Advances in Gas Phase Ion Chemistry, Volume 2 (Advances in Gas Phase Ion Chemistry)

ADVANCES IN GAS PHASE ION CHEMISTRY

Volume 2

1996

This Page Intentionally Left Blank

ADVANCES IN GAS PHASE ION CHEMISTRY Editors" NIGEL G. ADAMS LUCIA M. BABCOCK

Department of Chemistry The University of Georgia VOLUME 2

9 1996

Greenwich, Connecticut

@

JAI PRESS INC.

London, England

Copyright 91996 by JAI PRESSINC 55 Old Post Road, No. 2 Greenwich, Connecticut 06836 JAI PRESSLTD. The Courtyard 28 High Street Hampton Hill, Middlesex TW12 1PD England All rights reserved. No part of this publication may be reproduced, stored on a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, filming, recording, or otherwise, without prior permission in writing from the publisher. ISBN: 1-55938-703-3 Manufactured in the United States of America

CONTENTS

LIST OF CONTRIBUTORS PREFACE

Nigel G. Adams and Lucia M. Babcock

~

VII

ix

EFFECT OF MOLECULAR ORIENTATION ON ELECTRON TRANSFER AND ELECTRON IMPACT IONIZATION

Philip R. Brooks and Peter W. Harland

EXPERIMENTAL APPROACHES TO THE UNIMOLECULAR DISSOCIATION OF GASEOUS CLUSTER IONS

Terrance B. McMahon

NEW APPROACHES TO ION THERMOCHEMlSTRY VIA DISSOCIATION AND ASSOCIATION

Robert C. Dunbar

41

87

ALKYL CATION-DIHYDROGEN COMPLEXES; SILONIUM AND GERMONIUM CATIONS: THEORETICAL CONSIDERATIONS

Peter R. Schreiner, Henry F. Schaefer III, and Paul v. Ragu@Schleyer

SYMMETRY-INDUCED KINETIC ISOTOPE EFFECTS IN ION-MOLECULE REACTIONS

Gregory I. Gellene

125

161

vi

CONTENTS

ION-MOLECULE CHEMISTRY: THE ROLES OF INTRINSIC STRUCTURE, SOLVATION, AND COUNTERIONS John E. Bartmess

193

GAS PHASE ION CHEMISTRY UNDER CONDITIONS OF VERY HIGH PRESSURE W. Berk Knighton and Eric P. Grimsrud

219

INDEX

259

LIST OF CONTRIBUTORS

John E. Bartmess

Department of Chemistry University of Tennessee Knoxville, Tennessee

Philip R. Brooks

Department of Chemistry Rice University Houston, Texas

Robert C. Dunbar

Department of Chemistry Case Western Reserve University Cleveland, Ohio

Gregory I. Gellene

Department of Chemistry and Biochemistry Texas Tech University Lubbock, Texas

Eric P. Grimsrud

Department of Chemistry Montana State University Bozeman, Montana

Peter W. Harland

Department of Chemistry University of Canterbury Christchurch, New Zealand

W. Berk Knighton

Department of Chemistry Montana State University Bozeman, Montana

Terrance B. McMahon

Department of Chemistry University of Waterloo Waterloo, Ontario, Canada vii

viii

LIST OF CONTRIBUTORS

Henry F. Schaefer Iii

Center for Computational Quantum Chemistry University of Georgia Athens, Georgia

Paul v. Ragu~ Schleyer

Center for Computational Quantum Chemistry University of Georgia Athens, Georgia

Peter R. Schreiner

Center for Computational Quantum Chemistry University of Georgia Athens, Georgia

PREFACE Gas phase ion chemistry is a broad field with many applications which encompasses various branches of chemistry and physics. It is continually developing, with new approaches to obtaining kinetic (Knighton and Grimsrud) and thermochemical (McMahon; Dunbar) data under a wide variety of experimental conditions and with new insights into the mechanisms of ion--molecule reactions (Gellene; Bartmess) and the parameters which control them. It is becoming increasingly obvious that progress on this mechanistic aspect is being considerably advanced by the availability of structural information on the reactants, products and reaction intermediates (Schreiner, Schaefer, and Schleyer). As our understanding develops, there is a need for more detailed reaction studies. The effects of molecular orientation on reactivity (Brooks and Harland) is a case in point. The articles collected here represent only a subset of the advances that are being made in this rapidly developing area. Successive volumes will emphasize the progress being made in other areas of the subject. The editors are making a specific effort to include contributions from those relatively new to the field, who bring in new ideas and perspectives, as well as those more established in the field who also bring their wealth of experience. Throughout each volume, a balance will be sought between experiment, theory, and applications so that the reader, in addition to having up-to-date information on developments in forefront areas, will have a broad

x

PREFACE

base from which to view the subject as a whole. To edit such a series gives the opportunity and privilege to look into the laboratories and the minds of the scientists who are advancing our understanding in the research area of gas phase ion chemistry, a privilege which, through these volumes, will be passed on to our fellow scientists. Nigel G. Adams Lucia M. Babcock Editors

EFFECT OF MOLECULAR ORIENTATION ON ELECTRON TRANSFER AND ELECTRON IMPACT IONIZATION

Philip R. Brooks and Peter W. Harland

Abstract

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

II.

2

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

A.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

B.

Theoretical Aspects of Electron Transfer . . . . . . . . . . . . . . . . . . .

3

C.

Experimental Technique

D.

Results

E.

Discussion

Electron Transfer

. . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6 12

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

16

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

A.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

B.

Experimental Technique

C.

Results

D.

Theoretical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . .

30

E.

A Model For Electron Ionization . . . . . . . . . . . . . . . . . . . . . . .

31

......

Electron Impact Ionization

. . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27 28

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

Advances in Gas Phase Ion Chemistry Volume 2, pages 1-39. Copyright 9 1996 by JAI Press Inc. All rights of reproduction in any form reserved. ISBN: 1-55938-703-3

2

PHILIP R. BROOKS and PETER W. HARLAND

ABSTRACT The influence of molecular orientation on electron transfer and electron impact ionization has been probed with oriented target molecules in crossed molecular beams. Electron transfer frequently occurs in thermal energy reactive collisions involving the harpoon or spectator-stripping mechanism, but at thermal energies charged species can rarely escape their mutual Coulomb attraction, and only neutral products are formed. When the collision energy is increased to a few eV, the charged species are separated, and the role of orientation on the electron transfer process can be probed. Collisional ionization of fast (-3--25 eV) neutral K atoms has been measured with a variety of symmetric-top molecules, such as CH3I and CF3Br, which were oriented prior to collision. It has been shown that the orientation of the molecular dipole drastically affects overall probability of ion production through a combination of entrance channel (electron transfer) and exit channel (ion recombination) effects. The electron transfers preferentially to the most labile substituent irrespective of its polarity, the negative Cl-end of CH3C1 and the positive Br-end of CF3Br. Electron bombardment of several oriented symmetric-top molecules has shown that formation of positive molecular ions is favored for electron impact at the positive end of the dipole, the CH3-end of CH3C1 and the Br-end of CF3Br, or for broadside collisions on the molecule. In a few cases, where the molecular ion and a fragment ion have been measured, it has been shown that the ratio of ions (the fragmentation pattern or mass spectrum) is orientation-dependent.

I. ELECTRON TRANSFER A. Introduction The simple collision theory for bimolecular gas phase reactions is usually introduced to students in the early stages of their courses in chemical kinetics. They learn that the discrepancy between the rate constants calculated by use of this model and the experimentally determined values may be interpreted in terms of a steric factor, which is defined to be the ratio of the experimental to the calculated rate constants! Despite its inherent limitations, the collision theory introduces the idea that molecular orientation (molecular shape) may play a role in chemical reactivity. We now have experimental evidence that molecular orientation plays a crucial role in many collision processes ranging from photoionization to thermal energy chemical reactions. Usually, processes involve a statistical distribution of orientations, and information about orientation requirements must be inferred from indirect experiments. Over the last 25 years, two methods have been developed 1 for orienting molecules prior to collision: (1) orientation by state selection in inhomogeneous electric fields, which will be discussed in this chapter, and (2) "brute force" orientation of polar molecules in extremely strong electric fields. 2 Several chemical reactions have been studied with one of the reagents oriented prior to collision. 1'2

Molecular Orientation on Electron Transfer and Impact Ionization

3

Experimental studies of chemical reactions designed to explore the effect of spatial orientation have been heavily weighted toward the reactions between alkali metal atoms and alkyl halide molecules. The reagents have generally been prepared and introduced in cross particle beams where ultrasensitive detection of alkali metal atoms and the alkali metal halide products is made possible by surface ionization on transition-metal wires. This set of reactions involves an electropositive atom and an electronegative molecule, and the first step in the reaction mechanism is considered to involve an electron transfer between the metal atom and the molecule. Reactions involving electron transfer are ubiquitous in chemistry and biology, but under normal circumstances (thermal energies) very few neutral species react to form ions because reactions are rarely energetic enough to cause the intermediate ions to separate as charged species. Ions normally recombine to form a salt, an alkali halide in the case of alkali metal with alkyl halide reactions, but if the initial energy is increased to preclude recombination, the ions can be observed and the effect of molecular orientation on the electron transfer process can be probed more directly. We will discuss electron transfer collisions occurring with a collision energy of a few eV, where ions can be detected and where the processes are still expected to be similar to those occurring at thermal energies.

B. Theoretical Aspects of Electron Transfer Electron transfer can occur when ionic and covalent states of the same symmetry have the same energy. Coupling between these states results in an avoided crossing of the diabatic covalent and ionic potential energy surfaces, 3 as shown in Figure 1 for the atomic system, Na + I -+ Na § + I-. At internuclear distances near the equilibrium bond distance in the NaI molecule, re, the system is highly polar, Na§ -, and bonding is largely described by an ionic potential. The ionic salt molecule dissociates to give neutral atoms, 4 so at large distances the molecule is best described by a covalent potential. At r c these zeroth-order (diabatic) ionic and covalent curves appear to cross, but a dissociating molecule must make a smooth transition from the ionic to covalent potential. For states of the same symmetry, the crossing is avoided by the adiabatic potentials, shown in Figure 1, which result from solution of the two-state Schrrdinger equation using the Born-Oppenheimer approximation. The adiabats, e 1 and 82 are given in terms of the diabats by, 3 81 = 1/2{Hll + H22 + [(H, l _/-/22)2 + 4H~211/2}

(1)

where H O.are the matrix elements in the Hamiltonian describing the coupling of the two states. As shown in Figure 1, the adiabatic curves resulting from ionic--covalent coupling do not cross, and the character of the system changes smoothly from covalent at long range to ionic at short range. The behavior of a colliding system at the avoided crossing depends on the speed with which the crossing is traversed, as well as the separation and slopes of the adiabatic curves. If the atoms approach slowly enough on the covalent curve, the

4

PHILIP R. BROOKS and PETER W. HARLAND Na"+ r

V(r) / eV 6

. ' ~ ' ~ ' ~ ~ Na.l

--Na+l

-4 0

2

4

6

8

10

12

Figure 1. Diabatic potential energy curves for Nal with an expanded view of the adiabatic potential curves, el and e2, near the diabatic curve crossing.

uncertainty principle allows the energy to be relatively well defined, and the system stays on the lowest, adiabatic curve. This adiabatic process results in what we loosely call an electron "jump." On the other hand, if the atoms approach at high speed and traverse the crossing quickly, the energy will be less well defined and it is possible that the system will remain on the diabatic curve (making a non-adiabatic or diabatic crossing) and will continue to be described by the covalent potential. The diabatic crossing represents a "hop" from one adiabatic potential curve to the other, but the electron stays on the atom and doesn't jump. The probability of adiabatic hop, Pd, is given to good approximation by the Landau-Zener (LZ) relation, 3

Pd=e -'c/v

(2)

where K = (2rcHic)Z/hAS, AS = It3Ei/Or- c3Ec/c3rl, OEi/Or and OEc/Or are the slopes of the ionic and covalent potential energy surfaces at the crossing, v is the speed, and Hic is the matrix element in the Hamiltonian that couples the two states. For the simplest crossing of an ionic curve with a covalent curve, the slope of the covalent potential can be regarded as zero with zero energy compared to the separated atoms. The crossing radius is given approximately by the condition that V(rc)ionic = V(rc)covalen t = A E 0 _ q Z / r e ,

or,

re = q2/AE0

(3)

where AE0 = I P - EA, the difference between the ionization potential of the electron donor (Na) and the electron affinity of the aeceptor (I), and q is the charge on the electron. AS = (q /r~) 2 and: Ir = (4rcZqZ / h ) [HIc(rc)/AEo] 2

(4)

Molecular Orientation on Electron Transfer and Impact Ionization

5

Thus, from Equation (2), low speeds or large ~r (large Hic or large separation between the curves) gives a small Pd, and the probability of adiabatic hop between potential curves is low. Under these circumstances, the crossing is adiabatic and the system smoothly changes from a covalent to an ionic description. In this process the electron jumps from the Na atom to the I atom. A complete collision requires the crossing to be traversed twice, once on the way in and once on the way out, as shown in Figure 2a. In order for ions to be produced from neutrals, the atomic system must traverse one crossing adiabatically and the other diabatically. For the atomic system shown in Figures 1 and 2, the two crossings are identical, and the overall probability of ionization is P = (1 - Pd)Pd. If the electron jumps at the first crossing the ions interact in close proximity to one another, leading to "ionic scattering." If the first crossing is diabatic, the close proximity encounter occurs between weakly interacting neutrals leading to "cova-

Figure 2. Simplified picture of atom-atom collisional ionization with crossing distance rc. Heavy solid lines represent trajectories of neutral systems. At the first crossing (r = rc) some fraction (1 - Pd) of trajectories make adiabatic transitions and are represented by dashed lines (ion pairs). Those making diabatic transitions remain neutral and continue their flight relatively unaffected. Each of these trajectories then encounters r - re again, and again each trajectory can make an adiabatic or diabatic transition, resulting in ion pairs or neutrals depending on the trajectory. The ultimate production of ions requires one transition to be diabatic and one to be adiabatic, in either order. The inner circle represents the repulsive core.

6

PHILIP R. BROOKS and PETER W. HARLAND

lent scattering," and the difference can be resolved in the differential scattering cross section. This has been extensively reviewed. 3 For atom-molecule collisions the situation is much more interesting. Many more dimensions need to be taken into consideration, and the interaction is likely to be dependent upon the orientation. This is shown schematically in Figure 2b, where the radius of the second crossing is shown to be different from the first. Even a minute change in crossing distance can have a profound influence on the dynamics because the coupling matrix element, H~2, depends exponentially 3'5 on r e and the LZ probability depends exponentially on H12! Moreover, the internal state of the molecule can change between the crossings, and the second crossing might be between surfaces quite different from those of the original system. This has been called "bond stretching" in the earlier work. 3 As an example of how the internal state of the molecule influences the crossing, consider the effect of adding an electron to a diatomic molecule, such as Br 2. The negative ion is less tightly bound than the neutral, and attachment of the electron (at fixed internuclear distance) results in a negative ion formed in a highly excited vibrational state. Following the electron jump, the Br nuclei begin to move apart and the apparent electron affinity of the Br 2 increases. According to Equation (3) this increases the crossing radius, decreases the ionic-covalent interaction, and greatly enhances the probability of the system making adiabatic transition. Since vibration of Br 2 is periodic, the bond stretching causes the electron affinity and crossing radius to vary with time, and the electron transfer probability at the second crossing will depend on the time required (i.e., on the speed) for the atomic ion to arrive, as observed experimentally. 6 In the extreme limit of bond stretching, complete dissociation of the molecular ion may occur between the crossings, leaving only the atomic ions to undergo a diatomic crossing.

C. Experimental Technique Overview of the Cross-Beam Experiments In these experiments, collisions are studied between spatially oriented molecules and neutral potassium atoms which are accelerated to energies of 3-25 eV. The orientation of the molecule can be changed so that either end of the molecule can be presented to the incoming K atom. Positive ions formed in the collision are detected by one of two particle multipliers, depending on the orientation, and pulse counted. The apparatus is schematically shown in Figure 3. Details concerning the construction may be found elsewhere. 7 The molecular beam is formed from an expansion of a pure gas sample or a 10% seeded mixture in He from the nozzle, labeled N. The central core of the expanding jet is passed by a thin-walled skimmer into the buffer chamber, labeled C, where it is modulated by a rotating chopper wheel. The beam then passes through a second skimmer into chamber H where it traverses an inhomogeneous hexapole electric field (-~ +5 kV on adjacent rods) that filters out the lower Stark states of the symmetric-top beam component and brings

Molecular Orientation on Electron Transfer and Impact Ionization

7

Figure 3. Illustration of the cross-beam machine. N is the nozzle source for the molecular beam, C is the buffer chamber with a beam chopper (not shown), H is the hexapole electric field quantum state selector, U are the homogeneous electric field plates, Q is an on-axis quadrupole mass filter, O is the fast atom beam source, and Co and C180are channeltrons.

the upper Stark states to a focus at the exit aperture. 8 Symmetric-top molecules such as CH3I are good candidates for orientation because the criterion for quantum state filtering is that the dipole moment does not average to zero during the course of rotation. Unlike diatomic molecules (which rotate in a plane, thereby causing the dipole moment to average to zero), symmetric-top molecules rotate in an electric field like a child's top in a gravitational field: the symmetry axis precesses about the field, and the dipole moment does not average to zero. The potential energy of interaction W of an electric dipole in an external electric field is given by, w = -~t.E

(5)

where Ix is the electric dipole moment vector and E is the electric field vector. For a symmetric-top molecule with dipole moment ~t0 oriented at an angle 0 with an applied field E the potential energy is given by the first-order Stark effect, 9 W = -~toE = -lttoE MK/J(J + 1)

(6)

where J, K, and M are quantum numbers for the total angular momentum, the component along the top axis, and the component along the field, respectively. Hyperfine interaction is neglected. Classically, ~ MK/J(J + 1), where 0 is the average angle between the symmetry axis and the electric field. In an inhomogeneous electric field, symmetric-top molecules experience a force F = - V W depending on the sign of M.K (or ), with each molecule moving to minimize its energy. Any inhomogeneous field will suffice in principle to separate the orientations, but it is useful experimentally to use a hexapole field because molecules with negative are focused by the field. ~~ Molecules with negative can thus be spatially separated from those with positive

8

PHILIP R. BROOKS and PETER W. HARLAND

, and the hexapole field can serve as a state-selecting filter, rejecting molecules in states with positive values of, and passing molecules in states with negative values of . These molecules are oriented with respect to the local, nonuniform electric field inside the hexapole field. At the exit of the inhomogeneous field, an additional uniform electric field is imposed by parallelplate electrodes. The E field thus gradually changes from the inhomogeneous field inside the hexapole to a uniform field in the collision center. The field changes very slowly in comparison to the rotation of the molecule, and the molecular rotation is quantized on the local field encountered by the molecule. In the collision zone, each molecule thus has a negative value of , and true orientation is achieved. An ideal hexapole field consists of six alternately charged hyperbolic rods, and the electrostatic potential inside this array is given by, V= Vo(r/rL)3COS 3~

(7)

where r is the distance from the axis, r L the axial distance to each electrode, V0 the magnitude of the voltage on the rods, and ~ is the polar angle. (Circular rods are usually used experimentally.) ~d The radial force on a symmetric-top molecule in such a field is independent of ~, and is given by: F r = l.t0 6 Vo(r/rz) 3

(8)

For negative values of , a molecule thus experiences a restoring force towards the axis, and the molecule can execute simple harmonic motion about the axis. Newton's equations predict that molecules entering the field with no radial component of velocity will be focused to a point on the axis when the voltage is: rl:2v2mr3L Vf~

(9)

241ttoL2 < - c o s 0 >

If only a few rotational states are populated, assumes a few discrete values, and if the exit aperture is small enough, the hexapole field will transmit individual J,K,M states depending on the Voltage selected (see below). Molecular orientation is effected in the homogeneous field, the negative end of the molecular dipoles ( negative) pointing toward the negative field plate. Reversal of the polarity of the homogeneous field inverts the orientation such that either end of the molecule can be presented to the potassium atom beam that passes through the molecular beam in the crossing region. Holes are cut in the field plates to pass the K atom beam and to allow a view of the intersection by two channeltron cones. A quadrupole mass filter on axis is used for beam detection and characterization. The beam of fast potassium atoms is generated by resonant charge transfer ~ of K + formed by surface ionization on a heated W filament in the oven labeled O. The K + ions are accelerated through the required potential and charge exchanged with K vapor at about 0.01 mtorr in the same oven. Ions passing through

Molecular Orientation on Electron Transfer and Impact Ionization

9

the exit orifice of the oven are swept out of the beam with a deflecting field of 20 V/cm, and thermal energy K atoms are unable to form ions in collisions with the oriented molecules and do not interfere with the measurements. ~2

Hexapole Characteristics and Orientation Distribution Figure 4 shows the hexapole transmission of a CH3Br beam at 10 K calculated for two exit apertures under our experimental conditions. At these temperatures, the most populated state is ~/K> = D0>, which does not focus, but there is some population in the I l l > , 121>, and 13l> states, and these states are transmitted individually at appropriate voltages as shown. Molecules are thus focused by the hexapole field. If only a few rotational states are populated, it is possible to select individual J, K, M states by use of appropriate combinations of applied voltage and beam apertures, la Focusing curves, such as that in Figure 4, have been measured experimentally, and reactive scattering has been observed for a few cases in which the beam is in a single quantum state. ~4 Unfortunately, the intensity of such state-selected beams is extremely low; for this reason we have selected conditions that transmit oriented beams with a distribution of states in order to facilitate cross-beam studies of reactive systems. Our experiments show that, although the beam intensity increases with the hexapole voltage, the hexapole voltage has no major qualitative effect upon the orientation distribution. Figure 5 compares calculated distributions for several molecules. As anticipated, the very prolate-top CH3Br (which, like a pencil, does not rotate stably about its symmetry axis), represents the least well oriented sample, and the oblate top CF3H (which, like a bicycle wheel, rotates easily about its symmetry axis) the best. Even though each resulting distribution is quite broad, a large effect is observed on the reaction. 0.04

w

"

'

l

'

i

~

|

w

~. 0.03 ->' 0.02

.E O3 t" (.-

-

o.01

4

8

12

Focussing Voltage / kV

Figure 4. Calculated focusing curves (intensity vs. V) for CH3Br at 10 K for a 1.4-m

long hexapole with exit aperture radii of 4.45 mm (solid line) and 0.145 mm (dashed line). Rotational states for the smaller aperture are resolved; the larger aperture completely loses rotational structure but gains in intensity.

10

PHILIP R. BROOKS and PETER W. HARLAND =

I

I

....... I

- CH3Br

-o~

0.8

_

9 -CF3Br

,

oE

-

"

- CF3H

~.,,r

/ , , //./,2"

.N

0.6

,

/

~y _

/ _

0.4s

0.2

0 ~,~.~"~" i - 1

-0.6

t

l

J

-0.2

0.2

0.6

1

cos O = p

Figure 5. Distribution of orientations of molecules state selected by an inhomogeneous hexapole electric field. ion Detection K + ions formed in the collision are detected by one or the other of the two channeltrons (C180 or Co) arranged schematically as shown in Figures 3 and 6. The voltage applied depends upon the orientation studied. The channeltron that protrudes through whichever uniform plate is negatively biased is activated to count positive ions. The active cone is biased at-1200 V while its uniform plate is held at-50 V. The opposing plate and cone are held at +50 V, and the channeltron anodes are held at +300 to +700 V, depending on gain requirements. For these operating conditions, the field at the intersection region is roughly determined by the parallel field plates because it was observed that the channeltron counts decreased if the plates were biased much above 50 V, indicating that at higher voltages the ions would be collected only by the plates and not by the channeltrons. Ions are less efficiently detected by channeltron C~80, apparently because the K + ions formed in the collision zone are initially moving away from Cl80. The orientation of the molecules is determined by the direction of the uniform electric field and may be reversed by a reversal of the polarity of the uniform field plates. As shown in Figure 6, the positive end of the molecule is presented to the incoming K atom in the 0 ~ configuration, and the ions counted by channeltron C 0. The negative end is presented in the 180 ~ configuration and the ions counted by channeltron C]80. The experiments thus directly determine the polarity of the more reactive end; the

Molecular Orientation on Electron Transfer and Impact Ionization

11

Figure 6. Polarities of the homogeneous orienting field and channeltrons used for the 0 ~ and 180 ~ configurations. The orientation of the polar molecule is indicated for each configuration using CH3Br and CF3Br as examples. chemical identity of the more reactive end must be deduced from electronegativities, dipole trends, and the reactivity itself.

Data Acquisition The active channeltron is capacitively coupled to a quad scaler that counts signal pulses and those from an 86-Hz clock. Beam on-off signal differences at focusing voltage, V, S(V)i-- [ S ( V ) o n - S(V)off]i, are measured for each channeltron i (i = 0 or 180) and then corrected for the different multiplication efficiencies and ion collection efficiencies of each channeltron in order to decouple these from orientation effects. The relative detection efficiency, F(e) = S(O)lso/S(O)o, is measured for each relative beam energy e, interspersed with measurements of S(V), by use of the small flux of randomly oriented molecules obtained when no voltage is applied to the 6-pole field (0 kV). The relative signal due to the oriented molecules, S'(V), is the (HVon)- (HVoQ signal difference corrected for the multiplier efficiencies at beam energy e: S'(I0180 = S(V)180 and S'(V)0 = F(e).S(V)o. For further details, see Reference 7.

12

PHILIP R. BROOKS and PETERW. HARLAND

D. Results

Raw Signals In every system studied, the orientation of the molecule clearly affects the signal, and examples of this effect are shown in Figure 7 for CHaBr and CFaBr. We compare the methyl and perfluoromethyl halides because the polarity of the molecules is different. The X-end in CH3X is usually negative, whereas the X-end in CF3X is usually positive. This demonstrates that these data arise from a real molecular effect, and not from stray electric fields. From the data in Figure 7 we conclude that the positive end of CFaBr is more reactive and the negative end of CHaBr is more reactive. The Br-end of CH3Br is assumed to be the negative end, and dipole moment trends and reactivity suggest that in CFaBr the Br is the positive end. In CFaI, the I has been directly 15 and indirectly 16 established (by use of oriented molecules) to be the positive end. Both molecules are thus more reactive on the Br-end, which we call the heads end (to emphasize the analogy with the heads/tails orientation of a coin). Similar conclusions are reached, with less refined data, in comparisons of the CF3I/CH3I and CF3C1/CH3C1 systems. The data are thus not explicable by the electron's simply jumping to the positive end of the dipole.

Cross Section The energy dependence of the K beam intensity and the energy dependence of the reaction cross section obscure the orientation dependence of the signals themselves. It is thus useful to remove the beam intensity variation by a comparison of the relative cross sections S'/I(K) for heads/tails orientation as shown in Figure 8. The heads/tails difference is much more apparent and seems largest at low energies. The space charge limited relationship, I K oc E 3/2, is used here to normalize the ion signals at different K beam energies, because the neutral intensity is expected to be proportional to E 3/2, as experimentally observed by Aten and Los 17 and roughly confirmed here.

Steric Effect The effect of orientation on the cross section is striking, but is still hidden by the variation of the cross section with energy. The steric factor, G, the signal difference normalized to the cross section as, ?

f

f

G = (S180 - S~))/(Sl8 0 + So),

(10)

emphasizes the salient features of the orientation itself, and is shown in Figure 9 for the currently best studied systems, CF3Br and CH3Br. The effect of orientation is striking: G must lie in the range - 1 < G < 1, yet at low energy for both molecules G can clearly be extrapolated to 1. This means that at low energies one orientation is completely unreactive. At higher energies G tends to 0 and the orientation makes almost no difference. The difference in molecular polarity is immediately apparent,

1500

,

, o

, S'

9

S'

~" 1 0 0 0

i

,

,

,

,

0 i

180

r

t'-" C7~

9

500

O

O

!

o

8 O

s

CHBr 3

O

I

I

8

,

I

o

!

I

I

'

1

'

I

.D t,,,.. col

S'

180

l

12

'

I

S' ~ 9

1500

,.

10 11 E (lab) e V

9

2000

I

13

' O

o

O

O

--~ 1 0 0 0 cOD

O

8

500 8 0

-

6

A

O

r !

9

7

8

i ,

E(lab)

CFBr 3

1

9

,

I

10

,

11

Figure 7. Relative signals for producing K§ ions on collision with oriented CH3Br and CF3Br. The negative end of CH3Br and the positive end of CF3Br are more reactive.

13

.Q

40

i

o

l__

~

tO

3O

,

,

,

CH

,

end

'

'

3 9 Br end

I

. . . .

,6

o

"o

&o

=l.-i

o

{D

'

o9

-

o

'

'

0

6r

o

*8

20

I

O l__

O ll}

AO

10

,8

O

K + C H Br 3

m

{D IT

t,~-~

|

,

,

I

,

,

,

,

10

80

I

tO 0

'

I

,

,

'

I

,

20

'

Br end o ~ ~ i ~ ~ r t

CF3end

60

. u

40 O 0 Q) > c~

,

15

E (cm) eV

.D

I

,

i Ir

L

8~

20

i

8~ i

. . m

K + C F Br

i

Q)

n"

0

~ 0

~

3

1

' 5

10

15

, ~ 20

E (CM)eV Figure 8. Relative cross section (corrected ion signal/K beam intensity) for heads and tails orientations of CH3Br and CF3Br.

14

~r"---~"--[--X O,

T

,O

x

oo',,

"r

!

r ~

*(~3Br -

0.5 0

o

U.I 0 o

u L _

-0.5

-1

~

0

q~'~" 9 CF

3

5

Br+

10 E (CM)eV

15

20

Figure 9. Steric factor G vs. center-of-mass energy, E(CM), for CFHBr and CH3Br. Horizontal line is G = 0 (no steric effect), and dashed line is the negative of a smooth fit to the CH3Br data plotted to compare the curvature of CHjBr and CF3Br.

!

I

I

0.6-

(.9

I

~,8\ 8

0.2-

-0.2 -

<> 9 o 9 Q 9

(:;HI CF31 CH3Br CF3Br CH3CI CF~CI

2.

[]

um

/. .

