrational levels, together with highly temperature dependent KIEs [70]. One expects ground-state tunneling through a static barrier, Eq. (10.17a), to be temperature independent [32, 70]. According to Eq. (10.17a), D20 is the square of the coupling between hydrogen donor and acceptor wavefunctions referenced to a given donor–acceptor distance, and S is the tunneling action, Eq. (10.17b), with limits of integration corresponding to classical turning points on the barrier through which the system tunnels. A fluctuating barrier originating from an environmental vibration, as invoked by Bruno and Bialek, can give rise to the observed temperature dependencies through its impact on the tunneling action, S. In order to understand the rate and KIE behavior that originate from a fluctuational barrier model, it is necessary to understand the physical origins of such a model. Similar in form to the development of the Bell correction, the rate of tunneling results from the multiplication of two probability distributions which depend on the available thermal energy. One probability distribution describes the deformability of the barrier, Eq. (10.18), while the other factor describes the probability of tunneling through the barrier at a given energy, Eq. (10.17a). Ptunnel z D20 expð2S=hÞ ð b pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi SWKB ¼ 2m½VðxÞ E dx
ð10:17aÞ ð10:17bÞ
a
b Pdeformation z exp kðl leq Þ 2 2
ð10:18Þ
The tunneling action is influenced by the energy difference between the barrier ðVðxÞÞ and the energy of the tunneling particle (E) and the distance traversed under the barrier by the tunneling particle (x). In the fluctuating barrier model, the rate is the result of a compromise between the amount of energy needed to reduce the distance between the hydrogen donor and acceptor and the rate enhancement due to deformation of the barrier (Fig. 10.4). In general, hydrogen tunneling is expected to be facilitated by attenuating the barrier in either a lateral or vertical direction (cf. Fig. 10.5). In their treatment, Bruno and Bialek made two simplifying assumptions: first, that there was no need for a vertical deformation and second,
10.4 Concepts and Theories Regarding Hydrogen Tunneling
Figure 10.4. Plot showing the peaked nature of the transfer rate as a function of distance in the fluctuational barrier model. The compromise between the probability of attaining a favorable configuration for
tunneling ðPDeformation Þ and the probability of tunneling for compressed barriers ðP Tunnel Þ is reached for a very small number of configurations centered at rS .
Figure 10.5. The protein environment can influence hydrogenic wavefunction overlap via asymmetrically coupled modes which bring hydrogenic wavefunctions into energetic coincidence [vertical perturbation, shown on left-hand side of figure]. These modes give rise to terms analogous to the Marcus theory of electron transfer [122]. Additionally,
symmetrically coupled modes (gating modes) spatially modulate the hydrogenic wavefunction overlap (horizontal perturbation, shown on right-hand side of figure). The separation of the hydrogenic wells when the gating coordinate is at its minimum energy is r0 .
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10 Nuclear Tunneling in the Condensed Phase: Hydrogen Transfer in Enzyme Reactions
that the energy required to alter the distance between the proton donor and acceptor could be modeled as a classical harmonic oscillator model. Ultimately, Bruno and Bialek achieved an equation for the KIE with only two adjustable parameters that could accommodate the data for the oxidation of benzylamine by BSAO collected by Grant and Klinman. However, given the modest temperature range and error inherent in the experimental studies, it was not possible to determine whether the observed numbers possessed the curvature in the Arrhenius KIE plot that was predicted from the model. Ultimately, the predominant value of the work of Bruno and Bialek was that it could explain, via a fluctuating barrier model, data that had previously been treated using a tunnel correction through a static barrier. It is notable that earlier, others had observed that ‘‘forcing vibrations’’ which modulate the hydrogen transfer barrier shape can substantially increase hydrogen transfer rates [71]. A more detailed ‘gating’ model has recently been presented by Kuznetsov and Ulstrup [33]. Once again, the physical picture underlying their model is that modulation of distance between hydrogen donor and acceptor can have enhancing effects on the quantum mechanical rate of H-transfer (Fig. 10.5). This phenomenon has been noted by many authors concerning hydrogen transfer in condensed phase systems [30, 31, 71–76]. In the gating model, a gating coordinate is represented by a classical harmonic oscillator whose temperature dependent motion modulates the distance between donor and acceptor, with the isotope dependence of gating arising from the well-known fact that tunneling is more distance dependent for heavier nuclei [77]. The gating model, described by Kuznetsov and Ulstrup [33] and adapted by Knapp et al. [43], is similar in concept to the model of Bruno and Bialek in two ways: (i) It is a full-tunneling model. (ii) The rate is expressed as the product of the probability of attaining a configuration and the probability of hydrogen transfer at that configuration (Eqs. (10.19)–(10.20)).
k tun ¼
X
Pv
v
X
kvw ¼
w
X v
X expðbEv Þ kvw w X expðbEv Þ
ð10:19aÞ
v
kvw ¼ kvw
oeff expðDGzvw =RTÞ 2p
DGzvw ¼ ðl þ DG þ Evib Þ 2 =4l qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðF:C: termÞ kvw ¼ jVel j 2 4p 3 =lRTh 2 oeff vw ð r0 2 ðF:C: termÞv; w ¼ ½eðmH oH r H Þ =2h eðEx =kb TÞ d X r1
k tun ¼
X v
Pv
X jVel j 2 w
2
ð10:19bÞ ð10:19cÞ ð10:19dÞ ð10:19eÞ
sffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! 4p 3 ðDG þ Evib þ lÞ 2 ðF:C: termÞv; w exp 4lRT lRTh 2 ð10:20Þ
10.4 Concepts and Theories Regarding Hydrogen Tunneling
Equation (10.19a) shows that the overall tunneling rate is computed for transfer from each donor hydrogen vibrational level (v) to each acceptor hydrogen vibrational level (w), where kvw is a level-specific rate and Pv is the Boltzmann population level v. This rate is thus summed over all acceptor vibrational levels and Boltzmann weighted for each donor vibrational level. This level-specific rate, Eq. (10.19b), is the product of an exponential term which reflects the probability of attaining a solvent or environmental configuration at which the donor and acceptor vibrational states are isoenergetic and a term, kvw , which reflects the probability of transmission of the hydrogen atom from donor to acceptor; oeff is the characteristic average frequency of the environmental modes that are treated classsically. Note that, kvw , Eq. (10.19d), contains the electronic coupling term jVel j 2 , under the assumption that the reaction is electronically diabatic, and the Franck–Condon term (originally developed in an ungated context by Ulstrup and Jortner) [78]. The expression in Eq. (10.19e) integrates the probability of the wavefunction overlap 2 ðemH oH r H =2hÞ, where mH , oH and rH are the mass, frequency, and distance, respectively, travelled by the tunneling particle over a range of distances that begin at r0 and move to the closest possible approach between H-donor and acceptor, r1 . For simplification, this expression is restricted to tunneling from an initial ground state to a final ground state vibrational level. Expressions for the F.C. terms that include excited reactant and product levels can be found in the appendix of ref. [43]. The fluctuating barrier is described by Ex ¼ 1=2mx ox 2 rx 2, where mx , ox and rx represent the mass, frequency and distance traversed by the heavy atoms that control the distance between the H-donor and acceptor (such that Dr ¼ r0 rx ). According to this model, the configuration at which tunneling occurs is comprised of three coordinate systems: (i) the environmental or solvent coordinate parametrized by the reaction driving force ðDG Þ and environmental reorganization ðlÞ; (ii) the gating coordinate parametrized by the gating frequency, ox and the reduced mass of the heavy atom motion, mx ; and (iii) the hydrogen transfer coordinate parametrized by the transfer distance ðDrÞ (Fig. 10.5). The enzyme, soybean lipoxygenase-1 (SLO), offers an excellent system in which to illustrate the power of Eq. (10.20) in reproducing experimental data. Several characteristics of SLO are impossible to interpret through a Bell-like tunneling correction. The KIE on kcat , D kcat ¼ 81 G 5, is nearly temperature independent, (Ea ðDÞ Ea ðHÞ ¼ 0:9 G 0:2 kcal mol1 ), and leads to an isotope effect on the Arrhenius pre-factor of AH =AD ¼ 18 G 5 [43]. In the case of several point mutants, D kcat is found to be almost unchanged while DEa becomes inflated and AH =AD is decreased to below unity. Using Eq. (10.20), the experimental observables, ½Ea ðDÞ Ea ðHÞ, AH =AD and KIE (30 C) could be reproduced for both WT-SLO and its three active site mutants. Details of this process are included in Knapp et al. [43]. These results show that a stiff gating frequency (ox G 400 cm1 , >kT ) leads to a D kcat that is nearly temperature independent, as seen for WT-SLO, while the increased temperature dependences seen for L546A/L754A and I553A can be reproduced by reducing the magnitude of the gating frequencies to 165 cm1 and 89 cm1 , respectively. To summarize, the gating coordinate modulates the height and width of the bar-
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10 Nuclear Tunneling in the Condensed Phase: Hydrogen Transfer in Enzyme Reactions
rier which separates the reactant and product hydrogenic wells. This type of motion has been referred to as symmetrical coupling to the reaction coordinate, which is rate-enhancing or rate-promoting and affects the system directly along the tunneling coordinate [30, 73, 74]. This occurs because of the extreme distance dependence of tunneling: as the donor and acceptor are forced together, the transfer probability increases extremely rapidly (Fig. 10.4). Antisymmetrically coupled motions modulate the relative energies of the reactant (hydrogen attached to donor) and product (hydrogen attached to acceptor), and arise because of the reorientation that must occur to yield the requisite equivalent energies for a tunneling event. Because of this requirement, antisymmetric modes which can be parametrized into the reorganization energy, l, have been referred to as ‘‘demoting modes’’ [73, 76]. As a result of the distinctions that have been made between antisymmetrically and symmetrically coupled environmental modes, Knapp et al. referred to the gating coordinate as an example of ‘‘active’’ dynamics; whereas, ‘‘passive’’ dynamics results from the collection of antisymmetrically coupled environmental coordinates [43]. In reality, both types of motions may arise from statistical sampling of a very large number of protein configurations. Hammes-Schiffer and coworkers have extended the work of Knapp et al. using a multi-state valence bond model, representing the solvent as a dielectric continuum and treating the transferred hydrogen quantum mechanically [80]. An important difference in their approach is that they introduce quantum effects into the oscillating environmental barrier and allow the shape of the tunneling barrier to change as a function of the proton donor–acceptor gating mode. Modeling the data for WT-SLO-1, they reach similar conclusions to Knapp et al. [43]. If they allow the initial donor–acceptor distance to ‘‘relax’’ to a longer value (that is close to the van der Waals radii), they find that the frequency of the gating mode must decrease to allow the donor and acceptor atoms to approach one another [80]. 10.4.4
Overview
As our understanding of the tunneling phenomenon evolves, enzyme-catalyzed reactions provide some of the most versatile systems for exploring the experimental parameters and theoretical models associated with different degrees and types of tunneling. In this laboratory we began by considering tunneling as a minor component of reaction rates and, furthermore, thought of reaction barriers as static. Systems like yeast alcohol dehydrogenase led to an understanding of the types of experimental parameters which were indicative of tunneling. Much of this behavior could be explained initially using the Bell correction and the assumption of a static barrier. However, as new data began to emerge, conventional theories were challenged. Beginning with bovine serum amine oxidase, the idea of a fluctuational barrier was introduced to reconcile the large primary KIE with a large temperature dependence in the KIE. Most recently, WT-SLO and its corresponding mutants have provided data that directly implicate a role for ‘‘active’’ dynamics in enzymatic processes. We are now at a critical juncture where our view of hydrogen transfer in the condensed phase has been transformed from a tunnel correction to
10.5 Experimental Systems
a semi-classical barrier to a fully quantum mechanical, dynamically enhanced reaction coordinate for hydrogen. This impacts our view not only of the origin of kinetic hydrogen isotope effects but also of all probes of hydrogen transfer that derive from the traditional approach of transition state theory.
10.5
Experimental Systems 10.5.1
Hydride Transfers Alcohol Dehydrogenases Alcohol dehydrogenase (ADH) oxidizes primary alcohols to their corresponding aldehydes via a hydride transfer to the cofactor nicotinamide adenine dinucleotide (NADþ ) (Scheme 10.1). The kinetic mechanism of ADH is well understood, the enzyme has a wide substrate tolerance and, furthermore, ADH has been cloned from several organisms. Cha and Klinman experimentally demonstrated hydrogen tunneling in ADH from yeast (YADH) as the first clear cut example of hydrogen tunneling in an enzyme [10], making ADH one of the bedrocks of enzymatic hydrogen tunneling research. The kinetic mechanism of ADH is shown in Scheme 10.1 (B) under conditions of saturating NADþ and the steady state. Saturating NADþ converts all free enzyme into the ENADþ form, which reversibly binds the alcohol to form the enzyme–substrate complex ENADþ RCH2 O where alcohol is indicated as the deprotonated alkoxide. The reaction can be driven irreversibly forward by chemically scavenging free aldehyde, making k3 irreversible. The degree of rate limitation by chemistry depends on the source of the enzyme and the substrate used. In general, kcat is less controlled by hydride transfer and frequently reflects the rate of cofactor dissociation from enzyme. By contrast, through the use of aromatic alcohols as substrates with YADH [10], and with mutagenesis of the ADH from horse liver (HLADH) [6], chemistry can be made to be rate limiting on kcat =K M . As defined above, the macroscopic rate constant kcat =KM reflects all steps from alcohol binding up to and including the first irreversible step, and is probed by competitive isotope effect measurements (cf. Eq. (10.4) in Section 10.2). As pointed out by Northrop, the observed isotope effect on kcat =KM can be formulated in terms of the intrinsic isotope effect on the chemical step ððkH =k T Þint Þ, and the commitment to catalysis CH [60]. CH accounts for the relative importance of chemical and nonchemical steps that contribute to kcat =K M when H is the isotope under study; a similar expression results for D/T isotope effects involving CD . Under all conditions, CD a CH =ðkH =kD Þint , making D/T KIEs less susceptible to kinetic complexity than H/T KIEs. 10.5.1.1
ðkcat =KM ÞH ðkH =k T Þint þ CH ¼ ðkcat =KM ÞT 1 þ CH
ð10:21Þ
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10 Nuclear Tunneling in the Condensed Phase: Hydrogen Transfer in Enzyme Reactions Table 10.2.
Kinetic isotope effect data for various ADH enzymes[a].
˚
˚
˚
˚
Enzyme
1 kD /kT
a -2 kH /kT
a -2 kD /kT
2 RS [b,c]
ht-ADH (60 C)[d] YADH WT (p-H)[e] YADH WT (p-Cl)[f ] HLADH L57F[h] ht-ADH (20 C)[d] HLADH F93W [h] HLADH V203A[g] HLADH L57V [h] HLADH V203L [g] HLADH WT [h] HLADH ESE[h] HLADH V203A:F93W[g] HLADH V203G[g] YADH WT (p-MeO)[f ]
1.626 G 0.03 1.73 G 0.02 1.59 G 0.03 1.827 G 0.01 1.64 G 0.013 1.858 G 0.01 1.88 G 0.02 1.902 G 0.021 1.89 G 0.01 1.894 G 0.013 1.872 G 0.006 1.91 G 0.02 1.89 G 0.01 1.94 G 0.06
1.23 G 0.015 1.35 G 0.015 1.34 G 0.01 1.318 G 0.007 1.257 G 0.013 1.333 G 0.004 1.316 G 0.006 1.332 G 0.003 1.38 G 0.005 1.335 G 0.003 1.332 G 0.004 1.325 G 0.004 1.358 G 0.007 1.34 G 0.04
1.0158 G 0.006 1.03 G 0.006 1.03 G 0.01 1.033 G 0.004 1.028 G 0.009 1.048 G 0.004 1.058 G 0.004 1.065 G 0.011 1.074 G 0.004 1.073 G 0.008 1.075 G 0.003 1.075 G 0.004 1.097 G 0.007 1.12 G 0.02
13.2 G 5.03 10.2 G 2.4 9.9 G 4.2 8.5 G 1 8.28 G 2.6 6.13 G 0.5 4.9 G 0.3 4.55 G 0.75 4.5 G 0.2 4.1 G 0.44 3.96 G 0.16 3.9 G 0.2 3.3 G 0.2 2.78 G 0.82
values G the standard error of the mean. b Exponent relating kD =kTðobsÞ and kH =kTðobsÞ : ½kD =kTðobsÞ RS ¼ kH =kTðobsÞ . c The error was calculated as follows: error ¼ exp½fq lnðkH =kT Þ=lnðkH =kT Þg 2 þ fq lnðkD =kT Þ=lnðkD =kT Þg 2 1=2 . d Ref. [24]. e Ref. [10]. f Ref. [83]. g Ref. [23]. h Ref. [6].
a Reported
Observed isotope effects will approach intrinsic values when the commitment to catalysis is small ðC ¼ 0Þ. Prior to tunneling analyses, earlier single-turnover experiments [81] and steady-state studies [82] had indicated conditions under which CH would be small or zero. Cha et al. provided the first experimental proof of hydrogen tunneling on an enzyme by reporting an elevated RS exponent for benzyl alcohol oxidation by yeast ADH (YADH) [10]. Isotope effects for benzyl alcohol oxidation were determined by the mixed-label tracer method, in which the primary and a-secondary positions of benzyl alcohol are either H or D, with stereochemically random, trace-level T incorporation. In this fashion, the observed ratios between the a-secondary ðkH =k T Þ1 H and ðkD =k T Þ1 D KIEs are susceptible to both Swain–Schaad and RGM deviations and, thus, are sensitive probes for tunneling (see Section 10.3.3.3). The observed a-secondary RS exponent, kH =k T ¼ ðkD =k T Þ 10:2 at 25 C, greatly exceeded the semi-classical value of 3.3, (Table 10.2). The results of Cha et al. [10] verified an earlier interpretation of elevated asecondary KIEs in dehydrogenase reactions as arising from a large tunnelcorrection to a semi-classical reaction coordinate [25]. Subsequent force-field calculations on the alcohol oxidation catalyzed by YADH were consistent with the view of a semi-classical reaction coordinate with a significant tunneling correction to the rates and KIEs [52]. As noted by Huskey, the only way to reproduce a large RS exponent is to include a significant tunnel correction [51]. Substituted benzyl alcohols were used to demonstrate that hydrogen tunneling in YADH does not require an isoenergetic reaction [82]. The internal thermody-
10.5 Experimental Systems
namics of hydrogen transfer were varied over a 1.9 kcal mol1 range by the use of three para-substituted benzyl alcohol substrates. For these substrates, kcat , as well as kcat =KM , is largely limited by hydride transfer; the finding that kcat at 25 C varied by less than a factor of two for these substrates indicated a very small change in the rate of hydride transfer [83]. Mixed-label isotope effects on kcat =KM revealed that the RS exponent for p-chlorobenzyl alcohol was very similar to that for benzyl alcohol, while the RS exponent for the reaction with p-methoxybenzyl alcohol was below the semi-classical value of 3.3 (Table 10.2). These observations led to the conclusion that tunneling is operative for both the p-chloro and the parent benzyl alcohol, despite the fact that the reaction driving force differs by 1.4 kcal mol1 , and that the p-methoxy substrate may be kinetically complex. Hydrogen tunneling in HLADH was examined using active site mutants [23, 84]. While wild-type HLADH is partly limited by binding of aromatic substrates, site-directed mutations in the substrate pocket altered the rate of substrate binding/product release leading to an ‘‘unmasking’’ of chemistry. Mutants produce a 100-fold variation in kcat =KM , which shows a positive correlation with the magnitude of the a-secondary RS exponent, Table 10.3. At that time, the data were interpreted to indicate that tunneling contributes ca. 100-fold to the catalytic efficiency of HLADH as the RS value increases from 3.3 to 9. A simple energetic argument implies that a reduction in the classical barrier height of 4.5 kcal mol1 would be required to produce an equivalent rate enhancement, making tunneling a significant contributor to catalysis. The X-ray crystal structures of two HLADH mutants revealed a correlation between the hydride transfer distance and the RS exponent [23]. The high-tunneling F93W mutant was compared with the low-tunneling V203A mutant, each of which was crystallized with the nonreactive substrate-analog trifluoroethanol. It was observed that the distance between the hydride donor and acceptor (C-1 of alcohol Rates and a-2 RS exponent for HLADH and mutants, pH 7.00, 25 C[a]. Table 10.3.
LADH mutant
kcat /KM (mMC1 sC1 )[b]
RS [c]
L57F F93W L57V ESE V203L V203A V203A:F93W V203G
8.6 4.7 3.5 3.3 1 0.2 0.13 0.071
8.5 G 1 6.13 G 0.5 4.55 G 0.75 3.96 G 0.16 4.5 G 0.2 4.9 G 0.3 3.9 G 0.2 3.3 G 0.2
[22, 23]. b Errors on kcat =KM are less than 10% of value. relating kD =k TðobsÞ and kH =k TðobsÞ : ½kD =k TðobsÞ RS ¼ kH =k TðobsÞ .
a Refs.
c Exponent
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10 Nuclear Tunneling in the Condensed Phase: Hydrogen Transfer in Enzyme Reactions
and C-4 of NADþ , respectively) was smaller in the F93W mutant (3.2 A˚) than in the V203A mutant (4.0 A˚) [23]. This implied that the barrier width will play a role in hydride tunneling and, therefore, must be considered in understanding the factors that impact catalysis. Hydrogen tunneling was demonstrated over a wide temperature range for the alcohol oxidation catalyzed by a thermophilic ADH (ht-ADH) from Bacillus stearothermophilus [24]. For this ADH, both kcat and kcat =KM appear to be primarily controlled by hydride transfer over a large temperature range. Mixed label substrates were used to measure primary and a-secondary KIEs between 5 C and 65 C. As with YADH and HLADH, the a-secondary KIEs were shown to have RS exponents elevated from the semi-classical value of 3.3 (cf. Table 10.2). The RS exponent varied from ca. 5 to almost 20 as the temperature was increased from 5 C to 65 C, suggesting that the extent of tunneling increased as the temperature increased. This contrasts with a simple tunnel correction, which would predict that the extent of tunneling should decrease at elevated temperature. Thermophilic proteins are thought to undergo a thermally driven phase transition, from a flexible phase near physiological temperatures, to a more rigid phase at reduced temperature. ht-ADH was shown to exhibit a change in catalytic behavior at 30 C: above this temperature, the activation energy ðEa Þ for kcat was moderate (Ea ¼ 14:0 kcal mol1 ), while below this temperature Ea increased by nearly a factor of two (Ea ¼ 23:0 kcal mol1 ) [24]. Support for a mechanistic phase transition that is due to altered protein flexibility was obtained from FT-IR H/D amide exchange experiments, which showed a greatly reduced global exchange rate below the 30 C transition [85]. In more recent studies [86] mass spectrometry was used to quantitate H/D exchange, allowing a spatial resolution of the structural changes that accompany the increase in tunneling above 3 C. Out of a total of 21 peptides analyzed, 5 showed changes in H/D exchange at the same temperature as the change observed in Ea cited above. All 5 peptides map to the substrate binding domain and 4 out of 5 have loop regions that are positioned to interact with substrate directly. These studies implicate a direct link between changes in local protein flexibility/dynamics and changes in H-transfer efficiency [86]. The primary KIEs on kcat also indicated a transition at 30 C, below which the primary kH =kD ratio is very temperature dependent, extrapolating to AH =AD f 1 [24]. This inverse Arrhenius prefactor ratio is predicted within the Bell tunnel correction for a moderate extent of tunneling, and is consistent with an elevated a-secondary RS exponent. Above 30 C, the primary kH =kD ratio is nearly independent of temperature, resulting in an isotope effect on the prefactor of AH =AD ¼ 2 [24]. A tunnel correction would also predict such an elevated Arrhenius prefactors ratio when both H and D react almost exclusively by tunneling; however this condition requires a very small activation energy for kcat, while a value of Ea ¼ 14 kcal mol1 is observed [24]. The data from ht-ADH raise provocative questions regarding hydride transfer processes. In particular, it would appear that a model that goes beyond a simple tunnel correction is needed to explain the composite data for ht-ADH. One possible explanation is that, at elevated temperatures, hydride transfer is a full tunnel-
10.5 Experimental Systems
Figure 10.6. Graphical representation of the exponential relationship between lnðkH =k T Þ and lnðkD =k T Þ for a-secondary KIEs in alcohol dehydrogenases (YADH, LADH and ht-ADH), open circles. The exponential Swain–Schaad relationship is shown as a line of slope ¼ 3.3.
ing process that is driven by thermal fluctuations of the protein; the latter would give rise to the observed Ea . As the temperature is reduced below 30 C and the protein stiffens, a new process dominates with the properties of a tunneling correction, leading to the much larger observed Ea value. Given the change in AH =AD from >1 (above 30 C) to <1 (below 30 C), remniscent of the trends in AH =AD on mutagenesis of soybean lipoxygenase [43], an alternate explanation is full tunneling at all temperatures with varying contributions of the gating mode above and below 30 C (Figure 10.5). The a-secondary KIE data for all of the ADHs from this laboratory have been summarized (Table 10.2), encompassing ADH from three sources, two alternate substrates with YADH, and two distinct temperature regimes for ht-ADH [6, 10, 23, 24]. A wide range of RS values is represented, suggesting, at first glance, that the extent of tunneling varies appreciably over this series. A graphical representation of the exponential relationship between lnðkH =k T Þ and lnðkD =k T Þ for the a-secondary KIEs is shown in Fig. 10.6. The semi-classical model predicts that RS is equal to 3.3, indicated as a solid line of slope 3.3. Data points above this line indicate an elevated RS exponent, which is a signature of tunneling. Most of the ADH data clearly deviate from the semi-classical prediction. Inspection of Table 10.2 reveals that the magnitude of the a-secondary kD =k T decreases as the RS exponent increases. This phenomenon, illustrated in Fig. 10.7, appears paradoxical in that more extensive tunneling for H than D might be expected to elevate the a-secondary kH =k T while leaving the a-secondary kD =k T relatively unchanged. When viewing the ADH reactions through a tunnel-correction model, the kD =k T measurements are expected to be a much closer monitor of the semi-classical hydride-transfer coordinate [50]. Thus, it was possible that the small a-secondary kD =k T KIEs near the top of Table 10.2 simply reflected an early transition-state structure. This interpretation would require that the slowest LADH mutants (e.g. V203G) have the latest transition states, while the faster LADH mutants (e.g.
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10 Nuclear Tunneling in the Condensed Phase: Hydrogen Transfer in Enzyme Reactions
Figure 10.7. Comparison of the a-secondary kD =k T values and RS for benzyl alcohol oxidation by alcohol dehydrogenases (YADH, LADH and ht-ADH).
L57F) have the earliest transition states. It is notable that the equilibrium limit for the a-secondary kD =k T ratio is 1:09 G 0:02 [10], approximately what is observed for those entries near the bottom of Table 10.2. While this would be consistent with the Hammond postulate [87] which predicts that earlier transition-state structures should correlate with faster reaction rates [88], a concomitant change in the primary kD =k T would also be predicted across this series, assuming relatively little tunneling for the D-transfer. In particular, the primary KIE should be maximal for a symmetric transition-state structure, and decrease for either an early or late structure. This trend is not observed; rather, the primary KIE shows a general increase toward the bottom of Table 10.2. An alternate view would be that the primary and secondary KIEs simply reflect the properties of tunneling along the reaction coordinate, with tunneling occuring far below the semi-classical transition state, a situation often referred to as large curvature tunneling [89, 90]. We note that a computational study of the ADH reaction could reproduce the large RS exponents with a Bell tunneling correction, but could not reproduce the small a-secondary kD =k T ratios unless many vibrational modes were coupled into the hydride transfer coordinate [52]. This calculation showed that the a-secondary kD =k T KIEs indicated the extent of tunneling, rather than the structure of the transition state under conditions of pronounced coupled motion. Furthermore, coupled motion can increase or decrease the a-secondary kD =k T KIEs [52], making a simple explanation for the trends in Table 10.2 elusive. Krishtalik [77] has, in fact, proposed that the RS exponents may decrease under the conditions of a full tunneling model. Clearly, more work is needed before we have a complete theoretical framework for the deviant secondary isotope effects seen in hydride transfer reactions (see note added in proof ). Glucose Oxidase Glucose oxidase (GO) catalyzes the oxidation of sugars to their corresponding lactone products, coupled to the reduction of O2 to H2 O2 , Scheme 10.3. The reaction 10.5.1.2
10.5 Experimental Systems
Scheme 10.3
occurs via a ping-pong mechanism that leads to a cycling of the bound flavin between a reduced and oxidized form, Flred and Flox , respectively. Isotopes have been used to probe both the reductive and oxidative half reactions, using hydrogen isotopes in the former [91, 92] and oxygen isotope effects in the latter case [93–96]. Recent studies of the reductive half reaction using enzyme that has been substituted with flavins of modified redox potentials indicate a structure reactivity correlation in support of hydrogen movement from substrate to flavin as a hydride ion [97]. Hydrogen isotope measurements have been carried out primarily for the reaction of the 2 0 -deoxy-form of sugar rather than glucose itself, as hydride transfer is largely rate determining for 2 0 -deoxyglucose. Very interestingly, expression of the GO gene in a yeast host gives rise to proteins of varying degrees of glycosylation that yield final molecular masses for the protein rising from 136 kDa (deglycosylated enzyme) to 320 kDa (extensively glycosylated enzyme). Initial studies using the 136, 155 and 205 kDa forms of GO at pH 9 showed similar rates and isotope effects, but different temperature dependences for the isotope effects [91]. It is important to point out that, unlike other enzyme systems where very significant deviations from classical behavior have been observed, the size of the KIEs and their temperature dependences are all seen to hover around the classical values in GO. In a very careful study, Seymour examined the impact of surface modification on the parameters describing H-transfer in GO. The impact of the surface modifier was assessed, by comparing H-transfer in proteins modified with polyethylene glycol to those modified by glycosylation [92]. Although both primary H/T and D/T isotope effects were measured as a function of temperature, the focus of the interpretation was on primary D/T isotope effects, since the smaller commitment for D- than H-transfer leads to a more complete contribution of the chemical step to the measured parameters (see e.g. Section 10.21). The results obtained from this study [92], as well as the earlier work [91], indicate a striking trend in which the value of AD =AT moves from near unity to below unity as the surface of the protein is modified (either by glycosylation or addition of polyethylene glycol). A similar type of pattern has been seen in other enzyme systems, such as the thermophilic ADH [24] (Section 10.5.1.1) and soybean lipoxygenase (SLO) [43] (see Section 10.5.3.1 below) where modification of reaction conditions away from either optimal temperature (ht-ADH) or optimal protein packing (via
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10 Nuclear Tunneling in the Condensed Phase: Hydrogen Transfer in Enzyme Reactions Table 10.4.
Enzymatic examples where perturbations lead to a decrease in A1 =A2 .
Enzyme
A1 /A2
Glucose Oxidase WT: surface modified:
@1 <1
Thermophilic Alcohol Dehydrogenase above 30 C: below 30 C:
>1 <1
Soybean Lipoxygenase WT: mutants:
g1 @1 or <1
Ref.
92
24
43
site specific mutagenesis in SLO) causes the value of AH =AD to fall from greater than unity to less than unity (Table 10.4). In the context of a full tunneling model (cf. Eq. (10.24)), values for A1 =A2 less than one reflect a greater need for distance sampling (gating ) to achieve the optimal distances between reactant and product that support efficient tunneling. One curious feature of the data for GO is that surface modification does not, in contrast to an earlier report [91], give rise to greater values for the experimental enthalpies of activation [98]. In the full tunneling model with gating, Eq. (10.20), and in the absence of compensating changes, the value of DH z is expected to increase as gating plays a greater role in achieving the optimal configuration(s) for catalysis. As an alternative to a full tunneling model, the hydride transfer catalyzed by GO has also been considered in the context of a tunnelingcorrection model. In this case, the increased stiffness of protein resulting from surface modification could reduce the distance sampling between reactants, resulting in a higher overall barrier and increased tunneling relative to WT-GO. In this instance the inverse value for AD =AT would reflect the greater ease for the lighter isotope to move under the reaction barrier. Within this model, the very small changes in DH z among the enzyme forms could reflect the interplay between increases in barrier height, which would increase DH z , and increased tunneling which would decrease DH z . The above discussion of GO illustrates the complexity of this H-transfer systems and the ambiguity that can arise in trying to distinguish between systems in which a tunneling correction [15] is appropriate and systems in which a full tunneling model [33] must be invoked. As will be discussed in Section 5.3.1, there are some enzyme systems where a tunneling correction will simply not apply, providing a contextual understanding for tunneling models that can then be applied to systems with less dramatic deviations from classical behavior.
10.5 Experimental Systems
10.5.2
Amine Oxidases Bovine Serum Amine Oxidase Bovine serum amine oxidase (BSAO) is a copper-containing amine oxidase which utilizes a covalently bound 2,4,5-trihydroxyphenylalanine quinone (TPQ) cofactor in the two-electron oxidation of a broad spectrum of primary amines [99]. The oxidation is thought to proceed via the formation of an iminium complex between the oxidized form of the cofactor and the primary amine (1 in Scheme 10.4). The substrate imine undergoes deprotonation to form product imine, which, after hydrolysis, releases aldehyde product and reduced cofactor [100]. Proton transfer is either partially or largely rate-limiting for the oxidation of benzylamines, as evidenced by a large deuterium isotope effect at the methylene adjacent to the amino group [36, 101, 102]. 10.5.2.1
Scheme 10.4
Competitive kinetic isotope effects (H/T and D/T) for the BSAO-catalyzed oxidation of benzylamine were determined using remote labeling methods. The values for primary H/T isotope effects on kcat =KM average 35:2 G 0:8 for 6 separate experiments composed of approximately 8 time points each. Correspondingly, the primary D/T isotope effects average to 3:07 G 0:07 [36]. These values exceed semiclassical expectations of 27 and 2.7 for H/T and D/T primary kinetic isotope effects on elementary reaction steps, respectively [15], over the temperature range 0–45 C. Arrhenius parameters also exhibit signatures of tunneling from both H/T and
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10 Nuclear Tunneling in the Condensed Phase: Hydrogen Transfer in Enzyme Reactions
D/T isotope effects. The predicted lower limits for Arrhenius pre-factors ðAL =AT Þ are 0.6 and 0.9 for L ¼ H and L ¼ D, respectively [19], in contrast to the measured values for this system of 0.12 and 0.51. The temperature dependence of the isotope effects far exceeds that anticipated by zero-point energy differences in the CaH stretch: for the complete disappearance of the CaH stretching zero-point energy with no compensation from transverse bending modes at the transition state, one would expect DEa values of 2.0 kcal mol1 for the H/T isotope effect and 0.6 kcal mol1 for D/T isotope effects in contrast to observed values of 3.4 and 1.1 kcal mol1 , respectively. What was most striking in the BSAO system was the evidence for deuterium as well as protium tunneling. First, the value of the D/T isotope effect on kcat =KM at 25 C is greater than the maximum expected value arising from zero-point energy differences. Second, the isotope effect on the Arrhenius pre-factor is well below that which is expected from semi-classical predictions. Finally, the differences in enthalpy of activation for D vs. T in the primary position well exceed differences predicted from zero point energies. While it is conceivable that one could attribute some of the differences in the Arrhenius parameters to kinetic complexity, it is unlikely that kinetic complexity would be present to any significant degree with either deuterium or tritium in the primary position given the significant values of the H/D and H/T primary KIEs. The enthalpy of activation for the oxidation of benzylamine has been computed from the temperature dependence for the BSAO-catalyzed consumption of 1,1-d2 benzylamine and the difference in the enthalpy of activation, Ea ðDÞ Ea ðHÞ. The value obtained is 13 kcal mol1 , close to the value of 14 kcal mol1 obtained directly from the temperature dependence for the corresponding oxidation of benzylamine [102]. This close correspondence indicates that little of the observed temperature dependence in the H/T isotope effect can be due to the contribution of other partially rate-limiting steps. It should be emphasized that the invocation of kinetic complexity would mean that the absolute magnitude of the intrinsic KIE on the isotopically-sensitive step would be larger than the observed values for the primary competitive kinetic isotope effects, which would further implicate a tunneling mechanism in the BSAO system. Although it seems evident that tunneling is operative in the proton abstraction step of BSAO-catalyzed oxidations, results obtained regarding competitive secondary isotope effects were initially puzzling in the light of those obtained for the ADH-catalyzed oxidation of alcohols, where secondary kinetic isotope effects have been one of the primary determinants of tunneling behavior. As noted in Section 5.1.1, RS exponents of 10.2 were measured for the a-secondary isotope effect for YADH. In the BSAO-catalyzed oxidation of benzylamines, the Swain–Schaad exponents for both primary and secondary KIEs are near the anticipated 3.26 for relating H/T and D/T isotope effects. Over the temperature range explored, the Swain– Schaad exponent was perhaps slightly reduced from the semi-classical value for the primary position and slightly elevated for the secondary position. These findings were taken to mean that there is much less coupling between the motion of the secondary position and the transferred hydrogen in BSAO than in ADH [36].
10.5 Experimental Systems
From a historical perspective, the BSAO system has played an important role, inspiring a new way of approaching the concept of hydrogen tunneling in enzymes. Bruno and Bialek determined that ground-state tunneling would give rise to H/T isotope effects that far exceed the measured values [32], and introduced a model in which the enzyme environment modulates the barrier for proton transfer. Using a rectangular barrier whose width is altered by thermally-induced protein motions, Bruno and Bialek were able to fit both D/T and H/T kinetic isotope effect data with the same pair of adjustable parameters, changing only the mass of the tunneling particle (see Section 10.4). While their choice of barrier shape was not physically realistic, it illustrated how protein-mediated motions can alter the contribution of tunneling to the reactive flux in enzyme-catalyzed hydrogen/ hydride/proton transfers. Monoamine Oxidase B Monoamine oxidase B (MAO-B) is a membrane-bound flavoprotein that catalyzes the two-electron oxidation of primary, secondary, and tertiary amines with a preference for primary amines. Extensive studies have addressed the issue of whether the hydrogen transfer occurs via a step-wise mechanism (i.e. electron transfer followed by Hþ ) or a concerted process (H) (e.g. Refs. 103, 104). Regardless of the precise nature of the mechanism, the amine must lose an a-hydrogen atom in the course of its oxidation. Jonsson et al. have determined primary and secondary H/T and D/T kinetic isotope effects for the MAO-B catalyzed oxidation of p-methyoxybenzylamine [65]. Initially, these isotope effect studies were performed at pH 7.5; however, it was found that the observed competitive H/T KIE was larger at 25.0 C than at 2.0 C. Because the KIE was substantially larger at the higher temperature, it could be ascertained that kinetic complexity was contributing markedly to the kinetic isotope effects. Kinetic complexity was corroborated by the value of the Swain–Schaad exponents for the primary and secondary KIEs. Primary KIEs rarely exhibit abnormal Swain–Schaad exponents due to tunneling, such that a value far below 3.26 relating H/T to D/T isotope effects is indicative of kinetic complexity. The primary Swain–Schaad exponent at pH 7.5 and 2.0 C is 2:57 G 0:05, and the exponent for the secondary KIE under the same conditions is 1:20 G 0:15. At pH 6.1, however, Swain–Schaad exponents for the primary KIEs at all temperatures studied (10.0–43.0 C) fell very near to the semi-classical expectation of 3.26. The exponents for the secondary KIEs were still somewhat low, however, averaging 2:36 G 0:13 over the temperature range studied. It is noteworthy that the Swain–Schaad exponents are temperature independent for both primary and secondary isotope effects at pH 6.1. Two scenarios can be considered. The first is that there is a significant commitment to catalysis which is obscuring the full value of the isotope effect on kcat =KM . It is anticipated that, because the primary and secondary exponents are temperature independent, this commitment would be temperature independent. Jonsson et al. have used Northrop’s expression [60] for correcting observed isotope effects based on the assumption of a temperature-independent commitment (Eq. (10.22)). A commitment of 0.6 for the oxidation of benzylamine brings the secondary exponent to about 3.3, 10.5.2.2
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10 Nuclear Tunneling in the Condensed Phase: Hydrogen Transfer in Enzyme Reactions
the semi-classical prediction. The commitment for deuterium abstraction is related to the commitment for protium abstraction by the intrinsic deuterium isotope effect, which is about 10 for MAO-B. Using these values, the Arrhenius parameters do not change appreciably from those computed from fits of observed isotope effects. The isotope effect on the Arrhenius pre-factors are still indicative of tunneling with the inclusion of this temperature-independent commitment (C). ðkH =k T Þintrinsic ¼ ½ðkH =k T Þobserved ð1 þ CÞ C
ð10:22Þ
The second scenario which might give rise to the observed temperature dependences is a temperature-dependent commitment factor which is exactly compensated by the portion of the reaction which is achieved via tunneling. While it seems highly unlikely that such a scenario could fortuitously exist, the motivation for such a consideration is that the degree to which tunneling participates in reactive flux inversely correlates with temperature. This phenomenon has been clearly demonstrated in the crystalline solid phase and in solid rare gas matrices [105]. Thus, it seems conceivable that, while a larger degree of tunneling at low temperatures could raise the Swain–Schaad exponent, a larger commitment at low temperatures could reduce the exponent, leading to the observed temperature invariant values. 10.5.3
Hydrogen Atom (H) Transfers Soybean Lipoxygense-1 Some of the most striking evidence for hydrogen tunneling under ambient conditions comes from the kinetic studies of soybean lipoxygenase-1 (SLO) [38, 43, 79, 106]. The D kcat b 80 for WT-SLO at room temperature [38] makes typical views of hydrogen transfer, including tunneling corrections, of dubious relevance. SLO catalyzes the production of fatty acid hydroperoxides at 1,4-pentadienyl positions, and the product 13-ðSÞ-HPOD is formed from the physiological substrate linoleic acid (LA) (Scheme 10.5). SLO is a substrate-activating dioxygenase, activating LA by homolytic CaH cleavage, and is the simplest example of metalloenzyme-catalyzed H abstraction, in that a stable form of the cofactor rather than a metastable species cleaves the CaH bond. Studies of SLO are useful in illuminating apolar H transfers, which may have implications for a wide variety of metalloenzyme CaH cleavage reactions. SLO follows an ordered, bi-uni mechanism, in which linoleic acid (LA) binds and reacts prior to O2 encounter [8], which has permitted a variety of steady-state and single-turnover studies into chemistry on SLO. The kinetic mechanism can be divided into a reductive half-reaction, described by the rate constant kcat =KM (LA), and an oxidative half-reaction described by the rate constant kcat =K M (O2 ). On the reductive half-reaction, SLO binds LA ðk1 Þ, then the Fe 3þ aOH cofactor abstracts the pro-S hydrogen from C-11 of LA ðk2 Þ, forming a substrate-derived radical inter10.5.3.1
10.5 Experimental Systems
Scheme 10.5
mediate and Fe 2þ aOH2 (Scheme 10.5) [8]. H abstraction is kinetically irreversible [8], making this the final step that appears on kcat =KM (LA) and kcat =KM (LA) partially rate limited by both substrate binding and chemistry. Molecular oxygen rapidly reacts with this radical in the oxidative half-reaction, eventually forming 13-(S)HPOD and regenerating free enzyme at a rate that appears to be limited by local structural features of the protein [107, 108]. Much of the work substantiating hydrogen tunneling in this reaction has relied on steady-state kinetics, in which D kcat is determined. The magnitude of the KIE was corroborated by viscosity effects, solvent isotope effects, and single-turnover studies [7–9]. One notable study confirmed the magnitude of the KIE as ca. 80 at room temperature, while excluding magnetic effects as the origin of this KIE [38b]. Potential complications in assigning D kcat to a single chemical step, for example due to a branched reaction mechanism, were also ruled out [7]. All the data indicate that the chemical step (H abstraction) is fully rate limiting on kcat , in WTSLO, and that the steady-state KIE ð D kcat Þ represents an intrinsic value. The bulk of the KIE studies with SLO have used substrate that is dideuterated at the C-11 position. In order to differentiate the impact of deuteration on the cleaved [11,S] vs. the noncleaved position [11,R], stereospecifically deuterated [11,S- 2 H] – linoleic acid was synthesized. Analysis of enzyme kinetics using either WT- or mutant forms of the enzyme initially yielded anomalously large secondary KIEs. This was subsequently shown, by mass spectrometric analysis of the enzymatic product, to be due to a loss of stereochemistry at C-11, arising, in fact, from the enormous KIE at the primary position. Through a combination of kinetic and mass spectrometric analyses, it could be shown that the bulk of the observed KIE with dideuterated substrate arises from the primary position, D ½k intrinsic ð1 Þ ¼ 75 and D ½k intrinsic ð2 Þ ¼ 1:1 [79].
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10 Nuclear Tunneling in the Condensed Phase: Hydrogen Transfer in Enzyme Reactions
Though the large KIE is striking, several other enzymatic and nonenzymatic reactions exhibit KIEs of greater than 50 at or near room temperature. Methane monooxygenase exhibits an H/D KIE of between 50 and 100 in the cleavage of the CaH bonds of methane [39] and acetonitrile [109]. A number of polypyridyl ruthenium-oxo compounds of the general formula [LRu 4þ bO] 2þ exhibit large KIEs in H and Hþ transfer reactions [110–113]. An example of a KIE of ca. 50 has been reported for H transfer catalyzed by a Cu 2þ -phenoxyl radical complex [114]. The variable-temperature kinetic data for SLO are unusual, in that the temperature dependence of the rate is very small (Ea ¼ 2:1 kcal mol1 ) [43]. An Eyring treatment of the variable temperature kinetic data for WT-SLO suggests that the barrier to reaction is mainly entropic, as the enthalpic barrier (DH z ¼ 1:5 kcal mol1 ) is much less than the entropic barrier (TDS z ¼ 12:8 kcal mol1 ). Such a treatment becomes meaningless when the KIEs are considered, as the isotope effect is predominantly on the entropic term rather than the enthalpic term. In particular, the bond-stretch theory of KIEs predicts that the KIE results entirely from the enthalpic term [16]. It is clear that the bond-stretch model fails to account for the rate and KIE data. Furthermore, a tunnel correction cannot simultaneously reproduce the magnitude and temperature dependence of this KIE, as such corrections result exclusively in inverse Arrhenius prefactors ðAH =AD f 1Þ. As discussed in Section 10.4, WT-SLO exhibits a large Arrhenius prefactor KIE ðAH =AD ¼ 18Þ, while mutations near the active site reduce the temperature-dependence of the KIE in a regular manner, leading to an inverse Arrhenius prefactor KIE (AH =AD ¼ 0:12 for I553A). That the KIE in WT-SLO and its mutants remains large (kH =kD > 80 at 30 C) forces the use of a model in which hydrogen transfer always occurs by tunneling [115]. The variable temperature-KIE behavior observed as a function of mutational position indicates that the active site of SLO plays an important role in optimal positioning of the substrate for H tunneling. Altering three of the bulky hydrophobic residues at or near the active site residues (Leu 546 , Leu 754 , Ile 553 ) makes this positioning sub-optimal, and introduces the requirement for a fluctuating barrier in effecting catalysis. The KIE arises from the differential tunneling probabilities of H and D at the reactive configuration, while the environmental vibration (gating) modulates the width of the tunneling barrier, and leads to the various temperature dependent KIEs. The net rate is always a compromise between an increased tunneling probability at short transfer distances and the energetic cost of decreasing the tunneling barrier (Fig. 10.4). These features directly link enzyme fluctuations to the hydrogen transfer reaction coordinate, making a quantum view of H-transfer necessarily a dynamic view of catalysis. Explicit tunneling effects are required to accommodate the kinetics of SLO, and may be equally important in many other hydrogen atom transfer reactions. Many H transfer reactions are characterized by very large inherent chemical barriers, such that movement through, rather than over, the barrier may dominate the reaction pathway as the lowest energy path for conversion of reactants to products.
10.5 Experimental Systems
10.5.3.2 Peptidylglycine a-Hydroxylating Monooxygenase (PHM) and Dopamine b-Monooxygenase (DbM) DbM and PHM belong to a small class of copper-containing oxygenases that catalyze the formation of norepinephrine and the precursor to C-terminally amidated peptide hormones, respectively (Scheme 10.6A and B) [116]. PHM is often found covalently linked to a second protein domain that is responsible for the hydrolytic breakdown of the immediate hydroxylated intermediate (Scheme 10.6B) to the final peptide product and glyoxylate [117]. Although DbM is significantly larger than PHM, the two proteins share a core of conserved residues that contributes the ligands to the two copper centers per polypeptide chain.
Scheme 10.6
The nature of H-transfer in these reactions is intrinsically linked to the identity of the oxygen species capable of CaH activation. The mechanism of PHM and DbM has been subjected to extensive investigations, including an X-ray structure for PHM that shows the two coppers per subunit located at a distance of ca. 10 A˚ across a solvent interface [118]. This structure has raised questions regarding how electrons are transferred between the metal centers and how the chemically difficult O2 and CaH activation reactions can occur at a solvent interface. Recently, Evans et al. have put forth a mechanism that is able to accommodate the very large array of experimental data for both PHM and DbM [119]. As described in Ref. [119], the O2 and CaH activation chemistry occur at a single copper site (CuB ), with the donation of the second electron required to complete the reaction sequence (from CuA ) occurring subsequent to H transfer from substrate to activated O2 . Although the reactive oxygen species is written as Cu(ii)a(O2 ), the failure to observe any uncoupling of O2 from CaH activation suggests that the amount of this species accumulates to only a very small extent at the enzyme active site [119]. As discussed below, the mechanism of hydrogen transfer displays the properties indicative of H-tunneling, implicating a role for environmental reorganization terms, both to generate the reactive metal superoxo-
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10 Nuclear Tunneling in the Condensed Phase: Hydrogen Transfer in Enzyme Reactions
species and to facilitate a quantum mechanical hydrogen atom transfer from donor to acceptor atoms. Early experiments with DbM, that provided intrinsic primary and secondary KIEs for the CaH cleavage step, showed a puzzling discrepancy in the context of the bond-stretch model for hydrogen transfer. This discrepancy was that the primary KIE implied a symmetrical transition state while the secondary KIE indicated that the transition state was very product like [120]. The failure of multiple probes of transition state structure to converge on a consistent pattern of behavior is one of the criteria available for the diagnosis of tunneling (cf. Section 10.3.3.2). In a more recent set of experiments, Francisco et al. turned to the magnitude of the intrinsic KIE in the PHM reaction as a function of temperature [13]. Observing that hydrogen transfer was only partially rate limiting for kcat =K M, substrate samples were prepared that allowed precise competitive measurement of both H/D and H/T isotope effects between 5 and 55 C. Subsequent analysis of the breakdown from the Swain–Schaad relationship of the experimental KIEs, according to the methods of Northrop [80], led to the magnitude of the intrinsic primary KIE at each temperature. Although breakdowns from the Swain–Schaad relationship can also be seen under conditions of tunneling, these breakdowns seem restricted to secondary KIEs and, in particular, when comparisons are made between D/T and H/T KIEs (cf. Section 10.3.3.3). The plot of the intrinsic KIEs for PHM as a function of temperature yielded isotopic Arrhenius parameters of AH =AD ¼ 5:9 (3.2) and Ea ðDÞ Ea ðHÞ ¼ 0:37 (0.33) kcal mol1 . These data are reminiscent of the data for SLO (Section 5.3.1), with the exception of the smaller magnitude of the KIEs in the case of PHM. Using the expression for the KIE derived by Kuznetsov and Ulstrup and modified by Knapp et al. [43], successful modeling of the temperature dependent KIE data for PHM data has led to a value for the gating term that controls the distance between donor and acceptor atoms that is significantly smaller than that for SLO (ox ¼ 400 cm1 for SLO versus 45 cm1 for PHM) [119]. These differences must reflect the very large differences in active site structures, with the SLO active site being deeply buried while the PHM active site is solvent exposed. The results suggest that the SLO site is stiffer and more optimized for H-tunneling, while that of PHM requires more extensive environmental reorganization to achieve the geometries that permit optimal wavefunction overlap between donor and acceptor. This type of analysis opens a new ‘‘window’’ into the properties of enzyme active sites and the nature of the differences from one system to another. One important aspect of the work on PHM is the demonstration of relatively small KIEs in the context of environmentally modulated H-tunneling reactions.
10.6
Concluding Comments
The last 15 years has seen a transformation in our understanding of the nature of H-transfer in the condensed phase. Much of this change is due to studies of en-
References
zyme catalyzed reactions, though the literature of ‘‘anomalous’’ KIEs in small molecule reactions has received increasing consideration as a result of the findings in enzymatic systems. There is no question that the available data force us to move beyond the simple bond-stretch picture for hydrogen transfer, with the best available explanation for the repeated deviations from semi-classical behavior being the quantum mechanical properties of hydrogen. Theoretical advances have appeared hand in hand with experimental findings, beginning with the treatises by Bell that discuss deviations from semi-classical behavior in the context of a tunneling correction. While this approximation was sufficient for many years, it is no longer able to explain the large body of data that has emerged for numerous enzyme systems. A more satisfactory picture has begun to emerge in which the H particle is treated fully quantum mechanically, with the barriers to reaction and the accompanying energies of activation reflecting the environmental reorganizations that must accompany hydrogen tunneling. This theoretical context is much closer to Marcus theory for electron transfer, with the additional caveat of the importance of distance sampling (gating) between hydrogen donor and acceptor atoms. In the last several years, with the growing recognition that both small molecule and enzyme hydrogen transfer reactions involve tunneling, investigators have begun to examine the degree to which enzymes may enhance tunneling in relation to the solution reactions. This issue has been discussed in a recent review [121], which points out the different kinds of experimental approaches for analysis of the extent of rate acceleration provided by tunneling in enzymes, together with the likelihood that the degree to which an enzyme uses tunneling for its rate acceleration will depend on the nature of the reaction undergoing catalysis. Note added in proof: A model for the RS deviations in the ADH reactions (Table 10.2) has been recently presented: Klinman, J. P., Phil. Trans. R. Soc. B 2006, 361, 1323–1331; Nagel, Z., Klinman, J. P., Chem. Rev. 2006, 106, 3095–3118.
References 1 Segel, I. H., Enzyme Kinetics, Wiley
2
3 4
5
Classics Edition, 1993 edn. John Wiley & Sons, New York, 1975. Cleland, W. W., Steady State Kinetics, in The Enzymes, 3rd edn., Boyer, P. (Ed.), Academic Press, New York, 1970, Vol. 2, pp. 1–65. Villa, J., Warshel, A., J. Phys. Chem. B 2001, 105, 7887–7907. Fersht, A., Enzyme Structure and Mechanism, 2nd edn., W. H. Freeman, New York, 1985. Some selected references: (a) Su, Q., Klinman, J. P., in 1998 Steenbock Symposium on Enzyme Mechanism, pp. 20–31; (b) Blacklow, S. C., Raines,
6
7 8 9
10
R. T., Lim, W. A., Zamore, P. D., Knowles, J. R., Biochemistry 1988, 27, 1158–1167; (c) Hardy, L. W., Kirsch, J. F., Biochemistry 1984, 23, 1275–1282. Bahnson, B. J., Park, D. H., Kim, K., Plapp, B. V., Klinman, J. P., Biochemistry 1993, 32, 5503–5507. Glickman, M. H., Klinman, J. P., Biochemistry 1995, 34, 14077–14092. Glickman, M. H., Klinman, J. P. Biochemistry 1996, 35, 12882–12892. Jonsson, T., Glickman, M. H., Sun, S. J., Klinman, J. P., J. Am. Chem. Soc. 1996, 118, 10319–10320. Cha, Y., Murray, C. J., Klinman, J. P., Science 1989, 243, 1325–1330.
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12
13
14
15
16
17
18 19 20
21 22 23
24
25 26
27
N. S., J. Biol. Chem. 2001, 276, 24581– 24587. Harris, R. J., Meskys, R., Sutcliffe, M. J., Scrutton, N. S., Biochemistry 2000, 39, 1189–1198. Francisco, W. A., Knapp, M. J., Blackburn, N. J., Klinman, J. P., J. Am. Chem. Soc. 2002, 124, 8194–8195. Sikorski, R. S., Wang, L., Markham, K. S., Rajagopalan, P. T. R., Benkovic, S. J., Kohen, A., J. Am. Chem. Soc. 2004, 126, 4778–4779. Bell, R. P., The Tunnel Effect in Chemistry, Chapman and Hall, New York, 1980. ¨ hnel, J., Schowen, R. L., Su Theoretical Basis for Isotope Effects, in Enzyme Mechanism from Isotope Effects, 1st edn., Cook, P. F. (Ed.), CRC Press, Boca Raton, FL, 1991, Vol. 1, pp. 3–35. (a) Melander, L., Saunders, W. H., Reaction Rates of Isotopic Molecules, R. E. Krieger Publishing, Malabar, FL, 1987; (b) Bigeleisen, J., GoepertMayer, M., J. Phys. Chem. 1947, 15, 261. Westheimer, F. H. Chem. Rev. 1961, 61, 265. Schneider, M. E., Stern, H. J., J. Am. Chem. Soc. 1972, 94, 1517–1522. Schowen, R. L., in Progress in Physical Organic Chemistry, Streitweiser, A., Jr., Taft, R. W., Jr. (Eds.), WileyInterscience, New York, 1972, Vol. 9, p. 275. Klinman, J. P., Adv. Enzymol. Relat. Areas Mol. Biol. 1978, 46, 415–94. Chin, J. K., Klinman, J. P., Biochemistry 2000, 39, 1278–1284. Bahnson, B. J., Colby, T. D., Chin, J. K., Goldstein, B. M., Klinman, J. P. Proc. Natl. Acad. Sci. USA 1997, 94, 12797–12802. Kohen, A., Cannio, R., Bartolucci, S., Klinman, J. P., Nature 1999, 399, 496–499. Huskey, W. P., Schowen, R. L., J. Am. Chem. Soc. 1983, 105, 5704–5706. Cook, P. F., Oppenheimer, N. J., Cleland, W. W., Biochemistry 1981, 20, 1817. Welsh, K. M., Creighton, D. J.,
28
29
30
31 32 33 34
35
36 37 38
39 40
41 42
43
44 45
Klinman, J. P., Biochemistry 1980, 19, 2005–2016. Parkin, D. L., Theoretical Basis for Isotope Effects, in Enzyme Mechanism from Isotope Effects, 1st edn., Cook, P. F. (Ed.), CRC Press, Boca Raton, FL, 1991, Vol. 1, pp. 269–290. Cleland, W. W., in Isotope Effects in Chemistry and Biology, Kohen A., Limbach, H. H. (Eds.), Taylor and Francis – CRC Press, Boca Raton, FL, 2006, pp. 915–929. Antoniou, D., Schwartz, S. D., J. Phys. Chem. B 2001, 105, 5553–5558. Borgis, D. C., Lee, S. Y., Hynes, J. T. Chem. Phys. Lett. 1989, 162, 19–26. Bruno, W. J., Bialek, W., Biophys. J. 1992, 63, 689–699. Kuznetsov, A. M., Ulstrup, J., Can. J. Chem. 1999, 77, 1085–1096. Levich, V. G., Dogonadze, R. R., German, E. D., Kuznetsov, A. M., Kharkats, Y. I., Electrochim. Acta 1970, 15, 353–367. Decornez, H., Hammes-Schiffer, S., J. Phys. Chem. A. 2000, 104, 9370– 9348. Grant, K. L., Klinman, J. P., Biochemistry 1989, 28, 6597–6605. Chowdhury, S., Banerjee, R., J. Am. Chem. Soc. 2000, 122, 5417–5418. (a) Glickman, M. H., Wiseman, J. S., Klinman, J. P., J. Am. Chem. Soc. 1994, 116, 793–794; (b) Hwang, C. C., Grissom, C. M., J. Am. Chem. Soc. 1994, 116, 795–796. Nesheim, J. C., Lipscomb, J. D., Biochemistry 1996, 35, 10240–10247. Abad, J. L., Camps, F., Fabrias, G., Angew. Chem. Int. Ed. 2000, 39, 3279– 3281, 3157. Meschede, L., Limbach, H. H., J. Phys. Chem. 1991, 95, 10267–10280. Basran, J., Sutcliffe, M. J., Scrutton, N. S., Biochemistry 1999, 38, 3218–3222. Knapp, M. J., Rickert, K., Klinman, J. P., J. Am. Chem. Soc. 2002, 124, 3865–3874. Klinman, J. P., J. Biol. Chem. 1972, 247, 7977–7987. Klinman, J. P., Biochemistry 1976, 15, 2018–2026.
References 46 Miller, S. M., Klinman, J. P., 47 48
49 50 51 52 53
54
55 56
57 58 59 60
61
62
63
64
65
Biochemistry 1983, 22, 3091–3096. Miller, S. M., Klinman, J. P., Biochemistry 1985, 24, 2114–2127. Francisco, W. A., Merkler, D. J., Blackburn, N. J., Klinman, J. P., Biochemistry 1998, 37, 8244–8252. Kurz, L. C., Frieden, C., J. Am. Chem. Soc. 1980, 102, 4198. Saunders, W. H., Jr., J. Am. Chem. Soc. 1985, 107, 164–169. Huskey, W. P., Phys. Org. Chem. 1991, 4, 361–366. Rucker, J., Klinman, J. P., J. Am. Chem. Soc. 1999, 121, 1997–2006. Amin, M., Price, R. C., Saunders, W. H., J. Am. Chem. Soc. 1990, 112, 4467–4471. Alston, W. C., Kanska, M., Murray, C. J., Biochemistry 1996, 35, 12873– 12881. Lin, S., Saunders, W. H., J. Am. Chem. Soc. 1994, 116, 6107–6110. Swain, C. G., Stivers, E. C., Reuwer, J. F., Schaad, L. J., J. Am. Chem. Soc. 1958, 80, 5885–5893. Kohen, A., Jensen, J. H., J. Am. Chem. Soc. 2002, 124, 3858–3864. Bigeleisen, J., J. Chem. Phys. 1955, 23, 2264–2267. Grant, K. L., Klinman, J. P., Bioorg. Chem. 1992, 20, 1–7. Northrop, D. B., in Isotope Effects in Enzyme-Catalyzed Reactions, Cleland, W. W., O’Leary, M. H., Northrop, D. B. (Eds.), University Park Press, Baltimore, MD, 1997, pp. 122–152. Bahnson, B. J., Klinman, J. P., Methods Enzymol. 1995, 249, 373– 397. Kwart, H., Acc. Chem. Res. 1982, 15, 401–408. Kwart’s attribution of temperature independent kinetic isotope effects to a bent transition state was subsequently corrected. Whittaker, M. M., Ballou, D. P., Whittaker, J. W., Biochemistry 1998, 37, 8426–8436. Harris, R. J., Meskys, R., Sutcliffe, M. J., Scrutton, N. S., Biochemistry 2000, 39, 1189–1198. Jonsson, T., Edmondson, D. E., Klinman, J. P., Biochemistry 1994, 33, 14871–14878.
66 de Broglie, L., Nature 1923, 112,
540. 67 Bell, R. P., Trans. Faraday Soc. 1959,
55, 1. 68 Northrop, D. B., J. Am. Chem. Soc.
1999, 121, 3521. 69 Garcia-Viloca, M., Gao, J., Karplus,
70
71
72 73 74 75
76 77 78 79 80
81 82 83
84 85 86
87 88
M., Truhlar, D. G., Science 2004, 303–186–195. Merzbacher, E., in Quantum Mechanics, 2nd edn., John Wiley & Sons, New York, 1970, Ch. 18. Borgis, D., Hynes, J. T., in The Enzyme Catalysis Process; Cooper, A, Houben, J. L., Chien, L. C. (Eds.), Plenum, New York, 1989, p. 293. Borgis, D., Hynes, J. T., Chem. Phys. 1993, 170, 315–346. Antoniou, D., Schwartz, S. D., J. Chem. Phys. 1998, 109, 2287–2293. Caratzoulas, S., Schwartz, S. D., J. Chem. Phys. 2001, 114, 2910–2918. Caratzoulas, S., Mincer, J. S., Schwartz, S. D., J. Am. Chem. Soc. 2002, 124, 3270–3276. Cui, Q., Karplus, M., J. Phys. Chem. B 2002, 106, 7927–7947. Krishtalik, L. I., Biochim. Biophys. Acta 2000, 1458, 6–27. Ulstrup, J., Jortner, J., J. Chem. Phys. 1975, 63, 4358–4368. Rickert, K. W., Klinman, J. P., Biochemistry 1999, 38, 12218–12228. Hatcher, E., Soudacker, A. V., Hammes-Schiffer, S., J. Am. Chem. Soc. 2004, 126, 5763–5775. Sekhar, V. C., Plapp, B. V., Biochemistry 1988, 27, 5082–5088. Klinman, J. P., Biochemistry 1976, 2018–2026. Rucker, J., Cha, Y., Jonsson, T., Grant, K. L., Klinman, J. P., Biochemistry 1992, 31, 11489–11499. Chin, J. K., Klinman, J. P., Biochemistry 2000, 39, 1278–1284. Kohen, A., Klinman, J. P., J. Am. Chem. Soc. 2000, 122, 10738–10739. Liang, Z-X., Lee, T., Resing, K. A., Ahn, N. G., Klinman, J. P., Proc. Natl. Acad. Sci. USA 2004, 101, 9556–9561. Hammond, G. S., J. Am. Chem. Soc. 1955, 77, 334. Lowry, T. H., Richardson, K. S., in
1283
1284
10 Nuclear Tunneling in the Condensed Phase: Hydrogen Transfer in Enzyme Reactions
89 90
91
92 93 94 95
96
97 98
99
100 101 102 103 104
105
Mechanism and Theory in Organic Chemistry, 3rd edn., Harper and Row, New York, 1987. Kim, Y., Kreenoy, M. M., J. Am. Chem. Soc. 1992, 114, 7116–7123. Truhlar, D. G., Isaacson, A. D., Garrett, B. C., in Theory of Chemical Reaction Dynamics, Baer, M. (Ed.), CRC Press, Boca Raton, FL, 1985, Vol. 4, pp. 65–137. Kohen, A., Jonsson, T., Klinman, J. P., Biochemistry 1997, 36, 2603– 2611. Seymour, S., Klinman, J. P., Biochemistry 2002, 41, 8747–8758. Su, Q., Klinman, J. P., Biochemistry 1999, 38, 8572–8581. Roth, J. P., Klinman, J. P., Proc. Natl. Acad. Sci. USA 2003, 100, 62–67. Roth, J. P., Wincek, R., Nodet, G., Edmondson, D. E., McIntire, W. S., and Klinman, J. P. J. Am. Chem. Soc., 2004, 126, 15120–15131. Roth, J. P., Klinman, J. P., in Isotope Effects in Chemistry and Biology, A. Kohen, H. L. Limbach (Eds.), Taylor and Francis – CRC Press, Boca Raton, FL, 2006, pp. 645–669. Brinkley, D. W., Roth, J. P., J. Am. Chem. Soc., 2005, 127, 15720–15721. Seymour S. L., The Influence of Enzyme Surface and Environmental Modification on Catalysis Examined with Probes for Hydrogen Tunneling, Ph.D. Thesis, University of California, Berkeley, CA, 2001. Janes, S. M., Mu, D., Wemmer, D., Smith, D., Kaur, A. J., Maltby, D., Burlingame, A. L., Klinman, J. P., Science 1990, 248, 981. Klinman, J. P., J. Biol. Chem. 1996, 271, 27189. Palcic, M. M., Klinman, J. P., Biochemistry 1983, 22, 5924. Hartmann, C. Klinman, J. P., Biochemistry 1991, 30, 4605. Silverman, R. B., Acc. Chem. Res. 1995, 28, 335–342. Miller, J. R., Edmondson, D. E., Grissom, C. B., J. Am. Chem. Soc. 1995, 117, 7830–7831. Benderskii, V. A., Makarov, D. E.,
106
107
108 109
110 111
112 113
114
115 116 117
118
119
120
121
122 123
Wight, C. A., Adv. Chem. Phys. 1994, 88, 1. Lewis, E. R., Johansen, E., Holman, T. R. J. Am. Chem. Soc. 1999, 121, 1395–1396. Knapp, M. J., Seebeck, F. P., Klinman, J. P., J. Am. Chem. Soc. 2001, 123, 2931–2932. Knapp, M. J., Klinman, J. P., Biochemistry 2003, 42, 11466–11475. Ambundo, E. A., Friesner, R. A., Lippard, S. J., J. Am. Chem. Soc. 2002, 124, 8770–8771. Roecker, L., Meyer, T. J., J. Am. Chem. Soc. 1987, 109, 746–754. Binstead, R. A., McGuire, M. E., Dovletoglou, A., Seok, W. K., Roeker, L., Meyer, T. J., J. Am. Chem. Soc. 1992, 114, 173–186. Binstead, R. A., Meyer, T. J., J. Am. Chem. Soc. 1987, 109, 3287–3297. Binstead, R. A., Moyer, B. A., Samuels, G. J., Meyer, T. J., J. Am. Chem. Soc. 1981, 103, 2897–2899. Chaudhuri, P., Hess, M., Muller, J., Hildebrance, K., Bill, E., Weyhermuller, T., Wieghardt, J., J. Am. Chem. Soc. 1999, 121, 9599–9610. Knapp, M. J., Klinman, J. P., Eur. J. Biochem. 2002, 269, 3113–3121. Stewart, L. C., Klinman, J. P., Annu. Rev. Biochem. 1988, 57, 551–592. Eipper, B. A., Stoffers, D. A., Mains, R. E., Annu. Rev. Neurosci. 1992, 15, 57–85. Prigge, S. T., Kolhekar, A. S., Eipper, B. A., Mains, R. E., Amzel, L. M., Science 1999, 278, 1300–1305. Evans, J. P., Ahn, K., Klinman, J. P., J. Biol. Chem. 2003, 278, 49691– 49698. Miller, S. M., Klinman, J. P., Biochemistry 1983, 22, 3096– 3106(b). Liang, Z.-X., Klinman, J. P., Curr. Opin. Struct. Biol., 2004, 14, 648– 655. Marcus, R. A., Sutin, N., Biochim. Biophys. Acta. 1985, 11, 265–322. Singleton, D. A., Thomas, A. A., J. Am. Chem. Soc. 1995, 117, 9357.
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Multiple-isotope Probes of Hydrogen Tunneling W. Phillip Huskey 11.1
Introduction
Forty years ago, Bell and Goodall [1] and Lewis and Funderburk [2, 3] carried out experimental studies of proton transfers that demonstrated the importance of hydrogen tunneling in chemical reactions. Chemists had recognized for years that tunneling should contribute significantly to observed rates of reactions involving hydrogen transfers, but convincing experimental verification was not available [4– 6]. Bell, Goodall, Lewis, and Funderburk found that hydrogen (H/D) isotope effects on proton transfers from 2-nitropropane to substituted pyridines (Fig. 11.1) were too large to be consistent with any reasonable explanations that did not invoke hydrogen tunneling. These isotope effects varied from 9.8 to 24.3 for a series of substituted pyridine bases at room temperature, with the largest isotope effects for proton transfers to the bulkiest bases. In several cases, the researchers measured the temperature dependence of the isotope effects and found that extrapolations to infinite temperature were also consistent with expectations for tunneling. However, it was the fact that the Lewis and Funderburk kinetic isotope effects were too large to be explained without invoking tunneling that proved to be particularly convincing. Not all tunneling systems are expected to show such large isotope effects. Additional experiments, typically involving multiple-isotope probes, are needed to identify reactions with significant tunneling, and to characterize the nature of the tunneling process. Researchers are now addressing questions about the nature of tunneling and its possible role in catalysis that require comparisons of experimental isotope effects, including multiple-isotope probes, with the results of exacting theoretical and computational efforts [7–14]. This chapter first recounts the basis for the use of simple kinetic isotope effects in studies of tunneling, followed by expectations for H/D/T isotope effect comparisons (Swain–Schaad exponents) and isotope effect on isotope effect experiments (tests of the Rule of the Geometric Mean). The last section reviews the background for experiments to determine mixed isotopic exponents that combine the effects of H/D/T comparisons with isotope effects on isotope effects. Notably, much of this chapter concerns non-tunneling mechanistic effects on Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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Figure 11.1. Isotope effects on a proton transfer from carbon (24.9 C) measured by Lewis and Funderburk [3] and Lewis and Robinson [29].
multiple-isotope experiments. Appreciating the possible non-tunneling contributions to experimental results is often essential when efforts are made to identify specific tunneling effects. The isotope effects of particular interest in this chapter are those that arise from substitution of protium, deuterium, or tritium at one or two hydrogenic sites as described in Fig. 11.2. With this many isotopic labels, a few comments about nota-
Figure 11.2. Possible hydrogen isotope effects in a study with two isotopic sites. Lines show H/D/T isotope effect comparisons. Ratios of pairs of isotope effects within one of the six
boxes constitute isotope effects on isotope effects (tests of the Rule of the Geometric Mean). The subscript shows isotopes at site 1, and the superscript shows isotopes at site 2.
11.2 Background: H/D Isotope Effects as Probes of Tunneling
tion are needed. For descriptions of isotope effects and relationships between isotope effects, the notation expressed in Eq. (11.1) below will be used. For any parameter, x, the subscripts i (and sometimes j) refer to isotopes at one site in a reacting system, while the superscripts, k (and sometimes l) refer to isotopes at a possible second site. xijkl
D kH =k D T
kH =k T ¼ ðkH =kD Þ rHD
ð11:1Þ
In cases where one site is thought to give rise to a primary isotope effect – one in which bonds are being made or broken at the isotopic element – the subscripts will be used. In cases where secondary isotope effects (by definition, those that are not primary) need to be distinguished, the superscripts will be used. The middle part of Eq. (11.1) illustrates one use of the notation, as a primary H/T isotope effect measured when D occupies a secondary site. As a final example, the right-hand part of Eq. (11.1) shows a Swain–Schaad exponent r defined for a single site of isotopic substitution. The HD subscript serves to connect the exponent to the H/D isotope effect it acts on to produce the H/T isotope effect. In this example, the superscripts were omitted because there is either no second site of isotopic substitution or, in all cases, the isotope is protium.
11.2
Background: H/D Isotope Effects as Probes of Tunneling
Descriptions of the influence of tunneling on isotope effects often use conventional transition state theory (TST) as a convenient reference for discussion. Conventional TST is amenable to a straightforward theory of kinetic isotope effects, and tunneling contributions can be included or discarded. Conventional TST also serves as the starting point for numerous sophisticated modern theories of reaction rates [15], and it can be reduced to very simple terms, as is next described for isotope effects on hydrogen transfers. 11.2.1
One-frequency Models
The useful benchmarks for the Swain–Schaad exponents described in Section 11.3 are obtained from simple one-frequency models for hydrogen transfer reactions. The theoretical basis for the approach comes from the Bigeleisen–Wolfsberg [16] formalism for isotope effects on gas-phase reactions according to transition state theory in the limit of the harmonic approximation for vibrations, and with classical treatments for translations and vibrations. Using reasonable empirical force fields for model reactant-state and transition-state structures, the resulting vibrational frequencies yield isotope effects through the Bigeleisen equation. At this level of theory, primary kinetic hydrogen isotope effects are very well approximated by re-
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ducing the problem to very simple one-frequency models [17–20] that can be applied to the reaction shown in Eq. (11.2). CaH þ C ! ½Ca aHa aCz ! C þ HaC
ð11:2Þ
The one-frequency model represented by Eqs. (11.3)–(11.8) shows single isotopic frequency expressions for the MMI (mass/moment of inertia), ZPE (vibrational zero-point energy), and EXC (excited vibrations) terms of the usual Bigeleisen equation [21]. The extra term tun is the truncated Bell tunnel correction [22], used here to provide a simple way to express a tunneling effect in terms of a reactioncoordinate frequency, n z . u i ¼ ni hc=kB T
ð11:3Þ
uzH =uzD R =u R uH D
ð11:4Þ
mmi ¼
zpe ¼ expð½uHR uDR =2Þ exc ¼ tun ¼
R 1 expðuH Þ 1 expðuDR Þ
uzH sinðuzD =2Þ uzD sinðuzH =2Þ
kH =kD ¼ mmi zpe exc tun
ð11:5Þ ð11:6Þ ð11:7Þ ð11:8Þ
The utility of the one-frequency model for hydrogen transfer reactions is demonstrated in Fig. 11.3, showing isotope effects calculated down to 250 K (at lower temperatures, the truncated Bell tunnel correction is likely to be particularly unrealistic). The symbols show isotope effects calculated using a more elaborate vibrational model with a 9-atom transition state characterized by 20 real frequencies and one imaginary reaction-coordinate frequency. One set of symbols shows results for a model in which the reaction-coordinate frequency is large enough to make the tunneling term significant. The other set of points shows isotope effects from a model with a reaction-coordinate frequency so small that the tunneling term is not significant. The curves drawn though the two sets of points are least-squares fits to the one-frequency model of Eqs. (11.3)–(11.8). The fact that the one-frequency model is a good approximation for the more complete vibrational model is undoubtedly why the Swain–Schaad exponent of 1.44 (described in Section 11.3) has proved to be a useful benchmark for H/D/T isotope effect studies in many hydrogen transfer reactions. At 298 K, the one-frequency model without tunneling predicts an isotope effect of 6.4, which is considerably lower than the kH =kD of 24.2 observed by Lewis and Funderburk [3]. Observed isotope effects that are larger than expected based on
11.2 Background: H/D Isotope Effects as Probes of Tunneling
Figure 11.3. Temperature dependence of the primary hydrogen isotope effect calculated using a 9-atom vibrational model for hydrogen transfer (model HHIE3 [37] with simple stretch–stretch coupling to generate a reaction-coordinate frequency). Triangles mark calculated results for models with a reactioncoordinate frequency for H transfer of 984i cm1 including the truncated Bell tunnel correction [6, 22]. The circles show results for models with a sufficiently low reactioncoordinate frequency (90i cm1 ) to make the
tunnel correction insignificant. The solid curves are least-squares fits to the one-frequency model described in the text represented by Eqs. (11.3)–(11.8). The least-squares estimates of fitted parameters in cm1 were for the triangles, nHR ¼ 3090, nDR ¼ 2343, nHz ¼ 983i, and nDz ¼ 708i. For the circle data, the fits gave nHR ¼ 3124, nDR ¼ 2380, and the ratio of reaction coordinate frequencies nHz =nDz ¼ 1:40. The dashed lines show tangents at 25 C with intercepts corresponding to AH =AD ¼ 0:226 (triangles), and 1.078 (circles).
non-tunneling models still provide the most convincing evidence for tunneling in reacting chemical systems, although other explanations may be important in special cases [23, 24]. 11.2.2
Temperature Dependence of Isotope Effects
The results from the rudimentary model for isotope effects on a hydrogen transfer reaction shown in Fig. 11.3 are plotted in Arrhenius style as their logarithmic form versus inverse temperature. An analysis based on the temperature dependence of isotope effects is another standard method for detecting tunneling [25, 26], and again, non-tunneling models are helpful as a basis for comparison. For many ex-
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periments, particularly in solution, the range of temperatures that can be studied is fairly narrow, so linear extrapolations of Arrhenius plots are used to determine the intercept at infinite temperature, AH =AD . Models without tunneling tend to predict AH =AD near unity. The low temperature curvature predicted from models that include tunneling is expected to produce, by extrapolation, values of AH =AD that are much less than unity. The tangent at 298 K for the tunneling model in Fig. 11.3 gives AH =AD ¼ 0:23. An Arrhenius analysis of the isotope effects measured for the proton transfer shown in Fig. 11.1 gives AH =AD ¼ 0:15, providing further evidence for tunneling. Theories of hydrogen transfer that involve little or no overbarrier reaction and proceed entirely by tunneling predict temperature-independent isotope effects [27], with AH =AD A kH =kD . The effects of complex mechanisms with serial or parallel shifts in rate limiting steps must also be considered in the analysis of the temperature dependence of isotope effects [28]. In addition, tedious attention to details of temperature effects on pH, acidity constants, reaction volumes, and substrate or catalyst stabilities may be needed in some cases to avoid problematic interpretations. For these reasons, temperature studies of isotope effects may not be as convincing as the observation of very large isotope effects in providing evidence for tunneling. For reactions involving hydrogen transfer that may have substantial tunneling contributions to reaction rates, but do not show exceptionally large isotope effects, other experimental measures that are sensitive to tunneling would be useful. Many researchers have considered the comparisons between tritium and deuterium hydrogen isotope effects as possible tunneling criteria. As the next section describes, these comparisons have not proved to be generally useful for detecting tunneling.
11.3
Swain–Schaad Exponents: H/D/T Rate Comparisons
Soon after the discovery of proton transfers from 2-nitropropane showing large isotope effects consistent with tunneling, Lewis and Robinson [29] wondered if they could use the reaction to develop a tunneling criterion based on relationships between H/D and H/T kinetic isotope effects. Their work did not produce experimental support for a new tunneling criterion, and their early computational results, along with those from More O’Ferrall and Kouba [30] and Stern and Weston [31], further diminished enthusiasm for the idea. Over the ensuing years, most results from studies that involve a single site of isotopic substitution have failed to provide a basis for tunneling criteria, although the temperature dependence of the relationship may prove to be useful [32]. The starting point for defining the relationships between H/D/T isotope effects is the set of equations (11.9) shown below, with exponents rHD and rDT as leading parameters for study. The subscript in the notation used here refers to the type of isotope effect, H/D or D/T, used to predict the H/T effect in an exponential relationship. The two exponents are algebraically related for systems with a single site
11.3 Swain–Schaad Exponents: H/D/T Rate Comparisons
of isotopic substitution [33]. In this section, results that have been published as rDT were converted to rHD using Eq. (11.9) to simplify comparisons. kH =k T ¼ ðkH =kD Þ rHD
kH =k T ¼ ðkD =k T Þ rDT
rDT ¼ rHD =ðrHD 1Þ
ð11:9Þ
11.3.1
Swain–Schaad Limits in the Absence of Tunneling
Early estimates of the exponent rHD were made by Swain et al. [34] and Bigeleisen [35]. Swain et al. [34] showed that the H/T isotope effect could be predicted from the H/D isotope effect using the one-frequency model described above (Eq. (11.2)) assuming that only the zero-point energy term (zpe, Eq. (11.5)) contributed to the kinetic isotope effect. If the single frequency of the model is a diatomic-type stretch, the isotopic zpe ratios depend only on the reduced masses for the vibration. For reduced masses of 1, 2, and 3 atomic mass units for H, D, and T transfer, the exponent rHD in Eq. (11.9) turns out to be 1.44. Bigeleisen [35] proposed a range of 1.38–1.55 for rHD. To establish these limits, he first calculated isotope effects for the set of hypothetical equilibria that could be envisioned for pairs of reactants and products selected among H2 , HF, HCl, HBr, HI, and H2 O at 298 K, 600 K, and 1000 K. He next estimated the effects of a reaction-coordinate frequency for hydrogen transfer in rate processes without tunneling, and then reasoned that his limits calculated for equilibria should also apply to rate processes. The Bigeleisen limits are probably too broad to be of general use in hydrogen transfers for most polyatomic systems. The model calculations discussed below provide better guides for expectations of primary kinetic isotope effects in non-tunneling reactions. For similar reasons, Melander and Saunders [21] recommended non-tunneling limits of 1.40–1.45 (or rDT ¼ 3.2–3.5). Calculations using conventional TST and the Bigeleisen–Wolfsberg [16] treatment for isotope effects have demonstrated that rHD ¼ 1:44 is a useful benchmark for primary hydrogen isotope effects. Using empirical harmonic force fields and various reactant-state and transition-state geometries, More O’Ferrall and Kouba [30] found, for proton-transfer models, that the exponents were within 2% of the 1.44 value, and similar computational approaches gave rHD ¼ 1.43–1.45 (343 K) [36] and 1.43–1.45 (298 K) [37] for calculations that included a wide range of transition-state models and reaction-coordinate motions with insignificant tunneling effects. In their study of tunneling and variational effects on hydride-transfer reactions Kim and Kreevoy [33] obtained vibrational frequencies from extended LEPS potential energy surfaces that also allowed them to calculate results for conventional TST, giving rHD ¼ 1:47. Similarly, the theoretical treatments used by Cui et al. permitted conventional TST calculations from their QM/MM (DFT/CHARMM) potentials for studies of liver alcohol dehydrogenase (1.42) [38] and triosephosphate isomerase (1.43) [32]. Melander and Saunders [21] recommended that nontunneling limits of 1.40–1.45 (or rDT ¼ 3.2–3.5) appear to be reasonable for many primary hydrogen isotope effects, at temperatures less than about 1000 K. Given
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that so many treatments give rHD very near 1.44 for primary H/D isotope effects larger than about 2 at moderate temperatures, rDH for conventional TST could perhaps be taken as a measure of the quality of a potential surface near stationary points for primary hydrogen isotope effect studies. Limits proposed by Kohen and Jensen [39] should not be considered with the single-site Swain–Schaad values discussed in this section. Kohen and Jensen [39] proposed that a value of 4.8 be treated as an upper limit in a non-tunneling system DT in Section 11.5 describing for a secondary isotope effect exponent defined as rDD ‘‘mixed-label’’ experiments. As shown in Section 11.5, it useful to separate these mixed-label exponents into two factors: one that arises from H/D/T substitutions, and one that arises from isotopic substitution that amounts to an isotope effect on an isotope effect. Also note that it is not straightforward to convert a mixed-label exponent based on D/T isotope effects into one based on H/D isotope effects as Eq. (11.9) shows for single-site exponents. 11.3.2
Swain–Schaad Exponents for Tunneling Systems
Early experimental tests in systems thought to involve significant tunneling were carried out by Lewis and Robinson [29]. In their work, they first extended the treatment of Swain et al. [34] by supposing that tunneling components ðQÞ could be factored out of the kinetic isotope effect, similar to the approach shown in Eq. (11.8). They used Eq. (11.10), using k to represent a rate constant without a tunneling correction, to conclude that tunneling should not cause Swain–Schaad exponents to deviate strongly from a value of 1.44, unless the exponent for the tunnel effect, sHD , is very different from 1.44 and most of the kinetic isotope effect arises from Q H =Q D . kH =k T ¼ ðkH =kD Þ 1:44 ðQ H =Q D Þ sHD rHD ¼ 1:44 þ ðsHD 1:44Þ
lnðQ H =Q D Þ ð11:10Þ lnðkH =kD Þ
Lewis and Robinson [29] explored the relationship between H/D and H/T kinetic isotope effects predicted by several one-dimensional models for tunneling, and found no conspicuous deviations from the prediction made by Swain et al. [34]. Noting that there were many uncertain factors in their model calculations, they proceeded to make experimental measurements on systems thought to react with significant tunneling, based on the fact that they showed large kinetic isotope effects. For the proton transfer reaction shown in Fig. 11.1, they measured rHD ¼ 1:42. Lewis and Robinson concluded that their results along with the results from five additional proton or hydride transfer reactions were consistent with predictions made using rHD ¼ 1:44. The one case that deviated significantly in the direction expected for tunneling was the oxidation of leuco crystal violet by chloranil which showed rHD ¼ 1:31. The Lewis and Robinson work demonstrated that Swain–Schaad exponents were not sensitive to the extent of hydrogen tunneling
11.3 Swain–Schaad Exponents: H/D/T Rate Comparisons
in a reaction, but it did not exclude the possibility of large deviations in the exponents for cases of extreme tunneling. Jones also summarized early work on H/D and H/T isotope effects on eight reactions [40] with H/D isotope effects large enough to suggest rate-limiting hydrogen transfers that may or may not involve significant tunneling. The values for rHD were in the range 1.38–1.50, except for the case of proton transfer from acetone to hydroxide ion, which requires an uncertain correction for secondary isotope effects. He also reported rHD for proton transfers from 2-carbethoxycyclopentanone to deuterium oxide (1.48 G 0.02), chloroacetate (1.72 G 0.05), and fluoride (1.32 G 0.05). At 298 K, the H/D isotope effects were modest at 3.4, 4.1, and 2.6. In studies of a different class of proton transfers, Limbach and coworkers [41, 42] used lineshape analysis of 1 H and 3 H NMR spectra of porphyrin and its monoanion conjugate base to obtain H/D/T rate constants for fast intramolecular proton transfers. They fit their temperature dependence of rate constants to a modified one-dimensional Bell tunneling model [43]. The fit of the data gave rHD very near 1.44 over the temperature range of the data where tunneling was thought to be significant, and down to about 240 K. At lower temperatures, the extrapolated fit predicted rHD to rise to a constant value near 1.7, although the Bell model for tunneling may not be as valid at the very low extrapolated temperatures. 11.3.3
Swain–Schaad Exponents from Computational Studies that Include Tunneling
Computational work has generally agreed with the the conclusions reached from experimental studies of tunneling systems. Vibrational analysis calculations using model reactant and transition states for primary isotope effects on hydrogen transfer reactions give Swain–Schaad exponents that are within 3% of the 1.44 value when tunneling effects are treated using the truncated Bell [22] equation [30, 36, 37]. A slightly wider range for rHD was seen in Stern and Weston’s [31] study of tunneling barriers. These authors included tunneling through one-dimensional Eckart barriers [44] for a series of model calculations on hydrogen transfer reactions, and showed that rHD is generally within the Bigeleisen limits [35] of 1.33– 1.58 discussed above. However, values as low as 1.25 were calculated for models with the highest reaction barriers. Grant and Klinman tested the exponents that could be generated using the full Bell tunnel correction [22] using assumed barrier heights for H, D, and T transfer and found a very wide range of possible values for rHD from 1.2 to 2.0. Studies involving multidimensional tunneling treatments have similarly not provided support for rHD as a criterion for tunneling. In their work on hydride transfer reactions, Kim and Kreevoy [33] using extended LEPS potential energy surfaces found rHD to be 1.27–1.50 for six model surfaces using conventional TST with the tunnel correction included, and 1.32–1.50 for the same surfaces using variational TST, again with the tunneling treatment included. The calculations reported by Cui et al. [38], also using variational TST and a multidimensional tunneling treatment gave rHD ¼ 1:50. In their study of the triosphosphate isomerase reaction, Cui
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and Karplus [32] found rHD to be 1.47 for two tunneling treatments at 300 K, and like Tautermann et al. [45], concluded that single-site Swain–Schaad exponents are not reliable indicators for tunneling. 11.3.4
Swain–Schaad Exponents for Secondary Isotope Effects
For secondary isotope effects, no simple one-frequency vibrational models have been devised analogous to the Swain et al. [34] treatment for primary isotope effects. Still, some vibrational analysis calculations tend to give rHD close to 1.44. A few single-site Swain–Schaad experimental results and several computational studies have been reported for secondary isotope effects. One experimental example comes from the triosephosphate isomerase reaction, which shows a large secondary H/T kinetic isotope effect of 1.27 G 0.03 and rDT ¼ 4:4 G 1:3 (therefore, rHD ¼ 1:29 G 0:38). Vibrational analysis calculations for elimination reactions [36] gave rHD ¼ 1.36–1.39 for models with and without truncated Bell [22] tunnel corrections in all cases where kH =kD was larger than 1.02. Similar calculations for hydride-transfer reactions gave rHD ¼ 1.42–1.44 for a range of models with and without tunnel corrections. Conventional TST produced a single-site secondary exponent of 1.46, and 1.31 for variational TST with multidimensional tunneling in the alcohol dehydrogenase study [38], and for the triosephosphate isomerase reaction [32], rHD ¼ 1:32 with conventional TST, and 1.85 and 2.27 for variational TST with respective one-dimensional and multidimensional tunneling treatments. The paper by Cui and Karplus [32] includes a very detailed discussion of the secondary Swain–Schaad exponents, and Hirschi and Singleton [46] report a wide range of secondary Swain–Schaad exponents from a large number of electronic-structure calculations. The fact that secondary kinetic isotope effects tend to be small causes an additional concern because Swain–Schaad exponents will become very large when one of the isotope effects approaches unity. Cautions about small uncertainties in computational results have been given [47], and a similar sensitivity is expected from experimental errors [48]. Large exponents from small isotope effects may also be quite real. If a secondary isotope effect arises from competing factors involving increasing and decreasing sensitivity of isotopic zero-point energies (from weakening some force constants while tightening others), it can be possible to have a D/T isotope effect very near unity to produce a large exponent. 11.3.5
Effects of Mechanistic Complexity on Swain–Schaad Exponents
Multiple rate-limiting steps can give rise to Swain–Schaad exponents that differ significantly from 1.44. Figure 11.4 gives the general form of the observed isotope effect in cases where two rate-limiting steps appear in series with one or more steady-state intermediates separating the steps, and in cases where rate-limiting steps occur in parallel, after a branch point in a mechanistic scheme. To get a sense
11.3 Swain–Schaad Exponents: H/D/T Rate Comparisons
Figure 11.4. Observed isotope effects as weighted averages of isotope effects on steps in mechanisms showing either serial or parallel changes in the rate-limiting step.
of the size of the Swain–Schaad deviations, Fig. 11.5 shows predicted exponents that would be observed if only one of two rate-limiting steps has an isotope effect. If that step is arbitrarily identified as the one corresponding to ka , the equations of interest are shown in Eqs. (11.11) and (11.12).
Figure 11.5. Changes in the observed Swain– Schaad exponent as the relative importance of an isotope-dependent step is adjusted by wa for mechanisms with serial or parallel changes in rate limiting step (see Fig. 11.4). The numbers near the curves show the isotope
effect on ka , which is also the limit of ðkH =kD Þobs when wa ¼ 1. When wa ¼ 0, the isotope-sensitive step no longer limits the reaction rate, so the observed isotope effect becomes 1.
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Serial:
ðkH =kD Þobs ¼ wa ðkH =kD Þa þ 1 wa ; ðkH =k T Þobs ¼ wa ðkH =kD Þa1:44 þ 1 wa
ð11:11Þ
Parallel: ðkH =kD Þobs ¼ wa ðkH =kD Þ1 a þ 1 wa ; ðkH =k T Þobs ¼ wa ðkH =kD Þa1:44 þ 1 wa
ð11:12Þ
Note that the weighting factors correspond to the common H-isotopomer in the H/D and H/T isotope effects, and expressions for wa are different for the serial and parallel cases. The equations in Eq. (11.11), developed by Northrop [49, 50], have proved to be useful in obtaining intrinsic kinetic isotope effects in enzymatic reactions with multiple rate-limiting steps that partially mask the full effect of an isotope-sensitive step. The exponents ðrHD Þobs calculated from Eqs. (11.11) and (11.12) are shown in Fig. 11.5 for various values of ðkH =kD Þa . For mechanisms with multiple rate-limiting steps in series, the observed exponents rHD tend to be larger than 1.44, while a mechanism with parallel rate-limiting steps will give an exponent less than 1.44. The corresponding trends for rDT, according to Eq. (11.9), will be just the opposite: rDT will be less than the benchmark 3.3 value for serial cases and greater than 3.3 for the parallel cases. The effects of changing rate-limiting steps may appear in temperature studies. With a few assumptions, the Eqs. (11.11) and (11.12) can be modified to allow for a temperature dependent ðkH =kD Þa and weighting factor, wa . Equation (11.13) shows wa expressed using an Arrhenius-type expression for a rate-constant ratio, such that a ¼ Aa =Ab and e ¼ ðEa Þa ðEa Þb . The temperature dependence on the isotope effect for ka assumes the effect arises entirely from zero-point energy terms; a value of z can be generated using a specified value for ðkH =kD Þa at a particular temperature. wa ðserialÞ ¼
1 1 þ aee=RT
wa ðparallelÞ ¼
1 1 þ a1 e e=RT
ðkH =kD Þa ¼ e z=RT ð11:13Þ
For an assumed H/D isotope effect of 7 for kH =kD at 298 K, the effects of temperature on observed values of rHD (upper panels) and the two steps observed H/D isotope effects (lower panels) are shown in Fig. 11.6. The values that define the temperature dependence of the weighting factors for the two steps are also shown on the figure. The range of possible temperature dependences is broad, and more complex temperature effects should be expected if additional rate-limiting steps are included in a mechanism [51]. As has been noted before, serial changes in mechanism only increase rHD from the 1.44 benchmark [52]. Parallel changes tend to decrease the observed exponent. The effects of mechanistic complexity apply potentially to many types of reactions, for both nonenzymic and enzymic systems, and for experiments involving steady-state turnover, rapid-mixing, relaxation kinetics, and other types of rate measurements. The Swain–Schaad exponents as described here, refer to the use of multiple iso-
11.4 Rule of the Geometric Mean: Isotope Effects on Isotope Effects
Figure 11.6. Influence of temperature-induced changes in rate-limiting steps on observed Swain–Schaad exponents, ðrHD Þobs , and observed H/D isotope effects. Shown above each curve are variables a and e (kJ mol1 ) for the ratio of rate constants ka =kb (defined in Fig. 11.4) expressed as aeðe=RTÞ . The curves were generated from a model that had isotope effects arising solely from zero-point energy
changes such that ðkH =kD Þa ¼ 7 at 298 K and ðrHD Þa ¼ 1:44. The curve for a ¼ 10, e ¼ 5 is not shown for the serial changes in the ratelimiting step (panels A and B) because the observed isotope effect is very small. For the same reason, the curve for a ¼ 0:1, e ¼ þ5 is not shown for the parallel changes in the ratelimiting step (panels C and D).
topes at a single site. The remaining sections concern experiments involving a second site of isotopic substitution.