-0.6 -1

/

/l 0

5

9

9

i

10

I

I

15 20 E (cm) eV

1

25

30

Figure 10. Comparison of experimental G values for CH3X and CF3X. The recent values of Reference 7b are included as dashed lines and dot-dash lines; other data are from Reference 12. 15

16

PHILIP R. BROOKS and PETER W. HARLAND

with the heads end, or Br-end, being more reactive in either case. This difference persists throughout the CH3X/CF3X family, as shown in Figure 10. Other types of systems, such as t-butyl X and CX3H , display somewhat similar features. ~2

Threshold Behavior Extrapolation of G to low energies yields IGI = 1, at least for CF3Br, CF3C1, and CH3Br. This implies that at the threshold one orientation is unreactive and is consistent with our early suspicion 12 that different orientations have different kinetic energy thresholds. This is indeed the situation, as illustrated by the example shown in Figure 11. E.

Discussion

All chemical reactions begin as the reagents approach and end as the products separate. The system must traverse both the entrance channel and the exit channel. Our hope is that, by specifying the reagent orientation in the entrance channel and monitoring the appearance of ions in the exit channel, we may learn how orientation affects the transfer of an electron from one species to another. Strictly speaking, we cannot separate the electron transfer, presumed to occur in the entrance channel, from the process of the ions separating, which is in the exit channel. Under certain circumstances, one or the other of these interactions may dominate. We have thus interpreted the data under certain assumptions, but what we really learn is how the

0.25

'

'

'

1

'

'

'

I

'

"

9 Br end

0.2

9

OF

3

',,

I

'

'

'kl

/

'

'

'

A/

_

en

~" 0.15 I1,..

tO) co ~

0.1 0.05

S

o7 -0.05

,

3

,

,

I

3.4

" "./'"

, ,

,

,

/-

I

,

,

_

-

,

I

3.8 4.2 E (CM)eV

,

,

~

I

4.6

~

,

,

5

Figure 11. Relative cross sections versus center-of-mass energy, E(CM), for heads and tails orientations for the K + CF3Br reaction near the threshold for ion production.

Molecular Orientation on Electron Transfer and Impact Ionization

17

entire process is affected by the initial molecular orientation, and conclusions regarding the electron jump must be regarded in this light.

Exit Channel Interactions Angular distributions of the products of many chemical reactions bear a resemblance to the distributions obtained from photodissociation, suggesting that the products are formed in an impulsive event similar to photolysis. ~8It has thus been useful to compare experiments with a "direct interaction with product repulsion" (DIPR) model. We have found this concept to be useful in interpreting the angular distributions of the neutral products of thermal energy collisions of oriented molecules. Early studies of the oriented CF3I + K reaction suggested that the (uncharged) KI product molecule was scattered in the direction in which the CF3I figure axis was originally pointing. 16 The neutral KI molecule is found to be scattered backwards for K incident on the I end of the molecule and forwards for K incident on the CF3-end. Cross sections for the heads and tails orientations were roughly equal. Because the LUMO receiving the electron might be rather diffuse, we had originally assumed (mainly for simplicity) that the initial electron jump might be relatively unaffected by the orientation of the molecule, and further analysis indicates that the angular distribution of heads, tails, and sideways-oriented molecules is primarily described by the distribution of directions of the molecular axes. 19These experimental results are semiquantitatively reproduced by the impulsive DIPR model sketched in Figure 12 when the effect of the incoming K atom's

Figure 12. Schematic mechanism for impulsive reaction of thermal energy reaction of K with oriented CF31.The electron is assumed to be transferred at large distance to the molecule irrespective of orientation. The molecular ion is formed in a repulsive state that promptly dissociates, ejecting the I- ion in the direction of the molecular axis, and the K+ is dragged off by the departing i- resulting in backward scattering for heads orientation and forward scattering for tails as observed.

18

PHILIP R. BROOKS and PETERW. HARLAND

momentum is included. Moreover, this model also accounts for the totally different angular distribution observed if the molecule is oriented sideways. 2~ It only partially accounts for the angular distribution observed for the analogous CF3Br reaction, 21 possibly because the orientation might affect the electron transfer. It thus appears that the breakup of the molecular negative ion plays an important role in determining the angular distribution of the products and may be important also in describing the higher energy ionization collisions. The collisional ionization experiments of unoriented molecules (mentioned in Section IA,B) provide the key to an understanding of the exit channel interactions for oriented molecules: there must be two ionic/covalent surface crossings, one as the particles approach, and the second as they recede, qualitatively sketched in Figure 2b. In a limiting case of "bond stretching," the molecular ion might be in the process of dissociating by the time the second crossing is encountered. This is shown very schematically in Figure 13, where the covalent K + RX surface crosses the ionic K + + RX-surface at rcl. The first crossing distance rcl q2/AEo is =

EXIT /'/'] CHANNEL ~

II

~

I

ENTRANCE CHANNEL

Figure 13. Highly schematic one-dimensional representations of the electron jump in a dissociating molecular system. Neutral K and RX approach on a covalent surface on the right, crossing the ionic surface at re1, which is at sufficiently short range for the surfaces to be separated and for the system to traverse the crossing adiabatically (the electron "jumps"). After electron transfer, the negative ion can undergo a dissociation (migrating to the left panel), and the system can evolve along another surface to give fragments K§ X-, and R. These undergo a crossing re2 at larger distances with neutral fragments K, X and R, where the surfaces are not well separated. The system is more likely to traverse this crossing diabatically, and the fragments will separate as charged species.

Molecular Orientation on Electron Transfer and Impact Ionization

19

calculated from ionization potentials and electron affinities to be about 4 .~, and Hic about 300 meV. At the nominal collision speeds used in these experiments (vr .~ 5.6 km/sec (56 A/ps) for K + CH3I at 5 eV), the Landau-Zener relation, Equation (2), predicts that Pd z 0, and the first crossing will be completely adiabatic: the electron will jump to the molecule. The electron is expected to occupy an antibonding C-X o* orbital, and the molecular ions produced, CF3X-and CH3X-, are expected to dissociate promptly along yet another surface (in another dimension on the left panel), indicated as K § + R + X-. This surface will intersect the K + R + X covalent surface at a much larger distance, re2. Since Hic decreases exponentially with distance, 5 this crossing is less avoided, and the system is more likely to traverse this crossing diabatically with the electron remaining on the X- ion. At energies a few volts above threshold, the CH3I, CF3I, CH3Br, and CF3Br molecules undergo dissociative electron attachment 22 and in collisional ionization give X- ions in about 98% yield. 23 The scenario suggested above (the electron jumping at the first crossing and the molecular ion dissociating before the second crossing is encountered) is thus very likely to occur. If the molecule were to remain unchanged upon the addition of the electron, the second crossing would be exactly equivalent to the first and would again be traversed completely adiabatically. The electron would be smoothly transferred back to the K § ion, the products would separate on the covalent surface, no ions would be produced, and there would be no dependence on orientation. If, on the other hand, the molecular ion were to decompose explosively, the second curve crossing would be an asymptotic crossing between the emerging X- ion and the incident K § This second crossing occurs at large R where Hic z 0. The LZ relation then predicts that the second crossing would be completely diabatic; the electron stays on the X- ion and the products separate on the ionic surface. In this latter limiting case, every collision would lead to ionization and the orientation would again not be important. The behavior observed is clearly intermediate between these two limits: ions are produced and the orientation is important. The existence of an orientation effect shows that every collision does not lead to ionization. As discussed previously, we expect the electron to be transferred adiabatically at the first crossing. However, at the second crossing the K + ion must be encountering something intermediate between a bound CF3Br- molecular ion and a free Br- atomic ion. It must encounter a species in the act of breaking apart, and we can use the experimental orientation data to extract some information about this species. We thus assume that the first crossing is completely adiabatic, and that the probability of K escaping as K + is the probability that the second curve crossing is traversed diabatically as described by Equation (2). This is sensitive to the relative speed of ions at the crossing, which, as shown in Figure 14, is different for the heads and tails orientation. When the zeroth-order approximation that K is independent of orientation is made, then the probability of formation of an ion in the heads or tails orientation is, P~ = Pd = exp(-K/v~)

(11)

20

PHILIP R. BROOKS and PETER W. HARLAND

Figure 14. Schematic illustration of velocity components as the molecular ion dissociates in heads and tails orientations. In the heads orientation, the nascent ions collide head on with a higher relative velocity than in the tails orientation, where one ion must catch up with the other.

where ~ refers to either heads or tails. The heads:tails ratio then becomes, R = Ph/Pt = exp(-~:/v h + r./vt) = exp(-r~Av/v 2)

(12)

where: Av = vt - vh and v2 = VhVt

"

-

2E'/go"

(13)

A plot ofln R vs. 1/E' is thus expected to be linear, where E' is the final translational energy, E ' < E - E t h , E is the relative collision energy, and Eth is the threshold energy for ion formation. This is shown for CF3Br in Figure 15. For energies a few volts above threshold, the orientation effect is well described by Equation (2). At high energies the first crossing may become diabatic, thereby invalidating the assumption made in Equation (11). Uncertainty in Eth and fluctuations in the very low signals probably account for deviations near Eth. The impulsive model described in Figure 14 therefore accounts nicely for the energy dependence of the orientation effect. In the exit channel, the ions are trying to get away from one another, and this is easiest if they are traveling in opposite directions, which occurs in the heads orientation. The second ionic/covalent surface crossing occurs between species in the act of reacting, and an experimental value for K:at this second crossing can be obtained from the slope of a plot such as Figure 15. Semiempirical estimates for Hic have been used to obtain rough values of re2 and suggest that rc2 may be an angstrom or two larger than rcl, consistent with the

Molecular Orientation on Electron Transfer and Impact Ionization

2.5

,

,,

,

I,

,

,,

i,

,

,

,

i,

,

,

,

i

,

,,

,

21

1

,

,

O!

O

_

,,

1.5 rr t"-

1 0.5

-0.5

. . . .

0

1

0.1

. . . .

I

0.2

. . . .

I , , , , I

. . . .

0.3 0.4 1/(E-Eth )

I

. . . .

0.5

0.6

Figure 15. In R vs. (E- Eth)-1 for CF3Br. Circles are from Reference 7b and squares from Reference 12. Deviations from the line are accentuated for low E.

notion that the crossing is between a K § ion and a species in the act of coming apart. 12 Thus, many aspects of the collisional ionization experiments can also be described by the impulsive DIPR mechanism, provided the very strong interaction between the ions in the exit channel is recognized. This is qualitatively depicted in Figure 16, which differs from Figure 12 in two major respects: (1) the incoming K atom is faster, and (2) ions are detected, not neutrals. As shown, the approach, the electron transfer, and the dissociation steps are similar to those at lower energy, and the negative atomic ion is again ejected in the direction of the molecular axis. The K atom is now much faster and the K + ion is more likely to continue in the forward direction. If the X- ion is ejected antiparallel to the incoming K+, the ions have less time to interact, and in the heads orientation the K* is more likely to escape the Coulomb attraction of the X-and be detected as an ion. On the other hand, in the tails orientation the X- travels parallel to the K § the ions are more likely to either recombine or to neutralize one another, and fewer K + ions escape the Coulomb attraction. Independent support for these conclusions regarding the orientation effects in the exit channel is provided by the experiments of Kalamarides et al. 24 Reaction of K atoms in high Rydberg states with CFaI , K** + CFaI -~ K + + F + CF3, was studied by passing a beam of K** through a scattering gas containing low-pressure CF3I

22

PHILIP R. BROOKS and PETERW. HARLAND

Figure 16. Schematic mechanism for impulsive reaction of high energy K with oriented CR3X, e.g., CF31. It is similar to Figure 12, but the higher energy K atom is much less perturbed by the lower energy X-, although parallel trajectories (in the tails orientation) allow for longer contact time resulting in some neutralization and a concomitant reduction in ion signal.

and measuring the angular distribution of the resulting V ions with a microchannel plate and position-sensitive detector. For large principal quantum numbers, n ~ 26, the Rydberg electron is essentially free of the core and behaves as a free electron. The CFaI was a gas and all orientations of the molecules were equally likely, so CF3I- ions were expected to be formed in all orientations by attachment of the free electron. Dissociation of CFaI- would eject I- along the randomly oriented molecular axes, and the I- ions were expected to be distributed isotropically, which was confirmed by experiment. However, as n decreased to 9, the angular distribution became anisotropic, with fewer I- ions moving in the direction of the initial K**. The electron is more tightly bound for n - 9 and is more comparable to those of this study (n - 4): the Rydberg electron in this case is not free, but carries with it the positively charged core. Kalamarides et al. thus observed that fewer I- ions were scattered in the forward direction and concluded that the diminution of I- in the forward direction was due to a greater likelihood of charge neutralization if I- and K § were traveling in the same direction, as concluded from the oriented-molecule experiments and shown in Figure 16.

Entrance Channel--Electron Transfer The Landau-Zener theory is comparatively successful in explaining the overall behavior of the reactions of oriented molecules at thermal energies where neutral

Molecular Orientation on Electron Transfer and Impact Ionization

23

products are formed, and at elevated energies where the transient ions have enough energy to separate. This is, in a sense, frustratingly successful, because there seems to be no room to accommodate an orientation-dependent electron transfer, which chemical intuition suggests must be operative. The role of the electron transfer in the post-threshold behavior discussed previously is apparently overshadowed by the strong Coulomb forces in the exit channel. Orientation-dependent exit channel interactions are possible when three or more species are produced in the collision, as shown in Figure 14, and, as discussed above, this is likely to be the situation for several of the molecules studied. However, if the collision energy is sufficiently low, decomposition of the molecular negative ion may not be energetically allowed. If only two particles are formed, a positive ion and a negative ion, conservation of momentum requires that they must recede with antiparallel velocities regardless of the orientation. The strong, orientation-dependent forces in the exit channel suggested in Figure 14 are thus not present, and any orientation effect may be due to the electron transfer in the entrance channel. The different threshold behaviors for heads and tails orientations shown in Figures 7 and 8 indicate that, at very low energies, reaction is restricted to only one end of the molecule. We directly observe that there is no reaction for attack in the unfavored orientation. The different thresholds for attack at different "ends" of these molecules requires the final state of the system, at the respective thresholds, to be somehow different for attack at the opposite ends of the molecule. For CF3Br, we believe that different products may be formed, depending on the end attacked, but the same species in different internal states could also be a possibility. 25 In these experiments there are two likely low-energy reaction channels, K + CX3Y ~ K § + Y - + CX 3 K § + CX3Y-

(14) (15)

that we are not yet able to differentiate because only the K § ion was detected. (KY salt molecules might also be formed, but, because only charged particles are detected, the neutrals are not observed.) At energies a few volts above threshold, fragmentation reaction (14) accounts for about 95% of the products, 23 and the early experiments were interpreted on the basis of reaction (14). At sufficiently low energies, however, the parent ion may not have enough energy to fragment and reaction (15) can be observed. The negative ions formed in collisions of Na atoms with unoriented CF3Br have been directly observed by Compton et al. 23 They observed the parent ion, CF3Br-, and determined the vertical electron affinity, EAv, to be 0.91 + 0.20 eV. Their data predict that the threshold for electron transfer to CF3Br to give the parent ion [reaction (15)] is 3.43 eV and the threshold for fragmentation [reaction (14)] to give Br- is 3.97 eV. These threshold energies for formation of the parent ion, CF3Br-, and for fragmentation into CF 3 and Br- agree closely with the apparent thresholds

24

PHILIP R. BROOKS and PETERW. HARLAND

of 3.4 eV and 4.0 eV obtained for the oriented molecules. Since the threshold laws are not known, we have linearly extrapolated the data to yield apparent thresholds. The threshold differences are expected to be significant because the cross sections for heads and tails orientations are similar over a large energy range (Figure 8). We thus conclude that, at the lower (heads) threshold, parent CF3Br- is produced, and it is produced by attack at the Br-end of the molecule. In the energy range 3.4--4.0 eV, reaction occurs exclusively at the heads end (Br) of the molecule producing only two particles, K § and CF3Br-, which must leave the collision traveling in opposite directions to conserve momentum. The strongly orientation-dependent 3-body exit channel interactions, which were adequate to explain the high-energy (10-eV) orientation behavior, are therefore absent. Effects of orientation between 3.4 and 4.0 eV must arise mostly from the electron transfer in the entrance channel, and we conclude that for energies near threshold the electron is transferred preferentially to the Br end of the molecule. At the higher (tails) threshold, tail-end attack results in fragmentation and produces Br- fragments. Formation of the parent negative molecular ion by tails attack is apparently prevented by some barrier that can be overcome with 0.5 eV of translational energy, but the CF3Br- molecular ion is too weakly bound to accommodate this much energy, and the negative molecular ion breaks up according to reaction (14). Above the tails threshold, heads attack may also produce Br- fragments because enough energy would probably be deposited in the parent ion to cause it to break apart, and above about 5 eV, Br- is the dominant negative ion. For the other molecules studied, less is known about the negative ions formed and their thresholds. It is, of course, tempting to speculate that different products are being formed for different orientations in a manner analogous to that for CF3Br and for the electron bombardment experiments. For CF3C1, the parent ion has been observed, 26 and we have measured a difference between heads and tails thresholds of 0.6 eV. Again, the Cl-end is more reactive and at low energies only Cl-end attack produces ions. However, the apparent threshold is in poorer agreement with that calculated, possibly a result of the extrapolation or of our weaker signals because the reaction cross section is smaller than that for CF3Br. The parent CH3Br ion has not been observed in previous studies. 23'27 Nevertheless, only one end of the molecule, the Br-end, is reactive at energies near threshold. The difference in thresholds is 0.2 eV, and the tails threshold is in rough agreement with the threshold calculated to produce Br- and with the observations of Compton et al. 23 for formation of Br-. If the analogy with CF3Br is pursued, these data indicate that the parent ion is bound only by 0.2 eV (+0.2 eV), suggesting that the parent may be so fragile that it might not be observed. These data thus suggest that different products are formed by attack at different ends of the molecule, which are manifested here by different energetic thresholds for the two orientations. The electron probably jumps to an antibonding per* orbital composed largely of p orbitals from carbon and bromine, 26 which is expected to be more accessible from the Br-end of the molecule. The threshold results show that transfer through the

Molecular Orientation on Electron Transfer and Impact Ionization

51

\'

4

'

'1

i

L

3

4

eads

25

'

'

I

I

!

i

,

5

6

7

8

ails

3 ~-

2

L

>

1

-

0 -1 -2

2

RK.Br (A)

Figure 17. Approximate one-dimensional ionic and covalent diabatic potentials adapted from Reference 48for CF3Br. Solid and dashed ionic curves are Rittner-type potentials for parent and fragment ions respectively, and heads and tails are covalent curves. The ionic asymptote is denoted by the arrow. The crossings are avoided; dotted curves for the "crossing" near 4.3 g, are the adiabatic curves resulting from configuration interaction s between the diabatic ionic and covalent curves. (Adiabatic curves for the other crossings are omitted for simplicity.)

CF3-end is apparently impeded by a barrier of about 0.6 eV (14 kcal/mol), which can be overcome by an increase in the collision energy, resulting in fragmentation of the anion. This is qualitatively illustrated by the potential curves in Figure 17, where the covalent potential for tails approach includes an extra repulsion term to account for the CF 3 group being interposed between K and Br. This extra repulsion forces the tails orientation crossing to be at larger distances (and higher energies) where electron transfer is much less likely because the orbital overlap is less. The interaction between the ionic and covalent configurations falls exponentially with distance, 5 and, at a given collision energy, the likelihood of an adiabatic crossing (electron jump) is greatly decreased, which mostly accounts for the lack of ions formed in the tails orientation. The higher energy of the crossing provides some rationale for the barrier to tails attack. This description and Figure 17 are highly simplified because additional dimensions, such as the C-Br distance, must be considered to explain salt formation as well as the fragmentation observed at higher energy. The conclusion that electron transfer is localized is likely to apply to other systems, even at lower energies. As the energy is decreased towards thermal energy,

26

PHILIP R. BROOKS and PETERW. HARLAND

the electron is more likely to jump although the electron will jump back if the energy is below threshold, which is most likely the case for tails attack below tails threshold. Salt formation (exoergic by 20 kcal/mol) and ion production compete with one another above the ion threshold, and it is reasonable to conclude that these processes share the same entrance channel. The preference for the Br-end is thus expected to extend to lower energies, and indeed, in an earlier study of K + CFaBr at thermal energies, E1 we found that the neutral salt, KBr, was more likely to be formed by Br-end attack. Although overall production ofK § is greater at all energies from heads attack, we are as yet unable to assess the relative importance of heads vs. tails attack on the Br-channel at the onset of Br- formation. In summary, ions are formed in electron transfer collisions between beams of neutral K atoms and beams of oriented target molecules. In every case studied so far, the orientation of the target molecule greatly affects the reactivity, consistent with "chemical intuition." The electron is not, however, simply transferred to the positive end of the molecule, because in the methyl halides the negative end is more reactive. At energies a few eV above threshold, where molecular negative ions might fragment, the dynamics seem to be dominated by the ions getting away from one another. More than two particles can form, and the initial molecular orientation can be manifested in the exit channel as ions traveling with parallel or antiparallel velocities. Ions with antiparallel velocities are most likely to survive as ions, consistent with observation. At low energies, several molecules exhibit different thresholds for different orientations. There is consequently an energy region where no reaction occurs at the "wrong" end of the molecule.

il.

ELECTRON I M P A C T I O N I Z A T I O N

A. Introduction The experiments involving the collision of fast potassium atoms with oriented symmetric-top molecules have demonstrated that the efficiency of the initial electron transfer step in the entrance channel is orientation-dependent, with the reaction threshold, cross section, and reaction products exhibiting an orientation dependence. The fast atom experiments were designed to probe the electron transfer step, although it is recognized that the LZ description of the electron transfer step in the entrance channel is an oversimplification. It is unlikely that a discrete electron particle jumps from the approaching alkali metal atom to the molecule at a well-defined separation. The wavefunctions corresponding to the two particles mix during the approach, and the system takes the characteristics of the transition-state species in a manner changing smoothly with time. In impulsive encounters, such as these, it is likely that the electron transfer is only complete when the reaction products emerging from the transition state have assumed their asymptotic identities. Whether the electron is transferred as a discrete particle or not, these results beg the question: Would the ionization of a molecule by a free electron also exhibit

Molecular Orientation on Electron Transfer and Impact Ionization

27

an orientation dependence? Recent cross-beam experiments have shown 28 that this is indeed the case, the ionization cross section and the fragmentation pattern exhibiting an orientation dependence. A number of excellent reviews and books have included consideration of the fundamental electron impact ionization process, 29-36 and the attention afforded the experimental measurement of ionization potentials and fragment ion appearance energies over the years is reflected in the comprehensive database of ionization potentials and gas phase ion enthalpies of formation published through the National Bureau of Standards in printed and electronic forms. 37 In contrast, few absolute ionization cross sections have been measured. The most comprehensive compilation of molecular ionization cross sections are relative values measured with a modified commercial electron impact mass spectrometer ion source using the cross section for Ar as a reference. 38

B. ExperimentalTechnique Experiments are carded out 28 with crossed beams of spatially oriented symmetric-top molecules and near-monochromatic electrons. The dimensions of the hexapole were chosen to optimize transmission at the expense of specific quantum state selectivity. The focused beam of upper Stark-state selected molecules passes through an 8.0-mm diameter exit aperture into a highly screened, weak, homogeneous orienting electric field (20 V cm-1) maintained between parallel field plates 200 mm long and 10 mm apart and is detected on axis by (1) a quadrupole mass filter or (2) a mass-insensitive rotatable particle multiplier. The electron beam passes through apertures in the field plates, through the molecular beam, and into a screened Faraday cup. The electron-beam-guiding elements, homogeneous field plates, screening grids and plates, Faraday cup assembly, and the ion-guiding lens are all coated with colloidal graphite. A diagram of the scattering region is shown in Figure 18. Collisions involving neutral reactants and products are unaffected by the presence of a uniform electric field in the crossing region. This is not the case where charged particles are involved. Ions formed between the homogeneous field plates would be accelerated towards the field plate of opposite polarity and be discharged. In collisions between fast K atoms and oriented symmetric-top molecules, the K § ion products are collected by use ofchanneltrons protruding through the field plates. This approach cannot be used for electron impact, where the proximity of the channeltron cones to the beam crossing would shatter the electron beam integrity and the geometry of the beam crossing volume, and attract ions produced by ionization directly to the negative field plate. To overcome this problem, experiments are carried out by use of a pulsed nozzle operating at 10 Hz with a 1.8-ms open time. One field plate is maintained at ground potential and the other at +_20 V. The energized field plate is switched to <0.1 V from ground (polarity preserved) in <1 ~ts as the leading edge of the gas pulse reaches the electron beam crossing. The

28

PHILIP R. BROOKS and PETERW. HARLAND

Figure 18. Illustration of the molecular beam-electron beam crossing region used in the electron impact ionization experiments. The molecular beam source, buffer, and hexapole chambers are similar to those shown in Figure 3.

segment of oriented beam between the homogeneous field plates at the time the field is collapsed corresponds to 300 laS in flight time. Ions produced by the electron impact ionization of this 300 ~ts segment of spatially oriented beam in the absence of the uniform orienting field are gated at the detector located 25 mm downstream on the molecular beam axis. An Einzel lens assembly fitted to the entrance of the quadrupole is designed to guide ions into the mass filter without disrupting the homogeneous field in the beam crossing region when it is energized. Measurements are repeated with the hexapole high voltage switched off and the rods set to ground potential, i.e., in the absence of the inhomogeneous field in the hexapole. The method of data analysis is the same as that described previously for the fast potassium experiments. The steric effect is expressed either as the steric ratio, R = S+/S_, which is the ratio of the corrected (for background) signal for ionization at the positive end of the dipole to the signal for ionization at the negative end of the dipole, or as the steric factor G, [Equation (10)]. Equal ionization probability at both ends of the molecule would give R = 1 and G = 0, preferential ionization at the positive end of the molecule would give R > 1 and G < 0, and preference at the negative end of the molecule would give R < 1 and G > 0. C. Results

The results for all experiments carried out to date are shown in Table 1. The symmetric-top molecules exhibit a clear effect that disappears if the homogeneous field is switched off as the gas pulse enters the field plates. Under identical experimental conditions, the ion signal produced by the electron ionization of the nonpolar molecules fails to display any effect on the field potentials or polarities. CH3C1 exhibits the highest steric ratio for the molecules investigated. This is also found in studies of the elastic scattering of high-energy electrons from oriented molecules. 39 Electron impact ionization is more efficient at the positive end for all of the molecules studied, with the possible exception of the CH~ fragment ions

Molecular Orientation on Electron Transfer and Impact Ionization

29

Table 1. Steric Factors and Steric Ratios for 200-eV Electron Impact Ionization

System

Ion

Ar

Ar +

SF 6

SF~

CH3C1

G = (S_ - S+)/(S_ + S§ 0.00 + 0.01 ~ 0

CH3C1 §

- 0 . 4 2 + 0.12

CH~3

+ 0.02 + 0.03

CH3Br a

CH3Br §

CC13H

CC12H §

CH~

~ - 0.1 ~ 0 - 0.17 + 0.08

R = S+/S_ 1.0 ~ 1 2.6 1.0 ~ 1.2 -- 1 1.4

Note: apreliminary results

formed from CH3C1 and CH3Br, which are independent of orientation or weakly favored for electron impact on the negative end of the molecule. The CH3Br results are preliminary and serve only to establish that the formation of the molecular ion, CH3Br +, exhibits an orientation effect that is in the same direction as that determined for CH3C1§ and that the orientation effect in the formation of the CH~/CH3Br fragmentation product is similar to that for CH~/CH3C1. The experiments were carried out with a nozzle stagnation pressure of about 1,000 torr at room temperature, resulting in low signal levels (low S/N). The only ion detected from CC13H was the fragmentation ion CC12H§ which was produced with higher efficiency at the positive H-end of the molecule. The distribution of orientations within the molecular beam is broad. However, the positive end of all molecules points towards the positive field plate and the negative end towards the negative field plate. Irrespective of the polarity on the field plates, the beam includes a substantial fraction of molecules that can best be described as sideways or broadside oriented. In the case of CH~ formation, a G factor close to zero may point to the domination of sideways orientations in the fragmentation channel. The molecular ion state leading to fragmentation may involve excitation of a molecular orbital that is relatively inaccessible to collinear electron approaches. To exclude the possibility that the ion-guiding lens was somehow discriminating against CH~ ion transmission, two tests were performed. First, the potential on the leading element was varied from -50 V to-200 V with an effect on ion signal but no significant effect on G. Secondly, the Einzel lens and quadrupole detector were replaced by a mass-insensitive particle multiplier detector fitted with a single-plane electrostatic lens element. From the measured steric ratio for CH3C1 (R = 2.58 for CH3C1+ andR = 0.96 for CH~) and the fragmentation pattern (CH3C1+ = 100 and CH~ = 54), a value of 1.78 can be calculated for the expected steric ratio for CH3C1 (all ions) measured with a mass-insensitive detector. The experimental result ofR = 1.62 (G =--0.23) is considered to be in accord with the

30

PHILIP R. BROOKS and PETERW. HARLAND

predicted value, showing that instrumental anomalies are not significant, and lending support to the evidence for fragment-dependent steric ratios.

D. Theoretical Considerations Theoretical models of the electron impact ionization process have focused on the calculation of the ionization cross section and its energy dependence, and can be characterized as quantum, semiclassical, and semiempirical. The theoretical treatment of the ionization process has been seen as a complex problem with the involvement of three charged particles in the exit channel. 4~ Even for atomic hydrogen, the simplest ionization case, the long-range Coulomb force restricts free movement of the particles even at very large interparticle separations. 4~ Quantum methods use a partial wave approximation. The Born approximation 35 considers the incident electron as a plane wave with limited interaction with the molecule, and it has had limited s u c c e s s . 40 A series of higher order approximations, including distorted wave theories, 35'42 have found some success in describing the absolute electron ionization cross section and the energy dependence for light neutral atoms such as H, He, and Ne and for light ion targets such as He +, Be +, Na § and Mg 2+ (within about 25%). There has been limited success with heavier atoms and ions, giving calculated ionization cross sections within a factor of two or better of experiment. 43 A number of semiclassical and semiempirical expressions 35have been developed for modeling the energy dependence of the electron ionization cross section for atoms, although no generally applicable model has yet emerged. There has been less effort invested in electron ionization of molecules, resulting in models that exhibit limited success for specific examples. A simple qualitative model of the ionization process that describes the threshold behavior involves the classical picture of the electron as a particle projectile transferring kinetic energy to the target molecule. At the ionization threshold, all of the energy carried by the incident electron is transferred in a head-on collision. At higher incident electron energies, where only a fraction of the energy is transferred, glancing collisions become important with a concomitant increase in the (collision) ionization cross section. This model could accommodate a spatial asymmetry in the cross section through the influence of the molecular orbitals (shape of the molecule) on the impact parameters for the glancing collisions effective in the ionization process. One model proposed to account for the maximum in ionization efficiency curves considers that the passage of the incident electron subjects the molecule to a pulsed disturbance. The probability for energy transfer would depend on the magnitude of the Fourier component in the pulse, which is in resonance with the transition energy in the molecule. As the electron energy increases, the ionization cross section would decrease as the pulse width and the magnitude of the lower energy components decreased. Semiempirical additivity rules 35 have been devised to estimate ionization cross sections for specific molecular groups with some success, and a correla-

Molecular Orientation on Electron Transfer and Impact Ionization

31

tion between experimental ionization cross section and polarizability, first reported by Lampe et al., 38 has been more recently reported for several series of organic molecules by Bartmess and Georgiadis. 44 An inverse relationship between the product of ionization cross section and the maximum in the ionization efficiency curve with the square of the ionization potential has been reported by Franco and Daltabuit. 45 Little progress has been made on the theoretical prediction of fragmentation patterns since the original quasi-equilibrium theory, which was based on statistical mechanics and transition-state theory.46 In summary, there is no simple model at present that adequately describes all aspects of the electron ionization process (threshold behavior, total ionization cross section, energy dependence of the cross section, and fragmentation) in terms of simple equations that could be used confidently in a predictive manner. S. M. Younger comments on this situation in Reference 35 with the statement: "It may be said that there currently exists no rigorous theory of the electron impact ionization of atoms and ions. Indeed, developments since the early work of Thomson (1912) have concentrated on increasingly sophisticated approximations to an as yet undefined formal theory." Investigation of the electron impact ionization of spatially oriented molecules was initiated in order to extend the work on electron transfer, to gain a deeper insight into the electron ionization process, and to provide data useful for the development of semiempirical models of practical value. E. A Model For Electron Ionization The investigation of electron ionization is clearly in the early stages in comparison with the electron transfer studies, and additional work on the influence of orientation on fragmentation will be required before a coherent pattern emerges and a model for fragmentation can be attempted. However, a simple model that considers ionization in terms of the Coulomb potential developed between the electron and the polar molecule, taking the electron transition probability into account, reproduces the main experimental features. This model accounts qualitatively for the steric effect measured and leads to simple, generally applicable, expressions for the maximum (70 eV) ionization cross section. As the electron approaches the molecule, an electric field is established that is described in terms of a Coulomb potential, ~c" It is assumed that when the Coulomb potential reaches the electron transition energy (the ionization potential, E0) the orbital electron involved in the transition absorbs energy from the field, the efficiency of the ionization depending on the transition probability, P~. When the electron-induced dipole contribution is neglected, a cross section, o c, which will be an underestimate, can be calculated from the interparticle separation when ~c = E0" In order to deduce the maximum ionization cross section, o~, the transition probability P~ must be taken into account:

32

PHILIP R. BROOKS and PETERW. HARLAND

~i = acPi

(16)

An Expression for ~c

The target molecule can be considered in terms of the isolated electron involved in the transition, charge q, and a charge, q", determined by the dipole moment of the molecule, ~to, and its orientation with respect to the electron projectile. The effective charge in the collision is given by qeff = q + q", where,

and ~ = 0, +1. For an electron collision on a nonpolar molecule or a broadside collision on a polar molecule, then { = 0, q " = 0, qee= q, and the electron is considered to be incident on a molecule exhibiting zero charge (electrically neutral). If the molecule has a permanent dipole moment g0 and separation of charge centers d, then ~ = +1 and q " = +go~d, depending on the orientation of the dipole with respect to the projectile electron. The length of the dipole, d, for prolate and oblate symmetric-top molecules, CY3X, is taken arbitrarily as the distance along the C-X molecular axis between the center of atom X and the Y atom plane perpendicular to the C-X axis. As the projectile electron approaches the positive end of the dipole, the field will be higher at a given separation and ~ = +1, q " = g0/d, and qee-q(1 + g0/d). As the projectile electron approaches the negative end of the dipole, the field will be lower at a given separation and ~ = - 1 , q " = - g 0 / d , and qe~'- q(1 - g0/d). The Coulomb potential is then given by, qefr q[1 + ~(bt0/d)] ~c - 4he0 r 4he o r

(18)

where e0 is the permittivity of free space. A plot of the Coulomb potentials for an electron approaching broadside, the CH3-end (~5+),and the Cl-end (~5-) for CH3C1, are shown in Figure 19. When ~c = E0, r = bmax, where bmax is the maximum impact parameter for the 2 electron transition process (ionization). Then, assuming that Pi = 1, t~c = ~bmax, where t~c is the calculated (Coulomb) maximum electron impact ionization cross section: t

qeff ] 2

(4 o)Eo)

for P~ = 1. With substitution of the appropdate quantities,

(19)

Molecular Orientation on Electron Transferand Impact Ionization

33

201816-

il O-" eV

12 Ix. lO ,~

o to

64 ....

0

t 1

'

1 '

I

'

I

2 3 4 5 Electron-Molecule

'

I

'

I'

6 7 Separation

I'

1J

8 0 I A

9

....1 10

Figure 19. Coulomb potential versus the electron-molecule separation for three ideal orientations of the CH3CI molecule as indicated. The electron-molecule separations corresponding to an equivalence between the Coulomb potential and the ionization potential for CH3CI are shown by the vertical lines.

in units of A 2 where z ~ =

t 0j

q~/q. The model requires that ionization

is favored at

the positive end of the molecule, and this has been observed to be true for CH3X and CCI3H, even though the positive end of the dipole corresponds to the CH3-end for CH3X and the H-end for CCI3H. To consider CH3CI in detail, the dipole moment is 6.24 x 10-3~ Cm (1.87 D) and the effective dipole length is 215 pm, giving the charge on the dipole as +_2.90 x 10-20 C or+0.18q, where q is the electron charge. From Equation (20), the ionization cross sections for electron impact on the 5+ end, 6i,8+, on the ~5- end, 6i,~-, and broadside, 6i,0, are calculated to be 7.2, 3.5, and 5.2 ~2, respectively. Therefore, these equations predict that the ionization cross section will be highest for electron impact on the ~5+end of the dipole, lowest for impact on the ~5- end of the dipole, and intermediate for broadside collisions. The calculated steric ratio, 6i,r,/6i,t,_ = 2.1, is close to the experimental ratio of 2.58 for the CH3C1§ ion and 1.62 measured using the mass insensitive detector. Table 2 lists the calculated steric ratios for several polar molecules. For the systems that have been studied experimentally, CHaC1 is predicted to exhibit the highest steric ratio in accord with experiment.

34

PHILIP R. BROOKS and PETER W. HARLAND

Table 2. Calculated and Experimental Steric Ratios

Species

k t / 1 0 -30 Cm

1/pm

R(calc)

R(expt) 2.6

CH3C16-

6.24

215

2.1

CH3Br ~

6.04

230

1.9

CH3IaCC13H~+

5.40 3.37

251 168

1.7 1.6

CBr3Ha+

3.30

175

1.6

CF3C1a+ CF3Br~

1.67 2.17

220 240

1.2 1.3

1.4

The experimental electron impact ionization cross sections reported in the literature correspond to values for a random orientation of dipoles, g;,r" For this model, where Ad~/Ar is approximately constant in the vicinity of ~ = E o, then (ai,5+- ~i,o) ~ (ai,o- ~i,5-) and ~;,r ~ c~i,o. Despite the simplicity of the model and its obvious limitations, the calculated cross sections lie within a factor of two of the measured values, 38 as shown in Figure 20.

0< c

O u

,== ,4,,i

o

9 8 --

O c

.o

_

HCN

6 --

C2H6 9 CH3CHO CH2CHtlD 9

9

~2H4

Kr

/

jFI2S

9

-

,e=l

~

.

xe

_

=o

C3H6 9

CH3CI

10 --

9

C2t-~tf

c

o

>=

4 -

Ar

~'CH4

H.Oo.

o

h,, m

c

E "C Q

2 H2

-

n_ X IM

o

r

0

Figure 20.

,

1

"

1

'

I

'

I

'

1

'

I

'

1

1 2 3 4 5 6 7 Calculated Ionization Cross-section I/~2

~

, . .

I

8

Experimental ionization cross section 38 versus the cross sections calculated from Equation (20) with Zeff = 1.

Molecular Orientation on Electron Transfer and Impact Ionization

35

An Expression for Pi

I,ifl

If the transition probability, Pi, is taken to be proportional to 2, where ,/fis the orbital overlap integral for the dipole transition from state i (neutral molecule) to statef(ion), then, . i f = ~V; "~ vfd'c

(21)

where ~ is the electric dipole moment operator. [~if] 2 is related to the quantum mechanical expression for mean molecular polarizability, or, by: 47 =

I,,fl =

2

(I, -~Z Ef_ E i

(22)

f

If

discrete states are assumed:

Pi I,wl = ~

= cct'E o.

(23)

This expression introduces a dependence of ionization efficiency on or', the polarizability volume, or'= ot/(4neo).

An Expression for t~ i An expression for the ionization cross section, o;, can be written from Equations (16), (20) and (23), ~i = ~c Pi ~ C'~cct'Eo

(24)

where c' is a constant. With substitution from Equation (20) for o c, oi = c"~fr ot' / E o

(25)

where c" is a constant. Thus, this model predicts a linear relationship between ionization cross section and ct'/E o (Lampe et al. 38in 1957 noted a linear relationship between their measured ionization cross sections and the corresponding values for a'). Plots of the experimental 70-eV ionization cross sections (Zeff= 1) reported by Lampe et al. 38 versus or' and ct'/E o are shown in Figure 21. The plots are linear and the equations obtained by least-squares fitting are, O"i ----

1.947 c t ' - 0.309

(26)

(3"i =

18.79 ix'/E o + 0.626

(27)

o" i is expressed in units ofA 2, a' in units ofA 3, andE 0 in eV. Table 3 compares ionization cross sections calculated from Equations (20), (26) and (27) with the experimental values reported by Lampe et al. 38 (which are assumed to be accurate).

where

14

13

13

9

12

~

~~

11

1

O O~

10

9 8 7

6 5 4

9 9

,.,

~

3

/i: '

2 1

0

0123456789

'1'1

0 0.0

d/,/~3

I ' ' I ' I 0.2 0.4 0.6 0.8

(o~ I Eo)/Xa. eV qmI

Figure 21. Experimental ionization cross section 3a versus the polarizabilty volume and versus the polarizabilty volume/ionization potential.

Table 3. Calculated and Experimental Maximum Ionization Cross Sections for a Range of Species

t~C/~2 Ar Xe N2 CO CO2 CH 4

CH3C1 CH3Br CCI3H

2.62 (-25.6%) d 4.43 (-39.4%) 2.68 (-2.6%) 3.32 (+ 11.0%) 3.44 (-20.2%) 4.16 (-10.5%) 5.17 (-45.3%) 5.86 (-47.7%) 5.04

Oi a/,~2 2.92 (-17.1%) 8.32 (+13.8%) 3.14 (+14.2%) 3.55 (+ 18.7%) 4.81 (+11.6%) 4.75 (+2.2%) 8.51 (-I0.0%) 10.30 (-8.0%) 16.24

Oi b//i2 2.61 (-25.9%) 6.88 (-5.9%) 2.76 (+0.4%) 3.28 (+9.7%) 4.22 (-2.1%) 4.53 (-2.6%) 8.21 (-13.2%) 10.34 (-7.7%) 14.67

Oi c//i2 3.52 7.31 2.75 2.99 4.31 4.65 9.46 11.2

Notes: aFromEquation(26). ~rom Equation(27). CFromRef. 38. aPercentagesgiven in parenthesesare for the differencesbetweenexperimentalvaluesand calculatedvalues. 36

Molecular Orientation on Electron Transfer and Impact Ionization

37

The discrepanciesbetween the calculated and experimental values, shown in

parentheses in the Table, are well within the uncertainties expected from experimental measurements. The closeness of fitexhibited in Figure 2 l, covering a factor of 20 in cross section,gives some confidence in the model. In summary, preliminary experiments have demonstrated that the efficiencyand outcome of electron ionization is influenced by molecular orientation.That is,the magnitude of the electron impact ionization cross section depends on the spatial orientation of the rnoleculc with respect to the electron projectile.The ionization efficiencyis lowest for electron impact on the negative end of the molecular dipole. In addition, the mass spectrum is orientation-dependent: for exarnplc, in the ionization of CHHCI the ratio CHHCI +:CH~ depends on the molecular orientation. There are both similaritiesin and differences between the effect of orientation on electron transfer (as an elementary step in the harpoon mechanism) and electron impact ionization, but there is a substantial effect in both cases. It seems likely that other types of particle interactions, for example, free-radical chemistry and ion-molecule chemistry, may also exhibit a dependence on relative spatial orientation. The information emerging from these studies should contribute one more perspective to our view of particle interactions and eventually to a deeper understanding o f complex chemical and biological reaction mechanisms.

ACKNOWLEDGMENTS The authors would like to acknowledge financialsupport from the Robert A. Welch Foundation (US), the National Science Foundation (US), the Petroleum Research Fund (U.S.), the Foundation for Research, Science and Technology (NZ), the New Zealand LotteriesBoard, and the Universityof Canterbury (NZ).

REFERENCES 1. For reviews see: (a) Brooks, P. R. Science 1976, 193, 11. Co)Bernstein, R. B.; Herschbach, D. R.; Levine, R. D. ,I. Phys. Chem. 1987, 91, 5365. (c) Harren, F.; Parker, D. H.; Stolte, S. Comments At. MoL Phys. 1991, 26, 109. (d) Parker, D. H.; Bernstein, R. B. Ann. Rev. Phys. Chem. 1989, 40, 561. (e) Stolte, S.Atomic and Molecular Beam Methods; Scoles, G., Ed.; Oxford: New York, 1988, Vol. 1., p. 631. 2. For example: (a) Loesch, H. J.; Remscheid, A. J. J. Chem. Phys. 1990, 93, 4779. Co) Loesch, H. J.; Remscheid,A. J.J. Chem. Phys. 1991, 95, 8194. (c) Loesch, H. J.; M611er,J. Chem. Phys. 1992, 97, 9016. (d) Friedrich, B.; Herschbach, D. R. Z. Physik 1991, D18, 153. (e) Slenczka, A.; Friedrich, B.; Herschbach, D. R. Phys. Rev. Lett. 1994, 72, 1806. 3. For reviews ofcollisional ionization, see: (a) Kleyn, A. W.; Los, J.; Gislason, E. A. Physics Reports 1982, 90, 1. Co) Lacmann, K. Potential Energy Surfaces; Lawley, K. P., Ed.; Wiley: New York, 1980; p. 513. (c) Baede, P. M. Adv. Chem. Phys. 1975, 30, 463. (d) Los, J.; Klein, A. W. Alkali Halide Vapors; Davidovits, P.; McFadden, D. L., Eds.; Academic: New York, 1979; p. 279. 4. Berry, R. S.J. Chem. Phys. 1957, 27, 1288. 5. Grice, R.; Herschbach, D. R. Mol Phys. 1974, 27, 159. 6. Kleyn, A. W.; Khromov, V. N.; Los, J. J. Chem. Phys. 1980, 72, 5282.

38

PHILIP R. BROOKS and PETERW. HARLAND

7. (a) Carman, H., Jr. Ph.D. Thesis, Rice University, 1985. (b) Xing, G. Ph.D. Thesis, Rice University 1993. 8. Bemstein, R. B. Chemical Dynamics via Molecular Beam and Laser Techniques; Oxford University: London, 1982, p. 45. 9. Townes, C. H.; Schawlow, A. L. Microwave Spectroscopy; Dover: New York, 1975. 10. (a) Bennewitz, H. G.; Paul, W.; Schlier, Ch. Z. Physik 1955, 6, 141. (b) Kramer, K. H.; Bemstein, R. B.J. Chem Phys. 1965, 42, 767. (c) Brooks, P. R.; Jones, E. M.; Smith, K. J. Chem. Phys. 1969, 51, 3073. 11. Helbing, R. K. B.; Rothe, E. M. Rev. Sci. Instrum. 1968, 39, 1948. 12. (a) Harland, P. W.; Carman, H. S., Jr.; Phillips, L. F.; Brooks, P. R.J. Chem. Phys. 1989, 90, 5201. (b) Harland, P. W.; Carman, H. S., Jr.; Phillips, L. F.; Brooks, P. R.J. Chem. Phys. 1990, 93, 1089. (c) Harland, P. W.; Carman, H. S., Jr.; Phillips, L. F.; Brooks, P. R.J. Phys. Chem. 1991, 95, 8137. 13. (a) Gandhi, S. R.; Xu, Q.-X.; Curtiss, T. J.; Bernstein, R. B. ,I. Phys. Chem. 1987, 91, 5437. (b) Kasai, T.; Fukawa, T.; Matsunami, T.; Che, D.--C.; Ohashi, K.; Fukunishi, Y.; Ohoyama, H.; Kuwata, K. Rev. Sci. Instrum. 1993, 64, 1150. 14. Janssen, M. H. M.; Parker, D. H.; Stolte, S.J. Phys. Chem. 1991, 95, 8142. 15. Gandhi, S. R.; Bernstein, R. B. J. Chem. Phys. 1988, 88, 1472. 16. Brooks, P. R. Faraday Discuss. Chem. Soc. 1973, 55, 299. 17. Aten, J.; Los, J. 3". Phys. E 1975, 8, 408. 18. (a) Ktmtz, P. J.; Mok, M. H.; Polanyi, J. C. J. Chem. Phys. 1969, 50, 4623. (b) Herschbach, D. R. Faraday Discuss. Chem. Soc. 1973, 55, 233. 19. Brooks, P. R. J. Phys. Chem. 1993, 9 7, 2153. 20. Brooks, P. R.; McKillop, J.; Pippen, H. G. Chem. Phys. Lett. 1979, 66, 144. 21. Carman, H. S.; Harland, P. W.; Brooks, P. R. J. Phys. Chem. 1986, 90, 944. 22. (a) Stockdale, J. A.; Davis, F. J.; Compton, R. N.; Klots, C. E.J. Chem. Phys. 1974, 60, 4279. (b) Heni, M.; Illenberger, E. Chem. Phys. Lett. 1986, 131, 314. 23. Compton, R. N.; Reinhardt, P. W.; Cooper, C. D. J. Chem. Phys. 1978, 68, 4360. 24. a) Kalamarides, A.; Walter, C. W.; Lindsay, B. G.; Smith, K. A.; Dunning, E B. J. Chem. Phys. 1989, 91, 44 11. (b) Kalamarides, A.; Marawar, R. W.; Ling, X.; Walter, C. W.; Lindsay, B. G.; Smith, K. A.; Dunning, F. B.J. Chem. Phys. 1990, 92, 1672. 25. (a) Lobo, R. F. M.; Moutinho, A. M. C.; Los, J. Chem. Phys. 1994, 179, 179. (b) Lobo, R. F. M.; Moutinho, A. M. C.; Lacmann, K.; Los, J. J. Chem. Phys. 1991, 95, 166. 26. Hasegawa, A.; Williams, F. Chem. Phys. Lett. 1977, 46, 66. 27. McNamee, P. E.; Lacman, K.; Herschbach, D. R. Faraday Discuss. Chem. Soc. 1973, 55, 318. 28. Aitken, C. G.; Blunt, D. A.; Harland, P. W.J. Chem. Phys. 1994, 101, 11074. 29. Massey, H. S. W.; Burhop, E. H. S. Electronic and Ionic Impact Phenomena; Oxford University: London, 1952. 30. Rudge, M. R. H. Revs. Mod. Phys. 1968, 40, 564. 31. Massey, H. S. W.; Burhop, E. H. S. Electronic and Ionic Impact Phenomena; Oxford University: London, 1969; Vol. 1. 32. Weingold, E.; McCarthy, I. E. (e, 2e) Collisions, Advances in Atomic and Molecular Physics; Bates, D. R.; Benderson, B., Eds.; Academic: New York, 1978; Vol 14. 33. McCarthy, I. E.; Stelbovics, A. T. In Theoretical Methods for Ionization in Atomic and Molecular Processes in Controlled Thermonuclear Fusion; McDowell, M. R. C.; Ferendeci, A. M., Eds.; Plenum: New York, 1980. 34. Younger, S. M. Comm. At. Mol. Phys. 1982, 11, 193. 35. Electron Impact Ionization; Mark, T. D.; Dunn, G. H., Eds.; Springer-Verlag: Wein, New York, 1985. See also (a) Deutsch, H.; Mark, T. D. Int. J. Mass Spectrom. Ion Procs. 1987, 79, R1. (b) Margreiter, D.; Deutsch, H.; Schmidt, M.; Mark, T. D. Int. J. Mass Spectrom. Ion Procs. 1990, 100, 157, and references therein.

Molecular Orientation on Electron Transfer and Impact Ionization

39

36. Electron-Molecule Interactions and Their Applications, Christophorou, L. G., Ed.; Academic: New York, 1984, Vol. 1. 37. (a) Franklin, J. L.; Dillard, J. G.; Rosenstock, H. M.; Heron, J. T.; Draxl, K.; Field, E H. "Ionization Potentials, Appearance Potentials, and Heats of Formation of Gaseous Positive Ions"; Nat. Stand. Ref Data Set, NBS (US), 1969. (b) Levin, R. D.; Lias, S. G. "Ionization Potential and Appearance Potential Measurements, 1971-1981"; Nat. Stand. Ref Data Ser., NBS (US), 1982. (c) Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. "Gas-Phase Ion and Neutral Thermochemistry"; Nat. Stand. Ref Data Ser., NBS (US), 1988. 38. Lampe, F. W.; Franklin, J. L.; Field, E H. J. Am. Chem. Soc. 1957, 79, 6129. 39. (a) Volkmer, M.; Meier, C.; Mihill, A.; Fink, M.; B6wering, N. Phys. Rev. Lett. 1992, 68, 2289. (b) B6wering, N.; Volkmer, M.; Meier, C.; Lieschke, J.; Fink, M. Z. Phys. D 1994, 30, 177. (c) Meier, C.; Volkmer, M.; Lieschke, J.; Fink, M.; B6wering, N. Z. Phys. D 1994, 30, 183. 40. Ehrhardt, H.; Jung, K.; Knoth, G.; Schlemmer, P. Z. Phys. D 1986, 1, 3. 41. Brauner, M.; Briggs, J. S.; Klar, H. Jr. Phys. B 1989, 22, 2265. 42. Jones, S.; Madison, D. H.; Franz, A.; Altick, P. L. Phys. Rev. A 1993, 48, R22. 43. McGuire, E. J. Phys. Rev. 1977,A16, 62; 1977, A16, 73; 1979,A20, 445. 44. Bartmess, J. E.; Georgiadis, J. E. Vacuum 1983, 33, 149. 45. (a) Franco, J.; Daltabuit, E. Rev. Mex. Astron. Astrof 1978, 2, 325. (b) Franco, J. Rev. Mex. Fisica 1981, 27, 475. 46. (a) Rosenstock, H. M.; Krauss, M. In Mass spectrometry of Organic Ions; McLafferty, F. W., Ed.; Academic: New York, 1963. (b) Rosenstock, H. M.; Krauss, M. InAdvances in Mass Spectrometry; Elliott, R. M., Ed.; Pergamon: Oxford, 1963; Vol. 2. 47. See for example, Atkins, P. W. Physical Chemistry, Fifth ed.; Oxford University: London, 1994; Chapter 2. 48. Faist, M. B.; Levine, R. D. J. Chem. Phys. 1976, 64, 2953.

This Page Intentionally Left Blank

EXPERIMENTAL APPROACHES TO THE UNIMOLECULAR DISSOCIATION OF GASEOUS CLUSTER IONS

Terrance B. McMahon

Io II.

III.

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. The Pulsed Ionization, High-Pressure, Reverse Geometry, Double-Focusing Mass Spectrometer . . . . . . . . . . . . . . . . . . . . B. The External High-Pressure Source Fourier Transform Ion Cyclotron Resonance Spectrometer . . . . . . . . . . . . . . . . . . . . . Unimolecular Dissociation of Cluster Ions . . . . . . . . . . . . . . . . . . . . A. Thermal Unimolecular Dissociation of the Proton-Bound Methoxide Dimer . . . . . . . . . . . . . . . . . . . . . . . B. Unimolecular Dissociation Lifetime of a Transient SN2 Intermediate . . . . C. Radiative and Unimolecular Dissociation Lifetimes of Chemically Activated Ions . . . . . . . . . . . . . . . . . . . . . . . . . . D. Metastable Ion Cyclotron Resonance Spectrometry . . . . . . . . . . . . . E. Thermal Infrared-Induced Dissociation of Cluster Ions . . . . . . . . . . . F. Infrared-Laser-Induced Thermal Dissociation . . . . . . . . . . . . . . . .

Advances in Gas Phase Ion Chemistry Volume 2, pages 41-85. Copyright 9 1996 by JAI Press Inc. AH rights of reproduction in any form reserved. ISBN: 1-55938-703-3 41

42 42 44 44 46 48 48 54 59 64 71 80

42

TERRANCE B. McMAHON

IV. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82 83 83

ABSTRACT The use of high-pressure mass spectrometric (HPMS) and Fourier transform ion cyclotron resonance (FTICR) techniques is described for the elucidation of unimolecular dissociation of gaseous ions. (1) The kinetics of clustering of CH30- onto CH3OH in the HPMS system are used to deduce the thermal unimolecular dissociation rate constant of the proton-bound methoxide ion. In addition a second, more weakly bound electrostatic complex is implicated as an entrance channel complex on this potential energy surface. (2) The kinetics of formation of CI-(CH3C1) from C1- and CH3C1 at high pressure is used to deduce the lifetime of the initially formed, chemically activated, adduct ion on the SN2 potential energy surface. Comparison with trajectory studies carried out by Hase shows good agreement with the experimental data. (3) FTICR studies of unimolecular dissociation of chemically activated proton-bound dimers give both unimolecular dissociation and radiative rate constants. Data for a variety of deuterium-substituted variants of the acetone system reveal that structures other than the proton-bound dimer may play an important role. (4) A metastable ion cyclotron resonance technique is described that provides a means of obtaining product branching ratios as a function of the transient intermediate lifetime. (5) Finally, thermal, blackbody-radiation-induced unimolecular dissociation of weakly bound cluster ions is strongly suggested on the basis of pressure and temperature dependencies of these dissociations at extremely low pressures.

I. I N T R O D U C T I O N Unimolecular reactions occupy a venerable position in the history of the development of modern physical chemistry. ~-3 The determination of the "activation energy" for such reactions was the earliest means by which reasonably accurate bond dissociation energies could be determined. 4 The subsequent development of transition-state theory 5 and statistical methods such as R R K M theory 6 for the treatment o f these reactions then gave a good quantitative understanding of the processes o f activation and energy flow within molecular systems. This understanding has advanced to an extent that quantitative predictions o f the rates of unimolecular dissociation are possible, given appropriate energetic and spectroscopic data. Current studies of unimolecular reactions can be broadly divided into three categories, based on different methods of activation of the decomposing species. The first, most classical, method is that of thermal activation o f the type first envisioned by Lindemann 7 to explain unimolecular dissociation phenomena brought about by heat energy. The second method involves chemical activation, 8

Unimolecular Dissociation of Gaseous Cluster ions

43

in which an exothermic bimolecular reaction results in the formation of transient species whose internal energy is the superposition of the exothermicity of the transient formation onto the Maxwell-Boltzmann distribution of thermal energies (corresponding to the temperature at which the bimolecular reaction occurs). In general, this chemical activation reaction efficiently deposits in the transient species considerably more energy than can be easily added via the thermal activation process. The final method is photoactivation, 9 in which a single-frequency radiation source, typically a laser, is matched to a resonant absorption by the species of interest to selectively deposit energy. The subsequently induced unimolecular dissociation is then monitored. The speed and extent of energy randomization within the molecule can then also be frequently inferred. There is curremly a considerable degree of interest in this last activation method with respect to the possibility of carrying out mode-specific chemistry resulting from a failure of the energy randomization process to compete on the timescale taken for dissociation of the molecule, l~ Although there has been a large number of studies of the metastable 11 and collision-induced 12 unimolecular dissociations of gas phase ions with a view to understanding the mechanisms by which these processes occur, there have been relatively few studies of this type that probe the more quantitative details of the reactions. Metastable dissociations are typically carried out in reverse geometry double-focusing mass spectrometers. 13 Although the mass-selected decomposing ions have a known range of lifetimes determined by the physical parameters of the system, the portion of the imemal energy distribution to which this range of lifetimes corresponds is unknown. ~4In addition, depending upon the method of ion formation, the actual form of the imemal energy distribution may also be completely unknown. 15 Hence it is not possible to extract quantitative details of the unimolecular dissociation for a well-defined ion population. Collision-induced decomposition studies are similarly unable to characterize the unimolecular reaction quantitatively, because the energy deposition function resulting from the collision of a fast ion with a stationary, usually monoatomic, target is not well understood. 16 To date, by far the best quantitative studies ofunimolecular dissociations of ions with a well-defined energy distribution have been those using the photoelectron photoionization technique (PEPICO). 17 These reactions have been discussed in detail elsewhere, most notably by Baer. ~8 In the present review, a new variation on an existing experimental method will be used to show how accurate unimolecular dissociation rate constants can be derived for thermal systems. For example, thermal bimolecular reactions are amenable to study by use of several, now well-known, techniques such as (Fourier transform) ion cyclotron resonance spectrometry (FTICR), 19'2~flowing afterglow (FA), 21'22 and high-pressure mass spectrometry (HPMS). 23 In systems where a bimolecular reaction leads to products other than a simple association adduct, the bimolecular reaction can always be thought of as containing a unimolecular

44

TERRANCE B. McMAHON

reaction in the form of the unimolecular dissociation of the chemically activated intermediate ion--molecule complex, as in Equation (1).24 Experiments investigating the lifetimes of such complexes will be detailed below. A + + B ~ - [AB+]* -+ C + + D

(1)

The study of photoinduced dissociation of molecular ions is also an active area of study, perhaps best exemplified by the work of Dunbar reviewed elsewhere in this volume. 25 Some of our own new work at Waterloo in this area will also be briefly outlined below.