11.4
Rule of the Geometric Mean: Isotope Effects on Isotope Effects
In systems with multiple sites of isotopic substitution, it is possible to determine if isotopic substitution at one site will alter the isotope effect at a second site. One example is the reaction catalyzed by glutamate dehydrogenase shown in Fig. 11.7. Srinivasan and Fisher [53] used stereospecifically labeled NADPH as the hydride
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Figure 11.7. Isotope effect on an isotope effect (298.15 K) in Srinivasan and Fisher’s study of catalysis by glutamate dehydrogenase [53]. When the isotope at the secondary site A is deuterium (L ¼ H or D), the primary isotope effect at site B is reduced by a factor of 1.14.
donor in the reaction to measure the H/D primary isotope effect when the nontransferring A-side site contained either protium or deuterium. The ratio of the two values, 1.14, is a significant ‘‘isotope effect on an isotope effect’’, also known as a nonadditive isotopic free energy effect or as a breakdown in the Rule of the Geometric Mean (RGM) [54]. Observations of RGM breakdowns can be indicators of tunneling in reacting systems, and more generally they signify departures from simple two-state models for rates and equilibria. The notation used here to express the RGM effect seen by Srinivasan and Fisher is shown in Eq. (11.14), where the subscripts on g denote the isotopes used in the primary site, and the superscripts denote secondary-site isotopes. HD ¼ gHD
H kH =kDH D kH =kDD
ð11:14Þ
11.4.1
RGM Breakdown from Intrinsic Nonadditivity
A common use of the RGM is to compare isotope effects among studies with equivalent chemical sites but having different levels of isotopic substitution. The secondary isotope effect arising from H/D substitution at a single hydrogenic site on a methyl group could be compared, for example, with the isotope effect obtained from isotopic substitutions at all three methyl hydrogens [55]. In this case,
11.4 Rule of the Geometric Mean: Isotope Effects on Isotope Effects
the RGM predicts that the d1 effect will be the cube root (the geometric mean) of the d3 effect. The effects on isotopic free-energy differences are therefore additive, and isotopic substitution at one site does not change the effect of isotopes at other sites. In this way, the RGM predicts no isotope effects on isotope effects. Experience with model calculations for equilibrium isotope effects and kinetic isotope effects, when using conventional TST, shows that the RGM is valid in the common circumstance in which the effects of coupled vibrational motions cancel between reactant and product states, or between reactant and transition states. The natural coupling expected between the various bends and stretches of the bonds in a methyl group is largely the same in the reactant state and transition state in the acetyl transfer example, so the free-energy effects of multiple isotopic substitutions are strictly additive. In the case of the glutamate dehydrogenase reaction of Fig. 11.7, the RGM would be expected to hold as the effects of coupled LA –LB motions cancel between reactant and transition states. Model calculations using conventional TST show that the cancellation of nonadditive effects is nearly exact in spite of the fact that the C–LB bond is reacting, so the RGM is predicted to hold [56, 57]. Knowing that the experiments show an RGM breakdown is therefore an indication that the simple transition-state picture must be modified to explain this reaction. In some types of experiments, the effects of vibrational coupling cannot cancel and the RGM breaks down. The case of the isotopic exchange of HOH and DOD to produce HOD is one example [58] of such intrinsic nonadditivity . The reaction is predicted to have an equilibrium constant of 4 on statistical grounds if the RGM holds, while experimental and theoretical results show smaller values of 3.85. The effect of the coupled motions between the two deuterium atoms in DOD cannot cancel in the isotope exchange reaction, and the effect of the extra isotope lowers the zero-point energy by more than expected from the RGM and the singly substituted HOD. In contrast to this specific isotope exchange reaction, most kinetic solvent isotope effect experiments would be expected to show substantial cancellation of nonadditive isotopic effects, and notably, the commonly used theory of reaction rates and equilibria in mixed HOH/DOD solvents relies on the validity of the RGM in these cases [59–62]. A second classic example of intrinsic nonadditivity is the nitrogen isotope effect on the acidity of pyridinium ion in HOH and DOD. Kurz and Nasr [63] found that K að14Þ =K að15Þ (298 K) was 1.0211 G 0.0003 in HOH and 1.0250 G in DOD, and they attributed this isotope effect on an isotope effect to the fact that in the reactant state the nitrogen and hydrogen isotopes are located on the same molecule, while in the product state they are on different molecules. Consequently, the nonadditive, coupled-motion effects of the reactant cannot be expected to be similar in the products. The RGM is therefore expected to hold for kinetic isotope effects that can be explained with conventional TST involving a single reactant state and a single transition state, with all isotopic sites in roughly similar bonding arrangements in the two states. For equilibrium isotope effects, the RGM should be similarly valid for two-state situations that do not involve the separation of the isotopic sites, as would occur if one isotope is transferred in the reaction.
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11.4.2
RGM Breakdown from Isotope-sensitive Effective States
The RGM breakdown reported by Saunders and Cline [64] illustrates a second class of RGM breakdowns for systems with isotope-sensitive effective reactant, product, or transition states. Saunders and Cline used deuterium shifts in carbon13 NMR signals to measure equilibrium isotope effects on rearrangements of carbocations with different levels of deuterium substitution for protium. The equilibrium constants shown for one set of their results in Fig. 11.8 represent bdeuterium isotope effects for the equilibrium shown, since the reaction with nondeuterated cations must equal unity. The fact that the observed isotope effects are normal (greater than one) can be explained by weaker binding of the isotopes through hyperconjugation with the empty p-orbital of an adjacent sp 2 -hybrid carbon. A breakdown in the RGM is apparent as can be see by showing that the cube of the d1 effect (1.6339) is significantly smaller than the observed d3 effect (1.7664). Electronic structure calculations were used to show that the RGM breakdown did not arise from intrinsic nonadditivity of isotope effects among single conformers of reactants and products. Instead, Saunders and Cline concluded that the relative populations of isotopically distinguished conformers were shifted by different levels of isotopic substitution. As is shown in Fig. 11.8, the product for the rearrangement with the d1 isotopomer can adopt conformations that reduce the sensitivity of the equilibrium to isotopic substitution. In this way, the effective product state for the equilibrium is altered by different levels of isotopic substitution, leading to the RGM breakdown.
Figure 11.8. Isotope effects (162.5 K) on a carbocation rearrangement studied by Saunders and Cline [64]. The rule of the geometric mean predicts that the three-isotope equilibrium isotope effect should be the cube of the single-isotopic-site effect: ð1:1778Þ 3 ¼ 1:6338.
11.4 Rule of the Geometric Mean: Isotope Effects on Isotope Effects
Figure 11.9. Mechanistic pathways for the malic enzyme reaction. Asterisks show the positions of the labels for some of the isotopeeffect-on-isotope-effect experiments of Hermes, Cook, Cleland and others [66–70]. The upper pathway shows concerted hydride transfer and
decarboxylation; the lower pathway shows the two chemical processes in separate steps. The carbon isotope effects they measured decreased when the transferring hydrogen was deuterium, ruling out the concerted pathway.
Isotope-sensitive effective states can also lead to RGM breakdowns for kinetic isotope effects. In cases involving multiple rate-limiting steps, the effective or virtual states [65] that can be deduced from a transition-state analysis may be sensitive to isotopic substitution. The malic enzyme story [66–70] is a comprehensive example of the use of isotope effects on isotope effects to resolve mechanistic details from effective transition states. Two possible routes for the oxidative decarboxylation of the substrate malate are shown in Fig. 11.9, and the two isotope effects of interest are the carbon isotope effect on decarboxylation and the hydrogen isotope effect on hydride transfer. Also of interest is the influence of the two isotope effects on each other – the hydrogen isotope effect on the carbon isotope effect. The distance between the two isotopic sites, along with likely cancellation of coupled-vibration effects, eliminates the possibility of an RGM breakdown from intrinsic nonadditivity. However, there is a chance that an RGM breakdown will be observed if the reaction follows the stepwise path and that path happens to have both steps partially limiting the reaction rate. In this case, the effective transition state is a weighted average of the decarboxylation and hydride-transfer transition states, and the relative weighting of the two states becomes sensitive to isotopic substitution. The effective transition state will be different for protium and deuterium transfer. Hermes, Cook, Cleland, and their coworkers [66–70]. found that the 12 C/ 13 C isotope effect on k cat =K m at saturating concentrations of NADPþ was 1.0324 G 0.0003 for protium transfer and 1.0243 G 0.0004 for deuterium transfer. These results are consistent with a stepwise path in which decarboxylation is less
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11 Multiple-isotope Probes of Hydrogen Tunneling
rate-limiting for the deuterated substrate (the hydride transfer step is more rate limiting when deuterium is transfered). In general, shifting effective states will cause RGM breakdowns according to equations similar to Eqs. (11.15) and (11.16), derived from the equations for serial and parallel changes in the mechanism shown in Fig. 11.4. These equations were simplified from a general set of equations for two isotopic sites and two ratelimiting steps (a and b) by identifying isotopes for one site to be H and D, and using I and J for the isotopes of the other site. A further simplification is the assumption that the H/D isotope effect on step a is unity and the I/J isotope effect on step b is also unity. Intrinsic nonadditivity and tunneling effects are also excluded by using the same ðkI =k J Þa in both equations. Serial:
gIJHD ¼
ðkIH =k H J Þobs ðkID =k D J Þobs
Parallel: gIJHD ¼
¼
ðkIH =k H J Þobs ðkID =k D J Þobs
waH ðkI =k J Þa þ 1 waH waD ðkI =k J Þa þ 1 waD
¼
waD ðkI =k J Þ1 a þ 1 waD waH ðkI =k J Þ1 a þ 1 waH
ð11:15Þ ð11:16Þ
These equations show that if the H/D isotope effect is normal, the isotope effect ðkI =k J Þobs will decrease (move toward unity) for the serial change in the rate-limiting step when H is replaced with D. If the H/D isotope effect is inverse, or the reaction involves a parallel change in mechanism, the RGM breakdown will be reversed and the I/J isotope effect will become larger (move away from unity) when H is replaced with D. There exist a wide range of possible RGM breakdowns from the shifting effective states in complex mechanisms. The full and elaborate analysis of the malic enzyme studies demonstrates the potential for using RGM breakdowns to sort out the details of multiple rate-limiting steps in enzymatic reactions [66–70]. Other approaches to the use of RGM breakdowns to distinguish between mechanistic pathways include studies of proline racemace [71, 72] and studies of multiple intramolecular proton transfers in porphyrins and related systems [43, 73–79], and in hydrogen-bonded dimers [80–82]. Special effects arising from variational TST [15, 83] can also be expected to produce RGM breakdowns in reacting systems with isotopomers having different free-energy bottlenecks. These variational effects are expected to be particularly significant for hydrogen transfer reactions with nearly symmetrical structures at the classical transition-state location at a potential-energy saddle point [14, 84]. The diagram in Fig. 11.10 gives a rough view of how the bottleneck can end up in a different position for hydrogen isotopes. If, near the saddle point, the vibrational potential corresponding to a triatomic symmetric stretch tightens relative to the potential at the saddle point, the resulting difference in the isotopic vibrational energies can be sufficient to shift the bottleneck for the protium isotopomer further from the saddle point than the deuterium isotopomer. In this way, the variational transition state is different for the two isotopomers, and a second isotopic probe would report on the different vibrational properties of the H-transfer and Dtransfer bottlenecks. An RGM breakdown is possible since the effective transition state is changed upon isotopic substitution.
11.4 Rule of the Geometric Mean: Isotope Effects on Isotope Effects
Illustration showing how variational transition state theory allows for different bottleneck structures for H and D transfer.
Figure 11.10.
11.4.3
RGM Breakdown as Evidence for Tunneling
The RGM breakdown seen for the glutamate dehydrogenase reaction (Fig. 11.7) was interpreted by Srinivasan and Fisher [53] as evidence for tunneling. Intrinsic nonadditivity had been ruled out based on earlier vibrational analysis calculations for related systems [56, 85]. The same vibrational-analysis studies [56, 85] used truncated Bell tunneling corrections to predict that RGM breakdowns could occur when both isotopic sites in Fig. 11.7 were moving together in the same reaction coordinate. The effective mass for the tunneling motion becomes sensitive to isotopic substitution at both sites giving tunneling terms Eq. (11.7) that are different for the HH, HD, and DD isotopomers. When only one isotopic site has significant reaction-coordinate motion, there is no RGM breakdown. The vibrational analysis calculations predicted that substitution of protium for deuterium could decrease the primary H/D isotope HD ¼ 1:14 measured by Srinivasan effect by about 10%, in good agreement with gHD and Fisher [53]. Other early reports of isotope effects on isotope effects in related systems include values of 1.13 and 1.09 for nonenzymic model hydride-transfer reactions [86] and 1.15 for the reaction catalyzed by yeast formate dehydrogenase [87]. The RGM studies in multiple proton transfers also provide valuable insights into tunneling processes [73–76, 80–82, 88].
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Cui et al. found an RGM breakdown in their computational study of alcohol dehydrogenase of when tunneling was included, but no breakdown when tunneling was omitted from the calculation. They found for the primary hydrogen isotope efHD ¼ 1:10 at 300 K and attributed it to the coupled motion of the secondary fect, gDT and primary hydrogen sites along the reaction path.
11.5
Saunders’ Exponents: Mixed Multiple Isotope Probes
In 1985, Saunders [36] proposed a new type of isotope-effect experiment to detect tunneling that required using H, D, and T isotopes similar to a Swain–Schaad experiment, but with an additional site of isotopic substitution. The extra isotopic site was shown to be the key reason for the sensitivity to tunneling because it allowed for an RGM breakdown when the two isotopic atoms move together in a tunneling motion [37]. 11.5.1
Experimental Considerations
The exponents described by Saunders, sometimes called ‘‘mixed isotopic expoDD describes the relationship nents’’, are shown in Eq. (11.17). The exponent rDT between the H/T isotope effect from substitution at site one (determined when protium is at site two), and the site-one D/T isotope effect (determined when deuterium is at site two). If the two sites are distinguished as giving primary and secondary isotope effects, the first exponent in Eq. (11.17) resembles the single-site Swain–Schaad exponent rDT Eq. (11.9) for a primary isotope effect, and the second exponent in Eq. (11.17) resembles a single-site secondary Swain–Schaad exponent. However, the mixed isotopic exponents necessarily involve isotopic substitution at two sites and should not be confused with single-site Swain–Schaad exponents. DD
H D D rDT =k H kH T ¼ ðkD =k T Þ
DT
T kHH =kH ¼ ðkDD =kDT Þ rDD
ð11:17Þ
One reason Saunders proposed using the set of isotopomers presented in Eq. (11.17) was for synthetic considerations. For reactants with two hydrogenic sites attached to the same atom, it is typically much simpler to prepare the DD isotopomer than it is to synthesize a compound with high abundance D in an HD compound. The HT and DT isotopomers are generally easier to prepare because the tritium is at tracer levels. Figure 11.11 shows an example [89] of the labeled reactants needed for an experiment. 11.5.2
Separating Swain–Schaad and RGM Effects
The Swain–Schaad and RGM components of mixed isotopic exponents can be readily identified by first defining relevant isotope effects on isotope effects [37].
11.5 Saunders’ Exponents: Mixed Multiple Isotope Probes
Example of competitive experiments used by Saunders et al. [89, 97] to measure isotope effects for mixed-isotope exponent determinations. The primary and secondary isotope effects were determined using the starting tritium activities of the bromide substrate, the product styrene, and the solvent ethanol, all at a known fractional
extent of reaction [21]. In double-tracer-label experiments like those used by Cha et al. [90] to study a reaction catalyzed by yeast alcohol dehydrogenase, 14 C is included in a remote site (the aromatic ring) to monitor the reaction rates for CD2 or CH2 substrates while simultaneously using tritium to monitor reaction rates for the CHT or CDT substrates.
Figure 11.11.
Equation (11.18) shows g1 as the ratio of primary D/T isotope effects when the secondary site is either H or D, and g2 as the corresponding H/D isotope effect on a secondary D/T effect. It is also convenient to define the RGM effect in an alternate way using the exponents g1 and g2 , as in Eq. (11.19). DH g1 ¼ gDT ¼
kDH =k H T kDD =k D T
DH g1 ¼ gDT ¼
lnðkDH =k H TÞ lnðkDD =k D TÞ
DT g2 ¼ gDH ¼
T kHD =kH kDD =kDT
DT g2 ¼ gDH ¼
T lnðkHD =kH Þ lnðkDD =kDT Þ
ð11:18Þ ð11:19Þ
With these definitions, a mixed isotopic exponent can be shown to be the product of an RGM exponent and a single-site Swain–Schaad exponent Eq. (11.20). As was noted in a previous section, single-site Swain–Schaad exponents tend to be close to rDT ¼ 3:3 (for rDH ¼ 1:44, Eq. (11.9)) even for reactions with substantial tunneling. When this is true, a mixed isotopic exponent greater than 3.3 can be explained by g, the RGM breakdown. And if the RGM breakdown is thought to arise from tunneling, a large mixed isotopic exponent further indicates that the effective tunneling mass is sensitive to both isotopic sites. DD ¼ rDT g1 m 1 ¼ rDT
DT m 2 ¼ rDD ¼ r DT g2
ð11:20Þ
Several experimental studies have shown that the secondary mixed exponents can be especially large. In cases where the single-site Swain–Schaad exponents
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ðr DT Þ are expected to be near 3.3, the relationships in Eq. (11.21) demonstrate the extra sensitivity of the secondary mixed isotopic exponents to RGM breakdowns. The RGM effect defined as a ratio of isotope effects tend to be similar in magniHD ). In the form of an exponent, however, tude for g1 and g2 (they are identical for gHD Eq. (11.21) shows that a large primary kD =k T isotope effect will diminish the effect of g1 on g1 . A smaller secondary D/T kinetic isotope effect will allow for a greater effect of a similarly valued g2 on g2 . g1 ¼ 1
lnðg1 Þ lnðkDH =k H TÞ
1
g2 ¼ 1
lnðg2 Þ D =k T Þ lnðkH H
1
ð11:21Þ
The results of Cha et al. [90] illustrate these tendencies. Their isotope effect HD results give an unexceptional primary mixed exponent, rDT ¼ 3:58 G 0:08, and a DT much larger secondary mixed exponent, rHD ¼ 10:2 G 2:0. These mixed exponents have been studied recently in several large-scale computational projects [14, 38, 47, 91]. Many other experimental studies [89, 92] involving mixed isotopic exponents are the subject of several reviews [93–96]. 11.5.3
Effects of Mechanistic Complexity on Mixed Isotopic Exponents
Efforts to test the influence of mechanistic complexity on the Saunders mixed isotopic exponents would be best approached by first considering the separate treatments presented above for single-site Swain–Schaad exponents and RGM effects according to Eqs. (11.11) and (11.12), (11.15) and (11.16), and (11.21). The net effect on mixed isotopic exponents can then be computed from the product according to Eq. (11.20). The resulting equations needed to explore the influence of either parallel or serial changes in rate-limiting steps will be simpler and the analysis more straightforward than any treatment that does not begin by separating the two components of a mixed isotopic exponent. The combined effects of mechanistic complexity on single-site Swain–Schaad exponents and RGM ratios should provide considerable modeling latitude in explaining the environmental or temperature influences on mixed isotopic exponents.
11.6
Concluding Remarks
Single-site Swain–Schaad exponents have not been found to be useful diagnostics for tunneling. Experimental results in systems thought to involve tunneling typically do not give single-site Swain–Schaad exponents that are outside the range of expected values for non-tunneling reactions, and computational studies have similarly failed to find good evidence for single-site H/D/T tunneling criteria. More work is needed to know if Swain–Schaad criteria could be established for reactions with extreme tunneling but, generally, the effects of H/D/T substitution on reac-
References
tion rates can arise from a comparatively global influence on vibrational frequencies. Special effects on tunneling coordinates are therefore difficult to distinguish as Lewis and Robinson [29] noted in their discussion of Eq. (11.10) many years ago. Reactions that involve the motions of two potential sites of isotopic substitution offer better opportunities for studies of tunneling through determinations of isotope effects on isotope effects (RGM tests). The influence of multiple mass sites on a reacting coordinate is somewhat special and can more directly report on tunneling. Mixed isotopic exponents include both Swain–Schaad exponents and RGM tests in a single experiment, and can therefore be expected to provide information related to tunneling if motions of two or more isotopic sites are significant in a tunneling coordinate. The RGM test within the mixed isotopic exponent is unfortunately clouded by the Swain–Schaad component of the experimental probe, particularly for secondary isotope effects. However, for laboratory work, the mixed isotopic probes often prove to give the best precision, and through comparisons with computational results, desired connections can be made between experimental findings and ideas about tunneling, catalysis, and reaction-rate theories. Finally, the effects of mechanistic complexity must be addressed in any study of tunneling, particularly for enzyme-catalyzed reactions. There is no simple way to avoid the complications from multiple rate-limiting steps – they may appear in rapid-mix experiments, relaxation kinetics, and steady-state turnovers. There is good reason to believe, however, that with sufficient numbers of isotopic probes, many interesting mechanistic details can be resolved.
References 1 R. P. Bell, D. M. Goodall. Proc. R.
2
3 4 5
6
7
8 9
Soc. (London) Ser. A, 1966, 294, 273–297. L. H. Funderburk, E. S. Lewis. J. Am. Chem. Soc., 1964, 86, 2531– 2532. E. S. Lewis, L. H. Funderburk. J. Am. Chem. Soc., 1967, 89, 2322–2327. R. P. Bell. Proc. R. Soc. (London) Ser. A, 1935, 148, 241–250. R. P. Bell, J. A. Fendley, J. R. Hulett. Proc. R. Soc. (London) Ser. A, 1956, 235, 453–468. R. P. Bell. The Tunnel Effect in Chemistry, Chapman Hall, London, 1980. M. Garcia-Viloca, J. Gao, M. Karplus, D. G. Truhlar. Science, 2004, 303, 186–195. J. Gao, D. G. Truhlar. Annu. Rev. Phys. Chem., 2002, 53, 467–505. D. G. Truhlar, J. Gao, C. Alhambra, M. Garcia-Viloca, J. C. Chorchado,
10 11 12 13
14
15
16 17
M. L. Sa´nchez, J. Villa`. Acc. Chem. Res., 2002, 35, 341–349. A. Warshel. Acc. Chem. Res., 2002, 35, 385–395. J. Villa`, A. Warshel. J. Phys. Chem. B, 2001, 33, 7887–7907. S. Hammes-Schiffer. Biochemistry, 2002, 41, 13335–13343. D. Antoniou, S. D. Schwartz. Proc. Natl. Acad. Sci, USA, 1997, 94, 12360–12365. G. Tresadern, P. F. Faulder, M. P. Gleeson, Z. Tai, G. MacKenzie, N. A. Burton, I. H. Hillier. Theor. Chem. Acc., 2003, 109, 108–107. D. G. Truhlar, B. C. Garrett, S. J. Klippenstein. J. Phys. Chem., 1996, 100, 12771–12800. J. Bigeleisen, M. Wolfsberg. Adv. Chem. Phys., 1958, 1, 15–76. A. Streitwieser, Jr., R. H. Jagow, R. C. Fahey, S. Suzuki. J. Am. Chem. Soc., 1958, 80, 2326–2332.
1307
1308
11 Multiple-isotope Probes of Hydrogen Tunneling 18 L. Melander. Isotope Effects on
19 20 21
22 23 24 25 26 27
28
29 30 31 32 33 34
35
36 37 38 39 40
Reaction Rates, Ronald Press Co., New York, 1960. F. H. Westheimer. J. Am. Chem. Soc., 1961, 1, 265–273. J. Bigeleisen. Pure Appl. Chem., 1964, 8, 217–213. L. Melander, W. H. Saunders, Jr. Reaction Rates of Isotopic Molecules, Wiley, New York, 1980. R. P. Bell. Trans. Faraday Soc., 1959, 55, 1–4. C. B. Grissom, C.-C. Hwang. J. Am. Chem. Soc., 1994, 116, 795–796. A. Thibblin, P. Alhberg. Chem. Soc. Rev., 1989, 18, 209–224. V. J. Shiner, Jr., M. L. Smith. J. Am. Chem. Soc., 1961, 83, 593–598. M. J. Stern, R. E. Weston, Jr. J. Chem. Phys., 1974, 60, 2808–2815. J. Basran, M. J. Sutcliffe, N. S. Scrutton. Biochemistry, 1999, 38, 3218–3222. L. Melander, W. H. Saunders, Jr. Reaction Rates of Isotopic Molecules, Wiley, New York, 1980, Ch. 10: Isotope Effects in Reactions with Complex Mechanisms. E. S. Lewis, J. K. Robinson. J. Am. Chem. Soc., 1968, 90, 4337–4344. R. A. More O’Ferrall, J. Kouba. J. Chem. Soc. B, 1967, pp. 985–990. M. J. Stern, R. E. Weston, Jr. J. Chem. Phys., 1974, 60, 2815–2821. Q. Cui, M. Karplus. J. Am. Chem. Soc., 2002, 124, 3093–3124. Y. Kim, M. M. Kreevoy. J. Am. Chem. Soc., 1992, 114, 7116–7123. C. G. Swain, E. C. Stivers, J. F. Reuwer, Jr., L. J. Schaad. J. Am. Chem. Soc., 1958, 80, 5885–5893. J. Bigeleisen. Tritium Phys. Biol. Sci., Proc. Symp., Vienna, Austria, 1962, 1, 161–168. W. H. Saunders, Jr. J. Am. Chem. Soc., 1985, 107, 167–169. W. P. Huskey. J. Phys. Org. Chem., 1991, 4, 361–366. Q. Cui, M. Eistner, M. Karplus. J. Phys. Chem. B, 2002, 106, 2721–2740. A. Kohen, J. H. Jensen. J. Am. Chem. Soc., 2002, 124, 3858–3864. J. R. Jones. Trans. Faraday Soc., 1969, 65, 2430–2437.
41 J. Braun, H.-H. Limbach, P. G.
42
43
44 45
46 47
48 49 50
51
52 53 54 55 56 57
58
Williams, H. Morimoto, D. E. Wemmer. J. Am. Chem. Soc., 1996, 118, 7231–7232. J. Braun, R. Schwesinger, P. G. Williams, H. Morimoto, D. E. Wemmer, H.-H. Limbach. J. Am. Chem. Soc., 1996, 118, 11101–11110. J. Braun, M. Schlabach, B. Wehrle, M. Ko¨cher, E. Vogel, H.-H. Limbach. J. Am. Chem. Soc., 1994, 116, 6593–6604. C. Eckart. Phys. Rev., 1930, 35, 1303–1309. C. S. Tautermann, M. J. Loferer, A. F. Voegele, K. R. Leidl. J. Chem. Phys., 2004, 120, 11650–11657. J. Hirschi, D. A. Singleton. J. Am. Chem. Soc., 2005, 127, 3294–3295. C. Alhambra, J. Corchado, M. L. Sa´nchez, M. Garcia-Viloca, J. Gao, D. G. Truhlar. J. Phys. Chem. B, 2001, 105, 11326–11340. D. B. Northrop. Bioorg. Chem., 1990, 18, 435–439. D. B. Northrop. Biochemistry, 1975, 14, 2644–2651. D. B. Northrop. in Istope Effects on Enzyme-Catalyzed Reactions, W. W. Cleland, M. H. O’Leary, D. B. Northrop (Eds), University Park Press, Baltimore, MD, 1977, pp. 122–152. I. M. Kovach, J. L. Hogg, T. Raben, K. Halbert, J. Rogers. J. Am. Chem. Soc., 1980, 102, 1991–1999. K. L. Grant, J. P. Klinman. Bioorg. Chem., 1992, 20, 1–7. R. Srinivasan, H. F. Fisher. J. Am. Chem. Soc., 1985, 107, 4301–4305. J. Bigeleisen. J. Chem. Phys., 1955, 23, 2264–2267. H. Fujihara, R. L. Schowen. Bioorg. Chem., 1985, 13, 57–61. W. P. Huskey, R. L. Schowen. J. Am. Chem. Soc., 1983, 105, 5704–5706. M. Amin, R. C. Price, W. H. Saunders, Jr. J. Am. Chem. Soc., 1988, 110, 4085–4086. E. K. Thornton, E. R. Thornton. in Isotope Effects in Chemical Reactios, C. J. Collins, N. S. Bowman (Eds), Van Nostrand Reinhold Co., New York, 1970, pp. 213–285.
References 59 A. J. Kresge. Pure Appl. Chem., 1964, 60
61 62
63 64 65
66
67
68 69
70
71
72
73 74 75
76
77
8, 243–258. K. B. Schowen, R. L. Schowen. Methods Enzymol. C, 1982, 87, 551–606. K. S. Venkatasubban, R. L. Schowen. Crit. Rev. Biochem., 1984, 17, 1–44. D. M. Quinn, L. D. Sutton. in Enzyme Mechanism from Isotope Effects, P. F. Cook (Ed), CRC Press, Boca Raton, 1991, pp. 73–126. J. L. Kurz, M. M. Nasr. J. Phys. Chem., 1989, 93, 937–942. M. Saunders, G. W. Cline. J. Am. Chem. Soc., 1990, 112, 3955–3963. R. L. Schowen. in Transition States of Biochemical Processes, R. Gandour, R. L. Schowen (Eds), Plenum Press, New York, 1978, pp. 77–114. J. D Hermes, C. A. Roeske, M. H. O’Leary, W. W. Cleland. Biochemistry, 1982, 21, 5106–5114. P. M. Weiss, S. R. Gavva, B. G. Harris, J. L. Urbauer, W. W. Cleland, P. F. Cook. Biochemistry, 1991, 30, 5755–5763. W. E. Karsten, P. F. Cook. Biochemistry, 1994, 33, 2096–2103. W. E. Karsten, S. R. Gavva, S.-H. Park, P. F. Cook. Biochemistry, 1995, 34, 3253–3260. W. A. Edens, J. L. Urbauer, W. W. Cleland. Biochemistry, 1997, 36, 1141–1147. J. G. Belasco, W. J. Albery, J. T. Knowles. J. Am. Chem. Soc., 1983, 105, 2475–2477. J. G. Belasco, W. J. Albery, J. T. Knowles. J. Am. Chem. Soc., 1983, 105, 6195. G. Scherer, H.-H. Limbach. J. Am. Chem. Soc., 1989, 111, 5946–5947. H. Rumpel, H.-H. Limbach. J. Am. Chem. Soc., 1989, 111, 5429–5441. M. Schlabach, G. Scherer, H.-H. Limbach. J. Am. Chem. Soc., 1991, 113, 3550–3558. H.-H. Limbach, G. Scherer, M. Maurer, B. Chaudret. Ber. Bunsenges. Phys. Chem., 1992, 96, 821–833. M. Schlabach, H.-H. Limbach, E. Bunnenberg, A. Y. L. Shu, B.-R. Tolf, Carl Djerassi. J. Am. Chem. Soc., 1993, 115, 4554–4565.
78 H.-H. Limbach, O. Klein, J. M. Lopez
79 80 81 82
83
84
85 86
87
88
89
90 91
92
93 94 95 96 97
Del Amo, J. Elguero. Z. Phys. Chem., 2003, 217, 17–49. G. Scherer, H.-H. Limbach. J. Am. Chem. Soc., 1994, 116, 1230–1239. D. Gerritzen, H.-H. Limbach. J. Am. Chem. Soc., 1984, 106, 869–879. L. Meschede, H.-H. Limbach. J. Phys. Chem., 1991, 95, 10267–10280. O. Klein, F. Aguilar-Parrilla, J. M. Lopez, N. Jagerovic, J. Elguero, H.-H. Limbach. J. Am. Chem. Soc., 2004, 126, 11718–11732. D.-H. Lu, D. Maurice, D. G. Truhlar. J. Am. Chem. Soc., 1990, 112, 6206–6214. B. C. Garrett, D. G. Truhlar, A. F. Wagner, T. H. Dunning, Jr. J. Chem. Phys., 1983, 78, 4400–4413. W. H. Saunders, Jr. J. Am. Chem. Soc., 1984, 106, 2223–2224. M. G. Ostavic´, M. G. Roberts, M. M. Kreevoy. J. Am. Chem. Soc., 1983, 105, 7629–7631. J. D. Hermes, S. W. Morrical, M. H. O’Leary, W. W. Cleland. Biochemistry, 1984, 23, 5479–5488. H.-H. Limbach, J. Hennig, D. Gerritzen, H. Rumpel. Faraday Discuss. Chem. Soc., 1982, 74, 229– 243. M. Amin, R. C. Price, W. H. Saunders, Jr. J. Am. Chem. Soc., 1990, 112, 4467–4471. Y. Cha, C. Murray, J. P. Klinman. Science, 1989, 243, 1325–1330. C. Alhambra, J. C. Corchado, M. L. Sa´nchez, J. Gao, D. G. Truhlar. J. Am. Chem. Soc., 2000, 122, 8197– 8203. W. E. Karsten, C.-C. Hwuang, P. F. Cook. Biochemistry, 1999, 38, 4398– 4402. J. P. Klinman. Pure Appl. Chem., 2003, 75, 601–608. A. Kohen. Progr. React. Kinet. Mech., 2003, 28, 119–156. A. Kohen, J. P. Klinman. Chem. Biol., 1999, 6, R191–198. A. Kohen, J. P. Klinman. Acc. Chem. Res., 1998, 31, 397–404. Rm. Subramanian, W. H. Saunders, Jr. J. Am. Chem. Soc., 1984, 106, 7887–7890.
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Current Issues in Enzymatic Hydrogen Transfer from Carbon: Tunneling and Coupled Motion from Kinetic Isotope Effect Studies Amnon Kohen 12.1
Introduction 12.1.1
Enzymatic H-transfer – Open Questions
Enzymes are the catalysts that direct, control and enhance chemical transformations in biological systems. Enzymes evolved to accomplish two almost contradictory tasks: (i) to catalyze a reaction at a rate most suitable for organism function and (ii) to prevent alternative side-processes that would commonly occur in nonenzymatic reactions. In other words, an enzyme not only catalyzes the reaction of interest, it also inhibits side reactions and the formation of by-products. Commonly, the first effect is denoted as catalysis and the second is denoted as specificity. The rate enhancement is often many orders of magnitude greater than the reaction in solution. How enzymes achieve this rate acceleration is a matter of great interest to both chemists and biologists. Different investigators have addressed this question using the tools available to them, sometimes leading to diverse, though not necessarily contradictory, suggestions. The question of whether physical phenomena such as ‘‘dynamics’’ or ‘‘quantum mechanical hydrogen tunneling’’ contribute to enzyme catalysis is one of the ‘‘hottest’’ and most controversial questions in enzymology today. In this chapter I will attempt to present theoretical and experimental approaches to this question. More importantly, I will try to suggest that in many cases the different views result from different definitions rather than from contradictory physical mechanisms. By way of introduction I will demonstrate this point for a basic, ‘‘old’’, example. The general notion entitled ‘‘induced fit’’ [1, 2] implies that the enzyme’s active site acts like a molecular laboratory in which the reactants (substrates) are first recognized during the binding process, and then both the enzyme and the substrate undergo conformational rearrangement. This leads to a substrate conformation that is closer to the desired transition state. This view leads to the generally accepted understanding of the role of transition state stabilization, since the free energy of the whole system is (by definition, as discussed below under Catalysis) Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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12 Current Issues in Enzymatic Hydrogen Transfer from Carbon
lower than that of the slower uncatalyzed reaction. Nevertheless, this has also led to the misconception of ‘‘ground state destabilization’’ [3, 4]. This term was coined since, in a two state system (ground and transition states), either stabilizing the transition state or destabilizing the ground state would have a catalytic effect (lowering the free energy of activation, DGz ). Upon binding and rearrangement, the substrate molecule may indeed adopt a conformation that would be less stable in solution, yet the free energy of the whole system ðDGz Þ is commonly lower in its bound-ground-state than in the free state, only the reactant is now in a distorted conformation that would be considered ‘‘destabilized’’ in solution.1) The reason why this is still a matter of controversy today is, in part, due to the different definitions used by different researchers [5–7]. In this chapter I attempt to distinguish between models that differ due to substantially different physical mechanisms from those that merely use different terminology. Consequently, the following section on terminology and definitions precedes the description of the mechanistic models and experimental examples. 12.1.2
Terminology and Definitions Catalysis Catalysis or ‘‘Catalytic Power’’ is the ratio between the reaction rate of the catalyzed reaction and that of the uncatalyzed reaction. It is defined as kcat =k un where kcat is the rate of the catalyzed reaction and k un is the rate of the uncatalyzed reaction. By definition, catalysis should be unit-less (a ratio of rate constants), thus care must be practised while determining ‘‘Catalytic Power’’ that kcat and k un have the same units. Alternatively, the second order uncatalyzed reaction’s rate (M1 s1 units) can be divided by kcat (s1 ) and the ratio then has units of concentration (M). This concentration is called ‘‘effective concentration’’ [2] and could be addressed as the concentration of functional groups or substrates in the enzyme’s active site. Since that effective concentration is often in the thousands of M range, it is not a physically meaningful concentration, but rather a manifestation of the role of correct orientation, dynamic, and other catalytic effects induced by the enzyme. A similar approach used the substrate concentration in which the enzymatic and uncatalyzed rates are equal as an indicator for catalytic power [8]. The advantage of the first 12.1.2.1
1) The binding process is a second order event
and the relative energies of the free and bound states are concentration dependent. Substrate concentration is reciprocal to the stability of the free state. At a low substrate concentration (kcat =kM conditions as defined below) the bound state is less stable than the free state but its stabilization or destabilization has no catalytic effect as the barrier for the reaction is now the difference between the free state and the transition state. At high substrate concentration the bound state is
more stable than the free state (lower free energy). The bound reactant may be ‘‘locally’’ distorted to a ‘‘locally’’ less stable conformation (one that would be less stable without the enzyme) but the whole complex is more stable than the free enzyme and substrate in solution. Destabilizing the bound state will have a catalytic effect only under these conditions ðVmax Þ, but most enzymes did not evolve under Vmax conditions (substrate concentration is rarely higher than kM ).
12.1 Introduction
Figure 12.1. An example of ground-state nuclear tunneling. The reactant well (R) is on the left and the product well (P) is on the right. The fine lines represent the probability (nuclear
c 2 ) of finding the nuclei in the reactant or the product wells. More overlap between the probability functions of the R and P results in higher tunneling probability.
approach is that the unit-less ratio of rates can be directly converted into the reduction of energy of activation ðDGz Þ induced by the enzyme, which is the most meaningful physical parameter. Enzyme catalysis can be studied from various points of view: regulation, structural aspects, order of reactant binding and product release, the role of functional residues (e.g., general bases or acids), etc. This chapter presents the use of kinetic isotope effects (KIEs) as tools for studying the physical nature of enzyme catalyzed CaH bond activation. Tunneling Quantum mechanical tunneling is the phenomenon by which a particle transfers through a reaction barrier by means of its wave-like properties [9]. Figure 12.1 illustrates this phenomenon graphically for a symmetric double well system such as the CaHaC hydrogen transfer. It is important to note that the tunneling probability is affected by both the distance between the R and the P wells and their symmetry. A lighter isotope has a higher tunneling probability than a heavier one, since a heavy isotope has a lower zero point energy and its probability function is more localized in its well. Consequently, kinetic isotope effects (KIEs) are effective tools for studying tunneling. Two practical applications are described in Section 12.3): the Swain–Schaad exponential relationship and the temperature dependence of KIEs. 12.1.2.2
Dynamics The definition of dynamics and their possible contribution to enzyme catalysis has been a matter of debate in recent years [10–13]. In a couple of recent reviews in Science, two groups of prominent researchers appear to disagree on the definition of dynamics [14, 15]. Ref. [15] and several textbooks of physical chemistry prefer the definition that ‘‘dynamics is any time dependent process’’. Any motion in a given system can be considered a dynamic process regardless of whether or not it 12.1.2.3
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12 Current Issues in Enzymatic Hydrogen Transfer from Carbon
is in thermal equilibrium with the environment (Boltzman distribution of states). On the other hand, other researchers, e.g., Benkovic, Hammes-Schiffer, Warshel and others, use the term dynamics only in cases of nonequilibrium motions [5, 11, 14, 16]. The reason is probably that motions that are in thermal equilibrium with the environment have no ‘‘interesting’’ dynamic contribution because these are already accounted for in transition state theory. According to these researchers, ‘‘dynamics’’ are only ‘‘nonstatistical’’ modes, namely motion along a coordinate that is not in thermal equilibrium. Direct contribution of such modes to the reaction is depicted as a non-RRKM system. Non-RRKM systems are indeed rare and so far have only been demonstrated in the gas phase [17, 18]. Consequently, such systems will not be discussed in this chapter as I intend to focus on biologically relevant systems in the condensed phase. Coupling and Coupled Motion These terms are also used extensively, and often loosely, in studies of enzyme catalysis. In mechanistic enzymology the term coupling is commonly used to describe two different phenomena: first, the transferred hydrogen is coupled to another hydrogen bound to the donor or acceptor heavy atom (primary–secondary coupled motion, Section 12.3.3). Second, the tunneling of the transferred hydrogen is coupled to the enzymatic environment (environmentally coupled tunneling, tunneling promoting vibrations, vibrationally enhanced tunneling and other terms are discussed in Section 10.4.1). A more general definition of physical coupling would be: two coordinates, for which a change in one coordinate affects the potential energy of the other are coupled to each other.2) This definition is vague because if the two modes of motion are orthogonal, they are not coupled and if they are coupled they do not establish two clearly separable modes. Indeed, if two modes in the same system are fully coherent (the ultimate coupling) they should be redefined as two new modes that result from the mixing of the two original modes. A simple resolution for this enigma is that the energy flow from one mode to the other is slower than the rate of excitation of that mode. For example, the infrared (IR) spectrum of a molecule reflects the different vibrational modes in that molecule. If one irradiates the molecule with a short IR pulse (<100 fs), at the frequency of one of its vibrational modes, then only this mode will be vibrationally excited at first. Within a few ps that vibrational energy will equilibrate among all the normal modes in the system. The energy dissipates due to coupling between the originally excited mode and the other modes in the system. The hydroxyl and the aldehyde of hexan-6-ol-1-al for example, are separated by six bonds and their IR absorbance peaks are separated by 1600 cm1 . Yet irradiation of the OH at 3300 cm1 will quickly lead to more excited carbonyl modes as the vibrational energy dissipates through the molecule via mode–mode coupling. 12.1.2.4
2) From the mathematical point of view,
coupling may be defined as mixing between two states (motion along two coordinates).
Coupling matrix elements will be proportional to the second derivative of the potential energy with respect to both coordinates.
12.1 Introduction
An example most relevant to the case studies presented in Section 3.3, is the coupling between two hydrogens bound to the same carbon. If the cleaving of one of them is directly affected by changes in the other they are considered coupled. The stretching mode of one (that is converted into translation at the cleavage event) is coupled to vibrational modes of the other, not only in the ground state but also in the TS. Alternatively, one can view these hydrogens as part of the same normal mode throughout. The antisymmetric stretch of the CH2 system is converted to translation of one of the hydrogens due to greater unharmonicity on one side of that vibration (induced by the environment and the acceptor if present). In such a case, the two hydrogens contribute equally to the same mode in the ground state but have unequal contributions in the transition state. However, both affect the reaction coordinate and the overall effect is commonly denoted as ‘‘coupled motion’’ (see Section 3.3). Kinetic Isotope Effects (KIEs) The KIE is the ratio of rates between two isotopolog reactants (molecules that only differ in their isotopic composition). For H-transfer reactions, this ratio of rates between light and heavy isotopes is characteristic of the reaction coordinate and the nature of the transition state (TS). The hydrogen KIE is particularly useful since the mass ratio of its isotopes is much larger than that of any other element, resulting in relatively large KIEs [19]. The KIE results from energy of activation differences for the different isotopolog reactants, and much of its magnitude is due to the differences in zero point energy (ZPE) between the ground state and the TS of the reaction [20–22]: 12.1.2.5
z
z
kH =kD A eðDGD DGH Þ=RT
ð12:1Þ
z þ ZPEHR , R is the gas constant and T where DGzD DGzH A ZPEDz ZPEDR ZPEH is the absolute temperature. Two other factors that contribute to the KIE to a lesser extent are the moment of inertia (MMI) and the effect of excitation (EXC). The Bigeleisen equation expresses the combined effects as KIE ¼ ZPE MMI EXC [19–21]. Other types of isotope effects, such as magnetic isotope effects are less relevant to enzymology and are not discussed in this chapter. The primary (1 ) KIE is the KIE measured for a bond cleavage or formation that is isotopically substituted on one of the bound atoms. The secondary (2 ) KIE is the KIE measured with isotopologs that are labeled on a position other than the one that is being cleaved. 2 KIEs result from a change in bonding force constants and vibrational frequencies during the reaction (e.g., s (s-sp 3 ) at the GS to s (ssp 2 ) at the TS). Equilibrium isotope effects (EIEs) are the fractionation of isotopes between stable states, namely, the different ratio between isotopes that are at equilibrium between two systems. 2 KIEs are normally smaller than or equal to the reaction’s 2 EIEs. The 2 EIE, results from the change in bond order from reactants to products, while the KIE is only affected by the change from the GS to the TS.
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12 Current Issues in Enzymatic Hydrogen Transfer from Carbon
Figure 12.2. A reaction energy profile for enzyme catalyzed A þ B ! Q þ P reaction. The chemical step is marked and the rate-limiting step is product Q release. The portions of this
reaction profile that are included in three common experimental rate constants (kcat , K cat =KM , and kPSS , for pre-steady-state rate) are marked.
12.2
The H-transfer Step in Enzyme Catalysis3)
Many experimental and theoretical studies have attempted to assess the specific contributions of physical phenomena to enzymatic rate enhancement. These contributions include: the relationship between the reactive complex’s structure and function; the location and structure of the transition state (TS) along the reaction coordinate; TS stabilization; ground state (GS) destabilization; the significance of quantum mechanical (QM) phenomena; the dynamics of the system; energy distribution through the normal modes of an enzyme; and contributions of entropy and enthalpy. KIEs are one of the most useful parameters that can provide direct information regarding the nature of the H-transfer and its potential surface. However, a major limitation in measuring the KIE on the H-transfer step, or on any other chemical transformation, is that the H-transfer step is rarely the rate limiting step of an enzymatic reaction. Figure 12.2 illustrates a minimal reaction profile for a bisubstrate, bi-product reaction. The kinetic steps included in common rate constants (kcat , kcat =KM , and pre-steady-state rate kPSS ) are marked. It is obvious that none of these kinetic rates represent solely the H-transfer (chemical) step. Conse-
3) All the examples and discussions presented
below are for CaH bond activation. Some of these discussions and models may not be
directly applicable to OaH activation and some other H-transfer phenomena.
12.2 The H-transfer Step in Enzyme Catalysis
quently, conducting measurement that will shed light on that step and will thus be relevant to molecular models and calculations is inherently challenging. In the investigation of KIEs and their temperature dependence in enzymatic systems (or any other kinetically complex system), explicit care must be exercised with regard to the following issues: 1. Is the KIE measured on a single kinetic step (e.g., internal KIE) or on a kinetically complex rate constant (e.g., kcat =KM or kcat )? 2. Is there an isotope effect on steps other than the one under investigation (e.g., substrate binding)? 3. What is the effect of kinetic steps that are not isotopically sensitive but still mask the isotope effect (e.g., substrate dissociation)? 4. Are the KIEs measured for the same rate constant throughout the whole temperature range (e.g., temperature dependent binding constants may change measurements under substrate saturation to nonsaturated measurements)? 5. Are all the experimental conditions (e.g., pH, ionic strength) consistent at all temperatures (e.g., temperature dependence of the buffer’s K a )? The first three points are related to ‘kinetic complexity’, which reflects the fact that the observed KIE ðKIEobs Þ is often smaller than the intrinsic KIE ðKIE int: Þ. This is due to the ratio between the isotopically sensitive step and the isotopically nonsensitive steps that lead to the decomposition of the same reactive complex. Its mathematical treatment is rigorously described in several published reviews [23, 24] and Chapter 10 (Knapp et al.) in this volume.
KIEobs ¼
KIE int þ C f þ C r EIE 1 þ Cf þ Cr
ð12:2Þ
where EIE is the equilibrium isotope effect and C f and C r are the forward and reverse commitments to catalysis, respectively. C f is the ratio between the rate of the isotopically sensitive step forward (e.g., kH-transfer ) and the rates of the preceding isotopically nonsensitive steps backward. C r is the ratio between the rate of the isotopically sensitive step backward and the rates of the succeeding isotopically nonsensitive steps forward. Techniques that allow estimation of the intrinsic effect from the observed one are discussed below (Section 3.2). The importance of the intrinsic KIE is that it imposes a strict constraint on any mechanism, theoretical model, analysis, or simulation addressing the chemical transformation under study. As described in the following section, intrinsic KIEs are unique as they are directly affected by the reaction potential surface and other physical features. In contrast to the KIEobs , KIE int can be compared to theoretical calculations, which commonly only reflect an effect on a single step. The following section presents several approaches towards studies of the H-transfer step in kinetically complex systems.
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12 Current Issues in Enzymatic Hydrogen Transfer from Carbon
12.3
Probing H-transfer in Complex Systems 12.3.1
The Swain–Schaad Relationship The Semiclassical Relationship of Reaction Rates of H, D and T Semiclassical in this context means that some quantum mechanical effects are taken into consideration (e.g., zero-point-energy: ZPE) but others are ignored (e.g., tunneling). When the main origin of KIEs is the differences between the isotopes’ ZPEs in the ground state (GS) and transition state (TS), the kinetic relationship between the three isotopes of hydrogen can be predicted [19, 25] and is depicted as the Swain–Schaad relationship. This relationship has wide usage as a mechanistic tool in organic and physical chemistry. The Swain–Schaad exponential relationship (EXP, as defined in Eqs. (12.3)–(12.5) is the semiclassical (no tunneling) correlation between the rates of the three isotopes of hydrogen, and was first defined by Swain et al. in 1958 [25]. This relationship can be predicted using the masses (or reduced masses) of the isotopes under examination [19]. Since H has a higher GS ZPE than D and T, it reacts faster than D and T (Fig. 12.3). The Swain– Schaad exponential relationship was originally defined for primary (1 ) KIEs [25]: 12.3.1.1
EXP kH kH ¼ kT kD
or
EXP ¼
lnðkH =k T Þ lnðkH =kD Þ
Figure 12.3. Different energies of activation (DEa ) for H, D, and T resulting from their different zero-point energies (ZPE) in the ground state (GS) and transition state (TS). The GS-ZPE is constituted by all degrees of
ð12:3Þ
freedom but mostly by the CaH stretching frequency, and the TS-ZPE is constituted by all degrees of freedom orthogonal to the reaction coordinate. This type of consideration is depicted as ‘‘semiclassical’’.
12.3 Probing H-transfer in Complex Systems
where k i is the reaction rate constant for isotope i. EXP can be calculated from [19]: EXP ¼
pffiffiffiffiffiffi pffiffiffiffiffi lnðkH =k T Þ 1= mH 1= mT ¼ pffiffiffiffiffiffi pffiffiffiffiffiffi lnðkH =kD Þ 1= mH 1= mD
ð12:4Þ
where mi is the reduced mass affecting the ZPE of isotope i. The original EXP was calculated for H/T vs. H/D KIEs and yielded a value of 1.44 (using atomic masses). Some labeling patterns use T as a frame of reference which is compared to H and D. Their EXP follows: EXP ¼
pffiffiffiffiffiffi pffiffiffiffiffi lnðkH =k T Þ 1= mH 1= mT ¼ pffiffiffiffiffiffi pffiffiffiffiffi lnðkD =k T Þ 1= mD 1= mT
ð12:5Þ
Equation (12.5) defines the relationship of H/T to D/T KIEs, for which the semiclassical EXP is 3.26 (for atomic masses: mi ¼ mi ). Several investigators examined this relationship under extreme temperatures (20–1000 K), and as a probe for tunneling [26–28]. This isotopic relationship was also used in experimental and theoretical studies to suggest coupled motion between primary and secondary hydrogens for hydride transfer reactions, such as elimination in the gas phase, and in organic solvents [29, 30]. The power of the Swain–Schaad relationship is that it appears independent of the details of the reaction’s potential surface and thus can be used to relate unknown KIEs (see Section 12.3.2). Effects of Tunneling and Kinetic Complexity on EXP Two features that might affect the observed Swain–Schaad relationship are kinetic complexity and tunneling. The first would make the fast H-transfer appear slower and would have a smaller such effect on D and T, which are more rate limiting in the first place. As a result EXP ¼ lnðH=TÞ=lnðD=TÞ will appear smaller and EXP ¼ lnðH=TÞ=lnðH=DÞ will appear larger than anticipated [26–28]. Tunneling, on the other hand, will make H-transfer even faster relative to D and T than predicted from ZPE considerations. This will have the opposite effect, namely EXP ¼ lnðH=TÞ=lnðD=TÞ will appear larger and EXP ¼ lnðH=TÞ=lnðH=DÞ will appear smaller than anticipated. Many researchers have suggested that this phenomenon can serve as an indicator for tunneling [19, 31–34]. Recently, three theoretically calculated phenomenological effects on 1 EXP using small molecular systems in the gas phase suggested that tunneling and kinetic complexity may have the same trend. Two of these calculations used a simple, linear double OaHaO transfer in formic acid [35] or a 2-dimensional linear CaHaC transfer (Zorka Smedarchina, personal communication). These calculations assumed parabolic reactant and product ground states, and calculated H-transfer rates while considering the CaH stretch and a symmetric vibration between these two states as two orthogonal modes (full tunneling model). Within this confined model the difference in rates between H and the heavier isotopes was smaller 12.3.1.2
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12 Current Issues in Enzymatic Hydrogen Transfer from Carbon
than that predicted from the difference between their ZPEs. Consequently, the Swain–Schaad EXP for lnðH=TÞ=lnðH=DÞ was predicted to be larger than the semiclassical limit (up to 1.58) and the EXP for lnðH=TÞ=lnðD=TÞ was smaller (down to 2.30). Since this trend is the same as that predicted from kinetic complexity, such a prediction could not be used to analyze experimental data. A somewhat more rigorous third study was conducted by Kiffer and Hynes [22, 36] and their conclusion was that, close to ambient temperature, the Swain–Schaad 1 EXP, range from 3 to 4. A recent study of 2 EXP [37] tested many 2 EIEs and 2 KIEs and concluded that for significant 2 KIEs (>1.1) inflated 2 EXP (>4.5) is an indication for tunneling (see more discussion below). In the future, this issue should be further explored to find more realistic models in the condensed phase. Two common uses of the Swain–Schaad relationship in enzymology are described in the following sections. 12.3.2
Primary Swain–Schaad Relationship Intrinsic Primary KIEs Both measurements (Eqs. (12.4) and (12.5)) establish the relationship between the three isotopes for a one-step reaction (single barrier). Intrinsically, these relationships are almost independent of the shape of the reaction potential surface [19]. If the chemical step is masked by kinetic complexity (Eq. (12.2)), the observed KIE ðKIEobs Þ will be smaller than the intrinsic one. In the case of Eq. (12.5), this will affect H/T KIE more than D/T KIE and the observed EXP will be smaller than the intrinsic one. For the experiment pertinent to Eq. (12.4), such kinetic complexity will have the opposite effect and the observed EXP will be larger than the intrinsic one. In the case of H-tunneling, a simple tunneling correction to TST (the Bell correction) [19, 32] predicts that the EXP of Eq. (12.4) will not be affected significantly. On the other hand, that of Eq. (12.5) will be inflated (larger than 3.3) for moderate tunneling and will decrease back to values close to 3.3 in the case of extensive tunneling [38]. As mentioned above, some recent calculations of two-dimensional systems have suggested the opposite trend but the relevance of these preliminary studies to H-transfer in the condensed phase is not clear (Ref. [35] and Zorka Smedarchina, personal communication). It is important to note that for 1 KIEs and the resulting 1 Swain–Schaad exponents, no EXP values larger than 3.6 are found in the literature. Even in cases in which tunneling was evident from mixed labeling experiments (Section 12.3.3) or from the temperature dependence of KIEs (Section 12.3.4), the 1 EXP did not significantly differ from the semiclassically predicted value of 3.3 for lnðkH =k T Þ=lnðkD =k T Þ or 1.4 for lnðkH =k T Þ=lnðkH =kD Þ. This observation suggests that the Swain–Schaad EXP can be used to reduce the number of unknowns in the comparison of observed KIEs to an equation with one unknown (an intrinsic KIE). Northrop [24, 39] developed a simple method for calculating the commitment to catalysis and the intrinsic KIE from the observed KIEs. This method assumes no significant deviation of the intrinsic 1 KIEs from their semiclassically predicted 12.3.2.1
12.3 Probing H-transfer in Complex Systems
values. By analogy to the method described by Northrop [24, 39], Eq. (12.3) can be written again while subtracting 1 from both sides of the equation:
kH kT
obs
1¼
ðkH =k T Þint þ C f þ C r EIE 1 1 þ Cf þ Cr
¼
ðkH =k T Þint þ C f þ C r EIE 1 C f C r 1 þ Cf þ Cr
¼
ðkH =k T Þint 1 þ C r ðEIE 1Þ 1 þ Cf þ Cr
ð12:6Þ
At the limit of the H/T EIE goes to 1, which is not a bad assumption for 1 EIE, Eq. (12.6) becomes:
kH kT
obs
1¼
ðkH =k T Þint 1 1 þ Cf þ Cr
ð12:7Þ
Now, Eq. (12.7) for H/T KIE is divided by the same equation for the H/D KIE. Since no isotopic rate constant appears in the denominator, this will cancel leaving the ratio of KIEint 1 on the right-hand side: ðkH =k T Þobs 1 ðkH =k T Þint 1 ¼ ðkH =kD Þobs 1 ðkH =kD Þint 1
ð12:8Þ
From Eq. (12.5): ðkH =kD Þint ¼ ððkH =k T Þint Þ 1=1:44
ð12:9Þ
And Eq. (12.8) can be rewritten as: ðkH =k T Þobs 1 ðkH =k T Þint 1 ¼ ðkH =kD Þobs 1 ððkH =k T Þint Þ 1=1:44 1
ð12:10Þ
Even though Eq. (12.10) (and equivalent equations for other KIE experiments) has only one unknown ðKIEint Þ, it cannot be solved analytically (due to transcendental functions). After dividing the observed KIEs minus one by each other, a numeric solution can be obtained.4),5) 4) In the original works of Northrop [24, 39],
tables for various KIE experiments offer solutions for a wide range of KIEs. Today this can be calculated with most calculators or any computer. 5) In cases where the chemical step is reversible and the assumption of a small 1 EIE is not
valid a solution is not possible without measuring the reverse commitment ðC r Þ. In this instance, Cleland [40] has identified a range for the KIEint values between the observed KIE ðKIEobs Þ and the product of EIE and KIEobs for the reverse reaction ðKIEobs-rev EIEÞ.
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12 Current Issues in Enzymatic Hydrogen Transfer from Carbon
12.3.2.2
Experimental Examples Using Intrinsic Primary KIEs
Peptidylglycine a-Hydroxylating Monooxygenase (PHM) PHM initiates the oxidative cleavage of C-terminal, glycine-extended peptides by H abstraction from the a-carbon of glycine. In the PHM reaction, substrate binding and product release contribute significantly to rate limitation under the conditions of steady-state turnover [41]. Francisco et al. [42] studied PHM using H/T and H/D competitive KIEs. The observed KIEs increased with temperature, but the intrinsic KIEs, calculated using the Northrop method, were all close to 10. These intrinsic KIEs exhibited a very small temperature dependence, leading to AH =AD of 5:9 G 3:2. This, together with a large energy of activation (Ea @ 13 kcal mol1 ) suggested ‘‘environmentally enhanced tunneling’’ [42]. This model is described in more detail in Chapter 10 Section 10.5.3.2). Dihydrofolate Reductase (DFHR) DHFR catalyzes the stereospecific reduction of 7,8-dihydrofolate (H2 F) to 5,6,7,8-tetrahydrofolate (H4 F), using nicotinamide adenine dinucleotide phosphate (NADPH) as the hydride donor. Specifically, the pro-R hydride is transferred from the C-4 of NADPH to C-6 of H2 F. The complete kinetic scheme for DHFR is complex and the H-transfer step is partly rate determining only at high a pH [43]. Pre-steady state stopped flow measurements resulted in H/D KIE between 2.8 and 3.0 [44]. In a recent study we measured H/T and D/T competitive KIEs and calculated an intrinsic H/D KIE of 3:5 G 0:2 [45]. This KIE is in excellent agreement with the calculated KIE of 3.4 [46]. This is significant because it demonstrates that the pre-steady state rate is not fully the ‘‘the H-transfer rate’’ (as illustrated in Fig. 12.2). A KIE of 3.5 exposed a commitment of 0.25 on the pre-steady state rate. This commitment suggested that the presteady state rate contains an additional step, most likely the reorganization of the nicotinamide ring in and out of the active site [45]. This conclusion is supported by stopped-flow FRET experiments conducted by Benkovic and coworkers with G121V ecDHFR [44]. The commitment was temperature dependent and so were the observed KIEs. Nevertheless, the calculated intrinsic KIEs were temperature independent with AH =AT ¼ 7:2 G 3:5, which served as evidence of H-tunneling [45]. Thymidylate Synthase Thymidylate synthase catalyzes the reductive methylation of 2 0 -deoxyuridine-5 0 -monophosphate (dUMP) to 2 0 -deoxythymidine-5 0 -monophosphate (dTMP). The cofactor N 5,N 10 -methylene-5,6,7,8-tetrahydrofolate (CH2 H4 folate) serves as a donor of both methylene and hydride [47]. We recently studied the hydride transfer step using competitive H/T and D/T KIEs [48], and the observed KIEs were used to calculate intrinsic KIEs. The observed and intrinsic KIEs were used to calculate the commitment to catalysis (Eq. (12.2)), and it was found that between 20 and 30 C the hydride transfer is fully rate determining, while at elevated and reduced temperatures the commitment increases. At 20 C, competitive KIE experiments resulted in 1 H/T KIE on kcat =KM and D/T KIE on kcat =KM KIEs of 6:91 G 0:05 and 1:78 G 0:02, respectively. The Swain–Schaad exponent for these KIEs is 3:35 G 0:07, suggesting that the hydride transfer is rate determining
12.3 Probing H-transfer in Complex Systems
overall [24, 48, 49]. H/D KIE on kcat ð D k ¼ 3:72Þ has been measured at 20 C by Spencer and coworkers [50] under the same experimental conditions as reported here. The Swain–Schaad exponent for the H/T KIEs on kcat =KM [48] vs. the H/D KIEs on kcat [50] is 1:46 G 0:4. Taken together, the exponential relationships of kcat and kcat =KM KIEs suggest no kinetic complexity on either kcat or kcat =KM, which strongly supports Spencer’s suggestion that the hydride transfer step is rate determining at 20 C. 12.3.3
Secondary Swain–Schaad Relationship
The secondary (2 ) Swain–Schaad relationship is calculated from 2 KIEs i.e., not the hydrogen whose bond is being cleaved but its geminal neighbor. In several cases a breakdown of this 2 Swain–Schaad relationship was used as evidence of a tunneling contribution. A number of these reported studies used mixed labeling experiments, as described below. In experiments of this type, the breakdown of the Swain–Schaad relationship indicates both tunneling and coupled motion between the primary and secondary hydrogens [33, 34]. 12.3.3.1 Mixed Labeling Experiments as Probes for Tunneling and Primary– Secondary Coupled Motion Mixed labeling experiments consist of an isotopic labeling pattern that is more complex than that considered in the original Swain–Schaad relationship. Several theoretical studies in the 1980s suggested that mixed labeling experiments would be the most sensitive indicators of H-tunneling [29]. In a mixed labeling experiment, the 1 H/T KIE is measured with H in the 2 position and is denoted as kHH =k TH , where k ij is the rate constant for H-transfer with isotope i in the 1 position and isotope j in the 2 position. The 2 H/T KIE is measured with H at the R position and is denoted as kHH =kHT . The 1 and 2 D/T KIE measurements, on the other hand, are conducted with D in the geminal position, and are denoted as kDD =k TD and kDD =kDT , respectively (Fig. 12.4 and Eq. (12.11)).
2
M
EXP ¼
Figure 12.4.
lnðkHH =kHT Þ lnðkDD =kDT Þ
The isotopic labeling pattern for a mixed-labeling experiment.
ð12:11Þ
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12 Current Issues in Enzymatic Hydrogen Transfer from Carbon
The exponential relationship resulting from such mixed labeling experiments is denoted as MEXP. If the 1 and 2 hydrogens are independent of each other, the isotopic labeling of one should not affect the isotope effect of the other. This is denoted as the rule of geometrical mean (RGM [51]): r¼
lnðkHi =kHT Þ ¼1 lnðkDi =kDT Þ
ð12:12Þ
where i is H or D. The RGM predicts that the isotopic label at the geminal position should not affect the MEXP: 2 EXP ¼
lnðkHH =kHT Þ lnðkHH =kHT Þ ¼ ¼ 2 lnðkHD =kHT Þ lnðkDD =kDT Þ
M
ð12:13Þ
EXP
If the motions of the 1 and 2 hydrogens are coupled along the reaction coordinate a breakdown of the RGM will result in an inflated 2 MEXP. The 1 KIE will have a secondary component, and will be deflated, but since the 2 H/D KIE is very small (@1.2), the expected deflation of the 1 MEXP is also very small. The 2 KIE on the other hand, will have a primary component and will be significantly inflated. Tunneling of the 1 H will induce a large 2 H/T KIE ðkHH =kHT Þ relative to the more semiclassical 2 D/T KIE ðkDD =kDT Þ, due to the reduced effect of Dtunneling in the primary position. In the mixed labeling experiment, when there is coupled motion between the 1 and 2 hydrogens, tunneling along the reaction coordinate will result in the inflation of the 2 MEXP because H tunneling is more significant than D tunneling. The MEXP is a product of the original Swain–Schaad EXP and RGM (r): rEXP ¼
lnðkHH =kHT Þ lnðkDH =kDT Þ lnðkHH =kHT Þ ¼ ¼ lnðkDH =kDT Þ lnðkDD =kDT Þ lnðkDD =kDT Þ
M
EXP
ð12:14Þ
A mathematically rigorous explanation of the high sensitivity of the mixed labeling experiment to H-tunneling can be found in Refs. [52, 53]. Both Huskey [53] and Saunders [54, 54] have shown independently that exceptionally large values of M EXP are only computed for 2 KIEs resulting from coupled motion and tunneling. They both concluded that the extra isotopic substitution is an essential feature of the experimental design. The mixed labeling experiment is also presented in similar terms in Chapter 10, Sections 10.3.3.2 and 10.3.3.3, where EXP is denoted S and r is R and MEXP is RS. Both presentations, are scientifically coherent and thus redundant, but they emphasize different aspects of the issue, so the reader may benefit from this redundancy. Upper Semiclassical Limit for Secondary Swain–Schaad Relationship For EXP as defined in Eq. (12.5), values smaller than its semiclassical lower limit can be explained by kinetic complexity and values larger than its upper limit serve as evidence of tunneling. Until recently, the upper semiclassical limit used was 12.3.3.2
12.3 Probing H-transfer in Complex Systems
3.34 [29, 56]. An upper limit that is more realistic and relevant to the commonly used mixed labeling experiment is calculated below [57]. This limit for EXP with no tunneling contribution was calculated using three different approaches: (i) ZPE and reduced mass considerations; (ii) vibrational analysis, and (iii) the effect of kinetic complexity. The results of these calculations suggest that for the mixed labeling method (kHH =kHT vs. kDD =kDT ) an experimental 2 MEXP larger than 4.8 (within statistical experimental error) may serve as a reliable indication of Htunneling [57]. In the case of experimental 2 MEXP between 3.3 and 4.8 additional evidence is needed to indicate H-tunneling. Such additional examination consists of simple analytical or numerical solutions such as those described above and, in more detail, in Ref. [57]. In accordance with our conclusion, ab initio calculations for many gas phase H-transfer reactions by Hirschi and Singleton [37] demonstrated that for sizable 2 KIEs (e.g., kH =k T > 1:1), only 2 EXP > 4 may indicate tunneling. Alternatively, a higher level of calculation for a specific enzymatic system could be employed, as discussed in Section 12.4.2. For ADHs, for example, several state of the art theoretical examinations have recently supported the tunneling contribution suggested by the inflated 2 MEXPs [58–61].
˚
Experimental Examples Using 2 Swain–Schaad Exponents To date, the only experimental examples where a 2 Swain–Schaad relationship resulted in a breakdown of semiclassical models and implicated tunneling and coupled motion were from studies of alcohol dehydrogenases (ADH). Furthermore, all these studies were conducted on the oxidation of the alternative substrate benzyl alcohol to aldehyde. The only attempt so far to conduct similar measurements used a very different system (DHFR). These experiments revealed no deviation from the semiclassical EXP [45]. Until such experiments are extended to other systems or at least extended to the reduction of aldehyde to alcohol for the same system, the generalization of their interpretation should be taken with some discretion. These examples are discussed in great detail in Chapter 10, Section 10.5.1.1, and only a concise summary of two seminal examples is presented below. 12.3.3.3
Horse Liver Alcohol Dehydrogenase (HLADH) Alcohol dehydrogenases (ADHs) catalyze the reversible oxidation of alcohols to aldehydes with NADþ as the oxidative reagent. HLADH has been extensively studied by means of 2 mixed labeling Swain–Schaad relationships [62–64]. Two interesting conclusions of these studies were that (i) For two mutants (F93T and F93T; V203G), a longer donor–acceptor distance (measured by X-ray crystallography) led to a smaller 2 exponent [64]; and (ii) for a series of mutants, a correlation exists between the catalytic efficiency ðK cat =KM Þ and the 2 exponent [63]. These findings are in accordance with tunneling models in which the barrier width plays a critical role. These models also included a contribution of coupled motion and tunneling to catalysis. Thermophilic ADH Secondary KIEs were measured using the mixed labeling pattern with thermophilic ADH from Bacillus stearothermophilus (bsADH) at temperatures ranging from 5 to 65 C. At the physiological temperature of this thermo-
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12 Current Issues in Enzymatic Hydrogen Transfer from Carbon
philic ADH (@65 C) inflated 2 Swain–Schaad exponents (@15) [65] indicated a signature of H-tunneling similar to that of the mesophilic yeast ADH at 25 C [66]. At temperatures below 30 C these exponents declined toward the semiclassical region and the enthalpy of activation increased significantly (14.6 to 23.6 kcal mol1 for H-transfer and 15.1 to 31.4 kcal mol1 for D-transfer). This phenomenon was interpreted as indicating a decreased tunneling contribution at reduced temperature due to different environmental sampling at high (physiological) and low temperatures. An alternative interpretation would result from using the environmentally coupled tunneling model. According to that model, at physiological temperature (30–65 C) the pre-arrangement of the potential surface (the Marcus term) is close to perfect and no gating is needed. At reduced temperature (5–30 C) the pre-arrangement is not so perfect, leading to gating, which modulates the donor–acceptor distance and results in temperature dependent KIEs. Interestingly, this effect is more pronounced for D-transfer than for H-transfer, possibly due to the higher sensitivity of D-tunneling to the distance between donor and acceptor. These findings were then correlated to the increased rigidity of the enzyme at lower temperatures [67, 68]. These studies suggested that similar enzymes that catalyze the same reaction at very different temperatures evolved to have similar rigidities in their respective physiological conditions and similar tunneling contributions to the H-transfer process. Interestingly, these results suggested possible relationships between protein rigidity and the degree of tunneling. Together with temperature dependence studies that are described below (Section 12.3.3.2), a model was suggested in which the enzyme’s fluctuations are coupled to the reaction coordinate [34, 60, 65, 69]. 12.3.4
Temperature Dependence of Primary KIEs Temperature Dependence of Reaction Rates and KIEs Traditional literature treats enzyme catalyzed reactions, including hydrogen transfer, in terms of transition state theory (TST) [4, 34, 70]. TST assumes that the reaction coordinate may be described by a free energy minimum (the reactant well) and a free energy maximum that is the saddle point leading to product. The distribution of states between the ground state (GS, at the minimum) and the transition state (TS, at the top of the barrier) is assumed to be an equilibrium process that follows the Boltzmann distribution. Consequently, the reaction’s rate is exponentially dependent on the reciprocal absolute temperature ð1=TÞ as reflected by the Arrhenius equation: 12.3.4.1
k ¼ A eðEa =RTÞ
ð12:15Þ
where A is the Arrhenius pre-exponential factor, Ea is the activation energy and R is the gas constant. Since the KIE is the ratio of the reactions’ rates, its temperature dependence will follow:
12.3 Probing H-transfer in Complex Systems
Figure 12.5. An Arrhenius plot of a hydrogen transfer that is consistent with a tunneling correction to transition state theory. (a) Arrhenius plot of a light isotope (i1) and heavy isotope (i2). (b) Arrhenius plot of their KIE (i1/i2). Highlighted are experimental temperature ranges for three regions: I, a
kl A l DEaðhlÞ =RT ¼ e kh A h
system with no tunneling contribution, II, a system with moderate tunneling, and III, a system with extensive tunneling contribution. The dashed lines are the tangents to the plot at each region. This illustration is similar to several schemes we and others have suggested in the past [33, 34, 49, 108].
ð12:16Þ
where h and l are the heavy and light isotopes, respectively. This equation is useful as long as the reaction is thermally activated. At low temperatures, the contribution of tunneling becomes significant, as no thermal energy is available for activation. This causes a curvature in the Arrhenius plot as illustrated in Fig. 12.5. Conventional tunneling, through a single, rigid barrier is temperature independent and may affect both the pre-exponential and the exponential factors. This treatment is confined to tunneling correction to TST and is not valid for any Marcus-like model (e.g., environmentally coupled tunneling). Thus, an Arrhenius plot of KIEs can distinguish between data that might be fitted by a tunneling correction model (e.g., A l =A h > 1 with DEa @ 0) and data that can only be fitted by a Marcus-like model (e.g., A l =A h > 1 with large DEa ). KIEs on Arrhenius Activation Factors Following Eq. (10.16), with no tunneling correction [19, 32] the KIE’s temperature dependence will reflect the differences in the energy of activation for the two isotopes, and the KIE on the pre-exponential factors ðA l =A h Þ should be close to unity (no-tunneling, region I in Fig. 12.5). Deviation from unity with no tunneling 12.3.4.2
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12 Current Issues in Enzymatic Hydrogen Transfer from Carbon Table 12.1. Semiclassical limits for the KIE on Arrhenius preexponential factors [19, 32, 74].
Upper limit Lower limit
AH /A T
AH /AD
AD /A T
1.7 0.3
1.4 0.5
1.2 0.7
seems to be confined to a limited prange, ffiffiffiffiffiffiffiffiffiffiffiffi as extensively discussed in the literature [33, 71–74]. These limits follow m h =m l > A l =A h > m l =m h where m is the reduced mass. These limits for hydrogen KIEs are summarized in Table 12.1. At a very low temperature, where only tunneling contributes significantly to rates, it is predicted that the KIEs will be very large (over six orders of magnitude [75]) and AH =AD will be much larger than unity (extensive tunneling, region III in Fig. 12.5). Between high and low temperature extremes, the Arrhenius plot of the KIEs will be curved, as the light isotope tunnels at a higher temperature than the heavy one. In this region, the Arrhenius slope will be very steep and AH =AD will be smaller than unity (moderate tunneling region II in Fig. 12.5). This has been deliberated in several previous reviews [33, 34] and has been used as a probe for tunneling in a wide variety of enzymatic systems (Table 12.2). According to this model, an AH =AD smaller than the semiclassical lower limit (Table 12.1) indicates tunneling of only the light isotope (‘‘Moderate Tunneling Region’’ [34]). Whereas an AH =AD larger than unity indicates tunneling of both isotopes (‘‘Extensive Tunneling Region’’ [34]). Table 12.2 summarizes several reports of H-tunneling based on pre-exponential Arrhenius factors that were outside the semiclassical range (Table 12.1). Several experimental AH =AD s, that do not match the criteria set by the above model are discussed in Section 12.3.3 and alternative models are presented in Section 12.4. 12.3.4.3
Experimental Examples Using Isotope Effects on Arrhenius Activation
Factors Soybean Lipoxygenase-1 (SBL-1) Lipoxygenases catalyze the oxidation of linoleic acid (LA) to 13-(S)-hydroperoxy-9,11-(Z,E)-octadecadienoic acid (13-(S)-HPOD) [76]. This reaction proceeds via an initial, rate-limiting abstraction of the pro-S hydrogen radical from C11 of LA by the Fe 3þ -OH cofactor, forming a substratederived radical intermediate and Fe 2þ -OH2 . Molecular oxygen rapidly reacts with this radical, eventually forming 13-(S)-HPOD and regenerating a resting enzyme. The abstraction of H or D from the pro-S C11 position of LA by the wild type SBL1 has very large KIEs (@80) and large AH =AD (@20) [76–78], which would suggest it fits region III in Fig. 12.5 (extensive tunneling). Yet, its KIEs are ‘‘only’’ around 80, while the above model would predict much larger KIEs [75]. For the wild type
12.3 Probing H-transfer in Complex Systems Table 12.2. Enzymatic systems for which tunneling was suggested by the temperature dependences.
Enzyme
kH /kD
AH /AD
Ref.
Soybean lipoxygenase, wt. Soybean lipoxygenase, mutants Methane monooxygenase Galactose oxidase Methylamine dehydrogenase Methylamine dehydrogenase (TTQ-dependent) Trimethylamine dehydrogenase Sarcosine Oxidase Methyl Malonyl CoA mutase Acyl CoA desaturase Peptidylglycine a-hydroxylating monooxygenase
82 93–112 50–100 16 17 12.9 4.6 7.3 36 23 10
18 4–0.12 0.25 13 9.0 7.8 5.8 0.08 2.2 5.9
76 76 98 99 100 101 102 103 104 105 42
Enzyme
kH /k T
AH /A T
Ref.
Bovine serum amine oxidase Monoamine oxidase Thymidylate synthase Dihydrofolate reductase
35 22 7 6
0.12 0.13 7 6
106 107 48 45
SBL-1, the Ea for the H-transfer was small (@2 kcal mol1 ) and the DEa was @1 kcal mol1 . Several mutants of SBL-1 were also studied and exhibited Arrhenius plots that range between regions II to III in Fig. 12.5 (see Chapter 10). Thermophilic ADH (ADH-hT) Another example for studies of temperature independent KIEs is taken from our work with thermophilic ADH from Bacillus stereothermophilus and is demonstrated in Fig. 12.6 [65, 67, 68]. Under physiological conditions (30–65 C), this enzyme had AH =AT and AD =AT larger than the semiclassical limits. However, its KIEs were relatively small (@3) and the enthalpy of activation for H and D was rather large (14.6 and 15.1 kcal mol1 , respectively). As discussed in Section 12.4.1, this can be explained by a ‘‘Marcus-like’’ model in which the temperature dependences of the reaction rate and of the KIE are separated. Below 30 C, both isotopes had a much larger energy of activation and large temperature dependence of the KIEs. This result was interpreted as ‘‘activity phase transition’’ due to increased rigidity of this thermophilic enzyme at reduced temperatures [65, 67, 68]. Using Marcus-like models, the low temperature behavior could be rationalized by imperfect pre-organization, more gating, or alternatively, using tunneling correction, the data would fit region II in Fig. 12.5.
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Figure 12.6. A thermophilic ADH (bsADH) with benzyl alcohol (f), [7- 2 H2 ] benzyl alcohol (n) and their KIEs (Y). Reproduced using data published in Ref. [65].
Dihydrofolate Reductase (DFHR) Measurements and calculations of intrinsic 1 KIEs with ecDHFR are described in Section 12.3.2.2.2 [45]. The commitment was temperature dependent and so were the observed KIEs. Nevertheless, the calculated intrinsic KIEs were temperature independent with AH =AT ¼ 7:2 G 3:5, which served as evidence of H-tunneling [45]. The energy of activation was measured by steady-state [45] and pre-steady state [79] kinetics and was found to be 4 G 1 kcal mol1 . Taken together with the large AH =AT , these findings were in accordance with ‘‘Marcus-like’’ models. Currently, attempts to reproduce these data using QM/MM calculations are being made [80] (see Section 12.4.1). Although this kind of simulation does not use phenomenological models (e.g., Marcus-like models) all the pre-, re-organization and so-called ‘‘gating effects’’ are embedded in the calculations. Such simulation may identify the specific motions that might be coupled to the H-transfer event, and may indicate protein normal modes that are coherent, or that otherwise affect the chemical transformation. Thymidylate Synthase Measurements and calculations of intrinsic 1 KIEs with ecTS are described in Section 12.3.2.2.3 [48]. These intrinsic KIEs were temperature independent with H/T KIEs close to 7 and AH =AT ¼ 6:8 G 2:8. These results served as evidence for QM tunneling, and together with the reaction’s energy of activation (Ea ¼ 4:0 G 0:1 kcal mol1 ) suggested a model in which the temperature dependence of the rate results from the reorganization of the system (isotopically insensitive), and an isotopically sensitive H-tunneling step that is temperature independent. In this specific system, since the intrinsic and observed KIES were close (small kinetic complexity), a similar qualitative conclusion would have been reached from the temperature dependence of the observed KIEs.
12.4 Theoretical Models for H-transfer and Dynamic Effects in Enzymes
In addition to the examples mentioned here, several studies by Sutcliffe, Scrutton and coworkers [81–83] have also resulted in temperature independent KIEs, with large AH =AD . These works are described in detail in Chapter 13. These systems had enthalpies of activation much larger than the semiclassical, rigid model prediction. As discussed in Section 12.4.1, such findings have led to many theoretical models attempting to explain the experimental results. It must be emphasized that the semiclassical limits for the energy of activation (the slope of the Arrhenius plot) are not well defined. Consequently, in order to establish that nonclassical features are evident from temperature independent KIEs, the pre-exponential Arrhenius factor must be outside their semiclassical limits. For example, a recent paper misinterpreted ‘‘nearly temperature independent’’ KIEs with AH =AD close to unity as ‘‘Evidence for environmentally coupled hydrogen tunneling during dihydrofolate reductase catalysis’’ [84]. Actually, the temperature dependence of the KIEs in that study (DEa ¼ 3:0 G 0:7 kcal mol1 above 20 C) was well within the semiclassical range. Over the years, TST has been modified and corrected for kinetic effects of tunneling, barrier recrossing and medium viscosity, yet, developing a theory that will explain such a phenomenon is an on-going challenge. The next section describes attempts to lay a general foundation for such a theory.
12.4
Theoretical Models for H-transfer and Dynamic Effects in Enzymes
Most of the studies described above could not be rationalized without invoking contributions from quantum mechanical tunneling and dynamic effects. This conclusion was based on deviations from semiclassical theory that exclude such phenomena. The following section presents attempts to explain those findings using models that were constructed from first principles and that include tunneling and dynamic effects. In the light of the above sections and specifically Section 12.2, it is important to note that all the theoretical treatments presented below assume a single step H-transfer phenomenon. Most of these treatments focus on the transition state of the chemical transformation catalyzed by an enzyme. Since most experimental data represent a more complex system the comparison between the calculations and their experimental counterpart has to be conducted with great care. An additional challenge when comparing theoretical to experimental results is that the experimental data carry an error that can be evaluated by standard statistical methods, while the theoretical results rarely address the accuracy of the calculated values. This having been said, it is well recognized that the only way to interpret the experimental findings on a molecular and energetic level is with a complementary theory, and that a theory that cannot be evaluated by relevant experimental data is rarely meaningful. The two approaches described below present several attempts to explain various experimental findings that could not be rationalized by semiclassical theory or classical phenomenological rate theories (e.g., transition state theory [70]).
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12.4.1
Phenomenological ‘‘Marcus-like Models’’
Models using a uni-dimensional (1D) rigid potential surface that attempted to reproduce temperature independent KIEs required the isotopically sensitive step to have little or no enthalpy of activation (e.g., H-transfer via QM tunneling). In the case of reactions with significant enthalpy of activation (e.g., Section 12.3. 4.3.2) an additional dimension has to be introduced. The temperature dependence of the reaction results from classically activated rearrangements of the potential surface prior to the H-transfer event. Several different models, which were constructed from very different basic principles, are successful because they separate the temperature dependence of the reaction’s rate from that of the KIEs [60, 69, 77, 83, 85]. Although these models use different terminology, their common theme involves two requirements for efficient tunnelling: degeneracy of the reactant and product energy levels, and narrow barrier width. These models were developed in an effort to rationalize H-transfer in the condensed phase and particularly in enzymes (e.g., Burgis and Hynes [86, 87], Kuznetzov and Ulstrup [88], Knapp and Klinman (Chapter 10), Benkovic and Bruce [7], Warshel [11, 89], and Schwartz [69]). These models resemble in part the approach of the Marcus theory [90], but with an additional term that accounts for the temperature dependence of the KIEs. Since, in contrast to electron transfer, H-transfer is very sensitive to the donor–acceptor distance, the additional term accounts for fluctuations of that distance (coordinate q in Fig. 12.7). Two common features of these models are the direct effects of the potential surface fluctuations on the reaction rate, and separation of the temperature dependence of the rate and the KIE. An example of a ‘‘Marcus-like’’ model is illustrated in Fig. 12.7. Environmentally coupled hydrogen tunneling models can accommodate the composite kinetic data for WT-SLO and its mutants [76, 77]. This model is described in more detail in Chapter 10 and was based on the model proposed by Kuznetsov and Ulstrup [88]. In this model, the rate for H transfer is governed by an isotope-independent term (const.), a Marcus-like term, and a ‘‘gating’’ term (the F.C. Term in Eq. (12.15)). In Eq. (12.15), the Marcus term relates l, the reorganization energy, to DG , the driving force for the reaction, where R and T are the gas constant and absolute temperature, respectively. This term has a weak isotopic dependence that arises when tunneling takes place from vibrationally excited states. The dominant isotopically sensitive term is the Franck–Condon nuclear overlap along the hydrogen coordinate (F.C. term), which is the weighted hydrogen tunneling probability. This term arises from the overlap between the initial and the final states of the hydrogen’s wavefunction and, consequently, depends on the thermal population of each vibration level. The F.C. term is also expected to be affected by the donor–acceptor distance, which is both temperature and isotope dependent. When distance sampling, or gating, occurs, the KIE can become very temperature dependent. The temperature dependence of KIEs arises from the thermal population of excited vibration levels. This model was developed for nonadiabatic radicaltransfer (H) reactions and the full scope of its applications is yet to be explored.
12.4 Theoretical Models for H-transfer and Dynamic Effects in Enzymes
Figure 12.7. Illustration of ‘‘Marcus-like’’ models: energy surface of environmentally coupled hydrogen tunneling. Two orthogonal coordinates are presented: p, the environmental energy parabolas for the reactant state (R) and the product state (P); and q, the H-transfer potential surface at each p configuration. The gray shapes represent the populated states (e.g., the location of the
k ¼ ðconst:ÞeðDG þlÞ
2
=ð4lRTÞ
particle). The original Marcus expression would have fixed q distance between donor and acceptor. By adding fluctuations of that distance (see gating by Knapp et al., Chapter 10) a temperature dependence of the KIE can be achieved. For three alternative graphic illustrations of such models see Refs. [33, 34, 109].
ðF:C: termÞ
ð12:15Þ
Do such models suggest that the protein dynamics or the environmental dynamics enhance the reaction rates and maybe contribute to catalysis? The fact that studies of enzymes at this level are so interdisciplinary can result in misunderstandings and disagreements between disciplines. As mentioned under ‘‘Definitions’’, most biochemists consider any motion of the protein or the enzymatic complex to be ‘‘dynamics’’. Most physical chemists on the other hand, will use that term only for motions along the reaction coordinate that are not in thermal (Boltzmann) equilibrium with their environment [14]. By their nomenclature, fluctuations that are in thermal equilibrium (like environmental rearrangement, gating motion, etc.) do not constitute a dynamical effect. For example, in Refs. [33, 34] we suggested models in which dynamic rearrangement of the reaction’s potential surface plays a key role in the enhancement of the reaction’s rate (illustrated in
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Fig. 5 in Ref. [34]). Vila´ and Warshel [11], offer a similar graphic presentation (Fig. 2 in Ref. [11]) to argue against such a role. Apparently, differences in terminology may lead to contradictory wording in the conclusions. To date, the temperature dependence of rates and KIEs is still a major challenge for explicit theoretical models or simulations and (to the best of our knowledge) only three studies have reproduced such phenomenon [60, 80, 91]. 12.4.2
MM/QM Models and Simulations
Recently, several computational studies and molecular simulations have been conducted in an attempt to reproduce and explain experimental findings such as the breakdown of the Swain–Schaad relationship and the nonclassical temperature dependence of KIEs. These studies employed a molecular mechanics (MM) based simulation of the exterior of a protein with high level ab initio calculations along the reaction coordinate and in the vicinity of the reacting atoms. Various methods were used to ‘‘buffer’’ the transition between these two regions. The general name for this kind of calculation is Molecular-Mechanics/Quantum-Mechanics (MM/ QM). Most of these studies investigated enzymatic systems for which ample kinetic, structural and other data were available (e.g., TIM [12, 92], carbonic anhydrase [93], ADH [11, 59, 61], LDH [16], methylamine dehydrogenase [94–96], SBL-1 [6, 91] and DHFR [46]). These state of the art simulations were able to reproduce rates and H/D KIEs but had little success in addressing temperature dependences (with the exception of Ref. [91]) and secondary KIEs (with the exception of Refs. [59, 97]). High level calculations of this kind are of critical importance as there is no other way to bring together all the molecular and kinetic data. While direct molecular dynamic simulations are limited to the nanosecond range, free energy perturbation/umbrella sampling calculations [5, 46] allow one to explore the effect of a much larger conformational space by forcing the system to move to different regions upon changing the charge distribution of the reacting system. Currently, the main limitations of QM/MM models are: (i) simulation of temperature dependence is not trivial in most existing methods; (ii) the limited time scale of the simulation; and (iii) the inherent compromise between accuracy (high level of theory) and conformational flexibility (large conformational space). This prohibits the coverage of a more substantial range of motion in the duration of an entire catalytic cycle while investigating quantum mechanical phenomena such as tunneling.
12.5
Concluding Comments
This chapter presents models for H-transfer that are relevant to enzymatic systems, and introduces experimental probes and case studies that have attempted to address this issue in recent years. The chapter focuses on CaH bond activation,
References
which requires significant rate enhancement by the catalyst. Hydrogen kinetic isotope effects, their temperature dependence, and the internal relationships between them, are presented as tools in studying the nature of H-transfer. Studies of Htransfer in enzymatic systems provide a unique opportunity to better understand H-transfer in the condensed phase in general, since the enzyme inhibits most of the side reactions that would take place in solution. Only one stereoselective and specific reaction takes place and can be studied in detail. Apparently, hydrogen transfer in the condensed phase is a complex phenomenon that includes not only the three atoms obviously involved (donor, hydrogen and acceptor) but many other atoms that constitute the environment of that chemical transformation. Part of this environment is in the immediate vicinity of the reacting atoms. Additionally, in an organized medium such as an enzyme, remote residues may also be coupled to the reaction coordinate. A major contemporary question in enzymology is whether the ability of a protein to serve as the reaction’s environment not only electrostatistically stabilizes the reaction’s transition state, but also dynamically enhances the reaction’s rate. This can occur by statistical reor pre-arrangement along the reaction path. Such rearrangement can be more efficient in the enzyme than in the uncatalyzed reaction. Several open questions are presented in this chapter, most of which focus on the issue of whether enzymes evolved to better rearrange the reaction’s environment, its electrostatics and relevant spins, to enhance the reaction’s rate relative to that in solution. Finally, it is suggested that close interaction between theory (calculations and simulations) and experiments is crucial to studying H-transfer in complex systems such as enzymes. The ability of theoreticians and experimentalists to communicate and produce data of relevance and use to each other is most likely to lead to a better understanding of enzyme catalysis and H-transfer phenomena.
Acknowledgments
I thank Judith Klinman for fruitful discussions and the NSF (CHE 01-33117) and the NIH (GM065368) for financial support.
References 1 Pauling, L. (1948) The nature of
forces between large molecules of biological interest, Nature 161, 707–709. 2 Jencks, W. P. (1987) Catalysis in Chemistry and Enzymology, Dover Publications, New York. 3 Schowen, R. L. (1978) Catalytic power and transition-state stabilization, in Transition States of
Biochemical Processes, Gandour, R. D., Schowen, R. L. (Eds.), Plenum Press, New York. 4 Fersht, A. (1998) Structure and Mechanism in Protein Sciences: A Guide to Enzyme Catalysis and Protein Folding, W. H. Freeman, New York. 5 Warshel, A., Parson, W. W. (2001) Dynamics of biochemical and biophysical reactions: insight from
1335
1336
12 Current Issues in Enzymatic Hydrogen Transfer from Carbon
6
7
8
9
10
11
12
13
14
15
16
17 18
computer simulations, Quart. Rev. Biophys. 34, 563–679. Olsson, M. H. M., Siegbahn, P. E. M., Warshel, A. (2003) Simulating large nuclear quantum mechanical corrections in hydrogen atom transfer reactions in metalloenzymes, J. Biol. Inorg. Chem. 9, 96–99. Bruice, T. C., Benkovic, S. J. (2000) Chemical basis for enzyme catalysis, Biochemistry 39, 6267–6273. Northrop, D. B. (1998) On the meaning of Km and Vmax/Km in enzyme kinetics, J. Chem. Ed. 75, 1153–1157. Steinfeld, J. I., Francisco, J. S., Hase, W. L. (1998) Chemical Kinetics and Dynamics, 2nd edn., Prentice Hall, Upper Saddle River, N.J. Mulholland, A. J., Karplus, M. (1996) Simulations of enzymic reactions, Biochem. Soc. Trans. 24, 247–54. Villa, J., Warshel, A. (2001) Energetics and dynamics of enzymatic reactions, J. Phys. Chem. B 105, 7887– 7907. Cui, Q., Karplus, M. (2002) Promoting modes and demoting modes in enzyme-catalyzed proton transfer reactions: A study of models and realistic systems, J. Phys. Chem. B 106, 7927–7947. Wilson, E. K. (2000) Enzyme dynamics, Chem. Eng. News 78, July 17, 42–45. Benkovic, S. J., Hammes-Schiffer, S. (2003) A perspective on enzyme catalysis, Science 301, 1196–1202. Garcia-Viloca, M., Gao, J., Karplus, M., Truhlar, D. G. (2003) How enzymes work: Analysis by modern rate theory and computer simulations, Science 303, 186–195. Hwang, J. K., Chu, Z. T., Yadav, A., Warshel, A. (1991) Simulations of quantum mechanical corrections for rate constants of hydride-transfer reactions in enzymes and solutions, J. Phys. Chem. 95, 8445–8448. Oref. I. (1998) Selective chemistry redux, Science 279, 820–821. Diau, E. W. G., Herek, J. L., Kim, Z. H., Zewail, A. H. (1998)
19
20
21
22
23
24
25
26
27
28
29
Femtosecond activation of reactions and the concept of nonergodic molecules, Science 279, 847–851. Melander, L., Saunders, W. H. (1987) Reaction Rates of Isotopic Molecules, Krieger, R.E., Malabar, FL. Bigeleisen, J., Mayer, M. G. (1947) Calculation of equilibrium constants for isotopic exchange reactions, J. Chem. Phys. 15, 261–267. Bigeleisen, J., Wolfsberg, M. (1958) Theoretical and experimental aspects of isotope effects in chemical kinetics, Adv. Chem. Phys. 1, 15–76. Kiefer, P. M., Hynes, J. T. (2003) Kinetic isotope effects for adiabatic proton transfer reactions in a polar environment, J. Phys. Chem. A 107, 9022–9039. Cleland, W. W. (1991) Multiple isotope effects in enzyme-catalyzed reactions, in Enzyme Mechanism from Isotope Effects, Cook, P. F. (Ed.), pp. 247–268, CRC Press, Boca Raton, Fl. Northrop, D. B. (1991) Intrinsic isotope effects in enzyme catalyzed reactions, in Enzyme Mechanism from IsotopeEeffects, Cook, P. F. (Ed.), pp. 181–202, CRC Press, Boca Raton, Fl. Swain, C. G., Stivers, E. C., Reuwer, J. F., Schaad, L. J. (1958) Use of hydrogen isotope effects to identify the attacking nucleophile in enolization of ketones catalyzed by acetic acid, J. Am. Chem. Soc. 80, 5885–5893. Bigeleisen, J. (1962) in International Atomic Energy Agency, pp. 161, Gerin, P., Vienna. Stern, M. J., Vogel, P. C. (1971) Relative tritium-deuterium isotope effects in the absence of large tunneling factors, J. Am. Chem. Soc. 93, 4664–4675. Stern, M. J., Weston, R. E. J. (1974) Phenomenological manifestations of quantum-mechanical tunneling. III. Effect on relative tritium-deuterium kinetic isotope effects, J. Chem. Phys. 60, 2815–2821. Saunders, W. H. (1985) Calculations of isotope effects in elimination reactions. New experimental criteria for tunneling in slow proton transfers, J. Am. Chem. Soc. 107, 164–169.
References 30 Amin, M., Price, R. C., Saunders,
31
32
33
34
35
36
37
38
39
40
W. H. (1990) Tunneling in Elimination Reactions – Tests of Criteria For Tunneling Predicted by Model Calculations, J. Am. Chem. Soc. 112, 4467–4471. Bahnson, B. J., Klinman, J. P. (1995) Hydrogen tunneling in enzyme catalysis, in Enzyme Kinetics and Mechanism, pp. 373–397, Academic Press, San Diego. Bell, R. P. (1980) The Tunnel Effect in Chemistry, Chapman & Hall, London & New York. Kohen, A., Klinman, J. P. (1998) Enzyme catalysis: beyond classical paradigms, Acc. Chem. Res. 31, 397–404. Kohen, A., Klinman, J. P. (1999) Hydrogen tunneling in biology, Chem. Biol. 6, R191–198. Tautermann, C. S., Loferer, M. J., Voegele, A. F., Liedla, K. R. (2004) Double hydrogen tunneling revisited: The breakdown of experimental tunneling criteria, J. Chem. Phys. 120, 11650–11657. Kiefer, P. M., Hynes, J. T. (2006) Interpretation of primary kinetic isotope effects for adiabatic and nonadiabatic proton transfer reactions in a polar environment, in Isotope Effects in Chemistry and Biology, Kohen, A., Limbach, H. H. (Eds.), pp. 549–578, Taylor & Francis, LLC CRC, Boca Raton, FL. Hirschi, J., Singleton, D. A. (2005) The normal range for secondary Swain-Schaad exponents without tunneling or kinetic complexity, J. Am. Chem. Soc. 127, 3294–3295. Grant, K. L., Klinman, J. P. (1992) Exponential relationship among multiple hydrogen isotope effects as probes of hydrogen tunneling, Bioorg. Chem. 20, 1–7. Northrop, D. B. (1977) Determining the absolute magnitude of hydrogen isotope effects, in Isotope Effects on Enzyme-catalyzed Reactions, Cleland, W. W., O’Leary, M. H., Northrop, D. B. (Eds.), pp. 122–152, University Park Press, Baltimore, MD. Cleland, W. W. (1977) Adv. Enzymol. 45, 273–303.