II.

EXPERIMENTAL

The instruments used for the experimental work detailed in this review are several high-pressure mass spectrometers (HPMS) and a Fourier transform ion cyclotron resonance spectrometer (FTICR). Each of the instruments was constructed, to a considerable degree, in-house at the University of Waterloo, and each contains features unique to its type of apparatus. The instruments in general and the unique features of the Waterloo apparatus in particular are described below.

A. The Pulsed Ionization, High-Pressure, Reverse Geometry, Double-Focusing Mass Spectrometer The technique of high-pressure mass spectrometry was pioneered by Kebarle and has been described in some detail in a recent review. 23 The two principle unique features of the Waterloo version of this instrument 26 are the incorporation of a very high pumping speed (8000 L s-l) diffusion pump on the source housing, which permits routine use of pressures as high as 50 torr in the ion source, and the use of a reverse geometry double-focusing mass spectrometer as the mass analysis stage. This permits observation of metastable and collision-induced dissociation of wellthermalized cluster ions in the second field-free region (FFR) of the spectrometer. A schematic view of the instrument is shown in Figure 1. The mass spectrometer itself is a VG 7070 instrument whose geometry was reversed via extensive redesign of the ion optics between source and magnet entrance slit, incorporation of a differentially pumped collision cell in the second field-free region, and modified ion optics for the transition from second field-free region to the electrostatic analyzer (ESA). The use of this instrument for investigating unimolecular dissociation of cluster ions is illustrated in Figure 2 where the collision-induced dissociation of [(CH3)20]3H3 O§ in the second FFR is shown. The sequence of dissociations, Equations (2a) and (2b), inferred from these data strongly favor structure I for this cluster ion with a central hydronium ion core. [(CH3)20]3H3 O+ __~ [(CH3)20]2H3 O§ + (CH3)20

(2a)

[(CH3)EO]EH3O+ --~ [(CH3)20]2 H+ + HEO

(2b)

0 .......,,I 14 " * ' 0

H/.t."~H

'~"'"

%'0

CH 3 ~m,' 0 ?*

CH 3

CH 3 "'o e l l l

tit 3

Clt 3

vo w e F ~

v

,T

Figure 1. Schematic of the reverse geometry double-focusing high-pressure mass spectrometer. 45

46

TERRANCE B. McMAHON 1,0

-

0.9

-

0.8

-

0.7

-

0.6

-

157 +

111 +

0 =.=,.

0 r

0.50.40.3

-

0.2

-

0.1

-

0

93+ 47* ~,~

40

i

65 + .....

I

60

~

139+ ___j ''"

"I

80

I

100

'

I-

.....

" '

120

A___J I

140

~1/ '

~.

160

m/z

Figure 2. Unimolecular dissociation spectrum (MIKES) of (H30)*[(CH3)20]3 illustrating major loss of (CH3)2O(m/z 111 ) and H2O + (CH3)2O(m/z 93). The peak near m/z 150 is an artifact peak due to ion reflections from the ESA walls.

B. The External High-Pressure Source Fourier Transform Ion Cyclotron Resonance Spectrometer The FTICR spectrometer used is a Bruker Spectrospin CMS-4727 that is coupled via a unique ion optical system to a high-pressure ion source. 28 This combination is illustrated schematically in Figure 3. The high-voltage ion optics permit the use of small apertures between pumping stages thus leading to a considerable saving in cost of pumps. The 500, 300, and 300 L s-1 combination used here permits pressures of 5 torr to be used in the external source with less than 5 x 10-l~ torr increase in the pressure in the FTICR cell region. In addition, the deceleration assembly permits even very weakly bound cluster ions to be trapped in the FTICR cell and to survive collisions with inert gases, such as Ar, without any significant collisional dissociation occurring. For example the H30+(CH4) cluster, which is bound by about 8 kcal mol-~, can, under ideal circumstances, be trapped for several seconds in the presence of 5 x 10--8 torr of Ar without a significant extent of dissociation. 29Thus the ion optics are ideal for the transfer ofweakiy bound clusters to the FTICR cell where their subsequent unimolecular as well as bimolecular chemistry can be readily examined.

Electron Gun

Ion Deceleration/Injection

Gate Valve

Ion Acceleration and Focusing

Gas Inlet

to ICR Cell

Ion Source 300 L/s u

41-

u 300 L/s

4-

u

"

500 L/s

41-

Figure 3. Schematic of the external high-pressure source mated to the FTICR spectrometer.

48

TERRANCE B. McMAHON

III. UNIMOLECULAR DISSOCIATION OF CLUSTER IONS A. Thermal Unimolecular Dissociation of the Proton-Bound Methoxide Dimer The kinetics of symmetric bimolecular proton transfer between alkoxide ions and their parent neutral alcohols have recently been studied by both Bierbaum and co-workers 3~and Brauman and co.workers. 31 For the reaction of labeled methoxide ions with methanol (and vice versa), the reaction was found to proceed at markedly less than a half of the collision rate, the value that might have been predicted for a thermoneutral reaction occurring on a barrierless potential energy surface. In contrast, the reaction of hydroxide ion with water is found to give proton transfer at a half of the collision rate. 32 These observations led Lim and Brauman 33 to propose that the reaction of methoxide with methanol involves a potential energy surface upon which the reaction is slowed owing to locking of the external rotations of the reactants, in addition to inhibited passage over the centrifugal barrier on an otherwise barrierless surface. In a related study, Dodd et al. 34 proposed that the reaction involves no substantive enthalpic barrier on the surface, which, however, might have one or more transition states along the association pathway. These transition states do inhibit formation of the minimum-energy proton-bound dimer intermediate through which proton transfer occurs. Lim and Brauman 33 noted, in discussion of the possible reasons for a low proton transfer rate, that if the value for the methoxide-methanol association rate to form the proton transfer intermediate were incorrect, this would alter the conclusions reached regarding the efficiency of proton transfer. They concluded that, given the substantial depth of the well associated With formation of the proton-bound dimer, this species is probably formed on every collision, and the use of the ADO model will give this rate sufficiently accurately. In order to better understand the detailed dynamics of this system, an investigation of the unimolecular dissociation of the proton-bound methoxide dimer was undertaken. The data are readily obtained from high-pressure mass spectrometric determinations of the temperature dependence of the association equilibrium constant, coupled with measurements of the temperature dependence of the bimolecular rate constant for formation of the association adduct. These latter measurements have been shown previously to be an excellent method for elucidating the details of potential energy surfaces that have intermediate barriers near the energy of separated reactants. 23 The interpretation of the bimolecular rate data in terms of reaction scheme (3) is most revealing. Application of the steady-state approximation to the chemically activated intermediate, [(CH30)2H-]*, shows that, kf ks[M] CH30-+ CH3OH ~-- [(CH30)2H-]* ~ [(CH30)2H-]

kr

(3)

49

Unimo/ecu/ar Dissociation of Gaseous Cluster Ions _

.=.._

. . . . . . . .

-- .

.

.

.

~_-__-:._-

.

~

-1 -2 ~9 -:3 c"

-5 -6

-7 0.2

1.2

2.2

3.2

4.2

5.2

Time (ms) Figure 4. Variation of relative ionic abundances with reaction time, in a high-pressure source at 5-tort CH4, for negative ions derived from deprotonation of methanol. The exponential decay of m/z 31 yields the bimolecular rate constant for formation of the proton-bound methoxide dimer, m/z 63. In addition, at this temperature (325 K) the subsequent reaction to generate the trimer anion (m/z 95) and attainment of equilibrium can be seen.

in the limit of ks[M ] >> kr, the collisionally stabilized association adduct will be formed with the collision rate constant, kf. Typical data showing these kinetics are given in Figure 4. These data reveal that, contrary to expectation, the collisionally stabilized association adduct is not formed at the collision rate at this temperature. Further, the variation of the association rate constant with temperature, as shown in Figure 5, reveals that, even at 300 ~ the rate constant remains well below the collision value of 1.9 x 10-9 cm 3 molecule -1 S--I. 35 In addition, the decrease of the association rate constant with increasing temperature is suggestive of a doubleminimum potential energy surface in which the transition state for formation of the proton transfer intermediate from an initially formed adduct lies slightly below the energy of the initial ion--neutral reactant pair. The variation of the association equilibrium constant, Keq, with reciprocal temperature is shown in Figure 6. These data yield a value of ~ = - 2 9 . 8 kcal mo1-1 for the enthalpy change in reaction (4), and z~ ~ = -26 cal mo1-1 K-~ for the corresponding entropy change. 36 As discussed previously, a combination of the

50

TERRANCE B. McMAHON 10 -e

-

Collision Limit 10 -e

o

o

o

I

Eo 10-1o

i0-11

2.0

I

I

I

2.2

2.4

2.6

,

IO00/T

I

I

I

I

2.8

3.0

3.2

3.4

K-I

Figure 5. Variation of the bimolecular rate constant at the high-pressure limit for methoxide/methanol clustering as a function of reciprocal temperature.

CH30- + CH3OH ~ - (CH30)2H-

(4)

equilibrium data and the forward rate constant data then yields the temperature dependence of the thermal unimolecular dissociation rate constant for the protonbound dimer adduct (see Figure 7). This can be interpreted in terms of a transitionstate theory model. Interestingly, the enthalpy of activation derived is in excellent agreement with a value that would be obtained from the enthalpy of the forward association reaction and its negative enthalpy of activation, consistent with the absence of any substantial barrier above that of reactants on the potential energy surface. The entropy of activation, derived from the pre-exponential factor for the unimolecular dissociation rate constant, is somewhat less negative than the entropy of activation associated with the bimolecular reaction involving passage from the first electrostatic well to the deeper proton-bound dimer well on the surface. The value of only 4 cal tool-] K-] indicates that the transition state for passage from the proton-bound dimer well to the electrostatic well is only marginally less constrained than the proton-bound methoxide dimer itself. Evidently, the greater bond lengths in the transition state will be compensated to a certain extent by the tightness resulting from a four-center-type intermediate in the "isomerization."

Unimolecular Dissociation of Gaseous Cluster Ions

51

24

201791

,._1

1310-

1,5

I

I

I

I

I

1.7

1.9

2.1

2.3

2.5

I O001T

2.7

K -I

Figure 6. Van't Hoff plot [In(Keq)vs. T-1] for the clustering reaction of methoxide onto methanol, from which AH~ and A5~ for the clustering reaction can be derived.

This model for the potential energy surface then leads naturally to the question of the detailed nature of the adduct initially formed between methoxide ion and methanol. As will be discussed in the following section, recent experiments from this laboratory have successfully determined the well depths for a number of SN2 electrostatic complexes between halide anions and alkyl halides, and these well depths are on the order of 11-13 kcal mol-l. 37 Although the molecular dipole moment of methanol is not aligned along the C-X bond axis as in an alkyl halide, the C-O bond dipole moment is still significant (-1.1 D), and it is therefore not unreasonable to expect that an electrostatic complex between methoxide and methanol could be formed which would be bound by some 5-10 kcal mo1-1. In fact, an examination of the total atomic charges determined from ab initio Mulliken population analysis reveals that the sum of the positive charges on the methyl hydrogens is greater than that on the hydroxylic hydrogen, as Thus a "backside attack" is feasible. The enthalpy of activation for dissociation of the proton-bound dimer indicates that the rate-determining step in this dissociation is evidently the isomerization from the proton-bound dimer form to the electrostatic form of the methoxide/methanol cluster. These data then allow the qualitative potential surface shown in Figure 8 to be proposed for the interaction of methoxide ion with methanol.

52

TERRANCE B. M c M A H O N

1000 100 -

I

II

10-

.=

0.1

0.01 2.0

I

1

I'

1

2.2

2.4

2.6

2.8

1000/T

.... 3.0

K-I

Figure 7. Variation of unimolecular dissociation rate constant vs. reciprocal temperature for the proton-bound methoxide ion, [(CH30)2H]. Arrhenius parameters derived are A = 1.9 x 1013 s-I and Ea = 23.6 kcal mol -I.

This interpretation of the potential energy surface for methoxide/methanol reactions might also serve to explain a number of observations concerning the apparent asymmetry of dissociation of what had previously been presumed to be protonbound complexes. For example, Baer and Brauman 39 found that, when labeled methoxide reacts with methyl formate to generate the protonated methoxide dimer in a Riveros reaction, there is a pronounced preference for subsequent formation of the methoxide that was originally in the neutral formate ester when pulsed IR is used to dissociate the dimer anion. 4~These results might be explicable on the basis of attack by the methoxide ion at the formyl hydrogen and, during the course of elimination of CO, attack by the ester ethereal oxygen at the backside of the nascent methanol. This is followed by a slow unimolecular, or possibly bimolecular, isomerization to the proton-bound dimer structure. The 13C-labeling experiments suggest that 15%--20% of the population examined in the IR laser photodissociation experiments might be in an electrostatic form not involving a strong symmetric hydrogen bond. The comparable deuterium-labeling experiments are complicated by a pronounced deuterium isotope effect that strongly favors formation ofmethoxide ion not containing deuterium, in both the pulsed and CW photodissociation

53

Unimolecular Dissociation of Gaseous Cluster ions CH30" + C H 3 O H

(o)

(T.S.) (-2)

\

.lO) [CH30" ... CH3OHI

t

(-3o)

[ C H 3 0 "'" H "'" OCH3]"

Figure 8. Qualitative potential energy surface proposed to explain the clustering of methoxide onto methanol and the "slow" rate of symmetric proton transfer. Energies in parentheses have units of kcal mo1-1.

experiments. This preference has also been observed in our own laboratory in low-energy collision-induced dissociation experiments at between 2.5- and 50-eV center-of-mass collision energy, which appear to very closely replicate the results of the pulsed IR photodissociation. 41 Thus, in this case, both collision-induced dissociation and pulsed-IR-induced dissociation might be said to yield more structurally significant information, actually sampling the ion structure rather than promoting an isomerization equilibrium between two, or more, possible structures. In contrast, the CW IR photodissociation seems to be a "gentler" process in which the isomerization is induced. This is most evident from the 13C experiments where a 1:1 ratio of labeled and unlabeled methoxide ions was observed. Dunbar has previously commented on the role that CW IR laser irradiation plays as a mimic for a blackbody s o u r c e . 42 It seems that this is also true of a thermal unimolecular isomerization equilibrium promoted by the CW laser.

54

TERRANCE B. McMAHON

In the case study presented here, the power of the HPMS technique as a probe for unimolecular dissociation kinetics and for elucidating the associated mechanism is thus evident. For this system, ample other experimental data are available to support the conclusions drawn, but in principle the same conclusions could have been reached solely on the basis of HPMS experiments.

B. Unimolecular Dissociation Lifetime of a Transient SN2 Intermediate It has been accepted for some time that gas phase SN2 reactions proceed on a double-minimum potential energy surface, as shown in Figure 9. Here, reactants combine to form an initial, primarily electrostatically bound, complex that then proceeds via a transition state, resembling the classical picture for such species in

X+

RY [XRY" ]t

Y'+

RX

x - (RY)

Y" (RX)

Figure 9. A qualitative double-minimum potential energy surface for gas phase SN2 reactions.

55

Unimolecular Dissociation of Gaseous Cluster Ions

solution, to a second electrostatically bound complex in which the leaving group is weakly bound to the newly formed alkyl halide moiety.43-5~Even when substantially exothermic, these reactions are found to be very slow, usually, at best, proceeding at only a few percent of the collision rate. This inefficiency is attributed to the height of the transition state on the potential energy surface, which is usually very close to the energy of separated reactants, such that entropic factors often significantly inhibit barrier crossing. This idea has appeared to have been bome out by a significant number of experimental and ab initio investigations of S~2 reactions of halide ions with methyl halides. Hase and co-workers have recently carried out extensive trajectory studies of the dynamics of a number of SN2 reactions, most notably the symmetric reaction between chloride ion and methyl chloride, Equation (5). 51-55 Experimental results CI- + CH3C1 ~--- [C1-...CH3C1]* ~-- [C1CH3...CI-]* ~ C1CH3 + Cl-

(5)

for this reaction, obtained by use of selected ion flow tube (SIFT) apparatus to study the chloride isotope exchange, 3~ show that, at thermal energies, reaction is extremely slow. This is also supported by the trajectory calculations, which indicate

5

"$ r r

J~ L) A

I-..CH3CI

4-

Cl3-

(/}

0

0

"-,:.;,;.;..,.

2-

e ~

eem

w

o

..J

9

eee

1-

0

0

I

I

I

I

5

10

15

20

25

Time (ms) Figure I0. Variation of relative ionic abundances with reaction time for CI- clustering onto CH3CI in a high-pressure source at 296 K and 4 torr of a 98:2 CH4-CH3CI mixture.

56

TERRANCE B. McMAHON 10

1:: =.J

m

_

5

!

2.5

2.8

3.1

IO00/T

3.4

K-1

Figure 11. Van't Hoff plot [In(Keq) vs. T -1] for the clustering reaction of CI- onto CH3CI, from which AH ~ and AS ~ for the clustering reaction can be derived.

that the intermediate barrier crossing in the double-minimum potential energy surface is extremely inefficient. However, this inefficiency is proposed, in large measure, to be due to the fact that the initially formed electrostatic adduct is extremely short lived and that there is insufficient time available for energy randomization among the internal degrees of freedom of the complex to permit energy flow into the reaction coordinate leading to barrier crossing. Using highlevel ab initio calculations for the potential energy surface, Hase et al. 53 arrive at a lifetime of the SN2 intermediate being on the order of 10 ps. This lifetime is sufficiently close to the order of magnitude of the time between collisions in a high-pressure ion source (--5 ns at 298 K and 5 torr) that it appears feasible to probe the lifetimes of such complexes experimentally. For example, as shown from the normalized intensities as a function of source residence time in Figure 10, despite this extremely short lifetime it is still possible to achieve clustering equilibrium between C1- and the collisionally stabilized C1-...CH3C1 adduct. From the clustering equilibrium constants obtained over a range of temperatures, the AH~ and z~S~ values obtained from the van't Hoffplot of the data, Figure 11, are-10.4 kcal mo1-1 and-15.3 cal mo1-1 K-1. These are in excellent agreement with the binding energy obtained from ab initio calculations as well as with the entropy change calculated

Unimolecular Dissociation of Gaseous Cluster Ions

==.,

0.8

--

0.6

--

0.4

--

e,. c

qO (U N .,=~, .,.=,

ee 9"

CI-

9eeoeOeOeo eeeeI|: eeeeeeeeeeeoeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeelleeeeeeeOeoeeeeeeeeeeeOeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeO e

ee

E

e

L

o Z

57

0.2

ee

.. 9

CI-..CH3CI

--

0

I '

0

0.2

I

I

I

0.4

0.6

0.8

1

Time (ms) Figure 12. Variation of relative ionic abundances with reaction time for CI- clustering onto CH3CI in a high-pressure source at 296 K with 4 torr of a 98:2 CHa-CH3CI mixture. From these observations at short reaction times the rate constant for formation of the SN2 adduct ion may be obtained.

by use of standard statistical thermodynamic treatment, with the ab initio geometries and harmonic vibrational frequencies. 56 Since it is possible to achieve clustering equilibrium under conditions of lower CH3C1 pressure, it should be possible to examine the kinetics of cluster formation. This can be readily seen from the kinetic scheme for Equation (6) outlined below and the experimental data shown in Figure 12. kf ks[M] CI-+ CH3C1 ~-- [C1-.-.CH3C1]* --~ C1-...CH3C1

(6)

kr Application of the steady-state approximation to the initially formed, chemically activated complex yields the rate equation for disappearance of the bare chloride ion and formation of the collisionally stabilized SN2 intermediate, Equation (7). The apparent bimolecular rate constant for the formation of the stabilized complex d[Cl-] = kf [CI-] PCH3C l dt

k r + ks[M ]

(7)

58

TERRANCE B. McMAHON

is then given by the combination of bimolecular and unimolecular rate constants and bath gas pressure in Equation (8). kapp =

kfks[M ]

(8)

kr + ks[M]

From this, it is evident that a plot of (kapp)-1 vs. [M] -1 should yield a straight line whose slope is kr/(kfks) and whose intercept is kf 1. The values for kapp can be obtained from fitting of experimental data, such as those shown in Figure 12, to a reversible first-order reaction system during the approach to equilibrium ion intensities. The resulting reciprocal plot is shown in Figure 13, which exhibits the anticipated linear behavior with a slope of 3.5 x 1028 s cm -6. Both kf and ks can be approximated from either the Su-Chesnavich trajectory algorithm for collisions of ions with polar molecules (kf = 2.28 x 10-9 cm 3 s-1) or the simple Langevin relation for the interaction of ions with nonpolar neutrals (ks = 1.03 x 10-9 cm 3 s-l), in this system CH4, which is being used as the bath gas in the HPMS experiment. Combination of these values with the experimentally determined slope then gives a value for the unimolecular dissociation rate constant of the initially formed SN2 intermediate of 8.2 x 10 l~ s-l, corresponding to a lifetime of 12 ps. Altematively,

0.5

9= Experimental o = ADO Rate

0.4I

E o

0.3-

I Q,

m

o

0.20.1-

w

0.0

I

I

0.0

0.1

!

I

0.2

0.3

'

0.4

(Ion Source Pressure) -1 Torr -1 Figure 13. Plot of reciprocal bimolecular clustering rate constant vs. reciprocal ion source pressure from which the transient SN2lifetime may be derived.

Unimolecular Dissociation of Gaseous Cluster Ions

59

Hase's trajectory value for the association rate constant, kf, of 1.04 cm 3 s-1 may 53 be used in conjunction with the above Langevin value of the collisional stabilization rate constant to yield a unimolecular dissociation rate constant of 3.75 x 101~ s-1 and a lifetime of 27 ps. In each case, these values are in excellent agreement with the order of magnitude of lifetimes predicted by Hase's calculations for C1-/CH3C1 collisions at relative translational energies of 1 kcal mol-~, rotational temperatures of 300 K, and vibrational energies equal to the zero-point energy of the system. These data thus show that high-pressure mass spectrometry can, in addition to its many other impressive capabilities, be a powerful tool for the determination of lifetimes of transient intermediates on the 10-12 s timescale.

C. Radiative and Unimolecular Dissociation Lifetimes of Chemically Activated ions One of the important processes believed to occur in interstellar environments, which leads to synthesis of molecular species of increasing complexity, is radiative association. 57 The neutral number density in these environments is generally sufficiently low that the only other possibility for direct association of ion and neutral to occur, collisional stabilization of the chemically activated intermediate, has a vanishingly low probability. The very low pressures attainable in the UHV system of a FTICR spectrometer (--5 x 10-l~ torr), coupled with the very long trapping time capability in the strong magnetic fields of superconducting magnets (>5000 s), renders FTICR experiments a nearly ideal tool for the investigation of competition between collisional and radiative stabilization of transient species formed by direct iorr-molecule association. 58-62 Just as in the experiments involving the formation of collisionally stabilized SN2 adducts previously described, the pressure dependence of the collisional stabilization rate yields the unimolecular dissociation lifetime of the chemically activated intermediate. The important difference between these two experiments is in the pressure regime used, which determines the intermediate lifetimes that may be probed. Thus, while the HPMS experiment uses pressures in the torr range and can determine lifetimes on the order of picoseconds, the FTICR experiment uses pressures 106 to 109 times lower and therefore probes lifetimes on the microsecond to millisecond timescale. The latter range of lifetimes is of the same order of magnitude as that for IR emission from ions, with the level of internal excitation resulting from the chemical activation via ion--molecule association. This can be seen from the reaction scheme in Equation (9) below. Application of the steady-state approximation to [AB§ * yields the

kf kr A + + B ~ [AB+]* ~ AB + + hv

kb

ks[M] AB +

(9)

60

TERRANCE B. McMAHON

kfkra kfkbks[M] kapp = kb + (kb + kra) 2

(1 O)

expression given in Equation (10) for the apparent rate constant for the overall conversion of reactants to association product. From this expression, it is clear that a plot of this apparent rate constant as a function of the pressure of the neutral, M, will give a straight line whose slope is given by Equation (11 a) and whose intercept is given by Equation (11 b). - -+ ~kra) slope = '(kf

intercept = ~ kb + kra

(11 a)

( 11b)

These equations give a system with four unknown rate constants and, nominally, only two equations to solve for. However, in general, two simplifying assumptions may be made that aid in the deduction of the two unimolecular rate constants of immediate interest, kb and kra. The first of these is, as discussed previously (Section IIIB), that the chemically activated intermediate is formed on every collision and this collisional rate constant can be calculated either from the Langevin expression or from the Su-Chesnavich algorithm, depending upon the nature of M. This assumption appears to be well justified for association reactions involving either simple covalent bond formation or, alternatively, the formation of strongly bound electrostatic complexes such as proton-bound dimers. 61 HPMS experiments have, in several instances, shown that this assumption is in fact true, 61 through the examination of the "saturated" association rate constant, because, in the limit of "infinitely" high pressure, all intermediates will be stabilized and the rate of formation of the initial complex then determines the overall association rate constant. The second assumption involves the rate constant for collisional stabilization, ks. Since the initially formed intermediate has an effective internal temperature that is typically very high, a collision with an ambient temperature neutral molecule, M, will, in the vast majority of such events, lead to a transfer of energy from the ion to the neutral. This transfer of energy can then be presumed to be adequate to significantly reduce the unimolecular dissociation rate constant to the extent that the adduct ion then lives a sufficiently long time to be further stabilized via either collisional or radiative processes. 63 Dunbar has added a deep theoretical understanding to the radiative stabilization process and has shown, using his "standard hydrocarbon model," that the radiative cooling of chemically activated adduct ions, with energy e n in the ith level of the nth normal mode, can be very accurately modeled by use of Equation (1 2). 63,64

Unimolecular Dissociation of Gaseous Cluster Ions

k~a=~

61

exp(-eT/kT)

exp(-8 7/kT)

A7

(12)

i

However, central to any truly accurate determination of the radiative rate are the integrated absorption (emission) intensities, A n, which for gaseous ions are almost completely unknown as are, usually, the vibrational frequencies. Fortunately, however, ab initio and density functional methods have recently been shown to be quite accurate in their predictions of vibrational spectra for a wide variety of systems, 56 and there is no reason to suspect that this accuracy would not carry over to comparable data for gaseous ions. The one caveat must be that the low-frequency modes that are common in cluster ions will be decidedly anharmonic, and prediction of both these frequencies and their intensities may be suspect. However, these modes are not generally expected to be dominant contributors to the overall radiative rate. In addition, standard RRKM procedures can be applied to the unimolecular dissociation of the same adduct ions and, in principle therefore, the overall kinetics of formation of stabilized association complexes can be accurately modeled. In order to assess the validity of such an approach, within the assumptions of the model outlined, we have recently undertaken an examination of deuterium isotope effects on both the radiative and unimolecular dissociation rates. 62'65 One such case is that of the protonated dimer of acetone in which either the methyl groups, the protonated oxygen, or both, are deuterium substituted. Results for these four systems are shown in Figure 14 and the rate data derived are summarized in Table 1.

Table 1. Summary of Rate Data for Low-Pressure Acetone Association Reactions

Temperature (~ kf(10-9 cm3 s-l) ks(10-9 cm3 s-i) kb(104 s-l), kra(S-l) correlation (r)

Temperature (~ kf(10-9 cm3 s-l) ks(10-9 cm3 s-1) kb(104 s-l), kra(S-1) correlation (r)

Acetone 1-1+

Acetone D +

Acetone t-1+

47 2.66 2.31 4.7 + 0.2 132 + 7 0.989

48 2.65 2.31 4.9 + 0.2 96 + 6 0.997

A c e t o n e - d 61-1+

Acetone-d 6 D +

Acetone-d 6 H +

47 2.54 2.20 1.49 + 0.06 147 + 7 0.994

47 2.53 2.20 1.69 + 0.06 106 + 6 0.990

24 2.61 2.23 0.89 + 0.03 141 + 8 0.994

27.5 2.73 2.37 2.44 + 0.06 103 + 4 0.998

62

TERRANCE B. McMAHON

((CD,),CO)=H ~

A

4 m

::3 o

3

-

_

~ . . ~ v .''~'~

/

/

/

((CD,),CO),D ~

0

E m

((CH,),CO),H"

o o

1

m

((CH,),CO),D"

i

I

I

I

I

I

0

5

10

15

20

25

P (10'mbar) Figure 14. Plots of apparent bimolecular rate constants for the association reaction of protonated acetone with acetone (and deuterium-substituted variants) as a function of neutral acetone (acetone-d6) pressure in the FTICR cell at a temperature of 47 ~

In addition, ab initio calculations of the geometries, energies, vibrational frequencies, and integrated absorption intensities have been carried out in order to attempt to reproduce the experimental data using the combined radiative and RRKM models. The RRKM calculations satisfactorily reproduce the experimental data for the unimolecular dissociation kinetics, including the effects of deuterium substitution. It has been experimentally verified by HPMS experiments that both the acetone and acetone-d 6 protonated dimers have the same binding enthalpy, and therefore the slower unimolecular dissociation rate of the acetone-d 6 protonated dimer can be readily ascribed to the lower vibrational frequencies associated with many of the normal modes of the deuterated species. This leads to a correspondingly higher density of states per unit energy and a lower probability of dissociation. Interestingly, the radiative cooling rates show no significant differences between acetone and acetone-d 6, which would seem to imply that it is the skeletal, carbonyl, or hydrogen-bonding modes in a proton-bound dimer structure that are the most important contributors to radiative relaxation. In apparent support of the last possibility is the fact that the species having deuterium in the presumed hydrogenbonding position have roughly 70% of the radiative rate of the hydrogenic analogues. Unfortunately, the theoretical calculations of the radiative rates, using the ab initio data for a proton-bound structure, do not appear to reproduce these trends

Unimolecular Dissociation of Gaseous Cluster Ions

63

because little difference is found in calculated rates between the hydrogen- and deuteron-bound species, yet significant differences are found between acetone and acetone-d6 species. 65 This lack of agreement between experimental and calculated radiative rates therefore suggests that the adduct structure may have been incorrectly identified as a proton-bound dimer of acetone. In apparent support of this are some metastable dissociation experiments using conventional MIKES techniques on our reverse geometry double-focusing HPMS. 66 When a 1:1 mixture of acetone and acetoned 6 in a bath gas of CH 4 is used in the high-pressure source, the dominant species generated are the three protonated dimers: [(CH3)2CO]2H+, [(CD3)2CO]2H+, and [(CH3)2CO][(CD3)2CO]H +. If the last, mixed, protonated dimer is selected by the magnetic sector and its metastable dissociation examined via MIKES techniques in the second field-free region of the spectrometer, a mixture of protonated monomers results: (CH3)2COH+ and (CD3)2COH§ If the structures of the protonated dimers were the commonly supposed proton-bound dimers, then the MIKES spectrum of the mixed dimer would be expected to yield virtually identical amounts of the two protonated monomers, because the barrier to proton transfer between the two basic oxygen sites in such a species is expected to be minimal and no pronounced isotope effect based on zero-point energy differences would be expected. However, at an ion source temperature of 300 K, a ratio of (CD3)2COH+: (CH3)2COH+ of 1.5 is observed. Thus, it appears that a structure other than the proton-bound dimer may be formed that favors deuterium in a position that leads to protonated acetone-d6 upon dissociation. This situation is reminiscent of that observed in the clustering reactions of methylated acetone with both acetone and dimethyl ether where, based on pronounced breaks in the van't Hoff plots, both covalently and electrostatically bound adducts were proposed to exist in relative amounts dependent upon the temperature involved. 67At low temperatures the more strongly bound but sterically congested, and therefore entropically less favorable, covalently bound structures dominate, whereas at higher temperatures the more weakly bound but entropically favorable electrostatically bound structures prevail. Deuterium substitution revealed pronounced isotope effects in the covalently bound adducts, arising from the measurably greater loss in entropy associated with restriction of CD3-rotors compared to CH3-rotors. In the case of the MIKES spectra of the protonated acetone dimers, when the source temperature was raised, as shown in Figure 15, the (CD3)2COH+ : (CH3)2COH§ ratio fell monotonically, reaching unity at about 500 K. Thus, it appears that there may indeed be two possible forms of the protonated acetone dimer whose relative amounts are determined by their thermochemistry and the temperature of the system. An ab initio search for an isomer other than the proton-bound dimer is currently being conducted. If such a structure exists, any attempt to model the radiative association kinetics in the absence of a more detailed knowledge of the potential energy surface will therefore be likely to be futile.

64

TERRANCE B. McMAHON

1.6

1.5 1.4 + m

+

1.3

tO m

1.2 1.1

l

16

18

~

I

20

w

I

'

22

I

w

24

(lIT)

I

26

'

I

28

'

I

30

'

l

32

34

x 10 4 K-1

Figure 15. Variation of the ratio of intensities of protonated acetone-d6 and protonated acetone, [(CD3)2CO]H§ § arising from the unimolecular dissociation of the mass-selected mixed protonated dimer of acetone and acetone-de (MIKES) as a function of the reciprocal ion source temperature.

D. Metastable Ion Cyclotron Resonance Spectrometry The relatively long timescales of the ionization, isolation, thermalization, reaction, and detection sequences associated with low-pressure FTICR experiments are generally thought to preclude the use of this technique as a means of examining the unimolecular dissociation of conventional metastable ions occurring on the microsecond to millisecond timescale. Nonetheless, as just demonstrated (Section IIIC), intermediates with this order of magnitude of lifetime are routinely formed in the bimolecular reactions of gaseous ions with neutral molecules at low pressures in the FTICR cell, as in Equation (13). A+ + B ~

[AB+] * --~ C + + N

(13)

Kleingeld and Nibbering et al. have shown that the intermediacy of such adducts can be demonstrated through the use of a double-resonance type of technique in which the transient [AB+] * is continuously irradiated at its cyclotron frequency throughout the entire reaction time, even though it is not detectable in the ordinary mass spectrum. 68 An overall decrease in the intensity of the product ion C + was then taken to indicate that the intermediate complex lived sufficiently long to be ejected,

Unimolecular Dissociation of Gaseous Cluster Ions

65

thereby reducing the amount of product ion formed. In this case, the information derived was essentially qualitative in demonstrating which ion must have undergone collision with which neutral molecule in order to yield a given product. In a significant extension of this methodology, using a conventional drift ion cyclotron resonance spectrometer, Anicich et al. 59 showed that the unimolecular dissociation lifetimes of such chemically activated intermediates could be sampled using variable rfpower to eject the transient on a timescale comparable to its range of lifetimes. Since the intermediates will have intemal energies corresponding to a room temperature thermal Boltzmann distribution superimposed upon the more significant amount of energy associated with the newly formed bond, the range of lifetimes is expected to be narrow. In the reaction of the radical cation ofcyanoacetylene with the parent neutral molecule, monitoring of the HCsN + product ion, corresponding to HCN loss from the intermediate, revealed a range of lifetimes from 50 ~ts to 500 ~ts. More recently, Audier and McMahon 69 have shown that the unimolecular dissociation spectrum of transient ions can be directly obtained from a simple manipulation of a series of FTICR spectra. The data arising from this approach very closely resemble those obtained from metastable dissociations in conventional sector spectrometers (MIKES), and it has been consequently dubbed metastable ion cyclotron resonance (MICR) spectrometry. Very briefly, the method functions as follows: 1. Following isolation and thermalization of the desired reactant ion, this species is trapped in the FTICR cell in the presence of the neutral reactant for a period of time sufficient to allow between 10% and 20% conversion to products to take place. If the product ions are each subsequently unreactive toward the neutral reagent, longer reaction times might be employed. 2. A second spectrum is then taken for which an rfelectric field at the frequency appropriate for the mass of the reaction intermediate is applied continuously throughout the same reaction delay as that employed in the first spectrmn, taken without this rf electric field. 3. The second spectrum is then subtracted from the first. This may be done either via subtraction of the time domain transients or, alternatively, via subtraction of the Fourier transformed spectra, provided that the absolute intensity of the second is referenced to the first according to the relative magnitudes of the time domain signals. If the distribution of transient intermediate lifetimes is similar to the time required for rf ejection, some of these species will be ejected from the FTICR cell before undergoing unimolecular dissociation and the overall intensity corresponding to the abundance of ejected ions will be lost from the second spectrum. The difference spectrum then corresponds to the mass spectrum of unimolecular dissociation products of those transient species that did live long enough to be ejected from the cell. If the intermediate is weakly bound, and/or contains relatively few atoms, a

66

TERRANCE B. McMAHON

simple RRKM analysis dictates that the lifetime will be much shorter than that resulting from formation of either a strongly bound adduct or, for the same binding energy, a species with a larger number of atoms (and vibrational degrees of freedom). For a cylindrical FTICR cell, 6 cm long and 6 cm in diameter, with use of rf amplitudes up to 400 V peak to peak, ejection times are 50 ~s and greater in a magnetic field of 4.7 T, as given by Equation (14). 4r 2 (14) Here the factor S E, equal to 0.814, corrects the rf electric field strength to account for the fact that the cell is not infinitely long. Those intermediates that are shorter lived than the time required for ejection undergo dissociation to products somewhere between the center of the cell, where they originated, and the cell walls. The fragment ions will then have the same linear velocity as their heavier parent; however, because their angular velocities are dictated by the mass and the magnetic field strength, these fragments will necessarily execute circular motion with orbits smaller in radii than that of the parent by the ratio of the masses of fragment and parent. This then leads to an unusual distribution of ions throughout the cell after dissociation. Ideally, the trajectories of all reaction products would decay back to the cell center and be detected with exactly the same efficiency as those ions that had never leit the center of the cell. However, the nature of the cyclotron and magnetron motions of the ions is such that this does not occur efficiently, and, as a result, those ions formed closest to the cell walls will be discriminated against in terms of intensity in the difference spectrum. However, implementation of quadrupolar excitation, as opposed to the dipolar excitation normally used for ejection or detection in FTICR experiments, accompanied by collisional relaxation of the fragment ions, should refocus them to the cell center where they again may be efficiently detected. 7~Although not attempted to date in conjunction with the MICR experiment, such implementation is currently being undertaken at Waterloo. This means that the MICR experiment in its current form is still not an ideal method for precise determination of intermediate ion lifetimes, although very good qualitative estimates of such lifetimes are readily obtained. In addition, however, the technique provides an extremely effective means for the examination of product distributions as a function of transient intermediate lifetime, and therefore of transient internal energy content. For example, consider the following hypothetical reaction scheme in Equation (15) with mixtures of products, each arising from a common chemically activated intermediate that is too short lived to be seen in a spectrum generated by the usual FTICR detection scheme. The chemically activated intermediate can undergo dissociation to yield either distinguishable products, C § D § and E § or the usually invisible product, A § whose formation cannot be readily seen since it is also the reactant ion. After formation of the initial [AB+] * complex, the system may proceed via one or more transition states to different complexes, which themselves may

UnimolecularDissociationof GaseousClusterIons

67

--)C + + N 1 A + + B ~ - [AD+] * -*

-* D + + N 2

(15)

E+ + N 3 undergo further rearrangement via other transition states leading to the various products. However, in many cases, it will be the transformation(s) from the initially formed complex that will determine the product branching ratio. The competition between return to initial reactants and conversion to new products will then depend on the relative energetics of the reactants, or their orbiting transition state, and that of the transition states leading to products, as well as the internal energy content of the individual [AB+] * species. Therefore, as the lifetime of the complex sampled in the MICR experiment is varied, so too is the internal energy content, and it can be expected that a change in the product branching ratio will result. In this respect, it can be readily understood that a change in the rf voltage, and therefore in the ejection time in the MICR experiment, is directly analogous to a change in the accelerating potential in a conventional reverse geometry double-focusing mass spectrometer in the examination of metastable dissociations. This is clearly illustrated in the example given below for the reaction of the methoxymethyl cation with pivaldehyde. 71 There are four possible reaction channels for the unimolecular dissociation of the initially formed adduct, which is presumed to be of the form of a covalent species resulting from the interaction of the carbocation center of the methoxymethyl cation with the carbonyl oxygen of the aldehyde, 2. For smaller carbonyl compounds this adduct has been demonCH 3OCH2-O'-CC(CH3) 3

I H 2

strated by ab initio calculations to be the energetic minimum on the potential energy surface, and its formation is also a mechanistically simple process. These four dissociation channels [see Equation (16)] are (1) the methoxymethyl cation plus neutral aldehyde, (2) the pivaloyl cation plus dimethyl ether, (3) methylated pivaldehyde plus formaldehyde, and (4) t-butyl cation plus CO plus dimethyl ether. I._~ CH2OCH{2+ (CH3)3CCHO (m/z 45)

CH3OCH~ + (CH3)3CCHO ~

~ (CH3)3C+ + (CH3)20 + CO (m/z 57) (CH3)3CCO+ + (CH3)20

l

(m/z 85) ---) (CH3)3CCHOCH~ + CH20 (m/z 1012)

(16)

I00

-

(a)

I01

85 80-

>t--

45

(/1

z 60-

ILl I--" Z m

40-

20 .

57

125

I

I00

I

!

I

I

I

I

(b) 85

J

80 >I.=_z

t

[ I

60

40

I

45

0

i

125

20

..............

-]'--T. . . . . .

"[~" -

I

i

l

50

60

70

--t

"~-~u

80

m/z

J u

i

90

100

......

&

-I

110

!

120

i

130

Figure 16. Metastable ion cyclotron resonance (MICR) spectra for the unimolecular dissociation of the chemically activated adduct ion derived from association of the methoxymethyl cation with pivaldehyde during a 2-s reaction delay at a pressure of pivaldehyde of 1.0 x 10-8 torr. The three spectra correspond to values of rf amplitude appropriate to eject transient intermediates with lifetimes longer than (a) 60 Its, (b) 80 Its, and (c) 170 Its. A partial pressure of CH 4 of 1.0 x 10-7 torr was also present to thermalize ions. The peak at m/z 125 is a secondary reaction product of m/z 85. 68

Unimolecular Dissociation of Gaseous Cluster Ions

I00

(c)

69

85 101

80 >.. I-v, z

60

UJ

I-Z

4O

125

20

I

50

I

60

I

70

8;

9'o

.

.

,;o

.

.

.

,,'o

.

.

m/z

Figure 16. (Continued)

The series of three MICR spectra, shown in Figure 16, illustrate the changing product distribution with internal energy. At high rf amplitudes, Figure 16a, the amount of time required to eject the transient intermediate is 60 Its and all species with lifetimes longer than this are ejected, giving the spectrum shown for the subsequent unimolecular dissociation products of all these ejected species. This is the fastest ejection time in this series and therefore corresponds to sampling of an ensemble of intermediates with the highest internal energy content. All four dissociation products are clearly visible in this spectrum. In Figure 16b, corresponding to an ejection time of 80 Its, the t-butyl cation has disappeared from the MICR spectrum, indicating that this product probably represents the most energy demanding dissociation process. In addition, significantly, the intensity of the methoxymethyl cation product has decreased relative to those of the pivaloyl cation and the methylated pivaldehyde. Finally, in Figure 16c, the ejection time is 170 Its and the methoxy methyl cation has completely disappeared and small changes in the ratio of the other two products have occurred. This, together with thermochemical data for reactants and products, allows the qualitative potential energy surface shown in Figure 17 for this system to be proposed. The S/N in each of these MICR spectra is significantly poorer than that in the ordinary spectra taken without ejection, indicating that the number of ejected species is small compared to the total number of complexes formed and therefore that most of the adducts formed undergo

70

TERRANCE B. McMAHON TSt

CHsOCH2 + +

(0)

tC, H,CHO

TS2

I,

t-C~H," + (CHjhO + CO (-2) _

TSj

12

~

/

(-20)

(CH3)jCCHOCHf + CH20

/ J

(-24) t-C4H,CO" + (CHj)zO

' (-40) [CHsOCHa-OCHC(CHj)~]"

Figure 17. Qualitative potential energy surface for the reaction of methoxymethyl cation with pivaldehyde. Energies in parentheses have units of kcal mol -~.

unimolecular dissociation on a timescale faster than that required for ejection. We are therefore probably in the low-energy end ofa Boltzmann distribution ofintemal energies for the species that are sampled in the MICR experiment. The rate constant for the overall reaction of the methoxymethyl cation with pivaldehyde of 1 • 10-9 cm 3 s-1 would also support the fact that the chemically activated intermediates are relatively short lived because virtually all complexes proceed to products other than regeneration of reactants. These, and similar data for other systems, demonstrate the tremendous potential that the MICR technique has for the qualitative elucidation of potential energy surfaces of relatively complex organic reactions. Once implementation of the quadrupolar excitation technique has been effected to relax ions to the cell center, the technique will become even more powerful, in that the determination of highly accurate unimolecular decomposition lifetimes of chemically activated intermediates will also become possible. No other technique offers such a powerful array of capabilities for the study of unimolecular dissociation mechanisms and rates.

Unimolecular Dissociation of Gaseous Cluster Ions

71

E. Thermal Infrared-Induced Dissociation of Cluster Ions One of the most surprising results, following the coupling of an external highpressure source to our FTICR spectrometer, was the observation of very slow unimolecular dissociation of apparently well thermalized cluster ions. 72 For example, as shown in Figure 18, the proton hydrate, (H20)4 H+, which has the Eigen structure of a core hydronium ion hydrogen bonded to three water molecules, is observed to dissociate via loss of a water molecule with smooth single-exponential decay on a timescale of hundreds of seconds. Given the strength of the bond broken of 17.5 kcal mo1-1 and the low pressures involved in the FTICR cell of the order of 10-9 torr, this dissociation appeared at first to be very difficult to rationalize. 73 One possibility immediately investigated was that the ions arriving at the FTICR cell were in fact not well thermalized and contained excess kinetic energy arising from the ion transfer optics. If this were the case, addition of a high pressure of a pulsed gas or a long prereaction delay in a static pressure of inert gas should change the rate of dissociation. Alternatively, a bimodal ion population might have been observed with a reactive component oftranslationally hot species and an unreactive component of relaxed ions. Neither of these behaviors was ever observed, with the rate constant for disappearance of a given cluster ion remaining invariant and single valued, independent of the times or means of supposed relaxation. Thus, excess translational or internal energy was not the cause of the unimolecular dissociation. Conventional wisdom concerning thermal unimolecular reactions would seem to dictate that this must then be a Lindemann-type collisionally activated dissociation reaction scheme such as is in Equation (17). ]-3 Application of the steady-state

1.0

0.e

c o

0.6-

o o

0.4

0.0

" 0

I 100

i 200

I 300

Reaction T i m e

i 400

I

500

($)

Figure 18. Variation of ionic intensities as a function of time, after isolation and thermalization in the FTICR cell, of the externally generated cluster ion, (H20)4H +.

72

TERRANCE B. McMAHON

k, A ++ M ~ [A+]* + M

(17)

[A+] * ---> B + + C approximation to [A+]* gives the general rate equation [Eq. (18)] and an apparent unimolecular dissociation rate constant given by Equation (19). This can be reduced in the low- and high-pressure limits to Equations (20) and (21) respectively. Thus

d[A +] dt

=

klk d k l[M] + kd

[M][A +]

klkd[M ] kuni = k I[M] + kd low pressure kun i = k 1 [M] (kd >> k_ 1[M])

klk d

(18)

(19)

(20) (21)

high pressure kuni - k 1 (kd >> k_l[M]) at low pressures the unimolecular rate constant should actually be linearly dependent on the pressure of M, whereas at high pressures it will be pressure-independent. Given the near pressure-independent behavior that is observed in our system, if this Lindemann model is valid, we must be approaching the high-pressure limit. However, given the very low pressures at which our experiments are carried out, this seems unlikely, and a comparison of realistic values for kd and k_l [M] supports this. For example, at the highest pressures of inert gas used in the FTICR cell (~ 10..6 torr) and a typical value of the bimolecular rate constant, k_ l, of 10-9 cm 3 molecule -1 s-1, a value of k_l [M] of the order of 10 S-1 is obtained. This must then be compared to the value of the unimolecular rate constant kd for activated species [A+] *. As seen from the chemical activation experiments discussed previously, values ofk d for species with this number of atoms and with exactly the fight amount of energy to undergo dissociation are typically on the order of 105 s-1. Thus we cannot be even approaching the high-pressure limit for a Lindemann mechanism. Indeed the pressures are much more appropriate for the low-pressure limit. However, if this is the case, the observed unimolecular rate constant should be a linear function of pressure and fall to zero in the limit of zero pressure. In contrast, the data in Figure 19 reveal that this is not at all the situation because there is only a slight dependence of the rate constant on pressure, and, furthermore, the zero-pressure intercept is decidedly nonzero.

Unimolecular Dissociation of Gaseous Cluster Ions

73

0.008

=,===,=

Tt,#}

C 0 .,=-

0.006

0.004

U m i._

0.002

I

I

I

l

I

20

40

60

80

100

pressure of CH4 [10 -e tuber]

Figure 19. Dependence of the unimolecular dissociation rate constant for H20 loss from the cluster ion, (H20)4 H§ on pressure of CH 4 in the FTICR cell.

A further feature expected of thermal, collisionally activated unimolecular dissociations is that the rate constants should exhibit an Arrhenius-type dependence on the temperature. ~-3 For the unimolecular dissociation of the (H20)5 H+ cluster, k = A e-~/Rr

(22)

shown in Figure 20 at 300 K, the temperature dependence shown in Figure 21 is obtained. The linearity ofln k with T -1 is of the expected Arrhenius form; however the activation energy, Ea, thus obtained of 7.2 kcal mo1-1 is much smaller than the value of near 13.9 kcal mo1-1 expected, based on the HPMS-determined bond dissociation energy. Furthermore, the supposed Arrhenius A factor obtained (2400 s-1) is far out of the range of values normally obtained, which are typically between 101~ and 1015 s-1. Thus, the combined evidence, based on both pressure and temperature dependencies, indicates that these unimolecular dissociations, as well as those of the other similar reactions 72, 74, 75 in Table 2, do not have the character of a Lindemann-type thermal process. The only apparently viable alternative mechanism to explain the observed unimolecular behavior is one that was originally proposed in 1919 by Perrin and became known as the radiation hypothesis. 76 In the absence of any significant body of kinetic data, Perrin proposed that reactant molecules obtain the energy required

1 . 0 -~,

0.8

=.Q -,9 c:

0.6

I) >_ e-, Q @:

0.4

0.2

0.0

Reaction Time Is)

Figure 20. Variation of ionic intensities as a function of time after isolation and thermalization in the FTICR cell of the externally generated cluster ion, (H20)sH §

0.5

0,0

-

T( / I .| .lg

i

I=

-0.5 -

-1

I

2.9

3.0

3.1

3.2

IO00/T

3.3

3.4

(K-1)

Figure 21. Dependence on the temperature of the FTICR cell of the unimolecular dissociation rate constant for H20 loss from the cluster ion, (H20)sH § 74

Unimolecular Dissociation of Gaseous Cluster Ions

75

Table 2. Unimolecular Rate Constants ku,~ and Associated Thermochemical Data a for the Loss of a Ligand from Cluster Ions (W: H20; E: (CH3)20) at Ambient Temperature

Reaction

(kc~Z~m2981 -l)

kuni[s-I ]

H+(Ws) -~ H+(W4) H+(W4) --~ H+(W3) H*(EW3) ~ H+(EW2) H+(EW2) ~ H*(EW)

0.49 _ 0.01 4.6(_+0.1) x 10-3 0.23 + 0.03 3.3(_+0.3) x 10-2

13.9 17.4 12.9 16.7

(15.3) b (17.5) b (13.8) c (15.3) r

H+(E2W2) ~ H+(E2 W) H+(E3W) --~ H+(E2) H*(E3 W) ~ H+(E2 W) Cl-(W3) --~ CI-(W2) CI-(W2) -~ CI-(W)

0.44 + 0.07 0.83 _+0.2 9.5(+1) x 10-2 8.6(_+1) x 10-2 2.4(-+0.4) x 10-3

14.3 (13.6) r 12.4 (16.3) c 21.7 (16.8) c 11.8 d 13.0 d

AG~298 1

(keal tool- ) 5.8 9.6 6.1 7.4

(5.5) b (9.3) b (6.2) c (7.5) c

6.2 (6.3) r 4.3 (4.7) c 9.3 (8.9) c 5.1 d 6.60

/~m2908/..1)

(keal 27.2 26.1 22.7 31.1

(32.6) b (27.3) b (25.4) c (26.3) c

27.2 (24.6) c 27.2 (38.8) c 41.6 (26.6) c 22.3 d 21.40

Note: aSzulejko and McMahon, unpublished results; literature value in brackets; bref. 73; CHiraoka, Grimsrud and Kebarle J. Am. Chem. Soc. 1974, 96, 3359; aHiraoka and Misuze, Chem Phys. 1987, 118, 457.

to promote unimolecular dissociation via absorption of radiation from the walls of the reaction vessel. Steinfeld et al. 77 have given an enlightening discussion of Perrin's hypothesis in which they note that, contrary to the claim of many kinetics textbooks, Langmuir's purported refutation of the idea is not valid because it was based on a calculated radiation flux at 400 nm rather than in the infrared where the blackbody radiation distribution peaks. 78 In fact, in the infrared region, there is sufficient energy available to account for the dissociation. Steinfeld et al., 77 however, subsequently state that "most importantly, a radiation-driven mechanism would have a rate truly independent of gas pressure." They then discuss the absence of any observation of a truly pressure-independent unimolecular dissociation and conclude that "it is primarily this observation which forces us to abandon the radiation hypothesis in favor of the collisional activation mechanism developed by Lindemann and Hinshelwood." As noted above, our observations do show pressure-independent unimolecular dissociation, and therefore it seems highly probable that the unimolecular dissociations that are observed are due to the continuous absorption of background infrared blackbody radiation from the cell walls by the ion population. The radiative mechanism can be summarized by the reaction scheme in Equation (23) where kabs and kem represent the "rate constants" for absorption and spontaneous emission of the infrared radiation. k~bs A + + hv ~-- [A+]* + M kem

[A+]" ~ B+ + C

(23)

76

TERRANCE B. McMAHON

As carried out above for the Lindemann mechanism, application of the steadystate approximation gives the apparent unimolecular rate constant in Equation (24) where [hv] represents the IR photon density. Again two limits may be considered,

kabskd kuni - Kd+'''T V ] k e m [h

(24)

Equations (25) and (26), depending upon the relative magnitudes of kd and kem.

kuni = kabs[hv]

kd >> kem

(25)

kabskd kuni = kem [hv]

kem >> kd

(26)

Again the radiative association kinetics described above allow a direct comparison for some realistic values of kem and k d. For most chemically activated systems at the threshold for unimolecular dissociation, the observed radiative rate constants are of the order of 10-100 s--I and hence are much below the values expected for kd of about 105 s--1. Therefore, the first limit is most likely to be valid, with the interesting conclusion that the observed unimolecular dissociation rate constant will depend only on the photon density and the absorption cross section (rate constant) at a given wavelength. The Arrhenius-like temperature dependence obtained, which however gives rise to unreasonable frequency factors, can then be rationalized on the basis of the temperature dependence of the blackbody radiation. At higher temperatures, the energy density per unit wavelength of the blackbody radiation increases with the maximum in the distribution shifted to higher frequency. Also, at a given frequency the intensity of radiation emitted varies approximatelyas In I oc - T -1.79 Therefore, as the temperature increases, so too does the intensity of the radiation and with it the rate ofenergization of the cluster ion and, consequently, the rate ofunimolecular dissociation. Thus the temperature dependence is entirely consistent with a radiative mechanism for dissociation. Variation of the cell temperature can be regarded as modifying the unimolecular rate constant via a shift in the photon density at the collection of frequencies for which a particular cluster ion absorbs infrared radiation. It would therefore also be desirable to effect the only other possible change, that is, to vary the value of/Cabs while leaving all other parameters unchanged. One intriguing way of doing this that suggested itself was to carry out identical unimolecular dissociation experiments with deuterated and undeuterated variants of the cluster ligands. 8~ In principle, if the dissociation energetics of deuterated and undeuterated species are very similar, then a pronounced deuterium isotope effect on the unimolecular rate constant might still result from a shift in absorption intensities from a region of relatively weak blackbody emission, in the hydrogenic case, to a region of lower frequency and

77

Unimolecular Dissociation of Gaseous Cluster Ions Table 3. Unimolecular Reaction Rate Constants for

Isotopically Analogous Reactions [Ac: ( C H 3 ) 2 C O , B: C6H6, E: (CH3)20, W: H20] kuni(S-1)

Reaction

(1)

CI-(Ac) --~ C1- + Ac

2.6(+0.1) x 10-3

(b) (c)

Cl-(Ac-d6) -~ C l - + A c - d 6 Cl-(B) -~ Cl- + B

5.7(_+0.25) x 10-3 3.2(_+0.16) x 10-2

(d)

Cl-(B-d6) --->C1- + B - d 6

3.7(+0.16) x 10-2

(e)

H+(E3W) --->H+(E2 w ) + E

0.095(_+0.005)

(f) (g)

H+(E-d6)3 w ---> H§ H+(E2 w ) --> H§ +W

(h)

H+(E-d6)2 w ~ H+(E-d6)2 + W

kdni/khni

2.2

1.2

1.4 w + E-d 6

0.13(_+0.006) 0.72(+0.04) a 1.2 0.85(-4-0.04) a

Notes: aThese rates were obtained from the consecutive dissociation of the products of reactions e and f, and thus

kuni (g) is different from that reported in Table 2.

higher blackbody emission intensity, in the deuterium case. Data obtained for several such isotopic pairs of cluster ions are shown in Table 3, where large deuterium isotope effects are in fact seen that are consistent with the radiative mechanism. This is perhaps more graphically illustrated by the qualitative presentation of the overlap of the room temperature blackbody emission distribution and the significant IR absorptions of the neutral ligands themselves 81 for the chloride adducts of acetone and benzene in Figures 22 and 23. Ideally this overlay would be done for the IR absorptions of the cluster ions themselves; however, these frequency and intensity data are not currently available from either experiment or ab initio calculation. As can be seen from these Figures, the shift in IR absorptions in acetone-d 6 is in fact to regions where the blackbody radiation is significantly more intense, and the isotope effect of 2.2 is the largest of those observed. In contrast, there are far fewer significant IR absorptions in benzene, and the frequency shifts in benzene-d 6 are not to regions of substantially greater blackbody intensity. Consistent with this, a considerably smaller isotope effect of only 1.2 is observed. In the case of the multiply solvated dimethyl ether-water clusters, as the number of deuterium-substituted ligands increases, so too does the magnitude of the increase in the unimolecular dissociation rate constant. Thus, the deuterium isotope effect data also support a radiative mechanism for the unimolecular dissociations observed here. Comparisons among some of the rate data obtained provide further support. For example, from the data in Table 2 it can be seen that both the EW3 H§ and W2C1-

TERRANCE B. McMAHON

78

(CHaIzCO

50-

T E u

#

40-

#

9

9 t

3:

,= I

tt tI

30

t #

0

i I

>., 2 0 "~ == -.

10

0

:

1.,' i i I'--............... II1 '

,

!

0

800

'

.

.

.

I

'

I

1600

.

2400

3200

(CDalzCO

50-

T E u

9

. . . . .

#

4O-

9

e

I i I t I

o! 0

30i

\

i i

>, 2 0 -

i

.==

i

..E = lO o I 0

: I

%

.

I

I

800

1600

2400

3200

Wavenumber (cm - I )

Figure 22. Schematic overlay of the most intense IR absorptions for neutral acetone and acetone-d6 with a 300-K blackbody emission spectrum. The intensity axis refers to the blackbody radiation only. ions bind the ligand lost by essentially 13.0 kcal mol-l. Despite this similarity in the energetic requirement for the dissociation, the former undergoes dissociation nearly two orders of magnitude faster than the latter. This is the opposite of what might have been expected from an RRKM analysis of the relative magnitudes of the kd values for species activated to the same extent in a high-pressure limit Lindemann case. Here it would have been expected that the larger species, EW3 H§ with the greater number of normal modes would have a higher density of states and therefore undergo dissociation more slowly than the smaller cluster ion. However, if as proposed in the radiative mechanism, the rate-determining step is in fact the IR absorption rate, it is quite logical to expect that the system containing the larger number of normal modes will be able to "harvest" energy at a faster rate

79

Unimolecular Dissociation of Gaseous Cluster Ions C6H6

50#e

9149149

'E U 40

till

~

2o

i

i

ID

.9

10

0

/,

,

0

800

i

9

I

~,ii

,

1600

5O o

3200

CsD6

40

,/

~ -1/! 20

~

i

24OO

'

10

o

0

j

800

I :'--. .... 1600

"T ....