41 Francisco, W. A., Merkler, D. J.,
42
43
44
45
46
47
48
49
50
Blackburn, N. J., Klinman, J. P. (1998) Kinetic mechanism and intrinsic isotope effects for the peptidylglycine a-amidating enzyme reaction, Biochemistry 37, 8244–8252. Francisco, W. A., Knapp, M. J., Blackburn, N. J., Klinman, J. P. (2002) Hydrogen tunneling in peptidylglycine-hydroxylating monooxygenase, J. Am. Chem. Soc. 124, 8194–8195. Fierke, C. A., Johnson, K. A., Benkovic, S. J. (1987) Construction and evaluation of the kinetic scheme associated with dihydrofolate reductase from Escherichia coli, Biochemistry 26, 4085–4092. Rajagopalan, P. T. R., Lutz, S., Benkovic, S. J. (2002) Coupling interactions of distal Residues enhance dihydrofolate reductase catalysis: mutational effects on hydride transfer rates, Biochemistry 41, 12618– 12628. Sikorski, R. S., Wang, L., Markham, K. A., Rajagopalan, P. T. R., Benkovic, S. J., Kohen, A. (2004) Tunneling and coupled motion in the E. coli dihydrofolate reductase catalyzed reaction, J. Am. Chem. Soc. 126, 4778–4779. Agarwal, P. K., Billeter, S. R., Hammes-Schiffer, S. (2002) Nuclear quantum effects and enzyme dynamics in dihydrofolate reductasecatalysis, J. Phys. Chem. B 106, 3283–3293. Carreras, C. W., Santi, D. V. (1995) The catalytic mechanism and structure of thymidylate synthase, Annu. Rev. Biochem. 64, 721–762. Agrawal, N., Hong, B., Mihai, C., Kohen, A. (2004) Vibrationally enhanced hydrogen tunneling in the E. coli thymidylate synthase catalyzed reaction, Biochemistry 43, 1998–2006. Kohen, A. (2003) Kinetic isotope effects as probes for hydrogen tunneling, coupled motion and dynamics contributions to enzyme catalysis, Progr. React. Kinet. Mech. 28, 119–156. Spencer, H. T., Villafranca, J. E.,
1337
1338
12 Current Issues in Enzymatic Hydrogen Transfer from Carbon
51
52
53
54
55
56
57
58
59
60
Appleman, J. R. (1997) Kinetic scheme for thymidylate synthase from Escherichia coli: determination from measurements of ligand binding, primary and secondary isotope effects, and pre-steady-state catalysis, Biochemistry 36, 4212–4222. Bigeleisen, J. (1955) The rule of the geometric mean, J. Chem. Phys. 23, 2264–2267. Huskey, W. P. (1991) Origin and interpretations of heavy-atom isotope effects, in Enzyme Mechanism from Isotope Effects, Cook, P. F. (Ed.), pp. 37–72, CRC Press, Boca Raton, Fl. Huskey, W. P. (1991) Origin of apparent Swain-Schaad deviations in criteria for tunneling, J. Phys. Org. Chem. 4, 361–366. Saunders, W. H. (1992) The contribution of tunneling to secondary isotope effects, Croat. Chem. Acta. 65, 505–515. Lin, S., Saunders, W. H. (1994) Tunneling in elimination reactions – structural effects on the secondary beta-tritium isotope effect, J. Am. Chem. Soc. 116, 6107–6110. Streitwieser, A., Jagow, R. H., Fahey, R. C., Suzuki, F. (1958) Kinetic isotope effects in the acetolyses of deuterated cyclopentyl tosylates, J. Am. Chem. Soc. 80, 2326–2332. Kohen, A., Jensen, J. H. (2002) Boundary conditions for the SwainSchaad relationship as a criterion for hydrogen tunneling, J. Am. Chem. Soc. 124, 3858–3864. Agarwal, P. K., Webb, S. P., Hammes-Schiffer, S. (2000) Computational studies of the mechanism for proton and hydride transfer in liver alcohol dehydrogenase, J. Am. Chem. Soc. 122, 4803– 4812. Alhambra, C., Corchado, J. C., Sa´nchez, M. L., Gao, J., Truhlar, D. J. (2000) Quantum dynamics of hydride transfer in enzyme catalysis, J. Am. Chem. Soc. 122, 8197–8203. Antoniou, D., Schwartz, S. D. (2001) Internal enzyme motions as a source of catalytic activity: rate-
61
62
63
64
65
66
67
68
69
promoting vibrations and hydrogen tunneling, J. Phys. Chem. B 105, 5553–5558. Cui, Q., Elstner, M., Karplus, M. (2002) A theoretical analysis of the proton and hydride transfer in liver alcohol dehydrogenase (LADH), J. Phys. Chem. B 106, 2721–2740. Bahnson, B. J., Park, D. H., Kim, K., Plapp, B. V., Klinman, J. P. (1993) Unmasking of hydrogen tunneling in the horse liver alcohol dehydrogenase reaction by site-directed mutagenesis, Biochemistry 32, 5503–5507. Bahnson, B. J., Colby, T. D., Chin, J. K., Goldstein, B. M., Klinman, J. P. (1997) A link between protein structure and enzyme catalyzed hydrogen tunneling, Proc. Nat. Acad. Sci. U.S.A. 94, 12797–12802. Colby, T. D., Bahnson, B. J., Chin, J. K., Klinman, J. P., Goldstein, B. M. (1998) Active site modifications in a double mutant of liver alcohol dehydrogenase: structural studies of two enzyme-ligand complexes, Biochemistry 37, 9295–9304. Kohen, A., Cannio, R., Bartolucci, S., Klinman, J. P. (1999) Enzyme dynamics and hydrogen tunneling in a thermophilic alcohol dehydrogenase, Nature 399, 496–499. Cha, Y., Murray, C. J., Klinman, J. P. (1989) Hydrogen tunneling in enzyme reactions, Science 243, 1325–1330. Kohen, A., Klinman, J. P. (2000) Protein flexibility correlate with degree of hydrogen tunneling in thermophilic and mesophilic alcohol dehydrogenase, J. Am. Chem. Soc. 122, 10738–10739. Liang, Z. X., Lee, T., Resing, K. A., Ahn, N. G., Klinman, J. P. (2004) Thermal activated protein mobility and its correlation with catalysis in thermophilic alcohol dehydrogenase, Proc. Nat. Acad. Sci. U.S.A. 101, 9556–9561. Antoniou, D., Caratzoulas, S., Kalyanaraman, C., Mincer, J. S., Schwartz, S. D. (2002) Barrier passage and protein dynamics in enzymatically catalyzed reactions, Eur. J. Biochem. 269, 3103–3112 and many cited therein.
References 70 Kraut, J. (1988) How do enzymes 71
72
73
74
75
76
77
78
79
80
work?, Science 242, 533–540. Stern, M. J., Schneider, M. E., Vogel, P. C. (1971) Low-magnitude, pure-primary, hydrogen kinetic isotope effects, J. Chem. Phys. 55, 4286–4289. Vogel, P. C., Stern, M. J. (1971) Temperature dependences of kinetic isotope effects, J. Chem. Phys. 52, 779–796. Schneider, M. E., Stern, M. J. (1972) Arrhenius preexponential factors for primary hydrogen kinetic isotope effects, J. Am. Chem. Soc. 94, 1517–1522. Stern, M. J., Weston, R. E. J. (1974) Phenomenological manifestations of quantum-mechanical tunneling. II. Effect on Arrhenius pre-exponential factors for primary hydrogen kinetic isotope effects, J. Chem. Phys. 60, 2808–2814. Moiseyev, N., Rucker, J., Glickman, M. H. (1997) Reduction of ferric iron could drive hydrogen tunneling in lipoxygenase catalysis: Implications for enzymatic and chemical mechanisms, J. Am. Chem. Soc. 119, 3853–3860. Knapp, M. J., Rickert, K., Klinman, J. P. (2002) Temperature-dependent isotope effects in soybean lipoxygenase-1: Correlating hydrogen tunneling with protein dynamics, J. Am. Chem. Soc. 124, 3865–3874. Knapp, M. J., Klinman, J. P. (2002) Environmentally coupled hydrogen tunneling. Linking catalysis to dynamics, Eur. J. Biochem. 269, 3113–3121. Glickman, M. H., Wiseman, J. S., Klinman, J. P. (1994) Extremely large isotope effects in the soybean lipoxygenase-linoleic acid reaction, J. Am. Chem. Soc. 116, 793–794. Maglia, G., Javed, M. H., Allemann, R. K. (2003) Hydride transfer during catalysis by dihydrofolate reductase from Thermotoga maritima, Biochem. J. 374, 529–535. Pu, J., Ma, S., Gao, J., Truhlar, D. G. (2005) Small temperature dependence of the kinetic isotope effect for the hydride transfer reaction catalyzed by Escherichia coli dihydrofolate
81
82
83
84
85
86
87
88
89 90
91
92
reductase, J. Phys. Chem. B. 109, 8551–8556. Scrutton, N. S., Basran, J., Sutcliffe, M. J. (1999) New insights into enzyme catalysis. Ground state tunnelling driven by protein dynamics, Eur. J. Biochem. 264, 666–671. Scrutton, N. S. (1999) Enzymes in the quantum world, Biochem. Soc. Trans. 27, 767–779. Sutcliffe, M. J., Scrutton, N. S. (2002) A new conceptual framework for enzyme catalysis. Hydrogen tunneling coupled to enzyme dynamics in flavoprotein and quinoprotein enzymes, Eur. J. Biochem. 269, 3096–3102 and many references cited therein. Maglia, G., Allemann, R. K. (2003) Evidence for environmentally coupled hydrogen tunneling during dihydrofolate reductase catalysis, J. Am. Chem. Soc. 125, 13372–13373. Schowen, R. L. (2002) Hydrogen tunneling. Goodbye to all that, Eur. J. Biochem. 269, 3095. Borgis, D., Hynes, J. T. (1991) Molecular-Dynamics Simulation For a Model Nonadiabatic Proton Transfer Reaction in Solution, J. Chem. Phys. 94, 3619–3628. Borgis, D., Hynes, J. T. (1993) Dynamical theory of proton tunneling transfer rates in solution – general formulation, Chem. Phys. 170, 315–346. Kuznetsov, A. M., Ulstrup, J. (1999) Proton and hydrogen atom tunneling in hydrolytic and redox enzyme catalysis, Can. J. Chem. 77, 1085–1096. Warshel, A. (1984) Proc. Natl. Acad. Sci. USA 81, 444–448. Marcus, R. A., Sutin, N. (1985) Electron transfer in chemistry and biology, Biochem. Biophys. Acta 811, 265–322. Hatcher, E., Soudackov, A. V., Hammes-Schiffer, S. (2004) Protoncoupled electron transfer in soybean lipoxygenase, J. Am. Chem. Soc. 126, 5763–5775. Cui, Q., Karplus, M. (2001) Triosephosphate isomerase: A theoretical comparison of alternative
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93
94
95
96
97
98
99
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pathways, J. Am. Chem. Soc. 123, 2284–2290. Hwang, J.-K., Warshel, A. (1996) How important are quantum mechanical nuclear motions in enzyme catalysis?, J. Am. Chem. Soc. 118, 11745–11751. Alhambra, C., Sa´nchez, M. L., Corchado, J. C., Gao, J., Truhlar, D. J. (2001) Quantum mechanical tunneling in methylamine dehydrogenase, Chem. Phys. Lett. 347, 512–518. Truhlar, D. G., Gao, J., Alhambra, C., Garcia-vilcoa, M., Corchado, J. C., Nchez, M. L. S., Villa, J. (2002) The incorporation of quantum effects in enzyme kinetics modeling, Acc. Chem. Res. 35, 341–349. Faulder, P. F., Tresadern, G., Chohan, K. K., Scrutton, N. S., Sutcliffe, M. J., Hillier, I. H., Burton, N. A. (2001) QM/MM Studies show substantial tunneling for the hydrogen-transfer reaction in methylamine dehydrogenase, J. Am. Chem. Soc. 123, 8604–8605. Garcia-Viloca, M., Truhlar, D. G., Gao, J. (2003) Reaction-path energetics and kinetics of the hydride transfer reaction catalyzed by dihydrofolate reductase, Biochemistry 42, 13558–13575. Nesheim, J. C., Lipscomb, J. D. (1996) Large kinetic isotope effects in methane oxidation catalyzed by methane monooxygenase: Evidence for C-H bond cleavage in a reaction cycle intermediate, Biochemistry 35, 10240–10247. Whittaker, M. M., Ballou, D. P., Whittaker, J. W. (1998) Kinetic isotope effects as probes of the mechanism of galactose oxidase, Biochemistry 37, 8426–8436. Basran, J., Sutcliffe, M. J., Scrutton, N. S. (1999) Enzymatic H-transfer requires vibration-driven extreme tunneling, Biochemistry 38, 3218–3222. Basran, J., Patel, S., Sutcliffe, M. J., Scrutton, N. S. (2001) Importance of barrier shape in enzyme-catalyzed reactions – vibrationally assisted tunneling in tryptophan tryptophyl-
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104
105
106
107
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quinone-dependent amine dehydrogenase, J. Biol. Chem. 276, 6234–6242. Basran, J., Sutcliffe, M. J., Scrutton, N. S. (2001) Deuterium isotope effects during carbon– hydrogen cleavage by trimethylamine dehydrogenase, J. Biol. Chem. 276, 24581–24587. Harris, R. J., Meskys, R., Sutcliffe, M. J., Scrutton, N. S. (2000) Kinetic studies of the mechanism of carbonhydrogen bond breakage by the heterotetrameric sarcosine oxidase of Arthrobacter sp. 1-IN, Biochemistry 39, 1189–1198. Chowdhury, S., Banerjee, R. (2000) Evidence for quantum mechanical tunneling in the coupled cobalt-carbon bond homolysis-substrate radical generation reaction catalyzed by methylmalonyl-CoA mutase, J. Am. Chem. Soc. 122, 5417–5418. Abad, J. L., Camps, F., Fabrias, G. (2000) Is hydrogen tunneling involved in acylCoA desaturase reactios? The case of a D9 desaturase that transforms (E )-11-tetradecenoic acid into (Z,E )-9,11-tetradeienoic acid, Angew. Chem. Int. Ed. 122, 3279–3281. Grant, K. L., Klinman, J. P. (1989) Evidence that both protium and deuterium undergo significant tunneling in the reaction catalyzed by bovine serum amine oxidase, Biochemistry 28, 6597–6605. Jonsson, T., Edmondson, D. E., Klinman, J. P. (1994) Hydrogen tunneling in the flavoenzyme monoamine oxidase B, Biochemistry 33, 14871–14878. Jonsson, T., Glickman, M. H., Sun, S. J., Klinman, J. P. (1996) Experimental evidence for extensive tunneling of hydrogen in the lipoxygenase reaction – implications for enzyme catalysis, J. Am. Chem. Soc. 118, 10319–10320. Kohen, A. (2006) Kinetic isotope effects as probes for hydrogen tunneling in enzyme catalysis, in Isotope Effects in Chemistry and Biology, Kohen, A., Limbach, H. H. (Eds.), pp. 743–764, Taylor & Francis, CRC Press, New York.
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Hydrogen Tunneling in Enzyme-catalyzed Hydrogen Transfer: Aspects from Flavoprotein Catalysed Reactions Jaswir Basran, Parvinder Hothi, Laura Masgrau, Michael J. Sutcliffe, and Nigel S. Scrutton 13.1
Introduction
Enzymes are extremely efficient catalysts that can achieve rate enhancements of up to 10 21 over the uncatalyzed reaction rate [1]. Our quest to understand the physical basis of this catalytic power – pivotal to our understanding of biological reactions and our exploitation of enzymes in chemical, biomedical and biotechnological processes – is challenging, and has involved sustained and intensive research efforts for over 100 years (for reviews see Refs. [2–6]). However, our understanding of how enzymes achieve phenomenal rate enhancements is far from complete. Recent years have witnessed new and important activity in this area, and these studies include roles for protein ‘motion’ [6–8], low barrier hydrogen bonds (for example see Refs. [9–11]), active site preorganization (for reviews see Refs. [4, 12]) and in particular the role of quantum mechanical tunneling in enzymic hydrogen transfer (for reviews see Refs. [13–16]). Understanding factors that drive this H-tunneling reaction is the key to understanding a large number of reactions in biology; CaH bond cleavage occurs in @50% of all biological reactions, and all of these are likely to involve tunneling to some degree. Studies of H-transfer by quantum tunneling focused initially on deviations from values predicted by semiclassical models (in which zero point energies, but not tunneling, have been taken into account) – namely kinetic isotope effects (KIEs), lnðkH =k T Þ > 3:26, where kH , kD , and k T Swain–Schaad relationships [17] (exp lnðkD =k T Þ are the rates of transfer for protium, deuterium and tritium, respectively) or Arrhenius prefactor ratios (g1 for a reaction proceeding purely by tunneling, <1 for moderate tunneling). Early examples in which H-tunneling was inferred from measurements of KIEs include the quinoprotein bovine serum amine oxidase [18], the Zn 2þ -dependent yeast alcohol dehydrogenase [19] and horse liver alcohol dehydrogenase [20], and the flavin-dependent monoamine oxidase [21]. These studies were shown to be consistent with the so-called Bell tunnel correction model of semiclassical transfer, which invokes tunneling (that is transfer occurs through the Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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13 Hydrogen Tunneling in Enzyme-catalyzed Hydrogen Transfer
energy barrier separating reactant from product) just below the classical transition state [22]. This correction model accommodates small corrections to the rate of a reaction and predicts inflated KIEs and Arrhenius prefactor ratios less than unity (the so-called Kreevoy criteria for tunneling [23]) when KIEs are measured as a function of temperature. Such nonclassical behavior is expected for a light particle such as the H-nucleus (for transfer over short distances): the de Broglie wavelength is 0.63 A˚ for protium and 0.45 A˚ for deuterium (assuming an energy of 20 kJ mol1 ), and this positional uncertainty gives rise to a significant probability of H-transfer by tunneling. Recent studies from our own group [24–28] and that of Klinman [29, 30] have now indicated that the simple Bell-correction model cannot adequately account for observed KIEs in a number of enzyme systems. This has led to full tunneling models, akin to the established models for electron transfer, in which protein and/or substrate fluctuations are required to generate a configuration compatible with tunneling (see for example Refs. [14, 30, 31]). These full tunneling models are consistent with the strong temperature dependence of reaction rates, the variable temperature dependence of KIEs and the observed range of the Arrhenius prefactor ratio. These new theoretical frameworks, which incorporate quantum mechanical tunneling coupled to protein motion, supported by experimental observations, have emerged in recent years [31–34]. The reaction itself (that is the breaking and making of bonds) can be modeled computationally based on the hybrid quantum mechanical/molecular mechanical (QM/MM) formulism, in which those atoms involved in the reaction are treated quantum mechanically and the rest of the system treated classically using molecular mechanics (for a review see [35]). Alternatively, the ‘‘quantum Kramers’’ method [15, 36, 37], which treats the whole enzymatic system using a simplified quantum mechanical formulism (note that current computers are not sufficiently powerful to treat the whole system with a full quantum mechanical formulism, hence the need for a simpler model), has been applied to small organic systems. The nature of the tunneling event itself is generally studied computationally using either a method based on variational transtition state theory with multidimensional tunneling corrections (VTST/MT) developed by Truhlar and coworkers (for a review see Refs. [38, 39]) or a method in which the electronic quantum effects are incorporated with an empirical valence bond potential and the hydrogen nucleus is represented as a multidimensional vibrational wavefunction developed by Hammes-Schiffer and coworkers (for a review see Ref. [39]). Given that protein ‘motion’ is thought to be an important factor in driving quantum tunneling in enzymic H-transfer reactions, methodology has also been developed for identifying computationally, residues important in creating reactionpromoting vibrations in enzymes [40, 41]. Our own studies, in which we have investigated H-tunneling in a number of quinoprotein and flavoprotein enzymes, have provided evidence consistent with H-transfer by quantum tunneling from the vibrational ground state of the reactive CaH bond of the substrate, and either H-tunneling in which the KIE is temperature independent – we interpret this to correspond to the absence of gated motion (that is no ‘compression’ of the transfer distance by substrate and/or protein fluc-
13.3 Interpreting Temperature Dependence of Isotope Effects in Terms of H-Tunneling
tuations) or H-transfer in which the KIE is temperature dependent – we interpret this to correspond to the involvement of gated motion. Our work [26] has also highlighted the importance of energy barrier shape in determining the rates of H-transfer, and the concomitant values of KIEs, obtained in experimental studies. We have recently reviewed our work on quinoprotein enzymes elsewhere [42]. In this chapter we review our studies of H-tunneling in flavoprotein enzymes.
13.2
Stopped-flow Methods to Access the Half-reactions of Flavoenzymes
The flavoprotein enzymes are ideally suited to studies of H-transfer during substrate oxidation using stopped-flow methods. Analysis using the steady-state approach is often compromised by the inability to focus on a single chemical step, owing to the existence of multiple barriers for binding, product release and a number of chemical steps, each of which may contribute to the overall catalytic rate. Using the stopped-flow method, the chemical step can often be isolated and the true kinetics of CaH bond breakage determined without complications arising from other events in the catalytic sequence. With flavoprotein enzymes, the reactions catalyzed are conveniently divided into reductive and oxidative half-reactions. Enzyme reduction occurs by breakage of substrate or coenzyme CaH bonds. The kinetics of bond breakage are conveniently followed by absorbance spectrophotometry since the reaction is concomitant with reduction of the redox centre. Thus, the alternative redox states of the flavin center provide a readily available spectroscopic probe for following the kinetics of CaH bond breakage. The oxidative half-reaction usually involves long-range electron transfer to acceptor proteins (for example cytochromes, copper proteins or other flavoproteins). Again, the absorbance changes associated with oxidation of the flavin provide a readily available signal for monitoring H-transfer to the oxidizing substrate. The ability to interrogate each halfreaction by stopped-flow methods simplifies substantially the kinetic analysis and this makes these enzymes attractive targets in studies of H-transfer employing KIEs as probes of enzymic H-tunneling. Our flavoenzyme work has focused on trimethylamine dehydrogenase (TMADH), heterotetrameric sarcosine oxidase (TSOX), morphinone reductase (MR) and pentaerythritol tetranitrate (PETN) reductase. We have also determined high resolution crystallographic structures for MR [43], PETN reductase [44] and TMADH [45].
13.3
Interpreting Temperature Dependence of Isotope Effects in Terms of H-Tunneling
As mentioned in Section 13.1, the temperature dependent behavior of KIEs (that is temperature dependent versus temperature independent) is a key experimental result when considering the nature of the tunneling. Based on the phenomenological model provided by the Marcus-like framework for H-tunneling [14, 30, 31], the
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13 Hydrogen Tunneling in Enzyme-catalyzed Hydrogen Transfer
Figure 13.1. Representation of the model for the hydrogen transfer reaction used to interpret the experimental data (see text, and Refs. [6, 84, 85], for more details); some of the parameters in Eqs. (13.1)–(13.3) are shown. The three axes are: E, energy; q, environmental coordinate (from which the transferred hydrogen atom is excluded); HC, hydrogen coordinate. The four vertical panels show the potential energy curve as a function of the hydrogen coordinate for three values of the environmental coordinate: q R is for the reactant, q is for the transition state and q P is for the product. The gray spheres represent the groundstate vibrational wavefunction of the hydrogen nucleus. The panel labeled M shows
a Marcus-like view of the free energy curves as functions of this environmental coordinate. The motions of the environment (related to the first exponential in Eq. (13.1)) modulate the symmetry of the double well, thus allowing the system to reach a configuration with (nearly) degenerate quantum states (q ¼ q ), from which the hydrogen is able to tunnel (F.C. Term in Eqs. (13.1) and (13.2)). The difference between panels a and b is a gating motion that reduces the distance between the two wells along the HC axis (rH ) away from its equilibrium value (r0 ). This motion increases the probability of tunneling at the (nearly) degenerate configuration q (active dynamics term in Eqs. (13.1) and (13.2)).
nature of the temperature dependence of the KIE can be interpreted as follows: (i) H-tunneling in which the KIE is temperature dependent corresponds to the involvement of gated motion (that is motion along HC in Fig. 13.1), and (ii) H-tunneling in which the KIE is temperature independent corresponds to either the absence of, or at least no detectable contributions from, gated motion (that is no significant motion along HC in Fig. 13.1). In other words, two types of motion are important in enzymic tunneling: (i) those which facilitate attaining a nuclear configuration compatible with tunneling (that is a configuration with degenerate quantum states) – termed ‘‘passive dynamics’’, and (ii) those which enhance the
13.3 Interpreting Temperature Dependence of Isotope Effects in Terms of H-Tunneling
probability of tunneling once (i) has been attained – termed ‘‘active dynamics’’. It is, however, not possible to completely decouple active and passive dynamics, since a given motion can contribute to both types of H-tunneling. However, such a role for gating in H-tunneling is not universally supported. For example: (i) the experimentally accessible temperature range is rather narrow, thus it is not always possible to show unambiguously that a given KIE is truly temperature independent; (ii) computational studies on a model system [46] have suggested that it is possible to have a temperature independent KIE in the presence of gating motion; and (iii) recent computational studies using the ensemble averaged variational transition state theory with multi-dimensional tunneling (EA-VTST/MT) framework [47] illustrate how, even with different tunneling behavior for H and D, nearly temperature independent KIEs can be observed. Thus, it is neither possible to map directly from the kinetic data to a detailed picture of the concomitant changes (motions) at the atomic level, nor, hence, to the nature of the (free) energy barrier separating reactants from products. Moreover, in cases where the KIE is temperature dependent (of which, from our own work, there are only two examples to date [26, 28]), a more traditional explanation is that the reaction takes place partly via the over-thebarrier route and partly by tunneling. In principle, this over/through the barrier explanation and/or the dominance of active gating is consistent with a temperature dependent KIE, and current methods for studying the KIE cannot unequivocally disentangle the contribution of each to the tunneling reaction. The realization that tunneling might be driven by thermally induced vibrations [48] in the protein scaffold (that is a thermally fluctuating energy surface), as described by the theoretical model of Kuznestov and Ulstrup [31] (analogous to electron transfer theory [49]) and illustrated in Fig. 13.1, has been a major step forward in recent years. This model has been adopted by Knapp and Klinman [14, 30], and is of the form: "
k tunnel
(
ðDG þ lÞ 2 ¼ ðconst:Þ exp 4lRT ðActive Dynamics TermÞ
)# ðF:C: TermÞ ð13:1Þ
Here, k tunnel is the tunneling rate constant; const. an isotope-independent term describing electronic coupling; the term in square parentheses is an environmental energy term relating the driving force of the reaction, DG , and the reorganizational energy, l (R is the gas constant and T the temperature in K); the F.C. Term is the Frank–Condon nuclear overlap along the hydrogen coordinate and arises from the overlap between the initial and the final states of the hydrogen’s wavefunction. In the simplest limit, when only the lowest vibrational level is occupied for the nuclear wavefunction of the hydrogen, the F.C. Term is independent of temperature; otherwise, the F.C. Term will be temperature dependent. Temperature dependent ‘gating’ (or ‘active’) dynamics, which can be likened to a ‘squeezing’ of the potential energy barrier, can modulate the F.C. Term. From Eq. (13.1), the KIE can be expressed as:
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13 Hydrogen Tunneling in Enzyme-catalyzed Hydrogen Transfer
Ð F:C:TermH ActiveDynamicsTermH KIE ¼ Ð F:C:TermD ActiveDynamicsTermD
ð13:2Þ
Thus, the KIE is temperature independent if the F.C. Term (which is distance independent) dominates, and temperature dependent if there is a significant contribution from a gating motion. To better understand how Eq. (13.2) can be used to describe active and passive dynamics, the case study of soybean lipoxygenase-1 [14, 30] will be discussed. In this study, Knapp and Klinman [14, 30] adopted the fully nonadiabatic approach of Kuznestov and Ulstrup to analyse their experimental data on hydrogen atom (H ) transfer. It should be noted that H transfer in soybean lipoxygenase-1 is nonadiabatic, whereas the quinoprotein systems discussed in this review, all of which involve proton transfer, are adiabatic in nature. In Knapp and Klinman’s studies of H transfer, the KIE (Eq. (13.2)) is written as [14]: Ð r0 KIE ¼ Ðrr10 r1
expðm H oH rH2 =2hÞ expðEX =kB TÞ dX expðm D oD rD2 =2hÞ expðEX =kB TÞ dX
ð13:3Þ
Where kB is Boltzmann’s constant, r0 is the equilibrium, and r1 the final, separation of the reactant and product potential wells along the hydrogen coordinate, oH and oD the frequencies of the reacting bond, and m H and m D the masses of the transferred particle for protium and deuterium, respectively. The H/D transfer distance, rH =rD , is reduced by the distance the gating unit moves, r X ðrH=D ¼ r0 r X Þ The energetic cost of gating (Ex ) is given by [14]: 1 1 o X X 2 ¼ mX o 2X r X2 EX ¼ h 2 2
ð13:4Þ
Here the gating coordinate (X) is related to the gating oscillation (o X ), the mass of the gating unit (mX ), and r X as follows: X ¼ rX
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi mX o X =h
ð13:5Þ
This model predicts that if the gating term dominates (that is h o X < kB T ), the observed KIE can be temperature dependent, since this leads to different transfer distances for the heavy and light isotope [14]. In this regime the A H =A D value is predicted to be less than unity. Alternatively, if the Frank–Condon term dominates (that is h o X > kB T ) the KIE will be temperature independent. In this latter scenario, occupation of excited vibrational levels could result in some temperature dependence [30]. However, the Boltzmann distribution at 298 K suggests that tunneling should be predominantly from the vibrational ground state of the nuclear wavefunction of hydrogen. In the regime where h o X @ kB T gating plays some role in modulating the tunneling probability, temperature dependent KIEs are observed and the A H =A D values decrease (compared with the regime where the Frank–Condon term dominates), and may approach unity [14].
13.4 H-Tunneling in Morphinone Reductase and Pentaerythritol Tetranitrate Reductase
Returning to the general case (Eq. (13.1)), studies of the temperature dependence of the KIE cannot disentangle unequivocally the contribution of each term to the tunneling reaction. Compounding the conceptual problem further, Warshel recently claimed [50, 51] that his work demonstrates that dynamical effects do not enhance enzyme catalysis over the equivalent reaction in solution, and he has suggested that the main contribution to catalysis comes from the fact that the barrier is lowered by electrostatic effects [52]. A key role for dynamics has, however, been advocated by others from theoretical studies and experimental observations, for example Bruno and Bialek [32], Klinman [53], Benkovic [7, 54–56], HammesSchiffer [41, 57–59] and Schwartz [15, 40, 48, 60–63]. The term ‘‘dynamics’’ is used by different authors to refer to very different events. For example, Schwartz uses ‘‘promoting vibrations’’ to refer to vibrations on the sub-picosecond timescale [61] that are coupled to the reaction coordinate and result in changes in the (quantum) free energy barrier. Hammes-Schiffer uses ‘‘promoting motions’’ to refer to motions averaged over Schwartz’s faster ‘‘promoting vibrations’’. These ‘‘promoting motions’’ occur on the much longer timescale of the chemical reaction being catalysed; these thermally averaged motions affect the free energy. The term ‘‘dynamical motions’’ refers to those that influence barrier re-crossing [6]. A similar definition has been used by Warshel [50, 52]. Also, the more general context of atomic and molecular motion has been used by others (for example Karplus [38]). Thus, the jury is still very much out as to exactly what properties of the enzyme give rise to the temperature dependent behavior of the KIE. The notion that enzymes have evolved to optimize H-tunneling by acquiring strategies during evolution to increase the probability of transfer remains controversial (see for example a recent News Feature in Nature [64]). In one study employing an adenosylcobalamin-dependent diol dehydratase model reaction it is argued by Finke and Doll [65, 66] that this B12 -dependent enzyme (which breaks a cobalt–carbon bond) exploits the same level of quantum mechanical tunneling that is available in the reaction occurring in the absence of enzyme (that is there is no ‘compressive’ motion that preferentially enhances H-tunneling in the enzyme over the reaction in solvent). Moreover, Siebrand and Smedarchina [67] have questioned the statistical significance of data reported over a relatively narrow temperature range for reactions of wild-type and mutant lipoxygenase – these data were originally presented as evidence for gated motion in this enzyme [30]. The same authors also argue, on theoretical grounds, that flexible proteins are ‘‘ill-equipped to cause strong local compression’’. One needs to be mindful of these issues, but our view is that it is not logical to generalize on the basis of a small number of studies and that a case-by-case analysis is appropriate.
13.4
H-Tunneling in Morphinone Reductase and Pentaerythritol Tetranitrate Reductase
We have used the formulism of Knapp and Klinman (see Section 13.3) to interpret the anomalous temperature dependences for H-transfer in FMN-containing mor-
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13 Hydrogen Tunneling in Enzyme-catalyzed Hydrogen Transfer
phinone reductase (MR) and the homologous pentaerythritol tetranitrate (PETN) reductase. In particular, we have studied the reactions of (i) PETN reductase with NADPH [28], (ii) MR with NADH [28], and (iii) MR in the oxidative half-reaction with 2-cyclohexenone [28], using stopped-flow and steady-state kinetic methods with protiated and deuterated nicotinamide coenzymes. 13.4.1
Reductive Half-reaction in MR and PETN Reductase
The temperature dependent behavior of the primary KIE for flavin reduction in MR and PETN reductase by nicotinamide coenzyme indicates that quantum mechanical tunneling plays a major role in hydride transfer. In PETN reductase, the KIE is essentially independent of temperature in the experimentally accessible range, and this contrasts with strongly temperature dependent reaction rates (Table 13.1). The data are consistent with a tunneling mechanism governed by passive dynamics and from the vibrational ground state of the reactive CaH/D bond. In MR, both the reaction rates with NADH and the KIE are dependent on temperature, and analysis using the Eyring equation (that is a plot of ln(k=T ) versus 1=T ) sug-
Table 13.1.
Tunneling regimes and associated parameters in various flavoprotein enzymes.
Enzyme
Substrate
AH /AD
DH H (kJ molC1 )
DH D (kJ molC1 )
KIE[a]
Passive[b]
MR[c]
2-cyclohexenone
3.7
17.6 G 0.9
17.1 G 0.9
3.5 TI[a]
4
0.126
35.3 G 0.5
43.5 G 0.8
MR[c]
NADH
Gated 2
Reference
28 4
3.9
TD[a]
36.6 G 0.9
4.1
TI[a]
4
28
41.2 G 2.6
41.7 G 2.6
4.6 TI[a]
4
25
2.5
42.1 G 0.9
45.1 G 1.6
8.7 TD[a]
5.8
39.4 G 0.9
40.0 G 1.2
7.3 TI[a]
PETNR[c]
NADPH
4.1
36.4 G 0.9
TMADH[c] (H172Q)
Trimethylamine
7.8
TMADH[c] (Y169F)
Trimethylamine
TSOX[c]
Sarcosine
a TI ¼ temperature independent KIE, TD ¼ temperature dependent KIE; KIE values for enzyme–substrate combinations displaying a temperature dependent (TD) KIE (that is reactions involving gated motion [14, 30]) are given at 298 K. b The terms ‘‘passive’’ (that is the KIE is [almost] temperature independent) and ‘‘gated’’ (that is the KIE is temperature dependent) dynamics are taken from the work of Knapp and Klinman [14, 30]. See text for a discussion of the current limitations of this, and other, interpretations of factors affecting the temperature (in)dependence of KIEs. c Enzyme abbreviations: MR, morphionone reductase; PETNR, pentaerythritol tetranitrate reductase; TMADH, trimethylamine dehydrogenase; TSOX, heterotetrameric sarcosine oxidase.
4 4
28
25 27
13.4 H-Tunneling in Morphinone Reductase and Pentaerythritol Tetranitrate Reductase
gests that hydride transfer has a major tunneling component, which unlike in PETN reductase, is gated by thermally induced vibrations in the protein (Table 13.1). We have suggested that PETN reductase is relatively more rigid than MR, consistent with gating being less dominant in PETN reductase, which in turn predicts that the KIE would be more temperature dependent in MR than in PETN reductase. Also, the active site of PETN reductase might be more optimally configured for hydride transfer than that of MR, thus requiring little (or no) vibrational assistance through gated motion. In other words, the active site of PETN reductase is ideally set up to transfer a hydride ion from NADPH to FMN, and nuclear reorganization associated with H-tunneling (that is passive dynamics) is the major dynamic component. We have compared the high resolution crystal structures of MR [43] and PETN reductase [44] in an attempt to provide insight into why gating is potentially more important in MR. Analysis of the structures of each enzyme suggest a key factor could be double stranded anti-parallel b-sheet D, against which the NAD(P)H coenzyme is thought to bind [43]. This region harbors arginine residues, important in the recognition of the 2 0 phosphate of NADPH (PETN reductase) and a glutamate residue required to form a H-bond with the 2 0 OH group of NADH (MR). The position of this sheet diverges at Leu-133 (PETN reductase)/ Val-138 (MR) and converges again at Ile-141 (PETN reductase)/Gly-146 (MR). Also, there is an insertion of a glycine residue (Gly-133) in MR immediately before the start of b-sheet D. These differences are consistent with MR being more mobile at physiological temperatures in this region than PETN reductase, which in turn might assist in a ‘squeezing’ or ‘compression’ of the energy barrier in MR. This suggestion is consistent with the temperature factors for MR (all Ca temperature factors > 40; PDB [68] accession code 1GWJ) and PETN reductase (all Ca temperature factors < 20; PDB accession code 1GVQ) in this region. The next stage of our work to test this hypothesis is to obtain structural information for the coenzyme complexes at high resolution and to perform a more detailed theoretical analysis involving QM/MM, variational transition state theory with multidimensional tunneling and molecular dynamics studies. 13.4.2
Oxidative Half-reaction in MR
The oxidative half-reaction of MR with the substrate 2-cyclohexenone and NADH at saturating concentrations is fully rate-limiting in steady-state turnover; this has enabled us to investigate potential tunneling regimes in this part of the reaction cycle. Reduction of 2-cyclohexenone involves hydride transfer from FMNH2 and protonation, and thus two H-transfer reactions are involved (Fig. 13.2). We have demonstrated that the KIE for hydride transfer from reduced flavin to the a=b unsaturated bond of 2-cyclohexenone is independent of temperature, contrasting with strongly temperature dependent reaction rates. A large solvent isotope effect (SIE) accompanies the oxidative half-reaction, which is also independent of temperature in the experimentally accessible range and double isotope effects indicate that hydride transfer from the flavin N5 atom to 2-cyclohexenone, and the protonation of
1349
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13 Hydrogen Tunneling in Enzyme-catalyzed Hydrogen Transfer
Figure 13.2. Proposed scheme for the oxidative half-reaction of morphinone reductase. The identity of the proton donor in the oxidative half-reaction is not known.
2-cyclohexenone, are concerted. Both the temperature independent KIE and SIE suggest that (i) gated motion is not required to compress the energy barrier, and (ii) this reaction proceeds by ground state quantum tunneling. Our work with MR is therefore the first to show that both passive and active dynamics are a feature of H-tunneling within the same native enzyme; in the reductive half-reaction we suggest barrier compression is required to facilitate hydride transfer from NADH to FMN, whereas in the oxidative half-reaction the active site is configured to catalyze hydride and proton transfer in a concerted fashion without vibrational assistance through gated motion.
13.5
H-Tunneling in Flavoprotein Amine Dehydrogenases: Heterotetrameric Sarcosine Oxidase and Engineering Gated Motion in Trimethylamine Dehydrogenase
The flavoprotein amine dehydrogenases have proven to be good model systems for studies of enzymic H-tunneling. Klinman and Edmondson provided early evidence for tunneling in mammalian monoamine oxidase, and the data were interpreted in terms of the Bell tunneling correction model [21]. More recent studies with heterotetrameric sarcosine oxidase (TSOX; [27]) and trimethylamine dehydrogenase (TMADH; [25]) indicate that the Bell tunneling correction model is inappropriate for these enzymes and that KIE data are consistent with the more recent full tunneling models. Although H-transfer in flavoprotein amine dehydrogenases has been shown to occur by tunneling, the mechanisms of amine oxidation by flavoproteins remain controversial. Over the years mechanisms involving the following have been con-
13.5 H-Tunneling in Flavoprotein Amine Dehydrogenases
sidered: (i) proton abstraction by an active site base to generate a carbanion species [69], (ii) an aminium radical cation species [70], (iii) H-atom abstraction by an active site radical species [71, 72] and (iv) nucleophilic attack by the substrate nitrogen on the flavin C4a atom, followed by proton abstraction by an active site base [73] or the flavin N5 atom [74] (analogous to a similar mechanism proposed for D-amino acid oxidase [75]). 13.5.1
Heterotetrameric Sarcosine Oxidase
TSOX is a diflavin enzyme containing FAD (the site of substrate oxidation) and 8a(N 3 -histidyl)-FMN (the site of oxygen reduction). Treatment of TSOX with sulfite provides the means for selective formation of a flavin-sulfite adduct with the covalent 8a-(N 3 -histidyl)-FMN [27]. Formation of the sulfite-flavin adduct suppresses internal electron transfer between the noncovalent FAD and the covalent FMN and thus enables detailed characterization of the kinetics of FAD reduction by sarcosine using stopped-flow methods. The rate of FAD reduction was found to display a simple hyperbolic dependence on sarcosine concentration, and studies in the pH range 6.5 to 10 indicate there are no kinetically influential ionizations in the enzyme–substrate complex. A plot of the limiting rate of flavin reduction/the enzyme–substrate dissociation constant (k lim =K d ) versus pH is bell-shaped and characterized by two macroscopic pK a values of 7:4 G 0:1 and 10:4 G 0:2, indicating two kinetically influential ionizations in the free enzyme or free substrate which remain to be assigned. The KIE for breakage of the substrate CaH bond is 7.3, and the value is independent of temperature (and pH – see below) in the experimentally accessible range; in contrast, reaction rates are strongly dependent on temperature (Table 13.1). The lack of a temperature dependence on the kinetic isotope effect suggests gated motion is not dominant in this reaction. 13.5.2
Trimethylamine Dehydrogenase Mechanism of Substrate Oxidation in Trimethylamine Dehydrogenase Over the years there have been a number of mechanistic proposals for substrate oxidation by TMADH. An early proposal considered a carbanion mechanism in which an active site base deprotonates a substrate methyl group to form a substrate carbanion [69]; reduction of the flavin was then achieved by the formation of a carbanion–flavin N5 adduct, with subsequent formation of the product imine and dihydroflavin. A number of active site residues were identified as potential bases in such a reaction mechanism. Directed mutagenesis and stopped-flow kinetic studies, however, have been used to systematically eliminate the participation of these residues in a carbanion-type mechanism [76–79], thus indicating that a proton abstraction mechanism initiated by an active site residue does not occur in TMADH. Early proposals also invoked the trimethylammonium cation as the reactive species in the enzyme-substrate complex, owing to the high pK a (9.81) of free 13.5.2.1
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13 Hydrogen Tunneling in Enzyme-catalyzed Hydrogen Transfer
trimethylamine. This was used to argue against mechanisms requiring trimethylamine base (or more explicitly a substrate nitrogen lone pair). However, more recent stopped-flow studies with trimethylamine and perdeuterated trimethylamine, which have taken advantage of force constant effects on the ionization of the trimethylammonium cation, have now established that trimethylamine base is in fact the reactive species in the enzyme–substrate complex [80]. Based on this finding, and the absence of residues in the active site that function as a base during amine oxidation, a mechanism involving addition of trimethylamine base at the C4a position of the flavin and abstraction of a substrate proton by the N5 atom of the flavin has been proposed [80]. This mechanism (Fig. 13.3(a)) is analogous to that proposed previously for monoamine oxidase A (MAO A) based on QSAR analysis with para-substituted benzylamines [74], and is consistent also with mechanisms arising from studies of model chemistry [73]. The proposed mechanism is likewise consistent with computational studies of TMADH that have indicated the C4a position is an electrophilic center [45], and with studies of inactivation of TMADH by phenylhydrazine where modification of the flavin occurs at the C4a position [81]. That said, other mechanistic possibilities exist, for example the equivalent of the aminyl radical cation mechanism proposed for MAO, but to date evidence for a protein-based radical to support such a mechanism in TMADH has not been obtained. A key issue that arises from the demonstration that trimethylamine base is the reactive form of the substrate is the mechanism by which the pK a for the ionisation of trimethylammonium cation is perturbed from 9.81 to @6.5 in the enzyme–substrate complex. The pH dependence of flavin reduction by trimethylamine and perdeuterated trimethylamine has been investigated in detail, and two kinetically influential ionizations have been identified [76]. The first ionization is perturbed by @0.5 pH units to higher pH when trimethylamine is replaced by perdeuterated trimethylamine, indicating that this kinetically influential ionization is attributed to deprotonation of substrate. The shorter CaD bond in the perdeuterated substrate results in a larger charge density, and is thus electron supplying relative to CaH. This has the effect of stabilizing the NaH bond, and thus elevating the pK a for the ionization of substrate. The second ionization is attributed to residue His-172 in the active site of TMADH; the ionization is lost in the H172Q mutant enzyme [78], and is perturbed in a Y169F mutant enzyme (Y169 forms a hydrogen bond to His-172 in native enzyme) (Fig. 13.4). Studies of the pH dependence of the H172Q mutant TMADH indicated that the substrate pK a in the enzyme-substrate complex is perturbed and elevated, indicating that His-172 is (partially) responsible for the lowing of the substrate pK a (by @1.5 pH units) when bound to enzyme [78]. Residue Tyr-60 also plays a major role: this residue is one of three aromatic side chains (Tyr-60, Trp-264 and Trp-355) involved in binding substrate through amino-aromatic interactions [79, 82]. Replacement of Tyr-60 by phenylalanine elevates the substrate pK a in the enzyme-substrate complex by about 1.3 pH units to a value of @8.8. In the double mutant (H172Q, Y60F) the substrate pK a is raised even further to @9.3, which is close to that of free trimethylamine base [76]. Combined, the data indicate key roles for His-172 and Tyr-60 in
13.5 H-Tunneling in Flavoprotein Amine Dehydrogenases
Figure 13.3. (a) A proposed mechanism for the oxidation of trimethylamine by TMADH [83]. (b) Kinetic scheme for the reaction of H172Q mutant TMADH with trimethylamine.
stabilizing the basic form of the substrate in the enzyme active site, thus facilitating catalysis at physiological pH values where the lone pair on the substrate nitrogen is required to initiate substrate oxidation. H-Tunneling in Trimethylamine Dehydrogenase We have investigated the effects of compromising mutations on tunneling in TMADH. Evidence from isotope studies (see below) supports the view that cataly13.5.2.2
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13 Hydrogen Tunneling in Enzyme-catalyzed Hydrogen Transfer
Figure 13.4. (a) Structure of the active site of TMADH showing ionizable residues and the aromatic ‘bowl’ (Tyr-60, Trp-264 and Trp-355) that interacts with the three methyl groups of the substrate through amino–aromatic interactions. Residues His-172 and Tyr-60 play key roles in stabilising the trimethylamine
base in the enzyme–substrate complex. (b) Kinetically influential ionizations in the fast phase of the reductive half-reaction of TMADH. Upper sequence, ionizations in native TMADH; lower sequence, the single ionization in the H172Q mutant enzyme.
sis by TMADH proceeds from a Michaelis complex involving trimethylamine base and not, as thought previously, trimethylammonium cation (Fig. 13.3(a)). Stoppedflow studies and analysis of tunneling regimes in this enzyme are not straightforward owing to the presence of four kinetically influential ionizations in the reduction of the 6-S-cysteinyl FMN of TMADH by substrate [two in the enzymesubstrate complex (pK a 6.5 and 8.2), one attributable to free trimethylamine (pK a 9.8) and one attributed to the free enzyme (pK a @ 10) which remains unassigned].
13.5 H-Tunneling in Flavoprotein Amine Dehydrogenases
In native TMADH, reduction of the flavin by substrate (perdeuterated trimethylamine) is influenced by two ionizations in the Michaelis complex with pK a values of 6.5 and 8.2 and maximal activity is realized in the alkaline region [83]. The latter ionization has been attributed to residue His-172 (through studies of the H172Q mutant enzyme; [78]) and, more recently, the former to the ionization of substrate itself [83]. Stopped-flow kinetic studies with trimethylamine as substrate have indicated that mutation of His-172 to Gln reduces the limiting rate constant for flavin reduction approximately 10-fold [78]. A kinetic isotope effect accompanies flavin reduction by H172Q TMADH, the magnitude of which varies significantly with solution pH. With trimethylamine, flavin reduction by H172Q TMADH is controlled by a single macroscopic ionization (pK a 6.8 G 0.1). This ionization is perturbed (pK a 7.4 G 0.1) in reactions with perdeuterated trimethylamine and is responsible for the apparent variation in the KIE with solution pH. The isotope dependence of this pK a value is of interest. The evidence suggests that this pK a represents the deprotonation of the substrate molecule itself [(CH3 )3 NHþ ! (CH3 )3 N] on moving from low to high pH. It is anticipated that perdeuteration of the substrate will affect this ionization since: (i) the shorter CaD bond results in a larger charge density, and thus it is electron supplying (i.e. stabilizing the NaH bond) relative to CaH; (ii) the perdeuterated substrate has a greater reduced mass for the (CD3 )3 NaH stretching vibration, and therefore lies lower in the asymmetric potential energy well (although the impact of this would be very small). Thus, the (CH3 )3 NaH bond dissociates more readily than the (CD3 )3 NaH bond, accounting for the elevated macroscopic pK a value seen with perdeuterated substrate in our kinetic studies. Figure 13.3(b) summarizes the prototropic control on flavin reduction in the enzyme–substrate complex. In Fig. 13.3(b) it is assumed that the rate of breakdown of the ES complex to EP is slow relative to the dissociation steps, so that the dissociation steps remain in thermodynamic equilibrium. Clearly, as a result of the elevated pK a value seen with perdeuterated substrate there is a greater concentration of the ESHþ (unreactive) complex (that is the lower branch of Fig. 13.3(b)). The effect of this partitioning between ES and ESHþ forms of the enzyme–substrate complex is that the observed KIE is inflated over the intrinsic value that would be realized if the concentration of the ES species were equivalent (at a given pH value) for both perdeuterated and protiated substrate. Only at pH values of 9.5 and above (where the group identified in the plot of k3 versus pH is fully ionized, and where the rate of flavin reduction is maximal), is the intrinsic isotope effect realized, owing to the enzyme being in the ES form for both protiated and perdeuterated substrate. In this regime, the KIE approaches a constant value of @4.5. In the enzyme–substrate complex, the pK a for the ionisation of trimethylamine (6.8) is more acidic than that of free trimethylamine (9.8). Consequently, in the Michaelis complex, the ionisation of substrate is substantially perturbed leading to a stabilisation of trimethylamine base by @10 kJ mol1 . We have shown by targeted mutagenesis and stopped-flow studies that this reduction of the pK a is a consequence of electronic interaction with residues Tyr-60 and His-172 and these two residues are therefore key for optimising catalysis in the physiological pH range. Formation of a Michaelis complex with trimethylamine base is con-
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13 Hydrogen Tunneling in Enzyme-catalyzed Hydrogen Transfer
sistent with a mechanism of amine oxidation that we advanced in our previous computational and kinetic studies which involves nucleophilic attack by the substrate nitrogen atom on the electrophilic C4a atom of the flavin isoalloxazine ring (Fig. 13.3). Substrate bond breakage by wild-type TMADH is too fast to be followed using the stopped-flow method in the regime where both His-172 and trimethylamine in the enzyme–substrate complex are deprotonated (that is @pH 10). Consequently, our tunneling studies have focused on the compromised mutant enzymes H172Q and Y169F (@10-fold and 40-fold reduction in the limiting rate constant for flavin reduction compared with wild-type enzyme, respectively). With H172Q TMADH flavin reduction is controlled by a single macroscopic ionization for substrate ionization (pK a 6.8), which is slightly elevated compared with the value obtained for wild-type owing to the stabilizing electronic effects of the His-172 side-chain in the latter. With H172Q TMADH this ionization is perturbed (pK a 7.4) in reactions with perdeuterated trimethylamine and is responsible for the apparent variation in the KIE with solution pH. At pH 9.5, where the substrate is fully ionized in the Michaelis complex, the KIE is independent of temperature in the range 277 to 297 K, whilst the reaction rates are still strongly dependent on temperature (Table 13.1); this is consistent with H-transfer by tunneling from the vibrational ground state of the reactive bond in a mechanism that is not dependent on gated motion (a possible alternative explanation is that there is still some gating, but this is not visible in the KIE temperature dependence as seen, for example, by Mincer and Schwartz [46]). With Y169F TMADH, the situation is different: the rate of flavin reduction is @4-fold more compromised than in H172Q TMADH and in the case of Y169F TMADH the KIE is dependent on temperature (Table 13.1). In this case, the temperature dependence of the KIE is consistent with the need for gated motion to facilitate the tunneling process.
13.6
Concluding Remarks
Quantum tunneling of hydrogen has emerged over recent years as a means by which enzymes catalyze reactions involving hydrogen transfer. The increasing body of experimental and computational evidence suggests that H-tunneling is likely to be adopted extensively by enzymes. The temperature dependent behavior of kinetic isotope effects has revealed that enzymes can catalyze reactions by ‘‘pure’’ quantum tunneling. KIEs give insight at the macroscopic level, but not at the atomic level. Computational studies are used to give insight into the atomic details of the mechanisms used by enzymes that invoke quantum tunneling. Protein dynamics (both ‘active’ and ‘passive’) drives these tunneling reactions, and a picture of how enzymes achieve this is beginning to emerge. However, many of the details at the atomic level remain to be discovered, and these will be probed in greater detail as more refined kinetic (for example at cryogenic temperatures) and computational techniques advance.
References
Acknowledgments
The authors are very grateful to Linus Johannissen, Kamaldeep Chohan, Richard Harris, Shila Patel, Adrian Mulholland and Kara Ranaghan for their valuable contributions to, and discussions about, the work presented. The BBSRC, EPSRC, University of Leicester and Wellcome Trust are thanked for providing financial support.
References 1 C. Lad, N. H. Williams, R.
2 3 4 5
6 7 8
9 10 11 12
13 14 15
16 17
Wolfenden, Proc. Natl. Acad. Sci. USA 2003, 100, 5607–5610. K. E. Neet, J. Biol. Chem. 1998, 273, 25527–25578. W. R. Cannon, S. J. Benkovic, J. Biol. Chem. 1998, 273, 26257–26260. A. Warshel, J. Biol. Chem. 1998, 273, 27035–27038. W. W. Cleland, P. A. Frey, J. A. Gerlt, J. Biol. Chem. 1998, 273, 25529–25532. S. J. Benkovic, S. Hammes-Schiffer, Science 2003, 301, 1196–1202. C. E. Cameron, S. J. Benkovic, Biochemistry 1997, 36, 15792–15800. P. T. Rajagopalan, S. Lutz, S. J. Benkovic, Biochemistry 2002, 41, 12618–21268. P. A. Frey, S. A. Whitt, J. B. Tobin, Science 1994, 264, 1927–1930. J. A. Gerlt, P. G. Gassman, Biochemistry 1993, 32, 11943–11952. W. W. Cleland, M. M. Kreevoy, Science 1994, 264, 1887–1890. W. R. Cannon, S. F. Singleton, S. J. Benkovic, Nat. Struct. Biol. 1996, 3, 821–833. M. J. Sutcliffe, N. S. Scrutton, Eur. J. Biochem. 2002, 269, 3096–3102. M. J. Knapp, J. P. Klinman, Eur. J. Biochem. 2002, 269, 3113–3121. D. Antoniou, S. Caratzoulas, C. Kalyanaraman, J. S. Mincer, S. D. Schwartz, Eur. J. Biochem. 2002, 269, 3103–3112. Z.-X. Liang, J. P. Klinman, Curr. Opin. Struct. Biol. 2004, 14, 648–655. A. Kohen, J. H. Jensen, J. Am. Chem. Soc. 2002, 124, 3858–3864.
18 K. L. Grant, J. P. Klinman,
Biochemistry 1989, 28, 6597–6605. 19 Y. Cha, C. J. Murray, J. P. Klinman,
Science 1989, 243, 1325–1330. 20 B. J. Bahnson, D. H. Park, K. Kim,
21
22
23 24
25
26
27
28
29
30
31 32
B. V. Plapp, J. P. Klinman, Biochemistry 1993, 32, 5503–5507. T. Jonsson, D. E. Edmondson, J. P. Klinman, Biochemistry 1994, 33, 14871–14878. R. P. Bell, The Tunnel Effect in Chemistry, Chapman and Hall, London, 1980, pp. 51–140. Y. H. Kim, M. M. Kreevoy, J. Am. Chem. Soc. 1992, 114, 7116–7123. J. Basran, M. J. Sutcliffe, N. S. Scrutton, Biochemistry 1999, 38, 3218–3222. J. Basran, M. J. Sutcliffe, N. S. Scrutton, J. Biol. Chem. 2001, 276, 24581–2587. J. Basran, S. Patel, M. J. Sutcliffe, N. S. Scrutton, J. Biol. Chem. 2001, 276, 6234–6242. R. J. Harris, R. Meskys, M. J. Sutcliffe, N. S. Scrutton, Biochemistry 2000, 39, 1189–1198. J. Basran, R. J. Harris, M. J. Sutcliffe, N. S. Scrutton, J. Biol. Chem. 2003, 278, 43973–43982. A. Kohen, R. Cannio, S. Bartolucci, J. P. Klinman, Nature 1999, 399, 496– 499. M. J. Knapp, K. Rickert, J. P. Klinman, J. Am. Chem. Soc. 2002, 124, 3865–3874. A. M. Kuznetsov, J. Ulstrup, Can. J. Chem. 1999, 77, 1085–1096. W. J. Bruno, W. Bialek, Biophys. J. 1992, 63, 689–699.
1357
1358
13 Hydrogen Tunneling in Enzyme-catalyzed Hydrogen Transfer 33 D. Borgis, J. T. Hynes, J. Phys. Chem. 34
35
36 37 38
39 40 41
42
43
44
45
46 47
48 49 50 51
1996, 100, 1118–1128. D. Antoniou, S. D. Schwartz, Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 12360–12365. J. Gao, M. Thompson, Methods and Applications of Combined Quantum Mechanical and Molecular Mechanical Methods, American Chemical Society, Washington DC, 1998. D. Antoniou, S. D. Schwartz, J. Chem. Phys. 1999, 110, 7359–7364. D. Antoniou, S. D. Schwartz, J. Chem. Phys. 1999, 110, 465–472. M. Garcia-Viloca, J. Gao, M. Karplus, D. G. Truhlar, Science 2004, 303, 186–195. S. Hammes-Schiffer, Curr. Opin. Struct. Biol. 2004, 14, 192–201. J. S. Mincer, S. D. Schwartz, J. Phys. Chem. B 2003, 107, 366–371. P. K. Agarwal, S. R. Billeter, P. T. Rajagopalan, S. J. Benkovic, S. Hammes-Schiffer, Proc. Natl. Acad. Sci. USA 2002, 99, 2794–2799. L. Masgrau, J. Basran, P. Hothi, M. J. Sutcliffe, N. S. Scrutton, Arch. Biochem. Biophys. 2004, 428, 41–51. T. Barna, H. L. Messiha, C. Petosa, N. C. Bruce, N. S. Scrutton, P. C. Moody, J. Biol. Chem. 2002, 277, 30976–30983. T. M. Barna, H. Khan, N. C. Bruce, I. Barsukov, N. S. Scrutton, P. C. Moody, J. Mol. Biol. 2001, 310, 433–447. P. Trickey, J. Basran, L.-Y. Lian, Z.-W. Chen, J. D. Barton, M. J. Sutcliffe, N. S. Scrutton, F. S. Mathews, Biochemistry 2000, 39, 7678–7688. J. S. Mincer, S. D. Schwartz, J. Chem. Phys. 2004, 120, 7755–60. J. Z. Pu, S. H. Ma, J. L. Gao, D. G. Truhlar, J. Phys. Chem. B 2005, 109, 8551–8556. D. Antoniou, S. D. Schwartz, J. Chem. Phys. 1998, 108, 3620–3625. R. A. Marcus, N. Sutin, Biochim. Biophys. Acta 1985, 811, 265–322. A. Warshel, J. Villa-Freixa, J. Phys. Chem. B 2003, 107, 12370–12371. M. H. Olsson, P. E. Siegbahn, A.
52 53
54
55
56
57
58
59 60 61 62
63 64 65
66 67 68
69 70 71
Warshel, J. Am. Chem. Soc. 2004, 126, 2820–2828. J. Villa, A. Warshel, J. Phys. Chem. B 2001, 105, 7887–7907. Z. X. Liang, T. Lee, K. A. Resing, N. G. Ahn, J. P. Klinman, Proc. Natl. Acad. Sci. USA 2004, 101, 9556–9561. C. J. Falzone, P. E. Wright, S. J. Benkovic, Biochemistry 1994, 33, 439–442. D. M. Epstein, S. J. Benkovic, P. E. Wright, Biochemistry 1995, 34, 11037–11048. M. J. Osborne, J. Schnell, S. J. Benkovic, H. J. Dyson, P. E. Wright, Biochemistry 2001, 40, 9846–9859. S. R. Billeter, S. P. Webb, P. K. Agarwal, T. Iordanov, S. HammesSchiffer, J. Am. Chem. Soc. 2001, 123, 11262–11272. P. K. Agarwal, S. R. Billeter, S. Hammes-Schiffer, J. Phys. Chem. B 2002, 106, 3283–3293. S. Hammes-Schiffer, Biochemistry 2002, 41, 13335–13343. S. Caratzoulas, S. D. Schwartz, J. Chem. Phys. 2001, 114, 2910–2918. D. Antoniou, S. D. Schwartz, J. Phys. Chem. B 2001, 105, 5553–5558. S. Caratzoulas, J. S. Mincer, S. D. Schwartz, J. Am. Chem. Soc. 2002, 124, 3270–3276. S. D. Schwartz, J. Phys. Chem. B 2003, 107, 12372. P. Ball, Nature 2004, 431, 396–397. K. M. Doll, B. R. Bender, R. G. Finke, J. Am. Chem. Soc. 2003, 125, 10877–10884. K. M. Doll, R. G. Finke, Inorg. Chem. 2003, 42, 4849–4856. W. Siebrand, Z. Smedarchina, J. Phys. Chem. 2004, 108, 4185–4195. H. M. Berman, J. Westbrook, Z. Feng, G. Gilliland, T. N. Bhat, H. Weissig, I. N. Shindyalov, P. E. Bourne, Nucleic Acids Res. 2000, 28, 235–242. R. J. Rohlfs, R. Hille, J. Biol. Chem. 1994, 269, 30869–79. R. B. Silverman, Progr. Brain Res. 1995, 106, 23–31. D. E. Edmondson, Xenobiotica 1995, 25, 735–53.
References 72 S. Rigby, R. Hynson, R. Ramsay,
73 74 75
76
77
78
A. W. Munro, N. S. Scrutton, J. Biol. Chem. 2005, 280, 4627–4631. J. Kim, M. Bogdan, M. PS, J. Am. Chem. Soc. 1993, 115, 10591–10595. J. R. Miller, D. E. Edmondson, Biochemistry 1999, 38, 13670–83. R. Miura, C. Setoyama, Y. Nishina, K. Shiga, H. Mizutani, I. Miyahara, K. Hirotsu, J. Biochem. 1997, 122, 825–855. J. Basran, M. J. Sutcliffe, N. S. Scrutton, J. Biol. Chem. 2001, 276, 42887–92. J. Basran, M. J. Sutcliffe, R. Hille, N. S. Scrutton, J. Biol. Chem. 1999, 274, 13155–13161. J. Basran, M. J. Sutcliffe, R. Hille, N. S. Scrutton, Biochem. J. 1999, 341, 307–314.
79 J. Basran, M. Mewies, F. S.
80
81
82
83
84 85
Mathews, N. S. Scrutton, Biochemistry 1997, 36, 1989–98. J. Basran, M. J. Sutcliffe, N. S. Scrutton, J. Biol. Chem. 2001, 276, 24581–24587. J. Nagy, W. C. Kenney, T. P. Singer, J. Biol. Chem. 1979, 254, 2684–2688. A. R. Raine, C. C. Yang, L. C. Packman, S. A. White, F. S. Mathews, N. S. Scrutton, Protein Sci. 1995, 4, 2625–2628. J. Basran, M. J. Sutcliffe, N. S. Scrutton, J. Biol. Chem. 2001, 276, 42887–42892. A. Kohen, J. P. Klinman, Acc. Chem. Res. 1998, 31, 397–404. A. Kohen, J. P. Klinman, Chem. Biol. 1999, 6, R191–R198.
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Hydrogen Exchange Measurements in Proteins Thomas Lee, Carrie H. Croy, Katheryn A. Resing, and Natalie G. Ahn 14.1
Introduction
Hydrogen exchange between protons in macromolecules and bulk solvent provides a powerful method to investigate global and local conformational changes, folding and stability, macromolecular interactions, and conformational mobility. This chapter describes techniques for monitoring hydrogen exchange processes that occur between acidic protons bound to proteins and hydrogen isotopes within bulk solvent (e.g., D2 O). Current methodologies are most appropriate for measuring slower exchange rates (half life @ 1 s or longer), which favor backbone amide hydrogens and certain slowly changing side chain hydrogens. In unstructured peptides, differences in exchange rate at various amide residues are primarily determined by inductive effects from surrounding residues. In proteins, the rate of exchange is controlled by additional environmental factors affecting proton acidity, as well as accessibility of protons to solvent molecules which catalyze abstraction. 14.1.1
Hydrogen Exchange in Unstructured Peptides
Amide hydrogens within peptides which lack secondary structure are constitutively exposed to solvent, thus their exchange rates are mainly governed by the concentration of available catalyst and inductive effects of side chains. Hydrogen exchange in peptides can be described by a chemical exchange rate constant (k ch ) for each hydrogen, which depends on an ‘‘intrinsic’’ rate constant of exchange (k int ) multiplied by the concentration of base or acid catalysts, which in water are represented by OH or H3 Oþ ions (k ch ¼ k int [catalyst]) (Fig. 14.1(a)). The chemical exchange rate constant for freely exposed amide hydrogens in peptides is minimal near pH 2.5 (k ch ¼ 101 –102 min1 at 5 C). Rates increase by 10-fold with each pH unit above or below this minima, due, respectively, to base-catalyzed or acid-catalyzed
These authors contributed equally to the preparation of this review.
Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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Figure 14.1. Hydrogen exchange mechanisms: (a) Amide exchange at neutral pH involves base catalyzed proton abstraction and acid catalyzed transfer of deuterium from solvent. Measurable isotope effects on the amide hydrogen and a lack of a solvent isotope effect indicate that proton abstraction is rate limiting [1]. (b) Schematic diagram of the two-state model for hydrogen exchange in native proteins and kinetic prediction. The rate of
observed hydrogen exchange (k obs ) depends on the fraction of conformers in the open state (e.g., breaking hydrogen bond) and the chemical exchange rate (k ch ¼ k int [catalyst]), where catalyst is OH or buffer. (c) In native proteins, the rate of opening is assumed to be much slower than the rate of closing. The observed rates of hydrogen exchange lie on a continuum described by EX1 and EX2 conditions, as described in the text.
proton abstraction [1]. Effects of pH, temperature, and neighboring residues on amide hydrogen exchange rate have been carefully measured in model peptides by the Englander laboratory [1–3]. From these measurements, chemical exchange rate constants can be calculated for amide residues between any combination of adjacent amino acid residues. In addition to catalyst concentration, the chemical exchange rates of amide hydrogens in peptides are influenced by surrounding amino acid residues. The intrinsic rate of exchange is dependent on local inductive effects which alter the pKa of the exchangeable proton, as well as steric effects from side chain groups which alter solvent accessibility of the amide hydrogens. A recent study also found that the effects of neighboring side chain on hydrogen exchange can be explained by residual structures of unfolded peptides which affect peptide backbone solvation and protection of amide groups from solvent [4].
14.1 Introduction
14.1.2
Hydrogen Exchange in Native Proteins
Exchange rates for amide hydrogens in native proteins can be much slower than the corresponding rates in peptides, typically differing by 10 2 –10 9 -fold. Protein folding, steric blocking, and hydrogen bonding interactions may reduce the local concentration of solvent catalyst by interfering with solvent accessibility, and may also alter chemical exchange rates by local perturbation of the pKa . Thus, protein tertiary and electrostatic interactions, as well as dynamic motions that lead to protein fluctuations or local unfolding, may strongly influence the exchange rates of amide hydrogens in native proteins. A two state kinetic mechanism, also referred to as the breathing or local unfolding model, has been a widely accepted model for hydrogen exchange processes [5, 6]. In this model, exchange reactions in native state proteins occur at or near protein–solvent interfaces at rates defined by the chemical exchange rate of unstructured peptides. However, reaction rates in the native protein are reduced by incomplete solvent accessibility, represented by the fraction of open or unfolded (open-state) versus closed or folded (closed-state) conformers (Fig. 14.1(b)). Thus, exchange rates can be influenced by transient protein fluctuations or flexibility, in addition to protein conformation. When the chemical exchange rate constant is much larger than the rate constant of structural closing (k close ), exchange occurs quickly after conversion of closed to open state (‘‘EX1 regime’’, Fig. 14.1(c)). At this limit, the observed rate constant of exchange approaches the rate constants for structural opening (k obs @ k open ). When the chemical exchange rate is slower than the rate for structural closing, conversion between open and closed states reaches equilibrium before exchange occurs (‘‘EX2 regime’’, Fig. 14.1(c)). At this limit, k obs approximates the product of the chemical exchange rate constant and the equilibrium constant for structural opening (k obs @ k ch K eq ¼ k ch k open =k close ). Thermodynamic parameters for hydrogen exchange events can be estimated from exchange rates measured under EX2 conditions. The rate of exchange for a given amide hydrogen in a protein can be reported as a protection factor, P, which equals the ratio between the theoretical chemical exchange rate in an unstructured peptide and the observed exchange rate (P ¼ k ch =k obs A k close =k open ¼ 1=K eq ). The logarithm of the protection factor is proportional to the apparent free energy for exchange, DGHX ¼ RT lnðK eq Þ A RT lnðPÞ, which reflects the change in state that a protein must achieve to enable structural opening and subsequent hydrogen exchange. Rates measured under EX2 conditions are proportional to the chemical exchange rate, which is in turn proportional to the catalyst concentration. This is not true under EX1 conditions where the observed rate reports structural opening, independent of chemical exchange. Therefore, measuring the pH dependence of the observed rate of hydrogen exchange allows one to distinguish between EX1 (pH independent) versus EX2 (pH dependent) mechanisms. In studies of native state proteins, the EX2 mechanism usually predominates under neutral pH condi-
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tions, where k close is typically greater than k ch . Under alkaline pH conditions, k ch may exceed k close , thus k obs approaches the EX1 regime. Measurements of k obs at varying pH can be fit to a two-state kinetic model [k obs ¼ ðk open k int ½OH Þ= ðk close þ k int ½OH Þ] from which individual rate constants for opening and closing can be reported [7]. The rate constant of opening can be directly and accurately estimated from these measurements. However, estimates of k close depend on the value of k int in the native protein, which may deviate from the measurements made in model peptides due to effects of tertiary environment. Therefore, measurements of k close should be interpreted carefully. In certain cases, biexponential rather than monoexponential time courses of hydrogen exchange from single backbone amide hydrogens may be observed, reflecting heterogeneous protein conformers that interconvert slowly. Such behavior can be observed in hydrogen exchange measurements of protein folding, under conditions where significant levels of open exchanging forms of a protein exist prior to initiation of the exchange reaction (e.g., K eq > 0:01), and are not in equilibrium with closed or structured forms (i.e., the conversion of open to closed conformers is slower than the chemical exchange rate; k close < k ch ). Rates of exchange from the pre-existing open forms are mixed with rates of exchange from closed forms, occurring with EX2 or EX1 kinetics [8, 9]. Examples include studies of protein folding intermediates of cytochrome c [10], where hydrogen exchange time courses were fit to a general biexponential pre-steady state rate equation, varying k ch by changing pH or pulse strength, in order to estimate k open , k close , and DGHX [9, 10]. Deviations in hydrogen exchange from monoexponential behavior have also been used as evidence for noninterconverting supramolecular forms of amyloid fibril molecules in solution [11]. 14.1.3
Hydrogen Exchange and Protein Motions
In addition to conformation and folding, hydrogen exchange measurements reveal information about internal motions of the folded state. Conversions in structure between open and closed conformers are assumed to be completely reversible in native proteins [12–14]. Such motions can be represented by a continuum between different hydrogen exchange mechanisms: Under the EX1 regime, where chemical exchange occurs rapidly after conversion from the closed to open conformers, motions can be described by local unfolding, involving timescales from milliseconds to seconds in native proteins [15]. A typical signature of EX1 exchange events is the correlation between exchange rates from individual hydrogens within a localized region of a protein. Rate limitation by k open leads to correlated exchange rates because the rate of reclosing is slow enough to allow exchange to occur from multiple hydrogens [16, 17]. Recent examples illustrate the determination of structural opening rates in a native protein from hydrogen exchange rates measured in the EX1 regime [15, 18]. Hydrogen exchange in the turkey ovalbumin third domain protein was monitored by NMR at varying pH. Observed rates were fit versus pH to a two-state
14.2 Methods and Instrumentation
kinetic model [k obs ¼ k open k int ½OH =ðk close þ k int ½OH Þ] from which estimates of k open ¼ 0.3–2.8 s1 and k close ¼ 0:8 10 3 –1:5 10 4 s1 were obtained for individual, slow exchanging amide hydrogens, and k open ¼ 40–200 s1 and k close ¼ 4–400 s1 were obtained for fast exchanging amides. A caveat with this method is that the EX1 exchange reactions were carried out at or above pH 10, conditions where many proteins are destabilized or unfolded. Therefore, protein stability and activity at high pH need to be examined carefully and confirmed when applying this method. While the approach is not suitable for all proteins, it provides a simple and valuable strategy to derive rate constants for conversion between open and closed protein conformers. Under EX2 conditions, where the rate of structural closing occurs faster than the rate of chemical exchange, individual hydrogens exchange in an uncorrelated manner, even when exposed to solvent in a single concerted motion. In this case, k obs reports the equilibrium between open versus closed conformers, from which the free energy of interconversion can be estimated. Motions that give rise to hydrogen exchange can be described by local fluctuations which are assumed to occur on millisecond to microsecond timescales [19]. Local fluctuations allowing hydrogen exchange events are assumed to involve breaking of hydrogen bonds, allowing solvent penetration into proteins and direct contact with solvent catalysts. In studies of hydrogen exchange by NMR, such fluctuations appear to occur over limited regions in proteins, typically less than 10 amino acids in length [15, 20–22]. In summary, the ability of hydrogen exchange measurements to report local protein changes at short timescales provides a powerful tool to measure solution behavior of proteins relevant to stability and conformational mobility.
14.2
Methods and Instrumentation 14.2.1
Hydrogen Exchange Measured by Nuclear Magnetic Resonance (NMR) Spectroscopy
NMR relaxation studies of nuclei in 15 N- and 13 C-labeled proteins, as well as heteronuclear Overhauser effects (NOE), have provided a wealth of insight into protein motions that occur in solution on picosecond–nanosecond and microsecond– millisecond timescales (reviewed in Refs. [23–25]). Hydrogen exchange NMR experiments provide complementary strategies to probe slower dynamic processes. Hydrogen exchange measurements are most often carried out by solvent exchange, reporting information about protons with slow or intermediate exchange rate constants (<0.1 s1 ). An alternative hydrogen exchange NMR strategy uses water magnetization transfer experiments, enabling rapidly exchanging protons, with exchange rate constants @0.1–100 s1 , to be observed. We briefly outline each experiment. For measurement of slower rates, solvent exchange is initiated either by dissolving lyophilized proteins into D2 O, or by solvent exchange into D2 O using rapid gel
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filtration. Proton signals are then monitored by collecting spectra at varying times after solvent exchange [26, 27]. A common collection method for 15 N-labeled protein would be a heteronuclear single quantum coherence (HSQC) experiment. The extent of exchange versus time can be measured by the reduction in the areas of the proton resonance peaks, normalizing intensities against the average intensity of multiple long-lived cross-peaks. The normalized data are then fit by nonlinear least squares to an exponential decay equation. Hydrogen exchange rates can be measured at specific residues when resonances for backbone amide protons are assigned. This is typically done by double labeling proteins with 13 C and 15 N amino acids and carrying out standard threedimensional experiments, which include HNCO and HN(CA)CO for backbone carbonyl assignments [28–31]; HNCA and HN(CO)CA for Ca assignments [31, 32]; HNCACB and CBCA(CO)NH for Cb assignments [33, 34], and all the above for amide resonance assignments. The dead time of the experiment is greater than 5 min, thus protons with slow exchange rate constants (<0.001 s1 ) are selectively monitored. These are assumed to be hydrogen bonded within regions of secondary structure, and typically represent more than half of the total amide hydrogens. Protons with faster rates of exchange, such as those found on surface exposed backbone atoms, cannot be monitored by methods involving change in solvent. Exchange can also be performed by measuring protons transferred from H2 O into deuterium-exchanged proteins, a strategy often used in protein folding experiments. For example, an early NMR protocol for monitoring slowly exchanging protons during folding, developed simultaneously by the Englander and Baldwin laboratories [17, 35], involved complete deuteration of unfolded proteins at low pH, initiation of folding followed by pulse labeling with H2 O at increased pH, and quenching exchange by decreasing pH. Transient states that showed partial exchange with hydrogen provided unequivocal support for the existence of intermediate states during refolding. Magnetization transfer techniques provide the means to measure rates at rapidly exchanging protons [36–38]. No change of solvent is involved; instead, water is excited with a selective 180 pulse which saturates the hydrogen spin states in solvent molecules, and exchange is detected by the appearance of proton resonances as magnetization from the solvent transfers to sites on the protein. Early magnetization transfer studies were often ambiguous due to signal contributions from other transfer mechanisms, such as NOEs arising from nonselective magnetization of Ca hydrogens whose chemical shifts are coincident with water, or exchange-relayed NOEs arising from nearby protons that undergo rapid exchange. Multiple pulse methods were therefore developed to suppress these distracting contributions. The Phase-Modulated CLEAN chemical EXchange (CLEANEX-PM) sequence [39] works by dephasing those protein NMR resonances that would give rise to distracting NOEs, while maintaining coherence of solvent protons. Amide proton peaks appear as exchange occurs during the mixing time, and increases in peak height versus time are used to determine k obs . Hwang and colleagues were able to measure accurate chemical exchange rates on submillisecond timescales using CLEANEX-PM and 2D-Fast HSQC (FHSQC) detection of 15 N-labeled staphylococ-
14.2 Methods and Instrumentation
cal nuclease. Tugarinov and Kay later demonstrated that CLEANEX-FHSQC experiments can be modified using a 3D-TROSY-HNCO type sequence in order to probe exchange processes in larger proteins [40, 41]. Magnetization transfer experiments on 13 Ca 15 N labeled malate synthase G were performed to reveal millisecond timescale motions occurring within the protein upon binding glyoxylate or pyruvate. NMR allows hydrogen exchange rates to be measured at specific amide hydrogens, enabling protection factors to be determined and related directly to the structural environment. However, determination of exchange rates with high resolution requires assignments of spectral peaks, which can be time consuming and require high concentrations of soluble protein. Furthermore, coverage of amide hydrogens is hampered by exchange rates outside the measurable range. 14.2.2
Hydrogen Exchange Measured by Mass Spectrometry
Mass spectrometry represents a complementary approach to NMR, providing faster analysis with high sequence coverage at lower protein amounts, although usually with reduced sequence resolution. MS enables detection at subpicomole sensitivity for hydrogen exchange measurements, which for many proteins is close to physiological concentration. Mass spectrometry detects hydrogen exchange in proteins by increased polypeptide mass, corresponding to 1 Da for each exchange event of a proton for solvent deuteron [42–44]. Initial studies measured exchange into intact proteins, for example by monitoring intact protein mass of ubiquitin to measure deuterium incorporation under native versus denatured conditions [45]. Later, strategies were developed to improve resolution by quenching exchange at varying times followed by proteolysis, and analysis of peptide weighted average mass [46, 47]. The sensitivity of mass spectrometers allows exchange reactions to be performed at submicromolar protein concentrations. Mass spectrometry is optimal for monitoring exchange into amide hydrogens. The exchange reaction is typically initiated by dilution of protein sample in water by @10–20-fold into D2 O. Reaction times are between seconds and hours, and reaction temperatures can easily be varied. Thus, rate constants for fast, intermediate and slow amides can be distinguished over 3 orders of magnitude (@0.00005– 0.05 s1 ). A larger range of rate constants can be captured by incorporating quench-flow methods to monitor exchange times down to 5 ms [48]. Exchange is quenched by rapidly lowering pH (pDread @ 2:4) and temperature (0 C) in order to reduce back-exchange, and the protein is diluted into water and rapidly (1–5 min) digested by proteolysis. Pepsin is used most often for proteolysis, due to its acidic pH optimum and stability against autolysis, although use of other proteases has also been reported [49, 50]. Proteolysis provides medium resolution that varies according to the lengths of peptide digestion products. Because pepsin cleavage specificities are not predictable, the cleavage sites must be inferred from peptide sequencing. This is performed most often by MS/MS, although accurate mass tag analysis, post-source decay, and C-terminal carboxypeptidase Y digestion
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have also been used. Often, coverage greater than 90% of amide hydrogens can be achieved. Weighted average masses of peptides are corrected for in-exchange during quenching and proteolysis (‘‘artifactual in-exchange’’) and back-exchange, from which the number of deuterons incorporated versus time is determined and fit to exponential models [51]. Because multiple exchange reactions occur on each peptide, the number of exponential terms theoretically equals the number of amides. However, in practice, rates of individual amides often cannot be distinguished and are instead grouped into classes with fast (>0.05 s1 ), intermediate (0.001– 0.05 s1 ), and slow (<0.001 s1 ) averaged rate constants, the latter includes those that are nonexchanging over the observation period. Examples of mass spectra along with a multi-exponential fitted curve are shown in Fig. 14.2 [52]. A feature unique to mass spectrometry datasets is that populations of molecules that exchange with greatly different rates but interchange slowly can be distinguished by the appearance of bimodal mass/charge distributions [53]. Thus, denatured populations within protein samples can be quantified by the appearance of peptides that show isotopic distributions at lower average mass, reflecting EX2 exchange by native forms, and higher average mass, reflecting rapid exchange by unfolded forms.
Figure 14.2. Quantifying deuterium incorporation into a protein detected by HX-MS. (a) MALDI-TOF mass spectra showing the incorporation of deuterium into a peptide from IkBa, EVIRQVKGDLAF (MHþ1 ¼ 1374.77), after indicated times of hydrogen/deuterium exchange. Apparent deuteration at each time point is measured by calculating the weighted average mass of the peptide and subtracting the weighted average mass at t ¼ 0. Average weighted mass is calculated as the P P ð i ðm=zÞi Ii Þ= i Ii , where ðm=zÞi is the mass/ charge for each isotopic peak and Ii is the
intensity of that isotopic peak. The number of deuterons incorporated into peptides at each time point are corrected for back-exchange and artifactual in-exchange. (b) Time course of deuteration, fit to a sum of three exponentials reporting fast (30 s1 ), intermediate (0.2 s1 ), and slow (0.01 s1 ) rate constants. Adapted with permission from Croy et al. [52]. Reprinted with permission from Croy C.H., Bergqvist S., Huxford T., Ghosh G., Komives E.A., Protein Sci., 2004, 13, 1767–1777. Copyright 2004 Cold Spring Harbor Laboratory Press.
14.2 Methods and Instrumentation
Mass spectral analysis is usually carried out by electrospray ionization (ESI), which generates multiply charged forms of peptides, or matrix assisted laser desorption/ionization (MALDI), which generates singly charged forms. These ionization methods require different sample preparation protocols. ESI enables peptide separation by reversed-phase HPLC in-line with the mass detector. Peptides are desalted on the column, leading to loss of deuteration at side-chains which rapidly back-exchange to water. As a result, amide hydrogens are observed almost exclusively. By embedding the column and injector in an ice/water slurry (0 C), and carrying out proteolysis in the sample loop or on a protease column, back-exchange of amide hydrogens to water during the liquid chromatographic (LC) separation can be minimized to @20% or less [54]. Matrix-assisted laser desorption ionization (MALDI) analysis involves mixing peptide analytes with matrix solution, typically a-cyano-4-hydroxycinnamic acid, and drying the mixture on a MALDI target prior to laser desorption and time of flight (TOF) detection. A 10–20 fold dilution into water is performed at the time of quenching in order to reduce deuteration of side-chains and preferentially monitor amide hydrogens [55, 56]. Back-exchange of amide hydrogens can be maintained between 35 and 50% by preparing the matrix solution in a mixture of acetonitrile, ethanol, and trifluoroacetic acid at pH 2.2–2.5, pre-chilling MALDI targets, and rapidly drying samples under vacuum [55]. Advantages of MALDI over ESI are that the spectra are simpler because singly charged ions are primarily observed, and HPLC is not required, therefore protocols and analyses are easier to perform. Advantages of ESI are that back-exchange is lower, ionization suppression is lower compared to MALDI, and LC separations reduce spectral overlap between peaks, increasing protein sequence coverage and allowing exchange reactions to be performed for longer times. ESI and MALDI interfaces can be coupled to various types of mass detectors including quadrupole, ion-trap, time-of-flight (qTOF), and Fourier transform ion cyclotron resonance (FT-ICR) mass analyzers. Mass spectral resolution, defined as observed mass divided by the full-width at half maximum peak height (FWHM) varies between instruments (quadrupole @800, ion-trap @3000, TOF @10 000, FTICR @70 000). ESI-quadrupole-TOF and MALDI-TOF instruments both provide baseline resolution of isotopic peaks and high data quality. The higher resolution of FT-ICR enables faster LC runs, thus reducing back-exchange, and enables analysis of large proteins or multiprotein samples with more complex peptide composition [57]. Recent protocols have automated hydrogen exchange measurements by LC-ESI-MS using a quadrupole ion trap instrument, or by MALDI-TOF using an autosampler for target plate spotting, allowing experiments to be performed with higher throughput [58, 59]. 14.2.3
Hydrogen Exchange Measured by Fourier-transform Infrared (FT-IR) Spectroscopy
Infrared detection represents one of the first strategies used to monitor protein hydrogen exchange [60]. Most IR studies measure the integrated intensity of the
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amide II band (@1550 cm1 ), assigned to a mode that couples NaH bond bending with CaN stretching. As amide protons are exchanged for deuterons, the wavenumber maximum decreases to @1450 cm1 (amide II 0 ), which mainly represents CaN stretching vibrations that are no longer coupled with NaD bending (reviewed in Refs. [61, 62]). The number of amide hydrogens that exchange over a given period, at slow or intermediate exchange rates, averaged over the entire protein, may be determined by fitting the normalized amide II intensity [ðAII; t AII; y Þ=AII; H20 ] against time using a multi-exponential decay equation. FT-IR measurements yield information about global hydrogen exchange into polypeptides, and can be used to reveal changes in tertiary structure or domain interactions in large protein complexes. A recent example measured overall hydrogen exchange changes which occur upon photoactivation of rhodopsin by monitoring the isotopic shift in the amide II band [63]. The authors used time resolved HXFT-IR to monitor conformational changes which occur within the 7-helix core of rhodopsin upon photoactivation, an event that allows binding of the ligand transducin. In order to monitor the solvent-protected core, the authors first allowed the accessible amides in the protein to exchange in D2 O for 48 h prior to photoactivation, after which 67% of the amide II intensity remained. Upon photoactivation, they observed a new population of exchangeable protons which consisted of fast (time constant @30 min) and slow (@11 h) components. Although they were not able to identify the regions in the protein that accounted for the increased exchange or measure whether these regions correlated to the appearance and decay of known rhodopsin intermediates, they were able to conclude that photoactivation caused buried portions of the core to become more accessible. A caveat of any method that monitors global hydrogen exchange is that exchange rates cannot be treated as occurring uniformly along the polypeptide backbone, thus information about exchange behavior in localized regions may be lost. This is illustrated by a study examining hydrogen exchange in different forms of alcohol dehydrogenase and comparing FT-IR versus mass spectrometry [64]. The ‘‘corresponding state’’ theory postulates that homologous thermophilic and psychrophilic proteins will show similar flexibility when measured at their physiological temperatures [65]. Global hydrogen exchange measured by FT-IR spectroscopy appeared to refute this prediction, showing overall lower exchange in psADH than htADH. However, analysis of individual peptides by HX-MS showed enhanced exchange in psADH compared to htADH, localized to regions involved in substrate and cofactor binding. Thus, localized flexibility within the active site is more likely relevant to catalysis than global motions. The amide I band region (1620–1680 cm1 ) can be used to monitor different classes of secondary structure, where absorbance is dominated by CbO vibrations. Second derivative peaks in this region are characteristic of secondary structure environments (b-sheet @ 1638/1628 cm1 ; a-helix @ 1655 cm1 ; b-turn @ 1686/1679 cm1 ; 310 helix @ 1660 cm1 ), and correlations between changes in these peaks with time of exposure in D2 O can be used to assign exchange rates to various secondary structures, thus improving resolution [66–68]. For example, a recent study of brain-derived neurotrophic factor (BDNF) binding to its receptor (trkB) used
14.3 Applications of Hydrogen Exchange to Study Protein Conformations and Dynamics
HX-FT-IR to monitor the global solvent accessibility of receptor in its unbound versus bound state, and then interpreted the observed hydrogen exchange differences by examining changes in secondary structure and thermal stability from the amide I 0 bands [66]. BDNF was metabolically labeled with 13 C- and 15 N-amino acids, resulting in isotopic shifts within the amide I 0 region. This enabled observation of both BDNF and trkB in the complex without spectral overlap, a method referred to as isotope-edited FT-IR. Amide I 0 band wavenumbers demonstrated that both proteins contained @50% b-sheet structure, and that a small percentage of loop structure in ligand-free trkB was converted into b-turn structure upon ligand binding. The overall stability of trkB decreased upon complex formation, indicated by a new amide I 0 band appearing at 1613 cm1 , a wavenumber associated with thermally denatured proteins. Correspondingly, HX into trkB increased significantly upon ligand binding, as observed by a 75% increase in amide II 0 band intensity, indicating that a large number of amides showed increased solvent accessibility in the complexed form. Raman spectroscopy showed significant conformational changes at six disulfide bonds upon ligand–receptor complex formation, consistent with loosening of tertiary structure, increased HX, and increased sensitivity to thermal denaturation. Attenuated total reflection Fourier transform infrared spectroscopy (ATR-FT-IR) involves depositing a thin film of protein on an internal reflection element, initiating deuteration by flushing the sample with nitrogen gas saturated with D2 O, and monitoring loss of signal from the amide II band. Advantages over normal transmission FT-IR are that the experiment requires lower amounts of analyte (1–100 mg), and can be performed within seconds after initiation, enabling amides exchanging with intermediate to fast rates to be observed. The solid support also enables sample orientation. By combining ATR with linear dichroism, secondary structures in membrane transporter proteins and orientation of helices relative to the membrane plane could be determined, allowing hydrogen exchange measurements to be selectively recorded from integral membrane-bound helices [69, 70].
14.3
Applications of Hydrogen Exchange to Study Protein Conformations and Dynamics 14.3.1
Protein Folding
Hydrogen exchange in proteins reports secondary and tertiary structures as well as loss of structure due to unfolding. From such measurements, protein folding intermediates and their kinetic and thermodynamic properties can be monitored. Most applications to examine protein folding use kinetic pulse labeling or equilibrium hydrogen exchange labeling strategies. In pulse labeling [71], an unfolded and fully deuterated protein, prepared in D2 O at high denaturant concentration, is diluted into H2 O to initiate refolding. The diluting solution is maintained at moderately low pH and temperature (e.g., pH 6,
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10 C) in order to slow chemical exchange rates at solvent accessible amides (halflife @ s). At various times during refolding, the pH is elevated (pH 8.5–10, halflife @ ms) to initiate pulsed back-exchange for short, fixed times (e.g. 50 ms) and then exchange is quenched by rapidly lowering the pH to 2.5. Backbone amide hydrogens in unstructured regions undergo back-exchange during the short pulse, whereas amide hydrogens in structured regions do not, providing a snapshot of folding in local regions at varying times. A recent study by Krishna et al. [10] provides an excellent example using hydrogen exchange by pulse labeling to investigate protein folding intermediates and their kinetics. Folding reactions with denatured cytochrome c were carried out with a fixed 100 ms prelabeling period at pH 6, followed by 50 ms pulses at varying pHs ranging from 7.5 to 10. NMR measurements of fractional back-exchange versus pH were fit to pre-steady state solutions, from which individual rate constants for opening and closing could be estimated (Section 14.1.2, Fig. 14.1(b)). The results revealed protection of N-terminal and C-terminal helices from back-exchange, indicating their secondary structure formation within 100 ms. In contrast, other regions of the protein showed partial or no protection. The free energies of unfolding (DGHX ) estimated from protection factors measured in the N and C-terminal regions were greater than those estimated for model helices in solution, suggesting that additional tertiary interactions formed within these helices which were more similar to the native state. Rates of structural closing indicated that folding in these regions occurred on a millisecond timescale, much slower than the nanosecond timescale observed for stable helices in solution. Importantly, these regions showed the highest free energy of unfolding in cytochrome c, and were proposed to represent the last step in a sequential unfolding pathway ([72]; see below), presumably due to steric hindrance and interactions between side chains. Rate constants of structural opening (k open ) in these regions were similar, suggesting that the two helices unfold in a concerted manner, and that unfolding begins at the ends of each helix. Overall, the results provided evidence for protein folding intermediates containing secondary and tertiary structures and resembling a partially constructed native state. Hydrogen exchange by equilibrium labeling monitors proteins at varying equilibria between folded and unfolded states, typically under conditions of added denaturants or lowered pH. Using this approach, protein folding intermediates of cytochrome c were monitored by measuring exchange rates and calculating DGHX versus increasing concentrations of guanidinium chloride (GdmCl) [72, 73]. A linear dependence of unfolding free energy on denaturant concentration [DGU ðGdmClÞ A DGHX ðGdmClÞ] was assumed (DGHX ðGdmClÞ ¼ DGHX ð0Þ m½GdmCl), where the slope (m) increases with the degree of denaturant-sensitive surface exposed during unfolding. At low [GdmCl], hydrogen exchange is dominated by local fluctuations and DGHX is independent of denaturant (m A 0). As GdmCl increases, global unfolding is enhanced and the slope increases in magnitude until linearity is observed between DGHX and [GdmCl]. Extrapolation to [GdmCl] ¼ 0 provided estimates of DGHX ð0Þ. It was observed in cytochrome c that groups of amino acids (usually within the
14.3 Applications of Hydrogen Exchange to Study Protein Conformations and Dynamics
Figure 14.3. HX reveals cooperative unfolding in cytochrome c. (a) A plot of DGHX versus guanidium chloride (GdmCl). Residues in cytochrome c with similar slopes at high GdmCl indicate similar free energies of global partial unfolding. Four of the five identified groups of unfolding units, termed ‘‘foldons’’ (red, orange, green, blue) are illustrated in this figure. The data suggest that residues in each foldon participate in a cooperative unfolding
unit and that cytochrome c unfolds in a sequential manner from the least stable foldon (red) to the most stable foldon (blue). (b) Foldons of cytochrome c, color coded against the X-ray structure in order of increasing stability (red, orange, green, blue). Adapted with permission from Bai et al. [72]. Reprinted with permission from Bai Y., Sosnick T.R., Mayne L., Englander S.W., Science, 1995, 269, 192–197. Copyright 1995 AAAS.
same secondary structure) were observed to have similar slope and intercepts, suggesting their participation as a cooperative unit (‘‘foldon’’) with the same DGHX ð0Þ. The results suggested that cytochrome c has five distinct foldons (named nested yellow, red, yellow, green, blue), which were proposed to unfold in a stepwise and sequential manner from lowest to highest DGHX ð0Þ (N < R < Y < G < B) (Fig. 14.3). The sequential unfolding model was further examined by introducing a point mutation (E62G) into the Y foldon, which disrupted salt bridge formation and destabilized the protein by 0.8 kcal mol1 [73]. The mutation decreased DGHX ð0Þ by @0.8 kcal mol1 in Y, R, and B foldons, but had little or no effect on N or R foldons. Changes in DGHX ð0Þ would be expected only for the Y foldon, if unfolding of each unit occurred independently. Therefore the results confirmed that the five units in cytochrome c unfold via a sequential, stepwise pathway. Hydrogen exchange by equilibrium labeling has also been used to study protein molten globules, a term that describes compact, partially folded species which lack complete tertiary interactions of the native state. In general, molten globules are viewed as an interconverting ensemble of structures, rather than a single conformational species. Creative means have been employed to observe such folding intermediates and to glean information about their behavior. Various proteins are known to exist in discrete molten globule states under mildly denaturing or acidic
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pH conditions [74]. Their isolation and characterization by NMR structural analysis is complicated by the propensity of these partially folded states to aggregate, leading to extreme line broadening and poor chemical shift dispersion. Use of hydrogen exchange can circumvent these problems, by allowing exchange to occur with the molten globule state, and then refolding the protein to the native structure. Well-resolved NMR spectra are obtained which report regions of solvent accessibility in the intermediate state. In this way, hydrogen exchange from a-lactalbumin was initiated in D2 O under pH conditions that favored the molten globule [74–76]. After varying times, the reaction was quenched and the protein was freeze-dried until NMR acquisition. Redissolving the protein in pH 5.5 buffer containing Ca 2þ promoted the native structure of a-lactalbumin, from which 2D-HSQC data were collected. Amides within A-, B-, and C-helices were protected from exchange and identified by retention of 1 H signal, evidence that these secondary structures were maintained in both the molten globule and the native state of the protein. Furthermore, the relative stability of these regions could be evaluated by titrating denaturant into the sample and measuring protection factors, demonstrating reduced stability of the molten globule state (P ¼ 100) compared to the native state (P > 10 7 ) [76]. Thus, by characterizing ‘‘molten globule’’ states, insights into kinetically transient intermediates in folding pathways were obtained. A practical application of folding analysis by hydrogen exchange is to screen proteins for crystallization optimization. A bottleneck in structural genomics is producing suitably diffracting protein crystals. Unstructured regions in proteins with higher flexibility cause structural heterogeneity in proteins, preventing crystallization. The ability of hydrogen exchange measurements to successfully reveal regions that interfere with crystallization was tested, using ESI-MS [77, 78]. Sites of proteolytic cleavage and regions of rapid deuteration (10 s) were mapped in 24 Thermotoga maritima proteins with known crystallization behavior. Regions of high deuteration were found to correlate with regions disordered in X-ray structures. Truncations were then made to remove rapidly exchanging regions in two proteins. Crystallization trials showed that one protein crystallized more readily in its truncated form (76 crystals out of 1920 attempts) than its corresponding full-length form (2 crystals out of 2400 attempts) and diffracted well (maximum resolution ¼ 1.9 A˚). Thus, hydrogen exchange measurements may be useful for distinguishing regions of flexibility from stable cores, facilitating protein analysis. 14.3.2
Protein–Protein, Protein–DNA Interactions
Comparing the extent of hydrogen exchange between bound versus unbound proteins provides a facile method for probing protein–protein interactions, macromolecular complexes, and protein–ligand interactions. Decreased hydrogen exchange (increased protection factors) around a binding interface can be interpreted by steric exclusion of bulk solvent from the binding interface, or alternatively, stabilization and reduced flexibility of the binding interface upon ligand binding.
14.3 Applications of Hydrogen Exchange to Study Protein Conformations and Dynamics
Both NMR and MS techniques have been used to analyze protein–protein interactions by hydrogen exchange, which reports interfaces between proteins as well as conformational changes induced upon protein complex formation. Early hydrogen exchange labeling studies were carried out by 2D-NMR to determine sites for antibody binding to horse cytochrome c [79]. Later, the same approach was used to map regions of association in a complex formed between yeast ferricytochrome c and cytochrome c peroxidase [80]. Although the X-ray structure of this complex had previously revealed an interface for protein–protein interactions, significant conformational differences between free versus complexed proteins were not observed. In contrast, the HX-NMR study revealed long distance conformational changes. In addition to expected chemical shifts of residues near the interface and around the exposed heme cofactor, hydrogen exchange protection was observed within the C-terminus of ferricytochrome c, a region located far from the protein– protein interface. A practical concern in mapping protein–protein interactions by HX-MS is the need for relatively high binding affinities. In order to identify protected interfaces and/or conformational changes upon binding, bound forms should ideally represent @75% of total protein. Given typical protein concentrations used in HX-MS experiments (1–5 mM), a 1:1 molar ratio of proteins is sufficient to achieve this level of binding when K d is less than @0.1 mM. However, lower affinities require higher molar ratios of one of the two proteins in order to maintain sufficient complex formation, which often leads to saturating signals and/or obscures peptides from the less abundant protein. In such cases, use of synthetic peptides in place of proteins, which are known to mimic protein interactions, allows examination of low affinity binding interactions. A recent example used HX-MS to locate binding sites on mitogen activated protein kinases (MAPKs) for substrate docking motifs, conserved regions in substrates and other proteins which enhance affinity and specificity of binding interactions [81]. Hydrogen exchange protection of MAP kinases p38 and ERK2 by peptide ligand revealed the location of homologous binding sites for a basic residue docking motif (K d @ 20 mM), confirming previous conclusions made from X-ray cocrystal structures of p38. In addition, a surface hydrophobic pocket in ERK2, protected by a separate hydrophobic docking motif (K d @ 10 mM), was found to be located in a region distal to the site of the basic residue docking motif (Fig. 14.4). Disruption of protein binding by site-directed mutagenesis confirmed the importance of the surface hydrophobic pocket as the relevant binding site for the hydrophobic docking motif. Together with the kinase catalytic cleft, these sites for docking motif binding revealed a new view of how tripartite interactions with enzyme confer substrate recognition. Two HX-MS studies investigated sites of interaction between regulatory (R) and catalytic (C) subunits of cAMP dependent protein kinase (PKA) where the affinity was in the nanomolar range, enough to maintain a stable complex between intact proteins [82, 83]. Kinase activity in PKA is inhibited by R and C subunit binding, and de-repressed when cAMP binds to R, which leads to subunit dissociation and release of the active C subunit. Hydrogen exchange by MALDI-MS was used to
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Figure 14.4. HX reveals the binding sites for substrate docking motifs on ERK2. (a) Three regions in ERK2 showed significant decreases in hydrogen exchange upon binding a docking motif peptide (open circles) compared to the unbound state of ERK2 (closed circles). (b) The regions represented in panel (a) are mapped onto the surface of ERK2 (red, green, and cyan). A model of substrate interactions with ERK2 (yellow) showing a sequence (PRSPAKLSFQFPS) from Elk1. Ser3 represents the site of phosphorylation, which is facilitated by a conserved Phe-X-Phe docking motif at res.
9–11. The model constrained the Ser hydroxyl (purple) to lie within hydrogen bonding distance of the catalytic Asp nucleophile (orange). The Phe-X-Phe motif (dark blue) was allowed to interact with a hydrophobic pocket that was revealed by HX-MS and confirmed by site-directed mutagenesis. Adapted with permission from Lee et al. [81]. Reprinted from Lee T., Hoofnagle A.N., Kabuyama Y., Stroud J., Min X., Goldsmith E.J., Chen L., Resing K.A., Ahn N.G., Mol. Cell, 2004, 14, 43–45. Copyright 2004 Elsevier.
14.3 Applications of Hydrogen Exchange to Study Protein Conformations and Dynamics
compare free R subunit, R–C holoenzyme complex in the absence of cAMP, and R þ C in the presence of cAMP. Binding of C resulted in protection of two alpha helices within a subdomain of the R subunit. This was located within a region adjacent to, but not overlapping with, residues previously shown by mutagenesis to be important for binding, suggesting that the mutations reduce affinity by perturbing direct binding interactions. Unexpectedly, C subunit binding also led to increased protection at a distal site in R that contained the cAMP binding pocket. Conversely, cAMP binding increased solvent accessibility within the helical subdomain in R comprising the R–C interface. Based on this evidence, the authors proposed that, in addition to sites of direct protein interaction, hydrogen exchange protection revealed transmission of conformational information between binding sites that were relevant to ligand allostery. Further resolution of the PKA binding interaction sites based on hydrogen exchange data were explored using a computational docking program. The docking program, DOT [84], was used to compute 117 billion potential docking structures based on X-ray coordinates of R and C subunits. The top 100 000 lowest energy structures were then filtered using hydrogen exchange information. For example, when amide exchange data showed two protected sites within a given region in R, docked structures would only be selected when two Ca atoms from this region were within 10 A˚ of the R–C subunit interface. After filtering, 15 structures remained, each showing a similar R–C interface, but differing in the rotational orientation between subunits. Further clustering of these structures yielded a subpopulation used to model the holoenzyme complex, which predicted R–C contacts consistent with previous mutational studies. Thus, data obtained from HX-MS are able to refine protein docking models generated computationally. Hydrogen exchange has also been used to probe specific interactions between proteins and DNA. Kalodimos et al. [85] characterized the mechanism of interactions between Lac headpiece (HP) protein and DNA operator sequences by HXNMR. Protection factor estimates in LacHP indicated greater structural stability in the DNA bound state (P @ 10 7 ) compared to the unbound state (P @ 10 2 ). Exchange rates were then measured under EX1 conditions by varying pH, in order to estimate k open and k close in LacHP, which were assumed to reflect respective rate constants of dissociation and association with DNA. The measurements revealed three distinct ranges for k open within the hinge helix, containing the DNA binding site (@0.20 h1 ), within Asn50 and the C-terminus of helix III (@0.1 h1 ), and within the rest of LacHP (@0.02 h1 ). These were interpreted to reflect sequential steps in the pathway of protein–DNA dissociation. Residues in each region showed similar values of k open , suggesting that each group of residues dissociates from DNA as a cooperative unit. Importantly, independent measurements of the macroscopic dissociation rate constant (@0.05 h1 , [86]) corresponded to the slowest and rate limiting value of k open . Parallel measurements of k close revealed that protein–DNA association is initiated by interactions between the recognition helix (helix II) in LacHP and the major groove of DNA, occurring with a rate constant @40 s1 , which is consistent with the macroscopic rate constant for asso-
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ciation. Overall, the data provided a model for LacHP–DNA association and dissociation, in which the rate limiting step for binding involves proper orientation between DNA and the LacHP helix-turn-helix, followed by association of the hinge helix with the minor groove of DNA. Greater flexibility of LacHP in the unbound state may enable initial DNA sliding, which is then followed by specific recognition of operator sequences in the major groove, formation of the hinge helix, and recognition of the minor groove. In contrast, LacHP–DNA dissociation is initiated by hinge helix unfolding which disrupts stable interactions in the major groove. This study illustrates the ability of HX measurements to elucidate details of protein– DNA interactions which cannot easily be monitored by conventional biochemical methods. 14.3.3
Macromolecular Complexes
An important advantage of HX-MS is its ability to study large proteins and macromolecular complexes. The size limitation is mainly governed by how well peptides in proteolytic digests can be uniquely identified and resolved from each other. Studies on macromolecular structures have been carried out using ESI-MS coupled to reverse phase-HPLC [87–89] as well as MALDI-MS without LC separation [90]. Examples described in this section illustrate analyses of heterotetramers, conformational changes in oligomeric capsid assemblies and formation of heterogeneous polymeric fibrils. A recent study compared nucleosome subcomplexes containing histone H3 or its centromeric variant, CENP-A, in an effort to explore differential packing in nucleosomes targeted to noncentromeric versus centromeric DNA [87]. Heterotetramers formed between CENP-A and histone H4 showed markedly reduced hydrogen exchange within two regions of H4 compared to the heterotetramers formed between histones H3 and H4, suggesting selective protection and subunit compaction by CENP-A association. Bimodal exchange behavior in 13 overlapping peptides was observed in H3-H4, revealing multiple discrete structural states. In agreement, analytical ultracentrifugation showed a smaller Stokes radius in CENP-A-H4 than H3-H4, implying greater compactness in the centromeric complex. Chimeras that substituted regions in H3 located at the H4 interface with homologous regions in CENP-A were then made and found to confer greater subunit compaction as well as centrometric targeting. The results support a model in which CENP-A directs centromeric targeting in part by conferring structural rigidity to nucleosome complexes. Viral capsids consist of large oligomeric assemblies, usually composed of single subunit types. High resolution models of viral capsids are often constructed from X-ray structures of individual subunits configured against capsids imaged by cryoelectron microscopy. However, these provide little information about intersubunit interactions and conformational changes that occur as the capsids change their form. Hydrogen exchange by ESI-MS of the @3.6 MDa brome mosaic virus
14.3 Applications of Hydrogen Exchange to Study Protein Conformations and Dynamics
(BMV) particle was performed to examine the behavior of the BMV capsid protein [89]. Reversible swelling of viral particles occurs when the pH is increased from 5 to 7, which has been linked to capsid stability and disassembly. After correcting for pH effects on chemical exchange, increased deuterium incorporation was observed at high pH, consistent with overall loosening of the protein assembly upon expansion. In contrast, solvent protection at the C terminus of the capsid protein was unaffected by pH, indicating that strong intersubunit interactions were still maintained. Hydrogen exchange by MALDI-MS was used to study the expansion of bacteriophage P22 capsids which occurs upon DNA packaging and viral maturation [90]. P22 maturation was initiated by raising temperature, identifying regions in the capsid protein that varied in flexibility between procapsid and mature capsid assemblies. In addition, a pulse exchange method was used to carry out inexchange during the expansion phase followed by back-exchange from the expanded form. Regions of the capsid protein that were solvent exposed only during the expansion period were identified by retention of deuterium, and interpreted as domains that were transiently exposed, then buried or stabilized in the mature form. Structures of fibril forming proteins have proven challenging to study at highresolution, due to the size and heterogeneity of the protein aggregates. However, HX-MS provides a method well suited to distinguish different aggregate forms. Studies of amyloid aggregation have explored protection patterns in amyloid Ab peptide (1-40), a proteolytic product of amyloid precursor protein, in unstructured monomeric, protofibril, and mature fibril forms [91–93]. Amyloid Ab protofibrils are oligomeric forms that are relevant to assemblies in Alzheimer’s disease, but are transiently observed and challenging to characterize. Hydrogen exchange monitored for 2 days showed strong solvent protection in protofibrils, covering 40% of backbone amides, in contrast to unstructured monomers which exchanged rapidly throughout the polypeptide. Strong protection of mature amyloid fibrils was also observed, covering 60% of backbone amides, indicating a significant core structure in protofibrils that approximates mature fibrils. Another study examined conformational changes in prion proteins during transition from soluble to aggregated states [93]. The soluble Het-S protein contains a well-ordered globular domain (residues 1–230) and an unstructured C-terminus (residues 240–289). Hydrogen exchange by MALDI-MS revealed that the Cterminal region is solvent accessible in the monomer but undergoes substantial solvent protection upon amyloid formation, suggesting that this region represents the site involved in aggregation. 14.3.4
Protein–Ligand Interactions
Hydrogen exchange has been used to map protein binding sites for ligands as small as metal ions. An early HX-MS study examined effects of Ca 2þ binding on recoverin, a sensor that enhances the lifetime of photoexcited rhodopsin by inhibit-
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ing rhodopsin kinase at high intracellular Ca 2þ concentrations. A ‘‘calciummyristoyl switch’’ model proposed that Ca 2þ binding promotes membrane association of recoverin by exposing an N-terminal myristoyl group. Neubert et al. [94] monitored hydrogen exchange on recoverin in myristoylated versus unmyristoylated states and in the presence and absence of Ca 2þ using ESI mass spectrometry. The results showed protection of a hydrophobic cleft in myristoylated recoverin that was abolished upon addition of Ca 2þ , supporting a model in which the myristoyl group interacts with the hydrophobic core in the absence of metal ion, but extends into the solvent after Ca 2þ binding. Interestingly, protection from hydrogen exchange was observed in only two of four helix-loop-helix ‘‘EF-hand’’ peptides, suggesting that only two EF-hands coordinate Ca 2þ . These conclusions were subsequently confirmed by NMR solution structures of myristoylated recoverin in the presence and absence of Ca 2þ [95, 96]. Hydrogen exchange also proves a powerful tool to identify sites on proteins targeted by pharmaceutical compounds. Eg5, a member of the kinesin superfamily, is essential for microtubule spindle formation and centrosome separation during mitosis, and a viable candidate for antimitotic drug development. Using hydrogen exchange mass spectrometry, Brier et al. [97] examined binding of S-trityl-lcysteine, a potent inhibitor of this enzyme (IC50 @ 1:0 mM). Global deuteration of intact protein for 120 min showed reduced exchange at @30 backbone amide hydrogens in inhibitor-bound versus free Eg5. Hydrogen exchange followed by proteolysis with pepsin revealed these amides to be located within the loop L5-a2 helix and b5-a3 regions, a domain containing the microtubule motor. Substitution of 21 residues in the motor domain of human Eg5 with equivalent residues from Neurospora Crassa Eg5 eliminated the effect of S-trityl-l-cysteine on ATPase activity, confirming the motor domain as the relevant binding site for the inhibitor. This study demonstrates that HX-MS can be used to rapidly probe interactions between small molecules and receptors prior to the high resolution structural determination. Development of high throughput methods for measuring protein–ligand binding is important in fields such as pharmaceutical therapeutics. ‘‘Stability of Unpurified Proteins from Rates of hydrogen EXchange’’ (SUPREX), is a MALDI-MS hydrogen exchange approach designed to rapidly quantify protein folding energy [59]. In this method, ligand interactions are assumed to increase protein folding energy, thus, ligand binding should increase the amount of denaturant needed to unfold the protein, which is indicated when the isotopic envelope shifts to high mass [98]. Hydrogen exchange rates in the presence versus absence of ligand are measured in the EX2 regime at increasing concentrations of denaturant, from which apparent dissociation constants and free energies for ligand binding can be calculated. For high-throughput applications, hydrogen exchange can be monitored at a fixed denaturant concentration (single point SUPREX). Powell and Fitzgerald [99] successfully identified high affinity ligands for a model protein (S protein), by screening combinatorial libraries containing peptides with affinities varying between K d @ 34 nM to 1000 mM. When fully automated, single point SUPREX was proposed to enable screening of 100 000 compounds per day.
14.3 Applications of Hydrogen Exchange to Study Protein Conformations and Dynamics
14.3.5
Allostery
Allosteric interactions between ligand binding sites play important roles in protein regulation. These involve changes in conformation or dynamics that may occur over long distances, which can be difficult to infer from static X-ray structures. Classically, allostery has been explained by transitions between discrete conformational states, which modulate binding affinity through changes in enthalpy [100, 101]. An alternative mechanism, proposed by Cooper and Dryden [102–104], suggested instead that ‘‘dynamic allostery’’ may involve modulation of affinity via changes in the distribution of fluctuations around the mean structure of a protein. Thus, allosteric regulation of binding may be attributed to entropic effects, e.g., due to altered side chain mobilities not observable by X-ray crystallography. The ability of hydrogen exchange measurements to report internal motions or conformational mobility within localized regions has led to increased use of this approach for documenting long distance communication in proteins. Due to protein size limitations with NMR, mass spectrometry is generally preferred for hydrogen exchange analyses of multidomain proteins, where allosteric interactions more often occur. Hemoglobin (Hb) represents a classic model for protein allostery, and structural and thermodynamic changes responsive to ligand (oxygen) binding were successfully examined by hydrogen exchange in tritiated water, using scintillation counting to monitor exchange [105–107]. Each of the 4 subunits in Hb (a2b2) contains a heme group, and sequential binding of oxygen to each subunit enhances the binding affinity to unoccupied sites. The basis of allostery has been modeled from X-ray structures of deoxy (T-state) versus oxy (R-state) forms of Hb, in which movement of Fe(ii) into the plane of the heme upon oxygen binding is propagated to the ab dimer interface and quaternary structure, affecting the binding affinity at each of the other subunits. Studies by the Englander laboratory [105–110] examined global hydrogen exchange into Hb with tritiated water, revealing changes in rate constants for amide exchange between different states of Hb. Later, higher resolution was obtained by digesting the protein with pepsin and separating the resulting peptides by HPLC [111]. In these studies, five amide hydrogens at the N-terminus of Hba showed 9-fold higher exchange rates in the R- versus T-state, while four amide hydrogens at the C-terminus of Hbb showed 190-fold higher exchange rates in the R- versus T-state. Allostery is indicated by the reduction in free energy upon oxygen binding (T to R) of 1.2 kcal mol1 monomer1 for Hba and 2.85 kcal mol1 monomer1 for Hbb. The free energy of allosteric destabilization upon oxygen binding (8.1 kcal mol1 at 0 C) is consistent with the value measured independently in binding studies (8.2 kcal mol1 at 5 C). Hydrogen exchange also revealed that ligand binding to Hba subunits altered exchange within unbound Hbb subunits, and vice versa, evidence for cross-subunit communications within the T-state Hb. Importantly, cross-subunit effects were not observed with the HbM (Milwaukee) mutant (Hbb–Val67Glu) in which Fe(ii) is 0.2 A˚ away from the heme plane, suggesting that cross-subunit communications depend on
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the movement of Fe(ii) with respect to the heme, rather than oxygen binding [110]. Analysis of thrombin illustrates the ability of hydrogen exchange mass spectrometry to reveal long distance interactions between an enzyme active site and distal regions in the protein. Thrombin regulates procoagulant pathways via proteolytic cleavage of fibrinogen, into fibrin, which then self-assembles to form insoluble fibrin clots. Binding of thrombomodulin (TM) alters the substrate specificity of thrombin to favor protein C, which initiates anticoagulant pathways. Biochemical studies indicated that TM binds to anion binding exosite 1 (ABE1), a site in thrombin distant from the active site. It was proposed that TM binding alters substrate specificity through allosteric regulation of the active site conformation, however, no conformational changes were apparent in X-ray cocrystal structures of TMthrombin [112]. However, hydrogen exchange experiments showed that TM binding reduced exchange within a surface loop adjacent to the active site as well as in the ABE1 [84]. Furthermore, binding of a competitive peptide inhibitor reduced hydrogen exchange at ABE1 as well as the active site [113]. The results provide evidence for reciprocal interactions between the TM binding site (ABE1) and the catalytic site via mechanisms that are more likely to involve changes in conformational mobility than structural perturbations. Hydrogen exchange measurements thus appear to be quite sensitive to perturbations in exchange within regions distal from ligand binding sites, and similar effects have been observed in many proteins. However, so far, the evidence for causality between binding and changes in hydrogen exchange are largely correlative, and the physical basis of effects reported by hydrogen exchange measurements, as well as their importance towards allosteric function, remains to be determined. Further studies are needed to explore this intriguing hypothesis by characterizing mutations in proteins that both eliminate allostery and disrupt effects on hydrogen exchange at long distances. These studies also illustrate an important caveat when examining sites for ligand binding interactions, that reduced hydrogen exchange does not always reflect steric effects from direct ligand binding interactions, and therefore require confirmation by independent methods.
14.3.6
Protein Dynamics
An exciting application of hydrogen exchange is to explore the relevance of global and local protein flexibility and dynamics in enzyme catalysis. It is often postulated that protein motions underlie conformational and entropic contributions to catalysis; however, motions in enzymes have been difficult to assay. Although NMR measurements of chemical relaxation and order parameters report local dynamics of proteins on timescales ranging from picoseconds to nanoseconds (see Section 14.2.1), the relevance of extremely fast motions in proteins to binding or catalysis is not clear (with the possible exception of electron or hydrogen tunneling). Hydrogen exchange can be used to probe local dynamics of proteins at timescales
14.3 Applications of Hydrogen Exchange to Study Protein Conformations and Dynamics
ranging from microseconds to seconds (Section 14.1.3), which overlaps timescales relevant to enzyme catalysis. An early study that correlated enzyme rate with hydrogen exchange behavior compared active versus inactive forms of the signaling enzyme, MAP kinase kinase 1 (MKK1) [114]. Two sets of activating mutations in MKK1 were examined, one which replaced regulatory phosphorylation sites with acidic residues, and another which deleted 8 residues from the N-terminus. Either mutation elevated the specific activity of MKK1 by 40–80-fold, and combining these mutations synergistically elevated activity by up to 600-fold. Localized changes in hydrogen exchange were examined in the single and combinatorial mutants, and compared to inactive WT enzyme. Noteworthy was a significant increase in exchange occurring within the N-terminal ATP-binding domain. This was attributed to enhanced flexibility upon activation and, due to overlapping proteolytic products, the sites of increased hydrogen exchange were able to be pinpointed to single amides in this domain. Such behavior was more consistent with fluctuations or breathing motions of the enzyme, which transiently enhance solvent accessibility in these regions, because local unfolding would be expected to alter hydrogen exchange at adjacent amides. Importantly, both sets of mutations individually increased the hydrogen exchange in the N-terminal domain and, in each case, the magnitude of the increase was intermediate to that observed in the combinatorial mutant. Thus, the increased hydrogen exchange in this region correlated qualitatively with increased specific activity. The authors hypothesized that enhanced flexibility within the N-terminal domain is important for MKK1 activation, perhaps to promote ATP binding, phosphoryl transfer, or ADP release. Local dynamic changes upon mutation that correlate with changes in enzyme activity were also suggested in glutathione transferase, GSTM1, which catalyzes the addition of glutathione to 1-chloro-2,4-dinitrobenzene (CDNB) with product release as the rate-limiting step [115]. Elevated activity of mutant GSTM1-Tyr115Phe was attributed to increased product release rates, whereas values of k chem for glutathione transfer and K d for CDNB binding were similar to those of WT enzyme. The high resolution X-ray structure of GSTM1-Tyr115Phe was identical to WT enzyme, except for loss of a hydrogen bond between Tyr115 and a neighboring backbone amide. However, comparison of GSTM1-WT versus GSTM1-Tyr115Phe by hydrogen exchange showed increased exchange rates, not only in the region containing the Tyr115Phe mutation, but also in an adjacent region containing the channel for product release. The results suggested that increased protein motions near the channel may explain how the mutation enhances the rate of product release. Other studies have used hydrogen exchange to reveal protein conformational and dynamic changes following covalent modifications of proteins. Hoofnagle et al. [116] monitored changes in conformational mobility in ERK2 following kinase phosphorylation, which increases the enzyme specific activity >1000-fold. Altered hydrogen exchange rates were observed upon phosphorylation in regions located >10 A˚ from the site of covalent modification. X-ray structures of unphosphorylated versus phosphorylated ERK2 revealed no conformational differences
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that could explain the altered hydrogen exchange rates, leading these investigators to hypothesize that the effects on hydrogen exchange reflect changes in conformational mobility or flexibility upon phosphorylation. Interestingly, regions of ERK2 that showed increased exchange upon kinase activation were those that would be expected to undergo motions during catalysis. Follow-up studies comparing active and inactive ERK2 using site-directed spin labeling (SDSL) and electron paramagnetic resonance spectroscopy (EPR) supported the conclusion that increased hydrogen exchange rates in these regions reflect increased flexibility in a manner correlated with enhanced turnover [117]. Perhaps the strongest evidence substantiating the connection between hydrogen exchange measurements and catalytic function has been made from correlations between exchange rates and hydrogen tunneling in related enzymes with differing temperature optima. Through a mechanism termed ‘‘environmentally coupled hydrogen tunneling’’, heavy atom motions in the active site control the probability of hydrogen transfer in the thermophilic alcohol dehydrogenase (htADH) from B. stearothermophilus [118]. Previous studies of temperature-dependent kinetic isotope effects showed discontinuities in Arrhenius plots which were attributed to a change in the properties of tunneling at elevated temperatures (Fig. 14.5(a)) [119]. Such results could be explained by invoking environmental coupling, in which hydrogen transfer is enhanced at high temperatures by increased sampling of a conformational space that is inaccessible at low temperature, thus reducing the reaction barrier width and enhancing coupling between reactant and product states. One test of the model was to demonstrate a transition in conformational mobility accompanying increased tunneling at high temperatures, which would reflect coupling to enzyme dynamics. HX-MS was carried out on htADH at 10–65 C, and averaged hydrogen exchange rate constants versus 1=T were evaluated for each peptide [120]. Overall, averaged hydrogen exchange rate constants increased with temperature, and most varied linearly with 1=T, as expected by Arrhenius behavior. But, unexpectedly, peptides that formed the cofactor and substrate binding sites underwent discrete transitions that increased temperature dependences above 30 C (Fig. 14.5(b) and (c)). Thus, regions in the active site undergo a transition in motion or conformation, which coincides with the change in the activation energy of k cat for hydride transfer and tunneling, indicating a direct correlation between hydride transfer and localized protein mobility in htADH. These results substantiate the ability of HX-MS to report changes in enzyme mobility, revealing locations in proteins that are relevant to catalytic function. Studies of enzyme orthologs with different temperature optima provide strong evidence for the importance of dynamics on enzyme catalysis, and their examination by HX has been insightful [64]. As mentioned above (Section 14.2.3), studies comparing HX behavior of thermophilic versus psychrophilic alcohol dehydrogenase by FT-IR versus mass spectrometry provided evidence that localized motions within discrete regions of the molecule are more likely relevant to catalysis than global motions. Similar conclusions were reached by hydrogen exchange NMR studies of thermophilic versus mesophilic rubredoxin. Structural comparisons suggest that the enhanced thermal stability of proteins from thermophilic organisms
14.3 Applications of Hydrogen Exchange to Study Protein Conformations and Dynamics
Figure 14.5. HX reveals a temperaturedependent transition in mobility. (a) Arrhenius plot for the oxidation of protonated (circles) or deuterated (squares) benzyl alcohol by htADH. The discontinuity at 30 C indicates a transition in activation energy for the reaction. (b) Weighted averaged HX rate constant (kHXðWAÞ ) for peptides from htADH plotted versus 1=T shows discontinuities at 30 C in five peptides. The weighted averaged kHX is defined as ðAk1 þ Bk2 þ Ck3 Þ=NH where NH is the total number of amide hydrogens in the peptide, and A, B, and C are the number of amide hydrogens exchanging with rate
constants k1 , k2 , and k3 , respectively. (c) The X-ray structure of htADH monomer where the five peptides from panel (b) (coded by number) are mapped onto the structure. All five peptides are located within the substrate binding domain, suggesting that localized changes in protein mobility proximal to the active site are linked to changes in the catalytic rate. Adapted with permission from Liang et al. [120]. Reprinted from Liang Z.X., Lee T., Resing K.A., Ahn N.G., Klinman J.P., Proc. Natl. Acad. Sci. U.S.A., 2004, 101, 9556–9561. Copyright 2004, National Academy of Sciences, U.S.A.
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may be caused by increased accumulation of salt bridges and other intramolecular interactions [121, 122]. To address whether global conformational rigidity may also account for increased thermostability, hydrogen exchange rates at fast exchanging amide protons (k ex > 0:2 s1 ) in thermophilic versus mesophilic rubredoxin were measured at varying pH and temperature by CLEANEX-PM [123]. At room temperature, mesophilic rubredoxin underwent significantly faster hydrogen exchange in regions surrounding the catalytic metal binding site and a three-stranded b-sheet compared to its thermophilic ortholog, suggesting higher flexibility at equivalent temperatures. In contrast, reduced hydrogen exchange occurred within a multiple turn domain in mesophilic compared to thermophilic rubredoxin. This was explained in part by ion pair interactions found only in the thermophilic enzyme; however, the exchange rates in this region showed no temperature dependence in thermophilic rubredoxin, unlike the mesophilic ortholog. These results suggest that thermal stability in the thermophilic compared to the mesophilic enzyme are due to localized rather than global conformational rigidity of the protein.
14.4
Future Developments
Further developments promise to broaden the technical capabilities and scope of problems that can be addressed by hydrogen exchange measurements. New TROSY techniques that yield high resolution spectra for large proteins, new methods for measuring residual dipolar couplings, and cryoprobe technologies are extending the range of protein sizes and concentrations that can be observed by NMR, from which improved protocols for HX-NMR are expected to follow. Major advances in hydrogen exchange measurements by mass spectrometry are needed to increase spatial resolution, by localizing deuteration events at specific amides and allowing measurement of individual protection factors. Increased resolution can be obtained to some degree by comparing the exchange rates between peptides with overlapping sequences. These are often generated by incomplete proteolysis by pepsin, and may also be enhanced using multiple proteases to produce variable patterns of cleavage [49, 114]. However, exchange rates can rarely be measured at more than a few amides. Several attempts have been made to achieve higher resolution by MS/MS, examining fragment ions for incremental mass shifts that report deuteration at specific residues, and requiring that the sum of deuterated sites equals the total deuterium incorporation into the peptide (reviewed in Ref. [124]). However, so far, the results have been mixed. A significant problem with MS/MS is that the high energy required to induce fragmentation often leads to nonspecific exchange along the peptide, a phenomenon termed scrambling. Some studies have shown significant scrambling behavior, particularly using model peptides deuterated at specific residues. However, other studies reported deuteration of b-ion fragments at individual amides without scrambling [125, 126], which in each case correlated well with corresponding hydrogen exchange rates determined by NMR. Residue-specific deuter-
References
ation has also been reported, upon inducing collision activated dissociation of an intact protein in the nozzle-skimmer region of the ESI source [127]. Most likely, scrambling occurs in a nonrandom fashion, determined by mechanisms for gas phase peptide bond cleavage. The most common cleavage mechanism involves formation of an oxazolone b ion and y ion, via attack of the backbone carbonyl oxygen at the n–1 position at a protonated peptide bond [128–132]. Very rapid cleavages probably occur at sites protonated during the ionization processes, while slower cleavages probably involve interchange of proteins by vibrational motion (mobile proton model). Thus, it is likely that scrambling is problematic at some peptide bonds, but not others. Recent computational algorithms based on classical kinetics and the mobile proton hypothesis have successfully simulated peptide MS/MS fragmentation generated in a 3D ion trap mass spectrometer [133]. Predictive models for fragmentation may be useful for improving the design of fragmentation experiments, in order to define conditions that minimize intramolecular proton interchange. Further improvement of hydrogen exchange methods will involve methods for improving throughput as well as better computational tools to facilitate data reduction. Such goals for hydrogen exchange experiments can be useful for screening compound libraries for protein binding, providing complementary information to high throughput structure determination by NMR and X-ray crystallography. In contrast to high resolution analyses, which show limited compatibility with many proteins and are often carried out under restrictive conditions, HX-MS shows applicability towards a wide range of proteins, accommodating greater diversity in protein sizes, solubilities, concentrations, and solution conditions. Furthermore, HX-MS is readily adaptable to high-throughput protocols. A prototype for automated acquisition and analysis in HX-MS studies was reported by Hamuro et al., who described a fully-automated sample handling system that carries out 100 labeling and quenching reactions, an automated LC system that performs in-line proteolysis and RP separation prior to MS detection, and a software analysis package which can rapidly analyze time courses of exchange [58]. Further development of these methods as well as approaches such as SUPREX (Section 14.3.1) will broaden applications of HX-MS for gaining insight into protein structure and dynamics.
References 1 G. P. Connelly, Y. Bai, M. F. Jeng,
S. W. Englander, Proteins, 1993, 17, 87–92. 2 Y. Bai, J. S. Milne, L. Mayne, S. W. Englander, Proteins, 1993, 17, 75–86. 3 R. S. Molday, S. W. Englander, R. G. Kallen, Biochemistry, 1972, 11, 150–158. 4 F. Avbelj, R. L. Baldwin, Proc. Natl.
Acad. Sci. U.S.A., 2004, 101, 10967– 10972. 5 A. Hvidt, C. R. Trav. Lab. Carlsberg, 1964, 34, 299–317. 6 S. W. Englander, N. R. Kallenbach, Quart. Rev. Biophys., 1983, 16, 521–655. 7 T. Sivaraman, A. D. Robertson, Methods Mol. Biol., 2001, 168, 193–214.
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10
11
12
13 14
15 16
17
18 19
20 21
22
23 24 25
26
1999, 286, 607–616. M. M. Krishna, L. Hoang, Y. Lin, S. W. Englander, Methods, 2004, 34, 51–64. M. M. Krishna, Y. Lin, L. Mayne, S. W. Englander, J. Mol. Biol., 2003, 334, 501–513. K. Yamaguchi, H. Katou, M. Hoshino, K. Hasegawa, H. Naiki, Y. Goto, J. Mol. Biol., 2004, 338, 559–571. Y. Bai, J. J. Englander, L. Mayne, J. S. Milne, S. W. Englander, Methods Enzymol., 1995, 259, 344–356. J. Clarke, L. S. Itzhaki, Curr. Opin. Struct. Biol., 1998, 8, 112–118. S. W. Englander, N. W. Downer, H. Teitelbaum, Annu. Rev. Biochem., 1972, 41, 903–924. C. B. Arrington, A. D. Robertson, J. Mol. Biol., 2000, 296, 1307–1317. A. Miranker, C. V. Robinson, S. E. Radford, R. T. Aplin, C. M. Dobson, Science, 1993, 262, 896–900. H. Roder, G. A. Elove, S. W. Englander, Nature, 1988, 335, 700–704. C. B. Arrington, A. D. Robertson, Biochemistry, 1997, 36, 8686–8691. G. Hernandez, F. E. Jenney, Jr., M. W. Adams, D. M. LeMaster, Proc. Natl. Acad. Sci. U.S.A., 2000, 97, 3166–3170. K. Kuwajima, R. L. Baldwin, J. Mol. Biol., 1983, 169, 299–323. G. Wagner, C. I. Stassinopoulou, K. Wuthrich, Eur. J. Biochem., 1984, 145, 431–436. H. Maity, W. K. Lim, J. N. Rumbley, S. W. Englander, Protein Sci., 2003, 12, 153–160. L. E. Kay, Nat. Struct. Biol., 1998, 5, 513–517. R. Ishima, D. A. Torchia, Nat. Struct. Biol., 2000, 7, 740–743. J. Cavanagh, W. J. Fairbrother, A. G. Palmer III, N. J. Skelton, Protein NMR Spectroscopy: Principles and Practice, Academic Press, San Diego, 1996. B. K. John, D. Plant, R. E. Hurd, J. Magn. Reson., Ser. A, 1992, 101, 113–117.
27 L. E. Kay, P. Keifer, T. Saarinen,
28 29
30
31
32 33 34 35 36
37
38 39 40 41 42
43
44 45
46 47 48 49
J. Am. Chem. Soc., 1992, 114, 10663– 10665. S. Grzesiek, A. Bax, J. Magn. Reson., 1992, 96, 432–440. H. Matsuo, E. Kupce, H. J. Li, G. Wagner, J. Magn. Reson., Ser. B, 1996, 111, 194–198. R. T. Clubb, V. Thanabal, G. Wagner, J. Magn. Reson., 1992, 97, 213–217. L. E. Kay, M. Ikura, R. Tschudin, A. Bax, J. Magn. Reson., 1990, 89, 496–514. A. Bax, M. Ikura, J. Biomol. NMR, 1991, 1, 99–104. ¨ller, J. Magn. M. Wittekind, L. Mu Reson., Ser. B, 1993, 101, 201–205. S. Grzesiek, A. Bax, J. Am. Chem. Soc., 1992, 114, 6291–6293. J. B. Udgaonkar, R. L. Baldwin, Nature, 1988, 335, 694–699. G. Gemmecker, W. Jahnke, H. Kessler, J. Am. Chem. Soc., 1993, 115, 11620–11621. S. Mori, M. Johnson, J. M. Berg, P. C. M. van Zijl, J. Am. Chem. Soc., 1994, 116, 11982–11984. S. Grzesiek, A. Bax, J. Biomol. NMR, 1993, 3, 627–638. T. L. Hwang, P. C. van Zijl, S. Mori, J. Biomol. NMR, 1998, 11, 221–226. V. Tugarinov, L. E. Kay, J. Am. Chem. Soc., 2003, 125, 13868–13878. V. Tugarinov, L. E. Kay, J. Mol. Biol., 2003, 327, 1121–1133. A. N. Hoofnagle, K. A. Resing, N. G. Ahn, Annu. Rev. Biophys. Biomol. Struct., 2003, 32, 1–25. L. S. Busenlehner, R. N. Armstrong, Arch. Biochem. Biophys., 2005, 433, 34–46. S. J. Eyles, I. A. Kaltashov, Methods, 2004, 34, 88–99. V. Katta, B. T. Chait, Rapid Commun. Mass Spectrom., 1991, 5, 214–217. Z. Zhang, D. L. Smith, Protein Sci., 1993, 2, 522–531. R. S. Johnson, K. A. Walsh, Protein Sci., 1994, 3, 2411–2418. H. Yang, D. L. Smith, Biochemistry, 1997, 36, 14992–14999. L. Cravello, D. Lascoux, E. Forest,
References
50
51
52
53
54
55
56
57 58
59
60 61 62
63
64
65
66
Rapid Commun. Mass Spectrom., 2003, 17, 2387–2393. J. J. Englander, C. Del Mar, W. Li, S. W. Englander, J. S. Kim, D. D. Stranz, Y. Hamuro, V. L. Woods, Jr., Proc. Natl. Acad. Sci. U.S.A., 2003, 100, 7057–7062. A. N. Hoofnagle, K. A. Resing, N. G. Ahn, Methods Mol. Biol., 2004, 250, 283–298. C. H. Croy, S. Bergqvist, T. Huxford, G. Ghosh, E. A. Komives, Protein Sci., 2004, 13, 1767–1777. D. M. Ferraro, N. D. Lazo, A. D. Robertson, Biochemistry, 2004, 43, 587–594. K. A. Resing, A. N. Hoofnagle, N. G. Ahn, J. Am. Soc. Mass Spectrom., 1999, 10, 685–702. J. G. Mandell, A. M. Falick, E. A. Komives, Anal. Chem., 1998, 70, 3987–3995. J. G. Mandell, A. M. Falick, E. A. Komives, Proc. Natl. Acad. Sci. U.S.A., 1998, 95, 14705–14710. J. Lanman, P. E. Prevelige, Jr., Curr. Opin. Struct. Biol., 2004, 14, 181–188. Y. Hamuro, S. J. Coales, M. R. Southern, J. F. Nemeth-Cawley, D. D. Stranz, P. R. Griffin, J. Biomol. Technol., 2003, 14, 171–182. S. Ghaemmaghami, M. C. Fitzgerald, T. G. Oas, Proc. Natl. Acad. Sci. U.S.A., 2000, 97, 8296– 8301. H. Lenormant, E. R. Blout, Nature, 1953, 172, 770–771. A. Barth, C. Zscherp, Quart. Rev. Biophys., 2002, 35, 369–430. R. B. Gregory, A. Rosenberg, Methods Enzymol., 1986, 131, 448– 508. P. Rath, W. J. DeGrip, K. J. Rothschild, Biophys. J., 1998, 74, 192–198. Z. X. Liang, I. Tsigos, V. Bouriotis, J. P. Klinman, J. Am. Chem. Soc., 2004, 126, 9500–9501. P. Zavodszky, J. Kardos, Svingor, G. A. Petsko, Proc. Natl. Acad. Sci. U.S.A., 1998, 95, 7406–7411. T. Li, J. Talvenheimo, L. Zeni, R. Rosenfield, G. Stearns, T. Arakawa, Biopolymers, 2002, 67, 10–19.
67 H. H. de Jongh, E. Goormaghtigh,
68
69
70
71 72
73 74 75
76
77
78
79 80 81
82
83
J. M. Ruysschaert, Biochemistry, 1997, 36, 13593–13602. H. H. de Jongh, E. Goormaghtigh, J. M. Ruysschaert, Biochemistry, 1997, 36, 13603–13610. V. Grimard, C. Vigano, A. Margolles, R. Wattiez, H. W. van Veen, W. N. Konings, J. M. Ruysschaer, E. Goormaghtigh, Biochemistry, 2001, 40, 11876–11886. C. Vigano, M. Smeyers, V. Raussens, F. Scheirlinckx, J. M. Ruysschaert, E. Goormaghtigh, Biopolymers, 2004, 74, 19–26. P. S. Kim, R. L. Baldwin, Biochemistry, 1980, 19, 6124–6129. Y. Bai, T. R. Sosnick, L. Mayne, S. W. Englander, Science, 1995, 269, 192–197. H. Maity, M. Maity, S. W. Englander, J. Mol. Biol., 2004, 343, 223–233. C. Redfield, Methods Mol. Biol., 2004, 278, 233–254. J. Baum, C. M. Dobson, P. A. Evans, C. Hanley, Biochemistry, 1989, 28, 7–13. V. Forge, R. T. Wijesinha, J. Balbach, K. Brew, C. V. Robinson, C. Redfield, C. M. Dobson, J. Mol. Biol., 1999, 288, 673–688. D. Pantazatos, J. S. Kim, H. E. Klock, R. C. Stevens, I. A. Wilson, S. A. Lesley, V. L. Woods, Jr., Proc. Natl. Acad. Sci. U.S.A., 2004, 101, 751–756. G. Spraggon, D. Pantazatos, H. E. Klock, I. A. Wilson, V. L. Woods, Jr., S. A. Lesley, Protein Sci., 2004, 13, 3187–3199. Y. Paterson, S. W. Englander, H. Roder, Science, 1990, 249, 755–759. Q. Yi, J. E. Erman, J. D. Satterlee, Biochemistry, 1994, 33, 12032–12041. T. Lee, A. N. Hoofnagle, Y. Kabuyama, J. Stroud, X. Min, E. J. Goldsmith, L. Chen, K. A. Resing, N. G. Ahn, Mol. Cell, 2004, 14, 43– 55. G. S. Anand, C. A. Hughes, J. M. Jones, S. S. Taylor, E. A. Komives, J. Mol. Biol., 2002, 323, 377–386. G. S. Anand, D. Law, J. G. Mandell, A. N. Snead, I. Tsigelny, S. S.
1389
1390
14 Hydrogen Exchange Measurements in Proteins
84
85
86
87
88
89 90
91
92
93
94
95
96
97
98 99 100
Taylor, L. F. Ten Eyck, E. A. Komives, Proc. Natl. Acad. Sci. U.S.A., 2003, 100, 13264–13269. J. G. Mandell, A. Baerga-Ortiz, S. Akashi, K. Takio, E. A. Komives, J. Mol. Biol., 2001, 306, 575–589. C. G. Kalodimos, R. Boelens, R. Kaptein, Nat. Struct. Biol., 2002, 9, 193–197. C. G. Kalodimos, G. E. Folkers, R. Boelens, R. Kaptein, Proc. Natl. Acad. Sci. U.S.A., 2001, 98, 6039–6044. B. E. Black, D. R. Foltz, S. Chakravarthy, K. Luger, V. L. Woods, Jr., D. W. Cleveland, Nature, 2004, 430, 578–582. J. Lanman, T. T. Lam, S. Barnes, M. Sakalian, M. R. Emmett, A. G. Marshall, P. E. Prevelige, Jr., J. Mol. Biol., 2003, 325, 759–772. L. Wang, L. C. Lane, D. L. Smith, Protein Sci., 2001, 10, 1234–1243. R. Tuma, H. Tsuruta, J. M. Benevides, P. E. Prevelige, Jr., G. J. Thomas, Jr., Biochemistry, 2001, 40, 665–674. I. Kheterpal, H. A. Lashuel, D. M. Hartley, T. Walz, P. T. Lansbury, Jr., R. Wetzel, Biochemistry, 2003, 42, 14092–14098. I. Kheterpal, S. Zhou, K. D. Cook, R. Wetzel, Proc. Natl. Acad. Sci. U.S.A., 2000, 97, 13597–13601. A. Nazabal, S. Dos Reis, M. Bonneu, S. J. Saupe, J. M. Schmitter, Biochemistry, 2003, 42, 8852–8861. T. A. Neubert, K. A. Walsh, J. B. Hurley, R. S. Johnson, Protein Sci., 1997, 6, 843–850. J. B. Ames, R. Ishima, T. Tanaka, J. I. Gordon, L. Stryer, M. Ikura, Nature, 1997, 389, 198–202. T. Tanaka, J. B. Ames, M. Kainosho, L. Stryer, M. Ikura, J. Biomol. NMR, 1998, 11, 135–152. S. Brier, D. Lemaire, S. Debonis, E. Forest, F. Kozielski, Biochemistry, 2004, 43, 13072–13082. K. D. Powell, M. C. Fitzgerald, Biochemistry, 2003, 42, 4962–4970. K. D. Powell, M. C. Fitzgerald, J. Comb. Chem., 2004, 6, 262–269. E. J. Goldsmith, Faseb J, 1996, 10, 702–708.
101 A. D. Robertson, Trends Biochem. Sci.,
2002, 27, 521–526. 102 A. Cooper, D. T. Dryden, Eur.
Biophys. J., 1984, 11, 103–109. 103 A. Cooper, Curr. Opin. Chem. Biol.,
1999, 3, 557–563.
104 A. J. Wand, Nat. Struct. Biol., 2001, 8,
926–931. 105 J. J. Englander, J. R. Rogero, S. W.
106 107
108
109
110
111
112
113
114 115
116
117
118 119
120
Englander, J. Mol. Biol., 1983, 169, 325–344. J. Ray, S. W. Englander, Biochemistry, 1986, 25, 3000–3007. G. Louie, J. J. Englander, S. W. Englander, J. Mol. Biol., 1988, 201, 765–772. S. W. Englander, J. J. Englander, R. E. McKinnie, G. K. Ackers, G. J. Turner, J. A. Westrick, S. J. Gill, Science, 1992, 256, 1684–1687. J. J. Englander, G. Louie, R. E. McKinnie, S. W. Englander, J. Mol. Biol., 1998, 284, 1695–1706. J. J. Englander, J. N. Rumbley, S. W. Englander, J. Mol. Biol., 1998, 284, 1707–1716. J. R. Rogero, J. J. Englander, S. W. Englander, Methods Enzymol., 1986, 131, 508–517. P. Fuentes-Prior, Y. Iwanaga, R. Huber, R. Pagila, G. Rumennik, M. Seto, J. Morser, D. R. Light, W. Bode, Nature, 2000, 404, 518–525. C. H. Croy, J. R. Koeppe, S. Bergqvist, E. A. Komives, Biochemistry, 2004, 43, 5246–5255. K. A. Resing, N. G. Ahn, Biochemistry, 1998, 37, 463–475. S. G. Codreanu, J. E. Ladner, G. Xiao, N. V. Stourman, D. L. Hachey, G. L. Gilliland, R. N. Armstrong, Biochemistry, 2002, 41, 15161–15172. A. N. Hoofnagle, K. A. Resing, E. J. Goldsmith, N. G. Ahn, Proc. Natl. Acad. Sci. U.S.A., 2001, 98, 956–961. A. N. Hoofnagle, J. W. Stoner, T. Lee, S. S. Eaton, N. G. Ahn, Biophys. J., 2004, 86, 395–403. M. J. Knapp, J. P. Klinman, Eur. J. Biochem., 2002, 269, 3113–3121. A. Kohen, R. Cannio, S. Bartolucci, J. P. Klinman, Nature, 1999, 399, 496–499. Z. X. Liang, T. Lee, K. A. Resing,
References
121
122
123 124
125
126 127
N. G. Ahn, J. P. Klinman, Proc. Natl. Acad. Sci. U.S.A., 2004, 101, 9556– 9561. K. S. Yip, T. J. Stillman, K. L. Britton, P. J. Artymiuk, P. J. Baker, S. E. Sedelnikova, P. C. Engel, A. Pasquo, R. Chiaraluce, V. Consalvi, Structure, 1995, 3, 1147–1158. N. Frankenberg, C. Welker, R. Jaenicke, FEBS Lett., 1999, 454, 299–302. G. Hernandez, D. M. LeMaster, Biochemistry, 2001, 40, 14384–14391. J. K. Hoerner, H. Xiao, A. Dobo, I. A. Kaltashov, J. Am. Chem. Soc., 2004, 126, 7709–7717. M. Y. Kim, C. S. Maier, D. J. Reed, M. L. Deinzer, J. Am. Chem. Soc., 2001, 123, 9860–9866. Y. Deng, P. Pan, D. L. Smith, J. Am. Chem. Soc., 1999, 121, 1966–1967. S. J. Eyles, P. S. Speir, G. H. Kruppa,
128
129
130
131
132
133
L. M. Gierasch, I. A. Kaltashov, J. Am. Chem. Soc., 2000, 122, 495– 500. V. H. Wysocki, G. Tsaprailis, L. L. Smith, L. A. Breci, J. Mass Spectrom., 2000, 35, 1399–1406. L. A. Breci, D. L. Tabb, J. R. Yates, 3 rd , V. H. Wysocki, Anal. Chem., 2003, 75, 1963–1971. G. Tsaprailis, H. Nair, W. Zhong, K. Kuppannan, J. H. Futrell, V. H. Wysocki, Anal. Chem., 2004, 76, 2083–2094. C. Gu, G. Tsaprailis, L. Breci, V. H. Wysocki, Anal. Chem., 2000, 72, 5804–5813. E. A. Kapp, F. Schutz, G. E. Reid, J. S. Eddes, R. L. Moritz, R. A. O’Hair, T. P. Speed, R. J. Simpson, Anal. Chem., 2003, 75, 6251–6264. Z. Zhang, Anal. Chem., 2004, 76, 6374–6383.
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Spectroscopic Probes of Hydride Transfer Activation by Enzymes Robert Callender and Hua Deng 15.1
Introduction
Dehydrogenases, reductases and a number of other enzymes, such as UDP-glucose epimerase, utilize NAD or NADP as an enzymatic cofactor and catalyze the oxidation/reduction of various substrates, facilitating the usually reversible stereospecific hydride transfer from the C4 position of the 1,4 dihydronicotinamide ring of NAD(P)H to substrate. The reaction catalyzed by lactate dehydrogenase and a schematic drawing of the putative hydride transfer reaction that takes place are shown in Fig. 15.1. The transition state paradigm states that enzymes achieve their high catalytic power by stabilizing the transition state and/or destabilizing (or activating) the ground state to reduce the reaction barrier. The forces that bring about transition state stabilization or ground state destabilization can be deduced typically from an examination of the distortions that enzymes bring about on bound substrates, or substrate mimics, or from the structures of bound transition state mimics. For example, stabilization of the transition state almost always brings the ground state of bound substrates structurally closer to the transition state compared to when unbound, even if the distortion may be small. Activation of the ground state typically shows up in larger distortions. Our purpose here is to review spectroscopic approaches, optical and vibrational, applied to the determination of enzyme structure and dynamics. We focus on hydride transfer reactions in protein catalysis. Vibrational spectroscopy is especially useful in the study of the molecular mechanism of enzymes because it is structurally specific and is of high resolution; bond distortions as small as 0.01–0.001 A˚ can be discerned by vibrational spectroscopy. It is at this level of atomic resolution that enzyme induced bond distortions usually manifest themselves. In addition, both enthalpic and entropic factors can be characterized by vibrational spectroscopy, sometimes in quantitative terms. Although most of the chapter is concerned with the structures of static protein–ligand complexes, the dynamics of how these complexes are formed and depleted has recently become a viable topic for scientific
Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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15 Spectroscopic Probes of Hydride Transfer Activation by Enzymes
Figure 15.1. Reaction catalyzed by LDH and active site contacts in LDH. It shows an A-side hydride transfer reaction from NADH to a substrate CbO which is accompanied by a proton transfer, either sequentially or simultaneously, from His195. The 1,4
dihydronicotinamide is in an ‘‘anti’’ conformation (relative to ribose) and its amide arm at C3 is in transoid conformation, and pro-R hydrogen at the C4 is in a pseudoaxial position.
research. Aspects of the dynamical nature of enzymes revealed by optical/ vibrational spectroscopies are also then discussed here. The reason that vibrational spectroscopy yields useful information on a quantitative basis is that the observed vibrational frequencies arise from interatomic force constants; these are a measure of the distribution of the electrons within the molecule [1–3]. This electronic distribution is disturbed, in some cases, by protein– ligand interactions, in direct proportion to the degree of interaction. For example, the strengths of hydrogen bonds in model systems can be determined directly from linear free energy correlations between frequency measurements and the DH of formation of the H-bonds. Besides the determination of electron density in a chemical bond, vibrational spectroscopy can also be used to relate molecular structure/conformation to the size of interactions between molecular groups, especially when complemented by vibrational analysis based on quantum chemical calculations. Thus, this spectroscopic method is well suited for the determination of the substrate activation using enzyme–ligand complexes that simulate the ground state or transition state of the enzyme catalyzed reaction. The vibrational approach to the study of enzyme–ligand interactions has been reviewed previously [4–7], and the reader may find these reviews quite useful and interesting. The chapter is organized as a series of summaries of actual uses of optical/ vibrational spectroscopies based on selected experiments of specific enzymes. We relate the results to the molecular mechanism. We feel this is the most productive
15.2 Substrate Activation for Hydride Transfer
way of providing an overview of spectroscopic probes of our enzyme class. Much of our past work on the NAD(P) linked enzymes, for example, concerns lactate dehydrogenase and dihydrofolate reductase, and we use these systems and others as selected specific examples in reviewing how various spectroscopic methods yield useful information on enzymatic catalysis within this enzyme group.
15.2
Substrate Activation for Hydride Transfer
For concomitant proton transfer to a substrate CbO oxygen or CbN nitrogen (see Fig. 15.1), the enzyme can activate the substrate for catalysis by increasing the partial positive charge on the carbon of the to-be-reduced substrate CbO or CbN bond. This can be achieved by forming a strong hydrogen bond, or other form of electrostatic interaction, to the oxygen of the CbO (CbN) bond, thereby polarizing it and stabilizing the polar nature of the transition state, or by protonation of the CbN bond. Both forms of activation have been found. 15.2.1
Substrate CyO Bond Activation
CbO stretch mode is quite strong in Raman or IR spectra and in some cases quantitative correlation between hydrogen bonding energy and CbO stretch frequency can be determined [8, 9]. Thus, it is ideally suited for studies of the substrate CbO bond activation in the enzyme complexes. Two dehydrogenases, LDH and LADH, have been studied in detail by vibrational spectroscopy. Hydrogen Bond Formation with the CyO Bond of Pyruvate in LDH Lactate dehydrogenase (LDH) accelerates the oxidation of lactate by NADþ to pyruvate and NADH by about 10 14 -fold relative to a corresponding model reaction [10]. This reversible reaction involves the direct transfer of a hydride ion, H to the proR, re-face of the nicotinamide moiety of NADþ from the C2 carbon of l-lactate forming NADH and pyruvate with a high degree of stereochemical fidelity [11]. The nature of the LDH/NADHpyruvate complex was originally studied by examining an adduct complex, E/NAD-pyr, that is formed by the addition of the C3 carbon of pyruvate enol to the C4 position of the nicotinamide ring of NADþ in the presence of LDH [12, 13]. It is believed that the interactions between the enzyme and pyruvate in the E/NADHpyr central complex are largely maintained in the adduct complex, in spite of the additional covalent linkage present in the adduct complex. The frequency of the CbO stretch of pyruvate in solution lies at 1710 cm1 . The bond order, hence stretch frequency, of this polar bond is modulated by electrostatic interactions. The stretch frequency is therefore a monitor of these interactions, which are believed to be quite important in stabilizing the transition state of LDH. It is obviously therefore of interest to determine the stretch frequency for 15.2.1.1
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Isotope edited difference Raman spectra between Cb 18 O pyruvate and 13 CbO pyruvate in solution and in LDH/ NAD-pyr adduct.
Figure 15.2. 13
pyruvate bound to the enzyme. Although this is just one CbO moiety in the enzyme–substrate complex among hundreds of others, it is possible to determine the CbO stretch of the bound pyruvate unambiguously using isotope editing approaches. In this approach, ternary E/NAD-pyr complexes are formed using pyruvate with and without 13 C (and/or 18 O) label on the CbO bond under identical conditions and their spectra are taken separately and then subtracted. The difference spectrum only shows the vibrational modes that are affected by the isotope labeling as positive and negative peak pairs, while all other protein and ligand peaks not affected by the isotope label are cancelled out. Isotope edited difference Raman studies showed that the frequency of the carbonyl stretch of pyruvate shifts downward by 35 cm1 relative to its solution value upon forming a complex with pig heart LDH (Fig. 15.2). This downward shift in frequency is associated with a strong bond polarization where a significant single bond, þ CaO , resonance form is mixed into the mostly double bond of the carbonyl upon binding. The net interaction energy between the protein and the carbonyl moiety that produces this bond polarization is about 14 to 17 kcal mol1 [14]. Further studies with a number of mutant LDHs revealed that there is a good correlation between the hydride transfer rate and the pyruvate CbO stretch frequency shifts in the E/NAD-pyr complex [15]; Fig. 15.3. The reasonable agreement observed in Fig. 15.3 can be rationalized by supposing that the enthalpy of the transition state is stabilized to an even greater extent than the ground state, so that the net reaction barrier is lowered by the electrostatic interaction. This is true because the carbonyl moiety is substantially more
15.2 Substrate Activation for Hydride Transfer
Figure 15.3. The log of the rate of hydride transfer step (in s1 ) versus the observed change in CbO stretch frequency of pyruvate upon binding to LDH/NADH.
polarized in the transition state, with more negative character on the oxygen. Also, it seems likely that the proton located on the imidazole in the ground state is now closer to the oxygen in the transition state. For example, ab initio calculations on hydride transfer reaction in a model system place the proton closer to the oxygen than to the imidazole ring [16]. This analysis is in accord with a previous study that showed that the equilibrium towards enol-pyruvate from pyruvate is increased by 10 5:5 -fold at the active site in LDH compared to solution by the stabilization of CaO character into the pyruvate’s CbO. All these results prompted the suggestion that some 10 5:5 fold of LDH’s 10 9 -fold rate enhancement arises from the CbO His-195þ interaction [10]. Hydrogen Bond Formation with the CyO Bond of Substrate in LADH Horse liver alcohol dehydrogenase (LADH) catalyzes the reactions of aldehydes and their corresponding alcohols with the coenzymes NADH and NADþ . Activation of substrate complexes via polarization of substrate CbO bond has been observed in LADH by vibrational spectroscopy. Two enzyme complexes have been studied by difference Raman measurements, the E/NADHDABA complex [17, 18] and the E/NADHCXF complex [19]. DABA is a poor substrate while CXF is a substrate analog. X-ray crystallography has shown that the polarization of the substrate CbO bond is mainly due to a coordination to the active site Znþþ ion [20, 21]. For example, polarization of the CbO bond of DABA in the LADH complex was found to be substantial, half way between a single and double bond as compared to DABA in solution [18]. Vibrational studies revealed substantial features of how CXF binds to LADH/ 15.2.1.2
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NADH [19]. Ab initio normal mode analyses of the Raman data in solution and in the enzyme complex were carried out and empirical correlations were established that yielded bond stretch versus interaction enthalpy relationships. The total binding Gibbs free energy between CXF and LADH/NADH complex is about 7 kcal mol1 . Since this is made up of both enthalpic and entropic components, and the entropic TDS term of the Gibbs free energy is almost certainly unfavorable, the binding enthalpy is greater than 7 kcal mol1 . It was found that 4 kcal mol1 of the enthalpic binding energy is from the amide moiety. The binding of the carbonyl group of CXF to the catalytic zinc and the hydrogen bond between the oxygen and the hydroxy group of Ser-48 would account for about 5.5 kcal mol1 to the enthalpic term. The binding of the amide NaH moiety is destabilizing, although it would be even more destabilizing if not for the cation–p interaction at the binding site [19]. 15.2.2
Substrate CyN Bond Activation
The intensity of the CbN stretch mode is also quite strong in Raman or IR spectra. Activation of the CbN bond for hydride transfer can be realized by formation of hydrogen bonding to the CbN nitrogen or by protonation of the CbN nitrogen. These two cases can be distinguished conclusively by vibrational spectroscopy, as shown below. N5 Protonation of 7,8-Dihydrofolate in DHFR Dihydrofolate reductase catalyzes the reduction of 7,8-dihydrofolate (H2 folate) to 5,6,7,8-tetrahydrofolate (H4 folate) by facilitating the addition of a proton to N5 of H2 folate and the transfer of a hydride ion from the pro-R side of NADPH C4 to C6 (see Fig. 15.4). Despite extensive kinetic, site directed mutagenesis, X-ray crystallographic, and theoretical molecular modeling studies that have been performed on this enzyme, the reaction mechanism of DHFR is still under debate. In fact, the electronic nature of the ground state within the active site in the productive DHFRNADPHH2 folate complex is unclear, and this is key to an understanding of the reaction mechanism of DHFR. For example, X-ray crystallographic studies have revealed that the only ionizable group near the pteridine ring is a carboxylic acid, equivalent to Asp27 in E. coli DHFR and there is no protein residue in the immediate vicinity of H2 folate N5 that can act as a general acid/base or form a hydrogen bond to N5 [22–24]. Thus, activation of the H2 folate substrate, if it exists, is unlikely to be realized by a strong hydrogen bond to C6bN5. It is possible that there are one or more binding site water molecules interacting with the pterin ring and that the proton that ends up on N5 arrives from the binding site carboxyl group via these water molecules. In this regard, the rate of hydride transfer from NADPH to H2 folate has a pK a of around 6.5 compared with the pK a of 2.6 for N5 of DHF in solution [25, 26]. The possibility of activating the H2 folate substrate in DHFR/NADPHH2 folate complex by the protonation of N5 for the subsequent hydride transfer was pro15.2.2.1
15.2 Substrate Activation for Hydride Transfer
Figure 15.4.
Reaction catalyzed by DHFR.
posed [23] and later supported by the Raman difference spectroscopic studies of the DHFR/NADPþ DHF complex, which is a mimic of the DHFR/NADPHH2 folate Michaelis complex [27]. In the Raman spectrum of DHFR/NADPþ H2 folate complex, two N5bC6 stretch ‘marker’ bands indicating unprotonated (1650 cm1 ) or protonated (1675 cm1 ) N5 were identified. The assignments were based on isotope labeling, comparisons to the spectra of solution models, and the positioning of the bands. Based on these assignments, N5 in the binary DHFR/H2 folate complex was found to be unprotonated at near neutral pH values. In the ternary DHFR/NADPþ H2 folate complex, however, another band at 1675 cm1 was observed (Fig. 15.5). A titration study, using the 1650 and protonated 1675 cm1 marker bands as indicators for unprotonated and protonated species respectively, showed that the pK a of N5 is raised from 2.6 in solution [25] to 6.5 in this complex [27] (Fig. 15.6). Further studies based on ab initio vibrational analysis of the Raman data confirmed the original assignments and further indicated that the immediate environment of N5 in the DHFRNADPþ H2 folate complex is quite hydrophobic [28]. The activation of the H2 folate due to N5 protonation can be rationalized by the reduced electron clouds near the C6bN5 carbon [28, 29]. In summary, vibrational spectroscopic studies have shown that in the enzyme catalyzed hydride transfer reaction, the substrate CbO or CbN bond in the Michaelis complex may first be activated in two different ways for the subsequent hydride transfer. For a substrate that contains a CbO bond to be reduced by the enzyme, strong electron withdrawing interaction due to hydrogen bonding (in LDH) or electrostatic interaction (in LADH) can polarize this bond to reduce the electron cloud near the carbonyl carbon to facilitate the hydride transfer. This is consistent with theoretical studies that one of the driving forces for the hydride transfer is the large
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15 Spectroscopic Probes of Hydride Transfer Activation by Enzymes
Figure 15.5. Difference Raman spectra between DHFR/ NADPþ H2 folate and DHFR/NADPþ at pH 6.1 and pH 7.4.
Figure 15.6. pH dependence of the intensities of the CbNH band (1675 cm1 ) and the CbN band (1650 cm1 ) of H2 folate in the DHFR/NADPþ H2 folate complex. The pKa ¼ 6.5.
15.3 NAD(P) Cofactor Activation for Hydride Transfer by Enzymes
partial positive charge on the carbonyl carbon caused by the strong hydrogen bonding on the CbO bond [30]. For a substrate that contains a CbN bond, protonation of the nitrogen can be used by the enzyme to reduce the electron cloud near the Schiff base carbon to facilitate the hydride transfer. In this case, hydrogen bonding to NaH would be electron donating and thus not required for the activation of the substrate.
15.3
NAD(P) Cofactor Activation for Hydride Transfer by Enzymes
Previous theoretical and enzyme kinetic studies have identified a number of factors that could be important in activating the NAD(P) cofactor. Several of these factors can be studied by spectroscopy to determine if and how the cofactor NAD(P) is activated within the Michaelis complex to facilitate the hydride transfer. 15.3.1
Ring Puckering of Reduced Nicotinamide and Hydride Transfer
Theoretical calculations suggested that the features of the transition state structure of the hydride transfer reaction include a ring puckering of the dihydronicotinamide ring of NADH, which renders the transferred hydrogen at the psuedoaxial position [16, 30, 31]. The formation of a boat conformation may contribute to a reduction of the reaction barrier by as much as 4–6 kcal mol1 with C4 and N1 out of the ring plane by 10–15 degrees, as predicted by semiempirical AM1 studies of LDH [30]. Thus, if such a form of activation is significant, a pro-R hydrogen will be observed at the pseudoaxial position in A-side enzymes (in which the pro-R hydrogen is transferred) and pro-S hydrogen at the pseudoaxial position in B-side enzymes (in which the pro-S hydrogen is transferred). The frequencies of the carbon–hydrogen stretching mode of the pro-R and pro-S C4-H bonds of NADH are a sensitive indicator of the nicotinamide planarity; they have been determined in solution and when bound to pig heart lactate dehydrogenase (LDH) by isotope edited Raman spectroscopy [32]; Fig. 15.7. This was achieved by specifically deuterating the C4 pro-R or pro-S hydrogens of NADH and determining the frequencies of the resulting C4aD stretches by Raman difference spectroscopy. The frequencies of the two C4aD stretching modes for the two bonds are essentially the same for the unliganded coenzyme in solution. On the other hand, the position of the pro-S [4- 2 H]NADH stretch shifts upwards by about 23–30 cm1 in its binary complex with lactate dehydrogenase relative to that observed in solution, while that for the bound pro-R [4- 2 H]NADH is relatively unchanged. Semiempirical quantum mechanical calculations (MINDO/3, MNDO and AM1) suggested that the orientation of the amide arm, puckering of the reduced nicotinamide ring, and external charge or dipole are among the factors that can affect the C4aH stretch frequency. Within the range of the study, the positions of the C4aD stretches may be understood as the result of two conformational
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15 Spectroscopic Probes of Hydride Transfer Activation by Enzymes
Figure 15.7. Raman difference spectra of (a) 100 mM pro-R [4- 2 H]NADH at 4 C, G1=2 ¼ 45 cm1 ; (b) pro-R [4- 2 H]NADH in LDH (LDHNADH ¼ 1:5=5 mM) at 4 C, G1=2 ¼ 16 cm1 ; (c) pro-R [4- 2 H]NADH complexed with LDHoxamate (LDH/NADHoximate ¼ 1:5=5=5 mM) at 4 C, G1=2 ¼ 6 cm1 for either the 2112 or 2132 cm1 band; (d) 100 mM pro-S [4- 2 H]NADH at 4 C, G1=2 ¼ 45 cm1 ;
(e) pro-S [4- 2 H]NADH in LDH (LDHNADH ¼ 1:5=5 mM) at 4 C, G1=2 ¼ 22 cm1 ; (f ) pro-S [4- 2 H]NADH complexed with LDHoxamate (LDH/NADHoximate ¼ 1:5=5=5 mM) at 4 C G1=2 ¼ 6 cm1 for either the 2110 or 2124 cm1 band. All spectra were obtained by subtracting the corresponding NADH spectrum taken under the same conditions.
changes of the nicotinamide ring that occur when NADH forms a binary complex with LDH: the rotation of the amide group from a solution cisoid to transoid, in situ, (which results in a blue shift of the average of the two CaD stretch frequencies) and the adoption of a ‘half-boat’ of the dihydronicotinamide ring of NADH when bound to the enzyme from an essentially planar solution structure (this results in a higher CaD stretch frequency of the pseudoequitorial CaD bond). The estimated angle of the C4 ring carbon with respect to the other carbon atoms is around 10– 15 degrees, with the pro-R hydrogen at a pseudo-axial position and the pro-S hydrogen at a pseudo-equatorial position. Since LDH is a so-called A-side enzyme (trans-
15.3 NAD(P) Cofactor Activation for Hydride Transfer by Enzymes
fers the pro-R hydrogen), the ground state structural distortions imposed on the cofactor appear to populate preferentially the correct ring geometry for the hydride transfer reaction. Similar difference Raman studies have been carried out on two other enzymes in their binary and ternary (Michaelis mimics) complexes with pro-R or pro-S specifically labeled NAD(P)H: the A-side specific dihydrofolate reductase (DHFR) and the B-side specific glycerol-3-phosphate dehydrogenase (G3PDH) [33]. DHFR shows quite similar behavior to that of LDH. In the ternary complex data involving B-side enzyme G3PDH, only a single band is observed and, hence, only a single conformer. The nearly equal frequencies for the C4 deuteron of NADH bound in the G3PDH ternary complex suggest that the ring is essentially planar. For all three ternary complexes, the bandwidths of the C4aD stretch modes have narrowed by a factor of two from those of the binary complexes, indicating the flexibility of the nicotinamide is further limited upon binding of the inhibitor. This is discussed further in Section 15.3.3. 15.3.2
Effects of the Carboxylamide Orientation on the Hydride Transfer
Theoretical studies suggest that a transoid amide significantly reduces the activation energy for hydride transfer compared to a cisoid amide, even though the cisoid conformation is more stable in solution [31]. In addition, there is a clear preference for the amide carbonyl oxygen to be located on the same face as the transferring hydride when the amide is transoid. This orientation preference has been attributed to electrostatic attraction between the amide oxygen and the partially positively charged hydride acceptor that is absent with a cisoid amide [31]. Thus, hydride transfer activation can be achieved by orientating the amide arm to the transoid conformation. Several vibrational frequencies of the reduced nicotinamide are sensitive to the orientation of the amide. Besides the C4aD stretch modes, discussed in Section 15.3.1, the coupled ring CbC stretch and the CbO stretch modes of the reduced nicotinamide ring are also sensitive to the amide orientation. Vibrational analysis based on ab initio calculations suggests that the stretch motions of the two CbC bonds in the reduced nicotinamide ring and the CbO stretch of the amide are highly coupled to form three vibrational modes [32]. The vibrational mode formed by the anti-phase combination of the two CbC stretches is the highest frequency mode and is not sensitive to the orientation of the amide. The vibrational mode with the lowest frequency of the three modes is very sensitive to the amide orientation, shifts up by nearly 40 cm1 when the amide is changed from cisoid to transoid. Since this mode intensity is quite strong in the Raman spectrum of NADH, it can be conveniently used for the determination of the amide orientation. According to such criteria, the amide of NADH in LDH and cytoplasmic malate dehydrogenase binary complexes is transoid while in the mitochondrial malate dehydrogenase it is cisoid [34, 35]. Apparently, the orientation of the amide can be controlled by active site contacts
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15 Spectroscopic Probes of Hydride Transfer Activation by Enzymes
in the enzymes. Difference Raman studies of an NAD analog APAD, in which the amide group of NAD is replaced by an acetyl group, showed that the hydrogen bonding on the acetyl CbO bond in the LDH complex is 4–5 kcal mol1 stronger than in aqueous solution [36]. 15.3.3
Spectroscopic Signatures of ‘‘Entropic Activation’’ of Hydride Transfer
Entopic effects may play a role in enzymatic catalysis by lowering the TDS component of DG between the ground state and the transition state along the reaction coordinate for the enzyme catalyzed reaction, relative to the reaction pathway in solution (cf. Jencks, [37]). This may come about either by lowering the number of available states in the ground state (ground state entropic loss) or by increasing the number of available states in the transition state (transition state entropic gain). This concept has recently been developed quantitatively using numerical simulations [30, 38]. These computational studies emphasize bringing the substrates from the ground state to a state closely resembling the structure of the transition state that is called the ‘‘near attack conformation’’ (NAC’s). Several states may be accessible from the ground state enzyme–substrate complex, with some states approaching the NAC structure and, hence, being poised for bond breaking/ making to occur while others are not catalytically productive. The enzymatic rate enhancement is then proportional to the fraction of time that the complex spends in the NAC conformation. In the Raman difference spectroscopic studies of the C4 deuterated NADH bound to LDH, it was observed that the width of the C4aD stretches of [4,4D2]NADH decreases by a factor of @2.5 upon the formation of a ternary complex with LDH and oxamate [36] (Fig. 15.7). Such a change in the Raman spectrum of bound NADH from the binary to the ternary complex suggests that the protein conformational change that accompanies loop closure and the formation of the ternary Michaelis complex involves a ‘stiffening’ of the active site in addition to the changes in electrostatic interactions reviewed in the discussion above. The most likely explanation for the unusual width of the C4aD stretch bands in water and in the binary complex is that the reduced dihydronicotinamide ring adopts various boat conformations (as discussed in Section 15.3.1) since quantum mechanical calculations suggest there is little energy difference between various boat conformations, including the planar conformation [16, 32, 39]. Since the frequency of the CaD stretch is sensitive to this angle [32], a heterogeneous mixture of various boat forms results in the observed broad bands. Band narrowing arises from the selection of a particular ring conformation forced by the formation of the E/NADHoxamate Michaelis mimic complex. The data thus suggest that the protein conformational change driven by substrate binding decreases the number of nicotinamide ring conformations that are energetically available to the coenzyme in the ternary E/NADHsubstrate complex compared to the E/NADH binary complex and presumably aligns the C4aH (proR) bond along the direction of the reaction coordinate in the transition state. This
15.3 NAD(P) Cofactor Activation for Hydride Transfer by Enzymes
suggests that entropic effects are involved in substrate binding and probably influence catalytic activity. Indeed, Burgner and Ray [10] estimated that the immobilization of reactants at the active site of LDH contributes at least a thousand-fold (ca 4.2 kcal mol1 ) to the lowering of the transition state barrier for hydride transfer to and from NAD to substrate on the basis of a series of reactions catalyzed by LDH. The approximate change in entropy between the binary LDH/NADH and the ternary LDH/NADHoxamate complexes, as monitored by the changes observed on the C4aH bond, is estimated by assuming that the number of available states, W, is proportional to the heterogeneous bandwidth of the observed Raman band. For example, taking the bandwidth of the C4aD stretch in the ternary complex as arising from essentially homogeneous line broadening processes and using this to fit the profile of this normal mode in the binary data, we find that three bands of essentially equal strength are needed. Thus, there are three states available to the ring in the binary complex as opposed to one in the ternary complex. Since S ¼ R ln W, TDS ¼ RT ln 3 or 0.7 kcal mol1 . Of course, this just involves the entropy change associated with the available states of the coenzyme that affect the CaD stretch at the C4 position, and the total entropic change is likely to be larger [36]. 15.3.4
Activation of CxH bonds in NAD(P)B or NAD(P)H
It has been argued that the activation of the oxidized nicotinamide in the ground state complex should force the C4 of NAD(P)þ from sp2- to sp3-like. In this case, the C4aH bond order, and thus the bond stretch frequency, should be reduced [11, 31]. A relatively large equilibrium deuterium and tritium isotope effect (@1.1) on binding of Ca4H labeled NADþ to LDH was detected. If the entire isotope effect is assumed to be due to the frequency change of the C4aH stretch upon NADþ binding to LDH, the predicted downward shift of the C4aH stretch frequency is @100 cm1 for NADþ bound to LDH compared to free in solution [11]. By the same argument, activation of the NAD(P)H C4aH bond that is not involved in the hydride transfer should result in a bond order increase, thus a blue shift of the stretch frequency, by the distortion of the electronic nature of C4 from sp3 to sp2. It is less clear how the C4aH stretch frequency should change for the C4aH bond involved in the hydride transfer since this would depend on the nature of the hydride transfer process: two-electron transfer followed by proton transfer, or vice versa, or all at the same time. In any case, the stretch frequency of the C4aH bond is a direct monitor of its bond order and therefore presents an opportunity to test the concepts above. On the NADH side, large shifts in the frequency of the C4aD stretch are not observed when NAD(P)H binds to the enzymes studied thus far (the A-side specific lactate dehydrogenase (LDH) and dihydrofolate reductase (DHFR) and the B-side specific glycerol-3-phosphate dehydrogenase (G3PDH)), as would be predicted [33]. The observed frequency shifts are generally not larger than the heterogeneously broad-
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15 Spectroscopic Probes of Hydride Transfer Activation by Enzymes
ened band of the cofactor’s solution spectrum. In addition, the C4aH frequencies in these three enzymes also do not indicate a direct relationship between frequency and activity. This suggests that the rate enhancements accomplished by NAD(P)H dependent enzymes do not reside in the enzymes ability to activate C4aH in the ground state by changing the electronic nature of the C4aH bond. With regards to the NAD(P)þ side of the reaction, the C4aD stretch mode is essentially unaffected when NAD(P)þ binds to either LDH or DHFR [33]. Neither the position nor the bandwidth is changed by binding upon formation of enzyme NAD(P)þ . Small shifts in frequency are observed for NAD(P)þ in the ternary complexes made with LDH and DHFR compared to the respective binary complexes, but it is hard to discern any pattern since the shift is positive in one protein (DHFR) and negative in the other (LDH). 13 C NMR studies of the 13 C4 labeled NADþ bound to UDP-galactose 4-epimerase showed that the 13 C4 signal was shifted downfield by 3.4 ppm, consistent with electron withdrawing from C4 in the enzyme [40]. Studies on a series of NADþ analog N-alkylnicotinamides, whose rates of reduction by cyanoborohydride in aqueous solution differ by three orders of magnitude, did show a clear correlation between the C4 chemical shift reduction rate (3.4 ppm downfield chemical shift correlated to 3200-fold rate increase). However, the Raman studies found only small changes in the C4aD stretch frequencies of the same series of N-alkylnicotinamides (less than 1 cm1 , our unpublished observations). Thus, it seems clear that C4 can be activated without affecting the electronic nature of the C4aH bond [33].
15.4
Dynamics of Protein Catalysis and Hydride Transfer Activation
While the static structures of a substantial number of Michaelis complexes are known for many enzymes, little is known of the nature or degree regarding protein conformational flexibility that is required to form the Michaelis complex and to accommodate the changing chemical nature of the bound ligand as the system evolves along the reaction coordinate. Just how a ligand binds to a protein, the specific pathway(s), the time ordering of events, and the atoms and groups of atoms involved in the binding process, is largely uncharacterized. These dynamical processes cover a wide range of time scales, from picoseconds, involving small scale displacement of atoms or molecular groups, to nanoseconds/microseconds involving activated motions of atomic groups (such as motions of loops either on the surface of the protein or buried), to millisecond times or longer for activated motions of domains. In general, time scales shorter than milliseconds have been difficult to access experimentally, and this has been a major reason for the lack of characterization of enzyme associated dynamics. Over the past years, a number of approaches to the study of atomic motion within proteins have been developed and are undergoing continued development. These include NMR relaxation spectroscopies, line shape analysis of spectral bands,
15.4 Dynamics of Protein Catalysis and Hydride Transfer Activation
and others. Our purpose here is to discuss the uses that investigators have developed for the optical/vibrational spectroscopic study of protein dynamics. We further narrow this perspective to examine briefly experimental studies of the ‘pump–probe’ type that have been carried out on the NAD(P) linked enzymes. In this approach, the chemistry of the system is initiated by some perturbant, and the evolving structural changes are followed by a suitable probe. This is the typical arrangement for conventional stopped-flow experiments, the problem being that the normal resolution of this approach is no better than around one millisecond. This limitation is being remedied to an extent by the development of fast mixers that can achieve a resolution of 10–50 ms (see e.g. Ref. [41]). For the NAD(P) enzymes, the rather limited number of studies that access time scales faster than one millisecond have centered on the use of T-jump relaxation spectroscopy. This approach was developed in the 1960s [42] and has recently found new and fruitful uses. Here the temperature of a chemical system (any chemical system that is in equilibrium) is quickly raised by 10–30 C, typically now by irradiating, for example, a protein solution by a pulse of near-IR laser light tuned to weak water absorption bands. As the chemical system evolves to a new equilibrium point defined by the new temperature, structural changes are monitored by spectroscopic probes. The approach is capable of achieving a resolution of about 10 ps [43]. Optical/ vibrational spectroscopies can follow events and structural changes on such fast time scales since their characteristic time scales are sub-picosecond, even femtosecond. The methodology is therefore suitable to study the dynamics of enzymatic catalysis over multiple time scales from picoseconds to minutes [44]. 15.4.1
The Approach to the Michaelis Complex: the Binding of Ligands
The binding of substrate in LDH is ordered and follows the formation of LDH/ NADH binary complex. The substrate binding pocket is somewhat deep into the protein [45]. It supplies the catalytically crucial His195 which acts as a general acid/base in the catalyzed reaction and also polarizes pyruvate’s CbO bond and stabilizes the transition state, which contains a highly polarized aCaO -like bond; the preformed pocket also ‘solvates’ the substrate’s carboxyl group by supplying Arg171 [15]. Once the substrate reaches a position close enough to the enzyme’s active site, a number of events take place. A surface loop, or flap, of the polypeptide chain, residues 98–110 (often referred to as the ‘mobile loop’), closes over the active site entrance, the key residue Arg109 located on the loop is brought deep into the active site in close contact with the CbO bond of bound substrate, water leaves the binding pocket, the enzyme tightens around the bound substrate and NADH bringing them, as well as key protein residues, close together in a proper geometry for the catalyzed reaction to occur, much of which is outlined above. The rate limiting step in the kinetics of hydride transfer catalyzed by LDH is loop closure, which occurs on the 1–10 ms time scale [46]. Spectroscopic probes of the kinetics of structural changes in the NAD(P) linked enzymes on the atomic scale
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include the absorption and emission of NAD(P)H, which occurs in the near-UV and visible, respectively, and the absorptions of the various substrate specific vibrational bands. The sensitivities to structure of various IR bands have been discussed above. In addition, it can be possible to introduce strategically placed chromophores (typically Trp residues) at strategic places within a specific protein of interest; the folding kinetics of LDH [47] was monitored in just this way, as were the structural changes involved with loop closure [48]. The dynamics of the binding of NADH to LDH has been studied by laser induced T-jump spectroscopy and NADH emission [49]; the binding process was found to occur via a multiple-step process over multiple time scales from nanoseconds to milliseconds. The kinetics of substrate binding has been investigated in several studies [46, 50, 51] (and S. McClendon, N. Zhadin, and R. Callender, unpublished). Most of these studies have employed the substrate (pyruvate) mimic, oxamate, which is an unreactive inhibitor of LDH. For example, a laser induced T-jump relaxation study of oxamate binding to LDH/NADH monitoring the changes in emission of bound NADH is shown in Fig. 15.8 [52]. Several steps occurring at 1.5, 53, and 119 ms (the fast ca. 15 ns and slow ca. 5 ms transients in Fig. 15.8 are instrument response). A kinetic scheme of the binding process is built up by performing a series of studies varying the amounts of free [LDH/NADH] and [oxamate] (cf., Ref. [53], which we have recently performed (S. McClendon, N. Zhadin, and R. Callender, unpublished). NADH emission is a very direct probe of substrate (or inhibitor mimic) binding since the emission yield of NADH bound to LDH decreases by a factor of more than ten when the ternary complex is formed.
Figure 15.8. The kinetic response of NADH emission at 450 nm stimulated by energy transfer from excited Trp residues as a result of a T-jump from 20 to 41 C for the reaction of LDH/NADH with oxamate. The kinetics were fitted to a three exponential function with time
constants of 1.5, 53, and 119 ms, which is overlaid on the data. The relative initial concentration of LDH, NADH, and oxamate were 100, 200, and 500 mM, respectively. All samples were in 100 mM sodium phosphate, pH ¼ 7:2.
15.4 Dynamics of Protein Catalysis and Hydride Transfer Activation
Holbrook and coworkers [51] first studied the binding kinetics of oxamate with LDH/NADH using a LDH with Tyr-237 nitrated. Putting their results together (cf., Ref. [46] with our current results yields the following preliminary kinetic scheme for the binding of substrate to LDH to form the Michaelis complex (at 20 C): 37 mM1 s1
LDH=NADH þ oxamate ! LDH 1 =NADHoxamate 1 2000 s
4000 s1
! LDH 2ðloopOpenÞ =NADHoxamate 1 4000 s
700 s1
! LDH 3ðloopClosedÞ =NADHoxamate 1 180 s
In these studies, the temperature dependence of the rates can be tracked so that the thermodynamics of the various steps are determined. One of the most interesting findings is that the on rate to form the initial encounter complex (termed LDH 1/NADHoxamate in the kinetic scheme above) actually slows down with increasing temperature. This implies a temperature dependent activation enthalpy which is explained by the ‘melting’ or exposure of hydrophobic residues to water in the transition state of the encounter complex formation (cf., Ref. [54]). In order to understand numerically the size of the change in the rate of formation of the encounter complex, about 30–40 residues would have to become unfolded in the transition state. This suggests that the structure of the LDH/NADH binary complex is quite labile comformationally, perhaps designed this way so as to facilitate proper binding of ligands. On the other hand, the relative motions of key residues at the substrate binding site of LDH moving against the substrate in the LDH/NAD-pyruvate adduct complex, a complex that closely resembles the productive Michaelis complex of this enzyme, except that the substrate is effectively trapped at the active site by the noncovalent contacts between protein and the NADH-like moiety of NAD-pryuvate (see above), were probed on the 10 ns to 10 ms time scale using laser induced temperature jump relaxation spectroscopy while employing isotope edited IR absorption spectroscopy as a structural probe (Fig. 15.9, [52]). The frequencies of NADpryuvate adduct’s CbO stretch and aCOO antisymmetric stretch will shift substantially should any relative motion of the polar moieties at the active site (His-195, Asp-168, Arg-109, and Arg-171) occur. Apart from the ‘melting’ of a few residues on the protein’s surface, although the measurements were made with a high degree of accuracy, no kinetics were observed on any time scale in experiments on the bound NAD-pyruvate adduct, even for final temperatures close to the unfolding transition of the protein. This is contrary to simple physical considerations and models. These results were interpreted to mean that, once a productive protein–substrate complex is formed, the binding pocket becomes very rigid, with very little, if any, motion apart from the mobile loop, and that loop opening involves concomitant movement of the substrate out of the binding pocket.
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Figure 15.9. (a) Kinetic IR response of LDH/ NAD-pyr in 5 mM deuterated sodium phosphate buffer pH* ¼ 7:0 for a T-jump from 6 to 19 C at 1608, 1596, 1679 and 1696 cm1 for LDH/NAD-pyr (sample side, dashed line) and LDH/NAD-[ 13 C1,13 C2]pyr (reference side, solid lines). The path length is 50 mm. The total protein optical absorbances at 1652 cm1 (maximum of the amide-peak of LDH) is 561 mOD, sample side, and 782 mOD, reference. (b) The difference transients formed by taking
the difference between sample and reference signals, where the two responses have been scaled to take into account the difference in concentration. The vertical bars represent the peak absorption of the CbO and aCOO stretch bands at 1676 and 1635 cm1 , respectively, of the LDH/NAD-pyr adduct as deduced from static isotope edited IR spectroscopy scaled for path length and concentration.
15.4.2
Dynamics of Enzymic Bound Substrate–Product Interconversion
In general, the conversion of enzyme–substrate to enzyme–product occurs on the 1 ms time scale over a very wide range of enzymes [38]. Hence, if we are to understand how chemistry is catalyzed by enzymes, dynamical process on shorter time scales require investigation. For the NAD(P) systems, a very preliminary study was performed on LDH using laser induced T-jump relaxation spectroscopy [44]. In this study, at high initial concentrations of lactate and LDH/NADþ , an equilibrium was established minimally consisting of:
15.4 Dynamics of Protein Catalysis and Hydride Transfer Activation
Time resolved fluorescence at 450 nm (NADH emission) of a reactive LDH/ substrates mixture in response to a T-jump of 10 to 23 C. The l ex ¼ 290 nm. The sample
Figure 15.10.
initially contained 100 mN LDH, 100 mM NADþ , and 10 mM lactate and was allowed to reach equilibrium before the T-jump experiments.
LDH=NADH þ pyruvate ó LDH=NADHpyruvate ó LDH=NADþ lactate ðplus free lactateÞ The LDH/NADHpyruvate ternary complex concentration is quite low, and it was found that the concentration of LDH/NADH þ pyruvate equals approximately that of the LDH/NADþ lactate. A temperature increase tips the equilibrium from right to left. Figure 15.10 shows the time-resolved fluorescence emission of NADH at 450 nm in response to a T-jump from 10 to 23 C. There are two instrument response times: one near 30 ns, which is the pulse width of the laser irradiation heating the sample, and the second is diffusion of heat out from the laser interaction volume that occurs around 15 ms (the latter response is not shown). Fitting the data (solid line) with a function of multiexponentials yielded four rates, as indicated on Fig. 15.10, in addition to these instrument response functions. The data of Fig. 15.10 are remarkable in showing that there exists a number of fast processes previously unresolved in studies of enzymic dynamics. It is clear that the minimal number of steps shown above is not sufficient to explain the kinetic data. In general, the minimal number of species in a kinetic model of the data is equal to one more than the number of observed relaxation rates. Hence, the data can be fit by four processes involving five species. We believe that none of the transients correspond to the reaction LDH/NADH ! LDH þ NADH because we have measured this reaction [49], and none of the events of the binding reaction correspond to any of signals shown in Fig. 15.10. The dissociation of pyruvate from LDH/NADH would be observed on the millisecond time scale. Taking a binding constant of 0.27 mM and the bimolecular rate constant of 8:33 10 5 M1 s1 yields a kobs ¼ k binding ([LDHNDH] þ [pyruvate]) þ krelease of 3 ms. Tentatively, we assign the 3.4 ms transient to this event. Such an assignment is reinforced by the increasing signal associated with the 3.4 ms transient since there is a large emission increase as pyruvate comes off from LDH/NADH.
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15 Spectroscopic Probes of Hydride Transfer Activation by Enzymes
Acknowledgments
Supported by research grants GM068036, EB001958.
Abbreviations
LDH, lactate dehydrogenase; DHFR, dihydrofolate reductase; G3PDH, glycerol-3phosphate dehydrogenase; LADH, liver alcohol dehydrogenase; H2 folate, 7,8dihydrofolate; H4 folate, 5,6,7,8-tetrahydrofolate; H2 biopterin, 7,8-dihydrobiopterin; NADH, reduced b-nicotinamide adenine dinucleotide; NADþ , oxidized bnicotinamide adenine dinucleotide; NADPH, reduced b-nicotinamide adenine dinucleotide phosphate; NADPþ , oxidized b-nicotinamide adenine dinucleotide phosphate; DABA, p-(dimethylamino)benzaldehyde; CXF, N-cyclohexylformamide; NAD-pyr, adducts formed in the presence of LDH from pyruvate and NADþ ; T-jump, temperature-jump.