.~400

'

3200

Wavenumber (cm -I)

Figure 23. Schematic overlay of the most intense IR absorptions for neutral benzene and benzene-d6 with a 300-K blackbody emission spectrum. The intensity axis refers to the blackbody radiation only. from the broad-band IR radiation field and thereby dissociate more rapidly. Conversely, when two clusters of comparable size are compared, such as WsH + and EWEH+, which each have 16 atoms, as expected the more weakly bound system undergoes dissociation more rapidly, in this case by a factor of about 15. The blackbody radiative mechanism proposed here is in fact very reminiscent of the model advanced by Dunbar 42 in which CW infrared laser irradiation can be regarded as a blackbody source raising the effective temperature of the system. In this model, the population of ions achieves a "truncated Boltzmann distribution," which resembles that of a normal Boltzmann distribution characteristic of the effective temperature but which abruptly ends near the dissociation energy of the ion of interest because once this energy is exceeded, the species rapidly undergo

80

TERRANCE B. M c M A H O N

unimolecular dissociation. Dunbar 82 has now also carried out a similar analysis showing that this truncated Boltzmann distribution is again appropriate to describe our thermal blackbody-induced dissociations. Using ab initio values for vibrational frequencies and absolute absorption intensities, he has obtained quantitative agreement with our experimental data for chloride-water clusters. Thus, the thermal radiative mechanism for unimolecular dissociations can be considered to be on a firm theoretical as well as experimental foundation. F. i n f r a r e d - L a s e r - i n d u c e d Thermal Dissociation

The observation of blackbody-radiation-induced thermal dissociation of gaseous cluster ions suggests that very low power, CW infrared laser irradiation should also a)

1.0

(H=O)4H'~~'~'~'~'~--~.......~.~...~.......,

=,- 0.8 "~ 0.6 @

,-

r

0.4

o

0.2 0.0

!

0

10

i

!

1

i

20

30

40

50

,

1.0 ~

H

,

*

>, 0.8 ISI

=

o

=~"

0.6-

~

tD

"~ 0.4IQ

"~

0.2 0.0

. 1 t

0

, 10

J

(H=O)3H*

, 20

, 30

', 40

, 50

Reaction Time (s)

Figure 24. Variation of ionic intensities as a function of time after isolation and thermalization in the FTICR cell of the externally generated cluster ion, (H20)4H + at a pressure of CH4 of 2.0 x 10 -9 torr in the FTICR cell and irradiation by (a) 300-K blackbody emission, and (b) 1.8 W cm -2 CW CO2 laser.

Unimolecular Dissociation of Gaseous Cluster Ions

0~

81

-

slope = 0.871

T( f l =~

JK

I

0.01

0.001 I

,

,

,

0.1

!

9

9

,

, , I

,

,

1

|

,

,

, , I

10

Laser Intensity (W cm -z} Figure 25. Logarithmic plot of klaser-kun i vs. C W C O 2 laser intensity for the unimolecular dissociation of (H20)4 H§ in the FTICR cell at a CH4 pressure of 2.0 x 10-9 torr.

be effective in inducing unimolecular dissociation of cluster ions, provided that there is sufficient absorption intensity in a cluster Vibrational mode at the given laser frequency. Further, if the laser intensity can be systematically varied, then the order of the dissociation with respect to photon flux (i.e., whether the dissociation is a single or multiphoton process) and the absorption cross section for the ions at the laser frequency can both be determined. Because ab initio calculations report vibrational frequencies of 950 and 968 cm-1 for the W4H+ system, 83 and because this ion had been well studied for the blackbody-radiation-induced dissociation, it was chosen as a good candidate for study by CO2-1aser-induced dissociation at the laser frequency of 943 cm-1. The data shown in Figure 24 illustrate the extents of dissociation observed at up to 50 s without CO 2 laser irradiation and with CW laser irradiation at an intensity of 1.8 W cm-2. The CO2-1aser-induced process is seen to be about 2.5 times faster than that arising solely from the ambient temperature blackbody radiation. Thus, the blackbody radiation contribution to the dissociation at this low laser power continues to be a sizable fraction. If the laser intensity is varied, then the order of reaction with respect to photon flux can be obtained from Equation (27), where I is the laser intensity expressed as W c m -2 and O'1,2 is the photon absorption cross section. ln(klaser -

kuni)

-

n In I - n In hv + In c12

(27)

A plot ofln (klase r - kuni) vs. In I then should yield a straight line of slope n. Such a plot for this system is shown in Figure 25, which gives a slope of 0.87 that is sufficiently close to unity to demonstrate, not surprisingly, that the dissociation is

82

TERRANCE B. McMAHON 3500

3000

T

--? 0

E

2500

E

2000

>,

1500

~

o

1000

C

500

_!l,.. ,,J. lOOO

.

9

-

9

I

'

9

2000

I

I

3000

9

1 4000

Energy (cm -I)

Figure 26. Ab initio calculated vibrational spectrum of the (H20)4 H+ cluster ion. No attempt has been made to assign linewidths to peaks in the spectrum.

the result of single-photon absorption processes. 84 In addition, the 943 cm-~ absorption cross section is found to be 3 x 10-20 cm 2. The calculated absorption spectrum, given in Figure 26, shows that this is a relatively minor absorption for this ion and that if a CW, IR laser at about 2850 cm-~ could be employed, a dramatically greater extent of dissociation would be observed. This is essentially the region in which Lee and co-workers 85 have demonstrated the power of"consequence" spectroscopy. IV.

CONCLUSION

The systems described above demonstrate the considerable insight that may be gained into the details of unimolecular dissociation of gaseous ions by use of currently available techniques for the study of iorr-molecule reactions. At high pressures in a pulsed ionization high-pressure mass spectrometer, the temperature dependencies of both the kinetics of formation of collisionally stabilized, strongly hydrogen bonded adducts and the equilibrium distribution of monomer and dimer ions provide Arrhenius parameters for the thermal unimolecular dissociation of the dimer species. In addition, the kinetics of the methoxide--methanol reaction strongly implicate an important electrostatic complex in the entrance channel on the potential energy surface. Similarly, the temperature dependence at high ion source pressure of the kinetics of formation of the chloride-methyl chloride adduct yields important information concerning the lifetime of the initially formed chemically activated transient adduct.

Unimolecular Dissociation of Gaseous Cluster Ions

83

At low pressures, in FTICR experiments, examination of the pressure and temperature dependencies of kinetics of strongly bound adducts again gives unimolecular rate constants for the dissociation of the chemically activated adduct species. However, in this case, the low-pressure regime studied also gives rise to radiative rate constants for the stabilization of activated intermediates by IR emission. Use o f controlled RF ejection of transient intermediate species is shown to provide data concerning the variation o f product branching ratios with the lifetime of the intermediates sampled. Finally, a new type o f unimolecular dissociation, that of dissociation of weakly bound cluster ions, initiated by background blackbody radiation, has been demonstrated. With complementary data from lowpower CW IR-laser-induced unimolecular dissociation, this provides a strong indication that vibrational spectroscopy of gaseous cluster ions may be realizable through use of low-power, tunable IR sources.

ACKNOWLEDGMENTS It is a pleasure to acknowledge the considerable efforts of my co-workers at the University of Waterloo who have made the experiments described herein a reality. Jan Szulejko, Kim Norrman, and Chun Li have carded out all of the high-pressure mass spectrometric experiments, and Andrea McCormick, Detlef Th61mann, and Scott Tonner are responsible for the majority of the FTICR experiments. The MICR technique was conceived and the experiments executed during a sabbatical leave in the laboratory of Henri Audier in Paris. He was responsible for taking a bimolecular mind and giving it a decidedly unimolecular twist, for which I warmly thank him. Finally, generous financial support of the research carded out at Waterloo by the Natural Sciences and Engineering Research Council of Canada is also gratefully acknowledged.

REFERENCES 1. Robinson, P. J.; Holbrook, K. A. Unimolecular Reactions; Wiley-Interscience: London, 1972. 2. Forst, E Theory of Unimolecular Reactions; Academic: New York, 1973. 3. Gilbert, R. G.; Smith, S. C. Theory of Unimolecular and Recombination Reactions; Blackwell Scientific: Oxford, 1990. 4. Pacey, E D.J. Chem. Educ. 1981, 58, 612. 5. Glasstone, S.; Laidler, K. J.; Eyring, H. The Theory of Rate Processes; McGraw-Hill: New York, 1941. 6. Marcus, R. A.J. Chem. Phys. 1965, 43, 2658. 7. Hinshelwood, C. N. Proc. R. Soc. London, Set A 1927, 113, 230. 8. Rabinovitch, B. S.; Setter, D. W. Adv. Photochem. 1964, 3, 1. 9. Laser Induced Chemical Processes; Steinfeld, J. I., Ed.; Plenum: New York, 1981. 10. Miller, W. H. Chem. Rev. 1987, 87, 19. 11. Cooks, R. G.; Beynon, J. H.; Caprioli, R. M.; Lester, G. R. Metastable Ions; Elsevier: New York, 1973. 12. Cooks, R. G. Collision Spectroscopy; Plenum: New York, 1978. 13. Holmes, J. L. Org. Mass Spectrom. 1985,20, 169.

84

TERRANCE B. McMAHON

14. Levsen, K. Fundamental Aspects of Organic Mass Spectrometry, 4th ed., Verlay Chemie: Weinheim, 1978. 15. Holmes, J. L.; Terlouw, J. K. Org. Mass Spectrom. 1980, 15, 383. 16. Douglas, D. J. J. Phys. Chem. 1982, 86, 185. 17. Rosenstock, H. M.; Stockbauer, R. L.; Parr, A. C. J. Chem. Phys. 1979, 71, 3708. 18. Baer, T. Adv. Chem. Phys. 1986, 64, 111. 19. Freiser, B. S. In Techniques of Chemistry; Farrar, J. M.; Saunders, W. H., Jr., Eds.; Wiley: New York, 1988; Vol. 20. 20. Kemper, P. R.; Bowers, M. T. In Techniques of Chemistry; Farrar, J. M.; Saunders, W. H., Jr., Eds.; Wiley: New York, 1988; Vol. 20. 21. Adams, N. G.; Smith D. In Techniques of Chemistry; Farrar, J. M.; Saunders, W. H., Jr., Eds.; Wiley: New York, 1988; Vol. 20. 22. McEwan, M. J. In Advances in Gas Phase Ion Chemistry; Adams, N. G.; Babcock, L. M., Eds.; JAI: Connecticut, 1992; Vol. 1, Chapter 1. 23. Kebarle, P. In Techniques of Chemistry; Farrar, J. M.; Saunders, W. H., Jr., Eds.; Wiley: New York, 1988; Vol. 20. 24. Audier, H. E.; Berthomieu, D.; LeBlanc, D.; McMahon, T. B.; Morton, T. H. Int. J. Mass Spectrom. Ion Proc. 1992, 117, 327. 25. Dunbar, R. C. InAdvances in Gas Phase Ion Chemistry; Adams, N. G.; Babcock, L. M., Eds.; JAI: Connecticut, 1995; Vol. 2, Chapter 3. 26. Szulejko, J. E.; McMahon, T. B. Int. J. Mass Spectrom. Ion Proc. 1990, 109, 279. 27. Allemann, M.; Kellerhalls, Hp.; Wanczek, K. P. Int. ,1. Mass Spectrom. Ion Proc. 1983, 46, 139. 28. Kofel, P.; McMahon, T. B. Int. J. Mass Spectrom. Ion Proc. 1990, 98, 1. 29. Bennet, S. L.; Field, F. H. J. Am. Chem. Soc. 1972, 94, 5188. 30. Barlow, S. E.; Dang, T. T.; Bierbaum, V. M.J. Am. Chem. Soc. 1990, 112, 6832. 31. Moylan, C. R.; Dodd, J. A.; Han, C. C.; Brauman, J. I. J. Chem. Phys. 1987, 86, 5350. 32. Grabowski, J. J.; DePuy, C. H.; Bierbaum, V. M. J. Am. Chem. Soc. 1983, 105, 2565. 33. Lim, K.; Brauman, J. I.J. Chem. Phys. 1991,94, 7164. 34. Dodd, J.; Baer, S.; Moylan, C. R.; Brauman, J. I.J. Chem. Soc. 1991, 113, 5942. 35. Su, T.; Chesnavich, W. J. J. Chem. Phys. 1982, 76, 5183. 36. Paul, G. J. C.; Kebarle, P. J. Phys. Chem. 1990, 94, 5184. 37. Li, C. M.Sc. Thesis, University of Waterloo, 1990. 38. Audier, H. E.; Koyanagi, G. K.; McMahon, T. B., unpublished results. 39. Baer, S.; Brauman, J. I.J. Am. Chem. Soc. 1992, 114, 5733. 40. Blair, L. K.; Isolani, P. C.; Riveros, J. M. P. J. Am. Chem. Soc. 1973, 95, 1057. 41. Hop, C. E. C. A. Chem. Phys. Lett. 42. Dunbar, R. C.J. Chem. Phys. 1991, 95, 2537. 43. Pellerite, M. J.; Brauman, J. I. J. Am. Chem. Soc. 1980, 102, 5993. 44. Dodd, J. A.; Brauman, J. I. J. Phys. Chem. 1986, 90, 3559. 45. Caldwell, G.; Magnera, T. F.; Kebarle, P. J. Am. Chem. Soc. 1984, 106, 959. 46. van Doren, J. M.; DePuy, C. H.; Bierbaum, V. M. J. Phys. Chem. 1989, 93, 1130. 47. DePuy, C. H.; Gronert, S.; Mullin, A.; Bierbaum, V. M.J. Am. Chem. Soc. 1990, 112, 8650. 48. Viggiano, A. A.; Morris, R. A.; Dale, E; Paulson, J. F.; Giles, K.; Smith, D.; Su, T.J. Chem. Phys. 1990, 93, 1149. 49. Graul, S. T.; Bowers, M. T.; J. Am. Chem. Soc. 1991, 113, 9696. 50. Knighton, W. B.; Bognan, J. A.; O'Connor, P. M.; Grimsrud, E. P. J. Am. Chem. Soc. 1993, 115, 12079. 51. Vande Linde, S. R.; Hase, W. L. J. Phys. Chem. 1990, 94, 2778. 52. Vande Linde, S. R.; Hase, W. L. J. Phys. Chem. 1990, 94, 6148. 53. Vande Linde, S. R.; Hase, W. L. J. Chem. Phys. 1990, 93, 7962. 54. Cho, Y. J.; Vande Linde, S. R.; Zhu, L.; Hase, W. L. J. Chem. Phys. 1992, 96, 8275.

Unimolecular Dissociation of Gaseous Cluster Ions 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85.

85

Hase, W. L.; Cho, Y. J.J. Chem. Phys. 1993, 98, 8626. Tucker, S. C.; Truhlar, D. G.J. Am. Chem. Soc. 1990, 112, 3338. Herbst, E.; Dunbar, R. C. Mon. Not. R. Astr. Soc. 1991, 253, 341. Dunbar, R. C. In Unimolecular and Bimolecular Ion--Molecule Reaction Dynamics; Ng, C. Y.; Baer, T.; Powis, I., Eds.; Wiley: Chichester, 1994. Anicich, V. G.; Sen, A. D.; Hunters, W. T.; McEwan, M. J. J. Chem. Phys. 1991, 94, 4189. Kofel, P.; McMahon, T. B..1. Phys. Chem. 1988, 92, 6174. Fisher, J. J.; McMahon, T. B. Int. J. Mass Spectrom. Ion Proc. 1990, 100, 701. Th61mann, D.; McCormick, A.; McMahon, T. B. J. Phys. Chem. 1994, 98, 1156. Dunbar, R. C. Int. J. Mass Spectrom. Ion Proc. 1990, 100, 423. Dunbar, R. C. Mass Spectrom. Rev. 1992, 11,309. McCormick, A. M.Sc. Thesis, University of Waterloo, 1995. Norrman, K.; McMahon, T. B., unpublished results. Szulejko, J. E.; McMahon, T. B. Org. Mass Spectrom. 1993, 28, 1009. Kleingeld, J. C.; Nibbering, N. M. M. In Lectures Notes in Chemistry; Hartmann, H.; Wanczek, K. P., Eds.; Springer-Verlag: Berlin, 1982; Vol. 31. Audier, H. E.; McMahon, T. B.a. Am. Chem. Soc. 1994, 116, 8294. Savard, G.; Becker, St.; Bollen, G.; Kluge, H.-J.; Moore, R. B.; Otto, Th.; Schweilchard, L.; Solzenberg, H.; Weiss, U. Phys. Lett. A 1991, 158, 247. Audier, H. E.; McMahon, T. B., unpublished results. Th61mann, D.; Tonner, D. S.; McMahon, T. B. J. Phys. Chem. 1994, 98, 2002. Grimsrud, E. P.; Kebarle, P. J. Am. Chem. Soc. 1973, 95, 7939. Hiraoka, K.; Grimsrud, E. P.; Kebarle, P. J. ,I. Am. Chem. Soc. 1974, 96, 3359. Hiraoka, K.; Misuze, S. Chem. Phys. 1987, 118, 457. Perrin, J. Ann. Phys. 1919, 11, 5. Steinfeld, J. I.; Francisco, J. S.; Hase, W. L. Chemical Kinetics and Dynamics; Prentice-Hall: Englewood Cliffs, N.J., 1989. Langmuir, I. J. Am. Chem. Soc. 1920, 42, 2190. Atkins, P. W. Molecular Quantum Mechanics, 2nd ed.; Oxford University: Oxford, 1983. Tonner, D. S.; Th61mann, D.; McMahon, T. B. Chem. Phys. Lett. 1995, 233, 324. Shimanouchi, T. Tables of Molecular VibrationalFrequencies; NSRDS--NBS 39; U.S. Department of Commerce: Washington, D.C., 1972; Consolidated Vol. I. Dunbar, R. C..1. Phys. Chem. 1994, 98, 8705. Wei, D.; Salahub, D. R.J. Chem. Phys. 1994, 101, 7633. Tonner, D. S. M.Sc. Thesis, University of Waterloo, 1994. Okamura, M.; Yeh, L. I.; Meyers, J. D.; Lee, Y. T.J. Chem. Phys. 1986, 85, 2328.

This Page Intentionally Left Blank

N EW APPROACH ES TO ION TH ERMOCH EMISTRY VIA DISSOCIATION AND ASSOCIATION

Robert C. Dunbar

Io II.

III.

IV.

V. VI.

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction: Some Thermochemical Quantities Defined . . . . . . . . . . . . . Time-Resolved Photodissociation (TRPD) . . . . . . . . . . . . . . . . . . . . A. T R P D in the F T I C R Ion Trap . . . . . . . . . . . . . . . . . . . . . . . . B. Results for Specific Systems . . . . . . . . . . . . . . . . . . . . . . . . . Radiative Association Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . A. Metal Ion--Benzene Complexes . . . . . . . . . . . . . . . . . . . . . . B. Methyl-Substituted Benzenes . . . . . . . . . . . . . . . . . . . . . . . Thermal Dissociation by Ambient Infrared Radiation . . . . . . . . . . . . . A. Cluster Ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Tetraethylsilane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix: From R a t e - E n e r g y Curves to Bond Strengths . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Advances in Gas Phase Ion Chemistry Volume 2, pages 87-124. Copyright 9 1996 by JAI Press Inc. All rights of reproduction in any form reserved. ISBN: 1-55938-703-3 87

88 88 92 92 94 102 104 106 108 109 112 115 116 121 121

88

ROBERT C. DUNBAR

ABSTRACT The convenience and power of the FTICR ion-trapping mass spectrometer for studying slow kinetic processes leads to new ways of determining thermochemistry and bond strengths for gas phase ions. Three such approaches are discussed. (1) Dissociation rates measured as a function of ion internal energy by the time-resolved photodissociation technique can be extrapolated to zero rate to obtain the true threshold. A discussion of rate-energy curve extrapolation methods is appended. A number of dissociation energy assigmnents from use of this approach are reviewed. (2) The kinetics of formation of ion-neutral complexes by radiative association is a strong function of bond strength. By carefully accounting for other factors, including the surrounding temperature and the heat capacity and radiative properties of the complex, the bond strength can be assigned from the measured association rate. Examples are given for metal ion--benzene complexes and methyl-substituted benzene ion dimerizations. (3) Fairly weakly bonded ions can dissociate thermally at ordinary temperatures in the background equilibrium radiation from the walls. We have developed this as a quantitative route to bond strength determination. Approaches to the derivation of accurate dissociation energetics are described, and examples are given for cluster ions and for the tetraethylsilane ion.

INTRODUCTION: SOME THERMOCHEMICAL QUANTITIES DEFINED The determination of thermochemistry and bond strengths for gas phase ions is highly developed, with many experimental approaches and a large body of data. There is, however, still room for more powerful methods, and large territories of thermochemical values are still poorly explored. In particular, the number and reliability of measurements drop off sharply for larger ions, and thermochemistry in the emerging area of cluster ions and complex ions is being worked out intensively. The low-pressure ion-trapping environment of the Fourier transform ion cyclotron resonance (FTICR) instrument 1has some interesting possibilities for new ways of looking at bond energies, arising from the unique ability to study very slow kinetic processes on timescales of milliseconds or seconds. Much of the recent work of our group has been concerned with exploring the application of the FTICR ion trap to several kinds of slow kinetic processes and with thinking about the thermochemical information that can be derived from such measurements. We will describe three different kinds of investigation here from this point of view. First, the time-resolved photodissociation experiment gives a direct view of the kinetics of bond cleavage, which easily leads to bond strength information. Our laboratory has done most of the work so far reported in this area, and this chapter gives a fairly complete overview of the work. Second, radiative association kinetics is an area that is being actively explored by a number of groups, using several types of ion-trapping instruments, as well as other types of mass spectrometers. Our group

New Approaches to Ion Thermochemistry

89

has taken a unique interest in the application of these kinetics to determining bond strengths in radiatively stabilized complex ions. Although this idea is still in an early stage of development, its power as a precise quantitative tool is becoming clear, as the examples given here illustrate. Third, the low-pressure (or "zero-pressure") thermal radiation-induced dissociation of weakly bound ions is a very new idea, whose potential application as a thermochemical tool is only beginning to be explored. Our intention here is certainly not to survey either ion thermochemistry or methods for its study, but to describe and illustrate some new approaches particularly related to the ion-trapping FTICR instrument. The NIST tabulation 2 describes many of the standard techniques and collects most of the existing data. Reference 3 is a useful source of bond strength data and techniques for smaller ions and molecules, and Ref. 4 tabulates bond strength information for many cluster ions. Ion dissociation energetics are described by several terms that have often been used rather loosely. They are now being measured with sufficient precision by various techniques that it is important to be careful about the definitions of the various quantities. Figure 1 indicates the important energies on a schematic potential energy diagram showing the variation of potential energy along the reaction coordinate for two dissociation processes, one barrierless, and the other having a significant barrier. We will try to hold carefully to the following definitions:

Eintemal

Er] A+ E~

+B

BDE

AB+

Reaction Coordinate Figure 1. Potential energy plots along the reaction coordinate for two dissociation reactions, one with a barrier (Eo > BDE), and the other barrierless (Eo ~ BDE).

90

ROBERT C. DUNBAR

Thermochemical threshold, bond strength, bond dissociation energy (BDE) are equivalent terms giving the enthalpy difference (at temperature T) between parent ion and fragments for the dissociation, AB + --)A + +B,

(I)

BDE(T) = A/~f, T(A+) + A/~f, r(B) - A/~f, r(AB +)

(2)

that is,

where A/-/~f,r(X) is the standard heat of formation of X at temperature T. With this definition, the bond strength is a well-defined quantity even if the actual dissociation involves multiple bond breaking (as in the ferrocene ion discussed in Section liB) or extensive structural rearrangement (as in the halotoluene ions). The thermochemical threshold or BDE depends on the temperature. At zero kelvin, it is the potential difference between parent ion and products (see Figure 1). At nonzero temperature, there is an additional enthalpy correction that can be significant, BDE(T) = BDE(0 K) + H~

§ + H~

- H~.(AB+),

(3)

where H~(X) = H ~r, rotation(X)+ H ~7".vibration(X)+ H ~r, electronic(X)+ 5/2RT.

(4)

Here H~(X) is the enthalpy of X at temperature T, defined such that H~ is zero at zero kelvin. True threshold, critical energy (Eo) is defined as the energy that must be added to the ground-state ion to surmount the potential barrier to dissociation (see Figure 1). The true threshold is the intemal energy value at which (in principle) products just begin to appear (ignoring tunneling), although in practice, for larger ions, the probability of fragmentation on the experimental timescale is apt to be extremely small for internal energies in the vicinity of E o. The difference between the true threshold and the (zero kelvin) thermochemical threshold is called the reverse activation barrier, labeled E r in Figure 1. The true threshold E o is defined only as a zero-kelvin number, because at finite temperatures (for which the Boltzmann tail of the thermal population extends to arbitrarily high internal energy) there is no energy deposition value below which there is zero probability of observing fragments. The critical energy E 0 of transition-state theory is often taken to be the same as the true threshold, although this identification may not be strictly valid for barrierless dissociations and becomes problematic when rearrangements accompany dissociation. Apparent threshold, appearance energy, appearance potential is defined as follows. For a particular apparatus operated at a given temperature and a given sensitivity for fragment ion detection, and a given amount of time being allowed for fragmentation to occur, there is an apparent threshold Eapp at which fragments

New Approaches to Ion Thermochemistry

91

/"

Kinetic Shifts (Tight Transition State) 7-

Eo

.1 eV

,, '

6

E o = 1 . 8 6 eV-.

~5

.

r

~22 1 -

d ,"

~

~

. - "

0

0

, l.--"

I

50

Conventional

-

--,--Intrinsic

=,'~..,.-" '

I

100

'

I

150

'

I

200

'

I

250

'

300

Degrees of Freedom Figure 2. RRKM calculations of the kinetic shift for model hydrocarbon ion dissociations as a function of ion size. Calculations are shown both for a fairly weakly bonded ion (1.86 eV) and a fairly strongly bonded one (3.10 eV), and in each case both the conventional and the intrinsic kinetic shifts are plotted.

just become observable. This energy value is clearly dependent on the apparatus and its mode of operation, as well as on the temperature of the parent ions. The traditional "appearance energy" for fragment ions was either reported as equal to Eapp or was corrected from Lapp by one of a variety of procedures intended to correct for kinetic and/or thermal shifts. The reliability of such appearance energy values for larger systems is not good. As an illustration of when one should expect serious kinetic shift difficulties in measuring dissociation thresholds, Figure 2 shows some example RRKM model calculations, using a moderately tight transition state (AS~0oo K = 2 eu.; see Section VI for more discussion). Some time ago our group defined two quantitative measures of the kinetic shift that have proven useful: The "conventional" kinetic shift is defined with typical mass spectrometer operation being assumed, such that a fragment signal will be just observable if 1% of the ions dissociate within 10-5 s. The "intrinsic" kinetic shift is defined with the assumption that 10% of the ions must dissociate within 10-2 s, beating in mind that a dissociation will never be observable if its rate is not competitive with the rate of infrared radiative deactivation of the excited ion, which typically 6 occurs at about 100 s-1. As the figure

92

ROBERT C. DUNBAR

suggests, the kinetic shifts depend strongly on the size of the ion and also on the strength of the bond being broken. Interestingly, significant kinetic shifts appear rather suddenly at around 20-30 degrees of freedom and then rise approximately linearly with the number of intemal degrees of freedom of the ion. 7 It can be seen that severe kinetic shifts of the order of 1 eV or more should typically come into play somewhere in the region of 30 to 100 degrees of freedom (12 to 35 atoms), depending on the bond strength and on whether the conventional or the intrinsic shift is of concem.

II.

TIME-RESOLVED P H O T O D I S S O C I A T I O N

(TRPD)

A. TRPD in the FTICR Ion Trap The straightforward strategy for measuring a bond strength is to put progressively increasing amounts of intemal energy into the ion and observe the threshold at which bond cleavage begins. For larger ions, this strategy is decreasingly useful, as the dissociation becomes slow near threshold (the kinetic shift), and the Boltzmann distribution of internal thermal energies in the molecule becomes broad (thermal shift). Thermal shifts can in principle be overcome by cooling of the molecule, although this is not easy in practice for large molecules of low volatility. Kinetic shifts cannot be overcome by use of very long observation times, because the emission of infrared light from the excited ion provides an ion deactivation path that becomes competitive with dissociation on a timescale of milliseconds (the intrinsic kinetic shift). Since ion dissociation rates decrease dramatically with increasing number of degrees of freedom, this problem escalates rapidly with increasing size (number of atoms) of the ion (Figure 2). To get around the problems of kinetic and thermal shifts, recent accurate determinations of dissociation energetics have often followed the strategy of measurement of the dissociation rate at known intemal energies, and extrapolation to zero rate to determine the true threshold. The first work using this approach employed photoelectron-photoion coincidence (PEPICO) to generate ions of known intemal energy. 8'9 The success of this approach with use of both laboratory light sources and synchrotron sources is well known, and has given high-confidence thresholds for a number of dissociations of medium-sized ions. Dissociative resonance multiphoton ionization has more recently been successful for a small number of systems. 1~ Our work with the ICR ion trap has shown that photodissociation of already-ionized molecules is another viable way of observing ion dissociation kinetics of ions with known internal energy. This time-resolved photodissociation (TRPD) approach has been applied to a number of ions, some of them confirming and extending the PEPICO results, and others measuring dissociation energies of previously poorly characterized dissociation reactions. As compared with PEPICO, the TRPD approach has the advantage that it can be done just as well on fragment ions and reaction product ions as on molecular ions of available neutral molecules.

New Approaches to Ion Thermochemistry

93

It can take advantage of the power of the FTICR instrument for preparation and observation of high-mass compounds that are unattractive for PEPICO work. PEPICO has the advantage of working conveniently over a wide range of ion intemal energies, whereas TRPD is limited by the constraints of available wavelengths that are absorbed sufficiently well by the target ion. In several studies, we have combined TRPD data with results obtained over a broader energy range by the time-resolved photoionization mass spectrometer (TPIMS) technique of Lifshitz's group, ll which is not fully energy resolved but provides a successful complementary technique to TRPD, as shown in the examples below. In practice, a TRPD experiment follows the straightforward approach of generating and thermalizing the target ion in the ion trap, photoexciting it with one or more photons of pulsed laser light, and recording the subsequent buildup of fragment ions as a function of time. Figure 3 shows the appearance of typical TRPD mass spectra as a function of delay after the photoexcitation laser pulse, and Figure 4 shows plots of results for the two isotopic naphthalene ions. 12 Our group spent considerable effort developing the extraction of dissociation rate constants from such curves by deconvolution of the ICR signal equation and the thermal distribution of intemal energies. 13'14 Reliable dissociation time constants are available using this technique from a lower limit of the order of one microsecond (limited by the cyclotron frequencies of the ions) up to an upper limit of tens of milliseconds lOO-

C10D8+ TRPD Mass Spectra

>., (n c

CtoD6 +

.c_ r" ._0) 5 0 u) (1) .> (1) n-

1610 psec

CloD7 +

,,~.~_,_.___~

210 ~sec

10 I~sec o-

No light I~)

100

m/z

120

140

160

Figure 3. Slow dissociation of naphthalene-d8 ions resolved by TRPD. Naphthalene ions were generated by multiphoton ionization of naphthalene vapor at 193 nm. After thermalization for about 5 s at 3 x 10-8 torr, they were photoexcited by two photons at 355 nm, using an 8-ns pulse from the Nd:YAG laser. The plots show the extent of fragment ion signal observed at several delay times following the laser pulse and the competitive slow fragmentation to give the CIoD~, CIoD~, and CsD~ products.

94

ROBERT C. DUNBAR

A w

100 "~

80

g

60

~

40

Naphthalene

(C10H8+)

TRPD plot

20

100 =9

80 60

Naphthalene (CloD8 +)

O

~

40 20 0

1000

2000

3000

4000

5000

6000

7000

Time (tas)

Figure 4. Illustrative TRPD curves, showing the appearance of the CaH~(CaD~) fragment ion from naphthalene ion (naphthalene ion-da) dissociation by two photons at 355 nm. The dissociation rates measured from these curves are 6.4 x 103 (2.4 x 103) s-1 at 7.10 (7.13) eV of internal energy. (Reproduced by permission from Ref. 12.)

(limited only by the interference of the collisional and IR-radiative relaxation processes of the photoexcited ion). Along with other groups, we have given thought to the extrapolation of the rate-energy data from the TRPD technique to determine the true threshold E 0 for dissociation. Some of these considerations are discussed in Section VI. Here, we proceed directly to a review and discussion of the results obtained by this technique for specific ionic systems.

B. Results for Specific Systems TRPD has been applied to quite a number of ion dissociations, yielding new thermochemical values as well as insight into the dissociation mechanisms of nonsimple systems. In keeping with the theme of this chapter, we will emphasize

95

New Approaches to Ion Thermochemistry Table 1. TRPD Results Interpreted as Simple Bond Cleavages Yielding Direct

Thermochemical Thresholds

Parent Ion Benzene

Bond

BDE (e V)

C6I-1~5-H

3.88

Phenyl (C6H5+)

1.2

C 17H~7

4.48 3.23 3.24 3.7

Naphthyl (Cl0H~) ot-Naphthyl (Cl0H~) CsHsNi § CsHsFe+

Fragment Ion

z3J'IrofIon (kJ moF I) 1152a

t-Bu Tri-t-butyl-benzene

(~--C(CH3)2+----EH3 /--t-Bti Naphthalene CIoH~'-H 1-Bromo-naphthalene Cl0H~ -Br Nickelocene CsHsNi+-CsH5 Ferrocene CsH5Fe§

518 b

1175a 1176a 1026b 1009b

Notes: a0 K. b298 K.

the cases w h e r e n e w and reliable dissociation t h e r m o c h e m i c a l values have resulted, but we will note as well s o m e systems w h e r e simple threshold information is o b s c u r e d by m o r e c o m p l e x mechanistic' situations. The T R P D results discussed here are s u m m a r i z e d in two tables: Table 1 s h o w s those cases w h e r e the T R P D results pertain to apparently simple bond cleavage dissociations and can be interpreted as giving reliable bond energies directly from E o. Table 2 shows a n u m b e r

Table 2. TRPD Results Interpreted with Rearrangements and Complex

Mechanisms

AHrof lon Parent Ion Cyanobenzene o-Iodotoluene m-Iodotoluene p-Iodotoluene Toluene Styrene Methylnaphthalene n-Propylphenyl ether Thiophenol

Fragments C6H~ + HCN C7H~ + I C7H~ + I C7H~ + I C7H~ + H C6H~ + C2H2 C l 1~ + H C6HsOH§ + C3H6 CsH~ + CS C4H4S§ + C2H2

E o (e V) 3.02 2.11 2.24 2.41 2.18r 2.43 2.25 1.47 3.2 2.9

Fragment Ion Benzyne (C6H4+) o-Tolyl (o-CH3C6H~) m-Tolyl (m-CH3C6H~) p-Tolyl (p-CH3C6H4+) Benzyl (CH2C6H5+) C6H~ Cl l ~ Barrier Competing channels

(kJ mol-I)

1321 a 1080b 1091 b 1083b 919a 993 a <869b'd

Notes: ao K. b298 K. CBasedon the decompositionof the compoundTRPD curve by Lifshitz(Ref. 19). aThis value is interpreted as an upper limit because it may represent the barrier for rearrangement to benzotropyliumion, analogousto the tolueneion system.

96

ROBERT C. DUNBAR

of cases where the TRPD dissociation process (or competing processes) was not simple bond cleavage, and some mechanistic understanding and discussion is needed in order to extract useful thermochemistry. Our first TRPD study, on chlorobenzene ion, 15 concerned a system where the rate--energy curve from PEPICO was well established, and the point of this work was to confirm that TRPD results were consistent with expectations. Most of our subsequent TRPD work has resulted in new thermochemical information, or in major strengthening of existing values, and will be worth discussing here from a specifically thermochemical point of view. The study of cyanobenzene ion 14 treated an ion whose thermochemistry was already well studied by PEPICO. 16However, the TRPD result was at a substantially lower internal energy, so that the measured dissociation rate of 5 x 103 s-1 at 4.10 eV internal energy was slower by more than an order of magnitude than the slowest dissociations probed by PEPICO. By extension of the known rate--energy curve nearer to threshold, this added quantitative confidence to the RRKM extrapolation and considerably strengthened the E 0 value for Equation (51) of 3.02 eV assigned +

C6HsCN + ~ C6H 4 + HCN

(5)

by Rosenstock et al. 16 The corresponding heat of formation of the benzyne ion is currently the standard value for this number. 2 The benzyne radical ion can also be accessed by dissociation of benzene ion. The recent dissociative REMPI measurements by Neusser and co-workers 1~ for the reaction, C6H~ ~ C6H~ + H2

(6)

were extrapolated by RRKM to give an E 0 of 3.74 eV, corresponding to a AH ~f,o of 1354 kJ mo1-1 for benzyne ion, which is significantly higher than the 1321 kJ mo1-1 derived from cyanobenzene ion dissociation. 14'16 This difference could be due to extrapolation errors, but it seems quite possible that it reflects a substantial reverse activation barrier in the benzene system [Equation (6)]. At present, it is most justified to take the lower value, 1321 kJ mol-l, as the best estimate of the (zero kelvin) heat of formation of benzyne ion. Methylnaphthalene ion 18 presented an interesting case where the dissociation energy was essentially unknown, because a kinetic shift of the order of 2 eV completely masks the true threshold in threshold appearance measurements. TRPD at two wavelengths, with RRKM extrapolation, assigned an E 0 of 2.25 eV for the loss of H from the molecular ion, shown in Equation (7). We found that this energy

CIoH7CH ~ ----)CIIH~ + H

(7)

was not much differentfrom the recentassignment of the extrapolatedE o for toluene ion dissociation, 5 suggesting that a consistent picture of these systems is emerging.

New Approaches to Ion Thermochemistry

97

The best guess at present is that both of these E 0 values represent rearrangement barriers on the way to the low-energy tropylium (benzotropylium) fragment ion structures. 19 Another ion for which the large number of degrees of freedom results in unmanageable kinetic shifts is the tri-t-butylbenzene ion, 2~ Equation (8). This is C6H3[C(CH3.)3] ~ ~ C17H~7 + CH 3

(8)

notable in being the largest ion for which a well-characterized rate-energy curve and a reliably extrapolated E 0 have been obtained by this (or any) technique. When the TRPD results at four wavelengths were extrapolated by RRKM theory, an E 0 of 1.2 eV was found for the cleavage of a methyl group from the molecular ion. Gratifyingly, this bond strength was the same as that previously assigned (by PEPICO) to the t-butylbenzene ion, 2~ indicating that in a thermochemical sense the additional t-butyl groups in the larger ion are acting as inconsequential spectators, just as one would expect. This is a graphic illustration of the idea that addition of remote substituents to a framework like t-butylbenzene ion will have the effect of reducing its dissociation rate by many orders of magnitude, while at the same time having little or no effect on the bond strength of the dissociating group. Recently, we have given attention to the metallocene systems. As well as having a rather large number of degrees of freedom, these ions have quite high bond strengths, so that, as suggested by Figure 2, they are subject to extraordinarily severe kinetic shifts. Thus ferrocene 22 [Equation (9)] and nickelocene ions 23 [Equation (10)], the two cases completed so far, have conventional kinetic shifts of more than Fe(CsHs) ~ __~ Fe(CsHs) + + C5H5

(9)

Ni(CsHs) ~ ~ Ni(CsHs) + + CsH 5

(10)

2 eV, and intrinSic kinetic shifts of near 1.5 eV. Nevertheless, TRPD measurements with RRKM extrapolations are successful in extracting believable E 0 values, which are thought to be good estimates of the thermochemical thresholds. The thermochemistry of these ions is interesting, and is summarized in Table 3. One thing to note is that the metal-Cp bond strength is significantly stronger for the ion than for the corresponding neutral, probably reflecting simple electrostatic attraction between the charged metal and the Cp ring in the ionic cases. Second, the bond strengths in the ferrocene system are stronger than in the nickelocene system, presumably reflecting the presence of more electrons in antibonding orbitals in nickelocene. Third, to dissociate the first ligand from either ferrocene ion or nickelocene ion is significantly easier than to remove the remaining ligand; this is a normal situation for successive ligand removal from a metal ion, and may reflect electrostatic effects and/or electronic bonding effects.

98

ROBERT C. DUNBAR Table 3. Thermochemistry of Metallocene Ring Dissociations (eV) a'b M+CP2 --> M+Cp --->M +

NiCp2 Average BDE BDE (lst dissociation) BDE (2nd dissociation)

2.88

NiCp~ 3.59 3.24 + .07

F~Cp2 3.40

3.96 + .07

F~Cp~ 3.97 3.7 + .3 4.3 + .3

Notes." aCp is the cyclopentadienyl ligand CsHs.

bFor sources and further discussion of these data see Ref. 23.

As discussed in Section VI, the benzene ion 24 is the polyatomic ion that has received the most careful attention regarding the extrapolation of rate--energy data to find the true thermochemical threshold [Equation (I 1)]. The TRPD results over C6H~ --~ C6H~ + H

(11)

the range 4.48 to 4.79 eV were combined with the REMPI data of Neusser and co-workers 1~ over the range 4.57 to 5.55 eV to give the experimental rate-energy curve over a usefully wide energy range (Figure 5). Because benzene ion has a rather fast IR-radiative cooling rate, z5 the effect of radiative relaxation on the measured rate--energy points becomes important at the low end of the energy range. Based on previous IR cooling measurements on the ion, 25 an IR photon emission rate of 700 s-1 was expected, which would significantly distort the slope of the apparent rate--energy curve at the low end. In view of the uncertainty this introduces in the experimental points, it was particularly valuable to have a parameter-free, nonadjustable theoretical curve shape available from variational RRKM calculations. 24 It was found that the observed experimental values deviated from this expected curve shape just as predicted for the effects of IR radiative relaxation. When the correction for IR radiation was applied, the experimental points followed the variational RRKM predicted curve over the entire energy range, a fitted E 0 of 3.88 eV being used, as shown in Figure 5. This E 0 value is 0.23 eV higher than that derived by Neusser and co-workers. As discussed in Section VI, 0.07 eV of this discrepancy arises from the difference between the extrapolated values of the variational RRKM approach versus the simple RRKM approach. The remaining difference of 0.16 eV arises from the difference between our treatment and Neusser's of the low-energy portion of the fit, which reflects our inclusion of the IR-radiative relaxation effects in the data fitting. Our resulting A/-/~f,0 value of 1152 kJ mo1-1 for phenyl cation is in reasonable accord with the tabulated value of 1141 + 10 kJ mol-l from iodobenzene ion fragmentation, 26 and is in good accord with bond strength data for the benzene neutral. 3 In considering phenyl cation thermochemistry, note the problems intro-

New

C6H6 + ~

T,9 I/)

v

0

C6H5 + + H

5

r

2

99

Approaches to ion Thermochemistry

"J9

4 3

........ Variational RRKM ------- Simple RRKM 1

I

4.0

I

4.2

4.4

4.6

4.8

,

I

I

m

5.0

5.2

,

I

5.4

=

I

5.6

,

I

5.8

.

6.0

Eintema I ( e V )

Figure 5. Rate--energy curves for benzene ion dissociation. Circles are TRPD points (corrected for IR-radiative relaxation) from Ref. 24; squares are REMPI points from Ref. 10. The two points with (,) symbols are TRPD points uncorrected for radiative relaxation. The curves are from variational RRKM, with E0 = 3.88 eV, and simple RRKM, with E0 = 3.81 eV.

duced by the existence of multiple low-lying electronic states of the ion. The present value from benzene ion dissociation is considered to correspond to the lowest triplet state, which correlates with the benzene ion reactant. The phenyl cation ground state is a singlet state lying about 20 kJ mol-~ lower. Thus a lower z~f, 0 value would be expected from equilibrium measurements or from photoionization of the phenyl radical. It is not known which fragment ion state is reflected in the iodobenzene ion dissociation 26 that gives the tabulated value. 2 The studies of naphthalene 12 and bromonaphthalene ions 27 are companion studies in that they both access the thermochemistry of the naphthyl cation, C 10I-1~7,using a combination of TRPD energy-specific rate measurements with deconvoluted time-resolved photodissociation (TPIMS) results [Equations (12) and (13)]. In this CloH~ -~ CloH~ + H --~ C 10H~ + H 2

-~ CsH ~ + C2H 2

(12)

100

ROBERT C. DUNBAR Table 4. Aromatic C-H Bond Strengths (eV)

Neutral Radical cation

Benzene

Naphthalene

4.8 3.88

4.8 4.48

CloH7Br+ ~ C10H~ + Br

(13)

successful combination of techniques, the TRPD points provide absolute rate-energy points (see Figure 4), whereas the TPIMS spectra provide rate-energy information over a wide internal energy range. Together, they permit the rate-energy curve to be reconstructed with confidence over a wide range. The resulting thermochemistry is consistent between the two studies, as well as with independent thermochemistry for the CsH ~ fragment from naphthalene ion. A good value for the C-H bond strength in naphthalene ion having been assigned from these studies, it is interesting to look at the pattern of bond strengths in the aromatics, as shown in Table 4. It is clearly seen that removal of an electron from the aromatic system significantly weakens the C-H bonding, and that this effect is much stronger in the benzene case than in the naphthalene case. The dissociation ofiodotoluene ions has posed a complex puzzle in ion chemistry for many years, generating a large literature, but in a recent analysis of new TRPD data, along with prior information we offered, the hope that it is now understood in many respects. 28 It appears that two dissociation channels giving the same fragment ion at m/z 91 [Equation (14)] are in competition, cleavage yielding tolyl IC6H4CH ~ --4 CTH~ + I

(14)

ions, (CH3C6H~), and rearrangement yielding tropylium (C7H~) and/or benzyl (CH2-C6H~) ions. To make a long story short, we interpreted the TRPD results, along with previous information on dissociation rates, product ratios, kinetic energy releases, and thermochemistry, to give separated rate--energy curves for the two channels. Of interest here was the resulting assignments of E 0 values and AH ~ values for all three of the tolyl ion isomers, as given in Table 2. In the o-tolyl case, dissociation appears to go exclusively via cleavage in the energy region of the TRPD measurements, and we could assign E 0 with considerable confidence, giving the first useful thermochemistry of this ion. The toluene ion offers another long-standing puzzle, also involving the competition of two dissociation channels, yielding isomeric C7H~ products that have the same mass [Equation (15)]. Lifshitz's group has fully analyzed the kinetics of the C6HsCH ~ ~ C7H~ + H

(15)

New Approaches to Ion Thermochemistry

101

competing isomerizations and dissociations in this system. 19The TRPD curves 5 in the 2.7-3.1 eV region for hydrogen loss from C7H~,and for deuterium loss from C7D~, fit their picture (and in fact formed an important part of the basis for their analysis). The heat of formation of the benzyl cation of 919 kJ mo1-1 is confirmed from this analysis of the TRPD E 0 values. Since there is a barrier to tropylium ion formation, its heat of formation is not accessible from the toluene ion dissociation. 29 When TRPD measurements are combined with PEPICO results, the dissociation rate-energy curve for styrene ion is known over perhaps the largest of any polyatomic ion's range. 3~ Simple RRKM theory gives an excellent fit (as does Klots '31 thermodynamic formulation), and an extrapolated E 0 of 2.43 eV is derived. The thermochemistry for this dissociation to benzene ion plus acetylene [Equation (16)] is very well known from independent heats of formation, 2 giving a calculated C6HsC2H~- ._> C6H~ + C2H2

(16)

zero kelvin thermochemical threshold of 2.47 eV, in excellent agreement with the E 0 value from the styrene ion rate-energy curve. From a thermochemical point of view, this adds no new values, but does establish that for this dissociation, which involves a major structural rearrangement, the activation energy E 0 gives an excellent value for the true thermochemical threshold and rules out a reverse activation barrier. This underlines the point that the occurrence of a major rearrangement during dissociation does not, per se, imply a reverse activation barrier or invalidate the use of E 0 to derive thermochemistry. TRPD investigation of thiophenol ion dissociations (combined with additional information from TPIMS) 32 studied two competing dissociation channels whose thermochemistry was already well known [Equation (17)]. The time-resolved C6HsSH+ ~ C4H4S+ + C2H2 --~ CsH~ + CS

(17)

analysis confirmed that both channels displayed E 0 values corresponding well to the thermochemical thresholds. The only surprise in these results was the very loose transition state observed for the CS elimination channel, which was interpreted as implying a prior, non-rate-determining rearrangement transition state lying well inside the loose rate-determining transition state. Recent TRPD work on the rearrangement dissociation of the n-propylphenyl ether ion 33 [elimination of propene, Equation (18)] has shown that a substantial C6H5OC3H~ __) C6H5OH+ + C3H6

(18)

barrier exists in this dissociation path, so that the observed E 0 is significantly higher than the thermochemical threshold.

102

ROBERT C. DUNBAR

III.

RADIATIVE ASSOCIATION KINETICS

Radiative association 34'35 is the combination of ion and molecule to form a metastable complex that is then stabilized by emission of a photon: (19)

A + + B ~-- [A+B]* ---) A+B + hv.

The observation of such a low-pressure association reaction in the FTICR ion trap is illustrated in Figure 6, showing the association ofCd § with neutral benzene under conditions where collisional stabilization of the [A+B]" complex is unimportant. The emitted photon can in a few cases be a visible photon from an electronic transition, but for polyatomic molecules it is almost always an infrared photon emitted from a vibrational transition. The basis for use of the kinetics of this process as an avenue to binding energies is that the rate is extremely sensitive to the binding energy; this dependence is so strong that quite a good binding energy estimate can be made even with rate data of modest accuracy, and even in spite of the fact that there are otten uncertainties in the numerical values needed for the interpretation. The kinetics of an iotr--neutral association reaction are often considered in terms of the following scheme (see also Chapter 2): A+ + M ~

kf kb

~- (A+M)* ~

k~ kr

v'~ (A+M)

(20)

/

Four microscopic rate processes are considered: bimolecular formation of metastable complexes with rate constant kf; unimolecular redissociation of complexes to reactants with rate constant kb; complex stabilization by emission of an IR photon with first-order rate constant kr; and bimolecular collisional stabilization of complexes with rate constant kc. The strategy to draw rate constants from association data is to combine measurements of the association rate with some combination of theoretical calculations, other kinetic data, and empirical estimates, in order to assign values to these microscopic rate constants. After assignment of the redissocation rate constant kb, we can make an estimate of the bond strength through one of the approaches described in Section VI. Three general approaches can be applied to the problem of solving the kinetics of association to obtain kb: 1. Pressure dependence analysis. Kofel and McMahon 36 pointed out that if the apparent bimolecular association rate constant kapp is measured as a function of pressure, kr and kb can be obtained from the slope and intercept of the pressure plot, provided that kf and kr are independently known; ke is otten taken equal to the Langevin or ADO orbiting rate constant korb (the strong collision assumption), and kf is either taken equal to korb or is measured independently by high-pressure mass spectrometry.

New Approaches to Ion Thermochemistry

103

Cd + + C6H6 ~

Cd+C6H6

1

Cd +

~

o ,

80

.........

, .........

, .........

120

, .........

, .........

164:) m/z

, .........

, .........

2,00

, ........

~o'"

Figure 6. Association reaction of Cd + with benzene. 53 Cd + was formed by laser desorption/ionization from a cadmium-contaminated stainless steel surface and allowed to react with benzene at a pressure of about 5 x 10-8 torr. The spectrum shown is for a 6 s reaction time, after which the ions were excited by impulse excitation and detected by FTICR. The multiplets show the cadmium isotope pattern.

2. Standard hydrocarbon estimation. 37 Measurement of the low-pressure radiative association rate constant kra is sufficient for assignment of kb, if kr and kf are independently known, from the relation, 36

kr

kfkr

(21)

in which kr is usually taken equal to the orbiting rate constant ko~b, and k~ can be estimated by use of the semiquantitative estimation approach of Ref. 37. This approach takes the view that IR radiative strengths of hydrocarbon-type ions are all similar to a first approximation (after sealing by the size of the ion, since larger ions have more IR-radiating normal modes than small ions). Reference 37 assigns the numerical values for this scheme according to the standard hydrocarbon model, and gives a practical scheme for relating radiative association observations to complex binding energy. Reference 38 elaborates this idea in the context of low-temperature interstellar processes, including the possibility of exothermie reaction channels for the complex, and the use of improved PST calculations of kb. 3. Ab initio calculation of radiative intensities. Quantum calculations are now capable of giving reasonably believable values for the absolute IR emission intensities of normal modes of medium-sized ions, which gives the possibility of direct, nonempirieal assignment of k~. This leads to the assignment of the complex

104

ROBERT C. DUNBAR

binding energy in the same way as in the previous approach, but without the uncertainty of the empirical estimation. The AI+C6H6 case, described below by way of approaches 1 and 2, is the first example where it will be possible to apply this third approach. 39 A considerable body of work has been described on radiative association kinetics, both for small systems of direct interest to interstellar modeling, 34'4~and also for larger systems of interest both from the interstellar standpoint and from a more general chemical the point of view (see Refs. 35-37, 41-51 for some examples). Among these larger systems, most studies are of deliberately chosen systems where the complex binding energy is already reasonably well known, in order to expand and solidify our understanding of the radiative association process. However, one or two studies have given thermochemical information about less well understood complexes, 49'51 and we expect this point of view to become increasingly important. To illustrate the thermochemical aspect of radiative association studies, we will describe here two systems of current interest where we have deliberately set out to use the potentially high precision of this approach to verify and improve previously assigned bond strengths.

A. Metal Ion-Benzene Complexes As one illustration, we can consider association kinetics data recently reported by St6ckigt et al. 52 for the reaction: A1§ + C6H6 ~ AI+C6H6"

(22)

The bimolecular rate constant for this process at 300 K was measured as 1.7 x 10-12 cm 3 molecule-1 s-I (in the limit of zero pressure, where three-body collisional association is negligible). They also determined the termolecular collisional association rate constant to be 1.2 x 10-22 cm 6 molecule-1 s-1. By use of the pressure dependence method of analysis (approach 1 above), their data were analyzed to give the average rate of IR photon emission from the energized complex, kr= 16s -1 and the average rate ofunimolecular dissociation of the energized complex back to reactants: kb = 1.6 x 104 S-1. The association rate data determined in this study can be used to make quite a precise binding energy estimate for the aluminum ion-benzene complex. The relation between the association rate constant kra and the binding energy was made with use of phase space theory (PST) to calculate kb as a function of E b, with a convolution over the Boltzmann distribution of energies and angular momenta of the reactants (see Section VI). PST should be quite a reasonable approximation for

New Approaches to Ion Thermochemistry

105

this fairly weak complex dissociating into two heavy fragments, and we take the PST prediction of kra to be reliable within a factor of two. Thus, using the experimentally derived kr and the PST relation between kra and E b, we can calculate kraaS a function of E b, as displayed in Figure 7. Figure 7 shows how the experimental radiative association rate constant of 1.7 x 10-12 cm 3 molecule -I s-~ combines with the calculated curve to give a fitted binding energy of 1.53 + 0.10 eV, where the uncertainty is estimated from the uncertainty in the kr that was used in the PST calculation. The previous thermochemistry for this complex, as analyzed in Ref. 52, gives a value of 1.6 + 0.3 eV.

10-10

AI + + C6H 6 /

! r~

f

10-il O

/ ~0

J

J .

l 0-12

PST calculation Stockigt et al.

10 -13

'

1.2

I

1.4

'

I

'

1.6

I

1.8

2.0

Binding energy (eV) Figure 7. Determination of binding energy from the observed radiative association

rate. The solid curve is the calculation of kra as a function of the assumed binding energy of the AI§ complex, a Boltzmann distribution of initial reactant energies and angular momenta at 300 K being assumed, by use of the PST approximation for kb and the experimentally derived kr as described in the text. The square point displays the observed kra from Ref. 52, and it can be seen that this intercepts the calculated curve at a binding energy of 1.53 eV, with an estimated uncertainty of +0.1 eV. The interval on the binding energy scale, delimited by arrows, shows the assignment of this binding energy derived in Ref. 52 from previous data, and it is apparent that the assignment of Eb by the present approach agrees very well with the previous assignment but offers much smaller error limits. St6ckigt et al. s2 also made an ab initio calculation of the binding energy of 1.70 eV, which is not unreasonably far from the present result of 1.53 eV.

106

ROBERT C. DUNBAR

The present approach thus confirms the previous value, but with considerably better error limits. The standard hydrocarbon model, data analysis approach 2, does a poor job of estimating E b in this system (1.83 eV). This has led us to recognize 39 that the case of an atomic ion associating with a neutral is exceptional because of the small number of rotational degrees of freedom of the reactants. With an appropriate correction for this effect, the standard hydrocarbon model estimate is lowered to about 1.5 eV, which is an entirely acceptable estimate. This approach can obviously be carried on to look at other metal ions binding to to benzene. For instance, our group has determined the bond strength of Cd§ be 1.55 eV,53 and we are looking at other examples down the periodic table.

B. Methyl-Substituted Benzenes Another recent illustration of thermochemical information available from radiative association kinetics was a study of the association of several methyl-substituted benzene cations with their parent neutrals to form the dimer ions. 54 Mautner et al. 55 measured the enthalpies of dimerization some time ago by equilibrium in the high-pressure mass spectrometer source for these systems from benzene through trimethylbenzene (mesitylene), providing a chance to compare our results with reasonably reliable values. The data of Mautner et al. 55 included a surprising feature, which we might call the "mesitylene anomaly," which was that the bond strengths of the dimer ions declined steadily from benzene to xylene (dimethylbenzene) but jumped back up at mesitylene (trimethylbenzene). This trend was, however, not significant within their uncertainty, and it was interesting to see if it was reflected in the more precise comparison provided by radiative association rates, which are very sensitive to such small variations in binding energy. Figure 8 shows the observed rates for the complexes up to tetramethyl benzene (durene). These complexes are too weakly bound to be observed at room temperature under low-pressure conditions, so the experiments had to be done at reduced temperature, usually 196 K (dry ice temperature). We are not yet able to do as detailed a job of modeling this system as was described in Section IIIA for the benzene-metal ion complexes, but it is interesting to see how far we can get in estimating bond energies using the nonspecific standard hydrocarbon modeling scheme of approach 2 as previously described. This genetic model 37 predicts an approximate relation among the binding energy E b (in eV), the number of degrees of freedom of the complex, N, and the efficiency of radiative association, which is found to have the numerical values, loglo R (300 K) ~ 0.7Ebq-N - 9.6,

(23a)

loglo R (196 K) ~ 0.99Eb'fN - 10.6,

(23b)

New Approaches to Ion Thermochemistry 10-11

107

_

Mesitylene

,,7,u) "T,c.)

o 10 -12

Durene

r

m~

0

E O3

v

E to rL _

p-Xylene Toluene

10 -13 Benzene

o

247 K 9 196K

60

I

80

'

I

100

'

I

120

'

I

140

Degrees of Freedom of Complex Figure 8. Radiative association rate constants measured for dimerization of methylsubstituted benzene ions. s4 The binding energies derived from these measurements are shown in Table 5.

where R is the collisional efficiency of radiative association, calculated as kra/kor b, the Langevin orbiting rate constant korb (1.2 x 10-9 cm 3 molecule -~ s-l in this case) for the rate of formation of metastable complexes being used. Calculation of the E b values from the data in this approximation gives the estimates shown in Table 5. It is seen that the genetic approximation is quite good, giving E b values a few hundredths of an eV higher than the equilibrium numbers. More detailed analysis by the pressure dependence method, as in Ref. 54, indicates that this modest deviation is largely due to the complexes having a higher rate of photon emission (by a factor of 2 to 5) than assumed in the genetic scheme. The trend noted as the mesitylene anomaly is positively confirmed by these results, although we have no explanation as to why mesitylene dimer ion should be substantially more strongly bound than xylene dimer ion. The previously unknown value assigned in this way to the durene dimer ion binding energy is not surprising, but the fact that it is similar to mesitylene rules out the idea that the eclipsing methyl groups in this complex might substantially lower the binding energy. These results emphasize that the genetic modeling scheme is a useful source of fairly precise thermochemical information, even though the individual rate constants assumed may differ by

108

ROBERT C. DUNBAR

Table 5. Binding Energies Ebfor the Methyl-Substituted Benzene Dimer Cations

Based on Application of the Generic Standard Hydrocarbon Model to the Radiative Association Kinetic Data. Robsis the Efficiency per Collision of Radiative Association Robs

E b (Radiative E b (Equilibrium) Association) (e V) (e V) r

Benzene a

6 x 10-5

0.79

0.74

Toluene ( M e t h y l b e n z e n e )

1.3 x 10-4

0.73

0.70

p-Xylene (1,4-Dimethylbenzene)

2.8 x 10-4

0.70

0.68

M e s i t y l e n e (1,3,5-Trimethylbenzene)

6 x 10-3

0.77

0.75

D u r e n e b (1,2,4,5-Tetramethylbenzene)

9 x 10-4

0.79

0.77 a

Notes: aThe radiative association of benzene ion was not directly observed at 196 K. The value given is estimated from the measured k3, along with a kr of 7 s-l based on extrapolation of the kr values in Table 3 of Ref. 54. bThe measurement and the standard hydrocarbon prediction correspond to a temperature of 247 K. The other values are at 196 K. CValues from equilibrium measurements from Ref. 55. dThis binding energy was previously unmeasured. The value given is our assignment from Ref. 54, where a somewhat more elaborate fitting of the radiative association rate constant than the present very simple approach was carried out.

factors of two or three from reality. This success reflects the fact that kra is such a strong function of binding energy that errors in the assignment of the other parameters are strongly demagnified. IV.