References 1 Bellamy, L. J. (1975) Advances in
2
3
4
5
6
7
Infrared Group Frequencies, Vol. 1, Chapman and Hall, London. Bellamy, L. J. (1980) The Infrared Spectra of Complex Molecules: Advances in Infrared Group Frequencies, Vol. 2, 2nd edn., Chapman and Hall, London. Colthup, N. B., Daly, L. H., Wiberley, S. E. (1990) Introduction to Infrared and Raman Spectroscopy, 3rd edn., Academic Press, San Diego. Carey, P. R. (1999) Raman spectroscopy, the sleeping giant in structural biology, awakes, J. Biol. Chem. 274, 26625–26628. Deng, H., Callender, R. (1999) Raman spectroscopic studies of the structures, energetics, and bond distortions of substrates bound to enzymes, Methods Enzymol. 308, 176–201. Deng, H., Callender, R. (2001) in Infrared and Raman Spectroscopy of Biological Materials, Gremlich, H.-U., Yan, B. (Eds.), pp. 477–513, Marcel Dekker, New York. Callender, R., Deng, H. (1994) Nonresonance Raman difference spectroscopy: a general probe of protein structure, ligand binding,
8
9
10
11
12
13
enzymatic catalysis, and the structures of other biomacromolecules, Annu. Rev. Biophys. Biomol. Struct. 23, 215–245. White, A. J., Wharton, C. W. (1990) Hydrogen-Bonding in Enzymatic Catalysis, Biochem. J. 270, 627–637. Tonge, P. J., Carey, P. R. (1992) Forces, bond lengths, and reactivity: fundamental insight into the mechanism of enzyme catalysis, Biochemistry 31, 9122–9125. Burgner II, J. W., Ray, W. J. (1984) On the Origin of Lactate Dehydrogenase Induced Rate Effect, Biochemistry 23, 3636–3648. Anderson, V. E., LaReau, R. D. (1988) Hydride Transfer Catalyzed by Lactate Dehydrogenase Displays Absolute Stereospecificity at the C4 of the Nicotinamide Ring, J. Am. Chem. Soc. 110, 3695–3697. Burgner II, J. W., Ray, W. J. (1978) Mechanistic Study of the Addution of Pyruvate to NAD Catalyzed by Lactate Dehydrogenase, Biochemistry 17, 1654–1661. Burgner II, J. W., Ray, W. J. (1984) The Lactate Dehydrogenase Catalyzed Pyruvate Adduct Reaction:
References
14
15
16
17
18
19
20
Simultaneous General Acid-Base Catalysis Involving an Enzyme and an External Catalysis, Biochemistry 23, 3626–3635. Deng, H., Zheng, J., Burgner, J., Callender, R. (1989) Molecular properties of pyruvate bound to lactate dehydrogenase: a Raman spectroscopic study, Proc. Natl. Acad. Sci. U.S.A. 86, 4484–4488. Deng, H., Zheng, J., Clarke, A., Holbrook, J. J., Callender, R., Burgner, J. W., 2nd. (1994) Source of catalysis in the lactate dehydrogenase system. Ground-state interactions in the enzyme-substrate complex, Biochemistry 33, 2297–2305. Wu, Y., Houk, K. N. (1991) Theoretical Evaluation of Conformational Preferences of NADþ and NADH: An Approach to Understanding the Stereospecificity of NADþ/NADHDependent Dehydrogenases, J. Am. Chem. Soc. 113, 2353–2358. Jagodzinski, P. W., Peticolas, W. L. (1981) Resonance Enhanced Raman Identification of the Zinc-Oxygen Bond in a Horse Liver Alcohol Dehydrogenase-Nicotinamide Adenine Dinucleotide-Aldehyde Transient Chemical Intermediate, J. Am. Chem. Soc. 103, 234–236. Callender, R., Chen, D., Lugtenburg, J., Martin, C., Ree, K. W., Sloan, D., VanderSteen, R., Yue, K. T. (1988) The Molecular Properties of p-Dimethylamino Benzaldehyde Bound to Liver Alchohol Dehydrogenase: a Raman Spectroscopic Study, Biochemistry 27, 3672–3681. Deng, H., Schindler, J. F., Berst, K. B., Plapp, B. V., Callender, R. (1998) A Raman spectroscopic characterization of bonding in the complex of horse liver alcohol dehydrogenase with NADH and N-cyclohexylformamide, Biochemistry 37, 14267–14278. Cedergren-Zeppezauer, E., Samama, J. P., Eklund, H. (1982) Crystal structure determinations of coenzyme analogue and substrate complexes of liver alcohol dehydrogenase: binding
21
22
23
24
25
26
27
28
of 1,4,5,6-tetrahydronicotinamide adenine dinucleotide and trans-4(N,N-dimethylamino)cinnamaldehyde to the enzyme, Biochemistry 21, 4895– 4908. Ramaswamy, S., Scholze, M., Plapp, B. V. (1997) Binding of formamides to liver alcohol dehydrogenase, Biochemistry 36, 3522–3527. McTigue, M. A., Davies, J. F., II, Kaufman, B. T., Kraut, J. (1992) Crystal Structures of Chicken Liver Dihydrofolate Reductase Complexed with NADPþ and Biopterin, Biochemistry 31, 7264–7273. Bystroff, C., Oatley, S. J., Kraut, J. (1990) Crystal Structure of Escherichia coli Dihydrofolate Reductase: The Binding of NADPþ Holoenzyme and the FolateNADPþ Ternary Complex. Substrate Binding and a Model for the Transition State, Biochemistry 29, 3263–3277. Klon, A. E., Heroux, A., Ross, L. J., Pathak, V., Johnson, C. A., Piper, J. R., Borhani, D. W. (2002) Atomic structures of human dihydrofolate reductase complexed with NADPH and two lipophilic antifolates at 1.09 a and 1.05 a resolution, J. Mol. Biol. 320, 677–693. Maharaj, G., Selinsky, B. S., Appleman, J. R., Perlman, M., London, R. E., Blakley, R. L. (1990) Dissociation Constants of Dihydrofolic Acid and Dihydrobiopterin and Implications for Mechanistic Models for Dihydrofolate Reductase, Biochemistry 29, 4554–4560. Fierke, C. A., Johnson, K. A., Benkovic, S. J. (1987) Construction and Evaluation of the Kinetic Scheme Associated with Dihydrofolate Reductase from Escherichia coli, Biochemistry 26, 4085–4092. Chen, Y.-Q., Kraut, J., Blakley, R. L., Callender, R. (1994) Determination by Raman Spectroscopy of the pKa of N5 of Dihydrofolate Bound to Dihydrofolate Reductase: Mechanistic Implications, Biochemistry 33, 7021– 7026. Deng, H., Callender, R. (1998) The Structure of Dihydrofolate when
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29
30
31
32
33
34
35
36
37
Bound to Dihydrofolate Reductase, J. Am. Chem. Soc. 120, 7730–7737. Gready, J. E. (1985) Theoretical Studies on the Activation of the Pterin Cofactor in the Catalytic Mechanism of Dihydrofolate Reductase, Biochemistry 24, 4761–4766. Almarsson, O., Bruice, T. C. (1993) Evaluation of the factors influencing reactivity and stereospecificity in NAD(P)H dependent dehydrogenase enzymes, J. Am. Chem. Soc. 115, 2125–2138. Wu, Y.-D., Lai, D. K. W., Houk, K. N. (1995) Transition Structures of Hydride Transfer Reactions of Protonated Pyridinium Ion with 1,4-Dihydropyridine and Protonated Nicotinamide with 1,4Dihydronicotinamide, J. Am. Chem. Soc. 117, 4100–4108. Deng, H., Zheng, J., Sloan, D., Burgner, J., Callender, R. (1992) A vibrational analysis of the catalytically important C4aH bonds of NADH bound to lactate or malate dehydrogenase: ground-state effects, Biochemistry 31, 5085–5092. Chen, Y.-Q., van Beek, J., Deng, H., Burgner, J., Callender, R. (2002) Vibrational Structure of NAD(P) Cofactors Bound to Three NAD(P) Dependent Enzymes: an Investigation of Ground State Activation, J. Phys. Chem. B. 106, 10733–10740. Deng, H., Zheng, J., Sloan, D., Burgner, J., Callender, R. (1989) Classical Raman spectroscopic studies of NADH and NADþ bound to lactate dehydrogenase by difference techniques, Biochemistry 28, 1525–1533. Deng, H., Burgner, J., Callender, R. (1991) Raman spectroscopic studies of NAD coenzymes bound to malate dehydrogenases by difference techniques, Biochemistry 30, 8804–8811. Deng, H., Burgner, J., Callender, R. (1992) Raman Spectroscopic Studies of the Effects of Substrate Binding on Coenzymes Bound to Lactate Dehydrogenase, J. Am. Chem. Soc. 114, 7997–8003. Jencks, W. P. (1980) in Molecular Biology, Biochemistry, and Biophysics,
38
39
40
41
42
43
44
45
46
47
Chapeville, F., Haenni, A.-L. (Eds.), pp. 3–25, Springer Verlag, New York. Bruice, T. C., Benkovic, S. J. (2000) Chemical basis for enzyme catalysis, Biochemistry 39, 6267–6274. Cummins, P., Gready, J. (1989) Mechanistic Aspects of Biological Redox Reactions Involving NADH 1: ab initio Quantum Chemical Structure of the 1-Methyl-nicotinamide and 1-Methyl-Dihydronicotinamide Coenzyme Analogues, J. Mol. Struct. (Theochem) 183, 161–174. Burke, J. R., Frey, P. A. (1993) The Importance of Binding Energy in Catalysis of Hydride Transfer by UDPGalactose 4-Epimerase: A 13C and 15N NMR and Kinetic Study, Biochemistry 32, 13220–13230. Jamin, M., Yeh, S. R., Rousseau, D. L., Baldwin, R. L. (1999) Submillisecond unfolding kinetics of apomyoglobin and its pH 4 intermediate, J. Mol. Biol. 292, 731–740. Eigen, M., De Maeyer, L. D. (1963) in Techniques of Organic Chemistry, Friess, S. L., Lewis, E. S., Weissberger, A. (Eds.), pp. 895–1054, Interscience, New York. Dyer, R. B., Gai, F., Woodruff, W., Gilmanshin, R., Callender, R. H. (1998) Infrared Studies of Fast Events in Protein Folding, Acc. Chem. Res., 31, 709–716. Callender, R., Dyer, R. B. (2002) Probing protein dynamics using temperature jump relaxation spectroscopy, Curr. Opin. Struct. Biol. 12, 628–633. Holbrook, J. J., Liljas, A., Steindel, S. J., Rossmann, M. G. (1975) in The Enzymes, Boyer, P. D. (Ed.), pp. 191–293, Academic Press, New York. Dunn, C. R., Wilks, H. M., Halsall, D. J., Atkinson, T., Clarke, A. R., Muirhead, H., Holbrook, J. J. (1991) Design and Synthesis of New Enzymes based upon the Lactate dehydrogenase Framework, Philos. Trans, R. Soc. (London) Ser.B 332, 177–185. Atkinson, T., Barstow, D., Chia, W., Clarke, A., Hart, K., Waldman, A., Wigley, D., Wilks, H., Holbrook,
References J. J. (1987) Mapping Motion in Large Proteins by Single Tryptophan Probes Inserterd by Site-Directed Mutagenesis: Lactate Dehydrogenase, Biochem. Soc. Trans. 15, 991–993. 48 Waldman, A. D. B., W., H. K., Clarke, A. R., Wigley, D. B., Barstow, D. A., Atkinson, T., Chia, W. N., Holbrook, J. J. (1988) The Use of a Genetically Engineered Tryptophan to Identify the Movement of a Domain of B. Stearothermophilus Lactate Dehydrogenase with the Process which Limits the Steady-State Turnover of the Enzyme, Biochem. Biophys. Res. Commun. 150, 752–759. 49 Deng, H., Zhadin, N., Callender, R. (2001) Dynamics of protein ligand binding on multiple time scales: NADH binding to lactate dehydrogenase, Biochemistry 40, 3767–3773. 50 Parker, D. M., Jeckel, D., Holbrook, J. J. (1982) Slow structural changes shown by the 3-nitrotyrosine-237
51
52
53
54
residue in pig heart [Tyr(3NO2)237] lactate dehydrogenase, Biochem. J. 201, 465–471. Clarke, A. R., Waldman, A. D. B., Hart, K. W., Holbrook, J. J. (1985) The Rates of Defined Changes in Protein Structure During the Catalytic Cycle of Lactate Dehydrogenase, Biochim. Biophys. Acta S29, 397–407. Gulotta, M., Deng, H., Dyer, R. B., Callender, R. H. (2002) Toward an understanding of the role of dynamics on enzymatic catalysis in lactate dehydrogenase, Biochemistry 41, 3353–3363. Cantor, C. R., Schimmel, P. R. (1980) Biophysical Chemistry, Vol. 2, W. H. Freeman and Company, San Francisco. Fersht, A. (1999) Structure and Mechanism in Protein Science: a Guide to Enzyme Catalysis and Protein Folding, W.H. Freeman, New York.
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Part IV
Hydrogen Transfer in the Action of Specific Enzyme Systems Although the previous section of this volume refers to numerous enzyme reactions, the focus has been on the general properties of hydrogen tunneling and enzyme dynamics. In the next four chapters, specific enzyme systems are the focus. In the chapter by Tittmann and co-workers, an emphasis is on the C-H activation in thiamin diphosphate, i.e., loss of the C2-H proton to yield the reactive zwitterionic intermediate. The high pKa of the C2-H in solution implicates specific interactions within the enzyme that increase the rate of proton loss. Through the use of NMR to follow the H/D exchange kinetics, the authors show how functional groups within the cofactor, as well as specific active site protein side chains lead to large increases in the rate of deuterium exchange. One notable effect is that of an allosteric effector in yeast pyruvate dehydrogenase that increases the rate of H/D exchange by 3 orders of magnitude. The contribution by Benkovic and HammesSchiffer describes the E. coli dihydrofolate reductase (DHFR), which has been one of the major ‘‘players’’ in discerning the role of protein dynamics, and more recently, tunneling in hydride transfer reactions. Both NMR and X-ray crystallographic studies have implicated multiple conformations for DHFR, in particular a closed vs. occluded form, binding substrates and products, respectively. The key question has been how motions within specific regions of the protein correlate with these conformations and facilitate the hydride transfer from NADPH to dihydrofolate. The use of site-specific mutagenesis, coupled to detailed kinetic studies and computational analyses, implicates a network of residues whose correlated motions are coupled to the efficiency of H-transfer. These authors point out that the type of motions that they are measuring are not ‘‘dynamically coupled’’, but rather are equilibrium, thermally averaged conformational changes that change the active site structure in such a way as to favor the hydride transfer from NADPH to dihydrofolate. A focus on hydrogen-atom transfers occurs in the chapter by Banerjee and co-workers on the H-transfer reactions catalyzed by B-12 enzymes. One very interesting aspect of these B-12 enzymes is the coupling of cleavage of the cobaltcarbon bond of the B-12 cofactor to the hydrogen abstraction from substrate, i.e., significant isotope effects are observed on the formation of the cleaved Co(II) form of the cofactor. Stopped flow studies have allowed the measurement of very large, temperature-dependent kinetic isotope effects. QM/MM modeling of these data support a very substantial contribution of tunneling to the reaction coordinate. Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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In concluding, the authors contrast their data with recent model studies, which indicate isotope effects of a similar size and temperature dependence to the enzyme. Whereas the bulk of the currently available experimental studies increasingly implicate specific roles for a protein in facilitating tunneling, this comparison raises the question of the exact role of methylmalonyl-CoA mutase in catalyzing its tunneling reaction. The contribution by Stein is a departure from the above chapters, with its focus on the important class of proton transfers to and from heteroatoms (illustrated for enzymes catalyzing an addition of water to their substrates). The determination of the size of solvent isotope effects is emphasized as a diagnostic tool to interrogate whether protein-aided acid or base catalysis is occurring; as discussed, by extension of such studies to mixtures of H2 O and D2 O the number of transferred protons can be inferred.
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Hydrogen Transfer in the Action of Thiamin Diphosphate Enzymes Gerhard Hu¨bner, Ralph Golbik, and Kai Tittmann 16.1
Introduction
The coenzyme thiamin diphosphate (ThDP, I in Scheme 16.1), the biologically active form of vitamin B1 , is used by different enzymes that perform a wide range of catalytic functions, such as the oxidative and nonoxidative decarboxylation of a-ketoacids, the formation of acetohydroxyacids and ketol transfer between sugars. In these reactions, the C2-atom of ThDP must be deprotonated to allow this atom to attack the carbonyl carbon of the different substrates. In all ThDPdependent enzymes this nucleophilic attack of the deprotonated C2-atom of the coenzyme on the substrates results in the formation of a covalent adduct at the C2-atom of the thiazolium ring of the cofactor (IIa and IIb in Scheme 16.1). This reaction requires protonation of the carbonyl oxygen of the substrate and sterical orientation of the substituents. In the next step during catalysis either CO2 , as in the case of decarboxylating enzymes, or an aldo sugar, as in the case of transketolase, is eliminated, accompanied by the formation of an a-carbanion/enamine intermediate (IIIa and IIIb in Scheme 16.1). Dependent on the enzyme this intermediate reacts either by elimination of an aldehyde, such as in pyruvate decarboxylase, or with a second substrate, such as in transketolase and acetohydroxyacid synthase. In these reaction steps proton transfer reactions are involved. Furthermore, the a-carbanion/enamine intermediate (IIIa in Scheme 16.1) can be oxidized in enzymes containing a second cofactor, such as in the a-ketoacid dehydrogenases and pyruvate oxidases. In principal, this oxidation reaction corresponds to a hydride transfer reaction. In the next section, the mechanism of the C2-H deprotonation of ThDP in enzymes is considered, followed by a discussion of the proton transfer reactions during catalysis. Finally, the oxidation mechanism of the a-carbanion/enamine intermediate in pyruvate oxidase is discussed.
Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
16 Hydrogen Transfer in the Action of Thiamin Diphosphate Enzymes
Scheme 16.1
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16.2 The Mechanism of the C2-H Deprotonation of Thiamin Diphosphate in Enzymes
16.2
The Mechanism of the C2-H Deprotonation of Thiamin Diphosphate in Enzymes
The deprotonation of the C2-atom of ThDP is a key reaction in all ThDPdependent enzymes. For the reaction with different substrates, the C2-H of ThDP, having a pK a of 17–20 in solution (Breslow, 1962; Crosby et al., 1970; Kemp and O’Brien, 1970; Kluger, 1987; Washabaugh and Jencks, 1988), must be activated by the enzyme environment. 13 C NMR investigations on pyruvate decarboxylase containing 13 C-C2-labelled ThDP exclude the existence of a C2-carbanion of ThDP in detectable amounts under physiological conditions (Kern et al., 1997). Therefore, in the enzyme-catalysed reaction, the addition of the carbonyl group of any substrate to the C2-atom of ThDP requires essentially a fast dissociation of the C2proton. In order to determine the rate of this deprotonation, the proton/deuterium exchange kinetics (H/D exchange) of the proton bound to the C2-atom of ThDP in the enzymes pyruvate decarboxylase, transketolase, pyruvate oxidase, and in the pyruvate dehydrogenase multienzyme complex have been examined by 1 H NMR. The exchange reactions were initiated by dilution of a sample solution containing the enzyme (active site concentration 0.1–0.5 mM) with D2 O at a mixing ratio of 1þ1 in a chemical quenched-flow device. The exchange reactions were stopped by addition of DCl and trichloroacetic acid. In addition, this procedure causes a rapid and complete denaturation and precipitation of the protein and a release of the cofactor. After separation of the denatured protein by centrifugation, the 1 H NMR spectra of the supernatant containing the ThDP can be recorded (Kern et al., 1997). These spectra show the C2-H signal of ThDP at 9.55 ppm. For quantification, this signal can be compared with the C6 0 -H signal at 7.85 ppm as a nonexchanging standard (Fig. 16.1). Under the experimental conditions used, the
Figure 16.1. Kinetics of H/D exchange of the C2-H in pyruvate decarboxylase from Saccharomyces cerevisiae. The 1 H NMR spectra are expansions showing the ThDP signals C2-H at 9.55 ppm and C6 0 -H at 7.85 ppm as a nonexchanging standard for quantification.
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16 Hydrogen Transfer in the Action of Thiamin Diphosphate Enzymes
H/D exchange follows a pseudo-first order reaction. It must be noticed that the H/ D exchange rate constant at the C2-atom of enzyme-bound ThDP represents the lower limit of the C2-H deprotonation, because this observed value reflects not only the deprotonation, but also the exchange rate constant of the base responsible for the deprotonation with solvent protons. The observed rate constant of the H/Dexchange kobs is composed of the rate constant of deuteration kD of the carbanion intermediate, and that of its reprotonation kH according to the equation kobs ¼ 12 ðkH þ kD Þ (Tittmann, 2000). The fractionation factor f of this reaction is 1.03 (Tittmann, 2000). 16.2.1
Deprotonation Rate of the C2-H of Thiamin Diphosphate in Pyruvate Decarboxylase
Pyruvate decarboxylase catalyses the nonoxidative decarboxylation of pyruvate yielding CO2 and acetaldehyde. The H/D exchange rate constant of the C2-H of ThDP bound to the homotetrameric and allosterically regulated pyruvate decarboxylase from Saccharomyces cerevisiae is accelerated by three orders of magnitude compared with that of free ThDP (Table 16.1). However, this rate constant is still one order of magnitude too small to allow the enzyme catalysis to proceed at the observed catalytic constant of 10 s1 at 4 C for each active site. Since the value of the catalytic constant represents the rate constant of the allosteric enzyme in the activated state, the H/D exchange of the C2-H of ThDP was investigated in the presence of the allosteric activator pyruvamide (Hu¨bner et al., 1978). In this case, the deprotonation rate constant is at least three orders of magnitude higher than that of the nonactivated enzyme (Table 16.1). The C2-H dissociation of the coTable 16.1.
Cofactor activation in pyruvate decarboxylase
Sample
Rate constant (sC1 )
Free ThDP
9:5 G 0:4 104
Free 4 0 -deamino-ThDP
1:2 G 0:1 103
Yeast pyruvate decarboxylase (wild type)
9:7 G 0:9 101
Yeast pyruvate decarboxylase (wild type), pyruvamide activated
b 600
Yeast pyruvate decarboxylase E51Q variant
7:6 G 0:6 102
Yeast pyruvate decarboxylase (wild type), reconstituted with 4 0 -deamino-ThDP
3:4 G 0:1 105
Pyruvate decarboxylase (wild type) from Zymomonas mobilis
110 G 20
Pyruvate decarboxylase (E473D) from Zymomonas mobilis
104 G 20
Pyruvate decarboxylase (D27E) from Zymomonas mobilis
117 G 13
Pyruvate decarboxylase (H113K) from Zymomonas mobilis
96 G 24
16.2 The Mechanism of the C2-H Deprotonation of Thiamin Diphosphate in Enzymes
enzyme ThDP is not rate-limiting in the activated pyruvate decarboxylase from Saccharomyces cerevisiae, whereas it is indeed rate-limiting in the nonactivated enzyme. This indicates that the allosteric activation in the yeast enzyme is accomplished by an increase in the C2-H dissociation rate of the enzyme-bound ThDP. This model was substantiated by measuring the H/D exchange of C2-H of ThDP in pyruvate decarboxylase from Zymomonas mobilis, which shows no allosteric activation by the substrate (Bringer-Meyer et al., 1986). According to this model, the deprotonation rate constant of the cofactor in pyruvate decarboxylase from Zymomonas mobilis exceeds its catalytic constant of 17 s1 at 4 C for each active site (Table 16.1) and is not altered by pyruvamide. The crystal structure of pyruvate decarboxylase from Saccharomyces cerevisiae (Arjunan et al., 1996; Dyda et al., 1993) shows that the side chain of a glutamate is at a short distance from the N1 0 -atom of the pyrimidine ring of ThDP, indicating the formation of a hydrogen bond. On the other hand, studies involving ThDP analogs bound in various ThDP-dependent enzymes point to an essential requirement of the N1 0 -atom and the 4 0 -amino group for the catalytic activity (Golbik et al., 1991; Schellenberger, 1990; Schellenberger et al., 1997). In order to demonstrate the cofactor activation by the protein environment Glu51 in pyruvate decarboxylase from Saccharomyces cerevisiae was mutated to glutamine and, additionally, the 4 0 -amino group of the coenzyme was eliminated. The E51Q mutant enzyme binds ThDP as strongly as the wild type enzyme, shown by characteristic changes in the near-UV circular dichroism spectrum (Killenberg-Jabs et al., 1997). However, the residual catalytic activity of the variant was only 0.04% of that of the wild type enzyme. The slow dissociation rate constant of the C2-H of ThDP in the Saccharomyces cerevisiae pyruvate decarboxylase E51Q variant (Table 16.1) suggests that this glutamate is essentially involved in the proton abstraction of the enzyme-bound ThDP. Furthermore, pyruvate decarboxylase from Saccharomyces cerevisiae was reconstituted with 4 0 -deamino-ThDP to unravel the function of the 4 0 -amino group of the coenzyme. This modification of the cofactor results in an inactive enzyme after reconstitution and in a markedly decreased H/D exchange rate constant of C2-H of the analog compared with the enzyme containing the entire coenzyme (Table 16.1). These findings point to an essential function of the 4 0 -amino group in the deprotonation step. In order to investigate the functional contributions of side chains of the active site to the H/D exchange of ThDP (beside the substitution of the conserved glutamate interacting with the N1 0 -atom of ThDP) all putative residues were mutated in this location in pyruvate decarboxylase from Zymomonas mobilis. As shown in Table 16.1, these mutations have no influence on the C2-H deprotonation rate constant of the enzyme-bound cofactor. In order to further characterize the key role of the 4 0 -amino group of ThDP for cofactor activation, the influence of the chemical environment at the active site of pyruvate decarboxylase from Zymomonas mobilis on the electronic properties of the 4 0 -amino group was studied by two-dimensional proton-nitrogen correlated NMR spectroscopy (Tittmann et al., 2005a). Chemical shift analysis and its pH dependence indicate that the acceleration of C2 deprotonation by 5 orders of magnitude is not mainly of thermodynamic nature caused by a significant increase in basicity
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16 Hydrogen Transfer in the Action of Thiamin Diphosphate Enzymes
of the 4 0 -amino group, but rather of kinetic nature caused by an optimal spatial orientation of the activated amino group towards the C2 hydrogen enforced by the adopted V conformation of the cofactor in the active site. 16.2.2
Deprotonation Rate of the C2-H of Thiamin Diphosphate in Transketolase from Saccharomyces cerevisiae
In order to investigate whether the mechanism of ThDP activation is a common phenomenon in other ThDP-dependent enzymes, the H/D exchange of the C2-H of ThDP was measured in transketolase from Saccharomyces cerevisiae catalyzing the ketol transfer between aldo- and ketosugars. As observed for the above mentioned pyruvate decarboxylase, the C2-H deprotonation of ThDP is not ratelimiting in the wild type enzyme (Table 16.2). The crystal structure of transketolase from Saccharomyces cerevisiae (Lindqvist et al., 1992; Nikkola et al., 1994) shows the importance of the N1 0 -atom of the pyrimidine ring of the cofactor, which is located at a hydrogen bond distance from the side chain of Glu418. A mutation of this glutamate to alanine results in an enzyme with only 0.1% of the activity measured for the wild type enzyme and a slow H/D exchange rate constant. However, the mutation of the closest base to the C2-atom of ThDP in this transketolase, realized in the variant H481A, does not change the rate constant of C2-H deprotonation (Table 16.2). Therefore, a mechanism assuming His481 as the base for C2-proton abstraction could be essentially ruled out. In order to unravel the function of both the 4 0 -amino group and the N1 0 -atom of the coenzyme in transketolase from Saccharomyces cerevisiae, the apoenzyme was reconstituted with either the 4 0 -deamino-ThDP, or the N1 0 ! C-substituted ThDP analog (N1 0 -deaza-ThDP, N3 0 -pyridyl-ThDP). Both modifications of the cofactor result in inactive enzymes and a markedly decreased H/D exchange rate constant of C2-H compared with the enzyme containing the natural coenzyme (Table 16.2). Structural changes of the respective complexes of the wild type enzyme with the analogs were not detectable by X-ray crystallography (Ko¨nig et al., 1994). These results establish the essential function of both the 4 0 -amino group, and the N1 0 -atom in the deprotonation reaction of the coenzyme in this enzyme as well. Table 16.2.
Cofactor activation in transketolase
Sample
Rate constant (sC1 )
Free ThDP Free N1 0 ! C substituted ThDP Free 4 0 -deamino-ThDP Transketolase (wild type) Transketolase E418A variant Transketolase H481A variant Transketolase (wild type) reconstituted with 4 0 -deamino-ThDP Transketolase (wild type) reconstituted with N1 0 ! C substituted ThDP
3:0 G 0:1 103 1:6 G 0:1 104 3:2 G 0:1 103 61 G 2 3:7 G 0:1 101 61 G 2 9:5 G 0:1 105 1:6 G 0:2 104
16.2 The Mechanism of the C2-H Deprotonation of Thiamin Diphosphate in Enzymes
The same coenzyme binding pattern and no structural changes in the protein component were detectable for the mutant enzymes of transketolase from Saccharomyces cerevisiae and their complexes with coenzyme analogs studied by X-ray crystallography (Ko¨nig et al., 1994; Wikner et al., 1994). Summarizing, it can be ruled out that the differences in the H/D exchange rate constants of transketolase from Saccharomyces cerevisiae are a result of a different solvent accessibility of a base involved in the proton abstraction mechanism of ThDP. 16.2.3
Deprotonation Rate of the C2-H of Thiamin Diphosphate in the Pyruvate Dehydrogenase Multienzyme Complex from Escherichia coli
In the pyruvate dehydrogenase complex, catalyzing the oxidative decarboxylation of pyruvate with NADþ and coenzyme A as cosubstrates and yielding acetylcoenzyme A, the ThDP-containing E1 component catalyzes the rate-limiting step of the overall reaction (Akiyama and Hammes, 1980; Bates et al., 1977) and, for this reason, represents an ideal target for regulation. Due to the reversible binding of ThDP to the complex the H/D exchange experiments were carried out in the presence of equimolar amounts of ThDP. Considering the very slow H/D exchange rate constant of the small amount of free ThDP in the reaction mixture (kobs ¼ 3 103 s1 at pH 7.0 and 4 C), a value of 16 s1 at pH 7.0 and 4 C was calculated for the enzyme-bound ThDP in bacterial E1, which exceeds the catalytic constant of 2 s1 measured under the same experimental conditions. On the basis of the crystal structure of a Bacillus stearothermophilus pyruvate dehydrogenase subcomplex formed between the heterotetrameric E1 and the peripheral subunit binding domain of E2 with an evident structural dissymmetry of the two active sites, a direct active center communication via an acidic proton tunnel has been proposed (Frank et al., 2004). According to this, one active site is in a closed state with an activated cofactor even before a substrate molecule is engaged, whereas the activation of the second active site is coupled to decarboxylation in the first site. Our own kinetic NMR studies on human PDH E1 (unpublished) support the model suggested, but similar studies on related thiamin enzymes, such as pyruvate decarboxylase, transketolase or pyruvate oxidase reveal that half-of-the-sites reactivity is a unique feature of ketoacid dehydrogenases. In line with this, X-ray crystallography studies on intermediates in transketolase catalysis indicated an active site occupancy close to unity in both active sites (Fiedler et al., 2002 and G. Schneider, personal communication). 16.2.4
Deprotonation Rate of the C2-H of Thiamin Diphosphate in the Phosphate-dependent Pyruvate Oxidase from Lactobacillus plantarum
The pyruvate oxidase from Lactobacillus plantarum catalyzes the oxidative decarboxylation of pyruvate and the formation of acetylphosphate, CO2 and H2 O2 in the presence of oxygen and phosphate (Go¨tz and Sedewitz, 1990; Sedewitz et al., 1984a; Sedewitz et al., 1984b). Each subunit of the homotetrameric enzyme binds
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16 Hydrogen Transfer in the Action of Thiamin Diphosphate Enzymes Table 16.3.
Cofactor activation in pyruvate oxidase
Sample
Rate constant (sC1 )
Free ThDP in 50 mM phosphate buffer
9:5 G 0:4 104
Holo pyruvate oxidase in 50 mM phosphate buffer
314 G 12
Holo pyruvate oxidase without phosphate Holo pyruvate oxidase reconstituted with 5-carba-5-deaza-FAD in 50 mM phosphate buffer Apo-ThDP-Mg 2þ pyruvate oxidase in 50 mM phosphate buffer Pyruvate oxidase E59A variant in 50 mM phosphate buffer
20 G 0:8 8 G 0:3 1:0 G 0:05 102 0:49 G 0:12
one ThDP and one FAD in the presence of Mn 2þ or Mg 2þ . The presence of these metal ions provided both FAD, and ThDP alone can form binary complexes with the apoenzyme (Risse et al., 1992). The binary complexes, however, are enzymatically inactive in the native overall oxidation reaction. The deprotonation of the C2-H of ThDP is also an important catalytic step in the pyruvate oxidase reaction. As shown in Table 16.3, the H/D exchange rate constant of the C2-H of ThDP in the apoenzyme–ThDP binary complex is very slow and would not allow catalysis at the rate constant observed. FAD binding to this binary complex accelerates the H/D exchange rate constant by four orders of magnitude compared to that of free ThDP (Table 16.3) and exceeds the enzyme’s catalytic constant of 2 s1 at 4 C. This fast H/D exchange in the native holoenzyme does not appear to be mediated by a direct interaction of the FAD with the C2-H of the enzyme-bound ThDP, but rather by interactions with functional groups of the protein that are operative only in the holoenzyme. This interpretation is consistent with the observation that the rate constant of the H/D exchange of ThDP is only marginally reduced compared to that of the native holoenzyme in the ternary complex with 5-carba-5-deaza-FAD (Table 16.3). In the crystal structure, the distance of the closest FAD atom to C2-H of ThDP is 11 A˚ (Muller and Schulz, 1993; Muller et al., 1994). Based on the structural homology of the ThDP binding site to other ThDP-dependent enzymes, it may be assumed that Glu59 is the residue mediating this activation in pyruvate oxidase by interacting with the N1 0 -atom of ThDP. This principle would be in analogy to pyruvate decarboxylase and transketolase (see sections above) displaying the same type of interaction. The slow H/D exchange rate constant in the E59A variant of pyruvate oxidase confirms this presumed function of Glu59 (Table 16.3). Interestingly, the presence of the second substrate phosphate increases the rate constant of the H/D exchange of ThDP in the holoenzyme of pyruvate oxidase from Lactobacillus plantarum 16-fold compared to that measured in a phosphatefree buffer (Table 16.3). At present, this behaviour of the enzyme observed in the presence of phosphate cannot be interpreted in molecular detail.
16.2 The Mechanism of the C2-H Deprotonation of Thiamin Diphosphate in Enzymes
16.2.5
Suggested Mechanism of the C2-H Deprotonation of Thiamin Diphosphate in Enzymes
The data measured for the deprotonation of the C2-H of ThDP in different enzymes show that its N1 0 -atom and 4 0 -amino group are essential for coenzyme activation. In addition, a fast deprotonation of C2-H requires an interaction of a conserved acidic group with the N1 0 -atom of the pyrimidine moiety of ThDP. As described in Section 16.2.1 a fast deprotonation of enzyme-bound ThDP is not mainly a result of an increased basicity of the 4 0 -amino group shown by protonnitrogen correlated NMR spectroscopy, but is rather caused by an optimal orientation of the amino group towards the C2 hydrogen. This kinetic control of the C2 deprotonation is in agreement with the previously performed experiments with 13 C2-labeled ThDP showing that the enzyme-bound cofactor does not generate a significant population of the C2 carbanion intermediate (Kern et al., 1997). A significant tautomerization of the aminopyrimidine part to the 1 0 –4 0 imino tautomer, as detected for covalent intermediates in pyruvate decarboxylase from Saccharomyces cerevisiae (Jordan et al., 2002; Nemeria et al., 2004) and the E1 component of the pyruvate dehydrogenase complex from Escherichia coli (Jordan et al., 2003), is not a prerequisite for a fast deprotonation (Scheme 16.2).
Scheme 16.2
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16 Hydrogen Transfer in the Action of Thiamin Diphosphate Enzymes
16.3
Proton Transfer Reactions during Enzymic Thiamin Diphosphate Catalysis
Whereas the mechanism of the C2-H deprotonation of ThDP has been shown to be identical in all ThDP-dependent enzymes investigated, the following steps in catalysis of the different enzymes require different protonation and deprotonation reactions of the intermediates formed along the process. In order to identify side chains involved in proton transfer steps, the distribution of reaction intermediates during catalysis of any wild type enzyme can be compared with that of active site mutant enzymes. Rate constants for single steps in catalysis can be calculated from
Figure 16.2. (A) C6 0 -H 1 H NMR fingerprint region of ThDP (I in Scheme 16.1), 2-lactylThDP (II in Scheme 16.1) and 2-(ahydroxyethyl)-ThDP (protonated III in Scheme 16.1). (B) Intermediate distribution of the
covalent intermediates formed during the nonoxidative decarboxylation of pyruvate by pyruvate decarboxylase from Zymomonas mobilis and its active site variants.
16.3 Proton Transfer Reactions during Enzymic Thiamin Diphosphate Catalysis
Figure 16.3. Crystal structure of active site residues of pyruvate decarboxylase from Zymomonas mobilis with the enzyme-bound cofactor ThDP in its typical V-conformation.
the distribution of reaction intermediates and compared for the wild type enzyme as well as for variants carrying mutations in the active site. This leads to a functional assignment of the corresponding side chains (Tittmann et al., 2003). Fortunately, in ThDP-dependent enzymes the intermediates (ThDP-C2 adducts) can be discriminated using 1H NMR (Tittmann et al., 2003). The chemical shifts of the C6 0 -H singlets of the aminopyrimidine moiety can be used as a fingerprint region for the discrimination of all C2-derived covalent ThDP adducts (Fig. 16.2A). They can be separated from the respective enzymes working at steady state conditions by acid quench treatment (Tittmann et al., 2003). Pyruvate decarboxylase from Zymomonas mobilis was investigated to determine the function of interacting groups in the interconversion of the reaction intermediates as a first example of this method (Tittmann et al., 2003). This enzyme, showing four amino acid side chains located at a short distance from the cofactor ThDP (Fig. 16.3), catalyzes the nonoxidative decarboxylation of pyruvate yielding acetaldehyde and carbon dioxide. The minimal catalytic scheme (Scheme 16.3) comprises the reversible, noncovalent binding of the substrate to the Michaelis complex, carbon–carbon bond formation between the C2-atom of ThDP and the carbonyl carbon of pyruvate to yield enzyme-bound 2-lactyl-ThDP (LThDP), the subsequent decarboxylation to the a-carbanion/enamine of 2-(a-hydroxyethyl)-ThDP (HEThDP), and finally, the liberation of acetaldehyde. Although a covalent binding of pyruvate to ThDP can be assumed to be reversible, the rate constant of this step calculated from the intermediate distribution at steady state reflects mainly the forward reac-
Scheme 16.3
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16 Hydrogen Transfer in the Action of Thiamin Diphosphate Enzymes Table 16.4. Microscopic rate constants of catalysis in pyruvate decarboxylase wildtype and variants
kcat (sC1 )
ZmPDC wt ZmPDC wt (D2 O) ZmPDC Glu 473 Asp ZmPDC Asp 27 Glu ZmPDC His 113 Lys ZmPDC Glu 50 Gln ScPDC wt
150 G 5 100 G 4 0.10 G 0.004 0.05 G 0.002 0.24 G 0.03 0.04 G 0.003 45 G 2
Rate constant (sC1 ) CxC bonding
CO2 release
Acetaldehyde release
2650 G 210 685 G 70 0.60 G 0.08 >5 >25 0.07 G 0.01 294 G 20
397 G 20 530 G 45 0.13 G 0.01 >5 >25 >7 105 G 6
265 G 13 150 G 14 1.2 G 0.2 0.051 G 0.002 0.25 G 0.03 0.09 G 0.01 105 G 6
tion of this microscopic step because of the large forward commitment factor of LThDP decarboxylation (Sun et al., 1995). The analysis of the intermediate distribution of pyruvate decarboxylase and its active site variants at steady state (Fig. 16.2B, Table 16.4) revealed two independent proton relay systems working in this enzyme. Furthermore, the kinetic solvent isotope effect measured for the wild type enzyme indicates the binding of pyruvate to the C2-atom of ThDP and the release of the reaction product acetaldehyde (both processes require proton transfer steps) to be the mainly affected steps in catalysis. The proton relay, involving the amino group of the cofactor and the interaction of the Glu50 with the N1 0 -atom of ThDP, influences not only the C2-H deprotonation of the coenzyme, but also the carbon–carbon bond formation between the C2carbanion of ThDP and the carbonyl-carbon of the substrate pyruvate and the release of the reaction product acetaldehyde (Table 16.4). According to the primary isotope effect measured, it can be assumed that this proton relay protonates the carbonyl-oxygen of the substrate as a prerequisite for the addition of its carbonylcarbon to the C2-carbanion of the coenzyme (step 2 in Scheme 16.4). This proton relay and a second proton relay consisting of the side chains of His113 and Asp27 are involved in product release (Table 16.4). This reaction step requires a protonation of the a-carbanion/enamine formed after decarboxylation of LThDP and a deprotonation of the a-OH group of HEThDP (step 4 in Scheme 16.4). The His113/ Asp27 dyad seems to be responsible for the protonation of the a-carbanion of HEThDP, since a mutation of Asp27 to alanine leads to a variant of this pyruvate decarboxylase catalyzing the formation of acetolactate as a result of the perturbation of the protonation reaction and the accumulation of the a-carbanion/enamine of HEThDP. A second pyruvate has the chance to attack the accumulated acarbanion of HEThDP in this protein. This reaction is usually catalyzed by acetohydroxyacid synthase (AHAS), a ThDP-dependent enzyme in which the His/Asp dyad is missing. Interestingly, if the pyruvate decarboxylase reaction is carried out in a mixture of H2 O/D2 O, a deuterium discrimination at the C1-atom of acetaldehyde will be ob-
16.3 Proton Transfer Reactions during Enzymic Thiamin Diphosphate Catalysis
Scheme 16.4
served (Ermer et al., 1992). This discrimination of deuterium, indicating a specific protonation of the a-carbanion/enamine intermediate by an active site residue, can be attributed in its magnitude either to a protonation by a functional group with low fractionation factor, or to a kinetic isotope effect of the protonation involving an asymmetric transition state. A mutation of Glu50, perturbing the proton relay Glu50 – N1 0 -atom – 4 0 -amino group, drastically decreases the rate constant of acetaldehyde release (Table 16.4). Therefore, the deprotonation of the a-OH group of HEThDP is very likely catalyzed
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16 Hydrogen Transfer in the Action of Thiamin Diphosphate Enzymes
by the 4 0 -imino group of its 1 0 ,4 0 -imino tautomeric form and would indicate this group of the cofactor as the preferred acid/base catalyst for this reaction. Similar results were obtained in our studies on the thiamin-dependent indolepyruvate decarboxylase, where protonation and deprotonation reactions are also catalyzed by a Glu-cofactor proton shuttle and a His-Asp-Glu relay (Schu¨tz et al., 2005). 16.4
Hydride Transfer in Thiamin Diphosphate-dependent Enzymes
Hydride transfer reactions can be expected in those ThDP-dependent enzymes catalyzing the oxidative decarboxylation of a-ketoacids, such as a-ketoacid dehydrogenase complexes and pyruvate oxidases. The electron/proton transfer in a-ketoacid dehydrogenase complexes cannot be ascribed unambiguously to the reaction of the a-carbanion/enamine of HEThDP (formed by the E1 component of the complex) with the lipoate of the E2 component leading to enzyme-bound 2-acetylThDP. An alternative mechanism leading to 2-acetyl-lipoate is imaginable, which involves an initial CaS bond formation and SaS bond fission together with proton reorganisation. On the other hand, in pyruvate oxidases the target for the oxidation reaction by enzyme-bound FAD can be attributed unambiguously to the acarbanion/enamine of HEThDP. In this section, the mechanism of the electron transfer in pyruvate oxidase from Lactobacillus plantarum is discussed. This enzyme is a homotetrameric protein containing one ThDP and one FAD per monomer and catalyzes the conversion of pyruvate to acetylphosphate, CO2 and H2 O2 in the presence of phosphate and oxygen.
Figure 16.4. Absorption spectra of oxidized (solid line) and reduced (dotted line) pyruvate oxidase from Lactobacillus plantarum.
16.4 Hydride Transfer in Thiamin Diphosphate-dependent Enzymes
For investigating pyruvate oxidase the spectroscopic properties of the isoalloxazine system of FAD are an excellent probe for monitoring steps relevant to enzyme catalysis directly. In pyruvate oxidase from Lactobacillus plantarum the lowest p–p transition can be used to distinguish between oxidized and reduced FAD (Fig. 16.4). In this enzyme the reductive half-reaction, including the catalytic steps of substrate binding, decarboxylation and electron transfer from the a-carbanion of HEThDP to FAD (Scheme 16.5), can be monitored after complete removal of oxygen in the mixture before the reaction is started with pyruvate. A back electron transfer from FADH2 to 2-acetyl-ThDP is negligible, because in the absence of oxygen pyruvate completely reduces enzyme-bound FAD to FADH2 . The progress curves of these single-turnover experiments measured at different concentrations of pyruvate (Fig. 16.5) reveal rate constants for the catalytic steps of the reductive half reaction of kon ¼ 6:5 10 4 M1 s1 and koff ¼ 20 s1 for the reversible binding of pyruvate, kdec ¼ 112 s1 for the decarboxylation, and kred ¼ 422 s1 for the reduction of FAD, respectively (Tittmann et al., 2000). In addition, time-resolved absorption spectra of enzyme-bound FAD indicate that blue or red flavosemiqui-
Scheme 16.5
Figure 16.5. Reduction of oxidized pyruvate oxidase by different concentrations of the substrate pyruvate under anaerobic conditions in 0.2 M potassium phosphate buffer, pH 6.0. Pyruvate concentration: 2.5 mM (open diamond), 5 mM (open square), 20 mM (open circle), and 50 mM (open triangle).
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16 Hydrogen Transfer in the Action of Thiamin Diphosphate Enzymes
Figure 16.6. Time-resolved absorption spectra of enzymebound FAD in pyruvate oxidase from Lactobacillus plantarum during the first turnover reduction by pyruvate under anaerobic conditions.
none species are not kinetically stabilized at pre-steady state (Fig. 16.6) and at steady state (data not shown) of the catalytic reaction. The absorbance appears to be composed of oxidized and fully reduced flavin species only. Kinetic solvent isotope effect experiments were performed to address the question, whether the reduction in pyruvate oxidase proceeds in a two-step single electron transfer or possibly via a hydride transfer after protonation of the a-carbanion/ enamine of HEThDP. Single-wavelength stopped-flow experiments were carried out with pyruvate and phosphate at saturating concentrations and air-saturated buffer using different mole fractions of deuterium oxide at pL 6.0. No kinetic solvent isotope effect for the reduction of FAD was found (Fig. 16.7). However, the catalytic constant representing the rate-limiting steps of catalysis shows a kinetic solvent isotope effect of 1.8 and a linear dependence of the proton inventory curve. In summary, the reduction of enzyme-bound FAD by the HEThDP intermediate proceeds via a two-step single electron transfer. Recent results obtained from 1 H NMR measurements on pyruvate oxidase suggest the decarboxylation of the substrate to be the rate-limiting step of catalysis (Tittmann et al., 2005b). A mechanism that involves protonation of the a-carbanion/enamine of HEThDP and subsequent hydride transfer, which has been proposed for several flavinedependent enzymes (Pollegioni et al., 1997), is unlikely since no kinetic solvent isotope effect is evident for this catalytic step (Fig. 16.7). In accordance, after replacement of FAD by 5-carba-5-deaza-FAD, a FAD analog not catalyzing a transfer of single electrons but functioning as hydride acceptor, no reduction is observed by the HEThDP intermediate in pyruvate oxidase from Lactobacillus plantarum (Tittmann et al., 1998).
16.4 Hydride Transfer in Thiamin Diphosphate-dependent Enzymes
Figure 16.7. Proton inventory for both the reduction of pyruvate oxidase by the substrate pyruvate (filled triangle) and for the catalytic constant (open square).
A direct a-carbanion mechanism involving the formation of a covalent adduct is very unlikely due to the spatial orientation of the two cofactors and the long distance between ThDP and FAD. The distance between the C2-atom of ThDP and the C4a-atom of FAD in pyruvate oxidase from Lactobacillus plantarum is about 11 A˚ as derived from the X-ray crystallography structure (Muller et al., 1993; Muller and Schulz, 1993). The results are in good agreement with the findings that Cadeprotonated HEThDP reduces a flavin analog in a two-step electron-transfer reaction in solution. Moreover, it has been concluded from the electron-transfer properties of free HEThDP that it may act as a two-electron donor with potentials 0 0 ¼ 0:97 V and Eoxð2Þ ¼ 0:56 V (Nakanishi et al., 1997a; Nakanishi et al., of Eoxð1Þ 1997b). Despite these clear indications for a radical two-step transfer mechanism, populated flavin radicals could neither be detected during the first turnover electron transfer (Fig. 16.6), nor at steady state or during anaerobic reduction (Fig. 16.4). It is unclear how the electrons are transferred between HEThDP and FAD. Based on the X-ray crystallography structure, it has been supposed that a stepwise electron transfer may be related to the benzene rings of Phe479 of the one and/or Phe121 of the other subunit (Muller and Schulz, 1993; Muller et al., 1994). On the other hand, the electrons may simply tunnel from HEThDP to FAD as proposed by Dutton and coworkers (Page et al., 1999). Since the redox potentials of the enzymebound HEThDP in pyruvate oxidase from Lactobacillus plantarum is still unknown, it is difficult to calculate the theoretical rate constant of the electron transfer from HEThDP to FAD according to Dutton (Page et al., 1999). However, it is very unlikely that the rate of reduction reflects the intrinsic rate of electron transfer. The
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16 Hydrogen Transfer in the Action of Thiamin Diphosphate Enzymes
absence of a kinetic solvent isotope effect argues against a proton transfer being the rate-limiting step. Possibly, rather, a reduction-associated distortion of FAD impeded by the protein environment is rate-limiting for the reduction process.
References Akiyama, S. K., Hammes, G. G. (1980), Elementary steps in the reaction mechanism of the pyruvate dehydrogenase multienzyme complex from Escherichia coli: kinetics of acetylation and deacetylation, Biochemistry 19, 4208–4213. Arjunan, P., Umland, T., Dyda, F., Swaminathan, S., Furey, W., Sax, M., Farrenkopf, B., Gao, Y., Zhang, D., Jordan, F. (1996), Crystal structure of the thiamin diphosphate-dependent enzyme pyruvate decarboxylase from the yeast Saccharomyces cerevisiae at 2.3 A˚ resolution, J. Mol. Biol. 256, 590–600. Bates, D. L., Danson, M. J., Hale, G., Hooper, E. A., Perham, R. N. (1977), Self-assembly and catalytic activity of the pyruvate dehydrogenase multienzyme complex of Escherichia coli, Nature 268, 313–316. Breslow, R. (1962), Part II. Cocarboxylase: Mode of action, reaction mechanism, and role of the active acetate, Ann. N. Y. Acad. Sci. 98, 445–452. Bringer-Meyer, S., Schimz, K. L., Sahm, H. (1986), Pyruvate decarboxylase from Zymomonas mobilis. Isolation and partial characterization, Arch. Microbiol. 146, 105–110. Crosby, J., Stone, R., Lienard, G. E. (1970), Mechanism of thiamine-catalyzed reactions. Decarboxylation of 2-(1-carboxy-1hydroxyethyl)-3,4-dimethylthiazoliumchloride, J. Am. Chem. Soc. 92, 2891–2900. Dyda, F., Furey, W., Swaminathan, S., Sax, M., Farrenkopf, B., Jordan, F. (1993), Catalytic centers in the thiamin diphosphate dependent enzyme pyruvate decarboxylase at 2.4-A˚ resolution, Biochemistry 32, 6165–6170. ¨bner, G. Ermer, J., Schellenberger, A., Hu (1992), Kinetic mechanism of pyruvate decarboxylase. Evidence for a specific protonation of the enzymic intermediate, FEBS Lett. 299, 163–165.
Fiedler, E., Thorell, S., Sandalova, T., Golbik, R., Ko¨nig, S., Schneider, G. (2002), Snapshot of a key intermediate in enzymatic thiamin catalysis: crystal structure of the a-carbanion of (a,bdihydroxyethyl)-thiamin diphosphate in the active site of transketolase from Saccharomyces cerevisiae, Proc. Nat. Acad. Sci. USA 99, 591–595. Frank, R. A., Titman, C. M., Pratap, J. V., Luisi, B. F., Perham, R. N. (2004), A molecular switch and proton wire synchronize the active sites in thiamine enzymes, Science 306, 818–820. ¨bner, G., Ko¨nig, S., Golbik, R., Neef, H., Hu Seliger, B., Meshalkina, L. E., Kochetov, G. A., Schellenberger, A. (1991), Function of the aminopyrimidine part in thiamine pyrophosphate enzymes, Bioorg. Chem. 19, 10–17. Go¨tz, F., Sedewitz, B. (1990), Physiological role of pyruvate oxidase in the aerobic metabolism of Lactobacillus plantarum, in Biochemistry and Physiology of Thiamin Diphosphate Enzymes (Bisswanger, H., Ullrich, J., eds.), pp. 286–293. VCH, Weinheim. ¨bner, G., Weidhase, R., Schellenberger, Hu A. (1978), The mechanism of substrate activation of pyruvate decarboxylase: A first approach, Eur. J. Biochem. 92, 175–181. Jordan, F., Nemeria, N. S., Zhang, S., Yan, Y., Arjunan, P., Furey, W. (2003), Dual catalytic apparatus of the thiamin diphosphate coenzyme: acid-base via the 1 0 ,4 0 -iminopyrimidine tautomer along with its electrophilic role, J. Am. Chem. Soc. 125, 12732–12738. Jordan, F., Zhang, Z., Sergienko, E. (2002), Spectroscopic evidence for participation of the 1 0 ,4 0 -imino tautomer of thiamin diphosphate in catalysis by yeast pyruvate decarboxylase, Bioorg. Chem. 30, 188–198. Kemp, D. S., O’Brien, J. T. (1970), Base catalysis of thiazolium salt hydrogen
References exchange and its implications for enzymatic thiamine cofactor catalysis, J. Am. Chem. Soc. 92, 2554–2555. Kern, D., Kern, G., Neef, H., Tittmann, K., Killenberg-Jabs, M., Wikner, C., ¨bner, G. (1997), How Schneider, G. Hu thiamine diphosphate is activated in enzymes, Science 275, 67–70. Killenberg-Jabs, M., Ko¨nig, S., Eberhardt, ¨bner, G. (1997), Role I., Hohmann, S., Hu of Glu51 for cofactor binding and catalytic activity in pyruvate decarboxylase from yeast studied by site-directed mutagenesis, Biochemistry 36, 1900–1905. Kluger, R. (1987). Thiamin diphosphate: A mechanistic update on enzymic and nonenzymic catalysis of decarboxylation. Chem. Rev. 87, 863–876. Ko¨nig, S., Schellenberger, A., Neef, H., Schneider, G. (1994), Specificity of coenzyme binding in thiamin diphosphatedependent enzymes. Crystal structures of yeast transketolase in complex with analogs of thiamin diphosphate, J. Biol. Chem. 269, 10879–10882. Lindqvist, Y., Schneider, G., Ermler, U., Sundstro¨m, M. (1992), Three-dimensional structure of transketolase, a thiamine diphosphate dependent enzyme, at 2.5 A˚ resolution, EMBO J. 11, 2373–2379. Muller, Y. A., Lindqvist, Y., Furey, W., Schulz, G. E., Jordan, F., Schneider, G. (1993), A thiamin diphosphate binding fold revealed by comparison of the crystal structures of transketolase, pyruvate oxidase and pyruvate decarboxylase, Structure 1, 95–103. Muller, Y. A., Schulz, G. E. (1993), Structure of the thiamine- and flavindependent enzyme pyruvate oxidase, Science 259, 965–967. Muller, Y. A., Schumacher, G., Rudolph, R., Schulz, G. E. (1994), The refined structures of a stabilized mutant and of wild-type pyruvate oxidase from Lactobacillus plantarum, J. Mol. Biol. 237, 315–335. Nakanishi, I., Itoh, S., Suenobu, T., Fukuzumi, S. (1997a), Electron transfer properties of active aldehydes derived from thiamin coenzyme analogues, Chem. Commun. 19, 1927–1928. Nakanishi, I., Itoh, S., Suenobu, T., Inoue, H., Fukuzumi, S. (1997b), Redox behavior of active aldehydes derived from thiamin coenzyme analogs, Chem. Lett. 707–708.
Nemeria, N. S., Baykal, A., Ebenezer, J., Zhang, S., Yan, Y., Furey, W., Jordan, F. (2004). Tehtrahedral intermediates in thiamin diphosphate-dependent decarboxylations exist as a 1 0 ,4 0 -imino tautomeric form of the coenzyme, unlike the Michaelis complex or the free coenzyme, Biochemistry 43, 6565–6575. Nikkola, M., Lindqvist, Y., Schneider, G. (1994), Refined structure of transketolase from Saccharomyces cerevisiae at 2.0 A˚ resolution, J. Mol. Biol. 238, 387–404. Page, C. C., Moser, C. C., Chen, X., Dutton, P. L. (1999), Natural engineering principles of electron tunnelling in biological oxidation – reduction, Nature 402, 47–52. Pollegioni, L., Blodig, W., Ghisla, S. (1997), On the mechanism of d-amino acid oxidase. Structure/linear free energy correlations and deuterium kinetic isotope effects using substituted phenylglycines, J. Biol. Chem. 272, 4924–4934. Risse, B., Stempfer, G., Rudolph, R., Mo¨llering, H., Jaenicke, R. (1992), Stability and reconstitution of pyruvate oxidase from Lactobacillus plantarum: Dissection of the stabilizing effects of coenzyme binding and subunit interaction, Protein Sci. 1, 1699–1709. Schellenberger, A. (1990), Die Funktion der 4 0 -Aminopyrimidin-Komponente im Katalysemechanismus von Thiaminpyrophosphatenzymen aus heutiger Sicht, Chem. Ber. 123, 1489–1494. ¨ bner, G., Neef, H. Schellenberger, A., Hu (1997), Cofactor designing in functional analysis of thiamin diphosphate enzymes, Methods Enzymol. 279, 131–146. ¨ tz, A., Golbik, R., Ko¨nig, S., Hu ¨bner, Schu G., Tittmann, K. (2005), Intermediate and transition states in thiamin diphosphatedependent decarboxylases. A kinetic and NMR study on wild-type indolepyruvate decarboxylase and variants using indolepyruvate, benzoylformate, and pyruvate as substrates, Biochemistry 44, 6164–6179. Sedewitz, B., Schleifer, K. H., Go¨tz, F. (1984a), Physiological role of pyruvate oxidase in the aerobic metabolism of Lactobacillus plantarum, J. Bacteriol. 160, 462–465. Sedewitz, B., Schleifer, K. H., Go¨tz, F. (1984b), Purification and biochemical
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16 Hydrogen Transfer in the Action of Thiamin Diphosphate Enzymes characterization of pyruvate oxidase from Lactobacillus plantarum, J. Bacteriol. 160, 273–278. Sun, S. X., Duggleby, R. G., Schowen, R. L. (1995), Linkage of catalysis and regulation in enzyme action – carbon isotope effects, solvent isotope effects, and proton inventories for the unregulated pyruvate decarboxylase of Zymomonas mobilis, J. Am. Chem. Soc. 117, 7317–7322. Tittmann, K. (2000), Untersuchungen zu Katalysemechanismen von Flavin- und Thiamindiphosphat-abha¨ngigen Enzymen. Aktivierung von Thiamindiphosphat in Enzymen. Katalysemechanismus der Pyruvatoxidase aus Lactobacillus plantarum, PhD Thesis, Martin-Luther-University HalleWittenberg. Tittmann, K., Golbik, R., Ghisla, S., ¨bner, G. (2000), Mechanism of Hu elementary catalytic steps of pyruvate oxidase from Lactobacillus plantarum, Biochemistry 39, 10747–10754. Tittmann, K., Golbik, R., Uhlemann, K., Khailova, L., Schneider, G., Patel, M., Jordan, F., Chipman, D. M., Duggleby, ¨ bner, G. (2003), NMR analysis of R. G., Hu covalent intermediates in thiamin diphosphate enzymes, Biochemistry 42, 7885–7891. ¨bner, Tittmann, K., Neef, H., Golbik, R., Hu G., Kern, D. (2005a), Kinetic control of thiamin diphosphate activation in enzymes
studied by proton-nitrogen correlated NMR spectroscopy, Biochemistry 44, 8697–8700. Tittmann, K., Proske, D., Spinka, M., ¨ bner, G., Ghisla, S., Rudolph, R., Hu Kern, G. (1998), Activation of thiamin diphosphate and FAD in the phosphatedependent pyruvate oxidase from Lactobacillus plantarum, J. Biol. Chem. 273, 12929–12934. Tittmann, K., Wille, G., Golbik, R., ¨bner, G. Weidner, A., Ghisla, S., Hu (2005b), Radical phosphate transfer mechanism for the thiamin diphosphateand FAD-dependent pyruvate oxidase from Lactobacillus plantarum. Kinetic coupling of intercofactor electron transfer with phosphate transfer to acetyl-thiamin diphosphate via transient FAD semiquinone/hydroxyethyl-ThDP radical pair, Biochemistry 44, 13291–13303. Washabaugh, M. W., Jencks, W. P. (1988), Thiazolium C(2)-proton exchange: structurereactivity correlations and the pKa of thiamin C(2)-H revisited, Biochemistry 27, 5044–5053. Wikner, C., Meshalkina, L., Nilsson, U., Nikkola, M., Lindqvist, Y., Sundstro¨m, M., Schneider, G. (1994), Analysis of an invariant cofactor-protein interaction in thiamin diphosphate-dependent enzymes by site-directed mutagenesis. Glutamic acid 418 in transketolase is essential for catalysis, J. Biol. Chem. 269, 32144–32150.
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Dihydrofolate Reductase: Hydrogen Tunneling and Protein Motion Stephen J. Benkovic and Sharon Hammes-Schiffer
Dihydrofolate reductase (DHFR, EC 1.5.1.3) is an essential enzyme required for normal folate metabolism in prokaryotes and eukaryotes. Its role is to maintain necessary levels of tetrahydrofolate to support the biosynthesis of purines, pyrimidines and amino acids. Many compounds of pharmacological value, notably methotrexate and trimethoprim, work by inhibition of DHFR. Their clinical importance justified the study of DHFR in the rapidly evolving field of enzymology. Today, there is a vast amount of published literature (ca. 1000 original research articles) on the broad subject of dihydrofolate reductase contributed by scientists from diverse disciplines. We have selected kinetic, structural, and computational studies that have advanced our understanding of the DHFR catalytic mechanism with special emphasis on the role of the enzyme–substrate complexes and protein motion in the catalytic efficiency achieved by this enzyme.
17.1
Reaction Chemistry and Catalysis
DHFR catalyzes the reduction of 7,8-dihydrofolate (H2 F) to 5,6,7,8-tetrahydrofolate (H4 F) using nicotinamide adenine dinucleotide phosphate (NADPH) as a cofactor (Fig. 17.1). Specifically, the pro-R hydride of NADPH is transferred stereospecifically to the C6 of the pterin nucleus with concurrent protonation at the N5 position [1]. Structural studies of DHFR bound with substrates or substrate analogs have revealed the location and orientation of H2 F, NADPH and the mechanistically important side chains [2]. Proper alignment of H2 F and NADPH is crucial in enhancing the rate of the chemical step (hydride transfer). Ab initio, mixed quantum mechanical/molecular mechanical (QM/MM), and molecular dynamics computational studies have modeled the hydride transfer process and have deduced optimal geometries for the reaction [3–6]. The optimal CaC distance between the C4 of NADPH and C6 of H2 F was calculated to be @2.7 A˚ [5, 6], which is significantly smaller than the initial distance of 3.34 A˚ inferred from X-ray crystallography [2]. One proposed chemical mechanism involves a keto–enol tautomerization (Fig. Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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17 Dihydrofolate Reductase: Hydrogen Tunneling and Protein Motion
(a) The reaction catalyzed by DHFR. R and R 0 denote functional groups of H2 F and NADPH, respectively. (b) Structure of dihydrofolate (H2 F). pABG denotes the para-amino benzoyl group of H2 F. (c) Structure of cofactor NADPH. (Reproduced from Ref. [38].) Figure 17.1.
17.2) driven by the low dielectric environment of the DHFR active site [7–9]. In this pathway, H2 F binds initially as the 4-oxo tautomer and expels most of the water molecules from the active site. The resulting decrease in dielectric constant raises the pK a of Asp-27 and serves as the driving force for the tautomerization. The enol tautomer (4-hydroxy) results in a complex poised for chemical reaction. Hydride transfer then proceeds along with concerted proton transfers involving O4, N5 and N3 positions of the pterin and Asp-27 with the product H4 F formed as the 4oxo tautomer. The hydride transfer rate (k hyd ) displays strong pH dependence with an experimentally determined maximal value of 950 s1 and a pK a value of 6.5 [10]. However, there is some dispute as to whether the measured pK a reflects that of Asp-27, that of the N5 of H2 F, or both [7, 9]. These mechanistic issues have been studied via several different theoretical approaches. Cummins et al. assessed the energetically most likely substrate and enzyme protonation sites and pathways by performing QM/MM calculations [11]. In addition to explaining control of the likely protonation site by a structurally conserved water molecule that hydrogen bonds to both the carboxyl of Asp-27 and the O4 of the pterin, their results support a mechanism in which Asp-27 is protonated first, followed by direct protonation of the keto form of the pterin at the N5 position for H2 F reduction. Analysis of the hydrogen-bonding distances between water molecules and the N5 position in classical molecular dynamics simulations has been used to postulate a mechanism in which the hydride transfer occurs before
17.1 Reaction Chemistry and Catalysis
Figure 17.2. The keto/enol tautomerization that plays a role in one of the proposed chemical mechanisms for hydride transfer.
the proton transfer [12, 13]. Recent calculations [14] have provided more direct evidence that the reaction proceeds through an initial proton transfer followed by a hydride transfer. These calculations illustrated that the free energy barrier for hydride transfer is more than 30 kcal mol1 greater for nonprotonated H2 F than for protonated H2 F. Most molecular dynamics simulations of the hydride transfer reaction have assumed that the protonation of H2 F occurs prior to hydride transfer. 17.1.1
Hydrogen Tunneling
Theoretical simulations indicate that hydrogen tunneling plays an important role in the hydride transfer reaction catalyzed by DHFR. A hybrid quantum/classical
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Figure 17.3. Three-dimensional vibrational wavefunctions representing the transferring hydride for reactant, transition state, and product configurations obtained from hybrid quantum/classical molecular dynamics simulations of the hydride transfer reaction
catalyzed by DHFR. On the donor side, the donor carbon atom and its first neighbors are shown, and on the acceptor side the acceptor carbon atom and its first neighbors are shown. (Reproduced from Ref. [15].)
molecular dynamics method that includes electronic and nuclear quantum effects, as well as the motion of the entire solvated enzyme, has been applied to this hydride transfer reaction [6, 15, 16]. In this approach, the transferring hydrogen nucleus is represented by a three-dimensional vibrational wavefunction (Fig. 17.3), and the free energy profile for the hydride transfer reaction is generated as a function of a collective reaction coordinate. Nuclear quantum effects such as zero point energy and hydrogen tunneling were found to lower the free energy barrier by 2–3 kcal mol1 [15]. The calculated primary deuterium kinetic isotope effect was consistent with the experimental value of 3, and hydrogen tunneling in the direction along the donor–acceptor axis was found to be significant [15]. The subsequent application of an alternative semiclassical tunneling method led to similar conclusions [14]. Mixed labeling experiments with specifically isotopically substituted 4R- and 4SNADPH cofactors established the primary and secondary kinetic isotope effects and their temperature dependence for the hydride transfer reaction. Indeed, resulting data could be rationalized only by a reaction model featuring an extensive tunneling contribution that is environmentally coupled. The difference in the observed and calculated intrinsic kinetic isotope effects requires a commitment factor arising from dissecting the pre-steady state hydride step into kinetic steps, one the actual hydride transfer step itself and the other a motion of the protein and/or nicotinamide associated with the hydride transfer step [17].
17.2 Structural Features of DHFR
Figure 17.4. The pH-independent kinetic scheme for DHFR catalysis at 25 C. This scheme pertains to the reaction at pH less than 7. E is DHFR; NH is NADPH; Nþ is NADPþ ; H2 F is dihydrofolate; and H4 F is tetrahydrofolate. (Reproduced from Ref. [38].)
17.1.2
Kinetic Analysis
DHFR catalysis follows the kinetic scheme described in Fig. 17.4. Pre-steady state kinetic experiments augmented by equilibrium binding measurements were used to elucidate this scheme, which correctly predicts the full-time course kinetics as a function of substrate concentrations and pH [10]. The preferred pathway that produces a maximal rate of H4 F turnover involves DHFR cycling between five kinetically observable species. Initially, rapid hydride transfer within the Michaelis complex (ENHH2 F) produces the product complex (ENþ H4 F) from which NADPþ (Nþ ) dissociates to produce the EH4 F binary complex. A NADPH (NH) molecule then associates to form a reduced ternary complex (ENHH4 F) from which H4 F dissociates, returning the ENH complex poised for another round of turnover. The steady state rate is controlled by the rate of H4 F release from the reduced ternary complex (ENHH4 F). The presence of both reduced ligands in this complex causes negative cooperativity and an elevation in the off rates of both ligands. This complete kinetic analysis of DHFR catalysis served as the basis for comparative studies with numerous site directed mutants. Similar kinetic schemes were developed for these mutant DHFRs, thereby allowing an in-depth and unambiguous analysis of the function of these mutated regions [10, 18–26] when combined with structural considerations furnished by X-ray and NMR methods.
17.2
Structural Features of DHFR
From the standpoint of protein structure, DHFR possesses prominent structural features that guide the substrate and cofactor through the preferred catalytic pathway (Fig. 17.5). X-ray crystallographic studies have shown that the E. coli DHFR is
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Structural features of E.coli DHFR. The figure is an overlay of three crystallographically observed Met-20 loop conformations. They are open (blue), closed (red) and occluded (green). (Reproduced from Ref. [38].)
Figure 17.5.
a monomeric enzyme and has several secondary structural elements [2, 8, 27]. An eight stranded b-sheet (bA-bH) and four a helices are interspersed with loop regions that connect these structural elements. The protein structure can be divided into two subdomains, namely the adenosine binding subdomain and the loop subdomain [18]. The loop subdomain contains three flexible loops: the Met-20 loop, the bF-bG loop, and the bG-bH loop. Space between the two subdomains forms the active site cleft where NADPH and H2 F bind at a 45 angle to each other. The subdomains rotate open and closed during passage through the preferred catalytic pathway. 17.2.1
The Active Site of DHFR
Key hydrophobic contacts exist between the para-amino benzoyl glutamate (pABG) group of H2 F and active site residues Leu-28, Phe-31, Ile-50 and Leu-54 that could be enhanced during the hydride transfer step [2, 21, 26]. After reduction to H4 F, the resulting ring pucker at the pterin C6 position causes the disruption of these van der Waals contacts. This provides a basis for discrimination between H2 F and H4 F. The side chains of Leu-28 and Leu-54 are separated by 8 A˚ on opposite sides of the active site but interact through the bound H2 F. This coupling was revealed by double mutational analysis of the two residues, as shown in Fig. 17.6. Kinetic constants for key steps were measured for both the single mutants (L28Y and
17.2 Structural Features of DHFR
Figure 17.6. Representative double mutational cycle involving mutations L28Y and L54F. Mutational effects are calculated as free energy changes (DG x ) relative to wild type. Nonaddi-
tivity (DGI ) in the double mutational cycle is then calculated for any kinetic or thermodynamic parameter. (Reproduced from Ref. [38].)
L54F) and the double mutant (L28Y-L54F) (Table 17.1) and converted to changes in free energy (DG x ) [21]. If the residues act independently, the free energies for a given step in the two single mutants would sum to that for the double mutant with DGI ¼ 0. Nonadditive free energies (nonzero DGI ) indicative of side chain Table 17.1. Mutational effects on ligand binding (KD ) and hydride transfer rate (k hyd ). All data were obtained at pH ¼ 7.5.
Mutation
Wild type H2 F contacts L28Y L28F L54F L28Y-L54F L28F-L54F Met-20 loop DL1 bF-bG loop G121V G121S D122N D122S D122A bG-bH loop S148D S148A S148K
KD H2 F (mM)
KD NADPH (mM)
khyd (sC1 )
References
0.21
0.33
220
10
0.11 0.15 0.10 11.0 0.20
0.15 0.40 0.17 0.60 3.5
109 4000 20 77 126
21 39 21 21 26
2.0
5.3
1.7
22
0.36 NR 0.38 0.37 0.39
14.2 NR 0.92 1.1 1.3
1.4 40.1 9.4 5.9 4.0
20 20 23 23 23
0.18 1.06 0.72
0.15 0.05 0.16
319 157 162
25 25 25
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coupling were, however, observed for H2 F and NADPH binding and the hydride transfer rates. Additive effects were displayed for the rates of reverse hydride transfer and product dissociation, indicating that for these steps the side chains act independently. The conclusion is that the substrate complexes (ENH and ENHH2 F) are in conformations in which the side chains of Leu-28 and Leu-54 can couple, whereas the product complexes (ENþ H4 F and ENHH4 F) are in conformations in which these side chains cannot couple. Of particular note is the fact that the forward and reverse hydride transfer steps exhibit different DGI values, thereby excluding interaction by these residues in their common transition state. Collectively the data suggest that DHFR adopts different conformations involving Leu-28 and Leu-54 during the catalytic cycle. Later efforts examined the additivity of mutational effects caused by the L54F mutation in combination with the L28F mutation [26]. The nonadditive effects observed with the related double mutational cycle involving the L28Y mutation were essentially absent, showing that a single functional group change (aOH in L28Y to aH in L28F) can control the additivity of mutational effects. In general, the effect of the second mutation within the active site, although deleterious, did not alter the thermodynamic and kinetic parameters to the extent anticipated if they were additive. Similar trends were observed for double mutational cycles involving paired mutations at active site residues Phe-31 and Ile-50 in conjunction with paired Leu-28 and Leu-54 mutations. This resiliency to mutation may be thought of as a built in ‘‘active site redundancy’’ that conserves function and may have evolutionary significance.
17.2.2
Role of Interloop Interactions in DHFR Catalysis
Sawaya and Kraut compiled structures representative of all five complexes and the TS in the kinetically preferred pathway by cocrystallizing the enzyme with substrate and cofactor analogs and subsequently tracing variations in loop and subdomain positions [2]. DHFR, as mentioned earlier, has three flexible loops that cover 45% of the sequence [2, 28]. Several structural studies have shown that the Met-20 loop adopts either a closed or occluded conformation (Fig. 17.5) depending on the ligands bound. In the closed conformation, the Met-20 loop residues interact with NADPH through hydrogen bonding to the carboxamide group and through van der Waals contacts with the ribose unit. This closed conformation is observed in surrogate substrate complexes (ENH and ENHH2 F) and is stabilized by interactions with bF-bG loop residues. Specifically, the amide backbone of both Gly-15 and Glu-17 in the Met-20 loop forms hydrogen bonds with Asp-122 in the bF-bG loop. Mutagenesis of Asp-122 to Asn, Ser and Ala (in order of decreasing ability to hydrogen bond) showed two important trends [23]. First, a significant correlation was observed between decreased NADPH binding and lowered hydride transfer rates (Table 17.1). This finding suggests that the interactions of Asp-122 participate in the collective reaction coordinate leading to the TS. Secondly, the mutations in
17.3 Enzyme Motion in DHFR Catalysis
Asp-122 altered the preferred catalytic pathway, indicating that loop interactions actively control ligand affinity and turnover. The presence of H2 F or an analog has implications for the conformational state of the Met-20 loop. In the absence of a folate analog, the occupancy of the nicotinamide binding pocket by this moiety of the cofactor in the ENH complex is @75%. When H2 F binds, the occupancy shifts to 100% and the nicotinamide ring is positioned favorably for hydride transfer. After the chemical reaction, the nicotinamide pocket occupancy falls to zero in the ENADPþ H4 F complex [2, 27]. Concomitant disruption of hydrogen bonds between the Met-20 and bF-bG loops and formation of new ones between the Met-20 and bG-bH loops result in the Met-20 loop adopting an occluded conformation in the product complexes. The occluded conformation excludes the nicotinamide ring from its binding pocket. The closed/occluded Met 20 loop conformations were also assigned to various DHFR ligand complexes in solution through observation of chemical shift changes associated with alanine 1 Ha 15 N resonances [29]. The findings are in close agreement with those from crystallography, namely, the key substrate complexes ENH and ENHH2 F are closed, and the key product complexes EH4 F, ENþ H4 F and ENHH4 F are occluded. The HSQC spectrum of the ENþ binary complex revealed the presence of both closed and occluded forms, probably associated with fluctuation of the ribose-nicotinamide moiety into and out of the binding cleft. The chemical shift of the Ala 6 resonance shows that the pterin ring occupies the active site in all complexes (both closed and occluded conformations) and irrespective of whether the ring is planar or strongly puckered. On the other hand, if either the pterin or nicotinamide rings are non-planar, e.g. NADPH or H4 F, the conformation of the Met 20 loop is occluded with the nicotinamide ring excluded from its binding site. Consequently, during turnover, the enzyme must cycle between the closed and the occluded states at two steps in the reaction cycle: following hydride transfer it changes from closed to occluded, and after product release it changes from occluded to closed. Site directed mutagenesis of bG-bH loop residues (residues 146-148) in which the ability to hydrogen bond with the Met-20 loop was systematically varied included single mutant enzymes S148D, S148A, S148K and the deletion mutant enzyme D(146-148). (Note that the amide backbone of Asn-23 in the Met-20 loop hydrogen bonds to Ser-148 in the bG-bH loop.) Kinetic studies indicated that the Met-20 and bG-bH loop interaction modulated the ligand off rates and degree of cycling through the preferred kinetic pathway. Collectively, these kinetic and structural studies implicated a series of conformational states characterized by extensive loop movements that guide the reaction cycle.
17.3
Enzyme Motion in DHFR Catalysis
Structures derived from X-ray crystallography provide static images of different protein conformations and lack dynamical information. Moreover, deviations due
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to crystal packing forces can cause a different picture to be presented than the true situation in solution. To address these issues, NMR studies were initiated to examine the solution structure of DHFR in the presence and absence of ligands [28, 30]. The dynamics of the Met-20 loop were investigated by analyzing the 2D NOESY spectra of the apo-enzyme. The time dependence of Trp-22 cross peaks was used as an indicator of Met-20 loop exchange between the closed and occluded states [28]. The frequency of oscillation of the Met-20 loop was found to be 35 s1 , which is similar to the off rate of H4 F under steady state conditions, suggesting that loop movement may be a limiting step in substrate turnover. Replacement of the central portion of the Met-20 loop (residues Met-16 to Ala-19) with a single glycine (mutant DL1 in table 1) altered the loop dynamics and decreased substrate binding 10-fold and hydride transfer 400-fold [22]. Epstein et al. studied the backbone and tryptophan side-chain dynamics of the 15 N-labeled DHFRfolate complex [30]. Measurements of the 15 N spin–lattice (T1 ) and spin–spin (T2 ) relaxation times and 1 Ha 15 N heteronuclear Overhauser effects (NOEs) were made for the protonated backbone nitrogen atoms. Dynamic information for each residue was then calculated and expressed in terms of a generalized order parameter (S 2 ), an effective correlation time for internal motions (te ), and a 15 N exchange broadening contribution (R ex ). The values of S 2 lie between 0 and 1, where a lower S 2 value implies increased disorder. The average S 2 values of secondary structure elements are similar, but much lower S 2 values and larger te values are observed in the loop regions, indicating increased motions on the ns–ps time scale. Four notable regions of enhanced flexibility are the Met-20 loop (residues 16-22), the adenosine binding loop (residues 67-69), the hinge regions (residues 38 and 88), and the bF-bG loop (residues 119-123) [30]. The DHFRfolate complex studied represents the product binary complex (DHFRH4 F) in which the Met-20 loop occludes the nicotinamide binding site. Subsequent work included DHFRdhNADPHfolate and DHFRNADPþ folate species that represent the product ternary complexes (DHFRNADPþ H4 F and DHFRNADPHH4 F) and the Michaelis complex (DHFRNADPHH2 F), respectively [31]. Folate and dhNADPH (5,6-dihydro NADPH) serve as nonreactive substrate and cofactor analogs, respectively. Conformations of the Met-20 loop and occupancy of the nicotinamide binding pocket in each complex were identified using a diagnostic set of marker resonances. The ns–ps timescale backbone dynamics of the regions in the DHFRfolate and DHFRdhNADPHfolate complexes (Met-20 loop in the occluded state) are largely attenuated in the DHFRNADPþ folate complex (Met-20 loop in the closed state), as indicated by increased S 2 and decreased te values. The change in dynamics observed between the closed and occluded complexes can be rationalized from structural considerations [2]. In the occluded conformation, residues 14-16 of the Met-20 loop occupy the nicotinamide binding pocket while residues 16-22 and 119-123 (bF-bG loop) are solvent exposed, resulting in high flexibility. In the closed state, however, tight packing involving the Met20 loop, the bF-bG loop, and the nicotinamide group results in reduced flexibility. Despite the suggestive nature of the data, the available NMR measurements cannot alone conclusively link the backbone motions to catalysis.
17.3 Enzyme Motion in DHFR Catalysis
The relationship between dynamics and catalysis was probed by site directed mutagenesis of Met-20 and bF-bG loop residues guided in part by the NMR findings [20]. The mutant enzymes were characterized by building complete kinetic schemes as in Fig. 17.4. Mutagenesis of Gly-121 in the bF-bG loop weakened NADPH binding and slowed hydride transfer (Table 17.1). In particular, the G121V mutation caused hydride transfer to be reduced 200-fold and introduced a kinetically significant conformational change step in the ternary Michaelis complex preceding the hydride transfer step [20]. NMR studies of this mutant have shown that the closed Met 20 loop is destabilized so that key substrate complexes are in the occluded conformation. Structurally, this corresponds to insertion of the nicotinamide ring into its binding pocket. The rate of insertion has been reduced from a rate of >2000 s1 in the wild type enzyme to 2 s1 in the mutant. However, despite insertion into the binding pocket, the hydride transfer rate is still reduced [20]. Two interpretations are plausible: the population of productive ternary complexes at the active site is also reduced by the mutation and/or an important conformational motion along the reaction coordinate has been affected by the mutation. In order to determine if the dynamic motions observed by NMR methods are correlated with one another and catalysis, classical molecular dynamics (MD) simulations were performed on various DHFR complexes. Radkiewicz et al. generated 10 ns MD simulations on the three ternary complexes in the preferred pathway [32]. The starting points for the simulations were crystal structures that represented the DHFRNADPHH2 F, DHFRNADPþ H4 F and DHFRNADPHH4 F complexes. During the simulations the flexible loop region underwent conformational changes while the protein retained its overall secondary and tertiary structure. Furthermore, these changes were dependent on the nature of the ligand bound. Residue–residue based maps of correlated motions representing fluctuations about an average structure were generated for all three complexes analyzed. These fluctuations are local to the average structure and typically occur on the femtosecond to picosecond timescale. In these maps, regions of correlated and anticorrelated motions were defined in which the two residues moved in concert, either in the same or in opposite directions, respectively. Strong correlated and anticorrelated motions involving spatially distinct regions in the protein structure were observed for the Michaelis complex (DHFRNADPHH2 F) only. These correlated motions appeared in many of the same regions of the protein observed in the dynamic NMR measurements. The absence of these correlated motions in the product complexes implied that they may be tied to catalysis, although it is not known which correlations are essential. Their possible relevance to catalysis is underscored by the fact that mutations made in regions of correlated motion have a deleterious effect on DHFR activity. Classical MD simulations on the G121V mutant, which has a 200-fold lower hydride transfer rate, revealed an absence of similar patterns of correlated motion [33]. The collective analysis of kinetic data for site directed mutants, data from NMR spectroscopy for regions of dynamic motions, MD simulations for correlated motions, and genomic content for sequence conservation across 36 species has led to the identification of a conserved set of residues that are catalytically relevant (Fig. 17.7) [6].
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17 Dihydrofolate Reductase: Hydrogen Tunneling and Protein Motion
Figure 17.7. Chain of residues important for hydride transfer in E.coli DHFR. Substrate and cofactor structures are in red and green respectively with dot surfaces. Blue balls with adjacent numbering denote residue location. (Reproduced from Ref. [38].)
In addition, hybrid quantum/classical molecular dynamics simulations of hydride transfer catalyzed by DHFR provided evidence of a network of coupled motions extending throughout the protein and ligands [6, 15]. These coupled motions represent equilibrium thermally averaged conformational changes along the collective reaction coordinate, leading to configurations conducive to the reaction. These motions are averaged over the fast vibrational modes and reflect conformational changes that may occur on the much slower millisecond timescale of the overall hydride transfer reaction. The equilibrium molecular motions in this network are not dynamically coupled to the chemical reaction, but rather give rise to conformations in which the hydride transfer reaction is facilitated because of short transfer distances, suitable orientation of substrate and cofactor, and a favorable electrostatic environment for charge transfer. A portion of this network of coupled motions is illustrated in Fig. 17.8. Applications of two other computational approaches to hydride transfer catalyzed by DHFR have shown geometrical changes to be in agreement with this network of coupled motions [14, 34]. Moreover, subsequent
17.3 Enzyme Motion in DHFR Catalysis
Figure 17.8. Schematic diagram of a portion of the network of coupled motions in DHFR. The yellow arrows and arc indicate the coupled motions. This picture does not represent a complete or unique network but rather
illustrates the general concept of reorganization of the enzymatic environment to provide configurations conducive to the hydride transfer reaction. (Reproduced from Ref. [6].)
to the identification of Ile-14 as a key player in this network of coupled motions, NMR experiments confirmed the catalytic importance of this residue [35]. Specifically, the observed line broadening for Ile-14 in the measurement of methyl deuterium relaxation rates suggests motions on a microsecond or millisecond timescale. Applications of the hybrid quantum/classical molecular dynamics method to mutant DHFR enzymes have provided further insights into this network of coupled motions. Hybrid simulations of the G121V mutant lead to a rate reduction that is consistent with the experimental rate measurements and suggest that the mutation may modify the network of coupled motions through structural perturbations, thereby increasing the free energy barrier and decreasing the reaction rate [36]. Recently, a more comprehensive analysis of coupled motions correlated to hydride transfer was applied to the triple mutant M42F-G121S-S148A (Fig. 17.9) and the associated single and double mutants [37]. This analysis indicates that each enzyme system samples a unique distribution of coupled motions correlated to hydride transfer. These coupled motions provide an explanation for the experimentally measured nonadditivity effects in the hydride transfer rates for these mutants. Moreover, this analysis illustrates that site-specific mutations distal to the active site can introduce subtle perturbations that impact the catalytic rate by altering the conformational sampling of the entire enzyme. Since distal regions of the enzyme are coupled to each other through long-range electrostatics and extended hydrogen bonding networks [16], the introduction of a site-specific mutation alters the thermal motions of the entire enzyme. Altering the thermal motions of the enzyme affects the probability of sampling conformations conducive to the catalyzed chemical reaction, thereby impacting the free energy barrier and the rate.
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17 Dihydrofolate Reductase: Hydrogen Tunneling and Protein Motion
Figure 17.9. Three-dimensional structure of wild-type DHFR, with the NADPH cofactor shown in green and the DHF substrate shown in magenta. The residues involved in the triple mutant M42F-G121S-S148A are labeled with red spheres.
17.4
Conclusions
The participation of distant residues in catalysis is not unique to DHFR. Distant residues have been shown to determine the energetics of active site residues in serine proteases. Switching the substrate specificity of trypsin to chymotrypsin required a large set of multiple mutations at unexpected positions. In addition to catalysis, other physiologically important phenomena where protein motion may be involved are the allosteric behavior of enzymes and protein–protein interactions. In both cases an event such as the binding of a ligand can be signaled to regions far away from the binding site using protein motion as the medium of communication. Evidence for the biological significance of protein motion may be manifested in conservation of residues involved in key conformational changes. The combination of genomic analyses, kinetic studies, and theoretical calculations is continuing to provide insight into the role of protein motion in enzyme catalysis.
References 1 Charlton, P. A., Young, D. W.,
Birdsall, B., Feeney, J., Roberts, G. C. K. (1979) Stereochemistry of reduction of folic acid using
dihydrofolate reductase, J. Chem. Soc., Chem. Commun. 922–924. 2 Sawaya, M. R., Kraut, J. (1997) Loop and subdomain movements in the
References
3
4
5
6
7
8
9
10
mechanism of Escherichia coli dihydrofolate reductase: crystallographic evidence, Biochemistry 36, 586–603. Wu, Y. D., Houk, K. N. (1987) Theorectical transmition structures for hydride transfer to methyleneiminium ion from methylamine and dihydropyridine. On the nonlinearity of hydride transfers, J. Am. Chem. Soc. 109, 2226–2227. Wu, Y. D., Lai, D. K. W., Houk, K. N. (1995) Transition structures of hydride transfer reactions of protonated pyridinium ion with 1,4-dihydropyridine and protonated nicotinamide with 1,4-dihydronicotinamide, J. Am. Chem Soc. 117, 4100–4108. Castillo, R., Andres, J., Moliner, V. (1999) Catalytic mechanism of dihydrofolate reductase enzyme: A combined quantum-mechanical/ molecular mechanical characterization of transition state structure for the hydride transfer step, J. Am. Chem Soc. 121, 12140–12147. Agarwal, P. K., Billeter, S. R., Rajagopalan, P. T. R., Benkovic, S. J., Hammes-Schiffer, S. (2002) Network of coupled promoting motions in enzyme catalysis, Proc. Natl. Acad. Sci. USA 99, 2794–2799. Chen, Y. Q., Kraut, J., Blakley, R. L., Callender, R. (1994) Determination by Raman Spectroscopy of the pKa of N5 of dihydrofolate reductase: mechanistic implications, Biochemistry 33, 7021–7026. Lee, H., Reyes, V. M., Kraut, J. (1996) Crystal structures of Escherichia coli dihydrofolate reductase complexed with 5-formyltetrahydrofolate (folinic acid), in two space groups: evidence for enolization of pteridine O4, Biochemistry 35, 7012–7020. Cannon, W. R., Garrison, B. J., Benkovic, S. J. (1997) Electrostatic characterization of enzyme complexes: evaluation of the mechanism of catalysis of dihydrofolate reductase, J. Am. Chem. Soc. 119, 2386–2395. Fierke, C. A., Johnson, K. A., Benkovic, S. J. (1987) Construction and evaluation of the kinetic scheme associated with dihydrofolate
11
12
13
14
15
16
17
18
19
20
reductase from Escherichia coli, Biochemistry 26, 4085–4092. Cummins, P. L., Gready, J. E. (2001) Energetically most likely substrate and active-site protonation sites and pathways in the catalytic mechanism of dihydrofolate reductase, J. Am. Chem. Soc. 123, 3418–3428. Shrimpton, P. J., Allemann, R. K. (2002) Role of water in the catalytic cycle of E.coli dihydrofolate reductase, Protein Sci. 11, 1442–1451. Shrimpton, P. J., Mullaney, A., Allemann, R. K. (2003) Functional role for Tyr31 in the catalytic cycle of chicken dihydrofolate reductase, Proteins: Struct. Funct. Genet. 51, 216–223. Garcia-Viloca, M., Truhlar, D. G., Gao, J. (2003) Reaction-path energetics and kinetics of the hydride transfer reaction catalyzed by dihydrofolate reductase, Biochemistry 42, 13558–13575. Agarwal, P. K., Billeter, S. R., Hammes-Schiffer, S. (2002) Nuclear Quantum Effects and Enzyme Dynamics in Dihydrofolate Reductase Catalysis, J. Phys. Chem. B. 106, 3283–3293. Wong, K., Watney, J. B., HammesSchiffer, S. (2004) Analysis of electrostatics and correlated motions for hydride transfer in dihydrofolate reductase, J. Phys. Chem. B. 108, 12231–12241. Sikorski, R. S., Wang, L., Markham, K. A., Rajagopalan, P. T. R., Benkovic, S. J., Kohen, A. (2004) Tunneling and coupled motion in the Escherichia coli dihydrofolate reductase catalysis, J. Am. Chem Soc. 126, 4778–4779. Miller, G. P., Benkovic, S. J. (1998) Stretching exercises – flexibility in dihydrofolate reductase catalysis, Chem. Biol. 5, R105–R113. Benkovic, S. J., Fierke, C. A., Naylor, A. M. (1988) Insights into enzyme function from studies on mutants of dihydrofolate reductase, Science 239, 1105–1110. Cameron, C. E., Benkovic, S. J. (1997) Evidence for a functional role of the dynamics of glycine-121 of Escherichia coli dihydrofolate reductase
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21
22
23
24
25
26
27
28
29
obtained from kinetic analysis of a site-directed mutant, Biochemistry 36, 15792–15800. Huang, Z., Wagner, C. R., Benkovic, S. J. (1994) Nonadditivity of mutational effects at the folate binding site of E.coli dihydrofolate reductase, Biochemistry 33, 11576–11585. Li, L., Falzone, C. J., Wright, P. E., Benkovic, S. J. (1992) Functional role of a mobile loop of E.coli dihydrofolate reductase in transition-state stabilization, Biochemistry 31, 7826–7833. Miller, G. P., Benkovic, S. J. (1998) Strength of an interloop hydrogen bond determines the kinetic pathway in catalysis by Escherichia coli dihydrofolate reductase, Biochemistry 37, 6336–6342. Miller, G. P., Benkovic, S. J. (1998) Deletion of a highly motional residue affects formation of the Michaelis complex for Escherichia coli dihydrofolate reductase, Biochemistry 37, 6327–6335. Miller, G. P., Wahnon, D. C., Benkovic, S. J. (2001) Interloop contacts modulate ligand cycling during catalysis by Escherichia coli dihydrofolate reductase, Biochemistry 40, 867–875. Wagner, C. R., Huang, Z., Singleton, S. F., Benkovic, S. J. (1995) Molecular basis for nonadditive mutational effects in Escherichia coli dihydrofolate reductase, Biochemistry 34, 15671–15680. Bystroff, C., Oatley, S. J., Kraut, J. (1990) Crystal structures of Escherichia coli dihydrofolate reductase the NADPþ holoenzyme and the folate NADPþ ternary complex. Substrate binding and a model for the transition state, Biochemistry 29, 3263–3277. Falzone, C. J., Wright, P. E., Benkovic, S. J. (1994) Dynamics of a flexible loop in dihydrofolate reductase from Escherichia coli and its implication for catalysis, Biochemistry 33, 439–442. Venkitakrishnan, R. P., Zaborowski, E., McElheny, D., Benkovic, S. J., Dyson, H. J., Wright, P. E. (2004). Conformational Changes in the Active Site Loops of
30
31 32
33
34
35
36
37
38
39
Dihydrofolate Reductase during the Catalytic Cycle, Biochemistry 43, 16046–16055. Epstein, D. M., Benkovic, S. J., Wright, P. E. (1995) Dynamics of the dihydrofolate reductase – folate complex: Catalytic sites and regions known to undergo conformational change exhibit diverse dynamical features, Biochemistry 34, 11037–11048. Wright, P. E. (2002) personal communication. Radkiewicz, J. L., Brooks, C. L. I. (2000) Protein dynamics in enzymatic catalysis: Exploration of dihydrofolate reductase, J. Am. Chem. Soc. 122, 225–231. Rod, T. H., Radkiewicz, J. L., Brooks, C. L. I. (2003) Correlated motion and the effect of distal mutations in dihydrofolate reductase, Proc. Natl. Acad. Sci. USA 100, 6980–6985. Thorpe, I. E., Brooks, C. L. I. (2003) Barriers to hydride transfer in wild type and mutant dihydrofolate reductase fom E.coli, J. Phys. Chem. B. 107, 14042–14051. Schnell, J. R., Dyson, H. J., Wright, P. E. (2004) Effect of cofactor binding and loop conformation on side chain methyl dynamics in dihydrofolate reductase, Biochemistry 43, 374–383. Watney, J. B., Agarwal, P. K., Hammes-Schiffer, S. (2003) Effect of mutation on enzyme motion in dihydrofolate reductase, J. Am. Chem Soc. 125, 3745–3750. Wong, K., Selzer, T., Benkovic, S. J. (2004) Impact of distal mutations on the network of coupled motions correlated to hydride transfer in dihydrofolate reductase, Proc. Natl. Acad. Sci. USA, 102, 6807–6812. Rajagopalan, P. T. R., Benkovic, S. J. (2002) Preorganization and protein dynamics in enzyme catalysis, The Chemical Record 2, 24–36. Wagner, C. R., Thillet, J., Benkovic, S. J. (1992) Complementary Pertubation of the Kinetic Mechanism and Catalytic Effectiveness of Dihydrofolate Reductase by Side-Chain Interchange, Biochemistry 31, 7834–7840.
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Proton Transfer During Catalysis by Hydrolases Ross L. Stein 18.1
Introduction
Hydrolases are a large family of enzymes whose members catalyze the hydrolytic cleavage of a variety of chemical bonds, including esters, epoxides, amides, acetals, acid anhydrides, and halides. The generalized reaction that is catalyzed by these enzymes is shown in Scheme 18.1 and illustrates the two chemical imperatives of all hydrolytic enzymes:
Generalized reaction catalyzed by hydrolases. In this scheme, R–X is the completely generalized substrate for hydrolases, where R contains the electropositive carbon that undergoes nucleophilic attack and X is the electronegative leaving group.
Scheme 18.1.
Activation of nucleophilic attack by proton abstraction. Stabilization of intermediate formation and/or leaving group departure by proton donation.
In this chapter we will examine the catalytic strategies that hydrolases employ to meet these chemical demands. 18.1.1
Classification of Hydrolases
Table 18.1 summarizes the scheme that the Enzyme Commission has adopted to classify hydrolases. Each major division or class of hydrolase designates the chemHydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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18 Proton Transfer During Catalysis by Hydrolases Table 18.1.
EC Number
Summary of hydrolases and their mechanisms. Example
Mechanism
EC 3.1.0.0 Ester bonds 3.1.1.7 acetylcholinesterase 3.1.3.48 protein-tyrosine-phosphatase 3.1.27.5 pancreatic ribonuclease
acyl-Ser intermediate phospho-Cys intermediate non-covalent intermediate
EC 3.2.0.0 Acetyl bonds of glycosides 3.2.1.17 b-galactosidase 3.2.1.139 a-glucuronidase
galactosyl-Glu intermediate direct, Glu- and Asp-assisted
EC 3.4.0.0 Amide bonds of proteins 3.4.11.1 leucyl aminopeptidase 3.4.17.1 carboxypeptidase A 3.4.21.1 chymotrypsin 3.4.22.2 papain 3.4.23.1 pepsin 3.4.24.27 thermolysin
direct, diMþþ -promoted water attack direct, Znþþ -promoted water attack acyl-Ser intermediate acyl-Cys intermediate direct, Asp-promoted water attack direct, Znþþ -promoted water attack
EC 3.5.0.0 Carbon nitrogen bonds (other than peptide bonds) 3.5.2.6 b-lactamase acyl-Ser intermediate 3.5.3.3 creatinase direct, His-promoted water attack 3.5.4.4 adenosine deaminase direct, Znþþ -promoted water attack EC 3.6.0.0 Acid anhydrides 3.6.1.1 inorganic pyrophosphatase 3.6.1.7 acylphosphatase
direct, Mgþþ -promoted water attack direct, Arg-promoted water attack
EC 3.8.0.0 Halide bonds 3.8.1.5 haloalkane dehalogenase
alkyl-Asp intermediate
ical bond that the enzymes of that particular class hydrolyze (e.g., EC 3.4.0.0, amide bonds of proteins). Subclasses that are shown in this table represent individual enzymes (e.g., EC 3.4.22.2, papain). Each of the enzymes in Table 18.1 represents a specific mechanistic type and is accompanied by a brief statement of the defining mechanistic feature for this enzyme. Note that neither this table nor this chapter is intended to be comprehensive; there are a number of classes of hydrolase enzyme that are not listed in the table and will not be considered in this chapter. The enzymes listed in Table 18.1 will be used as illustrative examples throughout this chapter. 18.1.2
Mechanistic Strategies in Hydrolase Chemistry
Two broad strategies will concern us here. First, we will need to understand the two types of general chemical mechanism that hydrolases use and the heavy atom rearrangements that each entails. The two chemical mechanisms lead to differences
18.1 Introduction
in enzyme kinetic mechanism. Operationally, the practicing enzymologist is often able to use observation of a particular kinetic mechanism to draw conclusions about chemical mechanism. The second broad strategic concern is how these enzymes have used proton bridging as a means to stabilize the transition states of these chemical mechanisms. Proton bridging, and the proton transfer which often accompanies it, is the principle topic of this chapter. Heavy Atom Rearrangement and Kinetic Mechanism Scheme 18.2 illustrates the two classes of reaction that hydrolases catalyze: single displacement reactions, in which the enzyme catalyzes the direct attack of water on a substrate, and double displacement reactions, in which the enzyme catalyzes the initial attack of an enzyme-bound nucleophile with expulsion of the leaving group 18.1.2.1
Scheme 18.2.
Mechanistic strategies employed by hydrolases.
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18 Proton Transfer During Catalysis by Hydrolases
to form an intermediate which undergoes subsequent enzyme-catalyzed attack of water. In all but a very few cases, the enzyme-bound nucleophile is a side-chain heteroatom of an amino acid of the enzyme’s primary sequence. One exception that I will discuss in this chapter is ribonuclease which proceeds through the intermediacy of a cyclic phosphate ester. Both classes of reaction in Scheme 18.2 are shown as catalytic cycles to emphasize the often overlooked fact that hydrolase turnover depends on the exchange of products for substrate and water, and proton shuffling to ‘prime’ the system for another round of catalysis. We will see that this step can be kinetically significant, leading to rate-limiting product release or protein- conformational isomerization. The double-displacement mechanism with its covalent intermediate can often be distinguished from single displacement reactions by kinetic experiments in which an appropriate nucleophilic species is added to reaction solutions of enzyme and substrate and allowed to compete with water for the covalent intermediate. The dependence of initial velocity on the concentrations of substrate and added nucleophile will produce a distinctive kinetic pattern (i.e., ‘ping-pong’ kinetics). Observation of such a pattern constitutes strong evidence suggesting that the hydrolase under study effects catalysis through a double-displacement mechanism. Proton Bridging and the Stabilization of Chemical Transition States In the reactions of Scheme 18.2, the principle chemical events are nucleophilic attack and leaving group expulsion. These processes invariably proceed through transition states that can be stabilized by the formation of appropriate proton bridges. For single displacement reactions, the single catalytic transition state is depicted in Scheme 18.2 as having two critical proton bridges. One of these proton bridges, mediated by Ha , activates the attacking water molecule, and the other proton bridge, mediated by Hb , stabilizes the departing leaving group. Without the stabilization that these proton bridges afford, a transition state of much higher energy would form. Proton bridges are formed in exactly analogous manner in transition states II1 and II2 of the double displacement reaction of Scheme 18.2. In addition to the generic bridges mediated by protons Ha and Hb , enzyme-specific proton bridging occurs and will be described in this chapter as the occasion arises. Often, bridging protons of transition states will become fully transferred protons. In Scheme 18.2, protons Ha and Hb , which first participate in bridges, are ultimately transferred. This is not always the case for proton bridges; some that are formed do not result in transfer to a heteroatom different from the one on which it started. Again, these important exceptions are enzyme-specific and will be described in due course. 18.1.2.2
18.1.3
Focus and Organization of Chapter
My goal in this chapter is to describe the proton transfer reactions that occur during the course of hydrolase-catalyzed reactions and to provide some insight into how they contribute to the catalytic efficiency of these enzymes. Rather than pres-
18.2 Proton Abstraction – Activation of Water or Amino Acid Nucleophiles
ent a case study for each of the hydrolases of Table 18.1, I have chosen instead to organize the chapter around proton transfer reactions themselves, presenting proton abstraction and proton donation, in turn. When we consider proton abstraction, we will first examine how it activates active-site nucleophiles in the first step of double displacement reactions, and then how it is utilized by hydrolases to activate the water molecule for nucleophilic attack in both the second step of double displacement reactions and single displacement reactions. When we turn to proton donation, we first consider how this reaction stabilizes the formation of the covalent intermediate of double displacement reactions and then how proton donation helps to promote leaving group departure in both single displacement and double displacement reactions. Throughout this chapter, I illustrate key points using the specific enzyme examples from Table 18.1 together with data for enzymes related to those of the table. Since the stated goal of this chapter is to shed light on how proton transfer contributes to the catalytic efficiency of hydrolases, I will necessarily be concerned with the formation of proton bridges in catalytic transition states. Since, arguably, the only experimental technique that directly probes these bridges is the kinetic solvent deuterium isotope effect, much of the data cited here will be these effects, along with results from proton inventory studies. Solvent isotope effects are determined by measuring reaction rates in H2 O and D2 O and are expressed as ratios of the rate constants, typically kH /kD , while proton inventories are determined by measuring reaction rates in mixtures of isotopic waters and are expressed graphically as the dependence of rate on mole fraction of solvent deuterium. The numerical magnitude of the solvent isotope effect and the shape of the proton inventory are diagnostic of reaction mechanism and, upon detailed analysis, can often lead to novel mechanistic insights. So-called ‘‘low-barrier hydrogen bonds’’ [1] may also play a role in catalysis effected by hydrolases, but their catalytic role is less secure [2–5] relative to the role of transition state proton bridges. It is indeed ironic that while the structural origins of catalytically-questionable LBHBs can be determined with certainty, the structural origins of catalytically-critical TSPBs are elusive. The implications of the latter point will be the topic of the final section of this chapter where we examine several cases in which the results of solvent isotope effect studies that may have been interpreted in the context of the hydrolase chemistry, in fact reflect ratelimiting product release or conformational isomerization of the enzyme.
18.2
Proton Abstraction – Activation of Water or Amino Acid Nucleophiles 18.2.1
Activation of Nucleophile – First Step of Double Displacement Mechanisms
The enzymes that we consider in this section all react through doubledisplacement mechanisms that require nucleophile activation by proton abstrac-
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18 Proton Transfer During Catalysis by Hydrolases
tion during the mechanism’s first step. In all cases considered here, the nucleophile is an amino acid residue and proton transfer is through a general-base mechanism to another active site residue. Acyl-transfer reactions comprise the largest single group of enzymic process that we will be considering in this chapter, and among these enzymes the most thoroughly studied are the serine proteases. Chymotrypsin and other serine proteases are acylated by a process that begins with attack of the active site serine hydroxyl on the carbonyl carbon of the substrate’s scissile bond. This step is subject to general-base catalysis by the active site histidine residue (i.e., transfer of Ha in transition state II1 of Scheme II), which itself might be assisted by proton-bridging to the active-site aspartate residue. In chymotrypsin, the residues Ser 95-His 57 -Asp 102 comprise what has been called the ‘charge-relay system’ or the ‘catalytic triad’. Attack of serine leads to formation of a tetrahedral addition adduct, which decomposes with release of leaving group to form the acyl-enzyme. Thus, in contrast to the general picture of Scheme 18.2, the first step of the double-displacement mechanism for these enzymes is not concerted, proceeding through the single transition state II1 , but rather goes through a tetrahedral intermediate. An informative study which probed acylation was conducted with the serine protease human leukocyte elastase, where a solvent isotope effect on k c /K m of 2.0 was observed for hydrolysis of Z-Val p-nitrophenyl ester [6]. Unlike the chymotrypsincatalyzed hydrolysis of similar substrates (e.g., Ac-Tyr p-nitrophenyl ester) where acylation chemistry is rapid and k c /K m is rate-limited by the binding of substrate, producing solvent isotope effects of unity, the hydrolysis of Z-Val p-nitrophenyl ester by elastase is rate-limited by chemistry. More specifically, since acylation is ratelimited by attack of the active site serine to form the tetrahedral intermediate rather than departure of the p-nitrophenylate leaving group from the intermediate, the observed isotope effect reflects protolytic activation of the serine nucleophile for attack. Additional insight into this reaction step was gained from the proton inventory for this reaction which was observed to be linear, suggesting the existence of a single protonic bridge in the transition state. One-proton catalysis provides evidence against operation of the catalytic triad, which, if fully functional, would be expected to produce a ‘bowl-shaped’ proton inventory indicative of two proton catalysis [7–11]. However, as discussed below, Z-Val p-nitrophenyl ester is a minimal substrate for leukocyte elastase and does not fulfill the enzyme’s structural requirements of a specific substrate. For such substrates, linear proton inventories are the rule [6, 8, 11–14]. Acetylcholinesterase is mechanistically related to serine proteases and involves acylation of Ser 200 and contains the catalytic triad Ser 200-His 440 -Glu 327 . Precise data for acetylation by the natural substrate acetylcholine is difficult to obtain due to lack of a convenient assay method, so the mechanistically equivalent surrogate acetylthiocholine has frequently been used to probe mechanistic aspects of this enzyme [15]. To explore proton transfer reactions that accompany acetylation by this substrate, solvent isotope effect measurements and proton inventories on k c /K m have been conducted [16, 17]. The isotope effects are near unity and the proton inventories bowed-upwards, suggesting that the transition state for k c /K m is a virtual transi-
18.2 Proton Abstraction – Activation of Water or Amino Acid Nucleophiles
tion [18], partially rate-limited by the chemical steps of acylation and some physical process. Since acylation is likely rate-limited by attack of the active site hydroxyl rather than the leaving group departure from the tetrahedral intermediate, the isotope effect reflects, at least in part, general-base catalysis of nucleophilic attack by His 440 . To probe active site chemistry more directly, the active site mutant in which Glu 202 of the active site was replaced by Ala was studied. This mutant is accompanied by a 2–3 order of magnitude decrease in reactivity towards acetylthiocholine [16]; for this mutant, k c /K m reflects acylation only. The solvent isotope now becomes large and produces a linear proton inventory, suggesting one-proton, general-base catalysis by His 440 during acetylation. This conclusion is consistent with solvent isotope effect studies of acetylation by unnatural anilide and phenyl ester substrates [19–24]. These results all suggest that if Glu 327 participates in acetylation, it does not engage in formation of an isotope effect-generating proton bridge with the His 440 ; that is, it would stabilize the transition state for this reaction by a mechanism other than that of a general catalyst, perhaps electrostatically. Acyl-transfer of b-lactam and acyclic substrates to active site Ser 64 of the blactamase of Enterobacter cloacae P99 occurs with a unique mechanism for nucleophilic activation in which the phenolate of Tyr 150, stabilized in free enzyme by interaction with both the hydroxyl of Ser 64 and by ionic interaction with protonated Ly 367, acts as general-base [25]. The unusual hydrogen bonding system which exists in free enzyme is thought to manifest as a ground state fractionation factor that is less than unity and account for the inverse solvent isotope effects around 0.7 that have been observed on k c /K m [25–27]. Acyl-transfer to the sulfhydryl protease papain occurs on the thiolate form of the active site cysteine Cys 25 , which is thought to be stabilized by ionic interaction with the imidazolium form of an essential active site histidine His 159 [28–30]. So, unlike serine hydrolases, papain and other cysteine acyl-transfer enzymes do not activate their nucleophiles by general-base catalysis but rather through a mechanism involving a pre-equilibrium process in which the sulfhydryl proton of Cys 25 of the uncharged pair SH/Im is transferred to the imidazole of His 159 to produce the ion pair S/ImHþ . Such a mechanism manifests itself in solvent isotope effects on k c /K m whose magnitudes are largely dependent both on the equilibrium constant for tautomerization of SH/Im and S/ImHþ , and the proton fractionation factor for sulfhydryl SH [29, 31]. In cases where SH/Im predominates, or is at least not in very low concentration relative to S/ImHþ , inverse isotope effects ranging from 0.5–0.9 are predicted. However, small normal solvent isotope effects can also be observed if leaving group expulsion from the tetrahedral intermediate is ratelimiting and the leaving group requires general-acid catalysis for expulsion. In these cases, the observed isotope effect will have contributions from both the fractionation factor of the ground state sulfhydryl and the fractionation factor of the catalytic proton bridge in the transition state. Protein-tyrosine phosphatase has an active site Cys 403 with an unusually low pK a of 4.7 [32] that is thought to result from stabilization that the thiolate anion receives from an extensive network of H-bonding interactions, including one from the closest proton donor, Thr 410 [33]. Nucleophilic attack on substrate phosphate
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esters is thought to be by the thiolate of Cys 403 and thus to occur without the need of general-base catalysis. This mechanism is supported by the observation of solvent isotope effects of unity on k c /K m [34]. 18.2.2
Activation of Active-site Water
The oxygen atom of water is not especially reactive relative to other heteratoms that enzymes might employ as effective nucleophiles, such as the e-amine of Lys, the unprotonated heterocyclic nitrogen of His, or the sulfhydryl of Cys. So, to promote attack on an electropositve carbon atom, hydrolases have had to devise strategies for activating water for nucleophilic attack. Two strategies are employed by hydrolases: proton abstraction from water by a basic amino acid residue acting as a general-base catalyst or coordination of the oxygen of water to an active-site metal to promote deprotonation and formation of metal-bound hydroxide. Double-displacement Mechanisms – Second Step Other than ribonuclease, the enzymes we will be considering here all proceed by mechanisms in which the substrate has undergone covalent interaction with an active site nucleophile to form an intermediate species. In this section, we will examine the role of proton transfer in the enzyme-promoted hydrolysis of this intermediate to generate the second product of the reaction and liberate free enzyme. The mechanisms used by these enzymes all involve activation of the attacking water molecule by an active site residue participating as a general-base. Our discussion again begins with chymotrypsin and other serine proteases. Perhaps the earliest paper documenting the investigation of the proton transfer involved in the attack of water on an acyl-chymotrypsin was that of Myron Bender in 1962 where he reported a solvent isotope effect of 2.8 on k c for the hydrolysis of Ac-Trp methyl ester [35]. Since k c for this substrate and other esters is ratelimited by deacylation rather than acylation and, further, since deacylation is itself rate-limited by attack of water on the acyl-enzyme to form a tetrahedral intermediate rather than expulsion of carboxylate product from the tetrahedral intermediate, this value does indeed probe the protonic bridge that is established in the catalytic transition state between the attacking water and His 57 . Since 1962, results similar to these have been observed for a great many serine proteases and their ester substrates [11, 14, 36–41]. In addition, it has also been repeatedly observed that proton inventories of k c for reaction of serine proteases with specific peptide substrates are ‘‘bowl-shaped’’ and can be fit by a simple model involving two proton catalysis. This has been interpreted to suggest that in the transition states for these reactions the catalytic triad is fully engaged with proton transfer occurring from the hydroxyl of Ser 95 to the imidazole of His 57 and a catalytic proton bridge being established between His 57 and Asp 102 . It is unclear, however, if the operation of the catalytic triad imparts any catalytic advantage. This was investigated in a systematic study of human leukocyte elastase [14, 42]. For p-nitroanilides of substrates R-Val-, R-Pro-Val-, R-Ala-Pro-Val-, and R18.2.2.1
18.2 Proton Abstraction – Activation of Water or Amino Acid Nucleophiles
Ala-Ala-Pro-Val- (R ¼ methoxysuccinyl-), the first-order rate constant for acylation from within the Michaelis-complex increases as 0.06, 0.42, 43, and 43 s1 , respectively, indicating that substrates of increasing length are better able to fulfill the enzyme’s specificity requirements. When proton inventories were determined for hydrolyses of the acyl-enzymes derived from these substrates, it was found that while R-Val-HLE and R-Pro-Val-HLE hydrolyze by a mechanism of one-proton catalysis, presumably involving general-base catalysis by the active site His; R-AlaPro-Val-HLE and R-Ala-Ala-Pro-Val-HLE hydrolyze by a mechanism of two proton catalysis, presumably involving full engagement of the catalytic triad [14]. Curiously, deacylation rate-constants are essentially identical for the four substrates and equal 12 G 1 s1 . It still ‘‘remains to be established whether coupling of the charge relay system gives rise to any substantial acceleration or if, perhaps, it is a mere structural and dynamic coincidence that it is coupled with physiological substrates but not with small substrates’’ [43]. During hydrolytic deacetylation of acetylcholinesterase, His 440 acts as a generalbase catalyst to abstract a proton from a water molecule as it attacks the acetylSer 200 intermediate. This reaction generates a solvent isotope effect of around 2 and a linear proton inventory [17, 22, 44] suggesting, as we saw above for acylation of this enzyme, that if Glu 327 participates in deacetylation, it does not engage in formation of an isotope effect-generating proton bridge with the His 440 . The observation of single-proton catalysis during deacylation of the enzyme’s natural substrate should be contrasted with observation of two-proton catalysis that has uniformly been observed when serine proteases act on their specific substrates. The significance of this observation for catalysis by acetylcholinesterase is currently unclear. Like serine hydrolases, the thiol protease papain contains the catalytic triad Cys 25 -His 159 -Asp 158 and thus offers the possibility of two-proton catalysis. To investigate the possible operation of this structural feature in catalysis, solvent isotope effects and proton inventories were determined for hydrolysis of the acyl-enzymes that form during reaction of papain with the methyl esters of N-benzoyl-Gly and N(b-phenylpropionyl)Gly, and the p-nitrophenyl esters of Z-Gly, Z-Lys, and Nmethoxycarbonyl-Phe-Gly [45, 46]. Solvent isotope effects ranged from 2.0 to 2.6 and were all accompanied by linear proton inventories suggesting processes of one proton catalysis in which His 159 acts as a general-base to abstract the proton from the attacking water molecule and a catalytic proton bridge between His 159 and Asp 158 does not form. Thus, it appears that, at least for hydrolysis of these substrates, papain’s catalytic triad is not fully operative. It could be that two-proton catalysis would be observed if longer peptide substrates were used that fulfilled the enzyme’s specificity requirements. Hydrolysis of the phospho-Cys 403 intermediate that forms during reactions of protein-tyrosine phosphatase is accompanied by a solvent isotope effect of 1.5 [47, 48] and a linear proton inventory [47] suggesting a process of one-proton catalysis in which Asp 356 acts as a general-base to abstract the proton from the attacking water molecule [49]. The second step of ribonuclease catalysis involves the hydrolysis of cyclic nucleo-
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18 Proton Transfer During Catalysis by Hydrolases
side 2 0 ,3 0 -phosphate esters to 3 0 -phosphates. The nucleophilic water that attacks the phosphorus atom of the cyclic ester is activated by proton abstraction by His 119 acting as general-base catalyst [50]. This mechanism is supported by observation of a large solvent isotope effect of 3.1 on k c /K m for the ribonuclease-catalyzed hydrolysis of cytidine cyclic 2 0 ,3 0 -monophosphate [51, 52]. Interestingly, this system generates a bowed-downward proton inventory that can be fit with a model involving two-proton catalysis [52]. The second proton ‘in-flight’ in the rate-limiting transition state for which these data provide evidence is likely the proton that is thought to be donated by the imidazolium of His 12 to the 2 0 -oxygen [50]. Observation of an identical proton inventory during hydrolysis of a substituted phenyl cyclic 3 0 ,4 0 monophosphate by the ribonuclease model b-cyclodextrin 6,6 0 -bis(imidazole) supports this mechanistic proposal [53]. b-galactosidase proceeds through the intermediacy of a galactosyl-enzyme whose hydrolytic decomposition rate-limits k c for substrates with sufficiently reactive aglycone leaving groups where formation of this intermediate is rapid [54–57]. For this process, it is thought that Glu 461 acts as a general-base catalyst to abstract a proton from the attacking water molecule [55, 56]. In such a situation, one would anticipate observation of a large solvent isotope effect. Interestingly though, a solvent isotope effect on k c of only 1.1 was measured for the b-galactosidase-catalyzed hydrolysis of 3,4-dinitrophenyl b-D-galactopyranoside [54]. It is unclear why such a small isotope effect is observed for this reaction. Haloalkane dehalogenase catalyzes hydrolysis of carbon–halide bonds of alkyl halides by a double-displacement mechanism in which the carboxylate anion of Asp 124 (Xanthobacter autotrophicus GJ10) attacks the carbon of the carbon–halide bond and displaces the halide with formation of an alkyl ester intermediate [58– 60]. Interestingly, decomposition of this intermediate is rate-limited by one of three steps, depending on the bacterial species from which the enzyme is isolated [60]: hydrolysis (Sphingomonas paucimobilis), halide release (Xanthobacter autotrophicus), or alcohol release (Rhodococcus rhodochrous). To probe the possibility of catalyticallyimportant proton transfer during hydrolysis of the alkyl ester intermediate, presteady-state kinetic experiments were preformed for turnover of dibromomethane by the enzyme from Xanthobacter autotrophicus and reveal an isotope effect of 2.5 on the rate-constant and amplitude of a pre-state burst [59]. This was interpreted to reflect general-base catalysis of attack of water by His 289 . Single Displacement Mechanisms The enzymes we will be considering in this section all catalyze their hydrolytic reactions through mechanisms that lack the intermediacy of any species other than simple, noncovalent Michaelis complexes. While transient intermediates may form, such as oxocarbenium species during catalysis by inverting glycosidases or tetrahedral intermediates during catalysis by aspartyl- and metallo-proteinases, they are of insufficient stability to accumulate in the steady state and thus have structures that are similar to the transition states that precede and follow them on the reaction pathway. For these reactions, the single displacement mechanism of Scheme 18.2, with its single transition state, is not an inaccurate depiction. 18.2.2.2
18.2 Proton Abstraction – Activation of Water or Amino Acid Nucleophiles
In this section, we will be concerned with understanding how proton Ha of this mechanism is abstracted from the attacking water molecule. Two mechanisms of activation will be seen to be used by these enzymes: activation by an amino acid general-base and activation by virtue of complexation of the catalytic water to a metal atom. Activation by Amino Acid General-base a-Glucuronidases and other inverting glycosidases catalyze their hydrolytic reactions through an SN 1 mechanism with a transition state having substantial oxocarbenium ion character, as evidenced by large asecondary deuterium kinetic isotope effects of the order of 1.1–1.2 [55, 56, 61]. In these reactions, the attacking water molecule is usually activated by an active site carboxylate moiety. a-Glucuronidases from two bacterial species have recently had their X-ray structures determined [62, 63], revealing key aspartyl residues that play the role of general-base catalyst in the displacement of aglycone by water. However, in some cases another residue is used. For example, a His has been implicated in the active site of an inverting exo-b(1 ! 3)-glucanase [64]. Reactions of this enzyme proceed with large solvent isotope effects on k c of the order of 2.5 indicating the establishment of a proton bridge in the catalytic transition state and perhaps suggesting a role of general-base catalyst for the His residue. Pepsin catalyzes the hydrolysis of amide bonds of proteins using a unique mechanism in which water attack on the amide is activated by concerted action of two active site aspartyl carboxyl groups. Small normal solvent isotope effects are observed but cannot be unambiguously interpreted regarding their origins and how they relate to proton abstraction from water and/or proton donation to amine leaving group [65]. Creatinase catalyzes the hydrolysis of creatine to N-methyl-glycine and urea by a mechanism in which water is activated for attack on substrate guanidinium carbon by the imidazole of His 232 acting as general base [66]. Acylphosphatase is one of the smallest enzymes (98 residues; MW 11 kDa) and hydrolyzes acylphosphates, such as acetylphosphate, succinylphosphate, and basparatylphosphate [67]. While there is scant kinetic and no isotope effect data, structural and mutagenesis studies suggest a mechanism in which the amide functionality of Asn 41 aligns a water molecule for attack on the phosphorus atom of the substrate with substrate-assisted general-base catalysis of this attack by an anionic oxygen of the phosphate group. A pentacovalent phosphorous may form and carboxylate leaves unassisted. Activation of Metal-bound Water In this mechanism, a metal ion, usually a zinc, complexes a water molecule and lowers its pK a from 14 to values perhaps as low as 7 or 8, thus readily producing a nucleophilic metal-bound hydroxide anion [68, 69]. Proton transfer thus occurs in a pre-equilibrium step and does not participate, in the form of general acid–base catalysis, in the rate-limiting step. This mechanism may best be exemplified by metal-dependent proteases and peptidases such as thermolysin, leucine aminopeptidase, and carboxypeptidase A. Of these, the most systematic study of proton transfer has been conducted with ther-
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18 Proton Transfer During Catalysis by Hydrolases
molysin and the mechanistically related metalloendoproteinase stromelysin [68– 73]. For both of these enzymes, solvent isotope effects on k c /K m of about 0.75 have been observed [69–71] and support a mechanism in which the zinc-bound water molecule of free enzyme undergoes reaction with substrate to become part of a tetrahedral addition adduct with a fractionation factor of one. The inverse isotope effect thus originates from the fractionation factors of about 0.85 for each of the two protons of the zinc-bound water molecule. Leucine aminopeptidase is interesting in that its active site contains two zinc atoms which together bind and activate the water molecule [74]. Despite this enzyme containing a dinuclear metal center at its active site, its mechanism, and specifically its mode of proton transfers reactions, appear to follow the general theme established by thermolysin and carboxypeptidase Adenosine deaminase and other members of the family of nucleoside and nucleotide deaminases utilize zinc-bound water as the catalytic nucleophile to displace ammonia from the 6-position of purines or the 4-position of pyrimidines and in all cases display inverse solvent deuterium isotope effects ranging from 0.3 to 0.8 on k c /K m [75–80]. These effects are reminiscent of those observed for metalloproteases and have their origins, like those of the proteases, in fractionation factors for the protons of the bound water that are less than one.
18.3
Proton Donation – Stabilization of Intermediates or Leaving Groups 18.3.1
Proton Donation to Stabilize Formation of Intermediates
All of the enzymes to be considered here proceed through double-displacement mechanisms in which stabilization of the intermediate occurs with donation of a proton by an amino acid of the primary sequence of the enzyme. In chymotrypsin and other serine proteases, the oxyanion hole exists as a means of stabilizing intermediates. The oxyanion hole is a structural unit at the active sites of these enzymes that is thought to participate in stabilizing acyl-transfer transition states via hydrogen bonds from two protein backbone amide groups to the oxyanion that exists during the formation and collapse of tetrahedral intermediates. The evidence for the existence of the oxyanion hole and hypotheses regarding its role in catalysis come chiefly from X-ray crystallographic studies of these enzymes and their stable complexes with inhibitors [81]. Like serine proteases, acetylcholinesterase, appears to possess an oxyanion hole, comprised of the peptide NH groups of Gly 118, Gly 119, and Ala 201 that stabilizes oxyanionic transition states and tetrahedral intermediates by hydrogen bonding [82]. Linear proton inventories on k c suggest that these stabilizing interactions do not generate proton bridges that give rise to fractionation factors less than unity; if this were the case, the multiproton origin of the solvent isotope effect would produce bowed-downward proton inventories [17]. Papain also contains an oxyanion hole comprising hydrogen-bond donation from
18.3 Proton Donation – Stabilization of Intermediates or Leaving Groups
the amide side chain of Gln 19 and the backbone NH of Cys 25 [83]. Evidence for the existence of this structural features comes largely from X-ray crystallographic studies. The phospho-Cys 403 intermediate that forms during the course of reactions catalyzed by protein-tyrosine phosphatase is stabilized by hydrogen-bond donation from backbone residues of the so-called P-loop comprising Cys 403 , Arg 409 , and Thr 410 as well as the guanidinium moiety of Arg 409 [49]. These interactions also serve to stabilize the Michaelis complex. During turnover of creatine by creatinase, the transition state for attack by water is stabilized by hydrogen bonding by carboxylate residues of Glu262 and Glu358 to the departing guanidinium group [66]. 18.3.2
Proton Donation to Facilitate Leaving Group Departure Double-displacement Mechanisms For many of the reactions that have been considered here, leaving group departure during formation of the stable intermediate of double-displacement reactions requires protonation of the scissile heteroatom. This proton is thought to come either from solvent, if the active site is sufficiently accessible to solvent, or from a protonated active site residue serving as general-acid. Chymotrypsin and other serine proteases undergo acylation by amide and anilide substrates with at least partial rate-limiting expulsion of the amine or aniline leaving group. 15 N-isotope effects of 1.010 G 0.001 and 1.014 G 0.001 on k c /K m for reaction of chymotrypsin with N-acetyl-Trp amide [84] and N-succinyl-Phe pnitroanilide [85] are smaller than the theoretical limit of 1.044 and suggest that the observed transition state for these reactions may be a virtual transition state [18] reflecting both formation and decomposition of the tetrahedral addition adduct that exists as an intermediate between the Michaelis complex and acylenzyme. Thus, in studies which seek to examine proton bridging to the departing leaving group, care must be taken in the interpretation of the data, since it is likely compromised by partial rate-limiting water attack and the proton bridging that accompanies it. For example, the solvent isotope effect on the first-order rate constant for acylation of chymotrypsin by N-succinyl-Ala-Ala-Pro-Phe p-nitroanilide from the stage of the Michaelis complex is 3.1 [86]. From the previous analysis, it is likely that this value is a weighted average of the isotope effect on proton abstraction from the attacking water molecule and the isotope effect on proton donation to the departing leaving group. For acetylcholinesterase, it is thought that the protonated imidazole of His 440 acts as a general-acid to assist departure of aniline during hydrolysis of anilide substrates. Based on analysis of the 15 N isotope effect in light and heavy water, it was estimated that departure of o-nitroaniline during hydrolysis of o-nitroacetanilide is accompanied by a modest solvent isotope near 1.5, supporting the general-acid role of ImHþ -His 440 [19]. Protein-tyrosine phosphatase catalyzes the hydrolysis of aryl phosphates with ratelimiting dephosphorylation for k c. However, for alkyl phosphates, k c is rate-limited 18.3.2.1
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18 Proton Transfer During Catalysis by Hydrolases
by phosphorylation [34] and allows proton transfer in this process to be explored. Specifically for our present discussion, we would like to learn about proton transfer as involved in leaving group departure. For the hydrolysis of 4-phenylbutyl phosphate, a solvent isotope effect of 2.4 is observed along with a linear proton inventory. Since nucleophilic attack by the thiolate of Cys 403 cannot generate this isotope effect (see above), it seems likely that the effect originates in the general-catalysis of leaving group departure from the tetrahedral intermediate. Mutagenesis and structural studies suggest that the general-acid is Asp 356 [87, 88]. b-galactosidase from E. coli is thought to use Glu 461 as a general-acid to donate a proton to the departing aglycone leaving group during transfer of b-Dgalactopyranosyl to Glu 537 to form the intermediate galactosyl-enzyme species [55, 56]. Some of the most compelling evidence for this comes from recent mutagenesis experiments in which the E461G enzyme was shown to have pH-rate dependences and solvent isotope effects predicted for this mutant [57]. Specifically for the latter property, the solvent isotope effect on k c for hydrolysis of 4-nitrophenyl b-D-galactopyranoside of 1.7 for wild-type enzyme [54] was reduced to a value near unity with the E461G mutant [57]. Since k c is thought to be rate-limited by galactosyl-enzyme formation, and it is known that nucleophilic attack on the anomeric carbon by Glu 537 is not subject to general-catalysis [55, 56], the observed solvent isotope effect for the native enzyme must be due the establishment of a proton bridge between the protonated carboxyl moiety of Glu 461 and the oxygen of the leaving group. In the E461G mutant, catalysis of this type is unavailable and no significant isotope is observed. Single-displacement Mechanisms The a-glucuronidases from the two bacterial species mentioned above have been suggested to have aspartyl residues as part of hydrogen-bonding networks that participate in proton donation to the departing aglycone moiety [62, 63]. For the mechanistically related enzymes thermolysin and stromelysin, a strong case has been made supporting the hypothesis that the amine of leaving groups during turnover of peptide substrates is fully protonated in the transition state and thus requires no assistance from a general acid [71]. Departure of urea leaving group during turnover of creatine by creatinase is facilitated by proton donation by the imidazolium group of His232, the same residue that extracted the proton from water to promote nucleophilic attack [66]. 18.3.2.2
18.4
Proton Transfer in Physical Steps of Hydrolase-catalyzed Reactions 18.4.1
Product Release
For thermolysin and stromelysin, release of the carboxylate product is not a simple dissociation process but rather involves a ligand exchange reaction on zinc; that is, that step involves the attack of water on zinc to displace the carboxylate product.
References
Rate-limiting protolytic catalysis of this process is suggested by the observation of a solvent isotope effect of 1.6 on k c for peptide hydrolysis by stromelysin [71]. Since release of carboxylate product is the reverse of the association of carboxylate-based inhibitors with metalloproteinases, one might anticipate that much could be learned about the former by study of the latter. For reaction of such inhibitors [73], as well as phosphorus-containing inhibitors [72], inhibitor displaces zincbound water to form the enzyme–inhibitor complex and generate isotope effects on the association rate constant of 1.6 to 1.9 [69, 72, 73]. These large isotope effects arise from proton catalytic bridges that form in the transition state for association of enzyme and inhibitor. Insufficient data exist to say whether this mechanism can be generalized to leucine aminopeptidase and carboxypeptidase A. In fact for both of these enzymes, solvent isotope effects ranging from 1.3 to 2.6 on k c have been observed and interpreted to reflect general-acid catalysis of the amine leaving group departure by an active site carboxylate of a Glu residue [89, 90]. A solvent isotope effect of 3 was observed on k c for inorganic pyrophosphatase and was originally interpreted to reflect the chemistry of pyrophosphate hydrolysis [91]. However, this interpretation required revision in the light of microscopic rate constants that were calculated from the results of studies that measured Pi -dependent formation of enzyme-bound pyrophosphate and measured rates of H2 O/Pi oxygen exchange [92]. Based on these studies it now appears that the large solvent isotope effect is for Pi dissociation and likely reflects changes in the energetics of hydrogen bonds between Pi and enzyme. 18.4.2
Protein Conformational Changes
Haloalkane dehalogenase from Xanthobacter autotrophicus GJ10 exhibits a solvent isotope effect of 3 and linear proton inventories for k c for hydrolysis of dibromethane and 1,2-dichloroethane [58]. Stopped-flow fluorescence experiments under single-turnover conditions suggest that halide release limits k c . This isotope effect was interpreted to reflect a conformational change of the protein that allows departure of halide. Data is accumulating for pepsin and HIV protease to suggest that they may catalyze their reactions through a mechanism in which release of products leaves the enzyme in a conformation which must undergo isomerization before another round of catalysis can commence [65]. More work is needed here to eliminate other mechanistic possibilities.
References 1 Cleland, W. W. (2000) Arch. Biochem.
Biophys., 382, 1–5. 2 Warshel, A., Papazyan, A. (1996) Proc. Natl. Acad. Sci. USA, 93, 13665–13670. 3 Ash, E. L., Sudmeier, J. L., De Fabo,
E. C., Bachovchin, W. W. (1997) Science 278, 1128–1132. 4 Stratton, J. R., Pelton, J. G., Kirsch, J. F. (2001) Biochemistry, 40, 10411–10416.
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6 7
8 9 10
11 12 13
14
15 16
17
18 19
20 21
22
C., Dunlap, C. A., Andersen, N. H., Gelb, M. H., Tsai, M.-D. (2003) J. Mol. Biol., 329, 997–1009. Stein, R. L. (1985) J. Am. Chem. Soc. 107, 5767–5775. Elrod, J. P., Gandour, R. D., Hogg, J. L., Kise, M., Maggiora, G. M., Schowen, R. L., Venkatasubban, K. S. (1976) Faraday Symp. Chem. Soc., 10, 145–153. Venkatasubban, K. S., Schowen, R. L. (1984) Crit. Rev. Biochem., 17, 1–44. Mordy, C. W., Schowen, R. L. (1987) Adv. Biosci., 65, 273–280. Demuth, H. U., Heins, J., Fujihara, H., Mordy, C. W., Fischer, G., Barth, A., Schowen, R. L. (1987) Stud. Org. Chem., 31, 439–446. Schowen, R. L. (1988) Mol. Struct. Energ., 9, 119–168. Stein, R. L. (1983) J. Am. Chem. Soc. 105, 5111–5116. Stein, R. L., Elrod, J. P., Schowen, R. L. (1983) J. Am. Chem. Soc. 105, 2446–2452. Stein, R. L., Strimpler, A. M., Hori, H., Powers, J. C. (1987) Biochemistry 26, 1305–1314. Froed, H. C., Wilson, I. B. (1984) J. Biol. Chem. 259, 11010–11013. Malany, S., Sawai, M., Sikorski, R. S., Seravalli, J., Quinn, D. M., Radic, Z., Taylor, P., Kronman, C., Velan, B., Shafferman, A. (2000) J. Am. Chem. Soc. 122, 2981–2987. Pryor, A. N., Selwood, T., Leu, L. S., Andracki, M. A., Lee, B. H., Rao, M., Rosenberry, T., Doctor, B. P., Silman, I., Quinn, D. M. (1992) J. Am. Chem. Soc. 114, 3896–900. Stein, R. L. (1981) J. Org. Chem. 46, 3328–3330. Rao, M., Barlow, P. N., Pryor, A. N., Paneth, P., O’Leary, M. H., Quinn, D. M., Huskey, W. P. (1993) J. Am. Chem. Soc. 115, 11676–11681. Salih, E. (1992) Biochem. J. 285, 451–460. Barlow, P. N., Acheson, S. A., Swanson, M. L., Quinn, D. M. (1987) J. Am. Chem. Soc. 109, 253– 257. Acheson, S. A., Dedopoulou, D.,
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40
41 42
Quinn, D. M. (1987) J. Am. Chem. Soc. 109, 239–245. Acheson, S. A., Barlow, P. N., Lee, G. C., Swanson, M. L., Quinn, D. M. (1987) J. Am. Chem. Soc. 109, 246–52. Quinn, D. M., Swanson, M. L. (1984) J. Am. Chem. Soc. 106, 1883–1884. Page, M. I., Laws, A. P. (1998) Chem. Commun., 1609–1617. Page, M. I., Vilanova, B., Layland, N. J. (1995) J. Am. Chem. Soc., 117, 12092–12095. Adediran, S. A., Deraniyagala, S. A., Xu, Y., Pratt, R. F. (1996) Biochemistry 35, 3604–3613. Creighton, D. J., Schamp, D. J. (1980) FEBS Lett. 110, 313–318. Creighton, D. J., Gessouroun, M. S., Heapes, J. M. (1980) FEBS Lett. 110, 319–322. Wandinger, A., Creighton, D. J. (1980) FEBS Lett. 116, 116–122. Case, A., Stein, R. L. (2003) Biochemistry 42, 9466–9481. Zhang, Z. Y., Dixon, J. E. (1993) Biochemistry 32, 9340–9345. Stuckey, J. A., Fauman, E. B., Schubert, H. L., Zhang, Z.-Y., Dixon, J. E. (1994) Nature 370, 571–575. Zhang, Z. Y., Van Etten, R. L. (1991) Biochemistry 30, 8954–8959. Bender, M. L., Hamilton, G. A. (1962) J. Am. Chem. Soc. 84, 2570–2576. Pollock, E., Hogg, J. L., Schowen, R. L. (1973) J. Am. Chem. Soc. 95, 968–969. Elrod, J. P., Hogg, J. L., Quinn, D. M., Venkatasubban, K. S., Schowen, R. L. (1980) J. Am. Chem. Soc. 102, 3917–3922. Hogg, J. L., Elrod, J. P., Schowen, R. L. (1980) J. Am. Chem. Soc. 102, 2082–2086. Quinn, D. M., Elrod, J. P., Ardis, R., Friesen, P., Schowen, R. L. (1980) J. Am. Chem. Soc. 102, 5358–5365. Quinn, D. M., Venkatasubban, K. S., Kise, M., Schowen, R. L. (1980) J. Am. Chem. Soc. 102, 5365–5369. Enyedy, E. J., Kovach, I. M. (2004) J. Am. Chem. Soc. 126, 6017–6024. Stein, R. L., Strimpler, A. M., Hori,
References
43
44
45 46 47 48 49 50 51 52 53 54 55 56 57
58 59
60
61
62
63
H., Powers, J. C. (1987) Biochemistry 26, 1301–1305. Maggiora, G. M., and Schowen, R. L. (1977) in Bioorganic Chemistry, van Tamelen, E. E. (Ed.), Acedemic Press, New York. Kovach, I. M., Larson, M., Schowen, R. L. (1986) J. Am. Chem. Soc. 108, 3054–3056. Szawelski, R. J., Wharton, C. W. (1981) Biochem. J. 199, 681–692. Storer, A. C., Carey, P. R. (1985) Biochemistry 24, 6808–6818. Zhou, X., Medhekar, R., Toney, M. D. (2003) Anal. Chem. 75, 3681–3687. Zhang, Z.-Y. (1995) J.Biol. Chem. 270, 11199–11204. Zhang, Z.-Y. (2003) Acc. Chem. Res. 36, 385–392. Raines, R. T. (1998) Chem. Rev. 98, 1045–1065. Eftink, M. R., Biltonen, R. L. (1983) Biochemistry 22, 5123–5134. Matta, M. S., Diep Thi, V. (1986) J. Am. Chem. Soc. 108, 5316–5318. Anslyn, E., Breslow, R. (1989) J. Am. Chem. Soc. 111, 8931–8932. Selwood, T., Sinnott, M. L. (1990) Biochem. J. 268, 317–323. Sinnott, M. L. (1990) Chem. Rev. 90, 1171–1202. Zechel, D. L., Wither, S. G. (2000) Acc. Chem. Res. 33, 11–18. Richard, J. P., Huber, R. E., McCall, D. A. (2001) Bioorg. Chem. 29, 146– 155. Schanstra, J. P., Janssen, D. B. (1996) Biochemistry 35, 5624–5632. Schanstra, J. P., Kingma, J., Janssen, D. B. (1996) J. Biol. Chem. 271, 14747–14753. Prokop, Z., Monincova, M., Chaloupkova, R., Klvana, M., Nagata, Y., Janssen, D. B., Damborsky, J. (2003) J. Biol. Chem. 278, 45094–45100. Vasella, A., Davies, G. J., Bohm, M. (2002) Curr. Opin. Chem. Biol. 6, 619–629. Nurizzo, D., Nagy, T., Giblert, H. J., Davies, G. J. (2002) Structure 10, 547–556. Golan, G., Shallom, D., Teplitsky, A., Zaide, G., Shulami, S., Baasov,
64 65 66
67 68 69 70 71
72
73
74 75 76
77
78 79 80
81 82
83
T., Stojanoff, V., Thompson, A., Shoham, Y., Shoham, G. (2004) J. Biol. Chem. 279, 3014–3024. Jeffcoat, R., Kirkwood, S. (1987) J. Biol. Chem. 262, 1088–1091. Northrop, D. B. (2001) Acc. Chem. Res. 34, 790–797. Coll, M., Knof, S. H., Ohga, Y., Messerschmidt, A., Huber, R., Moellering, H., Russmann, L., Schumacher, G. (1990) J. Mol. Biol. 214, 597–610. Stefani, M., Taddei, N., Ramponi, G. (1997) Cell. Mol. Life Sci. 53, 141–151. Izquierdo, M. C., Stein, R. L. (1990) J. Am. Chem. Soc. 112, 6054–6062. Izquierdo-Martin, M., Stein, R. L. (1992) J. Am. Chem. Soc. 114, 325–31. Stein, R. L. (1988) J. Am. Chem. Soc. 110, 7907–7908. Harrison, R. K., Chang, B., Niedzwiecki, L., Stein, R. L. (1992) Biochemistry 31, 10757–1762. Izquierdo-Martin, M., Stein, R. L. (1992) J. Am. Chem. Soc. 114, 1527– 1528. Izquierdo-Martin, M., Chapman, K. T., Hagman, W. K., Stein, R. L. (1994) Biochemistry 33, 1356–1365. Holz, R. C. (2002) Coord. Chem. Rev. 232, 5–26. Lewis, A. S., Glantz, M. D. (1974) J. Biol. Chem., 249, 3862–3866. Weiss, P. M., Cook, P. F., Hermes, J. D., Cleland, W. W. (1987) Biochemistry 26, 7378–7384. Merkler, D. J., Kline, P. C., Weiss, P., Schramm, V. L. (1993) Biochemistry 32, 12993–13001. Merkler, D. J., Schramm, V. L. (1993) Biochemistry 32, 5792–5799. Wang, Z.-X., Quiocho, F. A. (1998) Biochemistry 37, 8314–8324. Snider, M. J., Reinhardt, L., Wolfenden, R., Cleland, W. W. (2002) Biochemistry 41, 415–421. Hedstrom, L. (2002) Chem. Rev. 102, 4501–4524. Sussman, J. L., Harel, M., Frolow, F., Oefner, C., Goldman, A., Toker, L., Silman, I. (1991) Science 253, 872– 879. Drenth, J., Kalk, K. H., Swen, H. M. (1976) Biochemistry 15, 3731–3738.
1471
1472
18 Proton Transfer During Catalysis by Hydrolases 84 O’Leary, M. H., Kluetz, M. D. (1970) 85 86 87
88
J. Am. Chem. Soc. 92, 6089–6090. Hengge, A. C., Stein, R. L. (2004) Biochemistry, 43, 742–747. Case, A., Stein, R. L. (2003) Biochemistry 42, 3335–3348. Zhang, Z., Harms, E., Van Etten, R. L. (1994) J. Biol. Chem. 269, 25947–25950. Keng, Y. F., Wu, L., Zhang, Z.-Y. (1999) Eur. J. Biochem. 259, 809–814.
89 Bienvenue, D. L., Mathew, R. S.,
Ringe, D., Holz, R. C. (2002) J. Biol. Inorg. Chem. 7, 129–135. 90 Suh, J., Cho, W., Chung, S. (1985) J. Am. Chem. Soc. 107, 4530–4535. 91 Konsowitz, L. M., Cooperman, B. S. (1976) J. Am. Chem. Soc. 98, 1993– 1995. 92 Welsh, K. M., Jacobyansky, A., Springs, B., Cooperman, B. S. (1983) Biochemistry 22, 2243–2248.
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Hydrogen Atom Transfers in B12 Enzymes Ruma Banerjee, Donald G. Truhlar, Agnieszka Dybala-Defratyka, and Piotr Paneth 19.1
Introduction to B12 Enzymes
B12 is a tetrapyrrolic-derived organometallic cofactor that supports three subfamilies of enzymes in microbes and in animals, the isomerases, the methyltransferases, and the dehalogenases [1]. The corrin ring system is more reduced than the porphyrin ring system, is heavily ornamented peripherally, and is distinguished by a central cobalt atom that is coordinated equatorially to four pyrrolic nitrogens. The cobalt can cycle between three oxidation states, þ1 to þ3, and the unique properties of each species are exploited in the chemistry of the reactions catalyzed by B12 enzymes. In both the methyltransferase and isomerase subfamilies of B12 enzymes, the upper axial ligand to cobalt is an alkyl group and the cobalt is formally in the þ3 oxidation state. The alkyl group is methyl and deoxyadenosyl in methylcobalamin (MeCbl) and coenzyme B12 (AdoCbl), respectively. Their structures are shown in Scheme 19.1. Dichotomous pathways for cleaving the organometallic cobalt–carbon bond yield different products with different reactivities. In the methyltransferases, the cobalt–methyl bond ruptures heterolytically, and the products are cob(i)alamin (vitamin B12 with cobalt in the þ1 oxidation state) and a carbocation equivalent that is transferred to a nucleophile. Cob(i)alamin is highly reactive and indeed, is regarded as nature’s supernucleophile [2]. Its reactivity is exploited in biology for transferring methyl groups from unactivated methyl donors, viz. 5methyltetrahydrofolate. In contrast, the cobalt–carbon bond is cleaved homolytically in the isomerases, where the upper axial ligand is a 5 0 -deoxyadenosyl group, and the coenzyme is called 5 0 -deoxyadenosyl cobalamin (AdoCbl). The radical products are cob(ii)alamin (vitamin B12 with cobalt in the þ2 oxidation state) and the reactive 5 0 -deoxyadenosyl radical, which is abbreviated dAdo. The reactivity of the latter is harnessed to effect hydrogen atom abstractions in unusual and chemically challenging 1,2 rearrangement reactions involving the exchange of a variable group with a hydrogen atom on adjacent carbons. Our understanding of the reaction mechanism of B12 -dependent reductive dehalogenations is quite limited [1]. However, the role of the cofactor appears to be subHydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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19 Hydrogen Atom Transfers in B12 Enzymes
Scheme 19.1
stantially different from its role in the other two groups of B12 -dependent enzymes. It appears likely that the low redox potential of the Co(i) state of the cofactor is exploited to drive the reductive dehalogenation reactions. The lower axial ligand in B12 derivatives is an extension of a peripheral propanolamine chain from ring D of the tetrapyrrolic structure. A variety of ligands are found in this position in nature, and the unusual base, 5,6-dimethylbenzimidazole, is the lower axial ligand in cobalamins. At acidic pH, the lower axial ligand is displaced via protonation. The cofactor can thus exist in two conformations, ‘‘base-on’’ and ‘‘base-off ’’. However, the crystal structure of methionine synthase revealed yet another conformation, ‘‘base-off/His-on’’, in which the endogenous ligand is displaced and replaced by a histidine residue donated by the protein [3]. This ligand switch by an active site histidine embedded in a conserved DXHXXG motif [4] has since been observed in a number of other B12 enzymes including methylmalonylCoA mutase [5], glutamate mutase [6], and lysine amino mutase [7]. In contrast, a
19.2 Overall Reaction Mechanisms of Isomerases
second subclass of AdoCbl-dependent enzymes, including diol dehydratase [8] and ribonucleotide reductase [9], binds the cofactor in the ‘‘base-on’’ conformation.
19.2
Overall Reaction Mechanisms of Isomerases
Isomerases that are dependent on coenzyme B12 constitute the largest subfamily of B12 enzymes and are components of a number of fermentative pathways in microbes [10, 11]. A single member of this group of enzymes, methylmalonyl-CoA mutase, is found in both bacteria and in mammals where it is a mitochondrial enzyme involved in the catabolism of odd-chain fatty acids, branched chain amino
Scheme 19.2
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19 Hydrogen Atom Transfers in B12 Enzymes
acids, and cholesterol [12]. The general reaction catalyzed by the isomerases is a 1,2 interchange of a hydrogen atom and a variable group such as a group containing a heteroatom (hydroxyl or amino) or a carbon skeleton (see Scheme 19.2). One member, ribonucleotide reductase, uses the B12 cofactor to effect reductive elimination in the conversion of ribonucleotides to deoxyribonucleotides and represents a third class of this subfamily. As might be expected, individual enzymes differ somewhat in their radical generating strategies, as discussed below. Whereas heterolytic cleavage in the methyltransferases is facilitated by methylcobalamin, homolytic cleavage is deployed by enzymes that resort to radical chemistry to effect difficult transformations. The preference for homolytic cleavage in AdoCbl may be related to the increased electron density on cobalt in the presence of the 5 0 -deoxyadenosyl group [13]. The chemical basis for the utility of the AdoCbl cofactor as a radical reservoir is the weak cobalt–carbon bond with a bond dissociation energy that is estimated to be @30 kcal mol1 (in aqueous solution) in the ‘‘base-on’’ state [14]. Reversible cleavage and reformation of the cobalt–carbon bond during catalytic turnover results in the formation of transient radical intermediates. The first common step in AdoCbl-dependent reactions is homolytic cleavage of the cobalt–carbon bond to generate a radical pair, cob(ii)alamin and the carboncentered dAdo radical (Scheme 19.3). This reaction experiences a @10 12 -fold rate enhancement in B12 enzymes [14, 15] in the presence of substrate, and the mechanism for this rate acceleration has been the subject of extensive scrutiny. Thus, in methylmalonyl-CoA mutase and in glutamate mutase, little if any destabilization of the cobalt–carbon bond is observed in the reactant state, as revealed by resonance Raman spectroscopy [16, 17], and the intrinsic substrate binding is utilized to labilize the bond. In contrast, approximately half of the destabilization of the cobalt–carbon bond in diol dehydratase is expressed in the reactant state. This re-
Scheme 19.3
19.2 Overall Reaction Mechanisms of Isomerases
actant destabilization may result in part from differences in the sizes of substrates that could translate into differences in binding energy. The destabilization renders the enzyme more prone to inactivation [10]; enzymes such as diol dehydratase can probably tolerate a higher inactivation rate due to the presence of repair chaperones that can catalyze the exchange of inactive cofactor for AdoCbl [18]. Rapid reaction studies on B12 enzymes reveal that homolysis is fast and not rate limiting [19–23]. Following homolysis, a series of controlled radical propagation steps result in migration of the organic radical (X in Scheme 19.3) to an adjacent carbon. The isomerization reaction is initiated by abstraction of a hydrogen atom from the substrate to generate a substrate-centered radical. This rearranges to a product-centered radical which reabstracts a 5 0 -hydrogen atom from 5 0 -deoxyadenosine. The dAdo and cob(ii)alamin radicals then recombine to complete a catalytic turnover cycle. In these 1,2 rearrangements, the hydrogen atom migrates intermolecularly, and a minimum of two hydrogen atom transfers, from substrate to dAdo and back, are involved. A mechanistic complication may involve some competition of a 1,2-hydrogen shift along with the dominant 1,2 shift of the carbon-centered radical [24]. A key issue to understanding these reactions is ascertaining the role of the protein [25]. In bacterial methylmalonyl-CoA mutase, the substrate is bound inside an a=b barrel, which may be important for shielding the radical intermediates [5, 26, 27]. More significant catalytically may be the role of an active-site tyrosine [28, 29], which appears to sterically drive the adenosyl group off the Co, as a result of a conformational change upon substrate binding. EPR spectroscopy provides information about the distance of the dominant product radical from cob(ii)alamin [30]. Finally, it is important to consider the role of entropy and the ‘‘solvating’’ power of the protein in promoting cobalt–carbon bond fission [31]. A critical issue for AdoCbl-dependent enzymes is controlling the timing of the homolysis step so that the radical pool is not dissipated. Homolysis of the cobalt– carbon bond takes place in the absence of substrate, as evidenced by the scrambling of label at the C5 0 position in methylmalonyl-CoA mutase [32]. However, the equilibrium favors geminate recombination, and formation of the spectrally visible cob(ii)alamin is not detected in the absence of substrate. Substrate binding triggers conformational adjustments, and the equilibrium shifts to favor the forward propagation of dAdo. Thus, homolysis and hydrogen transfer from the substrate are kinetically coupled; evidence for this was first obtained with methylmalonyl-CoA mutase [20] and later with other enzymes, viz. glutamate mutase [33] and ethanolamine ammonia lyase [34]. In methylmalonyl-CoA mutase, substitution of the protons on the methyl group of methylmalonyl-CoA with deuterons decelerated the appearance of cob(ii)alamin by @20-fold at 25 C [20]. This unusual sensitivity of the homolysis reaction of the cofactor to isotopic substitution in the substrate was interpreted as evidence for kinetic coupling, whereby the detectable accumulation of cob(ii)alamin was dependent on the extent of H-atom abstraction from the substrate. Kinetic coupling effectively shifts the equilibrium of the homolysis reaction, and it allows the substrate to gate mobilization of radicals from the AdoCbl reservoir.
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19 Hydrogen Atom Transfers in B12 Enzymes
Ribonucleotide reductase presents an exception to the above mechanism where the working radical is a thiyl derived from an active-site cysteine (C408 in the Lactobacillus leichmannii enzyme) rather than dAdo [35]. Mutation of C408 leads to failure of the mutant enzyme to generate detectable levels of cob(ii)alamin. However, the mutant catalyzes epimerization of AdoCbl that is stereoselectively deuterated at the 5 0 carbon bonded to cobalt [36]. This indicates that transient cleavage of the cobalt–carbon bond occurs, but when radical propagation to C408 is precluded, recombination of dAdo and cob(ii)alamin is favored.
19.3
Isotope Effects in B12 Enzymes
Large primary kinetic isotope effects have been measured for the H-atom transfer steps from substrate to dAdo and from dAdo to the product radical in a number of AdoCbl-dependent enzymes as indicated in Table 19.1. In methylmalonyl-CoA mutase, the steady-state deuterium isotope effect is 5-6 in the forward direction, and the intrinsic isotope effect of step (i) in Scheme 19.3 is masked by the kinetically coupled but slower later steps [37–39]. The steady-state tritium kinetic isotope effect (kH =k T ) in the forward direction has been reported to be 3.2 [38]. Note that the experiments with deuterium were performed with a fully deuterated methyl group, while those with tritium were carried out at the trace level and correspond to a single isotopic atom; therefore these two isotope effects should not be directly compared. For the reverse reaction, the deuterium kinetic isotope effect is also par-
Table 19.1.
Summary of kinetic isotope effects reported for B12 -dependent isomerases.
Enzyme substrate
Overall kinetic isotope effect
kH /kD on Co(II) formation
Ref.
kH /kT
kH /kD
Diol dehydratase propanediol
83 (10 C)
10 (37 C)
3–4 (4 C)
10, 45
Ethanoloamine lyase (EAL) ethanolamine
107 (23 C)
7.4 (23 C)
>10 (22 C)
34, 44
3.2 (@30 C)
5–6 (30 C) 3.4 (30 C)
43 (10 C)
37–40 29
21 (10 C) 19 (10 C)
3.9 (10 C) 6.3 (10 C)
28 (10 C) 35 (10 C)
33, 43 33, 43
Methylmalonyl-CoA mutase (MCM) methylmalonyl-CoA succinyl-CoA Glutamate mutase glutamate 3-methylaspartate
19.3 Isotope Effects in B12 Enzymes
tially masked by kinetic complexity (kH =kD ¼ 3:4) [38]. Under pre-steady-state conditions though, the measured kinetic isotope effects should not be affected by the product release step and, barring other complications, should be close to the intrinsic kinetic isotope effect. Under these conditions, a large deuterium isotope effect on cob(ii)alamin formation has been reported for the conversion of methylmalonylCoA to succinyl-CoA [20, 40]. Since a protein-based hydrogen pool in methylmalonyl-CoA mutase, which could account for the anomalously large isotope effects, has been excluded [38], the involvement of tunneling was invoked [20]. An Arrhenius analysis of the temperature dependence of the pre-steady-state isotope effect has provided compelling evidence [40] that tunneling dominates the reaction in that the observed values of the ratio, AH =AD (0.078 G 0.009), of preexponential factors and the difference, Ea; H Ea; D (3.41 G 0.07 kcal mol1 ), of activation energies lie outside the ranges expected [41] (AH =AD ¼ 0.5–1.4 and Ea; H Ea; D ca. <1.3 kcal mol1 ) in the absence of tunneling. The coupled homolysis/H-transfer steps catalyzed by methylmalonyl-CoA mutase are characterized by an equilibrium constant that is estimated to be close to unity and a phenomenological free energy of activation, DGz , of 13.1 G 0.6 kcal mol1 at 37 C that corresponds to a @10 12 -fold [42] rate acceleration. In contrast, thermolysis of AdoCbl in solution is characterized by an unfavorable equilibrium, and a DGz of 30 kcal mol1 at 37 C. In glutamate mutase [43], the forward and reverse steady-state deuterium (kH =kD of 3.9 forward and 6.3 reverse) and tritium (kH =k T of 21 forward and 19 reverse) kinetic isotope effects are both suppressed. However large deuterium isotope effects of 28 and 35 in the forward and reverse directions respectively have been observed for cob(ii)alamin formation under pre-steady-state conditions. These large kinetic isotope effects suggest that quantum mechanical tunneling also dominates this enzyme reaction. Diol dehydratase and ethanolamine ammonia lyase exhibit the largest overall tritium isotope effects that have been measured in B12 -dependent enzymes [44, 45], the overall deuterium kinetic isotope effect is also substantial [10, 34, 45]. The observation of a deuterium isotope effect on the pre-steady-state formation of cob(ii)alamin in diol dehyratase [10] and in ethanolamine ammonia lyase [25] is consistent with kinetic coupling between the homolysis and H-transfer steps. Recently the secondary kinetic isotope effect has been measured for the CoaC homolysis step in the pre-steady-state reaction of glutamate mutase [46]. The result obtained was kH =k T ¼ 0:76 G 0:02, which is a large inverse effect. The same study reported a secondary equilibrium isotope effect of kH =k T ¼ 0:72 G 0:04. Thus the kinetic and equilibrium effects agree within the error bars, the most straightforward interpretation of which, in the absence of tunneling, would be that the dynamical bottleneck is close to the product, i.e., late. However in the light of the large role expected for tunneling, this conclusion is not justified. Tunneling would be expected to raise the secondary kinetic isotope effect, so the fact that the kinetic isotope effect is inverse seems very significant. Recall that the CoaC homolysis and the hydrogen transfer from substrate to dAdo, though not likely to be concerted, are kinetically coupled. The homolysis step corresponds to a sp 3 ! sp 2 hybridiza-
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19 Hydrogen Atom Transfers in B12 Enzymes
tion change at C5 0 and this direction of hybridization change usually makes a normal contribution to the secondary kinetic isotope effect [47], whereas the hydrogen transfer involves the opposite trend at C5 0 . Hence the net inverse kinetic isotope effect would seem to place the dynamical bottleneck of the kinetically coupled two-step process at the hydrogen transfer step.
19.4
Theoretical Approaches to Mechanisms of H-transfer in B12 Enzymes
It is not easy to infer the details of the hydrogen atom transfer steps from the experimental kinetics, and theoretical methods provide one possible way to increase understanding. Although computational approaches to the CoaC bond dissociation and radical rearrangement steps in B12 -dependent enzymes have been attempted [48–56], the hydrogen atom transfer has received less attention. The radical nature of the dAdo reactant, the large size of the corrin moiety and the presence of a transition metal contribute to the difficulty of modeling this step in B12 enzymes. This difficulty is compounded by the paucity of reliable energetic data to calibrate the calculations. While good geometric information is sometimes sufficient for qualitative predictions of kinetic isotope effects for over the barrier processes, modeling the tunneling contribution [57–59] requires detailed knowledge of the ensemble of reaction paths, their barrier heights, the shapes (especially the widths) of the barriers, the curvature components of the reaction paths, and the potential energy in the tunneling swaths, which are the broad regions of configuration space through which tunneling from the reactant valleys to the product ones may proceed. Thus far only a few reports have been published on reactions that specifically aim at modeling the hydrogen atom transfer steps in B12 -dependent enzymes, and only one [60] addresses the tunneling contribution. Such calculations however are beginning to come within the realm of current computational technology, spurring new attempts at modeling H-atom transfer steps. Several studies have addressed the energetics and geometry of H-atom transfer in reactions that serve as models for this step in B12 -dependent enzymes [61–65]. Although these studies do not include active site residues and do not attempt to address the non-classical behavior of this step, they do provide useful information. Since combined quantum mechanical/molecular mechanical (QM/MM) calculations [66] of the enzyme kinetics may require the inclusion of a large number of atoms in the QM part due to the size of the corrin moiety, it is advantageous to use an inexpensive quantum mechanical model such as semiempirical molecular orbital theory. Therefore, a study was carried out in which the performance of semiempirical methods was critically evaluated and compared to high-end theory levels for Cn H2nþ1 þ Cn H2nþ2 (n ¼ 1; 2; 3) reactions [65]. Consensus values were evaluated from the high-level G3S//MP2(full)/6-31G(d), G3SX(MP3)//B3LYP/631G(2df,p), CBS-QB3//B3LYP/6-31G(dy), MCG3/3//MPW1K/6-31þG(d,p), MCQCISD/3//MPW1K/6-31þG(d,p), MC-QCISD/3, MPW1K/MG3S, and MPW1K/ MG3S//MPW1K/6-31þG(d,p) calculations. The energetics of the n ¼ 1 species
19.4 Theoretical Approaches to Mechanisms of H-transfer in B12 Enzymes Table 19.2. Calculated barrier heights (in kcal mol1 ) for Cn H2nþ1 þ Cn H2nþ2 (n ¼ 2; 3) reactions[a]
Method
C2 H5. B C2 H6
C3 H7. B C3 H8
Consensus barrier height AM1 PM3 AM1-CHC-SRP PM3-CHC-SRP PM3(tm) B3LYP/6-31þG(d,p)[b] MP2/6-31þG(d,p)[b]
16.7 16.0 12.0 18.3 17.0 16.3 15.7 19.4
16.0 15.6 12.5 17.9 16.3 15.6 15.5 18.6
a average
values for gauche and trans structures. b The basis set is given after the solidus, using conventional notation [67].
(CH3. and CH4 ) differ significantly from that obtained for the larger models, indicating the inadequacy of a methyl species as a model for the larger molecules. Some key results [65] for n ¼ 2 and 3 are shown in Table 19.2. This table shows that the general AM1 semiempirical parametrization [67] is capable of reproducing the barrier heights for transfer of a hydrogen atom between two carbons centers (the ‘‘CHC’’ motif ) within @1 kcal mol1 , which is quite encouraging. The equally inexpensive PM3 parametrization [67] is much less accurate, but the PM3(tm) method [67] is about as accurate as AM1. Use of specific reaction parameters (SRP) [68] for CHC systems [65] also improves PM3, but is unable to systematically improve AM1. Table 19.2 also shows a more expensive semiempirical method, B3LYP [67], which is a hybrid of Hartree–Fock theory and density functional theory, and it shows an ab initio post-Hartree–Fock level, MP2 [67]. Although B3LYP usually underestimates barriers for hydrogen atom transfers [69], for the CHC motif the magnitude of the underestimate is not large, only 0.5–1.0 kcal mol1 in Table 19.2. Toraya et al. [60–63] used B3LYP (with the 6-311G(d) basis set) for calculations on the H-atom transfer steps in diol dehydratase reaction. Both H-atom transfers, i.e., from the substrate and re-abstraction of a hydrogen atom from 5 0 deoxyadenosine, were considered. The models used in these studies included the substrate, 1,2-propanediol, a potassium cation found in the active site, and an ethyl radical as a mimic of the dAdo radical (Fig. 19.1). The activation barrier for the abstraction of the pro-S hydrogen atom of substrate by dAdo was calculated to be 9.0 kcal mol1 , while the activation barrier for the reverse reaction between product radical and 5 0 -deoxyadenosine was 15.7 kcal mol1 . In the absence of the potassium cation the forward activation barrier is 9.6 kcal mol1 indicating that coordination of the substrate by the potassium cation has a minimal energetic effect on the H-atom transfer step, but seems to hold the substrate and intermediates in
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19 Hydrogen Atom Transfers in B12 Enzymes
Figure 19.1.
Model [61–63] of hydrogen atom transfer steps in diol dehydratase reaction.
position for the multistep sequence. These calculations disagree with the experimental [70] determination of the rate-determining step in that the barrier for hydrogen atom abstraction is lower than that for OH group migration, which is probably a consequence of omitting active-site residues, since calculations on other model systems show strong environmental effects on the OH migration [48, 49]. For the re-abstraction step, two pathways were considered that differ in the timing of dehydration (Fig. 19.1). When the dehydration step precedes the H-atom transfer step, an activation barrier of 19.8 kcal mol1 is estimated. For the alternative pathway, in which hydrogen abstraction from deoxyadenosine by the product radical occurs prior to dehydration, the barrier is 15.1 kcal mol1 and was proposed to be more likely. However, the lack of active site residues in this model precludes unequivocal exclusion of the first pathway. The H-atom transfer steps in the reaction catalyzed by ethanolamine ammonia lyase reaction have also been examined computationally [64]. The simplest model employed a 1,5-dideoxyribose radical and 2-aminoethanol as the substrate (Fig. 19.2). The influence of full (R 2 ¼ Hþ ) or partial protonation (R 2 ¼ methyliminium ¼ NH2 CH2 þ ) of the nitrogen atom, as well as the synergetic presence of two (R 1 ¼ HCO2 , R 2 ¼ methyliminium ¼ NH2 CH2 þ ) hydrogen bonds, on the energetics of H-atom abstraction were evaluated. The hydrogen bonds mimic His and Asp residues in the active site, although the hydrogen bonds were arbitrarily placed since the 3D structure of the active site is not known. Two conformations of the ribose ring were considered. Calculations were carried out at B3LYP/6-
19.4 Theoretical Approaches to Mechanisms of H-transfer in B12 Enzymes
Figure 19.2. Model [64] of the hydrogen atom transfer between two CH2 groups in ethanolamine ammonia lyase. See Section 19.4 of text for an explanation of R 1 and R 2 .
311þþG(d,p)//B3LYP/6-31G(d) and MP2/6-311þþG(d,p)//B3LYP/6-31G(d) levels, and zero point vibrational energy was included. Activation enthalpies of 16.7 and 17.3 kcal mol1 were found for the unprotonated substrate (R 1 and R 2 missing) and the ribose C3-endo and C2-endo conformers, respectively. The results indicate that the H-atom transfer step would be facilitated by protonation or by hydrogen bonding interactions to the substrate. In particular, activation enthalpies for models of fully protonated or singly hydrogen-bonded substrate were smaller than 15 kcal mol1 , while the simultaneous presence of two hydrogen bonds to the nitrogen atom increased the activation barrier to over 25 kcal mol1 . Finally we consider some attempts to simulate the tunneling contributions in the hydrogen transfer step. This was first attempted using several models of differing complexity [60, 71]. PM3 calculations using conventional transition state theory (TST) [72] and a model comprising 37 atoms of the ribose radical and methylmalonyl with truncated CoA moiety (Fig. 19.3 with R 3 ¼ H and R 4 missing) give a hydrogen kinetic isotope effect (for CH3 vs. CD3 ) of only about 10, indicating that TST without tunneling corrections is insufficient to account for the experimental results, which are summarized in column 2 of Table 19.4. To include tunneling, the barrier shape was estimated from the energies of three stationary points (the substrate, the transition state, and the product of the hydrogen atom reaction) by an algorithm called IVTST-0 that was developed earlier [73] for gasphase reactions. This treatment allows the calculation of a multidimensional tunneling contribution. The resulting dynamical method [74, 75] is called TST/ZCT (where ZCT denotes zero-curvature tunneling, since this method ignores the curvature of the reaction path, which is discussed below). Calculated energetics (Table 19.3, column 3) and kinetic isotope effects (Table 19.4, column 4) compare reason-
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19 Hydrogen Atom Transfers in B12 Enzymes
Figure 19.3. Models [60] used in calculations of hydrogen kinetic isotope effects with tunneling contributions.
Table 19.3. Classical barrier heights and energies of reaction (in kcal mol1 ) for models[a] of the hydrogen abstraction for methylmalonyl-CoA mutase.
Ref.
PM3 H ... 60
M[b] H ... 71
PM3 Arg ... 60
PM3(tm) H ... 71
PM3(tm) Arg CorrinBHis 60
PM3 ... ... 60
barrier height[c] reaction energy[d]
11.9 0.2
14.4 0.7
12.0 0.6
16.2 0.1
19.9 9.5
4.5 2.6
QM R3 R4
a R3
and R 4 are explained in Fig. 19.3. b M denotes MPW1K/631þG(d,p). c The change in potential energy (exclusive of zero-point energy) in proceeding from reactants to the saddle point. d The change in potential energy (exclusive of zero-point energy) in proceeding from reactants to products.
Table 19.4.
˚
Primary kinetic isotope effects for hydrogen abstraction from methylmalonyl-CoA.
T ( C)
Exp.
Ref.
5 20
aM
40
PM3 H ... 60
M[a] H ... 71
PM3 Arg ... 60
PM3(tm) H ... 71
PM3(tm) Arg CorrinBHis 60
PM3 ... ... 60
50 36
47 37
42 32
49 38
118 84
63 49
9.4 8.6
QM R3 R4
denotes MPW1K/6-31þG(d,p).
19.4 Theoretical Approaches to Mechanisms of H-transfer in B12 Enzymes
ably well with results carried out at the MPW1K/6-31þG(d,p) level (Table 19.3, column 4 and Table 19.4, column 5), which has been validated to give reliable results for hydrogen atom transfer reactions [69]. Inclusion of arginine, which is hydrogenbonded to the carboxylate of the methylmalonyl moiety in the crystal structure, does not affect the results very much (Table 19.3 column 5 and Table 19.4, column 6). However, the agreement between these results and the experimental values is only coincidental. When the PM3tm method, which gives a higher barrier height is used (Table 19.3, column 6), the TST/ZCT hydrogen kinetic isotope effect is much higher (Table 19.4, column 7). Further enlargement of the model to include the corrin moiety with an imidazole ring (Table 19.3, column 7 and Table 19.4, column 8) does not change the isotope effect very much, but deprotonation of the carboxyl group leads to substantial lowering of the barrier (Table 19.3, column 8) and consequently, a much smaller kinetic isotope effect (Table 19.4, column 9), illustrating the sensitivity of the calculated isotope effect to the barrier height. As the next step in improving the dynamical description, it is important to include reaction path curvature (as well as zero point variation) in the description of the tunneling event. If the minimum energy path (MEP) from reactants to products were a straight line in the space of atomic Cartesian coordinates, there would be no internal centrifugal effect (bobsled effect) forcing the system’s motion, on average, to deviate from the MEP. But the MEP for most reactions is curved, and there is a bobsled effect. For tunneling processes the bobsled effect is negative (because the semiclassical kinetic energy is negative) [76–78] and thus the dominant tunneling paths are on the concave side of the MEP. This phenomenon is called corner-cutting tunneling [78, 79]. To describe the tunneling process in more detail, we need to define some terminology. A transition state (or generalized transition state) is a dividing surface (technically a hypersurface) in phase space (the space of the nuclear coordinates and momenta); here we define transition states entirely in terms of their location in coordinate space, which, after separating translation and rotational motion, has 3N 6 dimensions, where N is the number of atoms; and we consider transition states that are orthogonal to the MEP. Distance along the MEP is the reaction coordinate. Because the reaction coordinate has a fixed value in a transition state, a transition state has 3N 7 vibrations, which are called its generalized normal modes (the word ‘‘generalized’’ is included because conventional normal modes are defined only at stationary points such as equilibrium geometries and saddle points). The conventional transition state passes through the saddle point, but generalized transition states intersect the MEP both earlier and later than the saddle point. Reaction path curvature is actually a vector with 3N 7 components [80]. Each component is associated with a particular generalized normal mode, and it measures the extent to which the system curves into a particular direction as it progresses along the MEP. Corner-cutting tunneling involves a coupled motion involving the reaction coordinate and all the generalized normal modes that are associated with nonzero curvature components [81]. When reaction-path curvature is small, the tunneling is dominated by paths on
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19 Hydrogen Atom Transfers in B12 Enzymes
the concave side of the MEP whose locations are determined by the reaction-path curvature components [81, 82]. These small-curvature tunneling paths are typically located close enough to the MEP that the harmonic approximation is valid, and thus the dominant tunneling paths may be calculated (approximately) from the 3N 7 curvature components and the 3N 7 harmonic force constants of the generalized normal modes. From this information and the shape of the potential energy along the MEP, one can then calculate the tunneling probabilities. This is called the small-curvature tunneling (SCT) approximation [82, 83]. Describing tunneling in terms of definite paths in coordinate space [84] is a classical-like approximation. This kind of approximation (like the well known WKB method [85]) is called ‘‘semiclassical’’ in chemical physics (and here) because it involves calculating a quantum mechanical quantity by classical-like methods; thus it is partly classical or semiclassical. Unfortunately the kinetic isotope effect community uses the word ‘‘semiclassical’’ to denote an entirely different approximation, namely including quantized vibrational energies in the treatment of the 3N 7 transition state vibrations, but treating the transmission coefficient entirely classically and thus completely neglecting tunneling. (This is sometimes called ‘‘quasiclassical’’ in chemical physics.) We hope this warning is sufficient to prevent confusion. When reaction-path curvature is large, one requires a much more complicated semiclassical treatment to handle the tunneling. In the limit of large reactionpath curvature, tunneling tends to occur along straight-line tunneling paths because the shortest distance between two points is a straight line, and when reaction-path curvature is large, tunneling along short tunneling paths has a greatly enhanced probability [86]. In addition, tunneling tends to be much more delocalized, and systems may have appreciable probability of tunneling directly into vibrationally excited stretching modes [86, 87, 89]. A semiclassical theory that incorporates all of these features has been developed [82, 90, 91] and it is called the large-curvature tunneling (LCT) approximation. In the general case one could obtain a good semiclassical tunneling approximation by optimizing the tunneling path somewhere between the small-curvature and large-curvature limits by a least-action approximation [92]. In practice, it has been found that simply choosing between the SCT and LCT approximations on the basis of whichever yields a larger tunneling probability (the tunneling is dominated by the most favorable tunneling paths at each tunneling energy) is enough optimization to yield accurate results [91, 93]. This is called microcanonically optimized multidimensional tunneling or mOMT [91, 93]. Tunneling can be included most consistently in transition state theory in the context of variational transition state theory, e.g., canonical variational theory (CVT) [75]. CVT calculations were performed [71] with zero-curvature tunneling (see Table 19.5, column 3), and they show that the IVTST-0 calculations overestimate ZCT contribution to the hydrogen kinetic isotope effect. Calculations were also performed including corner-cutting tunneling, and these are shown in the last five columns of Table 19.5. As can be seen from the comparison of the results in these columns, large-curvature tunneling (LCT) plays the dominant role. Col-
19.5 Free Energy Profile for Cobalt–Carbon Bond Cleavage and H-atom Transfer Steps Table 19.5. Kinetic isotope effects for 37-atom model obtained using PM3 for electronic structure calculations.
T ( C)
˚
CVT[a]
CVT/ZCT
CVT/SCT
CVT/LCT
CVT/mOMT
QM model
PM3 M37[b]
PM3 M37
PM3 M37
PM3 M37
PM3 M37
PM3 M50[c]
AM1 M37
5 20
9.9 8.5
21 18
27 23
145 124
113 94
96 80
127 89
tunneling. b 37-atom model corresponding to R 3 ¼ H, and R 4 not present. c 50-atom model: M37 þ adenine.
a No
umns 6 and 7 of Table 19.5 show that comparable results are obtained when the model is enlarged to include adenine, the last column contains results obtained for the AM1 Hamiltonian instead of PM3. Barriers for the AM1 parameterizations are 14.9 and 16.6 kcal mol1 for the M37 and M50 models, respectively. The last three columns of Table 19.5 report results obtained with the microcanonically optimized multidimensional tunneling approximation, which represents the currently most trusted method for including a tunneling contribution. These results predict that the hydrogen kinetic isotope effect for the hydrogen atom step in methylmalonyl-CoA reaction in the direction of succinyl formation is @100. The dynamical calculations in Tables 19.4 and 19.5 were performed with the polyrate [88] and morate [90] computer programs.
19.5
Free Energy Profile for Cobalt–Carbon Bond Cleavage and H-atom Transfer Steps
The interpretation of kinetic isotope effects observed in enzymes must take account of kinetic complexity. For example, the deuterium kinetic isotope effect on the methylmalonyl-CoA mutase-catalyzed reaction was measured under presteady-state conditions with UV–visible detection of cob(ii)alamin formation [20, 42]. Thus, it reports on a combination of steps, including substrate binding and a concomitant conformational change in the enzyme, cobalt-carbon bond homolysis, and hydrogen-atom transfer to the dAdo radical. The kinetics could be further complicated in other enzymes such as diol dehydratase [95] and glutamate mutase [96], where conformational changes in the dAdo radical are expected to occur between the homolysis and hydrogen atom transfer steps, and in ribonucleoside triphosphate reductase, in which a protein-based cysteinyl radical functions as the working radical [97]. Because of these mechanistic complexities, observed kinetic isotope effects under pre-steady state conditions, although large, need not reflect
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19 Hydrogen Atom Transfers in B12 Enzymes
the full intrinsic values for the kinetic isotope effects on the H-atom transfer steps in the respective enzymes. Thus it is unclear whether the difference between the large intrinsic kinetic isotope effect calculated for the hydrogen atom transfer step in methylmalonyl-CoA mutase and the isotope effect observed experimentally (which is also very large, but not as large as the calculated one) indicates that kinetic complexity causes about half of the isotope effect to be masked by isotopeinsensitive steps in the observed pre-steady-state rate or whether it results from the quantitative uncertainty of the calculation. Since the calculation includes neither the full enzyme nor ensemble averaging, one should be very cautious about the former type of conclusion. Further progress toward a quantitative resolution of the size of the intrinsic kinetic isotope effect requires a more complete mechanistic analysis, which is sometimes [98], but not always, possible. A step in this direction has been made for methylmalonyl-CoA mutase [42], for which a free energy profile extending across seven steps has been constructed on the basis of available kinetic and spectroscopic data. Similarly, a three-step profile has been presented for ethanolamine deaminase [99], and a six-step profile has been presented for glutamate mutase [22]. A feature seen in the profiles of both methylmalonyl-CoA mutase and glutamate mutase, which is also seen for many other enzymes, is that the energetic barriers to the interconversion of the various chemical intermediates are similar in height, which may be a general consequence of the tendency of enzymatic transformations to be partitioned into a series of discrete steps without the inefficiency of high energy release or high energy consumption in any one of them. In any event, it is precisely this feature that makes it hard to sort out elementary-step rate constants and kinetic isotope effects for the individual chemical steps.
19.6
Model Reactions
We discussed above some theoretical studies of model systems. There is an even larger literature devoted to experimental studies of model systems, dating back at least 20 years [100, 101]. Most recently, some model studies have appeared that are directly related to the present concerns. In particular, Finke and coworkers [102, 103] have studied the reaction of b-neopentyl-Cbl with ethylene glycol (a model of the diol dehydratase reaction) at temperatures up to 120 C, and their results have engendered interesting discussions [104]. Their key finding is that the elevatedtemperature kinetic isotope effects observed for the model reaction in solution (where the enzyme is not present to stabilize the dAdo radical) are very similar to those obtained for methylmalonyl–CoA mutase at temperatures more typical of physiological action. The comparison is clouded by potential kinetic complexity, discussed above, that may suppress the intrinsic value of the kinetic isotope effect in the enzyme case. Nevertheless one clear conclusion of this work, which agrees with pure theoretical considerations as well as with studies of many nonenzymatic reactions, is that enzymes are not uniquely evolved to promote tunneling. Whether
References
the fraction of a reaction that proceeds by tunneling in an enzyme reaction is greater than that in a similar nonenzymatic reaction will depend on the individual enzyme and on many detailed mechanistic factors. One scenario is that the environment can exert a greater leverage on a reaction by lowering the effective barrier height (which appears in an exponent) than by changing the transmission coefficient, and lower barriers are often (not always) associated with broader barrier tops; a lower, broader barrier makes it harder for tunneling to compete with overbarrier processes so that the fraction of reactive events that occurs by tunneling may be lower in the enzymatic system. If the intrinsic methylmalonyl–CoA mutase kinetic isotope effect is as large as the calculated values given above, though, then this reaction may prove to be an exception to that scenario.
19.7
Summary
Deconvoluting the contributions of the individual steps in the observed pre-steadystate rate constant for cob(ii)alamin formation is challenging and awaits solution. In particular, details of the H-atom transfer steps elude direct determination. However, recent advances in the theoretical methodology hold promise for complementing the experimental analysis of a fundamental aspect of AdoCbl-dependent reactions, i.e., the H-atom transfer steps.
Acknowledgments
This work was supported by grants from the National Institutes of Health (Fogarty International Collaboration grant to P.P. and R.B. and DK45776 to R.B.) and the National Science Foundation (CHE-0349122 to D.T.).
References 1 Banerjee, R., Ragsdale, S. W. (2003)
The many faces of vitamin B12 : Catalysis by cobalamin-dependent enzymes, Annu. Rev. Biochem. 72, 209–247. 2 Schrauzer, G. N., Deutsch, E. (1969) Reactions of cobalt(i) supernucleophiles. The alkylation of vitamin B12S , cobaloximes(i), and related compounds, J. Am. Chem. Soc. 91, 3341– 3350. 3 Drennan, C. L., Huang, S., Drummond, J. T., Matthews, R., Ludwig, M. L. (1994) How a protein binds B12 : A 3 A˚ X-ray structure of
B12 -binding domains of methionine synthase, Science 266, 1669–1674. 4 Marsh, E. N. G., Holloway, D. E. (1992) Cloning and sequencing of glutamate mutase component S from Clostridium tetanomorphum, FEBS Lett. 310, 167–170. 5 Mancia, F., Keep, N. H., Nakagawa, A., Leadlay, P. F., McSweeney, S., Rasmussen, B., Bo¨secke, P., Diat, O., Evans, P. R. (1996) How coenzyme B12 radicals are generated: The crystal structure of methylmalonyl-coenzyme A mutase at 2 A˚ resolution, Structure 4, 339–350.
1489
1490
19 Hydrogen Atom Transfers in B12 Enzymes 6 Reitzer, R., Gruber, K., Jogl, G.,
7
8
9
10
11
12
13
14
15
Wagner, U. G., Bothe, H., Buckel, W., Kratky, C. (1999) Glutamate mutase from Clostridium cochlearium: the structure of a coenzyme B12 dependent enzyme provides new mechanistic insights, Structure Fold. Des. 7, 891–902. Chang, C. H., Frey, P. A. (2000) Cloning, sequencing, heterologous expression, purification, and characterization of adenosylcobalamindependent D-lysine 5,6-aminomutase from Clostridium sticklandii, J. Biol. Chem. 275, 106–114. Shibata, N., Masuda, J., Tobimatsu, T., Toraya, T., Suto, K., Morimoto, Y., Yasuoka, N. (1999) A new mode of B12 binding and the direct participation of a potassium ion in enzyme catalysis: X-ray structure of diol dehydratase, Structure Fold Des. 7, 997–1008. Sintchak, M. D., Arjara, G., Kellogg, B. A., Stubbe, J., Drennan, C. L. (2002) The crystal structure of class II ribonucleotide reductase reveals how an allosterically regulated monomer mimics a dimer, Nat. Struct. Biol. 9, 293–300. Toraya, T. (2003) Radical catalysis in coenzyme B12 -dependent isomerization (eliminating) reactions, Chem. Rev. 103, 2095–2127. Banerjee, R. (2003) Radical carbon skeleton rearrangements: catalysis by coenzyme B12 -dependent mutases, Chem. Rev. 103, 2083–94. Banerjee, R., Chowdhury, S. (1999) Methylmalonyl-CoA Mutase, John Wiley and Sons, New York. Jensen, K. P., Sauer, S. P., Liljefors, T., Norrby, P.-O. (2001) Theoretical investigation of steric and electronic effects in coenzyme B12 models, Organometallics 20, 550–556. Finke, R. G., Hay, B. P. (1984) Thermolysis of adenosylcobalamin: A product, kinetic and Co-C5 0 bond dissociation energy study, Inorg. Chem. 23, 3041–3043. Halpern, J. (1985) Mechanisms of coenzyme B12 -dependent rearrangements, Science 227, 869–875.
16 Dong, S., Padmakumar, R., Maiti,
17
18
19
20
21
22
23
N., Banerjee, R., Spiro, T. G. (1998) Resonance Raman spectra of methylmalonyl-Coenzyme A mutase, a coenzyme B12 -dependent enzyme, reveal dramatic change in corrin ring conformation but little change in Co-C bond force constant in the cofactor upon its binding to the enzyme, J. Am. Chem. Soc. 120, 9947–9948. Huhta, M. S., Chen, H. P., Hemann, C., Hille, C. R., Marsh, E. N. (2001) Protein-coenzyme interactions in adenosylcobalamin-dependent glutamate mutase, Biochem. J. 355, 131–137. Mori, K., Toraya, T. (1999) Mechanism of reactivation of coenzyme B12 dependent diol dehydratase by a molecular chaperone-like reactivating factor, Biochemistry 38, 13170–13178. Hollaway, M. R., White, H. A., Joblin, K. N., Johnson, A. W., Lappert, M. F., Wallis, O. C. (1978) A spectrophotometric rapid kinetic study of reactions catalyzed by coenzyme B12 -dependent ethanolamine ammonia lyase, Eur. J. Biochem. 82, 143–154. Padmakumar, R., Padmakumar, R., Banerjee, R. (1997) Evidence that cobalt-carbon bond homolysis is coupled to hydrogen atom abstraction from substrate in methylmalonylCoA mutase, Biochemistry 36, 3713– 3718. Brown, K. L., Li, J. (1998) Activation parameters for the carbon-cobalt bond homolysis of coenzyme B12 induced by the B12 -dependent ribonucleotide reductase from Lactobacillus leichmannii, J. Am. Chem. Soc. 120, 9466–9474. Chih, H. W., Marsh, E. N. (1999) Pre-steady-state kinetic investigation of intermediates in the reaction catalyzed by adenosylcobalamin-dependent glutamate mutase, Biochemistry 38, 13684–13691. Licht, S. S., Lawrence, C. C., Stubbe, J. (1999) Thermodynamic and kinetic studies on carbon-cobalt bond homolysis by ribonucleoside triphosphate reductase: the importance of
References
24
25
26
27
28
29
30
31
32
entropy in catalysis, Biochemistry 38, 1234–1242. Kunz, M., Re´tey, J. (2000) Evidence for a 1,2 shift of a hydrogen atom in a radical intermediate of the methylmalonyl-CoA mutase reaction, Bioorg. Chem. 28, 134–139. Garcia-Viloca, M., Gao, J., Karplus, M., Truhlar, D. G. (2004) How enzymes work: Analysis by modern rate theory and computer simulations, Science 303, 186–195. Branden, C., Tooze, J. Introduction to Protein Structure, 2nd edn., Garland Publishing, New York, 1999, pp. 50–51. Thoma¨, N. H., Evans, P. R., Leadlay, P. F. (2000) Protection of radical intermediates at the active site of adenosylcobalamin-dependent methylmalonyl-CoA mutase, Biochemistry 39, 9213–9221. Mancia, F., Smith, G. A., Evans, P. R. (1999) Crystal structure of substrate complexes of methylmalonyl-CoA mutase, Biochemistry 38, 7999–8005. Thoma¨, N. H., Meier, T. W., Evans, P. R., Leadlay, P. F. (1998) Stabilization of radical intermediates by an active site tyrosine residue in methylmalonyl-CoA mutase, Biochemistry 37, 14386–14393. Reed, G. H., Mansoorabadi, S. O. (2003) The positions of radical intermediates in the active sites of adenosylcobalamin-dependent enzymes, Curr. Opin. Struct. Biol. 13, 716–721. Pratt, J. M. Cobalt in vitamin B12 and its enzymes, in Handbook on Metalloproteins, I. Bertini, A. Sigel, H. Sigel (Eds.), Dekker, New York, 2001, pp. 603–668. Gaudemer, A., Zybler, J., Zybler, N., Baran-Marszac, M., Hull, W. E., Fountoulakis, M., Konig, A., Wolfe, K., Retey, J. (1981) Reversible cleavage of the cobalt-carbon bond of coenzyme B12 catalyzed by methylmalonyl-CoA mutase from Propionibacterium shermanii: The use of coenzyme B12 stereospecifically deuterated in position 5 0 , Eur. J. Biochem. 119, 279–285.
33 Marsh, E. N. G., Ballou, D. P. (1998)
34
35
36
37
38
39
40
Coupling of cobalt-carbon bond homolysis and hydrogen atom abstraction in adenosylcobalamindependent glutamate mutase, Biochemistry 37, 11864–11872. Bandarian, V., Reed, G. H. (2000) Isotope effects in the transient phases of the reaction catalyzed by ethanolamine ammonia-lyase: determination of the number of exchangeable hydrogens in the enzyme-cofactor complex, Biochemistry 39, 12069– 12075. Licht, S. S., Booker, S., Stubbe, J. (1999) Studies on the catalysis of carbon-cobalt bond homolysis by ribonucleoside triphosphate reductase: Evidence for concerted carbon-cobalt bond homolysis and thiyl radical formation, Biochemistry 38, 1221–1233. Chen, D., Abend, A., Stubbe, J., Frey, P. A. (2003) Epimerization at carbon-5 0 of (5 0 R)-[5 0 - 2 H]adenosylcobalamin by ribonucleoside triphosphate reductase: Cysteine 408independent cleavage of the Co-C5 0 bond, Biochemistry 42, 4578–4584. Michenfelder, M., Hull, W. E., Retey, J. (1987) Quantitative measurement of the error in the cryptic stereospecificity of methylmalonyl-CoA mutase, Eur. J. Biochem. 168, 659–667. Meier, T. W., Thoma¨, N. H., Leadlay, P. F. (1996) Tritium isotope effects in adenosylcobalamin-dependent methylmalonyl-CoA mutase, Biochemistry 35, 11791–11796. Chowdhury, S., Thomas, M. G., Escalante-Semerena, J. C., Banerjee, R. (2001) The coenzyme B12 analog 5 0 Deoxyadenosylcobinamide-GDP supports catalysis by methylmalonylCoA mutase in the absence of transligand coordination, J. Biol. Chem. 276, 1015–1019. Chowdhury, S., Banerjee, R. (2000) Evidence for quantum mechanical tunneling in the coupled cobalt carbon bond homolysis-substrate radical generation reaction catalyzed by methylmalonyl-CoA mutase, J. Am. Chem. Soc. 122, 5417–5418.
1491
1492
19 Hydrogen Atom Transfers in B12 Enzymes 41 Saunders, W. H. Jr. Kinetic isotope
42
43
44
45
46
47 48
49
50
effects, in Investigation of Rates and Mechanisms of Reactions, Part I, 4th edn., C. F. Bernasconi (Ed.), Wiley, New York, 1986, pp. 565–611. Chowdhury, S., Banerjee, R. (2000) Thermodynamic and kinetic characterization of Co-C bond homolysis catalyzed by coenzyme B12 -dependent methylmalonyl-CoA mutase, Biochemistry 39, 7998–8006. Chih, H. W., Marsh, E. N. (2001) Tritium partitioning and isotope effects in adenosylcobalamindependent glutamate mutase, Biochemistry 40, 13060–13067. Weisblat, D. A., Babior, B. M. (1971) The mechanism of action of ethanolamine ammonia-lyase, a B12 -dependent enzyme. VIII. Further studies with compounds labeled with isotopes of hydrogen: Identification and some properties of the ratelimiting step, J. Biol. Chem. 246, 6064–6061. Essenberg, M. K., Frey, P. A., Abeles, R. H. (1971) Studies on the mechanism of hydrogen transfer in the coenzyme B12 dependent dioldehydrase reaction II, J. Am. Chem. Soc. 93, 1242–1251. Cheng, M. C., Marsh, E. N. G. (2004) Pre-steady-state measurement of intrinsic secondary tritium isotope effects associated with the homolysis of adenosylbcobalamin and the formation of 5 0 -deoxyadenosine in glutamate mutase, Biochemistry 43, 2155–2158. Saunders, W. H. Jr., p. 598 of Ref 41. Smith, D. M., Golding, B. T., Radom, L. (1999) Understanding the mechanism of B12 -dependent methylmalonyl-CoA mutase: Partial proton transfer in action, J. Am. Chem. Soc. 121, 9388–9399. Smith, D. M., Golding, B. T., Radom, L. (2001) Understanding the mechanism of B12 -dependent diol dehydratase: a synergistic retro-pushpull proposal, J. Am. Chem. Soc. 123, 1664–1675. Andruniow, T., Zgierski, M. Z., Kozlowski, P. M. (2001) Theoretical
51
52
53
54
55
56
57
58
59
determination of the Co-C bond energy dissociation in cobalamins, J. Am. Chem. Soc. 123, 2679–2680. Jensen, K. P., Ryde, U. (2002) The axial N-base has minor influence on Co-C bond cleavage in cobalamins, J. Mol. Struct. (Theochem) 585, 239–255. Wetmore, S. D., Smith, D. M., Bennett, J. T., Radom, L. (2002) Understanding the mechanism of action of B12 -dependent ethanolamine ammonia-lyase: Synergistic interactions at play, J. Am. Chem. Soc. 124, 14054–14065. Freindorf, M., Kozlowski, P. M. (2004) A combined density functional theory and molecular mechanics study of the relationship between the structure of coenzyme B12 and its binding to methylmalonyl-CoA mutase, J. Am. Chem. Soc. 126, 1928–1929. Loferer, M. J., Webb, B. M., Grant, G. H., Liedl, K. R. (2003) Energetic and stereochemical effects of the protein environment on substrate: A theoretical study of methylmalonylCoA mutase, J. Am. Chem. Soc. 125, 1072–1078. Jensen, K. P., Ryde, U. (2003) Theoretical prediction of the Co-C bond strength in cobalamins, J. Phys. Chem. A107, 7539–7545. Doelker, N., Maseras, F., Siegbahn, P. E. M. (2004) Stabilization of the adenosyl radical in coenzyme B12 – a theoretical study, Chem. Phys. Lett. 386, 174–178. Truhlar, D. G. Variational Transition State Theory and Multidimensional Tunneling for Simple and Complex Reactions in the Gas Phase, Solids, Liquids, and Enzymes, in Isotope Effects in Chemistry and Biology, H. Limbach, A. Kohen (Eds.), Dekker, New York, pp. 579–619. Ferna´ndez-Ramos, A., Miller, J. A., Klippenstein, S. J., Truhlar, D. G. Modeling the Kinetics of Bimolecular Reactions, Chem. Rev. submitted for publication. Truhlar, D. G., Gao, J., GarciaViloca, M., Alhambra, C.,
References
60
61
62
63
64
65
66
67
Corchado, J., Sanchez, L., Poulsen, T. D. (2004) Ensemble-averaged variational transition state theory with optimized multidimensional tunneling for enzyme kinetics and other condensed-phase reactions, Int. J. Quantum Chem., 100, 1136– 1152. Dybala-Defratyka, A., Paneth, P. (2001) Theoretical evaluation of the hydrogen kinetic isotope effect on the first step of the methylmalonyl-CoA mutase reaction, J. Inorg. Biochem. 86, 681–689. Toraya, T., Yoshizawa, K., Eda, M., Yamabe, K. (1999) Direct participation of potassium ion in the catalysis of coenzyme B12 -dependent diol dehydratase, J. Biochem. (Tokyo) 126, 650–654. Toraya, T., Eda, M., Kamachi, T., Yoshizawa, K. (2001) Energetic feasibility of hydrogen abstraction and recombination in coenzyme B12 -dependent diol dehydratase reaction, J. Biochem. (Tokyo) 130, 865–872. Eda, M., Kamachi, T., Yoshizawa, K., Toraya, T. (2002) Theoretical study on the mechanism of catalysis of coenzyme B12 -dependent diol dehydratase, Bull. Chem. Soc. Jpn. 75, 1469– 1481. Semialjac, M., Schwarz, H. (2004) Computational investigation of hydrogen abstraction from 2-aminoethanol by the 1,5-dideoxyribose-5-yl radical: A model study of a reaction occurring in the active site of ethanolamine ammonia lyase, Chem.: Eur. J. 10, 2781–2788. Dybala-Defratyka, A., Paneth, P., Pu, J., Truhlar, D. G. (2004) Benchmark results for hydrogen atom transfer between carbon centers and validation of electronic structure methods for bond energies and barrier heights, J. Phys. Chem. A 108, 2475– 2486. Gao, J., Truhlar, D. G. (2002) Quantum mechanical methods for enzyme kinetics, Annu. Rev. Phys. Chem. 53, 467–505. Cramer, C. J. Essentials of Computa-
68
69
70
71
72
73
74
75
76
77
tional Chemistry: Theories and Methods, Wiley, Chichester, 2002. Gonza`lez-Lafont, A., Truong, T. N., Truhlar, D. G. (1991) Direct dynamics calculations with neglect of diatomic differential overlap molecular orbital theory with specific reaction parameters, J. Phys. Chem. 95, 4618– 4627. Lynch, B. J., Fast, P. L., Harris, M., Truhlar, D. G. (2000) Adiabatic connection for kinetics, J. Phys. Chem. A 104, 4811–4815. Eagar, R. G. Jr., Bachovchin, W. W., Richards, J. H. (1975) Mechanism of action of adenosylcobalamin: 3-Fluoro1,2-propanediol as substrate for propanediol dehydratase-mechanistic implications, Biochemistry 14, 5523– 5528. Dybala-Defratyka, A. (2004) Ph. D. Thesis, Technical University of Lodz, Poland; Dybala-Defratyka, A., Paneth, P., Truhlar, D. G., unpublished results. Eyring, H. (1938) The theory of absolute reaction rates, Trans. Faraday Soc. 34, 41–48. Gonza`lez-Lafont, A., Truong, T. N., Truhlar, D. G. (1991) Interpolated variational transition state theory: Practical methods for estimating variational transition state properties and tunneling contributions to chemical reaction rates from electronic structure calculations, J. Chem. Phys. 95, 8875–8894. Truhlar, D. G., Kuppermann, A. (1971) Exact tunneling calculations, J. Am. Chem. Soc. 93, 1840–1851. Garrett, B. C., Truhlar, D. G., Grev, R. S., Magnuson, A. W. (1980) Improved treatment of threshold contributions in variational transition state theory, J. Phys. Chem. 84, 1730–1748. Marcus, R. A. (1966) On the analytical mechanics of chemical reactions. Quantum mechanics of linear collisions, J. Chem. Phys. 45, 4493–4499. Kuppermann, A., Adams, J. T., Truhlar, D. G. (1973) Streamlines of probability current density and
1493
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19 Hydrogen Atom Transfers in B12 Enzymes
78
79
80
81
82
83
84
85
tunneling fractions for the collinear H þ H2 ! H2 þ H reaction, in Electronic and Atomic Collisions: Abstracts of Papers, Eighth International Conference on the Physics of Electronic and Atomic Collisions (VIII ICPEAC), Beograd, 1973, B. C. Cobic, M. V. Kurepa (Eds.), Institute of Physics, Beograd, pp. 149–150. Skodje, R. T., Truhlar, D. G., Garrett, B. C. (1982) Vibrationally adiabatic models for reactive tunneling, J. Chem. Phys. 77, 5955–5976. Kreevoy, M. M., Ostovic, D., Truhlar, D. G., Garrett, B. C. (1986) Phenomenological manifestations of large-curvature tunneling in hydride transfer reactions, J. Phys. Chem. 90, 3766–3774. Miller, W. H., Handy, N. C., Adams, J. E. (1980) Reaction path Hamiltonian for polyatomic molecules, J. Chem. Phys. 72, 99–112. Truhlar, D. G., Isaacson, A. D., Garrett, B. C. (1985) Generalized transition state theory, in Theory of Chemical Reaction Dynamics, M. Baer (Ed.), CRC Press, Boca Raton, FL, Vol. 4, pp. 65–137. Lu, D.-h., Truong, T. N., Melissas, V. S., Lynch, G. C., Liu, Y.-P., Garrett, B. C., Steckler, R., Isaacson, A. D., Rai, S. N., Hancock, G. C., Lauderdale, J. G., Joseph, T., Truhlar, D. G. (1992) POLYRATE 4: A new version of a computer program for the calculation of chemical reaction rates for polyatomics, Comput. Phys. Commun. 71, 235–262. Liu, Y.-P., Lynch, G. C., Truong, T. N., Lu, D.-h., Truhlar, D. G., Garrett, B. C. (1993) Molecular modeling of the kinetic isotope effect for the [1,5]-sigmatropic rearrangement of cis-1,3-pentadiene, J. Am. Chem. Soc. 115, 2408–2415. Marcus, R. A., Coltrin, M. E. (1977) A new tunneling path for reactions such as H þ H2 ! H2 þ H, J. Chem. Phys. 67, 2609–2613. Schatz, G. C., Ratner, M. A. (1993) Quantum Mechanics in Chemistry, Prentice-Hall, Englewood Cliffs, NJ, pp. 167–181.
86 Garrett, B. C., Truhlar, D. G.,
87
88
89
90
91
Wagner, A. F., Dunning, T. H. Jr. (1983) Variational transition state theory and tunneling for a heavylight-heavy reaction using an ab initio potential energy surface. 37 Cl þ H(D) 35 Cl ! H(D) 37 Cl þ 35 Cl, J. Chem. Phys. 78, 4400–4413. Marcus, R. A. (1979) Similarities and differences between electron and proton transfers at electrodes and in solution. Theory of a hydrogen evolution reaction, in Proceedings of the Third Symposium on Electrode Processes, S. Bruckenstein, J. D. E. McIntyre, B. Miller, and E. Yeager (Eds.), Electrochemical Society, Princeton, pp. 1–12. Chuang, Y.-Y., Corchado, J. C., Fast, P. L., Villa`, J., Hu, W.-P., Liu, Y.-P., Lynch, G. C., Jackels, C. F., Nguyen, K. A., Gu, M. Z., Rossi, I., ˜ o, E. L., Clayton, S., Melissas, Coitin V. S., Lynch, B. J., Steckler, R. B., Garrett, C., Isaacson, A. D., Truhlar, D. G. (2000) POLYRATE– Version 8.4.1.PL, University of Minnesota, Minneapolis. Garrett, B. C., Abusalbi, N., Kouri, D. J., Truhlar, D. G. (1983) Test of variational transition state theory and the least-action approximation for multidimensional tunneling probabilities against accurate quantal rate constants for a collinear reaction involving tunneling in an excited state, J. Chem. Phys. 83, 2252–2258. Truong, T. N., Lu, D.-h., Lynch, G. C., Liu, Y.-P., Melissas, V. S., Stewart, J. J. P., Steckler, R., Garrett, B. C., Isaacson, A. D., Gonza`lez-Lafont, A., Rai, S. N., Hancock, G. C., Joseph, T., Truhlar, D. G. (1993) MORATE: A program for direct dynamics calculations of chemical reaction rates by semiempirical molecular orbital theory, Comput. Phys. Commun. 75, 143–159. Liu, Y.-P., Lu, D.-h., Gonza`lezLafont, A., Truhlar, D. G., Garrett, B. C. (1993) Direct dynamics calculation of the kinetic isotope effect for an organic hydrogen-transfer
References
92
93
94
95
96
97
98
reaction, including corner-cutting tunneling in 21 dimensions, J. Am. Chem. Soc. 115, 7806–7817. Garrett, B. C., Truhlar, D. G. (1983) A least-action variational method for calculating multidimensional tunneling probabilities for chemical reactions, J. Chem. Phys. 79, 4931–4938. Allison, T. C., Truhlar, D. G. Testing the accuracy of practical semiclassical methods: Variational transition state theory with optimized multidimensional tunneling, in Modern Methods for Multidimensional Dynamics Computations in Chemistry, D. L. Thompson (Ed.), World Scientific Singapore, 1998, pp. 618–712. Chuang, Y.-Y., Fast, P. L., Hu, W.-P., Lynch, G. C., Liu, Y.-P., Truhlar, D. G. (2001) morate-version 8.5, University of Minnesota, Minneapolis. Masuda, J., Shibata, N., Morimoto, Y., Toraya, T., Yasuoka, N. (2000) How a protein generates a catalytic radical from coenzyme B12 : X-ray structure of a diol-dehydrataseadeninylpentylcobalamin complex, Structure Fold. Des. 8, 775–788. Gruber, K., Reitzer, R., Kratky, C. (2001) Radical shuttling in a protein: Ribose pseudorotation controls alkylradical transfer in the coenzyme B12 dependent enzyme glutamate mutase, Angew. Chem. Int. Ed. Engl. 40, 3377– 3380. Licht, S., Gerfen, G. J., Stubbe, J. (1996) Thiyl radicals in ribonucleotide reductases, Science 271, 477–481. Berti, P. J., Schramm, V. L. (1999) Enzymatic transition state structures constrained by experimental kinetic
99
100
101
102
103
104
isotope effects: Experimental measurement of transition state variability, ACS Symp. Ser. 721, 473–488. Warncke, K., Schmidt, J. C., Ke, S.-C. (1999) Identification of a rearranged-substrate, product radical intermediate and the contribution of a product radical trap in vitamin B12 coenzyme-dependent ethanolamine deaminase catalysis, J. Am. Chem. Soc. 121, 10522–10528. Dowd, P., Trivedi, B. K. (1985) On the mechanism of action of vitamin B12 . Model studies directed toward the hydrogen abstraction reaction, J. Org. Chem. 80, 206–217. Dowd, P., Wilk, B., Wilk, B. K. (1992) First hydrogen abstractionrearrangment modle for the coenyme B12 -dependent methylmalonyl-CoA to succinyl-CoA carbon skeleton rearranment reaction, J. Am. Chem. Soc. 114, 7949–7951. Doll, K. M., Finke, R. G. (2003) A compelling experimental test of the hypothesis that enzymes have evolved To enhance quantum mechanical tunneling in hydrogen transfer reactions: The b-neopentylcobalamin system combined with prior adocobalamin data, Inorg. Chem. 42, 4849–4856. Doll, K. M., Bender, B. R., Finke, R. G. (2003) The first experimental test of the hypothesis that enzymes have evolved to enhance hydrogen tunneling, J. Am. Chem. Soc. 125, 10877–10884. Kemsley, J. (2003) Enzyme tunneling idea questioned, Chem. Eng. News 81(38), 29–30.
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Part V
Proton Conduction in Biology The motion of protons from one place to another is important in several areas of biochemistry and biology, particularly in bioenergetics where transmembrane proton-transport is a mechanism of energy storage and energy transduction as in the synthesis of high-energy molecules from a pre-established proton gradient. In enzyme action, there are other proton relay systems as well, for example in the transport of protons out of the active site of carbonic anhydrase. A number of these phenomena are explored elsewhere in these volumes. The sole paper in this section is Gutman and Nachliel’s elegant examination of a paradigmatic system, the motion of protons at the surface of proteins in general and in such special circumstances as protein/membrane interfaces.
Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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Proton Transfer at the Protein/Water Interface Menachem Gutman and Esther Nachliel 20.1
Introduction
The bulk to surface proton transfer is the most voluminous of all reactions in the biosphere. Each O2 molecule generated by the chloroplasts is coupled with 20 moles of H3 Oþ ions, which are sequentially taken up and released by membranal enzymes. Similarly, the mitochondrial oxidative phosphorylation is operated by a coupled cross-membranal proton flux, which is comparable in its number of protons to that of the photosynthesis process. This high proton flux has been, for a long time, a subject of intensive biochemical–biophysical research, and each level of refinement of the mechanism generated a new set of experimental/theoretical uncertainties. One line of research was aimed at elucidating the contribution of geometric features and the special physical properties of the reaction space on the mechanism of proton transfer near the surface. The other was focused on the proton transfer events at specific loci on the membrane or on proteins where the proton pumping activity is located. In the present chapter we shall discuss both approaches, with emphasis on the new possibilities opened up by the prevalence of structural information and the ability to reconstruct in silico complex chemical processes. The free energy that mitochondria or chloroplasts generate is initially stored in the form of a proton gradient, which is utilized for the synthesis of ATP or other processes. Proton pumps, such as cytochrome c oxidase, are very efficient enzymes, having a turnover number of more than 1000 s1 . Under physiological conditions there is, on average, less than one free proton in a mitochondrion; however, the measured rate constant of proton uptake at a certain step of the catalytic cycle of cytochrome c oxidase is still exceptionally fast, and as high as 2 10 13 M1 s1 [1]. Such a rate is above the theoretical prediction by the Debye–Smoluchowski equation, implying that proton transfer within the cristae of the mitochondria utilizes an accessory mechanism that accelerates the reaction, either by imposing bias forces or high cross section for proton uptake events. Proton transfer reactions inside organelles are also mediated by the diffusion of mobile proton carriers, which facilitate the equilibration between the bulk and the surface. The density of proton Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
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20 Proton Transfer at the Protein/Water Interface
binding sites on the surface of a protein can be high, and the binding residues can form clusters that interact with each other. Thus, the formulation of the dynamics should account for the local conditions, rather than the average distribution of binding sites. The solvated proton is not a point charge; it exists in water in two solvated states of H3 Oþ aq and H5 O2 þ aq and the location of the positive charge is smeared over the complex, as determined by quantum mechanical calculations. Any attempt to predict the location of a proton with 1 A˚ resolution is an ‘overkill’. With the present advances in structural biology, ultra-fast kinetic measurements and computational capabilities, the understanding of the mechanism of proton transfer at the interface should be based on experimental measurements capable of observing molecular events at a real time [2], coupled with an analysis that matches the molecular details of the reaction space. The mechanism of proton transfer at the membrane/bulk interface has been investigated since the acceptance of the Mitchell hypothesis as the paradigm of bioenergetics [3]. The early experiments were based on rather slow reactions, where the electron flux in the respiratory system was used to drive the proton translocation across the mitochondrial membrane [4]. Later, faster reactions were introduced where the triggering was initiated by photochemical reactions, using either the photosynthetic apparatus or the proton translocating reaction of the Bacteriorhodopsin. These systems suffered from a common disadvantage: the inherent complexity of the driving reaction. As a result, there is very detailed information about the mechanism of proton transfer in specific sites [5–11], but the general properties of proton transfer at the surface were lagging behind. To obtain direct experimental measurements of proton transfer at the interface, the protons have to be generated by an external source that is not part of the system under study. The laser induced proton pulse [12–15] is capable of generating a short pulse of a few mM of H3 Oþ , within a nanosecond time frame, perturbing all acid–base equilibria in the reaction space. This technique enabled the monitoring of the reversible protonation of surface groups on the protein and membranes with high time resolution and the determination of the rate constants of these reactions [16–19]. The membrane/protein interface with the bulk is dominated by the discontinuity of the physical chemical properties of the reaction space. On one side of the borderline there is a low viscosity, high dielectric constant matrix where rapid proton diffusion can take place. On the other side of the boundary, there is a low dielectric matrix that is covered by a large number of rigidly fixed charged residues. The dielectric boundary amplifies the electrostatic potential of the fixed charges and, due to their organization on the surface of proteins, a complex pattern of electrostatic potentials is formed. These local fields determine the specific reactivity of the domain, either with free proton or with buffer molecules. In this chapter we shall discuss both the general properties of the interface and the manner in which they affect the kinetics of defined domains. A special complication of proton transfer is the interruption of the proton diffusion by the formation of covalent bonds with the various proton-binding sites. Each site that interacts with a free proton will bind it for a time frame that is propor-
20.2 The Membrane/Protein Surface as a Special Environment
tional to its pK value [13]. The combination of periods; where the proton is diffusing in the solution, is interrupted by the formation of covalent bonds, acquires the proton [2] a nature of ‘‘fly and perch’’ mode of propagation. The various protonbinding sites on the surface are unevenly dispersed, the distance between them being determined by the special structure of biomembranes [20–25] or a protein [2]. Clusters of nearby sites on a protein can serve as highly proton-reactive domains that fulfill special mechanistic roles, like the proton-collecting antenna of the bacteriorhodopsin [25]. For the most recent review see Ref. [26].
20.2
The Membrane/Protein Surface as a Special Environment
The motion of a proton near a protein or a membrane surface differs markedly from its random diffusion in the bulk, thus reflecting the inhomogeneity of the diffusion space. The various modes in which the proximity to the structure affects the ion are discussed below. 20.2.1
The Effect of Dielectric Boundary
The electric charging of a body requires investment of energy, called the selfenergy, E ¼ q 2 =2er, where q is the charge, r is the radius of the body and e is the dielectric constant of the surrounding medium. For a charged particle that is located in a high dielectric matrix at a distance of few nanometers from a low dielectric matrix, its self-energy will vary with the distance from the dielectric boundary. A convenient presentation of the charge’s electrostatic potential and its decay as a function of distance is through the ‘‘image charge’’ model [27]. Consequently, the potential of an ion approaching the membrane is raised through interaction with its imaginary ion, with a charge almost identical located behind the membrane/water interface at the same distance from the interface as the real ion. This function decays very rapidly; for a monovalent ion dissolved in water, the repulsion will exceed the thermal energy only when the ion is less than @4 A˚ from the surface. Thus, the first solvation layer of a neutral membrane can be regarded as ‘‘ion repellent’’ [28]. When the surface carries charges, the ‘‘image charge’’ formalism doubles their electrostatic potential. Thus, charged residues will serve as stronger attractors than the same charge dissolved in water. 20.2.2
The Ordering of the Water by the Surface
The charged residues on the surface of a membrane or proteins minimize their electrostatic potential through immobilization of the dipoles of the nearest water molecule. In parallel, stabilization can be gained through local interactions between adjacent residues with opposite charges. The competition between the two stabilization forces leads to a coupling between the solvation of a phospholipid
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20 Proton Transfer at the Protein/Water Interface
membrane and their internal organization [29]. Accordingly, it is expected that local stress on the membrane, generated at the boundary between the membranal enzymes and the membrane matrix, would modulate the solvation of the phospholipid head-group with a subsequent effect on the diffusion of a proton in that domain. The interaction of the water with the head-groups, was quantitated by the number of ‘nonfreezing’ water molecules per head-group [30], or through the dichroic ratio of the IR spectrum of the water at the interface [31–33]. These observations were also confirmed by molecular dynamics [34]. The extent of water immobilization by the phospho head-group is almost doubled in the presence of cholesterol [30], which acts as a spacer and allows more water molecules to get close enough to the head-group. Considering the high content of cholesterol in the mitochondrial membrane, one can imagine that the ordering of the water along the mitochondrial membrane will be nonhomogeneous. In some regions, the water will be more ordered than in others. This ordering of the water molecules has a direct effect on the dynamics of proton transfer, affecting two parameters, the rate of dissociation and the diffusion coefficient. The Effect of Water on the Rate of Proton Dissociation The dissociation of an acidic residue in water is essentially a downhill proton transfer between the donor and the solvent, and in the case of a large value for DpKa, the reaction can be as fast as a barrier-less reaction [35]. To achieve the maximal rate of the reaction, the proton-donor atom must establish a hydrogen bond with the acceptor, and the reaction then takes place along this bond. As the rate of the reaction can be as fast as the hydroxyl vibration frequency, @60–150 fs [36, 37], it is implicit that, for a fast reaction, the hydrogen bond must be established before the proton transfer event. In the case of proton transfer to water, pre-orientation of a few water molecules is required to stabilize the ejected proton and the conjugated base from which the proton was released. Accordingly, reduction in the availability of free water molecules will reduce the probability of the proton acceptor configurations, and this effect will appear as a reduction in the rate of dissociation. The correlation between the availability of water and the rate constant of proton dissociation was measured in two systems. In one system, the ratio water: methanol of a mixed solution modulated the availability of water [38]. In the other system, made of concentrated electrolyte solutions, the activity of the water was modulated by the salt [39]. The dependence of the measured rate of dissociation [60, 67, 68], either from photoacid or ground state acids, on the activity of the solvent yielded a straight log–log correlation function with respect to the activity of the water 20.2.2.1
kdis ¼ kdis 0 a watern where kdis 0 is the rate measured in pure water and the power n is specific for the dissociated acid. The rate of proton dissociation from the excited pyranine was measured in different bio-environments, such as the inter-bilayer space of multilamellar vesicles [39a]
20.2 The Membrane/Protein Surface as a Special Environment
and the heme-binding site of apomyoglobin and another protein [39b]. The results clearly indicated that the water molecules in such micro-spaces were highly immobilized, having a chemical potential well below that of bulk water. For example, in a small cavity such as the heme-binding site, the activity of the water was found to be as low as a water ¼ 0:6. The activity of the water in the inter-bilayer space of multilamellar phospholipid vesicles was determined to be of the order of a water ¼ 0:8– 0.9, depending on the nature of the head-group and the width of the aqueous layer. Thus, the interaction between acidic residues and the water located on a surface, which is limited to the innermost solvation shells [2], can alter its tendency to dissociate. The Effect of Water Immobilization on the Diffusion of a Proton The mechanism of proton diffusion, usually referred as the Grotthuss mechanism, differs from that of other ions. Instead of a self-diffusion process, where the mass and the charge are inseparable, the proton diffusion is the movement of the protonic charge independently from the transport of the particle. This mode of propagation leads to the diffusion of the proton DHþ ¼ 9:3 105 cm 2 s1 being faster than the diffusion of all other ions (D a 2 105 cm 2 s1 ), and of the selfdiffusion of the water molecules in water as a solvent (for details see Ref. [40]). The solvated proton assumes two basic structures in water: H3 Oþ aq and H5 O2 þ aq , which have almost the same potential [41, 42]. The diffusion of the proton in water is a sequence of transitions between these two states of the solvated proton, where the initiation of the transition is made by the random motion of water molecules in the second solvation shell of the proton [41, 43]. Naturally, the immobilization of the water molecules, which are in contact with the membrane or the protein’s surface, will reduce their rate of orientation, leading to diminished diffusivity of the proton. Indeed, measurements of proton diffusion in immobilized water, ice, yielded a diffusion coefficient that is @30% of the value in water at the same temperature [44]. It must be recalled that the ordering of the water next to the surface is limited to a few water molecules (4–7) per head-group, hardly enough to cover the surface with a continuous layer. Thus, the innermost solvation layer can exhibit lateral inhomogeneity, where ordered water forms patches over the surface of the membrane. Under such conditions, the most efficient trajectory for proton transfer between two sites on the surface will follow through the less ordered water molecules. This pathway may be longer, yet the overall passage time may be shorter. Indeed, direct measurements of proton dissociation in the ultra-thin water layers, only 8–11 A˚ thick, that are interspaced between the phospholipids layers in multilamellar vesicles, yielded values of 8–9 105 cm 2 s1 [45]. The diffusion coefficient of a particle, diffusing in a 3D space, is given by the expression D ¼ ðl 2 nÞ=6 where l is the length of the random step and n is the frequency (in s1 units) of making a random step. For a particle that is diffusing in a nonhomogeneous space, made for example of water and fixed proton binding sites, the apparent diffusion coefficient becomes a function of the observation time. For a proton in bulk water, l is the distance between the oxygen atoms in 20.2.2.2
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20 Proton Transfer at the Protein/Water Interface
the water and n is the frequency of proton transfer between them [41, 45]. The diffusion coefficient of a proton in the inter-bilayer space, when measured with subnanosecond resolution, was comparable with that in water [45]. In such a short time frame, encounters of the proton with the surface sites depleted the free proton population. When the observation time is longer, or measured at steady state [46], more protons are removed from the system and another process may take place: the bound protons dissociate at the frequency of kdiss and replenish the diffusing population. In this case, the value l will be the average distance between the proton binding sites. This mechanism makes a negligible contribution to proton diffusion. The calculated diffusion coefficient, using the experimental conditions of Zhang (l @ 5 A˚, kdiss @ 10 6 s1 , compatible with pK @ 4), is as small as @109 cm 2 s1 , four orders of magnitude smaller than the measured value 1:5 105 cm 2 s1 [46]. Accordingly, it must be concluded that the surface groups, when sufficiently close together, can very efficiently exchange a proton among themselves. This feature was noticed by Zundel and others, who termed it ‘proton polarizability’ [47, 48]. When the local configuration of proton binding sites can form a sequence of states where a proton is in more than one location, there is a rapid transition between them, at a frequency comparable to that of the IR spectrum. When the proximity between the sites and their pK values are suitable, the proton exchange reactions become intensive, leading to the appearance of a continuum IR absorption band.
20.3
The Electrostatic Potential Near the Surface
Biomembranes and proteins carry a large number of charges on their surface, generating a complex pattern of electrostatic interactions. In the case of proteins, where positive and negative residues can be packed together, the electrostatic potential is extremely nonhomogeneous, and local domains that differ in their charges from the surrounding structure are commonly found. Such local domains account for the kinetic peculiarities of the superoxide dismutase, where a local positive domain accelerates by funneling the encounter with the negative substrate [50]. Phospholipid membranes are more homogeneous in nature, due to the prevalence of the zwitterionic head-group of the PC, which contributes most of the membrane’s mass. Langner and coworkers [51] used a variety of experimental techniques to study the effect of the monovalent lipid phosphtidylinositol (PI) and the trivalent lipid phosphtidylinositol 4,5-diphosphate (PIP2) on the electric potential adjacent to the bilayer membrane. When the membranes were formed from a mixture of PI and the zwitterionic lipid phosphatidyl choline (PC), the smeared charge theory of Gouy–Chapman–Stern adequately described the dependence of the potential on the distance from the membrane, the density of the negative charges and the screening electrolyte concentrations. However, with PC/PIP2 membranes, anionic probes reported less negative potentials than the counterions. The deviations of the experimental results from the theoretical predictions were
20.4 The Effect of the Geometry on the Bulk-surface Proton Transfer Reaction
greater for the counterions than for the anions. To improve the predictions, the authors formulated a consistent statistical mechanical theory that takes into account three effects which were ignored in the Gouy–Chapman–Stern theory: the finite size of the ions in the double layer, the electrical interaction between pairs of ions (correlation effects), and the mobile discrete nature of the surface charges. The improved model could predict the experimental observations. However, it must be stressed that deviations from the Gouy–Chapman–Stern theory are significant only for trivalent lipid headgroups, and are greater for anions than for counterions. To test the limit of accuracy of the Gouy–Chapman–Stern theory, McLaughlin and coworkers [52] made a comparison between the predictions of the model with precise nonlinear Poisson–Boltzmann calculations of the electrostatic potentials in the aqueous phase adjacent to a molecular model of a phospholipid bilayers (phosphatidyl choline plus acidic lipids suspended in 0.1 M monovalent salt). When the bilayers contained less than 11% acidic lipid, the equipotential surfaces having a value of kB T were sufficiently separated from each other to form discrete domes centered above the anionic residues. When the bilayers contained more than 25% acidic lipid, the 25 mV equipotential profiles had merged into an essentially flat surface and agreed well with the values calculated using the Gouy–Chapman theory. The membrane surface is not perfectly flat and ions, due to the Van-derWaals repulsion, cannot get closer to the polar headgroups than 2 A˚. However, these refined features hardly affect the calculated potential in the aqueous phase. Thus, the electrostatic potential at the interface can be calculated with high accuracy, using either the Gouy–Chapman–Stern method or the precise nonlinear Poisson–Boltzmann equations, depending on the level of structural accuracy of the domain under study.
20.4
The Effect of the Geometry on the Bulk-surface Proton Transfer Reaction
The protonation of a given site on a surface can proceed by two pathways. The proton can either react directly with the site, propagating to the target in a three dimensional (3D) diffusion, or it may first adsorb to the surface, which is huge with respect to the target, and then propagate in a 2D mechanism until it encounters its target. This mode of reaction was first introduced in the classical manuscript of Adam and Delbru¨ck [53] and later developed by Berg and Purcell [54]. During a random three-dimensional walk in the bulk, a particle can encounter a surface many times. For a particle that is located at a given time at a distance of l i from a surface, there is a certain probability that, during a random walk, it will reencounter with the surface. This problem was treated by Berg and Purcell, who determined that the average number (n) of repeated encounters between the particle and the surface, before being ‘‘lost in the bulk’’, is given by by n ¼ R=l i [54]. This expression implies that a large surface will be a better target than a small one. A convex surface, as we find in the folding of the mitochondrial inner membrane, will even increase the probability of the particle as the surface engulfs the space
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20 Proton Transfer at the Protein/Water Interface
where the particle diffuses. This mechanism accelerates the reaction between a solute and a site on the surface by geometrical considerations, where the diffusion is all in 3D space. The second mechanism by which a particle can encounter a target on a surface is based on the concept of ‘‘reduction of dimensionality’’ introduced by Adam and Delbru¨ck [53]. The mechanism consists of two steps. At first, the particle encounters the surface by 3D diffusion and, due to attracting force, concentrates at the interface. The enhanced number of particles increases the probability of encounter with the target, which is further amplified by the higher efficiency of search on a 2D surface. The efficiency of the overall process is determined by two terms, the magnitude of the attractive force and the ratio between the diffusion coefficients in the 2D and 3D spaces. An intensive attraction will increase the density of particles at the interface, but may also reduce the frequency at which they execute a random stepping. As was argued by Berg and Purcell, for a ratio Dð2Þ =Dð3Þ ¼ 0:1 the attraction to the surface should be more intensive than 3 kcal mol1 , otherwise the surface will not facilitate the encounter between the particle and the target. For a proton near a phospholipid membrane, its tendency to concentrate near a negatively charged surface will lead to the formation of a covalent bond with the carboxylates on the surface, and in such state their diffusivity is zero. The macroscopic diffusion that Unwin and coworkers [46, 55] measured consisted of a binding of protons to the surface carboxylates providing the attractive force, and diffusion through the interspacing water molecules adjacent to the membrane’s surface. Stuchebrukchov and coworkers formulated a comprehensive reaction mechanism [56, 57]. According to this phenomenological model, the interaction of the low-pK protonable groups (carboxylates) with protons corresponds to the force detaining the particles near the surface, and their diffusion, either through the bulk or by the ‘proton polarizability’ mechanism of Zundel, corresponds to twodimensional diffusion. The model enabled the formulation of time and length criteria defining the coupling between a source and a sink on the membrane surface, while protons generated by the source are fully equilibrated with the bulk. What is more, the model accounts well for the role of mobile buffers on the dynamics of bulk-surface proton transfer and for the delayed presence of proton near the surface of Purple Membrane [10, 58, 59]. Because of its empirical compatibility with the experimental observations, the model merits elaboration, defining its specific features. The membrane of Stuchebrukchov’s model is an infinite surface, where the multitude of proton binding sites (carboxylates with pK ¼ 5) is represented by a density function ðsÞ. The dwell time of a proton on any of the sites is determined by the pK ðtdwell ¼ K dis kon Þ, but during this time interval the proton can diffuse on the surface with a diffusion coefficient that is @10% of the bulk value (Ds @ 0:1 Db ), screening an area with a radius L s . On the surface, there is a proton-channel acting either as an absorbing sink, or a source which affects the immediate proton concentration, both at the surface and in the solution. The bulk phase in this model is an infinite reservoir, which is sufficiently far from the proton-consuming cluster to satisfy the demand dC=dx ¼ 0, a definition that is based on a chemical function
20.4 The Effect of the Geometry on the Bulk-surface Proton Transfer Reaction
and not on physical properties. Encounter of a proton with the channel proceeds by two independent pathways; the direct collision of a free diffusing proton with the channel, or through surface diffusion. The former is a classical three-dimensional process, while the latter is described by an equation that incorporates the reduced dimensionality of the reaction space: ks ¼ 2pDs seq =lnðR c =r0 Þ The term R c denotes the capture radius; the distance from the target at which the probability of capture decreases to zero and r0 is the radius of the channel. Due to the logarithmic function, the radius of the channel r0 has a minor effect on the rate. The quantitation of the contribution of the surface diffusion to the overall flux is given by the term R 0 , which is the radius of channel that will support the same flux given that only the three-dimensional mechanism is operating. The typical values characterizing the proton flux in such a system are summarized in Table 20.1. The values in the table are characteristics for a negatively charged membrane suspended in unbuffered aqueous solution. The dwell time of a proton (@4 ms) was estimated from the pK of the proton binding sites [60]. During this time frame, the proton scans the surface sites that are within a radius of @600 A˚. Assuming that the surface carries a proton sink, which irreversibly consumes protons (or alternatively is a source of free protons), then the combination of repeated encounters plus the scanning of the surface during each encounter ðtdwell Þ increases the effective capture range of the channel to 17 mm, a value that exceeds the dimensions of many sub-cellular organelles. The flux supported by the surface diffusion is so high that, in order to support the same rate just by protons coming directly from the bulk, the pore should be as large as 2 mm in radius. This value is @104 times larger than the real size of a protonic channel (like gramicidin) which is @2 A˚. It is of interest to point out that the distance defined by Stuchebrukchov as the border with the bulk (@170 mm), is comparable to the width of the unstirred layer as measured by Pohl and coworkers (@200 mm) [61, 62]. In the presence of buffers, most of the proton flux is carried by the diffusion of Table 20.1. The characteristics parameters for the bulk-surface proton transfer in the absence of soluble buffers.
Parameter
Value
s (density of sites) tdwell (average time of a proton on the surface) L s (radius of search over the surface) R c (effective capture radius) R 0 (real radius of channel) R c =r0 (efficiency factor) L 0 (surface to bulk distance) teq (equilibration time between surface and bulk)
0.01 A˚2 4 ms 660 A˚ 17 mm 2 mm @10 4 170 mm @1 s
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20 Proton Transfer at the Protein/Water Interface
the buffer molecules. Indeed, the diffusion coefficient of buffer molecules is @10– 20% of that of the free proton yet the physiological concentration of the buffers (10–30 mM) exceeds the free proton concentration by 5 orders of magnitude. Consequently, in the presence of increasing buffer concentrations, the proton flux will shift from diffusion of free proton to a new regime, where the proton transfer is totally mediated by the diffusion of buffer molecules. This mechanism was first described by Junge and McLaughlin [63] and confirmed at the level of physiological systems. Vaughan-Jones and coworkers carried out measurements with single ventricular myocyte cells that were isolated from the rat, guinea pig, or rabbit. These measurements confirmed the accuracy of the Junge–McLaughlin equation [63] in predicting the rate of spreading of acidity on the surface and the role of the bicarbonate as a proton carrier [64]. It must be recalled that the model of Stuchebrukchov is phenomenological in nature and many discrete steps and events have been ‘lumped together’. The understanding of all intricate relations between the rate constants of the chemical reaction of the proton binding sites with free proton and the macroscopic descriptors calls for molecular modeling and direct measurements, where the local properties of the reaction space must be included in the analysis. Accordingly, the Stuchebrukchov mechanism can be taken as a guideline and its predictions are approximations. The basic feature derived by the model of Stuchebrukchov, that transient protonation of surface groups accelerated the migration of protons on the surface has been confirmed in real time measurements carried out by Nachliel and Gutman [17]. Figure 20.1 depicts time-resolved measurements of the protonation of the in-
Figure 20.1. Transient protonation of Bromocresol Green adsorbed on mixed micelles. The reaction was carried out at pH 7:3 G 0:1 in a solution containing 500 mM Bromocresol Green, 1 mM of the proton emitter 2-naphthol-3,6-disulfonate, 500 mM micellar concentration of Brij-58 (40 mg mL1 ),
and 3 mM of phospholipids. The transient protonation was measured at 633 nm through an optical path of 2.0 mm: (A) control, no phospholipids were added; (B) phosphatidylcholine; (C) phosphatidylserine; (D) phosphatidic acid.
20.5 Direct Measurements of Proton Transfer at an Interface
dicator Bromocresol Green, adsorbed on a neutral micelle, by a proton released in the bulk using a water-soluble photoacid. The kinetics were measured either in the absence of phospholipids (curve A) or in the presence of phosphatidylcholine (B), phosphatidylserine (C) and phosphatidic acid (D). As seen in the figure, the zwitterionic residues (PC), that can bind the proton for only a few nanoseconds, enhanced the protonation of the dye, confirming the mechanism of enhanced proton transfer between adjacent proton binding sites. On the other hand, residues with pK values that will retain the proton in a bound state for time frames that are comparable with the observation time appear as proton traps and reduce the probability of the proton reacting with the site under study.
20.5
Direct Measurements of Proton Transfer at an Interface 20.5.1
A Model System: Proton Transfer Between Adjacent Sites on Fluorescein The Rate Constants of Proton Transfer Between Nearby Sites The fluorescein molecule is a suitable model system for monitoring the mechanism of proton transfer between adjacent sites as it has two distinct proton binding sites @6 A˚ apart, each having a distinct pK and spectral properties. The first is the oxyanion attached to the xanthene ring, whose protonation is associated with a spectral shift of the dye, while the second is the carboxylate on the benzene ring. The protonation of this site has no effect on the absorption spectrum of the dye (Scheme 20.1). 20.5.1.1
The structure of fluorescein. The OH moiety of the xanthene ring controls the spectrum of the chromophore. In the ionized state, the dye has an intensive absorption at lmax ¼ 496 nm. The carboxylate of the benzene ring does not affect the spectrum of the dye.
Scheme 20.1.
The reversible protonation of the dye was measured in the time resolved domain using photoexcited pyranine as a proton emitter [65]. The rate constants of the various proton transfer reactions were determined by kinetic analysis [66, 66a] and the results are given in Table 20.2. The rate constants determined by the analysis are subjected to quantitative evaluation by comparison with the predicted value according to the Debye–Smolu-
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20 Proton Transfer at the Protein/Water Interface Table 20.2. The rate constants of proton transfer as measured for the pyranine fluorescein system in water, D2 O and in 100 mM NaCl at 25 C. All rate constants are given in M1 s1 .
Reaction
H2 O (MC1 sC1 )
D2 O (MC1 sC1 )
KIE
100 mM NaCl (MC1 sC1 )
Ea (kcal molC1 ) in H2 O
FLU þ Hþ COO þ Hþ COOH þ FLU
2:5 10 10 2:5 10 10 23:3 10 10
1:7 10 10 1:7 10 10 0:43 10 10
1.47 1.47 54.2
1:6 10 10 1:6 10 10 6:5 10 10
3.3 3.3 11.0
chowski equation, for the rate constant of the time independ diffusion controlled reaction an expression that correlates the rate constant with the radius of encounter ðSR j; i Þ, the diffusion coefficients of the reactants SDj:i and the Avogadro number Nav [60, 67, 68]. k max ¼ ð4pNav =1000ÞSR j; i SDj:i
ð20:1Þ
The rate constants corresponding to the diffusion-controlled reaction between a free proton and acceptor and the rate constants were found to be compatible with the values predicted by the Debye–Smoluchowski equation for diffusion-controlled reactions (Table 20.2 rows 1 and 2), and so were the reactions that describe a collisional proton transfer between two free-diffusing reactants (not shown). In contrast with these reactions, the rate constant calculated for the intra-Coulomb cage proton transfer (Table 20.2, bottom row) had an extremely high value. The rate constant calculated by the Debye–Smoluchowski equation for a vanishing ionic strength I ! 0, is k @ 3 10 9 M1 s1 . This value is smaller by two orders of magnitude than the measured one (2:3 10 11 M1 s1 ). Such a fast reaction negates a mechanism based on encounter between two fluorescein molecules. Accordingly, the mechanism must be identified as an intra-Coulomb cage proton transfer, where the proton is first released from the benzene’s carboxylate and then reacts preferentially with the nearest proton-binding site, the chromophore’s oxyanion that is 6.7 A˚ apart. It should be stressed that the magnitude and the units of the reaction utilize second order rate constant units. For these reasons, the calculated rate constant of the intra-Coulomb cage proton transfer is suitable for comparison between measurements carried out under varying conditions (temperature, ionic strength, D2 O etc.), reflecting how the efficiency of the process is affected by the experimental conditions. A high rate constant implies that the pathway competes successfully with a parallel pathway, where the proton is dispersed into the bulk of the solution before re-encounter with the Coulomb cage of the fluorescein. The kinetic features recorded for the intra-Coulomb cage proton transfer between the proton binding sites were reconfirmed with other dyes resembling the
20.5 Direct Measurements of Proton Transfer at an Interface Table 20.3. The solvent effect on the intra-Coulombic rate constant, determined by kinetic analysis of signals recorded at varying pH values. The second and third columns denote the rate constant for the proton transfer from the carboxylate to the chromophore as measured in water and in 100 mM NaCl. The column at the right denotes the KIE for the proton transfer reaction from the carboxylate to the chromophore.
Compound
Fluorescein Rhodol green 5 carboxy fluorescein 6 carboxy fluorescein
Rate constant
KIE
Water
100 mM NaCl
2.5 1011 2. 1012 9.3 1011 1. 1012
6.5 1010 1. 1011 4. 1011 2.5 1011
54 105 22.5 38
fluorescein molecule. Careful measurements were carried out with Rhodol green, and the 6 and 5 di-carboxy-fluorescein. The rate constants for the intra-Coulomb cage proton transfer were calculated. As seen in Table 20.3, the rate constant for the intra proton binding site are high, the screening electrolyte shows the reaction and the kinetic isotope effect exceeds 20. Proton Transfer Inside the Coulomb Cage The intra-Coulomb-cage proton transfer differs from the diffusion controlled reactions by its kinetic and thermodynamic parameters. The kinetic isotope effect measured for the intra-Coulomb-cage proton transfer is extremely high @50, sigpffiffiffi nificantly larger than the value of 2 measured for the reaction controlled by the diffusion of the proton. The same pattern is noticed when comparing the activation energies of the reactions. The protonation of the two proton binding sites of the fluorescein by free-diffusing proton (Ea @ 3 kcal mol1 ) is compatible with the temperature dependence of the water’s viscosity (Ea ¼ 4:2 kcal mol1 ). In contrast with these values, the intra-Coulomb-cage proton transfer has significantly higher activation energy. This is a clear indication of a different reaction mechanism. Addition of a screening electrolyte reduced the diffusion-controlled reactions of free proton in accordance with the Debye–Smoluchowski equation. The intra-Coulomb-cage proton transfer was much more sensitive to the screening effect, which is another indication of a reaction mechanism that differs from the homogeneous diffusion-controlled reactions [66a, 66b]. The high activation energy and the large kinetic isotope effect values assigned to the intra-Coulomb-cage proton transfer are characteristic of proton transfer through a hydrogen bond that is slightly stretched beyond its equilibrium length [69, 70]. Accordingly, we investigated whether the solute molecule, the fluorescein, 20.5.1.2
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20 Proton Transfer at the Protein/Water Interface
may affect the water molecules in its immediate vicinity, searching for the presence of hydrogen-bonded water molecules that may serve as pathways through which the proton can propagate from the carboxylate to the oxyanion. The distance between the two proton binding sites of the dye, 6.7 A˚, is too large to support a direct proton transfer between them. Consequently, the proton transfer involves the water as a carrier, which makes it suitable to characterize the water in the inner solvation shell of solutes. For a study of the fluorescein–water interactions, the fluorescein molecule with a single proton attached to the carboxylate moiety, in the presence of 639 water molecules and one Naþ , was simulated by molecular dynamics for 500 ps [66b]. The protonated carboxyl moiety of the fluorescein was hydrogen-bonded with water for 95% of the simulation time, and with an average of 5 hydrogen bonds. The acceptor oxygen atoms, attached to the xanthene rings, were permanently hydrogenbonded with the water, averaging 4 hydrogen bonds. The hydrogen bonds between the dye and the water had a lifetime that was @2 times longer (5.80 ps and 5.13 ps for the carboxylate and the chromophore, respectively) than the average hydrogen bond between water molecules in the bulk (2.94 ps). In the presence of so many water molecules, the proton can propagate from the donor to the acceptor by more than one trajectory. What is more, once the proton dissociates from the carboxylic moiety, it will affect the local structure of the water, by forming either H9 O4 þ or H5 O2 þ species. For these reasons, the search was limited to the water molecules in the vicinity of the dye that are at a suitable distance to form a hydrogen-bonded array, using the default value of the GROMACS program (r a 3:5 A˚) for the length of the hydrogen bond. The search was carried out with respect to the two oxyanions of the chromophore, and 10 superpositioned trajectories are presented in Fig. 20.2. The connection of the two sites by the water molecules is a flexible yet persistent feature. The length of the path varies with time, even within a 1 ps time-frame, and so does the shape of the path. Yet in all cases, the path remained close to the surface of the molecule, and did not extend out of the Coulomb cage of the molecule, which extends 14 A˚ into the bulk. The order imposed by the fluorescein on the inner solvation layer may account for the special features of the intra-Coulomb-cage proton transfer reactions. The proton transfer between two water molecules is regulated by the motion of the water molecules in the whole structure of the solvated proton; the hydrogen bonds in the second and third layer are rearranged, destabilizing bonds are broken and stabilizing ones are formed, and during the passage of the protonic charge, the hydrogen bonds are temporarily constricted [43]. These local rearrangements of structure are hampered by the structure imposed by the negative charges of the anion, thus forcing the proton transfer to take place in a more rigid environment where the OaO distances are larger than 2.4 A˚. As a result, both the activation energy and the kinetic isotope effect (KIE) increase. Scheiner and coworkers [70, 71] have investigated the effect of the interatomic distance on the activation energy and the KIE of proton transfer. These quantum mechanical calculations show that the energy barrier for proton transfer increases with the distance between the oxygen atoms of the water, reaching a
20.5 Direct Measurements of Proton Transfer at an Interface
Figure 20.2. The array of water molecules that are at a hydrogen bond distance and form a possible proton-conducting pathway between the protonated state of the carboxylate (donor) on the benzene ring of fluorescein and the
proton acceptor oxygen atoms on the xanthene ring. 10 trajectories are superpositioned. The figure also exhibiteds the structural fluctuations of the dye’s structure.
value of 15–20 kcal mol1 at a separation of @2.8 A˚ [70, 71]. Furthermore, under these conditions, the proton transfer operates both by a classical mechanism (transition state theory) and by tunneling, thus leading under certain conditions to a very high KIE [69]. In bulk water, the length of the hydrogen bond in the Eigen or the Zundel structures is of the order of 2.4 A˚ and the measured activation energy represents the reorganization of the solvent [43]. When the water molecules are held by the ordering forces of the charged scaffolding, the reaction operates under a different regime, where the concerted motion of the water molecule, as required to facilitate the proton transfer, is restricted. The rate-limiting step is shifted from the organization of the solvent to the passage of the proton, with subsequent enhancement of activation energy and KIE. A question to be answered is why the proton remains in the vicinity of the acceptor water molecule (which is part of the interconnecting trajectory, as in Fig. 20.2) instead of escaping to the bulk. This can be explained by the presence of the intensive electrostatic potential that detains the proton within the space defined by the Coulomb cage, as depicted in Fig. 20.3. This figure depicts the 1 kBol T/e boundary around the Rhodol green molecule either at vanishing ionic strength or at 100 mM NaCl. At low ionic strength, the Coulomb cage is almost spheric and the acceptor moiety of the chromophore, the amine, is well under the ‘‘umbrella’’ of the negative charged Coulomb cage. At higher ionic strength, the cage had contracted and the amine moiety is protruding out of the cage. As a result, a proton
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Figure 20.3. The electrostatic potential surrounding the Rhodol green molecule (at 1 kBol T/e) either in vanishing ionic strength (frame A) or in 100 mM NaCl (frame B). Please note that at high ionic strength the Coulomb cage had contracted, leaving the
amine moiety of the dye, which serves as a proton acceptor, protruding out of the Coulomb cage, forcing the passage of a proton from the carboxylates on the benzene ring towards the acceptor site, to escape out of the attractive Coulomb cage.
transfer from the donor residues, the carboxylate on the benzene ring, to the acceptor must climb up in the potential field, before it can interact with the acceptor site. This energy-barrier accounts for the marked effect of the screening electrolyte on the rate constant of the intra-Coulomb cage reaction. In the case of the di-carboxylate fluorescein, where the molecule bears a charge of Z ¼ 3, the Coulomb cage is large enough, both in low and high ionic strength, to allow proton transfer without breaching out of the cage. For this reason, the effect of the screening electrolyte on the intra-Coulomb cage reaction is much smaller. The diffusion out of the Coulomb cage is an uphill diffusion with escape time of the order of hundreds of picoseconds [67], while the intra-Coulomb-cage reaction hardly overcomes an electrostatic barrier. Thus, while the released proton attempts to diffuse out of the Coulomb cage, there are ample opportunities to propagate through the rigidified water molecules. The collapse of the local electrostatic potential brought about by high concentrations of electrolyte is consistent with our interpretation. In the presence of 100 mM NaCl, the ionic screening practically abolishes the wrapping Coulomb cage. In the absence of the retarding potential, the proton can readily disperse to the bulk and the intra-Coulomb-cage reaction is slowed to a level that reflects the proximity of the acceptor site to the site of release. 20.5.2
Direct Measurements of Proton Transfer Between Bulk and Surface Groups
Physically, the bulk phase of the solution is as close as a solute can get to a surface before it is affected by the image charges or the partial immobilization of the water molecules. We can surely assume that some 10–15 A˚ from the surface, equivalent to the third to fourth solvation layer, the solvent can be regarded as ‘‘bulk’’ [72, 73].
20.5 Direct Measurements of Proton Transfer at an Interface
A system suitable for measuring the rate constants of proton transfer between bulk and surface should be made on a single bilayer, which is fully equilibrated with bulk water on both sides, and should contain a marker present at very low content, yet sensitive enough to report the interaction of the membrane with free proton. A phospholipid black lipid membrane impregnated with a small amount of monensin meets these experimental requirements. Monensin is an ionophore that supports an electroneutral proton/Naþ exchange across a membrane. The kinetics of the exchange were measured by a system consisting of a black lipid membrane equilibrated with monensin and NaCl, with the photoacid pyranine added to the compartment facing one side of the membrane. When a laser pulse excited the pyranine, one face of the membrane was selectively acidified, and the released protons reacted with the membrane, thus initiating the exchange reaction. The first step is the formation of an unstable, ternary complex MonHNaþ that dissociates into MonH and Naþ ion. This enriches the MonH species concentration on one side of the membrane, and the perturbation is propagated to the other side by diffusion of MonH to one side of the back flux of MonNa. Each species, on arriving at the other side of the membrane, equilibrates with the bulk, releasing/binding either proton or Naþ ions. Due to the short duration of the perturbation, some 1–2 ms during which the free proton concentration is higher than the pre-equilibrium state, the exchange reaction is highly synchronized and can be followed by monitoring the capacitance current of the system [74]. The selective protonation of one side of the membrane consists, physically, of the charging of one side of a capacitor and the propagation of the charge from one side to the other is a discharging event. By monitoring the current passing through a short-circuit which connects the two faces of the membrane, the charge dynamics can be observed and the chemical reactions associated with the charge translocation can be deduced. The results of capacitance current, measured with increasing Naþ concentrations, are presented in Fig. 20.4. As the reaction mechanism hinges on the protonation of the MonNa species, the shape of the signal varies with the Naþ concentration. At low Naþ (10 mM), the signal is small, and increases in magnitude and shape as more Naþ ions are present. Above 100 mM, the signals are constant in shape and size. The perturbation has been expressed as a series of chemical reactions taking place simultaneously on the two sides of the membrane; it was converted into a set of chemical rate equations, and integrated over time to reconstruct the time derivative of the charge imbalance between the two faces of the membrane. The computed current and its variation with the Naþ concentration are presented in the figure. The accuracy of the reconstruction is so high as to fall within the narrow band set by the electronic noise. The rate constants determined for the binding and release of the ions are given in Table 20.4. The rate constants for the proton transfer between surface groups and the bulk, as well as the collisional proton transfer between the protonated surface sites and the soluble proton acceptors, are of the order of diffusion controlled reactions, with no indication as to an energy barrier that retains the free proton near the surface. The rate constants of the MonNa or the Mo imply that both species are located on the surface of the membrane, with the proton-binding site constantly exposed to
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20 Proton Transfer at the Protein/Water Interface
Figure 20.4. Capacitance current measured with monensin-impregnated, black lipid membrane subjected to pulse protonation of one side of the membrane. The traces represent the charge flux, already expressed in molar units as function of time. The signals
were measured in 100 mM choline chloride as a conducting electrolyte, and in the presence of 10, 50 and 210 mM NaCl. Each experimental curve was reconstructed by integration of differential rate equations corresponding with the reaction mechanism. For details see [24].
Table 20.4. The rate constants of proton transfer bulk and surface. The rate constants reproduce the experimental capacitance currents presented in Fig. 20.3. Data taken from Ref. [74].
Reaction
Rate constant (MC1 sC1 )
MonNa þ Hþ Mon þ Hþ Ps þ Hþ PsH þ FO MonH þ FO
1 10 10 1 10 10 1 10 10 1 10 10 1:2 10 10
Abbreviations: Monensin (Mon ); Phosphatidyl serine (Ps ); Pyranine (FO ).
20.6 Proton Transfer at the Surface of a Protein
the bulk. To confirm this assumption, Ben-Tal and coworkers calculated the electrostatic potential of the various complexes of monensin, their solvation energy and the free energy changes as the complex is inserted into a slab of a low dielectric constant matter [75]. The results of these calculations, based on the structure of the MonNa crystals, confirmed the conclusions derived by the kinetic analysis, i.e. the stable location of the monensin in the membrane is at the water membrane interface and is oriented so that the proton-binding site is preferentially exposed to the bulk.
20.6
Proton Transfer at the Surface of a Protein
The scarcity of free proton in the cytoplasmic space of bacteria, eukaryotic cells or the mitochondrial matrix imposes a time limitation on the rate at which a free proton can diffuse towards the enzyme’s active sites, so that the system appears to be rate-limited by the availability of free protons. However, the measured rates still seem to exceed the predicted values, for a review see Ref. [26], indicating that the protein’s surface participates in channeling the proton to the orifice of the protonconducting channels. This case was first demonstrated with bacteriorhodopsin, a membranal protein which utilizes the energy of a photon, absorbed by its chromophore, to drive protons from the cytoplasmic space of the bacteria to the external space. The late phases of the bacteriorhodopsin’s photocycle are kinetically limited by the intake of proton from the cytoplasmic side of the membrane, and by delivery of the proton to a carboxylate of residue D96, located below the surface of the protein. The carboxylate is connected to the surface through a shaft, which is too narrow to accommodate a water molecule [76]. To let the proton through, the shaft must expand to let the water in, an energy-consuming step estimated to be some 10–20 kcal mol1 . To overcome this barrier, the protein retains, next to the shaft, a reservoir of available space, stored as micro-cavities [77]. The fusion of the microcavities with the shaft assists in its expansion, lowering the required investment of energy by @2.5 kcal mol1 . Yet, even that makes the lifetime of the open state very short. To assure a rapid proton transfer to the D96, when the ‘‘moment of grace’’ is coming, the protein must retain an available proton in the immediate vicinity of the shaft’s opening. The local proton storage is provided by the carboxylate of D38, which is partially exposed to the surface and, due to its semi-hydrophobic environment, has a rather high pK value (pK ¼ 5:1) [25]. The partial exposure of D38 renders its reaction with free proton somewhat slow. To ensure that whenever the shaft is expanded, the proton will be available, an accessory mechanism is required. This enhancement of protonation of D38 is attained by a cluster of three carboxylates that assist in the protonation of D38 (the proton-collecting antenna) [78]. The proton-collecting antenna was first identified in studies carried out with the ground state form of the protein, which is a resting configuration. To establish the
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20 Proton Transfer at the Protein/Water Interface
physiological role of the antenna, evidence must be supported on the monitoring of the process on the surface of the M state, which is a short-time intermediate where the Schiff-base has lost its proton and is re-protonated from the cytoplasmic side. To monitor the dynamics at this state of the photocycle Nachliel and coworkers [79] used mutated BR preparation D96N and a triple mutant (D96G/ F171C/F219L). Both mutations permit, under steady background illumination, the accumulation of the late M state. The protein, while being kept in the M state, was subjected to reversible pulse protonation caused by repeated excitation of pyranine present in the reaction mixture, and the re-protonation dynamics of the pyranine anion were recorded and subjected to kinetic analysis. The calculated rate constants indicated that, in the late M state of bacteriorhodopsin, there is an efficient mechanism of proton delivery to the unoccupied and most basic residue on its cytoplasmic surface (D38), see Fig. 20.5. This machinery was even more efficient in the M state than in the ground state (BR) configuration of the protein. The presence of a proton-collecting antenna has been demonstrated for the matrix surface of bovine cytochrome c oxidase [26] and the intracellular surface of the Rhodobacter sphaeroides cytochrome oxidase [65]. These proteins operate under temporal restriction, where the protein must pump protons at a rate compatible with the physiological requirements of the cell. On the other hand, membranal proteins that utilize the proton-motive force for driving a slow reaction, whose rate-limiting step is the binding and release of the substrate, such as the Lacpermease or the transhydrogenase, are devoid of a proton-collecting antenna [80, 81].
20.7
The Dynamics of Ions at an Interface
The kinetic analysis of proton transfer at the bulk/surface interface is based on standard chemical kinetic formalism, a procedure that cannot account for the multitude of forces operating in the reaction space, or for the dynamics of the protein’s surface groups. A full account of the reaction mechanism can be compiled by molecular dynamics, with one drawback: the calculations carried out for a solvated proton are extremely laborious, due to the need to account for the breaking and formation of covalent bonds, which are the essence of the proton’s dissociation mechanism [82, 83]. An alternative procedure, which can shed light on the proton’s propagation at the interface, is to make a minimal generalization, and to substitute the proton, with its special chemistry, by charged ions which propagate by self-diffusion and with the assumption that the forces operating on a proton will affect other ions in the same manner. A molecular dynamics (MD) simulation was carried out, simulating the propagation of Naþ and Cl ions in the immediate vicinity of a small globular protein [85]. The protein selected as a model for this study is the S6, which forms part of the bacterial 30S ribosome central domain [84], and does not have a function associ-
20.7 The Dynamics of Ions at an Interface
Figure 20.5. Surface proton-transfer pathways on the cytoplasmic surface of bacteriorhodopsin in the BR and the M-states. (A) Atomic model of the carboxylic side chains at the cytoplasmic surface of bacteriorhodopsin. Initial
state is colored purple and the M state yellow. (B) Schematic representation of the proton conduction pathways in the Br and the M states. The numbers on the arrows represent the rate constants and are given in M1 s1 .
1519
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20 Proton Transfer at the Protein/Water Interface
Figure 20.6. The electrostatic potential surface around the small protein S6. (A): Residue His16 (which is transiently located in the vicinity of the ion) and the two attractor sites Glu41 and Glu95. Right: Residues Arg80 and Arg87, which are the strongest ion attractors and Lys92, which is located in their vicinity and
forms a weak ion attractor, are presented as the ion is detained by Arg80 and Arg87. The Coulomb cages for the positive (blue) and negative (red) domains are drawn at the distance where the electrostatic potential equals 1 kB T=e.
ated with ion transport on its surface. The S6 is a globular protein of 101 amino acids, 32 of which are charged at a physiological pH. Moreover, due to its high charge density and globular structure, no amino acid is totally buried in the protein matrix and all the amino acids are at least partially exposed to the bulk. The uneven distribution of the charged residues on the protein generates two potential lobes, one having a positive potential and the other a negative (Fig. 20.6). To follow the dynamics of the ions near the protein, molecular dynamics simulations were carried out in the presence of 6639 water molecules, and Naþ and Cl ions were added to a formal concentration of 30 and 120 mM. The simulations were carried out for a period of 10 ns, and the diffusion coefficients of the ions were calculated to be comparable with the values determined by experimental methods [85]. A great advantage of molecular dynamics calculations is the possibility to visualize the motion of each ion. On inspecting the various ions, it became evident that their spatial distribution was not random. There was a clear tendency of some anions and cations to remain in the vicinity of the protein, as if the local forces detained them next to the protein’s surface. Molecular dynamics simulation of the protein in the presence of a small number of ions (4 Naþ and 4 Cl ions, comparable with 30 mM NaCl solution) revealed that the ions were scanning the whole reaction space. Yet, the ions were not evenly distributed in the solution and had a tendency to linger in the immediate proximity (6 A˚) of the protein for a relatively long time, @1 ns (see Fig. 20.7). The simulation revealed fast exchange of the ions between the protein’s surface and the bulk, reflecting competition between two forces: the electrostatic attraction that favors the
20.7 The Dynamics of Ions at an Interface
Figure 20.7. The minimal distance, in nm, between any of the Cl (A) and Naþ (B) ions and the protein as a function of simulation time. The distances are given in nm and the time in ns. The minimal distance is dictated by the steric interferences between the Van-der-Waals radii of the ions.
detainment and the entropic drive that prefers the free state of the ion. Therefore, throughout most of the simulation time, the ions diffuse in a Brownian motion in the bulk, but once an ion is trapped by the protein’s Coulomb cage, it is drawn to the nearest attractor site. Sooner or later, depending on the strength of the attractor site, the ion will escape its detainment and will diffuse either within the Coulomb cage to the next attractor or out of the Coulomb cage. Thus, an ion that is already located inside the Coulomb cage has a higher probability to encounter with other attractor sites [85]. There is a strong resemblance between the mechanism of ion motion next to the protein and the proton-collecting antenna reported for bacteriorhodopsin [78, 79] or cytochrome c oxidase [2]. These domains consist of a cluster of carboxylates that function as proton binding sites. The protonation on any carboxylate of the cluster leads to rapid proton exchange reactions that finally deliver the proton to the immediate vicinity of the proton-conducting channel of the protein.
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20 Proton Transfer at the Protein/Water Interface
20.8
Concluding Remarks
Proton transfer at the surface of a protein or biomembrane is a cardinal reaction in the biosphere, yet its mechanism is far from clarification. The reaction, in principle, should be considered as a quantum chemistry event, and the reaction space as a narrow layer, 3–5 water molecules deep. What is more, local forces are intensive and vary rapidly with the precise molecular features of the domain. For this reason, approximate models that are based on pure chemical models or on continuum physical approximations are somewhat short of being satisfactory models with quantitative prediction power. At the present time, when the structure of the proton pumping protein and the membrane’s surface can be gained at atomic resolution, when the dissociation of a proton can be recorded with sub-nanosecond resolution and molecular dynamics can be extended to tens of nanoseconds, it seems that a combination of these methods will be required to elucidate the mechanism of the reaction. Thus, combination of specific labeling of sites of interest by a photoacid or indicator, coupled with time-resolved measurements and molecular dynamics of the reaction, will be the next step in the research. Once these combined experiments are available, the generalization of the process, like the role of local electrostatic potential, orientation of water and the relative motion of side-chains, will be quantitated, with a subsequent improvement in the theoretical predicting power.
Acknowledgments
The authors are grateful to Ran Friedman, from Tel-Aviv University, Israel for his help with the theoretical calculations. The research in the Laser Laboratory for Fast Reactions in Biology is supported by the Israeli Science Foundation (472/01-2) and the American Israel Binational Science Foundation (2002-129). The molecular dynamics calculations were carried out in the High Performance Computing Unit of the Inter University Computing Center.
References 1 Namslauer, A., et al., Intramolecular
3 Mitchell, P., Chemiosmotic coupling
proton-transfer reactions in a membrane-bound proton pump: the effect of pH on the peroxy to ferryl transition in cytochrome c oxidase, Biochemistry, 2003, 42, 1488–98. 2 Marantz, Y., et al., Proton-collecting properties of bovine heart cytochrome C oxidase: kinetic and electrostatic analysis, Biochemistry, 2001, 40, 15086–15097.
in oxidative and photosynthetic phosphorylation, Biol. Rev. Camb. Philos. Soc., 1966, 41, 445–502. 4 Wikstrom, M.K., Proton pump coupled to cytochrome c oxidase in mitochondria, Nature, 1977, 266, 271–273. 5 Paddock, M.L., et al., Pathway of proton transfer in bacterial reaction centers: replacement of serine-L22 by
References
6
7
8
9
10
11
12
13
14
alanine inhibits electron and proton transfers associated with reduction of quinone to dihydroquinone, Proc. Natl. Acad. Sci. USA, 1990, 87, 6803–6807. McPherson, P.H., et al., Protonation and free energy changes associated with formation of QBH2 in native and Glu-L212 ! Gln mutant reaction centers from Rhodobacter sphaeroides, Biochemistry, 1994, 33, 1181–1193. Lancaster, R.C., D., Michel, H., The coupling of light-induced electron transfer and proton uptake as derived from crystal structures of reaction centers from Rhodopseudomonas viridis modified at the binding site of the secondary quinone, QB, Structure, 1997, 5, 1339–1359. Axelrod, H.L., et al., Determination of the binding sites of the proton transfer inhibitors Cd2þ and Zn2þ in bacterial reaction centers, Proc. Natl. Acad. Sci. USA, 2000, 97, 1542– 1547. Dencher, N.A., et al., Structurefunction relationship of the lightdriven proton pump bacteriorhodopsin, J. Protein Chem., 1989, 8, 340–343. Heberle, J., et al., Proton migration along the membrane surface and retarded surface to bulk transfer, Nature, 1994, 370, 379–382. Riesle, J., et al., D38 is an essential part of the proton translocation pathway in bacteriorhodopsin, Biochemistry, 1996, 35, 6635–6643. Gutman, M., Huppert, D., Rapid pH and deltamuHþ jump by short laser pulse, J. Biochem. Biophys. Methods, 1979, 1, 9–19. Gutman, M., The pH jump: probing of macromolecules and solutions by a laser-induced, ultrashort proton pulse-theory and applications in biochemistry, Methods Biochem. Anal., 1984, 30, 1–103. Gutman, M., Application of the laserinduced proton pulse for measuring the protonation rate constants of specific sites on proteins and membranes, Methods Enzymol., 1986, 127, 522–538.
15 Viappiani, C., Bonetti, G., Carelli,
16
17
18
19
20
21
22
23
24
M., Ferrati, F., Sternieni A., Study of proton transfer processes in solutions using the laser induced pH jump: A new experimental setup and an improved data analysis based on genetic algorithm, Rev. Sci. Instrum., 1998, 69, 270–276. Gutman, M., et al., Time-resolved protonation dynamics of a black lipid membrane monitored by capacitative currents, Biochim. Biophys. Acta, 1987, 905, 390–398. Nachliel, E., Gutman, M., Time resolved proton-phospholipid interaction. Methodology and kinetic analysis, J. Am. Chem. Soc., 1988, 110, 2635. Yam, R., Nachliel, E., Gutman, M., Time-resolved proton-protein interaction. Methodology and kinetic analysis, J. Am. Chem. Soc., 1988, 110, 2636–2640. Kotlyar, A.B., et al., The dynamics of proton transfer at the C side of the mitochondrial membrane: picosecond and microsecond measurements, Biochemistry, 1994, 33, 873–879. Haines, T.H., Dencher, N. A., Cardiolipin: a proton trap for oxidative phosphorylation, FEBS Lett., 2002, 528, 35–39. Brzustowicz, M.R., et al., Molecular organization of cholesterol in polyunsaturated membranes: microdomain formation, Biophys. J., 2002, 82, 285–298. Samsonov, A.V., Mihalyov, I., Cohen, F.S., Characterization of cholesterol-sphingomyelin domains and their dynamics in bilayer membranes, Biophys. J., 2001, 81, 1486–1500. Shaikh, S.R., et al., Lipid phase separation in phospholipid bilayers and monolayers modeling the plasma membrane, Biochim. Biophys. Acta, 2001, 1512(2), 317–328. Bransburg, Z.S., Nachliel, E., Gutman, M., Utilization of monensin for detection of microdomains in cholesterol containing membrane, Biochim. Biophys. Acta, 1996, 1285, 146–154.
1523
1524
20 Proton Transfer at the Protein/Water Interface 25 Checover, S., et al., Mechanism of
26
27
28
29
30
31
32
33
34
35
proton entry into the cytoplasmic section of the proton-conducting channel of bacteriorhodopsin, Biochemistry, 1997, 36, 13919–13928. Adelroth, P., Brzezinski, P., Surface-mediated proton-transfer reactions in membrane-bound proteins, Biochim. Biophys. Acta, 2004, 1655, 102–115. Jaskson, J.D., Classical Electrodynamics, John Wiley & Sons, New York, 1975. Cohen, B., et al., Excited state proton transfer in reverse micelles, J. Am. Chem. Soc., 2002, 124(25), 7539– 7547. Binder, H., et al., Hydration of the dionic lipid dioctadecadienoylphosphatidylcholine in the lamellar phase. An infrared linear dichroism and Xray study on headgroup orientation, water ordering, and bilayer dimensions, Biophys. J., 1998, 74, 1908–1923. Milhaud, J., New insights into waterphospholipid model membrane interactions, Biochim. Biophys. Acta, 2004, 1663, 19–51. Bach, D., Miller, I.R., Attenuated total reflection (ATR) Fourier transform infrared spectroscopy of dimyristoyl phosphatidylserinecholesterol mixtures, Biochim. Biophys. Acta, 2001, 1514, 318–326. Miller, I.R., Bach, D., Organization of water molecules by adhering to oriented layers of dipalmitoylphosphatidyl serine in the presence of varying concentrations of cholesterol, Biochim. Biophys. Acta, 2000, 1468, 199–202. Bach, D., Miller, I.R., Hydration of phospholipid bilayers in the presence and absence of cholesterol, Biochim. Biophys. Acta, 1998, 1368, 216–224. Nicklas, K., et al., Molecular dynamics studies of the interface between a model membrane and an aqueous solution, Biophys. J., 1991, 60(1), 261–272. Kiefer, P.M., Hynes, J.T., Nonlinear free energy relations for adiabatic proton transfer reactions in a polar
36
37
38
39
39a
39b
39c
40
41
42
43
environment. II. Inclusion of the hydrogen bond vibration, J. Phys. Chem., 2002, 106, 1850–1861. Douhal, A., Lahmani, F., Zewail, A.H., Proton-transfer reaction dynamics, Chem. Phys., 1996, 207, 477–498. Rini, M., et al., Real-time observation of bimodal proton transfer in acidbase pairs in water, Science, 2003, 301, 349–352. Lee, J., Griffin, R.D., Robinson, G.W., 2-naphthol: a simple example of proton transfer effected by water structure, J. Chem. Phys., 1985, 82, 4920–4925. Huppert, D.K., Gutman, M., Nachliel, E., The effect of water activity on the rate constant of proton dissociation, J. Am. Chem. Soc., 1982, 104, 6944–6953. Gutman, M., Nachliel, E., Kiryati, S., Dynamic studies of proton diffusion in mesoscopic heterogeneous matrix. The interbilayer space between phospholipids membranes. Biophys. J., 1992, 63, 281–290. Shimoni, E., Tsfadia, Y., Nachliel, E., Gutman, M., Gaugement of the inner space of the apomyoglobin’s heme binding site by a single free diffusing proton. I. Proton in the cavity. Biophys. J., 1993b, 64(2), 472– 479. Yam, R., Nachliel, E., Kiryati, S., Gutman, M., Huppert, D., Proton transfer dynamics in the nonhomogeneous electric field of a protein. Biophys. J., 1991, 59(1), 4–11. Agmon, N., The Grotthuss mechanism, Chem. Phys. Lett., 1995, 244, 456–462. Agmon, N., Hydrogen bonds, water rotation and proton mobility, J. Chem. Phys., 1996, 93, 1714–1736. Agmon, N., Estimation of hydrogenbond lengths to H3 Oþ and H5 O2 þ in liquid water, J. Mol. Liq., 1997, 73/74, 513–520. Lapid, H., et al., A bond-order analysis of the mechanism for hydrated proton mobility in liquid water, J. Chem. Phys., 2005, 122, 14506.
References 44 Pines, E. Huppert, D., Kinetics of
45
46
47
48
49
50
51
52
53
54
55
proton transfer in ice via the pH-jump method: evaluation of the proton diffusion rate in polycrystalline doped ice, Chem. Phys. Lett., 1985, 116, 295–301. Bransburg, Z.S., et al., Biophysical aspects of intra-protein proton transfer, Biochim. Biophys. Acta, 2000, 1458, 120–134. Zhang, J., Unwin, P.R., Proton diffusion at phospholipid assemblies, J. Am. Chem. Soc., 2002, 124, 2379– 2383. Zundel, G., Merz, H., On the role of hydrogen bonds and hydrogen-bonded systems with large proton polarizability for mechanisms of proton activation and conduction in bacteriorhodopsin, Progr. Clin. Biol. Res., 1984, 164, 153–164. Zundel, G., Proton polarizability of hydrogen bonds: infrared methods, relevance to electrochemical and biological systems, Methods Enzymol., 1986, 127, 439–455. Wang, J., El-Sayed, M.A., Timeresolved Fourier transform infrared spectroscopy of the polarizable proton continua and the proton pump mechanism of bacteriorhodopsin, Biophys. J, 2001, 80, 961–971. Klapper, I., et al., Focusing of electric fields in the active site of Cu-Zn superoxide dismutase: effects of ionic strength and amino-acid modification, Proteins, 1986, 1, 47–59. Langner, M., et al., Electrostatics of phosphoinositide bilayer membranes. Theoretical and experimental results, Biophys. J., 1990, 57, 335–349. Peitzsch, R.M., et al., Calculations of the electrostatic potential adjacent to model phospholipid bilayers, Biophys. J., 1995, 68, 729–738. Adam, G.A., Delbruck., M., Reduction of dimensionality in biological diffusion processes, Struct. Chem. Mol. Biol., 1968, 198–215. Berg, H.C., Purcell, E.M., Physics of chemoreception, Biophys. J., 1977, 20, 193–219. Selevia, C.J., Unwin, P.R., Lateral proton diffusion rates along stearic
56
57
58
59
60
61
62
63
64
65
66
66a
monolayer, J. Am. Chem. Soc., 2000, 122, 2597–2602. Georgievskii, Y., Medvedev, E.S., Stuchebrukhov, A.A., Proton transport via coupled surface and bulk diffusion, J. Chem. Phys., 2002, 116, 1692–1699. Georgievskii, Y., Medvedev, E.S., Stuchebrukhov, A.A., Proton transport via the membrane surface, Biophys. J., 2002, 82, 2833–2846. Heberle, J., Proton transfer reactions across bacteriorhodopsin and along the membrane, Biochim. Biophys. Acta, 2000, 1458, 135–147. Heberle, J., et al., Bacteriorhodopsin: the functional details of a molecular machine are being resolved, Biophys. Chem., 2000, 85, 229–248. Gutman, M., Nachliel, E., The dynamic aspects of proton transfer processes, Biochim. Biophys. Acta, 1990, 1015, 391–414. Serowy, S., et al., Structural Proton Diffusion along Lipid Bilayers, Biophys. J., 2003, 84, 1031–1037. Pohl, P., Saparov, S.M., Antonenko, Y.N., The size of the unstirred layer as a function of the solute diffusion coefficient, Biophys. J., 1998, 75, 1403–1409. Junge, W., McLaughlin, S., The role of fixed and mobile buffers in the kinetics of proton movement, Biochim. Biophys. Acta, 1987, 890, 1–5. Zaniboni, M., et al., Proton permeation through the myocardial gap junction, Circ. Res., 2003, 93, 726–735. Marantz, Y., et al., The proton collecting function of the inner surface of cytochrome c oxidase from Rhodobacter sphaeroides, Proc. Natl. Acad. Sci. U.S.A., 1998, 95, 8590– 8595. Moscovitch, D., et al., Determination of a unique solution to parallel proton transfer reactions using the genetic algorithm, Biophys. J., 2004, 87, 47– 57. Mezer, A., Friedman, R., Noivirt, O., Nachliel, E., Gutman, M., The mechanism of proton transfer between adjacent sites exposed to
1525
1526
20 Proton Transfer at the Protein/Water Interface
66b
67
68
69
70
71
72
73
74
75
76
water. J. Phys. Chem. B. Condens Matter Mater. Surf. Interfaces Biophys., 2005, 109(22), 11379–11388. Gutman, M., Nachliel, E., Friedman, R., The mechanism of proton transfer between adjacent sites on the molecular surface. Biochim. Biophys. Acta., 2006b, in press. Gutman, M., Nachliel, E., The dynamics of proton exchange between bulk and surface groups, Biochim. Biophys. Acta, 1995, 1231, 123–138. Gutman, M., Nachliel, E., Time resolved dynamics of proton transfer in proteinous systems, Annu. Rev. Phys. Chem., 1997, 48, 329–356. Scheiner, S., Latajka, Z., Kinetics of Proton-Transfer in (H3ch..Ch3)-, J. Phys. Chem., 1987, 91, 724–730. Hillenbrand, E.A., Scheiner, S., Effects of Molecular Charge and Methyl Substitution on ProtonTransfer between Oxygen-Atoms, J. Am. Chem. Soc., 1984, 106, 6266–6273. Scheiner, S., Proton transfers in hydrogen-bonded systems. Cationic oligomers of water, J. Am. Chem. Soc., 1981, 103, 315–320. Parsegian, V.A., Rau, D.C., Water near intracellular surfaces, J. Cell Biol., 1984, 99, 196s–200s. Rand, R.P., et al., Variation in hydration forces between neutral phospholipid bilayers: evidence for hydration attraction, Biochemistry, 1988, 27, 7711–7722. Nachliel, E., Finkelstein, Y., Gutman, M., The mechanism of monensin-mediated cation exchange based on real time measurements, Biochim. Biophys. Acta, 1996, 1285, 131–145. Ben-Tal, N., et al., Theoretical calculations of the permeability of monensin-cation complexes in model bio-membranes, Biochim. Biophys. Acta, 2000, 1466, 221–233. Schatzler, B., et al., Sub-second
77
78
79
80
81
82
83
84
85
86
proton-hole propagation in bacteriorhodopsin, Biophys. J., 2003, 84, 671–686. Friedman, R., Nachliel, E., Gutman, M., The role of small intraprotein cavities in the catalytic cycle of bacteriorhodopsin, Biophys. J., 2003, 85, 886–896. Checover, S., et al., Dynamics of the proton transfer reaction on the cytoplasmic surface of bacteriorhodopsin, Biochemistry, 2001, 40, 4281– 4292. Nachliel, E., et al., Proton Transfer Dynamics on the Surface of the Late M State of Bacteriorhodopsin, Biophys. J., 2002, 83, 416–426. Nachliel, E., et al., Time-resolved study of the inner space of lactose permease, Biophys. J., 2001, 80, 1498–1506. Nachliel, E., Gutman, M., Probing the substrate binding domain of lactose permease by a proton pulse, Biochim. Biophys. Acta, 2001, 1514, 33–50. Laasonen, K., et al., Structures of small water clusters using gradientcorrected density functional theory, Chem. Phys. Lett., 1993, 207, 208– 213. Tuckerman, M.E., Marx, D., Parrinello, M., The nature and transport mechanism of hydrated hydroxide ions in aqueous solution, Nature, 2002, 417, 925–929. Agalarov, S.C., et al., Structure of the S15,S6,S18-rRNA Complex: Assembly of the 30S Ribosome Central Domain, Science, 2000, 288, 107–112. Friedman, R., Nachliel, E., Gutman, M., Molecular dynamics of a protein surface: ion-residues interactions. Biophys. J., 2005, 89(2), 768–781. Gutman, M., Nachliel, E., Friedman, R., The dynamics of proton transfer between adjacent sites. Photochem. Photobiol. Sci., 2006a, 5(6), 531–537.
1527
Index a absorbance 1410 absorbance, excited-state 450, 453, 471 absorbance, transient 465 absorption, excited state (ESA) 354, 356f. absorption spectroscopy 245, 256f., 386f., 388, 435, 463, 466, 530, 1408, 1432 absorption, transient (TA) 509, 532, 540, 544, 547, 555 – time-resolved 352ff., 468, 1434 absorption of H2 753 acceleration 1063, 1072, 1109 acceleration factor 1045ff. acetaldehyde 519, 957, 1037, 1430f. – hemiacetal 980 acetate anion 957, 980 acetic acid 173, 210f., 450, 519, 529, 967f., 1001 – methanol complex 932f. acetic anhydride 980f. acetone 952f., 955, 967 acetonitrile 172, 199, 400, 516ff., 529, 543, 887, 962, 1278 acetophenone 1004 acetyl group 225ff. acetylene 519 N-acetylmethionineethyl ester 1030 acids 1502 acids, mineral 387, 392, 394, 398 acid-base – catalysis 975ff., 1079ff., 1162, 1241, 1361 – mechanism 977, 980 – equilibrium 370, 410 – neutralization 445, 448f. – pairs 108f., 377f., 434, 1069, 1178 – reactions 110 – systems 303, 309, 400, 406f., 444 Acinetobacter calcoaceticus 1070 Aquifex pyrophilus 1161
acridinium 1051, 1066 activation energy 748 – of diffusion 753, 763 additives, electronegative and electropositive 773 adenine 934 adenosine triphosphate (ATP) 552, 1152, 1154ff., 1378, 1499 S-adenosylhomocysteine 1062 adiabatic longitudinal transport after dissociation engenders net alignment (ALTADENA) 657, 662ff. adiabatic regime 303, 307, 309ff., 315, 320ff., 327 – excited state 597 – ground state 588, 597 – ground state potential 837, 840f., 846f., 851 – PES 368 – surface 1185 – theory of reactions 834, 840, 845 adsorption 688ff., 698, 773ff. – activated H 756f. – activation barrier 757 – energetic heterogeinity 759 – energy 758, 771, 773 – kinetics 773 advanced materials 245 Aequorea victoria 435 Aeromonas caviae 1151 agostic interaction 611 alanine (Ala) 1026, 1081, 1092, 1102, 1129, 1139ff., 1147, 1161, 1161, 1218, 1397, 1430, 1447 Albery-Kreevoy-Lee approach 1054 alcohols 228f., 427ff., 775, 992f., 1037, 1048 – aromatic 400ff. – tertiary 993 aldehyde 1048, 1107
Hydrogen-Transfer Reactions. Edited by J. T. Hynes, J. P. Klinman, H.-H. Limbach, and R. L. Schowen Copyright 8 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-30777-7
1528
Index aldimine 1141, 1143f., 1150 aldol-keto isomerization 1120 Alexander-Binsch formalism 622, 670 alkali metals 773 alkaline fuel cells (AFCs) 709ff., 718 alkane 957 – aggregates, physical state 116ff. – as proton acceptors 105ff., 115ff., 126ff. – s-basicity 110f. – crystallisation 126, 128ff. – halogenated (Cl, Br) 112ff. – systems 991 alkene 1001 alkyne 1001 allostery 1381ff., 1422, 1452 alloys 771ff., 787, 804ff. AlO4 tetrahedron 685, 700 aluminium 779, 782, 809, 812 aluminophosphates (AlPOs) 686 aluminosilicates see zeolites Alzheimer’s disease 1029, 1379 amides 1017 amidines 196 amidines, diaryl- 203 amidines, N-N 0 -di-(p-F-phenyl) 193ff. amidines, fluoro 172 amines 205, 591, 1006, 1017ff. amines, chloro 1017 amines, tertiary 399 amino acid 232, 729, 1013, 1017, 1110, 1439, 1475 – activation 1459ff. – ester 967 – radical generation 548ff. aminopyrenes 398, 400, 445 1-aminopyrene (1-AP) 228ff., 382 8-aminopyrene-1,3,6-trisulfonate (APTS) 382, 400 2-amino-pyridine 446 aminopyrimidine 1427 1-amino-8-trifluoroacetylaminonaphthalene 979 ammonia 431f., 446, 593, 641, 688ff., 697 ammonium ions 688ff., 954, 1001 amphiphilic helices 1081 4-androstene-3,17-dione 1109, 1125 5-androstene-3,17-dione 1109, 1125 angular momentum 59 anion propagation 214 anisotropy, elastic 789 anisotropy experiments 226, 234, 238, 256ff., 262ff. – time-resolved 262
ansa-bridging 628 anthracene 517ff. antibiotics, petide-based 1154 antioxidants 1014 anvil cell, diamond 740, 742ff. anvil cell, sapphire 819 apomyoglobin 1503 approximate instanton method (AIM) 896, 904f., 914, 923, 927, 938f. aqueous solution 377f., 410, 428ff., 443f., 542, 714ff., 724, 867, 949, 992, 1014, 1052, 1098, 1116, 1186, 1507 – of KOH 711, 714 – NaOH 714 arginine (Arg) 528, 1084, 1099, 1145, 1407, 1485, 1519 Arrhenius behavior 333ff., 489, 577, 823 Arrhenius curves 135ff., 174, 176, 178ff., 188ff., 197ff., 205ff., 212ff., 264, 326, 337ff., 429f., 536f., 677, 765, 798, 877ff., 884ff., 891f., 917f., 923f., 927ff., 1255, 1289f., 1327, 1384f. – for single and multiple H transfer 146, 150f., 157, 160f., 163f., 167f., 181, 185ff. Arrhenius expression 1245 Arrhenius factor – pre-exponential factor 9, 135, 150, 167f., 185, 206ff., 213, 217, 719, 762, 798f., 877, 879, 884f., 891f., 1245 Arrhenius law 148, 162, 164, 167, 655, 797f., 812 Arrhenius prefactor 1254ff., 1268, 1274, 1276ff., 1326f., 1342 Arrhenius relation 762, 1060, 1172 Arrhenius rate 655f. arsenic 761 artificial light-harvesting 245 aryl groups 203f. asparagine (Asn) 1108, 1397 aspartate (Asp) 528, 1108, 1113, 1126f., 1131, 1145, 1154, 1161, 1398, 1440 atmospheric reactions 834 attractive forces 759 autoionisation 443f. autoprotolysis 216 – constant 214 – enthalpy 214 – mechanism 214 7-azaindole 925, 935f. azenes, diaryltri- 203 azenes, tri- 205f. azimuthal polarization mode 266 azophenine 155, 172, 176, 197ff.
Index
b Bacillus stearothermophilus 212f., 1143f., 1151, 1217, 1268, 1325, 1329, 1384, 1425 backbone, aromatic 445 backbone structure 377, 435 backdonation (BD) 604, 629 bacterial cell walls 1161 bacteriochlorin 175, 184 bacteriorhodopsin 1500f., 1506, 1516ff. Baker Campbell Hausdorf Theorem 1212 band mode 787 band model 767f. band structure, atomic 766f. barrier 141, 143, 147, 150ff., 157, 160f., 189, 193ff., 199, 203, 251ff., 265, 275, 278, 282f., 291f., 584ff., 596, 645, 652, 687, 834, 840ff., 855, 928ff., 1007, 1110f., 1190f., 1196, 1232, 1481ff. – above/over-the-barrier 84, 100, 199, 304, 309, 632, 810, 858, 869, 875, 904, 915, 936 – fluctuations 824, 1260ff., 1363 – oscillations 880 – quadruple-barrier 161, 163f. – through-the-barrier 84f., 100, 136, 307, 364, 904, 914 – two- /double- 162, 164 barrier, Eckart 879 barrier, Gaussian 879 barrier, reaction 315ff., 322ff., 328ff., 338f., 510, 513, 522, 1179 barrier, single 164, 211, 218 barrier, transition 34ff., 39, 44 barrier, triple 159ff. barrier, trunctuated parabolic 879 basal plane of crystals 809 base, scavenging 448ff. BaZrO3 , Y-doped 732 barrel domain 1134 BBO 352 Becke-Lee-Yang-Parr (BLYP) 288ff., 697ff. – B3LYP 249, 265, 571, 919f., 927f., 939, 1480ff. BDE 511, 516ff. – Bell tunneling model 136f., 144f., 146ff., 251, 584, 623, 641, 653ff., 656, 674, 676, 844, 847, 1250ff., 1257 – dependence on hydrogen isotope 1250 – tunnel correction 1258, 1270, 1293, 1341f., 1350 BDE, one-dimensional 1293 BDE, truncated 1288, 1294, 1303 Bell-Evans-Polanyi (BEP) principle 585, 590
Bell-Limbach model 135, 137f., 146ff., 153, 155, 174, 177, 189, 191f., 198f., 208, 216 – parameters 169ff. Bema Hapothle 584 benzaldehyde 1247, 1247 benzaldehyde acetals 983, 992, 998 benzene 517, 519, 689, 877 benzenesulfonate 239 benzimidazole 721, 727 benzisoxazole 989, 1006 benzoic acid 135, 171, 188, 296, 529 – crystalline 923, 1214ff., 1234 – dimer 278ff., 284, 919, 922 – methyl ester 568 p-benzoquinone 525f. S-benzoylglutathione 1099f. 1-benzoyl-3-phenyl-1,2,4-triazole 983 benzyl alcohol 1266 benzylamine 1162 1-benzyl-1,4-dihydronicotinamide 1049 benzylsulfonium cation 984f. bifurcation point 910, 920 Bigeleisen limits 1291ff. Bigeleisen theory 140f., 148 Bigeleisen-Wolfsberg formalism 1287, 1291 bilayer 737ff., 747, 749, 780 (of water molecules) bimetallic systems 771, 773 biological reactions 436 biological systems 232, 433ff., 537, 548ff., 729, 733, 778, 932, 1241 biomedical application 498 biomolecular processes 834 biomolecule 213, 224, 445 [2,2 bipyridyl]-3,3 0 -diol (BP(OH)2 ) 370f. 2,5-bis(2 0 -benzaoxazolyl)-hydroquinone (BBXHQ) 353, 358, 361, 365 1,3-bis(4-fluorophenyl)[1,3]-N2 ]triazene 203, 205 bleach 450, 464 Bloch orbitals 768f. Bloch states 812 body centered cubic cell (bcc) 737, 740, 789, 797ff., 814, 817, 825 Bloembergen, Purcell and Pound model (BPP) 791 Boltzmann constant 148 Boltzmann distribution 149, 655f. Boltzmann law 147 Boltzmann probability 1196f. Bombyx mori 1152 bond see also hydrogen bond – angle HaOaH 718, 737
1529
1530
Index bond, CaH 515f. – activation 1405 – order 1055 bond, CbN 1395ff., 1400 – activation 1398 bond, CbO 1395ff. – CaS 1432 – CoaC 1476ff., 1487 – dissociation energy 109f., 1018, 1023, 1027 – formation/breaking 1083, 1097, 1163, 1229, 1351, 1487 bond, CaC 1430 bond, s- 107f., 111 – rotation, CaC 1097 – rotation, CaN 1108 – stretch 1245f., 1250 bond, OaH 515 – three-centre three-electron bond 111 bond, ribosidic 1233 bond, SaS 1432 – valences 141ff. bond energy – bond order model (BEBO) 325, 394ff. Born-Oppenheimer 276, 461, 480, 837f., 1175 bottleneck 838ff., 1303, 1479f. brain-derived neurotrophic factor (BDNF) 1370f. – receptor (trkB) 1370f. Bravais sublattice 801 bridges, carbon 525 bridges, salt 494, 527ff., 554, 1081, 1386 Brillouin zone 766f. brome mosaic virus (BMV) particle 1378 bromocresol green 1508f. 4-bromopyrazole (4BrP) 193ff. Brønsted acidity 397, 962 Brønsted acids 377, 409f., 443, 585, 719, 954, 965f., 969f. Brønsted bases 377, 443, 585, 965f., 970, 1049 Brønsted coefficient 313, 317ff., 334f., 583ff., 599, 954, 1049, 1054ff., 1095, 1116f. Brønsted correlation 589f., 591ff., 1000f. Brønsted equation 977, 1001, 1093 Brønsted relation 585, 997 Brønsted site 685ff., 693ff., 700ff. Brønsted-type plot 427, 510 Brownian dynamics (BD) simulation 1193 buffers 954, 969, 976 Bruice’s proximity effect 1044 n-butylamine 691
c
Ca 2þ 597, 1152, 1374, 1378f. cage 223, 229 Calcium 808 calix[4]arene 173, 213ff., 223, 939f. – p-tert-butyl- 215, 939 CAMEL-SPIN 174 canonical ensemble 833 canonical mean shape (CMS) 862f. canonical variational theory (CVT) 836, 842, 867, 1486 carbanions 949ff., 958ff. – aromatic 566 – a-carbonyl carbon 957, 963ff., 968f. carbanions, a-cyanomethyl 955 – enamine 1419, 1429, 1434 – intermediates 565, 573ff., 581f., 1001, 1158 carbanions, vinyl 1001 carbenes 429 – /ylide 963 carbenium ions 106, 110, 116, 123f., 129f., 686ff., 703ff. – tert-butyl cation 704 – of xylene 704 2-carbethoxycyclopentanone 1293 carbon acid 949ff., 960, 964, 966f., 1107, 1110 carbocations 106, 1300 carbocations, oxo- 994 carbocations, 1-phenylethyl 983 carbohydrates 1023f. carbonium ions 106, 111, 116, 123f., 127 carbonyl groups 225, 230ff., 957, 963, 1002ff. carbonyl/carboxylate acceptor 1114ff. carboxylamide orientation 1403 carboxylate anions 1107 carboxylic acids 462, 466, 523, 1107 – dimeric 896 carboxylic bases 395, 426 Car-Parrinello – molecular dynamics (CPMD) 286ff., 293, 692ff., 696ff., 721f. – path 1185 catalytic cleavage 1375 catalytic cracking 686 catalytic mechanism – of cages 223 – of enzyme reaction (KSI) 1126, 1133, 1435 – one-base mechanism 1141, 1157 – two-base mechanism 1141, 1158 catalytic proficiency 1046f. catalytic triad 1460 cation propagation 214
Index cavity 1100 – CD 223ff., 230 – porphyrins 245, 248ff., 254, 267f. – zeolites 686, 691 CCl4 172, 208f. CCl3 F 208f. CCSD(T) 705 CDCl3 185 CD2 Cl2 172, 198 C2 D2 Cl4 198 CDFCl2 185 CDF2 Cl 185 cephalosporin 1156 3-center 2-electron bonding 604 centroid path integral approach 1183 cesium perfluorooctane 233 m/p-CF3 C6 H4 CHClCH2 Cl 578 CF2 bCCl 6 H5 575 CF2 bCl2 573 CF3 COOH 613 charge carriers 714ff. charge interactions 1079f., 1096, 1098 charge relay system 1460 charge separation 506 charge transfer 417 – intramolecular 420, 445 – metal-to-ligand 530f. CHARMM program 1219, 1291 – /MOPAC 1227 Chaudret 630 C6 H5 CHBrCH2 Br 580 C6 H5 CHBrCH2 Cl 580 C6 H5 CHBrCH2 F 580 C6 H5 CH(CF3 )2 571 C6 H5 C(CF3 )bCF2 573 C6 H5 CH(CF3 )CF2 OCH3 573 C6 H5 CH(CH3 )CH2 Br 577 C6 H5 CHClCF3 571 C6 H5 CHClCF2 Cl 577 C6 H5 CHClCH2 Cl 579 CH2 Cl2 523, 533 CHCl2 CF3 573, 580 chelate interaction 958f. chemical step 1316 chemical reactions 833f., 869, 875ff., 1175, 1227, 1447 – addition 1001, 1107 – bimolecular 834, 836, 843ff., 887ff. – Claisen-type 952 – carbocation-nucleophile addition 958 – catalysis 965ff., 980ff., 988ff. – catalysis, acidic 967, 982f., 993ff., 998ff., 1089, 1094
– catalysis, base 966, 983ff., 999ff., 1004ff., 1089 – cyclization 985, 1001, 1007 – dehydration 1107, 1188 – elimination 952, 1107 – E2 1006 – fragmentation 1018 – a-b- 1014 – 1,2-H-shift 1014ff., 1031, 1107, 1477 – 1,5-H-shift 1017f. – 1,1-proton transfer 1108, 1139, 1157 – hydration 1107 – hydride transfer 1107, 1187, 1230 – hydrolysis 976, 882ff., 976ff., 988ff., 993ff., 1002, 1005ff., 1086ff., 1101ff. – inversion 883ff. – intramolecular 987ff., 993ff., 998ff., 1002ff. – cyclisation 987 – mechanisms 835, 981ff., 1006 – acetal cleavage mechanism 991 – nucleophilic 958, 984f., 993ff., 998ff., 1089 – SN 1 994 – SN 2 984f., 994, 1008, 1187 – SN i 985 – oxidation 1013, 1328, 1353 – sterically hindered 876ff. – transesterification 1086 – unimolecular 1242f. chemisorption 754ff., 766 chirality 433, 448, 939 chlorine 175, 184, 849ff., 853ff. chloroacetate 1293 p-chlorobenzyl alcohol 1267 4-chlorobutanol 985 chlorodecanes 126, 130 1-chloro-2,4-dinitrobenzene 1383 chloroethene 860 1-chlorohexane 126 1-chloropentane 126, 129 chloroplasts 1499 2-chloropyridine 546 cholesterol 1476 CH3 OCF2 CHCl2 573 CH3 OHþ 692 2 chromophore 260, 266, 367, 378, 435, 448, 455, 528, 991, 1512 chromium 771, 798ff., 805ff. chromous acid 278 Chudley-Elliott model 801ff. circular dichroism (CD) 1085, 1142f., 1149ff., 1163 – magnetic 245 classical mechanics 639
1531
1532
Index m-ClC6 H4 CHBrCH2 Br 578 m-ClC6 H4 CHClCH2 Cl 578 m/p-ClC6 H4 CHClCH2 F 578 CLIO 69f. Clostridium stricklandii 1157 clusters 689 – of metals 774 cluster and slab approaches 758 CO 773, 777f. CO2 431, 777, 936, 1188 Co 1þ , Co 2þ , Co 3þ 1473, 1476 Co 2þ 1140, 1152 co-adsorbed molecules 771 coalescence 623 cobalt 771, 810 coenzymes 1064ff. – B12 (AdoCbl) 1473ff. – 4-chlorobenzoyl-CoA 1131 – 4-(N,N-dimethylamino)cinnamoyl-CoA 1128 – enoyl CoA 1128f. – flavin adenine dinucleotide (FAD/FADH2 ) 1039f., 1065, 1107, 1426, 1432ff. – flavin adenosine mononucleotide (FMN/ FMMH2 ) 1039f., 1064, 1113, 1350, 1354 – 4-fluorobenzoyl-CoA 1131 – N 5 ,N 10 -methylene-5,6,7,8-tetrahydrofolate 1322 – methylcobalamin (MeCbl) 1473 – nicotinamide 1048ff., 1060ff., 1071 – adenosine dinucleotide (NADþ/NADH) 212, 1038f., 1055, 1065, 1157f., 1165, 1217ff., 1265, 1325, 1393ff., 1425 – adenosine dinucleotide phosphate (NAPDþ/NADPH) 1038f., 1297, 1301, 1322, 1348f., 1393ff., 1439ff. – 4-nitrobenzoyl-CoA 1131 – pyridoxal 5 0 phosphate (PLP) 1139ff., 1151f. – quinone 1039, 1041, 1068 – cysteine tryptophyl (CTQ) 1041 – lysine tyrosyl-(LTQ) 1041 – pyrolloquinoline (PQQ) 1041, 1069 – 2,4,5-trihydroxyphenylalanine (TPQ) 1041, 1273 – tryptophan tryptophyl (TTQ) 1041 – thiamine diphosphate (ThDP) 1419ff. – Mg 2þ -, Apo- 1426 complex 432, 444, 451ff. – amidinium-carboxylate interfaces 492, 494, 527ff., 554 – DNA-acrylamide 492, 496 complex, encounter 960
complex, electron and proton donor 1075 – guanidinium-carboxylate 528 – dihydrogen 603ff., 640 – elongated 409 complex, macromolecular 1378f. complex, metal 480, 1064 complex, Michaelis 1154, 1354f., 1399ff., 1406, 1429, 1448f., 1463 complex, oxygen evolving 551 – phenol:py 544 complex, precursor 509 – stoichiometry 225ff. complex, thymine-acrylamide 496 – of cyclodextrin 225ff., 230ff. complex, transition 513ff., 519, 603ff. – coordination sphere 603ff., 633 – (m-h 2 : h 2 -peroxo)dicopper(II) 514 – bis(m-oxo)-dicopper(III) 514 – Cr 615 – Fe 613, 621, 627 – Fe IV bO 515ff., 549f. – Fe III aOH 550f. – Fe III bO 550 – iron bi-imidazoline (Fe III Hbim) 492f., 513f. – [Fe(H2 )H(dppe)2 ]þ 623, 632 – [Fe(H)2 (H2 )(PEtPh2 )3 ] 625 – [FeH2 (H2 )(PEtPh2 )2 ] 632 – cis-[FeH(H2 )(L)4 ]þ 624 – PFe III bO, P ¼ porphyrin 550 – [(N4 Py)Fe IV bO] 2þ 514ff. – Ir 613, 619 – IrClH2 (H2 )(P i PrR3 )2 622, 632 – [Ir(H2 )H(bq)(PPh3 )2 ]þ 623 – IrH2 X(P t Bu2 Ph)2 626 – IrXH2 (H2 )(PR3 )2 627ff. – [TpIrH(H2 )(PR3 )]þ 624 – [Mn(CO)(dppe)2 (H2 )]þ 620 – Mo 606, 615, 617, 624f. – MoH2 (CO)(Et2 OCH4 PEt2 )2 619 – [Cp*MoH4 (H2 )(PR3 )]þ 624 – [Cp2 MoH3 ]þ 628 – Me2 X(C5 R4 )2 Mo(H2 )]þ 628ff. – Nb 615, 619, 629 – Os 627 – [Os(H2 )(ethylenediamine)2 (acetate)]þ 605 – trans-[OsCl(H2 )dppe)2 ]þ 609 – OsH3 X(P i PR3 )2 626 – polyhydrides 619 – [ReH9 ] 2 – [ReH8 (PR3 )] 606 – [ReH4 (CO)(H2 )(PR3 )3 ]þ 624
Index – [Re(H2 )(H)2 (PMe2 Ph)3 (CO)]þ 625 – [ReH4 (CO)L3 ]þ 628f. – [Rh(cod)(dppb)]þ 664 – [(bpy2 )(py)Ru IV bO] 2þ 514, 517 – MeC(O)O-[Ru]-Y 540ff. – CpRuH(PP), PP ¼ diphosphine 613 – [Cp*Ru(h 4 -CH3 CHbCHCHbCHCOOH)] [CF3 SO3 ] 662f. – [CpRu(H2 )(dppm)]þ 619 – Tp*RuH(H2 )2 631 – Cp*RuH3 (PCy3 ), Cp* ¼ C5 Me5 622f. – RuH2 (H2 )2 (PCy3 )2 632f. – (L2 )(H2 )Ru(m-H)(m-Cl)2 RuH(PPh3 )2 671f. – trans-[Ru(D2 )Cl(dpp)2 ]PF6 671ff. – Ru 619ff., 627 – [RuH(H2 )(dppe)2 ]þ 621 – [RuH(H2 )(CO)2 (PR3 )2 ]þ 624f. – [RuH(H2 )(PR3 )]þ 628 – [RuH2 (H2 )2 (PCy3 )2 ] 630 – ruthenium polypyridyl 492ff., 524, 530f. – Cp*2 Zr(H2 ), deuterated 625 – SISHA interactions 632 – Ta 615, 629 – tris-bipyridine 497, 538 [Ru(bpy)3 ] 2þ 529ff. – W 606, 615, 617, 625 – W(CO)3 (PR3 )2(H2 ) 618, RbCy, iPr 603ff., 609f., 621ff., 674ff. – Zn II porphyrin 523ff., 528ff. – Zn II tetraphenylporphyrin 533f. compression variable 1058ff. comproportionation reaction 495 computer simulations 1171ff., 1193 condensed phase 597ff., 864, 867ff., 1241ff. Condon field emission 653 configuration 72, 372, 858 – boat-shaped 15 (tropolon) configuration interaction singles methodology (CIS) 21 confined geometry 223ff. conformation 228, 1371ff., 1394, 1447 – base-on, base-off 1474 – b-barrel 435f. – in alkane radical cations, alkanes 107f., 119f., 122, 128ff. – bowl-shape 1462 – helical 1027ff., 1080ff., 1097, 1102, 1112, 1370f. – wheel 1082 – helix-loop-helix 1080, 1086, 1089, 1096, 1378ff. conformation, b-sheet 1027, 1029, 1100, 1349, 1386, 1444
conformational – changes 1361, 1367, 1378 – dependence 213 – during H transfer reactions 197ff., 203ff. – E- and Z-isomers of vinyl ethers 575 conformational flexibity of glycopyranoside units 231 conformers 1362f. continuum theory 499, 539 copper 757, 759, 764, 772ff., 707, 800, 812, 1017, 1028f. corrin 1473, 1480 corner cutting 1209, 1215ff., 1485 corrphycene 245ff. Coulomb cage 1511ff., 1519 Coulomb cage, intra- 1510ff. Coulomb energy 163 Coulomb field 124f. Coulomb interaction 445 coumarins 230ff., 448 CPMD see Car-Parrinello molecular dynamics Cram boxes 223 criss-cross mechanism 1123 cryogenic matrices – chlorofluorocarbons 107f. – CCl3 F 105, 115ff., 129 – CCl2 FCF2 Cl 122 – electron acceptors – chloroalkane 123ff. – CO2 123ff. – SF6 122 – zeolites 122f. crystal structure – of enzyme complex 1153 – orthorhombic 289 crystal structure, single 794 CRYSTAL 286f. CsHSO4 732, 749 Cu 2þ 1279 – phenoxyl radical 1278 cubic force constants 470 Cumene 517f. cyanoalkanes 962 3-cyanomethyl-4-methylthiazolium cation 961ff. cyclic dimers 204, 462, 466ff., 523ff. cyclodextrin (CD) 223ff., 228ff. – structure 224 1,3-cyclohexadiene 359, 519 cyclohexane 350, 354f., 370, 519 cyclohexene 518 2-cyclohexenone 1348ff. N-cyclohexylformamide (CXF) 1397
1533
1534
Index cyclopentene 689 cyclopentadiene 519 cyclopropane 876f., 882 cysteamine 1025f. cysteine (Cys) 1023, 1027, 1086, 1145, 1159, 1161f. cytochrome 1342f. cytochrome c 1372 cytochrome oxidase 528, 1499, 1516ff. cytochrome P450 549f. cytoplasma 1515 cytosine 525, 542, 548, 934
d de Broglie 1256 – wavelength 765 Debye-length 727 Debye-Smoluchovski equation (DSE) 391, 422f., 448ff., 1499, 1510f. cis-decalin-d18 112ff. decane 129 decarboxylation 1018f., 1048, 1085f., 1130, 1301, 1419, 1425ff. decarboxylation, oxidative 1432 DeDp-ApAe systems 513, 524, 527, 531ff. De-[Hþ ]-Ae systems 528 deformation 932 degenerate four-wave mixing (DFWM) 5, 14 degree of freedom (DOF) 80f., 84, 88, 223f., 275, 643, 837, 841, 864, 1008, 1079, 1213f., 1232, 1245f. dehydrohalogenation 576ff. – alkoxide promoted 579 p-delocalization 566, 580 denaturing 1373, 1421 dendrimers 240 density functional theory (DFT) 8, 13, 41ff., 205, 245, 262, 286f., 296, 360, 493ff., 571, 627ff., 689, 692, 696ff., 704f., 758, 777, 930, 1174, 1291 density matrix 648, 661, 666f., 668 – evolution 1196 – theory 649ff. density operator 648, 659, 666 deoxyadenosine 542, 1477 5 0 -deoxy-5 0 -adenosylcobalamin 1023 deoxyuridine 542, 1020f. 2 0 -deoxyuridine-5 0 -monophosphate, cyclic (cUMP) 1322 depolarization 259ff. deprotonation 229, 496, 949ff., 960, 965ff., 1032, 1158, 1421, 1427 – energy 687 – rate 1422ff.
designed catalyst 1085ff., 1100 desorption 782 – kinetics 773 – spectroscopy (TDS) 755, 776f., 780 desorption, thermal 775 deuterium 764f., 767 Dewar-Chatt-Duncanson model 604 DFT see density functional theory DFWM see degenerate four-wave mixing DHAQ 365 diabatic – curves 588 – electronically 314, 327, 330f. – states 1173ff. diamond structure 737 diarylformamidines 204 dibenzo-tetraaza[14]annulene (DTAA) 171, 185f. Dieckmann condensation 1130 dielectric boundary 1501 dielectric constant 232, 377, 511, 529, 723 – electronic 480 – inertial 480 dielectric continuum 480 – of the environment 486ff., 936 dielectric environment 505f. dielectric relaxation 283 1,1-difluoroalkenes 573ff. b-b-difluorostyrenes 575 diffusion 717, 787ff. – barrier 764f. – control 976f., 1014 – coefficients 720, 739, 745, 748f., 765, 790, 795ff., 810, 1503 – equation 741 – energy 758, 764, 773 – long range 789, 817 – mechanism 770, 788, 801ff. – path 792 – tracer 792 diffusion, anomolous 811 diffusion, self- 727, 793 dihydroanthracene (DHA) 513ff. 7,8-dihydrofolate 1322, 1398, 1439f., 1440 dihydrogen (H2 ) 615ff. – bridging ðhÞ 607, 609, 615ff., 623ff., 632, 640 – cis-interaction 612 – cleavage 608, 610ff. – deuterated 639 – dynamic behavior 603ff., 633 – exchange 623ff., 627ff., 675 – pKa 612 – physisorbed 604
Index dihydroxyacetone phosphate (DHAP) 955, 967, 1088, 1101, 1109, 1118, 1157 diketopiperazines 1024f. diiron cofactor 549 diiron metalloprotein 1087 dimethylamine 205 p-(dimethylamino)benzaldehyde (DABA) 1397 8-dimethylamino-1-naphthol derivatives 992, 995f., 1004 N,N-dimethyl-1-aminopyrene (DMAP) 382 5,6-dimethylbenzimidazole 1474 dimethylbutane 517 1,3-dimethylcyclopentadiene 689 3,6-dimethylene-cyclohexa-1,4-diene 689 N-N 0 -di-(p-F-phenyl)amidine (DFFA) 194, 201 1,3-dimethyl-2-phenylbenzimidazoline derivative 1061 3,5-dimethylpyrazole (DMP) 172, 190f., 193ff. 3,4-dinitrobenzoic acid 523f., 529ff. 2,4-dinitrophenyl triester 984 dioxane 173, 208f., 237f., 992 dipeptides 1014 diphenylamine 888 3,5-diphenyl-4-bromopyrazole (DPBrP) 190, 193ff. 3,5-diphenyl-4-pyrazole (DPP) 172, 191, 193f. dipicolylamine ligands 545 dipole 266f., 527, 898, 1178 – moment 59, 63, 287, 1082 – relaxation 620, see relaxation dipole-dipole interactions 462, 791 Dirac exchange interaction 644f. direct methanol fuel cells (DMFCs) 709, 777f. discrete molten globule states 1373f. dispersed polaron 1181 dissolution 753 distance – dHH 630 – continuum 605f. – donor-acceptor 366ff., 484, 493, 499, 548, 1198, 1225, 1230, 1326, 1332f. – off-pathway 548 – in crystals 810 – equilibrium 277f., 289, 291 – NaN in porphyrins 245, 249ff., 255 – Om-H in zeolites 692 – OaH in water clusters in zeol 696ff. – OaO 919f., 940, 1512 – shrinkage 231 – reduction 362ff. – transfer 511, 754
distant residues 1452 – pattern 787f. 1,4-dithiothreitol 1020ff., 1025 di-tertbutyl-2-hydroxyphenoxyl radical 173 distortion 816 DMSO 386f., 399, 407ff., 431f., 542, 544, 950f., 1116 DNA 232, 240, 541, 752, 1374, 1377ff. – damage 1028 – repair 934 dividing surface 833, 843, 869, 905 docking motif 1375f. docking program (DOT) 1377 DOIT program 908, 923, 927, 938 doublet separation (DS) 4ff., 15, 17, 25, 27 DPBrP crystal 171 drugs 236 – metabolism 1020 dyads 536, 1131, 1430 dyes 225, 228ff., 1509ff. – aromatic 410 – Dansyl 234 – organic 378
e Escherichia coli 553, 1023, 1161, 1398, 1425ff., 1443f., 1450 echo attenuation 731 – spin- 790 Eckart barriers, one-dimensional 1293 effect of excitation 1315 effective molarity 987ff., 1001ff., 1008 Ehrenfest’s theorem 358 Eigen cation see H9 O4 þ ion eigenfunction 61, 64, 639ff. – nodes through CaC bonds 385 – symmetric (gerade) and anti-symmetric (ungerade) linear combinations 642 Eigen’s scheme of H-transfer 165, 174 Eigen solvation core 454 Eigen-type mechanism 962 eigenstates 24, 89, 98, 359, 644f., 768f. eigenvalues 61f., 768f., 802 eigenvectors 802, 1174 Eigen-Weller model 444, 451f. elastic after-effect see Gorsky effect elastic incoherent structure factor (EISF) 806 elbow plot 757 electrocatalysts 711 electrode 710ff., 771 electrolytes 709ff., 718, 732, 749, 771 electron – lone-pairs 110 – p-systems 110
1535
1536
Index electron attachment 124 electron – acceptor (Ae) 503, 507, 523 – bonding 480 – donor (De) 503, 507, 523 – relay 548, 552 – transfer (ET) 480, 503ff. – stepwise 511 electron capture 887 electron diffraction 42f. electron-energy loss spectroscopy 776 electron paramagnetic resonance (EPR) spectroscopy 105, 107, 115ff., 124, 127f., 876, 883ff., 1030, 1384, 1477 – powder spectra 112ff. – spin trapping 1017 – time resolved 265, 527 electron spin echo spectroscopy 265 electron-stimulated desorption ion angular distribution 780 electron transfer 378, 1048ff., 1178 electronic dipole transitions 371 electronic polarization 1233 electronic states – ground state 4, 19, 38, 48f., 100, 225ff., 398ff., 417, 463, 922ff. – of porphycenes 247ff., 253ff., 268 – excited state 4, 15, 38ff., 48f., 225ff., 369, 377ff., 396, 401, 420, 446, 544, 922ff. – of porphycenes 253ff., 258ff., 268 – models 445ff. – transitions 385ff., 399, 404ff., 447ff. electronic switching 363 electroosmosis 725 electroosmotic drag 711, 726f. electrostatic interaction 1395 electrostatic potential 1504 electrostatic stabilization 966, 997 emission decay 229 emission spectroscopy 225, 228, 230, 357, 425, 780, 1408 – time-resolved 534ff. enamine 1000 energy – binding 688 – deprotonation 687, 690 – electrical 709 energy hopping 224 energy of activation 156, 214, 394, 836, 866, 869, 1255 enol 237f., 1000 – ethers 1002ff. enolate 953f., 957, 966, 970, 1000, 1004, 1110ff., 1134
enolization 1002ff. Enterobacter cloacae 1461 enthalpy 1316 entrance channel 757 entropic activation 1404 entropy 213, 428, 978, 987, 1007, 1079, 1316, 1382 – contribution in water, protein 234 enzymatic system 135, 835, 1296 enzyme 212f., 224, 232, 523, 548ff., 598, 975ff., 1006, 1009, 1175, 1186f., 1196, 1209, 1393, 1473ff. – acetohydroxyacid synthase 1430 – acetylcholinesterase 1456, 1460ff. – aconitase 1107 – actinomycin synthetase II (ACMSII) 1140, 1156 – acylaminoacid racemase 1140, 1145 – acyl-CoA dehydrogenase 1107, 1114 – acyl CoA desaturase 1255, 1329 – acylphosphatase 1456 – adenosine deaminase 1456 – S-adenosylhomocysteine hydrolase 1062 – alanine racemase 1113, 1139ff., 1166 – alcohol dehydrogenase (ADH) 135, 212ff., 1037, 1069, 1209f., 1217ff., 1230ff., 1247f., 1251, 1255, 1291, 1304f., 1325f., 1334, 1370, 1384f. – horse liver (HLADH) 1218ff., 1265ff., 1341 – thermophile (ht-ADH) 1266ff. – yeast (YADH) 1244f., 1264ff., 1341 – amino acid racemases 1107, 1140, 1151 – amino acid transaminases 1107 – amino dehydrogenase 1231f. – d-L-(a-aminodipoyl)-L-cysteinyl-D-valine (ACV) 1140, 1156 – aspartate racemase 1140, 1145, 1159 – bovine serum amine oxidase (BSAO) 1262ff., 1273ff., 1329, 1341 – carbohydrate epimerases 1165 – carbonic anhydrase 597, 1334 – II 936ff. – III, human 1188ff. – carboxypeptidase A 1456 – catalytic efficiency 1458 – catalytic power 1045, 1071ff., 1312f., 1341 – chymotrypsin 1456, 1460ff. – citrate synthase 1107 – creatinase 1456 – diaminopimelate epimerase (DAP) 1140, 1145, 1159, 1162 – dihydrofolate reductase (DHFR) 528, 868, 1244, 1255, 1322, 1329f., 1334, 1398, 1403, 1405, 1439ff.
Index – diol dehydratase 1475, 1478ff. – dopamine b-monooxygenase (DbM) 1251, 1279f. – dTDP-L-rhamnose synthase 1140, 1165 – enolase 1107ff., 1131ff. – enoyl-CoA hydratase (ECH) 1109, 1116f., 1127ff., 1134 – ethanolamine ammonia lyase 1475, 1478f. – fumarase 1107 – galactose oxidase 549, 1329 – b-galactosidase 1456, 1464 – a-glucoronidase 1456 – glucose dehydrogenase 1070 – glucose 6-phosphate isomerase 967, 1107 – glucose oxidase 1270ff. – glutamate dehydrogenase 1297f., 1303 – glutamate mutase 1474ff., 1487 – glutamate racemase 1140, 1145, 1159ff. – glutathione transferase (GSTM1) 1383 – glycerol-3-phosphate dehydrogenase (G3PDH) 1403ff. – glycosidases 993 – haloalkane dehalogenase 1456, 1464 – hydrogenase 679 – hydrolases 1455ff. – classification 1455f. – inorganic pyrophsophatase 1456 – 3-isopropylmalate dehydrogenase 1217 – a-ketoacid decarboxylase 1048, 1432 – keto-L-gulonate 6-phosphate decarboxylase 969 – ketosteroid enolase 956 – ketosteroid isomerase (KSI) 956, 1109ff., 1125ff., 1134 – kinetic control 1223ff. – Lac-permease 1518 – b-lactamase 1456, 1461 – lactate dehydrogenase (LDH) 1062, 1209, 1223ff., 1394ff., 1405 – leucyl aminopeptidase 1456 – leukocyte elastase 1460, 1462 – lipoxygenase 492, 498f., 549, 1198, 1231, 1251 – soybean (SLO) 1244f., 1255, 1263, 1271f., 1276ff., 1329ff., 1334, 1345 – lysine 5,6 aminomutase 1474f. – lysozyme 988, 993, 998, 1179 – malate dehydrogenase – cytoplasmatic 1403 – mitochondrial 1403 – malate synthase 1367 – mandelate dehydrogenase 1113 – mandelate racemase 956, 1004, 1108ff., 1116, 1131ff., 1140, 1145, 1152ff.
– mannose 6-phosphate isomerase 967 – methane monooxygenase 1278, 1329 – methanol dehydrogenase 1070 – methylamine dehydrogenase 1251, 1255, 1329, 1334 – methylene glutarate mutase 1475 – methylmalonyl-CoA epimerase (MMCE) 1140, 1152, 1156f. – methylmalonyl-CoA mutase 1329, 1474ff., 1488f. – methylmalonyl-CoA racemase 1145 – microperoxidases 549 – mitogen activated protein kinases (MAPKs) 1375f. – kinase (MKK1) 1383 – monoamine oxidase B 1275f., 1329, 1352 – monooxygenases 1080 – morphinone reductase (MR) 1343, 1347ff. – nitric oxide synthase 528 – pancreatic ribonuclease 1456 – papain 1456, 1461ff. – pentaerythritol tetranitrate (PETN) reductase 1343, 1347ff., 1349 – pepsin 1456 – peptidylglycine-a-hydroxylating monooxygenase (PHM) 1244, 1251, 1255, 1279f., 1322, 1329 – phenylalanine racemase 1140, 1154f. – proline oxidase 1157 – proline racemase 1109, 1112, 1139, 1145, 1157ff., 1302 – prostaglandin H synthase 1016 – protein-tyrosine-phosphatase 1456, 1461ff. – purine nucleoside phosphorylase 1233 – pyruvate decarboxylase 1419ff. – multienzyme complex 1425 – pyruvate oxidase 1419, 1425f., 1432ff. – holo 1426 – D-ribulose 5-phosphate 3-epimerase 1140, 1145, 1157 – ribonuclease 985ff., 1458, 1463f. – ribonucleotide reductase 549, 553, 1028, 1475, 1478 – benzylsuccinate synthase 1020, 1022 – class I (RNR1) 1016, 1024 – class II (RNR1) 1023 – class III (RNR), pyruvate formate lyase 1020, 1022 – ribunucleoside triphosphate reductase 1487 – sarcosine dehydrogenase 1255, 1329 – heterotetrameric (TSOX) 1343, 1348, 1350f. – serine proteases 1452, 1459, 1463
1537
1538
Index – – – – – – – – – –
serine racemase 1140, 1152 serum albumens 1006 succinate dehydrogenase 1107 sugar epimerases 1157f., 1165 superoxide dismutase 1504 thermolysin 1456 thymidylate synthase 1322, 1329f. transhydrogenase 1518 transketolase 1424ff. trimethylamine dehydrogenase (TMADH) 1255, 1329, 1343, 1348, 1350ff. – triosephosphate-isomerase (TIM) 956, 967, 1080, 1101, 1107ff., 1115ff., 1134, 1291, 1334 – tyrosyl-tRNA synthetase 1114 – UDP-N-acetylglucosamine-2-epimerase (UDP-GlcNAc) 1140, 1163 – UDP-galactose-4-epimerase 1140, 1157, 1406 – vicinal oxygen chelate (VOC) superfamily 1152 – xylose isomerase 868 enzyme catalysts 34, 53, 860, 949ff., 955ff., 970, 988, 1079ff., 1195, 1316, 1341ff., 1428, 1439ff. enzyme motion 1447ff. enzyme-substrate complex 3, 28, 987, 1114ff., 1242f., 1265, 1352ff., 1393ff., 1439 enzyme reactions 137, 498ff., 834f., 1110, 1139ff., 1172, 1241ff., 1311ff., 1440 – mechanism 1045ff., 1052ff., 1351, 1421, 1426ff., 1456ff., 1475ff. – double displacement 1457ff., 1462ff. – merge 1054 – ping-pong 1271, 1458 – single displacement 1457 equations of motion 910 equilibrium constants 378, 388, 964, 1056f. – pKa 565, 949ff., 957ff., 967, 977, 981, 1002, 1085ff., 1090ff., 1101, 1107ff., 1127f., 1190, 1194, 1352ff., 1440 equilibrium overshoot 1142f., 1159, 1162ff. equilibrium perturbation 1146ff. – washout 1148f., 1160 ESI (electron spray ionization) 1369, 1378, 1387 ESIPT see excited-state intramolecular proton-transfer esters 976, 1086, 1089ff., 1097ff. – acetate 980 – cationic 963 ethanol 235, 385, 427, 519, 983, 1217ff., 1305 ethanolic sodium ethoxide 573ff.
ethyl acetate 954f. ethylbenzene 516ff. ethylene glycol 1024 ethylene oxide 729f. Euclidian action 904 eukaryotic cells 1515 Evans window 462 Evans-Polanyi relation 318, 510, 515, 517, 519, 588 excimer/exciplex formation 224 exit channel 757 excitation-emission cycle scenarios 387 excited-state intramolecular proton-transfer (ESIPT) 225, 228, 349ff., 357ff., 362, 366ff., 372f. – multidimensional model 363ff. Eyring equation 676ff. Eyring’s transition state theory 140, 217, 1245
f face centered cubic center (fcc) 755, 797ff., 810 facile intramolecular site exchange 623 fatty acids 1475 – hydroperoxides 1276 – polyunsaturated fatty acids 1014, 1025, 1028 – arachidonate 1015 – linoleate, linolenate 1015 – linoleic acid 498, 1276f., 1328f. FDMR see fluorescence detected magnetic resonance Fe 2þ 1140, 1152, 1381 Fe 3þ -OH 1276, 1328 Feit and Fleck approximate propagator 1212 FEL see free electron laser FELIX (free electron laser for infrared experiments) 56ff., 66ff., 75 femtochemistry 223ff. femtosecond studies 230ff., 471 FeaN bonds 493 Fe(III)aOH cofactor/Fe(III) center 498 fermentative pathways 1475 Fermi resonance 64f., 460, 462f., 469 Fermi symmetrization rules 639, 678 ferricinium ion 1049 ferricyanide 1049ff. ferrierite (FER) 704 Feynman’s path integral formulation 1184 fibrin 1382 fibrinogen 1382 Fick’s diffusion coefficient 793 Fick’s first law 762
Index Fick’s second law 741, 793, 796 field emission fluctuation method 763 flash spectroscopy 443 fluctuation dissipation theorem 1210 fluctuations 791, 803, 1333, 1342, 1447 – of the environment 1177ff. fluorescein 1509ff. fluorene 516, 518 fluoroethanols 591 fluorescence 226f., 239, 258f., 378, 383, 408, 434ff., 449, 523ff., 534 – decay 256, 262, 391, 935 – detected magnetic resonance (FDMR) 107 – detection 266 – dip IR spectra (FDIRS) 20, 41 – enhancement 224f. – excitation spectroscopy 14ff., 253ff., 259, 924 – lifetime 230, 236, 259, 264, 389ff., 431 – polarization 259 – quantum yields 392 – spectroscopy 256f., 350, 387f., 397, 400 – time resolved 1411 – titration 387ff., 422 fluorine bond 426 flux 870 – correlation function formalism 1212 – equilibrium one-way 833, 862 – net reactive 833 fluxional behavior 606, 610, 631 fly and perch propagation 1501 Fokker-Planck theory 86 folding 1363 – unfolding 1363, 1372 – foldons 1373 formaldehyde 519 formamide 386 – dimer 921 formamidine dimer 921 formamidine-formamide dimer 921 formic acid – dimer 897ff., 913, 918ff. – formic acid derivatives 983 – formic acid-formamidine dimer 921 Fo¨rster acidities 421 Fo¨rster calculation 422 Fo¨rster cycle 378f., 383ff., 389ff., 397f., 405f., 410 – energy gaps (FEG) 379, 383f., 406 Fo¨rster equation 417 Fourier transforms/transformation 355, 359, 370, 464, 467f., 471, 793f. fractal network 810 fractional negative charge 965
Franck-Condon 527, 907 Franck-Condon factors 461, 473f., 481, 1179 Franck-Condon overlap 485, 1332, 1345f. Franck-Condon region 349, 360, 363, 366f., 372 free electron laser (FEL) 56f., 66, 69, 75 free energy 310ff., 328, 949ff., 1072f., 1110, 1114, 1149, 1175, 1343ff., 1365, 1372, 1398 – activation 303, 310ff., 329, 339, 394, 512f., 1054, 1190 – bare 310f., 315 – contour plot 311 – correlation 393ff., 510f. – equilibrium 1008 – excited state 383f. – ground state 303, 307, 383 – perturbation (FEP) 1175, 1181f., 1185f., 1195 – perturbation-umbrella sampling 1176, 1185f. – relation (FER) 313, 315ff., 320ff., 332, 335, 597, 1187, 1193 – models 584ff., 590ff. – relation, linear (LFER) 583ff., 594, 1171ff., 1185ff., 1199 – reaction 303, 307, 342, 496, 503, 1054, 1186 – relaxed 383ff. – surface – ET diabatic 481ff. – reactant and product 486f., 510 – total 310, 394 Frenkel defects 804 freon 891 – mixture 185, 633 FTIR see infrared spectroscopy fuel cells 709ff., 732, 752, 771 fullerene (C60 ) 544ff. FWHM (full-width half-maximum) 632
g gallium 761 Gamow model 653 gas phase 383, 594, 679, 835 – clusters 431f., 446 – ionization 115 – reactions 834, 843, 863f., 870 – bimolecular 843ff. – unimolecular 857ff. – studies 580 gas phase spectroscopy 35, 41, 45, 53ff., 61ff., 256, 431f. gas phase ionization 115 gas voltaic battery 710
1539
1540
Index Gaussian model 810 Gaussian cross correlation 357 Gaussian98 program package 360 geminate recombination 445, 448f. generalized gradient approximations (GGA) 758 Gerlt-Gassman/Cleland-Kreevoy proposal 1114ff., 1126 giant planets 740 glass transition 188 glasses 256ff., 265f. – organic 887ff. – sol-gel 235, 240 D-glucanpyranose 224 glucosamines 1018f. a-glucosyl fluoride 983 glutamate (Glu) 1102, 1117ff., 1127ff., 1131, 1145, 1156, 1161, 1179, 1423f., 1430f., 1474ff., 1519 glutamine (Gln) 1092, 1354f., 1397 glutathione (GSH) 1014, 1028 glyceraldehyde 3-phosphate (G3P) 1088, 1102, 1109, 1118 glycine (Gly) 1017ff., 1026f., 1029f., 1349 glycolytic pathway 1107 glycosides 993f. glyoxylate 1367 germanium 757, 761 gold 757, 772f. Golden Rule calculations 931 Gorsky effect 789f., 795, 798ff., 802 gramacidin S 1154 green solvent 419 GROMACS program 1511 Grote-Hynes theory 313 Grotthus-type hopping proton 452f. Grotthuss mechanism 399, 418f., 443f., 454, 717, 1192, 1503 ground state destabilization 1316 group theory 639 Grove 710 guanine 525, 541f., 548, 932ff. guanidinium chloride (GdmCl) 1372f. guanidinium group 998 guest-host 224ff., 230, 236, 240 Guoy-Chapman theory 723 Guoy-Chapman-Stern theory 1504f.
h hafnium 800, 805ff. Hagen-Poisseuille 726 Hamiltonian 12f., 45, 59f., 81f., 84, 87ff., 489, 645ff., 657ff., 670, 813, 904ff., 1173, 1176ff., 1210ff., 1231, 1234
– model, 2D 275ff. – pure spin 644 – Zwanzig 1210 Hammes-Schiffer and coworkers’ model 541 Hammett – equation 401ff. – plot 568 – value 1095 Hammond see Bema Hapothle Hammond postulate 318, 590, 1054, 1269 Hangman porphyrin models 550 harmonic approximation 834, 844, 1287 harmonic frequency 854 – calculation 287, 288ff. harmonic twofold potential 643 Hartree – time-dependent Hartree approximation 82 Hartree-Fock theory 689, 1481 – methodology, restricted (RHF) 21ff. Haven ratios 722, 731, 790 heart 1223ff. Heaviside step function 839 Hessian matrix 838f. hexamethylphosphoramide 1062 H-bonded crystals 273ff. – NaHaN fragments 277 – containing quasi-symmetric O H O fragments 277ff., 288ff. H-chelate ring 361, 363, 366, 371 HCl 309ff., 394 HClO4 392, 425 HClO4 2H2 O 288ff. heat of solution 753 helix, coaxial 435 hemiporphycene 245ff. hemoglobin (Hb) 1381 heptane 126ff., 173 hexagonal close-packed (hcp) 770 hexafluoro-2-propanol (HFIPA) 546 hexamethylbenzene 689 hexane 386 hexan-6-ol-1-al 1314 3-hexyne-1-ol 662f. HF 308ff., 394, 593ff., 983 HgCdTe 749 high-resolution electron-energy loss spectroscopy (HREELS) 768, 776, 779ff. Hilbert space 643ff., 659, 670 histidine (His) 936, 1026, 1029, 1083f., 1087, 1090ff., 1097ff., 1108, 1113ff., 1120, 1131, 1145, 1155, 1188, 1193, 1228, 1352ff., 1394, 1430, 1474 H3 O2 þ (H2 O)2 699 H3 Oþ 1500
Index H5 O2 þ ion 286, 288ff., 454, 696ff., 714ff., 1500, 1504 – structures in crystal and in gas phase 289 H7 O3 þ ion 697 H9 O4 þ ion 454, 694, 715ff. Hoffmann-Lo¨ffler-Freytag reaction 1018 hole refilling 763 hole-burning experiments 256 homogeneous media 714ff. HOMO see molecular orbital, highest occupied homocysteine 1063 host 226, 230, 239 Hove correlation function 793 Hoz, Yang and Wolfe (HYW) 592, 595 HPLC 1369, 1378, 1381 Hu¨ckel aromaticity 184 human genome 1013 humidification 711 Hund 641f. Huppert-Agmon model 428 Hwang Aqvist Warshel (HAW) 1186ff. hydration 231ff., 655ff., 723ff. – shell 717 hydride 771, 804ff. – dynamic behavior 603ff. – transfer 136, 835, 1393ff., 1450 – 1,1- 1157 – alternate routes 1055, 1301, 1391 – formal 1037, 1048ff., 1052, 1071 – mechanism 1050, 1069f. – model studies 1037ff., 1045, 1048ff., 1061ff. – rate 1445 hydrocarbons 685, 704ff., 771 – ligands 516ff. – saturated 106 – unsaturated 658 hydrodynamic theory under stick conditions 227 hydrogen – dissociation 753, 775 – homolytic 747 – probability 771, 782 – spontaneous 761 – freezing point 755 – quantum delocalization 770 hydrogen atom abstraction 512ff., 522, 553, 887ff., 1023, 1322, 1351 hydrogen atom transfer (HAT) 136, 223f., 503ff., 509ff., 555, 843, 1013ff., 1473ff. – geometry 504ff. – mechanism 504ff. – synchronous 505f., 513, 522
hydrogen bond 426, 463ff. – bihalide anions 60ff., 91ff. – bihalide neutrals 95 – breaking 90ff., 511, 539, 565ff., 588, 878, 975, 981, 1000, 1362 – CHC 207 – compression 141, 144, 159, 196f., 200 – crystalline environment 274 – energy 715 – formation 775, 960f., 975, 981, 1007 – CaH 957 – geometric hydrogen bond correlation 142f. – geometry 141, 143, 193ff. – length 193ff., 248 – low barrier (LBHB) 1195, 1459 – OHN 207 – OHO 207 – pre-equilibria 203ff. – quasi-linear 274 – strength 53, 75f., 185, 188, 245, 274f., 280ff., 288ff. – halides (Br, I) 59 hydrogen bonded chain 776, 783 hydrogen bonding 459ff., 717, 730, 997 – polarized 527ff. – symmetric 523ff. hydrogen-bonding wire 423 hydrogen bromide 849ff. hydrogen cyanide 960 hydrogen diffusion 754 hydrogen halides 454 hydrogen jump 787ff., 801ff., 812ff., 823ff., 881ff. – in binary-hydrogen systems 802 – long-range 793 – low-temperature hopping 821ff. hydrogen migration 753 hydrogen subway 84 hydrogen motion 787ff., 807, 875 – quantum 812 hydrogen storage 825 hydrogen transfer (HT) – between carbon and oxygen 565ff. – in complex systems 212ff., 1318 – dynamics – ground state 368 – fast 224ff. – ultrafast 79ff., 224, 230ff., 236ff. – enzymatic 1209ff., 1241ff., 1316ff., 1419ff. – exchange 641, 1361ff. – intramolecular 670 – rates 1361ff., 1371 – excited state (ESHT) 410, 446 – from carbon 1311ff.
1541
1542
Index – four-state diagram 503, 510, 537 – heavy atom motions 174ff., 197ff. – environmental influence 187f. – HH 153ff., 160, 162, 170, 177f., 196ff., 210f. – free energy diagram, free energy correlation 155ff. – HHH 159ff., 210f. – HHHH 161ff., 196, 215 – in condensed phases 135ff. – application 168ff. – in liquids 136, 188 – in solids 136, 835 – intermolecular 137, 188ff. – intramolecular 83ff., 166, 185ff. – excited state 443f. – multiple 136, 1139ff. – concerted 151f. – stepwise 152ff., 159f., 161ff., 182, 185ff. – nonclassical 1245 – on metals 751, 754, 756, 761ff., 775ff. – photoinduced 460, 523f. – probability 1262 – single 136ff. – reactions 833 – with pre-equilibria 165ff. hydrogenation 658, 664, 771 – single/two-step 666ff. hydrogenolysis 771 hydrolytic cleavage 1455 hydronium ion 953ff., 967 hydroperoxides 1014 hydrophilic domain 723 hydrophilic pore 235 hydrophobic – core 1098 – interaction 239 – pocket 1376 – pore 235f. – residues 1082, 1091 hydrophobic/hydrophilic nano-separation 711 hydroxide 961f., 964, 967, 1188ff. hydroxy dimers 467ff. – deuterated 469ff. hydroxy groups 754 hydroxyacetone 968f. 1-hydroxy-2-acetonaphthone 350, 353ff., 361, 366 1 0 -hydroxy-2 0 -acetophenone (HAN) 225ff., 364 hydroxyarenes 420f. o-hydroxybenzaldehyde (OHBA) 350f., 353, 356f., 369
10-hydroxybenzo[h]quinoline (10-HBQ) 353, 360ff., 369 p-hydroxybenzylidenediazolone 435 3-hydroxybutyryl CoA 1109 3-hydroxybutyrylpanthetheine 1128 10-hydroxycamptothecin (10HCT) 434, 448 2-(2 0 -hydroxy-4 0 -methylphenyl)benzoxazole (MeBO) 206f. 2-(2 0 -hydroxy-5 0 -methylphenyl)benzotriazole (TINUVIN P) 353, 362, 366, 369, 473 9-hydroxyphenalenone derivatives 279 2-hydroxyphenoyxlradical 173 2-(2 0 -hydroxyphenyl)benzoxazole (HBO) 350f., 353ff., 360ff., 366 2-(2 0 -hydroxyphenyl)benzothiazole (HBT) 350f., 353ff., 360ff., 366ff., 463ff., 471ff. 1-(2 0 -hydroxyphenyl)-4-methyloxazole (HMPO) 236ff. 2-(2 0 -hydroxyphenyl)-5-phenyloxazole 362 2-(2 0 -hydroxyphenyl)-triazole 369 2-hydroxypropyl phosphate 997 1-hydroxypyrene (1HP) 382, 394ff., 396, 403, 405 8-hydroxypyrene-1,3,6-dimethylsulfamide (HPTA) 382, 401ff. 8-hydroxypyrene-1,3,6-trisdimethylsulfonamide 426 8-hydroxypyrene-1,3,6-trisulfonate (HPTS) 382, 289ff., 396, 401ff., 419, 446ff., 1502, 1509, 1515 – fingerprint spectrum 447 – photoexcited 1509 hydroxyquinoline 434 6-hydroxyquinoline (6HQ) 423, 434 6-hydroxyquinoline-N-oxide (6HQNO) 424f., 434 7-hydroxyquinoline (7HQ) 423 3-hydroxystilbene 420 4-hydroxystilbene 420 Hynes model 429 hyper-coordination 718
i Ibach’s and Lehwald’s structure model 779f. ice 737ff., 747, 749, 781 – crystal structure 737ff. – deuterated 745 – high pressure phases 742ff. – VII 737f., 740, 746ff. – VIII 737f., 740 – hot 740 ICR see photodissiociation, – ion cyclotron resonance image charge model 1501
Index imidazole 714, 720ff., 729f., 987, 1002, 1115 imidazolium cation 963 improved canonical variational theory (ICVT) 837, 847, 852f. impurities 1066 IN6 spectrometer 820 Indene 516, 517 indigodiimin 170f. inelastic electron tunneling spectroscopy (IETS) 770 inelastic neutron scattering (INS) 273, 283, 285ff., 291, 607, 616, 622, 627, 632f., 640f., 671, 675ff., 771f., 813ff., 817ff. inertial polarization potential 481 inflammatory conditions 1017 infrared array detectors 749 infrared reflection 742ff. – absorption spectroscopy (IRAS) 776f., 779 infrared spectroscopy (IR) 6ff., 16f., 20, 23, 25, 37, 63ff., 72ff., 79f., 248ff., 273, 278, 285ff., 609, 679, 688f., 694ff., 740ff., 1395ff. – 2D 555 – FTIR (fourier transform IR) 19, 26, 45ff., 1369ff. – attenuated total reflection 1371 – mid-IR 389, 471 – ultrafast 554 Ingold radical 173 INS see inelastic neutron scattering instanton 910f. – action 908, 913ff. interconversion 258, 266, 1088, 1162, 1223, 1365 – cis-trans 260, 263, 267 – trans-trans 259f., 263, 266f. intermediates 982ff., 1069, 1294, 1462 – quinoid 1145 – zwitterionic 159, 161f., 184, 199, 206, 921f. intermetallic compounds 788, 804ff. internal conversion 368f., 410 internal friction 789 internal return 1142 – mechanism 566, 572, 575 interstitial sites 787, 797f., 804ff., 818 intersystem crossing 535 intramolecular hypervalent interactions (IHI) 632 inverse electrolysis 710 ionization potential 517ff. ionizing radiation see radiation chemistry IR-PD see photodissociation, – infrared iridium 776, 779, 782 isobacteriochlorin 175, 184 isobestic point 535f.
isobutene 687ff., 704 isoinertial coordinates 836ff. isoleucine (Ile) 1029, 1278, 1444, 1451 isomerization 876ff. isopentane 877, 882 isoporphycene 245f., 932f. isooctane 882 isotope effects 45, 797, 1093, 1115, see also kinetic isotope effects – H and D 3, 7, 20f., 25f., 34, 65ff., 196f., 253ff., 277ff., 645, 678, 745f., 822, 896, 983, 1003, 1009, 1049, 1183, 1266ff. isotope effects, equilibrium (EIE) 618, 1315ff., 1321 isotope effects, heavy atom 576ff., 746, 1165 – carbon 1301 – oxygen 19, 25f. – metal 678 isotope effects, inverse 764 – on isotope effects 1297f., 1301 isotope effects, solvent 1349, 1463 isotopic exchange 1299 isotopic fractionation 154f., 157f., 161ff., 176 isotopic labeling 1253, 1365f., 1371, 1427 – 14 C 1248, 1305 – 1 H 1248 – 18 O 1396 – spin, site-directed 1384 isotopic labeling, mixed 1323f. isotopic labeling, stereospecific 1297 isotopic scrambling 755, 779, 783 isotopologs 193, 530 isotopomer 530, 639, 679, 920, 923 iron 759, 810, 1017
j Jacobian 848 jellyfish 435 Jencks 584 – anchor principle 1042 – libido rule 981, 989, 1002 JN 1092 JNII 1092, 1094 JNIIOR 1096 Johnston and Parr 585
k Kamlet-Taft analysis 409, 426, 445 Karplus calculations 1124 Kemp elimination 1006, 1007 dTDP-4-keto-6-deoxy-D-Glucose ketone (keto-type, keto-bonds) 225ff., 357, 363, 958, 962, 967, 1107 – mono-keto isomer, di-keto-form 370
1543
1544
Index K3 H(SO4 )2 291 kinematic coupling 275 kinetic acidity 566 kinetic analysis 1443 kinetic energy 838 kinetic experiments 509ff., 521f., 675 kinetic isotope effects 135f., 493, 513, 517, 522, 536, 539f., 835, 867 – H/D (hydrogen/deuterium) 140, 144, 148f., 151ff., 157f., 160ff., 169ff., 174, 176, 179, 189ff., 198ff., 205f., 210ff., 251, 303ff., 315ff., 323ff., 333ff., 429, 497, 511f., 544f., 573ff., 622, 843f., 878, 884ff., 914ff., 931, 938ff., 1142ff., 1162, 1241, 1271, 1285, 1313ff., 1342ff., 1478ff., 1512f. – competitive 1248f., 1273, 1305 – intrinsic 1320ff., 1442 – magnitude 1249 – masking 1215f., 1317 – measurement 1247 – model 1245 – kinetic isotope effects, multiple 1146ff., 1286ff., 1304ff. – non-competitive 1247f. – kinetic isotope effects, primary 154, 157, 162, 565ff., 574, 577, 858, 868, 1158ff., 1218f., 1246, 1251f., 1260, 1268ff., 1273, 1287, 1291, 1298, 1315 – kinetic isotope effects, secondary 154f., 157, 1052, 1060, 1247, 1252f., 1268ff., 1287, 1315, 1480 – kinetic isotope effects, temperature dependence of 1326 kinetics 975ff., 1045ff., 1108ff., 1164, 1242 kinetics, exchange 1421 – equivalence 979 kinetics, first order 876, 881f., 1046 kinetics, saturation 1087 kinetics, second order 571, 876, 1046 Kondo parameter 86, 816 KO-42 1087ff. Kreevoy model 1054
l
a-lactalbumin 1374 lactate 1223 Lactobacillus fermenti 1161 Lactobacillus leichmannii 1478 Lactobacillus plantarum 1425f., 1432f. Langevin equation 1210 Langevin dynamics (LD) simulations 1193 large-curvature tunneling (LCT) 842f., 850ff., 862f., 1486 Larmor frequencies 665 laser methods 509 (PCET)
laser-pulse 83ff., 362 – control 92 – infrared 83, 85, 91ff. – UV 90ff. laser-pulse, Ti:sapphire 352 laser spectroscopy 33, 39, 46, 75, 79ff., 423 lattice 816ff. – cubic (C15-type) 798ff., 805ff. – cubic (A15-type) 809 – hexagonal (C14-type) 805ff. – hexagonal (C36-type) 805 lattice expansion 787 lattice-hydrogen interactions 764 Laves phases 798, 805, 823 least-action tunneling (LAT) 852f. least motion 1009 Leffler 590 see Bema Hapothle Lennard-Jones potential, H on metals 756 leucine (Leu) 1278, 1349, 1444ff. leuco crystal violet 1292 level inversion 404 Lewis studies 420 ligand exchange 606 linear dichroism 248, 262, 1371 linear response approximation 1181 Liouville-von-Neumann equation 670 Liouville space 648ff., 659f., 670 Liouville super operator 648ff., 670 Liu-Siegbahn-Truhlar-Horowitz (LSTH) potential energy surface 843 lipid breakdown 1156 lipid vesicles 240 liquid chromatography (LC) 1369, 1378, 1387 liquids 459, 463, 732, 835, 860 liquid crystals 240 liquid films 752 London-Eyring-Polanyi-Sato 585 Lorentzian term 793ff., 801ff., 821 low-energy electron diffraction (LEED) 761, 765, 768, 772, 780 Lo¨wenstein rule 685 luminescence 509 LUMO see molecular orbital, lowest unoccupied lutetium 821 2,6-lutidine 984 lyonium/lyate species 975 lyoxide ion 955 lysine (Lys) 1006, 1083, 1085, 1092, 1099, 1120, 1133, 1143, 1154, 1188f., 1474f., 1519
m magic-angle – configuration 354 – emission decay 227
Index magnesium 810 – in enzymes 969 maleamic acids 988 mammalian brain tissue 1152 malonaldehyde (MA) 3ff., 14, 369 mandelamide 1001 mandelate 1109, 1131, 1152f. mandelic acid 956 manganese 788, 805f., 817ff. Mannich derivative 434 mapping potential 1175f. Marcus – barrier 489, 583f., 594f., 598 – intrinsic 958ff., 969, 1110 Marcus charge-transfer theory (MCT) 394ff. Marcus-Coltrin method 834, 842, 848 Marcus equation 394ff., 592, 600, 958ff., 1188ff. Marcus formalism 1110 Marcus-like model 1329ff. Marcus parabolas 1176, 1198 Marcus relation 305, 310, 597f. Marcus theory 417f., 493, 510, 522, 538ff., 587, 714, 962, 1049, 1054ff., 1185, 1214, 1261, 1332 MARI neutron spectrometer 819 Markov approximation 86 Markov process 793 mass-skew skew 849 mass spectrometry (MS) 432, 1277, 1367ff., 1375, 1378 – accurate mass tag analysis 1367 – C-terminal carboxypeptidase Y digestion 1367 – Fourier transform ion cyclotron resonance (FT-ICR) 1369 – MALDI- 1375ff. – MALDI-SUPREX (stability of unpurified proteins from rates of hydrogen exchange) 1380, 1387 – MALDI-TOF 1367f. – /MS 1367, 1386f. – post-source decay 1367 – radio frequency (RF) 57 – tandem MS 57 master equation 801f. matrix element 282, 642 Matthieu type differential equation 643 MCSCF calculations 918 mean-square-displacement of H 287 Me-BO 173 medical applications (porphyrins) 245 Meisenheimer complex 1131 membrane 240, 443, 552, 711, 724, 733, 752, 1330
– bilayers 1241, 1514 – transporter proteins 1371 membrane, biological 1499ff., 1504ff. 2-mercaptoethanol 1020 metal-hydrogen binding energy 758f. metal-hydrogen potential 765 metals 787ff. – amorphous 795, 810ff. metal surfaces 751ff., 766ff. – heterogenous 754 metallic fluid 740 metallic glass 812 metamorphosis 1152 methane 853ff., 1278 methanol 173, 210ff., 232, 350, 399, 402, 406, 425, 427ff., 565ff., 689, 691f., 711, 726, 775ff., 867, 887ff. – deuterated 567 – dimer 689, 691f. methanolic sodium methoxide 565 methionin (Met) 1026, 1029ff., 1448 methotrexate 1439 methoxide 214, 776ff. methoxonium ion 214, 693f. p-methoxybenzylamine 1275 methoxymethyl acetal 993, 993f. 1-methyl-1,10-dihydroacridan 1049 N-methylacridinium ion (MA(H)þ 1053 N-methyl-1-aminopyrene (MAP) 382 N-methyl-hydroxyquinolinium species 423 4-methylimidazole 1087, 1093, 1096, 1101 methylchlorocarbene 860, 864 methylcyclohexane 172, 199 methylethylether 203, 205 2-methyl-6-hydroxyquinoline-N-oxide (MeHQNO) 424f. 3-methylindene 689 methylisocyanide 887 methylmalonyl-CoA 1156 3-methylpentane 237 3-methylphenyl-(2,4-dimethylphenyl)-methane 689 methyl salicylate 351 2-methyltetrahydrofuran 537 methyl viologen acceptor 497 Mg 2þ 597, 1112, 1131ff., 1140, 1152, 1426 Mg-Mg breathing 868 micelle 229, 232ff., 240, 448, 752, 1509 Michael addition 1102 Michaelis mimics 1403f. microcanonical emsemble 833 microcanonical optimized curvature tunneling (mOMT) 856, 862, 867 microcanonical variational theory 837ff. microscopic reversibility 1049
1545
1546
Index microwave spectroscopy 13, 37 Miller-index 759 minimum energy for tunneling 135, 145, 150, 188f., 202, 213 minimum energy path (MEP) 835ff., 846ff., 854f., 863ff., 910ff., 1485f. Mitchell hypothesis 1500 mitochondria 1499f., 1505, 1515 mixed isotopic exponents see Saunders exponents MN 1092 Mn 2þ 1140, 1152, 1426 MNDO study 591, 1401 MO see molecular orbital molecular diffusion 746ff. molecular dynamics (MD) 230f., 287, 490ff., 692, 696, 1449, 1518 – classical 287f. – with quantum transition (MDQT) 1196 molecular hydrodynamic theory 231 mobile loop 1407 molecular mechanics (MM) 1171ff., 1193, 1228, 1233, 1291, 1334, 1342, 1349, 1440, 1480 molecular mechanics calculation 230 molecular memories 245 molecular orbital (MO) 583, 594f., 757, 1172 – computations 16, 20, 22f., 590ff. – highest occupied (HOMO) 107, 513 – of 2-naphtholate 420 – lowest unoccupied (LUMO) 245, 1022 – of 2-naphtholate 420f. – semi-occupied (SOMO) 107, 115, 1022 molecular pocket 223ff. molecular structures, derivatives of 2- and 4membered aromatic rings 380ff. Møller-Plesset perturbation theory (MP2, MP3, MP4) 21ff., 42ff., 71, 249, 596, 689, 695ff., 705, 1481 molybdenum 807 moment of inertia 40, 1288, 1315 – (a-type, b-type) 40, 47 monensin 1514f. monolayer 779, 774, 779 mono-p-nitrophenyl fumarate 1089, 1091ff. Monte Carlo calculations 761, 791, 939 – diffusion (DMC) 60, 71ff. More O’Ferrall 584 More O’Ferrall-Jencks diagram 592 Morse potential 1175 motion 1341 motion, coherent low-frequency 459ff. motion, coupled 1313, 1449ff. motion, gating 1345, 1350f.
motion, low-frequency 471ff. motion, primary-secondary coupled 1323 mouse brain enzyme 1152 Mulliken charge transfer picture 308f. multilamellar vesicles 1502f. multimode (MM) methodology 59f., 69, 71, 75 multiphoton process 55f., 66ff., 76 multishell continuum model 231 muonium 843ff. Murdoch 584 muscle 1223ff. mutagenesis 1217ff., 1375f., 1446ff. mutants 1029, 1099, 1102, 1108, 1132, 1145, 1154, 1161, 1189ff., 1263, 1267f., 1278, 1325, 1332, 1352ff., 1516 mutation 1383, 1430 – multiple 1445, 1452 – point 934
n
Naþ 597, 1514f. Nafion2 711, 724ff., 732 nanoscopic pools 232 nanostructure 228, 713 nanotubes 225, 240 NaOH 425 naphthalene 386, 420, 446 naphthalenediimide (NI) carboxylate 534ff. naphthazarin 896, 899, 913, 926, 942 naphthols 445, 448 – 1-naphthol (1-NP) 228ff., 380, 386f., 398f., 401ff., 420ff., 428, 431f., 446 – 2-naphthol (2-NP) 380f., 385f., 389, 398f., 401ff., 420ff., 428 – 1-naphthol-3,6-disulfonate (1N3,6diS) 380, 401ff. – 1-naphthol-4-chlorate (1N2Cl) 380, 403 – 1-naphthol-2-sulfonate (1N2S) 380, 403 – 1-naphthol-3-sulfonate (1N3S) 380, 403 – 1-naphthol-4-sulfonate (1N4S) 380 – 1-naphthol-5-sulfonate (1N5S) 380, 402 – 2-naphthol-6-sulfonate 449 – 5-cyano-1-naphthol (1N5CN/DCN1) 380, 401, 422, 449 – 5-tButyl-1-naphthol (1NtBu) 380, 402ff., 421 – 5-cyano-2-naphthol (2N5CN/5CN2) 380f., 401, 421ff., 428, 431f. – 6-cyano-2-naphthol (6CN2) 422f. – 7-cyano-2-naphthol (7CN2) 422f. – 8-cyano-2-naphthol (2N8CN) 380f., 401, 421 – 5,8-dicyano-2-naphthol (DCN2) 401, 421ff., 428ff.
Index – 2-naphthol-6,8-disulfonate (2N6,8diS) 380f., 401ff. – 5-methanesulfonyl-1-naphthol 448 – 5-methanesulfonyl-2-naphthol (5MSN2) 422 – 6-methyl-2-naphthol (2N6Me) 380f. – 5,8-dicyano-2-naphthol (2N5,8diCN) 380f. – 2-naphthol-3,6-disulfonate (2N3,6diS) 380f., 1508 – 3,5,8-tricyano-2-naphthol 421 naphthoquinone 547 narcisstic type of reaction 260 native chemical ligation 1086 near attack conformations (NAC) 1044, 1404 neopentane 877 Nernst-Einstein relation 719 Neurospora crassa 1380 neurotoxic effects 1029 neutralization 214 neutron diffraction crystallography 142f., 273, 277, 605, 695 Newtonian dynamics 1210 Newtonial principle of parsimony 1042 Ni 2þ 1140, 1152 nickel 755, 758f., 764ff., 771ff., 776, 779, 781, 800, 809ff. Nile Blue a 235 niobium 753, 762, 787f., 798f., 801f., 809, 814ff., 821ff. NIR 352 nitrogen monoxide 1020 nitrogen dioxide 1020 2-nitropropane 1285, 1290 p-nitrophenyl acetate 1087 4-nitropyrazole 192 p-nitrophenyl esters 987 NMR lineshapes 655ff., 677, 1293 NMR, natural abundance techniques 1248 NMR pulse sequence 174 NMR relaxation 188 NMR relaxometry 923, 939 NMR spectroscopy 15, 38, 136, 142f., 187, 197, 201ff., 238, 248ff., 265, 534, 610f., 615ff., 629f., 639ff., 666f., 787, 791, 927, 1080, 1084, 1098, 1364, 1375, 1451 – 13 C 615, 628, 1300, 1406, 1421 – CLEANEX (clean chemical exchange) 1366 – phase modulated (CLEANEX-PM) 1366f., 1386 – coupling constant 619, 662, 671 – downfield shift 693 – 1 H 671, 700ff., 951, 1092, 1115, 1428f. – pulsed field gradient (PFG) 716, 719ff., 731, 792, 798
1547
– 2 H 623, 671ff., 677 – HSQC (heteronuclear single quantum coherence) 1366, 1374 – FHSQC (2D-fast) 1266f. – liquid 615, 628, 251, 640, 646, 671 – NOE (heteronuclear Overhauser effects) 1365, 1427, 1448 – 17 O-PFG 716 – 31 P 628 – PFG 719f. – solid state 251f., 604f., 621ff., 627, 671ff. – TROSY 1367, 1386 NMR studies 283, 630ff. – 15 N CPMAS NMR 251ff. – magnetic field-cycling 283 m/p-NO2 C6 H4 CHbCF2 575 nonadiabatic coupling 483ff. nonaqueous solution 428ff. non-enzymic systems 1037 nonlinear vibrational spectroscopy 463 nonxollinearly phase matched optical parametric amplifiers (NOPAs) 352f. norbornene 547 NovoTim 1.2.4 1088 nuclear motion 349ff. nuclear spin 140 nucleoside – diphosphates 553 nucleoside, deoxy- 553 nucleoside, pyrene-modified 542
o octane 126ff. 2,3,6,7,11,12,17,18-octaethylcorrphycene 247 2,3,6,7,11,12,16,17-octaethylhemiporphyrene 247 2,3,6,7,11,12,16,17-octaethylporphyrene 247 olefin coordination 604 oligosaccharides 224 one-frequency models 1287, 1291 optical density 532 optical spectroscopy 38, 389, 927, 1147, 1219ff., 1407 optical trigger – ultrafast 445ff. – trigger pulse 443 optimized curvature tunneling (OCT) 842f. optimized multidimensional tunneling (OMT) 856f. Orange II 239f. organelles 1499 organic ethers 614 organic solution 528ff. organic solvent 399 organic solvent, aprotic 542
1548
Index – tritiated 565 2,3,4,5,6-pentafluorobenzyl alcohol 1219 pentane 129 pepsin 1367 peptide 435, 1013, 1017, 1027f., 1079ff., 1134, 1322, 1363 – backbone 1081, 1361ff., 1370, 1446ff. – EF hand 1380 – scaffolds 1079f., 1085, 1095ff., 1345 peptide, b-amyloid-(b-AP) 1029f. peptide, unstructured 1361 Perdew-Burke-Ernzerhofer (PBE) 697f. Perdew-Wang91 (PW91) 697f. perfluorocarbons – as cryogenic matrix 107 perfluorohexanesulfonyl-2-naphthol (6pFSN2) 425 permanganate, tetrabutylammonium (Bu4 NMnO4 ) 514ff. permeation methods 795f. permutation operator 645ff. peroxynitrite 1020 perturbation treatment 1174 PES see potential energy surface pH 975, 990f., 999, 1062, 1087, 1090ff., 1101f., 1128, 1150, 1361ff., 1371f., 1400 – dependence 496, 538ff., 1352, 1362, 1423 p – of a solution 397 palladium 753, 755, 759, 762, 771ff., 776f., – jump 378, 419, 445 779ff., 787, 796ff., 801, 810ff. phase diagram – film 796 – H-on-Ru(0001) 760 PAM 1140 – of ice 737f. (PAMAþ H3 PO4 )nH3 PO4 727f. – solid-solution 787 para-hydrogen 655ff., 665, 669 phase transition, 2D–3D 754 para-hydrogen induced polarization (PHIP) phenols 446, 519ff., 548 640, 657ff., 662ff., 668f., 679 – fluorinated 426 – 1 H PHIP 662ff. – oxidation potential 520ff. – 13 C PHIP NMR 664f. – oxidation rate constants 522 – lineshapes 665ff. para hydrogen and synthesis allow dramatically phenolate 981 enhanced nuclear alignment (PASADENA) phenol-ammonia clusters 410 phenylalanine (Phe) 1026, 1154f., 1218ff., 656ff., 662, 667ff. 1376, 1435, 1444 partition functions 140, 834, 844, 914f. 1-phenylcycloproanolate 1000 partition functions, reactant 836f. phenylethylbromide 1305 path integral quantum TST (PI-QTST) 869 9-phenylfluorene 419, 570, 572, 580 pathological processes 1013 – deuterated 572 Pauli exclusion principle 640, 670 – tritiated [9-PhFl-9-t] 565ff. Pauli matrices 660 phenyl glycidyl ether 426 Pauli repulsion 757 phonon-vibron coupling 764 P branch 7, 14 phosphate 1001 PDLD/S-LRA approach 1189 – monoesters 995 PEF see potential energy function phosphatidyl choline 1504, 1508f. penicillin 1156 phosphatidyl inositol 1504 1,3-pentadiene 858 phosphatidyl inositol 4,5-diphosphate 1594 pentafluorobenzene (PFB) 565ff., 576, 580 organometallic chemistry 640 orthoesters 982 ortho hydrogen 656 oscillator 461ff., 469ff., 642 oscillator, harmonic 81f., 84, 87f., 1211, 1258 – approximation 254, 258 – approximation, quantum mechanical 654ff. – undamped 491 oscillator, one-dimensional symmetric double 138f. overlayer-underlayer transitions 762 oxalamidines 155, 172, 177, 197ff. – OA5 200f. – OA6 200f. – OA7 198f., 200f. oxidative damage 541 oxidative cleavage 1322 oxidative stress 1014, 1020 oxidic support materials 771 oxo-acids 727, 732 oxolacetate 1085f. oxygen – carboxylic 1179, 1214 – glycosidic 1179
Index phosphatidyl serine 1508f., 1515 phosphatidylic acid 1508f. phosphazene 169 2-phosphoglycerate 956, 1109, 1131ff. phosphoglycolohydroxamate 1123 phospholipid 1501ff. – bilayer (membrane) 1503 – black lipid membrane 1514 – head group 1502, 1504 phosphonic acid 714, 720, 729ff., 732 4 0 -phosphopantethein (PAN) 1155 phosphorane dianion 986 phosphorescence enhancement 224 phosphoric acid 711f., 714, 719ff., 732 phosphoric acid fuel cells (PACFs) 709ff. phosphorolysis 1223 photoacidity 379ff., 389ff., 410 – determination 387 – effects of substituents 400ff. – solvent assisted 377ff. – 1 La 1 Lb paradigm 404ff. – solvent effects 398ff. photoacids 377ff., 383ff., 389ff., 397ff., 410, 417ff., 422ff., 433ff., 445ff., 1502 – biological 436 – in the gas phase 431 – pKa values 401f., 408, 419, 421ff., 445 – reactivity 393 photoacids, cationic 398 photoacids, neutral 398 photoacids, super 417, 422ff., 426ff. photoactivation 1370 photobases 377ff., 383ff., 390ff., 411, 429 photochemistry 224ff. photochemistry, radical organic 507 photocleavage 224 photodeoxygenation 424 photodetachment – of electrons 91ff. photodissociation 427ff., 782 – infrared (IR-PD) 55ff., 61ff., 65ff., 75, 91, 100 – ion cyclotron resonance (ICR) 106 – rate, protolytic 434 photodynamics 228 photoexcitation 57, 225, 266, 432, 435, 496 photohydrolysis 426 photoinitiation 509 photoisomerization 224f. photolysis 876, 882 photolysis, laser flash 1016 photon echo techniques 460 photons 55f. – absorption 387
– emission 387 photophysics 224ff., 436 photosynthetic systems 245, 418 – bacterial 552 photosynthesis 1499 Photosystem II 538 phototherapy 236, 245 photovoltaic systems 245 phthalocyanine 169, 176 physisorption 753ff. pigments of life 245 platinum 710ff., 763f., 771ff., 776ff., 779ff., 800 Platt’s notation 385 PMP 194 Poisson-Boltzmann equation 723, 1505 Polanyi see Bema Hapothle, Evans-Polanyi polar headgroup 229 polarity 232 polarity, solvent 325, 529 polarity reversal catalysis (PRC) 1021 polyacrylamide hydrogel 235 polybenzimidazole (PBI) 713, 727ff. polymer electrolyte membrane or proton exchange membrane fuel cells (PEM) 709ff., 725, 731f. polymeric fibrils 1378 polymers 240, 256, 685, 713, 727, 749 – films/sheets 256ff., 262ff. polymers, hydrated acidic 723ff. polymethylmethacrylate 267 polypeptide chains 523 polyphosphate 728 polystyrene 187 polyvinyl butyral 256, 258, 263f. population dynamics 85ff., 390f. porphine 928f. porphycenes 171, 185f., 193ff., 245ff., 896, 929f., 842 – crystalline 252f., 255, 265 – nonsymmetric 256 porphyrinoids 267 porphyrins 135, 155, 169f., 184f., 193ff., 206, 245ff., 266, 523ff., 529ff., 896, 913, 1293 – analogs of p. 174ff. – constitutional isomers (reshuffled) 245f. – hydroporphyrins 184ff. – inverted (N-confused) 245 – metal complexes 245f., 528ff. – symmetric 174ff. – unsymmetrically substituted 181ff. porphyrins, free base 547 positive hole density 105, 107, 109
1549
1550
Index positive hole transfer 125 potassium acetate 395 potassium bicarbonate potassium bromide 743 potassium formate 395 potential energy 760 potential energy curves 238 – enthalpy changes 591 potential energy diagram 753, 856 potential energy function (PEF) 3ff., 15f., 24, 180, 233, 1174 – double-well 4, 27, 40, 54, 79, 138, 143ff., 174, 275, 812 – inter-well transition 282 – intra-well transition 282 – single-well 53f. potential energy surface (PES) 3, 5, 8ff., 14, 21, 23, 27f., 36, 39f., 58, 61f., 68, 75, 79ff., 87, 90ff., 223, 358, 350, 365, 372, 461, 583, 589ff., 694, 835, 849, 870, 880, 885, 901ff., 910f., 961, 1174ff., 1190ff., 1227, 1245 – LEPS 1293 – multidimensional 843 – SPES 854 – topology 366ff. – two-dimensional 273ff., 280ff., 291ff. potential energy well 756ff. potential function see potential energy function potential of mean force (PMF) 863, 863 potential surface see potential energy surface power law potential 676 PQR rotational envelopes 6f. praseodymium 810 primary metabolic steps 548 probability density 88, 768 probability distribution function, phase-space 833 probability flux correlation function 490ff. proline 1157ff. propane 882 propanol 430 propene 689 propinquity catalysis see Bruice’s proximity effect Propionibacterium shermanii 1156 propionyl-CoA 1156 N-propylisonicotinamidine 533f. protein 232, 236, 240, 435, 490, 523, 598, 733, 1013ff., 1028, 1171ff., 1195ff., 1343, 1361ff. – design 1080ff., 1100 – dynamics 1209ff., 1313f., 1333, 1356, 1371ff., 1382ff., 1406, 1439ff.
– environment 1261 protein, flavo 1275, 1341ff. protein, globular 1518 protein, green fluorescent (GFP) 435f., 455 – human serum albumin (HSA) 236ff. – interactions 1374ff., 1379ff., 1452 – interactions, interloop 1446f. protein-ligand recognition 236 – mobility 1361, 1382, 1385 – Monellin 234 protein, native 1363 protein, photosensor 443 – Sublitsin Carlsberg (SC) 234 – structure 1112, 1373, 1443ff. – tertiary 549 – water interface 1499 proteolysis 1367 proteome 1013 protic solvent 448 protodetriation rate 565ff. proton – abstraction 1108f., 1118ff., 1351, 1455, 1459ff. – acceptor (Ap) 377, 444, 503, 507, 527, 1052 – donation 1455 – donor (Dp) 503, 507, 527 – flux 1507 proton affinity 689, 697ff., 704, 1110 proton, bridging 273, 278, 1458, 1462 – energy diagram for neutral alkyl radicals 109 proton-collecting antenna 1501, 1516ff. proton-conducting channel 1519 proton conduction 709ff., 715ff., 728, 731f. – confinement and interfacial effects 723 – mechanism 718 proton-coupled electron transfer (PCET) 479ff., 483ff., 503ff., 526ff., 552, 1015, 1017 – across interfaces 523ff. – asynchronous 505f., 510f., 513, 519, 522 – bidirectional 508, 537ff., 549, 553 – bimolecular 531ff. – concerted 503ff. – in protein 498f. – temperature dependence 499, 537 – in solution 492ff. – non-specific 3-point 538 – redox state 508, 523, 525, 537 – site differentiated 523ff. – solvent dependence 511 – study methods 509ff., 514 – temperature dependence 512 – theoretical formulation 480ff. – dynamical effects 485
Index – types 507, 512, 523, 537f., 541, 543, 549ff. – non-specific 3-point 538ff. – site-specified 3-point 543ff. – symmetric see H bond – polarized see H bond – unidirectional 508, 512ff., 553 – unimolecular 533 proton, defect 718 proton diffusion 737ff., 953, 960 – at high pressure 740 – spectral analysis 745ff. proton-dissociation 388, 392, 395, 398ff., 404, 1502f. – lifetimes 400 proton donor 377, 444 proton donor-acceptor 714, 932, 960 – motion 483, 492, 498 proton dynamics 273ff. proton, free 110 proton, geminate 377, 389 proton jump 700ff., 739f., 749, 1004 proton mobility 724, 727 proton polarizability 1503ff. proton-proton coupling/correlation 895ff., 908ff., 918ff., 927, 941 proton pump 771, 1499 proton recombination 388ff., 448f. proton repellent 1501 proton solvents – covalently bound 728 proton sponge 245 proton transfer 105ff., 112ff., 122ff., 136, 213ff., 223ff., 236, 370, 424, 481, 686ff., 1048, 1114, 1171ff., 1230, 1455, 1499 – asymmetric 110, 123ff. – proton-donor site selectivity 124f. – proton-acceptor site selectivity 125f. – at carbon 958ff., 965ff., 1107ff. – bimolecular 443ff. – by low-frequency mode excitation 279 – carbon acid to methoxide 565ff. – concerted 418, 895ff., 910, 940ff. – conduits 932ff. – coordinate 274, 279, 283 – exited state (ESPT) 420ff., 427ff., 433ff., 443f. – in a box 435ff. – intramolecular (ESIPT) 443f. – geometry 1505f. – in vivo 433 – intramolecular 926ff. – mechanism 1069 – methanol to carbanion 573 – methoxide promoted 576
– multiple 136, 370f., 895ff., 908ff., 919ff., 932f., 939ff. – photoinduced 226, 430 – rate 398 – rate constant 229, 394, 909, 918, 932 – reaction 228, 377f., 1185ff., 1428ff., 1499 – activation energy 394 – stepwise 418, 511, 895ff., 910, 921, 928, 941 – symmetric 110, 115ff. – proton-acceptor site selectivity 120f. – proton-donor site selectivity 119f. – thermoneutral 960ff. – theoretical aspects in polar environment 303ff. – theoretical simulations 583ff., 1171ff. – to and from carbon 949ff., 960, 970, 1000 – ultrafast 349ff., 424, 453 proton translocation (PTR) 1171, 1193, 1199 proton transport, long range 714ff., 732 Pseudomonas putida 1151 Pseudomonas qetrolens 1151 pseudorotation 986 pulse radiolysis 1014, 1018, 1025 pump-control scheme 91 pump-dump scheme 83, 90ff. pump-probe experiments 352, 360f., 447ff., 459, 463f., 466ff., 1407 purine 1439 purpurin 528ff. pyranine see 8-hydroxypyrene-1,3,6trisulfonate pyrazoles 135, 189ff., 721 pyrenols 445 pyridine (py) 545, 593, 689, 984 – substituted 1285 pyridinium 1062 pyridone group 434 2-pyridone-2-hydroxypyridine dimer 924f. pyrimidine – biosynthesis 1439 – nucleobases 542 pyrrole rings 245, 267 pyruvate 955, 1223ff., 1367, 1395ff., 1407f. PZD2 1087, 1101
q Q bands 245, 261f., 528 Q branch 14f. – spikes 7, 19 Q frequencies 312 quadrupolar Pake pattern 672 quantum average 317, 324f. quantum classical path (QCP) 1184f., 1196f.
1551
1552
Index quantum coherent vibrational dynamics 459 quantum correction factor 840 quantum dynamics 1209 quantum Kramers model 1209ff., 1231ff., 1342 quantum Kramers flux autocorrelation 1213 quantum mechanical activation barrier 1184 quantum mechanical exchange coupling (QEC) 619f., 629 quantum mechanical integrated reaction probability 148 quantum mechanical rotor, one-dimensional free 652 quantum mechanical studies 135, 143, 175, 217 quantum mechanics (QM) 639ff., 665, 1171ff., 1193, 1228, 1233, 1291, 1316, 1334, 1342, 1349, 1440, 1480 quantum mechanics, nuclear (NQM) 1177ff., 1195ff. quasiclassical hybrid 837 quasi-elastic neutron scattering (QNS/QENS) 283, 632f., 787, 792ff., 801ff., 807ff., 821f. quasiparticles 1184 quenching 225ff., 390ff., 523ff., 534, 544, 818, 1421 quinone 552 quinuclidines 943, 967 QSID (quadratic configuration interaction including single and double substitutions) 211, 596
r racemization 1142ff. radiation chemistry 106, 107, 1020 – g-irradiation 106, 112ff., 119ff., 126f. – radiolytic process, mechanism 115ff., 123ff. radicals 512f., 519, 542f., 544, 546, 553, 876ff., 1013ff. – acridine 1052 – alkoxyl 1014 – alkyl – cations 105ff., 115ff., 123ff. – electronic absorption 106 – neutrals 112ff., 123 – paramagnetic properties 107f., 117 – a-(alkylthio)alkyl 1029f. – bi- 542 – benzyloxyl 1015 – bis(trifluoromethyl)nitroxide 880ff. – bromine 513 – carbon centered 1019f. – chlorine 512f.
– cumylperoxide 521f. – cyclohexydienyl 1025 – cyclopropyl 883f. – cysteinyl 1016, 1023f. – deoxyuridin-1-yl 1020 – 2,3-dimethyloxiranyl 885 – N-(6,6-diphenyl-5-hexenyl)acetamidyl 1018 – dioxolanyl 886 – 3,5-di-tert-butylneophyl 207ff. – free 867ff. – 2-hydroxyphenoxyl 208f. – 3,6-di-tert-butyl-2-hydroxyphenoxyl 208f. – hydroxyl 1013, 1052 – iodine 512 – isobutyl 883 – methyl 887ff. – 1-methylcyclopropyl 883f. – nitrogen centered 1017 – amidyl 1017ff. – aminyl 1017ff. – in biological samples 1017 – octamethyloctahydroanthracen-9-yl 881 – oxiranyl 884f. – oxygen centered 1013 – phenoxyl 1020 – sulfur centered 1019ff. – cations, sulfide 1019, 1029ff. – sulfonyl 1027 – thiyl 553f., 1019ff., 1027 – tetramethylgermacene 882 – trapping 888f. – 2,4,6-tri(1 0 -adamantyl)phenyl 881 – tri-n-butyltin 882 – trifluoromethyl 883 – trimethyltin 876 – trimethylsilicon 876 – 2,4,6-tri-tert-butylphenyl 207ff., 876ff. – 2,4,6-tri-tert-butylneophyl 876 – tyrosyl 538, 553, 1015f., 1023 radiolytic processes 106 Raman spectroscopy 45, 285, 288, 361, 464f., 468ff., 1131, 1395ff., 1398, 1476 – third-order (TOR) 555 Raman studies 473f. rate constants 184, 188, 191, 197f., 210, 303, 337, 431, 837, 840, 867, 951ff., 958ff., 961, 964, 967, 1052, 1056, 1068, 1092, 1171, 1196, 1430 – first order 888ff., 987, 1046, 1463 – intrinsic 1361 – predictions 833 – pre-steady-state 1489 – pseudo-first order 166, 201, 544
Index – second order 949ff., 957, 967, 987, 1046, 1057, 1071, 1095 – third order 967 rate equilibrium – correlations 961 – studies 1058 rate law – second order 211 rate limiting step 1316 Rb3 H(SO4 )2 291 R branch 7, 14 reaction asymmetry 333, 341 reaction coordinate 505, 585, 587ff., 840ff., 908ff., 935, 841, 1316 – intrinsic 589 reaction dynamics 449ff. reaction mechanism – biochemical 419 – OA/RE type 633 reaction path 366, 373, 505 reaction progress – coordinate 1058 – variable 1058ff. reaction rates 388, 512, 869 reaction scheme 371, 484ff. rearrangement 204, 225, 411, 1027, 1031, 1300, 1473 – 1,2- 1477 – electronic 385 – heavy atom 1457f. – intramolecular, of H2 623ff. – of water molecules 452 – sigmatropic 858f. recoverin 1379f. redox reaction 515ff., 1057, 1062, 1067 reduced mass 274f., 838, 1325 reductive methylation 1322 refractive index 287f. regio-selectivity 668 regio-specificity 666 Rehm-Weller equation 417, 585 relaxation 235, 648 – anelastic 787ff., 825 – dynamics 223 – molecular 223 – rate 82f., 651, 790 – reorientation 789 – spin-lattice 282ff., 623, 673ff., 790, 821ff., 1448 – spin-spin 1448 – solvent 138, 140, 427ff., 446 – time 79, 186, 253, 618 – vibrational 138 reorganization 499
– inner-sphere 493 – outer-sphere 482f. repair reaction 1020 repulsive forces 758ff. resonance effects (of substitutents) 961ff. resonance frequency 791 resonance structure 1175 respiration 1223ff. – anaerobic 1224 reversible oxidation 1325 dTDP-L-rhamnose 1165 rhodium 759, 764, 767, 776, 779ff. Rhodobacter sphaeroides 1516 rhodopsin 1370, 1379 riboflavin tetraacetate 1067 ribonucleotide 1476 – in TTUTT 987 ribosome 1518 ribozyme 1241 ring opening 1006 RMS fitting error 72f. RNA 985ff., 1028, 1087 ROESY 174 rotamer 1091 – keto 225ff. rotation 225ff., 604, 609, 739 – dihydrogen 615ff., 627, 657 rotational constants 42f. rotational diffusion 262 rotational states 7, 13f. rotational transitions 19, 69 rotational-vibrational – state 39, 43, 46f. – lines 66 RRKM – system 1314 – theory 857 rubredoxin, mesophilic 1384 rule of geometric mean (RGM) 157, 160, 190, 210, 1252f., 1266, 1285f., 1297ff., 1304ff., 1324 – breakdown 1298ff. – RS (RGM and Swain-Schaad) exponents 1252, 1267 ruthenium 759f., 764, 770ff., 776f., 779ff. – Ru IV O 2þ 1051
s S-824 1087 SA-42 1090 Saccharomyces cerevisiae 1421ff., 1427 saddle-point (SP) 4, 12, 21, 589, 687, 757, 833f., 844, 850ff., 858 – first order 895ff., 909, 913, 926 – second order 249, 899ff., 909, 913, 930
1553
1554
Index salicylic acid derivatives 988ff., 995, 998, 1002 salicylaldimine 88ff. sapphyrin 267 sarcosine 1348 Saunders exponents 1304, 1306 scandium 788ff. scanning tunneling microscope (STM) 752, 770, 772, 781 scattering law 287 SCF see self-consistent field methodology Schiff base 554, 1069, 1401 Scho¨nbein 710 Schro¨dinger equation 5, 21, 276f., 280, 327, 643f., 670 SCSAG method 849 SD see spectral doublets self-consistent field methodology (SCF) 21, 926 semi classical method 8f., 21, 23, 36, 58, 136f., 938, 1179f., 1219, 1245, 1256, 1318, 1324, 1442, 1486 semi empirical method 837, 841, 1227, 1401, 1481 semiconductors 757, 761, 771ff. semiquinone 546 serine (Ser) 1026f., 1152, 1376 syn-sesquinorbornene disulfone 931 SHAKE algorithm 1220 shift – blue 227f., 230, 472 – red 232, 432, 460, 463 Sievert’s law 810 Silicon 757, 761, 810f. silicon-aluminiumphosphates (SAPOs) – (H-SAPO-34) 686, 695ff. siloxane backbone 732 silver 757, 772ff., 781 single crystal 759, 764, 802 single molecule spectroscopy 266 single photon counting detection 449 SiO4 tetrahedron 685, 700 skew angle 849, 857 small-curvature tunneling (SCT) 842f., 848ff., 855f., 862, 867, 1486 Snoek effect 788f. sodium bifluoride 285 sodium hydrogen bis (4-nitrophenoxide)dihydrage 278 solid acids 749 solute-solvent – interaction 1174 – system 491 – terms 1192
solution 1171, 1176 solvation 305, 398, 417, 490, 1501 – dynamics 230f., 447 – ultrafast 231 – layer 1503 – shells 451ff. solvatochromism 426, 445 solvent chaperoned 418 solvent configuration 310 solvent fluctuation 1196 solvent mixtures 427ff. solvent reaction coordinate 310, 330 solvent reorganization 955, 1197, 1513 – energy 1181ff., 1186, 1198 solvent-solvent terms 1192 SOMO see molecular orbital, – semioccupied Soret bands 245, 261f., 528 sorption energy 753 SP see saddle-point spacer 532f., 713, 732 spectral doublets (SD) 13, 27 spectroscopic signatures 1404 spill-over effect 754, 773f. spin 1/2 645f., 670, 790 spin 1 646f., 670 spin >1 790 spin 1/2 660 spin boson see dispersed polaron spin-lattice correlation rates 923 spin system, 2 state 1232 staphylococcal nuclease 1367 Stark effect 13 static-secondary-zone result 866 steady-state 1243, 1294 – studies 230, 389ff., 432 – velocity 1242 Stern-Volmer quenching analysis 449, 531 stereochemistry 433, 940 stereoinversion 1152ff., 1158f., 1165f. stereoselective reactions 662f. stereoselectivity 433, 1020 stereospecific reduction 1322 stereospecifity 433 Stokes-Einstein relation 719 Stokes radius 1378 Stokes shift 236, 378, 408 stopped-flow methods 1351, 1355, 1434 – FRET 1322 strain 821 – tensor 788 stress 1224 structure activity relationships 996, 999 structure diffusion 716f.
Index structure reactivity studies 1059 Stuchebrukchov’s model 1506ff. styrene 1305 substituent effects 957, 958ff. substrate activation 1395 substrate binding 1242 substrate transport 1241ff. subsurface-site population 754 succinyl-CoA 1156 sugars 992, 1158, 1165, 1271, 1419 – ketol transfer 1424 surface coverage 768ff., 778 surface diffusion 761ff., 762, 773ff. sulfonic acid groups 723 sulfuric acid 710 superacids 110, 686 – SFO3 H-SbF5 -SO2 692 supercritical fluids 419, 431 superionic fluid 740 supersonic jet studies 253 support materials (metals) 774 supramolecular chemistry 224 supramolecule 523, 528f. surface hopping method 1196 surface orientation 759, 764 surface reconstruction 753f. Swain-Schaad exponent 1259, 1275, 1280, 1285ff., 1290ff., 1304ff., 1318ff. – kinetic complexity 1319 – mechanistic complexity 1294 – primary 1320 Swain-Schaad relation 320, 322ff., 333, 340ff., 565ff., 577, 914ff., 920, 928f., 1252f., 1266, 1318ff. – primary 1320ff. – secondary 1323ff. swinging door 1142, 1157 symmetry – effects (on NMR lineshapes) 655, 670 – in dihydrogen transfer 639ff. symmetry groups – C2 19, 65f., 462 – C2h 36, 46, 49, 260, 897, 921 – C2v 5, 21ff., 260, 627, 897, 921f. – C4 939 – C4v 767 – Cyh 61 – Cs 262 – D2h 36, 46, 248, 261, 920f. – Dyh 61 – E-type 767 – inversion operations 4 – G4 4f. symmetry related quantum effects 640
p-System 420, 1000, 1007 Szabo-Collins-Kimball model (SCK) 451 Szymanski and Scheurer 649
t tantalum 753, 762, 788, 794, 798f., 801, 805ff., 814, 821ff. tautomer 4, 23ff., 184, 188, 202, 610, 618, 926, 996 – amidine-carboxylic acid 529 – phototautomer 225ff., 266, 425 tautomerism 135, 154f., 174ff., 181, 189f., 198ff., 207ff. tautomerization 15f., 19, 23, 27, 623ff., 934ff., 1124, 1427, 1461 – keto-enol 226ff., 237f., 366f., 372, 463, 471ff., 926, 976, 1439ff. – kinetics 259f. – in metal complexes 619 – in porphycenes 245ff., 251ff., 258ff. – in quinolines 424 – rates 262ff. temperature jump relaxation spectroscopy 1407ff. tensor 647ff. tetrachloroethylene 351 1,2,4,5-tetracyanobenzene (TCB) 545f. tetrahedral jump mechanism 606 tetrahydrofuran 428 5,6,7,8-tetrahydrofolate 1439, 1447 1,5,6,6-tetramethyl-3-methylene-cyclohexa1,4-diene 689 tetraphenylchlorin (TPC) 170, 183ff. tetraphenylbacteriochlorin (TPBC) 184f. tetraphenylisobacteriochlorin (TpiBC) 170, 183ff. tetraphenoloxalamidine (TPOA) 198ff. 2,7,12,17-tetra-n-propyl-9-acetoxyporphyrene 256ff. tetratoloylporphyrin (TPP) 174, 176ff., 185 TFXA spectrometer 818 thermal annealing 744ff. thermal equilibrium see canonical ensemble thermodynamic acidity 580 thermodynamic cycle 379 thermodynamic miscibility 773 thermodynamic parameters 569f., 1056 thermodynamically symmetric reaction 317 thermodynamics (of PCET) 503f., 513ff., 521ff., 1231ff. – pKa value/Ered value 504, 508, 523, 527, 537, 554 – coupling 548 Thermotaga maritima 1374
1555
1556
Index Thermus thermophilus 1217 THF 172f., 203, 210, 225ff., 529 – d8 672, 933 thiamine 958 thioacetylone 85ff. thioester 1107, 1156 thiol 984, 1020 thiophenol 1017 thioredoxin 1087, 1101 thorium 810 Thornton see Bema Hapothle threonine (Thr) 1026f., 1222 thrombin 1382 thrombomodulin 1382 through-atom axis ( 1 La state) 445f. through-bond axis ( 1 Lb state) 445f. thymine (T) 542, 934, 1028 tight-binding 758 time correlation function 490 TIP3P potential 1219 titanium 753, 761, 805, 810 titration 528 see fluorescence titration – Mataga’s titration treatment 544 a-tocopherol 1017 toluene 463, 516ff., 689, 877, 891 topoisomerase I inhibitors 434 topotecan 434 transition metals 772ff. – reductive cleavage 1014 transition moment 258ff. – directions 260ff. transition path sampling 1209 transition state 513, 590ff., 909, 924, 938, 958, 1008, 1098, 1110, 1245f., 1394, 1442, 1483 – descriptors 1056 – inhibitors 1209ff. – inhibitors, multiple 1073 – stabilization 1047, 1052, 1072, 1087, 1108, 1115, 1194, 1316, 1458 – structure 589ff., 919ff., 981ff., 994ff., 1251, 1268, 1280 – theory (TST) 309ff., 904, 918, 1056, 1074, 1186, 1195, 1241, 1287ff., 1299ff., 1326ff., 1513 – zero-curvature tunneling (TST/ZCT) 1483ff. transmission change 355f., 370 transmission coefficient 840f., 870 transmission factor 1196f. trapping of hydrogen 817 – rate 795, 803 trifluoroacetic acid (TFA) 546 trifluoroethanol (TFE) 546 trifluoroethanolysis 983f.
6-tri-fluoromethanesulfonyl-2-naphthol 425 trihydrogen 617 – in complexes 624 trimethoprim 1439 trimethylamine 205, 691, 1348, 1353f. N,N,N-trimethylammonium glycine methyl ester 954 triphenylmethane 516f. tripodal phoshphine 628 TRIS 1001 tritium 764f., 767 TRN see tropolone trolox C 1014 tropolone (TRN) 3ff., 8, 13ff., 79 – diethyl acetale 982 – derivatives 3, 26f., 82 Trouillier-Martins pseudo-potentials 288ff. tryptophan (W, Trp) 232, 540ff., 554, 1218ff., 1352ff., 1448 TSTH model 25 TTAA 171, 193ff. tungsten 763f. tunneling 136, 258, 303ff., 326ff., 333, 336, 340f., 364, 483, 499, 641, 783, 788, 812ff., 1007, 1187, 1195, 1217ff., 1241ff., 1255ff., 1279, 1285ff., 1475f. – coenzymatic reactions 1060ff., 1068 – coherent 3ff., 13ff., 35ff., 138ff., 183, 642ff., 649ff., 675, 817ff., 1314 – at higher temperatures 647 – hydrogen 817ff., 1285ff., 1341ff., 1347ff., 1439ff. – DNA 33f. – Eigenstates 21 – electron-proton 505 – fast 675 – frequency 147, 642, 645 – ground-state nuclear 1313 – hot bands 19 – phonon assisted 714, 797ff., 816 – intermediate (speed) 671ff. – masses 145f., 149ff., 189, 205 – modes 906f. – models 135ff., 251, 897ff. – one-dimensional 143ff. – two-dimensional 143ff., 505 – nonadiabatic 303, 307, 333ff., 429 – pathway 84f., 145, 156 – quantum mechanical (QMT) considerations 33f., 39, 48, 623, 678, 875ff., 884ff., 1341 – parameters 182, 188 – properties for carboxylic acids 35ff. – aromatic dimers 37 – benzoic acid dimer 35ff., 48f.
Index – cyclic carboxylic dimers 37 – N,N-dimethyl carbamic acid dimer 36f. – formic acid dimers (FAD) 36f., 42ff. – properties of malonaldehyde 5ff., 27f., 138, 279 – properties of tropolon 13ff., 138 tunneling, correction 148 tunneling, enhanced 1314 tunneling, environmentally coupled 1314 tunneling, incoherent 138ff., 649ff., 675 tunneling, multidimensional (MT) 834f., 842, 869, 1293f., 1342ff. tunneling, nonthermally activated quantum 770 tunneling, proton 3ff. – dynamics 904ff., 908ff. – fundamental, overtone, combination, hot band vibrational transitions 5 – rotation-tunneling transitions 14, 617, 634 – slow 671f. – splitting 9f., 15ff., 21, 23ff., 27f., 35, 37, 44, 48f., 254, 264, 267, 279, 283, 327, 652, 679, 813ff., 909, 914, 920, 926f. – damping 15ff., 21 – multidimensional tunneling splitting 9 – zero-point (ZP) 5, 12ff., 19, 21, 24, 27f., 48, 79 tunneling, vibrationally enhanced (VET) 1195 TURBOMOLE 288ff. turkey ovalbumin third domain protein 1364 turn-over rates 1243 two-mode linear model 274 two-dimension lattice gas behavior 761 two-state model 795 tyrosine (Tyr, Y) 538ff., 553f., 1015, 1118, 1126f., 1143ff., 1151, 1352ff. – oxidation 492, 496, 543 TZ2P calculation 249
v
valence bond (VB) 308f., 343, 583, 587, 595 – empirical (MS-EVB) 724, 1177, 1264 – model, four-state 480ff. valence bond, empirical (EVB) 1171ff., 1185ff., 1195 valence bond, multistate 1264 valine (Val) 1026, 1029, 1156, 1218, 1222 vanadium 761, 788, 794, 798f., 800ff., 805ff., 805ff., 814, 821ff. van-der-Waals forces 751, 778 van-der-Waals potential function 1175 van-der-Waals radii 1520 VASP see Vienna ab initio simulation program variational transition state theory (VTST) 833ff., 858, 869, 1303, 1342ff. – ensemble-averaged VTST with static secondary zone (EA-VTST-SSZ) 861, 865ff. – ensemble-averaged VTST with equilibrium static secondary zone (EA-VTST-ESZ) 861 – equilibrium solvation path (ESP-VTST) 861, 864f., 867f. – nonequilibrium solvation path (NESP-VTST) 861, 864, 867f. VCI see virtual configuration interaction vehicle mechanism 717, 726 vehicular diffusion 718 ventricular myocyte cells 1508 vibration 8, 137, 554 – aromatic ring 41 – bending 21, 64, 71, 140f., 289ff., 371f., 688, 845, 878, 1370 – SiOH 695 – cyclic 281 – CbO 1370, 1407ff. – coherently excited 359, 371 – coupling 1216, 1232 – stretch-stretch 1289 vibration, H atom 787 u – in-plane 8, 364, 372, 609 Ubbelohde effect 277f. ultrafast optical Kerr effects spectroscopy 235 – librational 233, 514, 616, 620 – out-of-plane 8, 19, 21, 24, 27, 469, 609 ultrafast transient lens measurements (UTL) vibration, promoting 1209, 1213ff., 1217ff., 239f. 1230ff., 1347, 1209, 1213ff., 1217ff., 1230ff., ultrasonic loss 789 1314 unpaired electrons 107, 109 – rotation-contortion-vibration electronic states a,b-, b,g-unsaturated 3-oxo-steroids 1125 4 uridine 3 0 -2,2,2-trichloroethylphosphte 1087 – skeletal 17, 24ff., 362, 472 uridyl esters 986 – stretching 61ff., 66ff., 94, 98, 140f., 144ff., UV photoemission (UPS) 776ff. 156, 460, 610, 849f., 878, 1246 UV pulse 354 – antisymmetric 1409 UV spectroscopy 14f., 38f., (80) – COO 1409 UV /vis 443, 447ff., 689, 1112
1557
1558
Index – asymmetric 277, 284, 289f., 609, 917 – 3-atom N-H O 536 – CaC 367 – CbC 1403 – CD 565, 1257 – CH 12f., 19f., 565, 854f., 859, 888, 918, 1180 – CaN 1370 – CbO 45ff., 284, 363f., 450, 453, 462, 471ff., 555, 918, 1395, 1403 – HaH 755, 845f. – HaCl 854 – MaH 608 – NH 248, 254, 258, 267, 471, 555, 720, 1355, 1370 – OD 453, 463ff., 466ff., 475 – OH 8, 12f., 17, 19f., 23ff., 27f., 41, 45f., 56, 71f., 74, 79, 88, 280ff., 289f., 364, 367, 459ff., 466ff., 474f., 539, 555, 688, 695, 743ff., 777f., 919f., 926 – O H O 284ff., 289f. – O O 12, 21, 23, 27, 70, 74, 280ff. – strong coupling 275ff., 296 – torsion 19 – twisting 16, 226 – wagging 16, 469 vibrational calculation 59f. vibrational frequencies 13, 16, 19, 42, 45f., 61ff., 98, 329 vibrational loss spectroscopy 768 vibrational marker 449 vibrational modes 55f., 74, 360, 447ff., 460, 476, 812, 837, 844, 848, 854ff., 1195 vibrational polarization 464 vibrational relaxation 39, 223, 459, 475 vibrational-rotational energy 839 vibrational-rotational transitions 35, 37 vibrational self-consistent field (VSCF) 7f., 71f. vibrational spectroscopy 12, 41, 45, 53ff., 61ff., 75, 287, 812, 1397, 1407 vibrational splitting 8 vibrational states 768 – anharmonicity 5, 7f., 10f., 20, 55, 68, 70, 460 – harmonicity 10f., 70f., 75 – quasiharmonicity 24f. – specific doublets 14, 17 vibrational structures 3 vibrational transitions 447 vibrationally adiabatic zero-curvature approximation 841
vibronic – absorption spectrum 14 – state 1179f. – surface 490 – transitions 253ff. Vienna ab initio simulation program 286f. viral capsids 1378 virtual configuration interaction (VCI) 69, 71ff. vitamin B1 1419 vitamin B12 1473 vitamin E 1014 volatile hydrides 761 VSCF see vibrational self-consistent field VTST, potential-of-mean-force (PMF-VTST) 861f., 864f. – based on a single-reaction-coordinate (SRC-PMF-VTST) 861 VTST, quantum mechanical effects 835ff., 840ff. VTST, separable equilibrium solvation (SES-VTST) 861f., 864f., 867f. VTZ 72, 288ff.
w Wasserstoff-Bru¨cken-Bindung 751 water 226ff., 230ff., 237, 311, 314ff., 377, 386, 395, 399f., 406f., 427ff., 443f., 446, 689ff., 723ff., 955ff., 967, 1116ff., 1192, 1502ff. – absorption 711 – activation 1459ff. – and DNA bases 932ff. – autodissociation 597 – biological 233, 240, 435, 1219 – bridges 453ff., 598 – channel, hard wired 550 – clusters 694ff., 718 – coordination 718 – cyclic hexamer 780 – diffusion 724 – dimer 689 – immobilization 1503 – interactions with proteins 232 – dynamic equilibrium 233 – magnetization transfer experiments 1365f. – migration 739 – Mn-bound 551 – nucleophile 977f., 993f. – on metal 775, 778ff. – ordering 1501 – ortho-/para 679 – solvent 962
Index – tetramer 689 – trimer 689, 697ff., 939f. Watson-Crick base bairs 525ff. wave function 36, 83ff., 92ff., 307, 309, 317, 329, 481ff., 639ff., 656, 679, 812f., 1174, 1257ff., 1313 – harmonic 275f. – overlap 1261, 1263 – vibrational 493, 499, 1442 wave packet 223, 238, 240, 349 – dynamics 370 – low-frequency 463, 474 – motion – ballistic 357ff., 363 – coherent 371, 468f. – oscillating 359 wave particle duality of matter 1256 well 139, 408, 813 – frequency 316 Wenzel, Kramers, Brillouin (WKB) approximation 34, 146, 653, 837, 845ff., 1486 Westheimer-effect 146 Westheimer and Melander (W-M) 304, 323f., 326, 565 Wigner tunneling correction 833, 844ff., 853
y YC6 H4 CHbCF2 571 yttrium 805ff., 821
z
Zassenhaus expansion 1212 zeolites 223f., 240, 685ff., 691ff., 700ff. – acidic catalysts 685ff. – chabasite H-CHA, CHA 686, 690ff., 696ff. – FER 692ff. – H-FAU, FAU 686, 690f., 700ff. – H-MFI (H-ZSM-5), MFI 685f., 692, 701ff. – H-SSZ-13 697ff. – MOR 690f., 704 – quantum mechanical studies 690 – sodalite (SOD) 691ff. – TON 692 – Z-ZSM-5 692, 695, 599 – unit cell 692 zero-curvature tunneling (ZCT) 842f. zero-point 60, 71 – energies 136, 143ff., 258, 305f., 309ff., 315ff., 321ff., 340, 511, 536f., 565, 599, 842, 845f., 878, 896, 907, 918, 1060, 1187, 1245ff., 1274, 1291, 1296, 1315, 1325 (ZPE) – excited state 1318 x – ground state 1318 Xanthene 516ff. – splitting 918, 939 Xanthobacter autotrophicus 1464 – vibration 275 X-ray crystallography 202, 969, 1325, 1387, – vibrational (EXC) 1288 1398, 1424, 1435, 1439, 1443, 1447 X-ray diffraction 65, 142, 273, 280, 288f., 435, zinc 810, 936ff., 1067 – in enzymes 968 605 X-ray photoelectron spectroscopy (XPS) 776, – Zn 2þ 597, 968, 1188, 1217, 1341, 1397 782 ZP see zero-point X-ray structure 236, 239, 248, 252, 598, 628, zirconium 761, 798ff., 805ff., 810f. 730, 937, 1120, 1127, 1192, 1279, 1374, Zundel ion see H5 O2 þ ion 1381ff. Zundel mechanism 1506 m-xylene 689 Zwanzig approach 1210, 1213 D-xylulose 5-phosphate 1165 Zymomonas mobilis 1422, 1428ff.
1559