THERMAL

DISSOCIATION

BY

AMBIENT INFRARED RADIATION

The possibility of thermally activated ion dissociation being used as a thermochemical tool has been around quite a long time. 56 However, this has not come to much in the past because of the experimental difficulties of heating a mass spectrometer sufficiently in order to cleave typical covalent bonds thermally, with further problems sometimes arising from surface chemistry. Recently, McMahon's group reinvigorated this idea with their observation of low-pressure thermal dissociation of a number of weakly bound cluster ions in the FTICR ion trap. 57'58 For the observation of dissociation of weak bonds it was unnecessary to use temperatures above room temperature, and low-pressure operation in the ion trap obviated any interfering surface reactions or ion--neutral reactions. They proposed that these dissociations were activated by exchange of thermal infrared radiation with the walls, an idea that received support from quantitative calculations by our group; based on our understanding of infrared absorption and radiation kinetics of gas phase ions, 59-61 we could confirm that absorption of blackbody infrared wall radiation was quantitatively able to produce the observed dissociation reactions.

New Approaches to Ion Thermochemistry

109

Our group has termed this process zero pressure thermal-radiation-induced dissociation (ZTRID). McMahon's group has continued to explore this new chemistry vigorously, and some of their findings are described in Chapter 2 of this volume. Our group's interest has centered on the possibilities of this experiment for accurate thermochemical determinations, building on our experience with quantitative study of infrared ion photodissociation kinetics using a laser s o u r c e . 59--61 We will describe here the basis for using ZTRID data to find accurate bond strengths, illustrating the idea with an example of a covalently bound ion studied in our instrument, and a collaborative study of cluster ions using data from McMahon's instrument. McMahon's group reported room temperature ZTRID values for dissociation of a number of cluster ions. 57'58 Particularly interesting for thermochemical analysis are recent measurements of the temperature dependence of several reactions, because the temperature dependence is directly related to the dissociation energy. A further promising development is the ab initio calculation of the absolute infrared intensities for the vibrational modes of two of these complexes, 62 which allows an independent derivation of E 0 from the data. For one of the complexes, (H20)3C1- , both the temperature dependence measurements and also the absolute IR intensity calculations have been done, and we have the opportunity to make an important comparison; the agreement of the dissociation energies derived by these two basically independent routes will provide a challenging test of the validity of ZTRID as a thermochemical tool.

A. Cluster Ions We will discuss here ZTRID bond strength determinations for the two clusterdissociation reactions,

(H20)2Cl- -->(H20)C1- + H20

(24)

(H20)3C1- ~ (H20)2C1- + H20.

(25)

and:

The measured dissociation rates constants at very low pressure are given in Table 6, and the temperature dependence as measured for Equation (25) is shown in Figure 9. The rate of ZTRID depends very strongly on the value of the dissociation energy E 0, but the relationship is not entirely simple. Having measured the dissociation rate, we must call on some theoretical analysis to make the connection that will enable us to derive a value ofE 0. We have discussed two approaches to doing this: 63 (1) The master equation modeling approach 59-61 amounts to a direct numerical simulation of the dissociation kinetics, in which E 0 is taken as an undetermined parameter to be adjusted to bring the simulation into agreement with experiment. As we will see below, this approach allows us to make a fully rigorous determination

110

ROBERT C. DUNBAR

Table 6. Thermochemistry Derived from the ZTRID Experimental Numbers (eV) E o or AH~ E o or AH~ (kdissapproach) (Ea approach)

kdiss (s-l) (I-I20)2C1- ---->(H20)CF

(H20)3C1- --~ (H20)2C1-

0.0024 (295 K) 0.11 (300 K)

0.45 0.32

0.31

z~a~ (ZTRID)

AHed98s (HPMS)

0.50

0.56b, 0.51c

0.41a

0.51b

Notes: aAverageof valuesfromthe two measurementapproaches. bRef.65. (Notethatwe believethesevaluesto be too high). CRef.62.

of E 0 to the extent that we can assign the needed optical properties of the ion accurately. (2) The Tolman theorem approach 63'64 takes the temperature dependence of the dissociation rate, views this as giving an activation energy E a for dissociation, and develops the relations that connect this activation energy withE 0. This approach illuminates the fact that the temperature dependence of the dissociation rate gives quite an accurate value of E 0, even if we know little about the ion's optical properties, and Ref. 63 provides an easily applied recipe for carrying this out. -1.4

(H20)3Cl-

-1.6

= (H20)2Cl- + H20

-1.8

'7, -2.0 .B "O V

C

-2.2

m

9

-2.4 E a -2.6

3.05

,

,

3.10

= 0.22 eV ,

,

3.15

,

=

3.20

,

,

3.25

,

,

3.30

,

,

3.35

,

,

3.40

,

3.45

1000/(T/K) Figure 9. Temperature dependence of the rate of low-pressure thermal dissociation of the (H20)3CI- cluster ion. (Data from Ref. 62.)

New Approaches to Ion Thermochemistry

111

Master Equation Modeling At low pressure, the only interactions of the ion with its surroundings are through the exchange of photons with the surrounding walls. This is described by the three processes of absorption, induced emission, and spontaneous emission (whose rates are related by the Einstein coefficient equations). In the circumstances of interest here, the radiation illuminating the ions is the blackbody spectrum at the temperature of the surrounding walls, whose intensity and spectral distribution are given by the Planck blackbody formula. At ordinary temperatures, this is almost entirely infrared radiation, and near room temperature the most intense radiation is near 1000 cm -~. If we know, or estimate, the infrared transition intensities for the ion, we can calculate the movement of the internal energy of the ion up and down the energy scale as it randomly absorbs and emits IR photons. This random walk on the energy axis can be treated either by direct random-walk simulations, 6~ or by solution of the master equation. 59'61'63 We have used both of these approaches. The master equation approach is easier to work with. To introduce ion dissociation into the kinetics, we can make the assumption that whenever an ion happens to absorb a photon that places its internal energy above the threshold E o, the ion immediately dissociates. (For larger ions, this assumption is inadequate because of kinetic shifts. Then we have to estimate the dissociation rate-energy curve, e.g., by RRKM calculations, and put the dissociation rate coefficients into the master equation matrix. This was not necessary for the examples described here, for which dissociation is fast near threshold.) Having put the dissociation process into the master equation matrix, we use the theorem that the dissociation rate constant is the lowest eigenvalue of the matrix to give the dissociation rate by simple matrix diagonalization.

Results for Cluster Ions For both cluster ions, the ZTRID rates for Equations (24) and (25) at room temperature (Table 6) were analyzed by the master equation method, the ab initio calculated IR intensities being used, 62 to give the fitted values of E 0 displayed in the Table. In addition, the temperature dependence of Equation (25) was fitted to the master equation simulation (the E a approach), to give an independent value of E 0 (0.31 eV) in excellent agreement with the value from the kdiss approach (0.32 eV). These values were corrected to 298 K by use of Equations (3) and (4) to give A/4298 (ZTRID). the BDE values displayed as "~'diss Literature values of "-~'diss A/-T298 are available from high-pressure mass spectrometry (HPMS) for these dissociations, 65 as shown in Table 6. The ZTRID values are significantly lower, and, particularly for (H20)3C1- , the discrepancy is much larger than the ZTRID experimental error. The strong evidence from the ZTRID analysis that these literature bond strengths are too high has led to a reexamination of the high-pressure equilibrium for the (H20)2C1- system, 62 resulting in a revision of the

112

ROBERT C. DUNBAR

HPMS value into good accord with the ZTRID value, as shown in the Table. We believe that the HPMS value for the (H20)3CV ion is also too high, and that the present ZTRID-derived value is to be preferred.

B. Tetraethylsilane We have seen that ZTRID can be successfully observed and interpreted for cluster ions. It is of interest to look as well at covalent molecular ions for new thermochemical information. The parent ion of tetraethylsilane illustrates these possibilities. 66 The ion is formed in ~adequate abundance directly in the FTICR cell by electron impact, and the more abundant triethylsilyl ion is readily removed by ion ejection. Temperatures substantially above room temperature are needed to give measurable ZTRID rates. Figure 10 shows the low-pressure dissociation chemistry at 403 K. At this temperature, some water vapor outgasses in the cell and reacts with the tetraethylsilane parent ion to give the Et3Si(H20) + ion, but this competing bimolecular reaction is well behaved and easily allowed for in the kinetic fitting. The parent ion undergoes the ZTRID process, Et4Si § ~ Et3Si § + Et

(26)

on a timescale of seconds. Pressure studies confirm that there is no collisional dissociation contribution to the kinetics at the pressure of these experiments, so this is a purely radiative thermal dissociation process. Temperature variation gives rate constants for the ZTRID reaction that can be plotted in Arrhenius form as in Figure 11. From the slope of the plot we can find an Arrhenius activation energy E a of 0.43 eV.

Master Equation Modeling As with the cluster ions, we can convert the E a value into a bond strength by doing master equation modeling with an accuracy limited only by our knowledge of the input parameters (most notably the IR absorption/emission properties of the ion.) The tetraethylsilane ion contrasts with the two cluster ions discussed previously in that, in this system, the absolute radiative strengths are not known. When this is the case, measurement of the ZTRID rate at one temperature gives us no information about E 0, but the temperature dependence of the dissociation still gives us a precise and useful way of determining E 0. In order to make this analysis by the master equation approach, we must assign a set of relative IR intensities to the vibrational modes, which can be done using the standard hydrocarbon model. 37The alternative analysis ofE a by the Tolman theorem approach described below, which does not depend on any IR intensity assignments, makes it clear that the choice of IR intensities is largely irrelevant to the final result derived from the temperature dependence. Application of the master equation procedure at several assumed temperatures gave a calculated value for the slope of In k,:tiss vs. T--1 that agrees with the

(a)

Experimental Pulse Sequence

e" beam

Quench

H-

Idle Time 8-18 sec

(b) 1.0

,

Detect

[I,,,,,,~

Thermalization

Delay

Tetraethylsilane Dissociation 9

L 8 08-J ~

I

9

I

'

!

9

Si(C2H5)4.

o t r

Eject

9

I

'

!

'

= Si(C2H5)3* + C2H5 I Si(C2Hs)3(H20)§ '

0

9

!

~

C

<

o.6-1

C

_o

.2 L-

.

u.o.2

oo 9

0

9

T

1

9

I

2

'

I

9

I

9

I

3 4 5 Reaction Delay Time (s)

9

I

6

'

7

Figure 10. (a) FTICR pulse sequence used in ZTRID work. The cell was allowed to equilibrate thermally during the idle time, after which ions were formed by electron impact ionization. Following thermalization, all ions except SiEt: were removed by cyclotron ejection, and the parent ion dissociation was allowed to proceed for a reaction time ranging up to about 10 s. The extent of fragmentation was sampled by FTICR detection at the end of the reaction period. (b) Low-pressure thermal dissociation of tetraethylsilane ion, showing the ZTRID dissociation and the competing bimolecular reaction with water. The pressure was 3 x 10-9 torr. Note that the first point, at 1 s reaction time, lies off the fitted lines, reflecting the fact that the ion population was not yet entirely thermalized at this time. The steady-state rate constants are derived from fitting data at longer reaction times where the ions are fully thermalized,

113

114

ROBERT C. DUNBAR -1.5

'

I

,

i

,

I

'

I

'

i

(C2H5)4Si*

-2.0

'

I

'

I

'

I

'

= (C2H5)3Si + + C2H 5

-2.5

-3.0 r 10

c

-3.5

...,...

-4.0

E a = 0.43

eV

-4.5 '

2.45

I

2.50

'

I

'

2.55

I

2.60

'

I

2.65

'

I

'

2.70

I

2.75

'

I

2.80

'

I

2.85

'

2.90

1000/(T/K)

Figure 11. Temperature dependence of the low-pressure thermal dissociation of

tetraethylsilane ion. The fitted line is the least-squares straight line, from which Ea is derived. The error bar suggests the uncertainty due to data scatter. The slope (and thus Ea) is estimated to be uncertain to _+10%.

experimental results shown in Figure 11 when the (zero kelvin) bond strength was taken to be: E o = BDE(Et3Si + - Et) - 0.71 eV.

Tolman Theorem Approach The corrected Tolman theorem that uses a truncated Boltzmann approximation provides a much easier approach for converting E a into a bond strength. 63 In a case like the present one, where the IR radiative strengths are not known accurately, it is probably no less reliable than master equation modeling, and far easier to carry out. This approach was described and tested in some detail in Ref. 63, and a brief summary will be enough here. The classical Tolman theorem relates the Arrhenius E~ to the bond strength E 0 for reactions in the high-pressure limit where thermal equilibrium of the dissociating reactant population is always maintained. It can be reformulated and corrected to apply to the zero pressure, radiation-activated system. 63 The exact solution has several complicated terms, but the small terms can be estimated, yielding a very good approximate relation: E 0 = E a + < E ' > - 0.04 eV.

(27)

New Approaches to Ion Thermochemistry Table 7.

115

Comparison of E0Values Derived from the ZTRID Temperature Dependence by Two Approaches (eV) E a (ZTRID)

<E'>

E 0 (Tolman)

Et4Si §

0.43

0.31

0.70

0.71

(H20)3C1-

0.22

0.11

0.29

0.31

E o (Master Eq.)

Here <E'> is the average energy of the parent ion population under conditions of reactive depletion, as discussed in detail in Ref. 64. Exact assignment of <E'> requires master equation modeling and is thus difficult, but in Ref. 63 we showed that the tnmcated Boltzmann picture gives a simple, and quite accurate, approximation. The prescription is to take the thermal Boltzmann distribution of molecular internal energies, truncate it at the energy (E 0 - 1/2hvav) (where hVav is the peak photon energy of the blackbody distribution), and set <E'> equal to the average energy of this truncated distribution. E0, calculated from E a in this simple way, is found to agree with the master equation fit within one or two hundredths of an eV. For the examples described here, where the temperature dependence of kdiss w a s analyzed both by master equation modeling and by Equation (27), it is interesting to see how well the Tolman theorem approximation compares with the detailed modeling. This is shown in Table 7 for the cases of tetraethylsilane ion and (H20)3C1-. It is seen that these two approaches give nearly identical results.

V. C O N C L U S I O N Three approaches to ion thermochemistry have been described that are diverse in their underlying strategies but have in common the use of the FTICR ion trap to make accessible very slow kinetic processes. The TRPD approach is a well-established and successful source of rate-energy data and bond strength information. An obvious future area for fruitful application is in the dissociation of ions that are not molecular ions of stable neutrals. For instance, the bond energies of numerous transition-metal complex ions have been bracketed by ion neutral reactions and by photodissociation threshold determinations, but we can hope for an order-of-magnitude greater accuracy by TRPD determination of the rate--energy curve. As a different sort of example, the TRPD study of H cleavage from the fragment ion phenyl cation, C6H~, could improve the thermochemistry of benzyne ion. Finally, many cluster ions like the carbon clusters have very uncertain energetics, which could be clarified by TRPD measurements. As a promising step in this direction we have been able to observe a TRPD c u r v e 67 for C 1 loss from C~l. The derivation ofthermochemical information from radiative association seems to have promise for precise and rapid relative bond strength comparisons among related complexes. Comparisons among different metal ions binding to the same

116

ROBERT C. DUNBAR

ligand, as suggested by the examples described here, seem ideally suited to this technique. For extensive work along this line, it is desirable to have temperature control of the ion trap, since it is desirable to be able to work at a temperature where the radiative association in a particular system is slow (for discrimination), but not so slow as to make observation hard. Temperature adjustment is the only way of tuning the association efficiency in a given system into a convenient range. Low-pressure thermal dissociation, ZTRID, is only at the threshold of application to bond strength problems. It is inherently best suited to weakly bonded systems. Room temperature studies are appropriate to bond strengths in the 0.5 to 1.0 eV region.

VI. APPENDIX: FROM RATE-ENERGY CURVES TO BOND STRENGTHS All of the approaches to bond strength measurement that are based on observation of dissociation (photodissociation, dissociative photoionization, dissociative electron impact ionization, collision-induced dissociation, etc.) face the same set of questions about how to relate the observed dissociation rates to the true threshold. Problems come from two sources: first, the thermal shift (the effect of the thermal internal energy of the parent ions), and second, the kinetic shift (the effect of the slow unimolecular dissociation of the ions). For ions of up to six or eight atoms, these effects are small, and it is easy either to ignore them or to make simple approximate corrections. However, these effects become rapidly overwhelming for ions with a dozen or more atoms, and careful treatment is necessary before bond strengths can be derived with even semiquantitative validity. For larger ions, techniques that do not include energy or time resolution (namely, dissociative electron impact and dissociative photoionization) are especially difficult to quantitate. In the methods considered in this chapter, the dissociation rate is typically measured for some known internal energies well above the true threshold. An essential consideration then is how to extrapolate from the observed rates back to the true threshold. This is not a trivial question and has received quite a lot of attention. Three approaches used in recent work are worth description and commentary.

Fitting to Detailed Theory The most satisfactory situation for making an extrapolation of rate data to the true threshold arises when the threshold is uncertain, but we can confidently calculate the functional form of the rate-energy curve from accurate kinetic theory. For small systems, it is feasible to calculate dissociation rates by quantum methods, but this is not yet feasible for the systems of interest to us. Various approaches to variational transition-state theory (VTST) provide classical or semiclassical calculations that are feasible for large systems and seem to be accurate when carefully

New Approaches to Ion Thermochemistry

117

done. Our group, in collaboration with S. J. Klippenstein, has followed the variational RRKM approach developed with success by Marcus's group. 68 This combines a quantum treatment of most of the vibrational degrees of freedom with a classical treatment of the "transitional" vibrations and rotations that are intimately involved in the dissociation dynamics. Such a theoretical approach calculates the dissociation rate-energy function with no adjustable parameters besides E o. If the calculation is fitted to a dissociation rate measured at even a single energy, E 0 can be assigned in a completely nonarbitrary way. Our application of this approach to the benzene ion dissociation in collaboration with Klippenstein was noted in Section II. When it can be carried out, this is by far the most satisfactory way currently available for extrapolation to E o. The necessary VTST calculations, whether by way of the Marcus variational RRKM approach or other approaches (e.g., statistical adiabatic channel theory 69) are laborious, involving the quantum chemical construction of large potential maps for the interaction of the separating fragments and extensive statistical calculations for the dissociation process. Application of this approach to a variety of interesting systems is one of the outstanding opportunities for future work.

Phase Space Theory Phase space theory 7~ (PST) has been widely used for estimation of rates and energy partitioning for ion dissociations. It can be considered within the framework of transition-state theory as the limiting case of a loose transition state, in which all product degrees of freedom are statistically fully accessible at the transition state. As such, it is expected to give an upper limit for dissociation rates and to be best suited to barrierless dissociations involving reaction coordinates with simple bond cleavage character. It is both a strength and a weakness of PST that it has no freely adjustable parameters other than E o. For dissociations (generally, simple bond cleavages) that seem likely to have very loose transition states, it offers a judgement-free rate-energy extrapolation to E 0 that can be fitted to a single rate--energy point. However, the totally loose transition state is probably not really correct for many reactions, and PST offers no clear way to adjust this. When data are available over a good range of energies, simple RRKM theory gives an adjustable way of making the transition state tighter, while still retaining PST as a limiting case. PST was concluded to be quantitatively accurate in reproducing experimental rates for the dissociation of bromobenzene ion 7~ (although complete variational calculations are not yet available for comparison). On the other hand, PST gave rates a factor of 5 higher than the best variational RRKM rates for benzene ion dissociation 24 (the same E 0 being assumed), and in this case would lead to an overestimate of E 0 by about 0.15 eV. This argues against the unquestioning use of PST as the rate-energy extrapolation tool even for simple bond cleavage dissociations.

118

ROBERT C. DUNBAR

Simple RRKM Theory Computationally, simple RRKM theory 72 is easy to apply, and it has been used as the extrapolation tool in many studies. By "simple" RRKM we mean the rate derived from,

N~,(E_Eo) kRRKM= Cr

(28)

hO(g)

where N ~ is the number-of-states function of the activated complex, p is the density-of-states function of the molecule, and c~ is the reaction path degeneracy factor. The statistical functions are calculated by use of harmonic oscillator vibrations (along with internal rotors if appropriate). Often, no attempt is made to account for angular momentum effects, or a correction factor may be included to correct crudely for angular momentum constraints on available energy. An outstanding characteristic of this approach is the large degree of flexibility (arbitrariness) in the assignment of the parameters, particularly the frequencies of the transition state. Deriving absolute rates is rather uncertain, but the RRKM curve is an excellent fitting and extrapolation function. It is usefully regarded as a two-parameter fitting function, one parameter being E 0 and the second being the "looseness" of the transition state. The transition state is made looser by a decrease in the frequencies of the vibrations (and internal rotors) used to calculate N :, the result being that as the transition state is made looser, the rate-energy curve rises more steeply. When rate-energy data are available over a range of energies, an unambiguous fit can be made by adjustment of E 0 and the looseness such that the RRKM function matches both the value and the slope of the experimental rate-energy points. We do not know of any system for which the experimental data are so good as to justify using more than two adjustable fitting parameters. Since the looseness or tightness of the transition state can be varied by an unlimited number of different frequency variations, it is vital to the usefulness of this approach that the shape of the resulting rate-energy curve be reasonably independent of the particular frequency set chosen. Tests show this to be a reasonably good assumption. For instance, Figure 12 compares RRKM curves calculated for a model hydrocarbon system with 60 degrees of freedom. The transition state was made quite loose by three widely different variation approaches: (1) All the molecular frequencies were scaled down by a uniform factor of about 0.9. (2) Four of the low-frequency modes (700, 700, 300, and 150 cm -1) were drastically reduced in frequency (by about a factor of 2). (3) One low-frequency vibration (at 150 crn-1) was converted to an internal rotor with a rotational constant of about 1 cm -~. For each of the calculations, the transition-state looseness was adjusted so that the rates were the same in the 105 s-~ region. The comparisons were made for two cases, a rather low (1.86 eV) and a rather high (3.10 eV) E 0 value. The RRKM curves are shown in Figure 12, and are seen to be quite similar. If these were used as extrapolation functions, the largest resulting variation in fitted E 0

New Approaches to Ion Thermochemistry

119

5

=

4

~ .'y ,77

-N3

Eo

B 2

1

2.0

2.5

3.0

I''

3.5

oo~ J ./~,jllS

I

4.0 Einternal

4.5

I

I

I

5.0

5.5

6.0

I

6.5

(eV)

Figure 12.

Comparison of simple RRKM rate--energy curves, using three different loose activated complexes giving the same rates at the energy corresponding to about 105 s-1. Calculations are shown for Eo values of 1.86 and 3.10 eV. The three transition states are: (a) uniform frequency multiplier of 0.9 (---); (b) four low-frequency vibrations (--); (c) low-frequency vibration to internal rotor (.... ). The corresponding AgoooK values are as follows: 1.86 eV, (a) = 8.2 eu, (b) = 4.9 eu, (c) = 1.6 eu; 3.10 eV: (a) = 6.9 eu, (b) = 4.9 eu, (c) = 2.9 eu. Also shown is the semiclassical RRK functional form (.... ).

would be of the order of 0.1-0.2 eV, which suggests the extent of error in fitted E 0 that would result from a very incorrect choice of transition-state frequencies. Following the original suggestion of Rosenstock, 73 the practice has developed of use of the activation entropy at 1000 K, A S~ooo r~, as a parameter characterizing the looseness or tightness of the activated complex. '4 Values more negative than about zero have been found to correspond to tight complexes characteristic of rearrangement dissociations, positive values of 5--10 cal K -~ to loose complexes characteristic of simple bond cleavages. The results shown in Figure 12 suggest that this is a qualitatively useful parameter, but should not be taken in a very quantitative spirit. These three RRKM calculations give nearly the same rate--energy curves, and thus should represent effectively the same looseness of the activated complex. The actual AS~000 K values for these three models are noted in the caption to Figure 12. The AS~00o K values are all positive, as appropriate to this rather loose complex, 9

.

4-

o

.

120

ROBERT C. DUNBAR

but they exhibit a substantial spread of values. This underlines the need for caution in consideration of ASi000 K as more than a semiquantitative signal of activated complex looseness. The ASi000 K calculation has particular problems when the passage from energized molecule to transition state involves a gain or loss of internal free rotations. Using the simple RRKM curves as extrapolating functions, this example suggests that variations of the order of 0.1 eV in the assignment of E o are expected depending on how the activated complex frequencies are chosen. Hydrogen atom loss from the benzene ion is a particularly poor reaction for application of PST or simple RRKM theory because of the weak long-range interaction and the large orbital angular momentum barriers. We noted previously in this Section that PST fails to a significant extent in this case. Simple RRKM theory is compared with variational RRKM theory in Figure 5 for this system. The simple RRKM parameters were adjusted to give a superimposable curve over the range of the experimental data, as shown. The E 0 value for simple RRKM is 3.81 eV, compared with 3.88 eV for the more accurate variational approach. This difference of 0.07 eV for the two approaches encourages our belief that simple RRKM is a good extrapolation tool for E 0 assigmnents within an uncertainty of 0.1 eV, even in a badly behaved example like this one. Figure 12 has another point of interest. The so-called semiclassical RRK function,

k=A

)

(29

coming from old unimolecular dissociation theory is still sometimes used as a functional form describing rate-energy curves 75 (where A is an adjustable frequency factor, E~ is the molecular zero-point energy and s is the number of degrees of freedom). 76 This function is also displayed in the Figure, using the same E 0 values, and is seen to be wildly inaccurate and entirely useless as a fitting or extrapolation function. This is not surprising, since such a semiclassical expression would only be expected to be useful for (E-Eo)much larger than E~ (5.5 eV in this c a s e ) . 77

When the RRKM transition state becomes loose enough, the calculation is expected to approach PST as a limit. It is interesting to ask how well the functional forms of PST and simple RRKM theory agree when the RRKM transition state is chosen to be very loose. Figure 13 shows model calculations with these two formalisms for one example, the complex ion AI+(C6H6). The PST calculation assumes J = 75 for the molecule, as an approximation to the thermal angular momentum distribution. The simple RRKM calculation uses a transition state in which the two low-frequency metal-ring rocking vibrations were loosened from 123 c m -1 to 7.0 cm-~. As the Figure shows, the rate-energy curves have very similar shapes except at the lowest energies.

New Approaches to Ion Thermochemistry

6

121 ,

v

,

.,

,

Rate-Energy Calculations

5

"N 0

..'~'

3

2

........PST

; 0.0

E o - 1 69 eV !

!

0.1

0.2

0.3

Excess Energy (eV) Figure 13, Comparison of phase space and RRKM extrapolation curves by use of parameters for the Al+(benzene) complex. The E0 value was the same for both curves. The RRKM curve was adjusted to give the same rate as PST at 10 s s-1 by variation of transition-state frequencies as described in the text.

ACKNOWLEDGMENTS Research described in this chapter has received support from the National Science Foundation and from the donors of the Petroleum Research Fund, administered by the American Chemical Society. Collaboration with Prof. Terrance McMahon has been indispensable to the evolution of our ideas about ZTRID. We are grateful to Prof. Stephen Klippenstein for help with PST calculations. We thank Prof. Helmut Schwarz and the other authors of Ref. 52 for communicating ab initio results and prepublication data.

REFERENCES AND NOTES 1. For an introductory review, see Dunbar, R. C. In Analytical Applications of FT-ICR Mass Spectrometry; B. Asamoto, Ed.; VCH: New York, 1991; Chapter 1. 2. Lias, S. G.; Bartmess, J. E.; Liebman, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. J. Phys. Chem. Ref. Data 1988, 17, Supplement 1. 3. Berkowitz, J.; Ellison, G. B.; Gutman, D. Jr. Phys. Chem. 1994, 98, 2744. 4. Keesee, R. G., Jr.; Castleman, A. W. J. Phys. Chem. Ref. Data 1986, 15, 1011. 5. Huang, F. S.; Dunbar, R. C. lnt. d. Mass Spectrom. Ion Proc. 1991, 109, 151. 6. Dunbar, R. C. Mass Spectrom. Rev. 1992, 11, 309.

122

ROBERT C. DUNBAR

7. The near-linear dependence of the kinetic shifts on the number of degrees of freedom N is notable, but not surprising. A reasonable functional form for the energy dependence Ofkdiss is the modified semiclassical RRK expression

k--AtE+_s E+EE0/) where A and ot are adjustable constants, E 0 is the critical energy, and E z is the total zero-point energy. In the high-energy limit where (E + Ez) >> E 0 this becomes Emin - E0 = N

8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.

30. 31. 32. 33. 34.

f, ol

' - (E0 + Ez) n (A/kmin)

where Emin - E 0 is the kinetic shift necessary to exceed the dissociation rate kmin. In the situations under consideration the high-energy limit is a good approximation, so the kinetic shift is approximately linear in N. Stockbauer, R.; Rosenstock, H. M. Int. J. Mass Spectrom. Ion Phys. 1978, 27, 185. Baer, T. Adv. Chem. Phys. 1986, 64, 111. Neusser, H. J.J. Phys. Chem. 1989, 93. 3897. Malinovich, Y.; Arakawa, R.; Ha,ase, G.; Lifshitz, C. J. Phys. Chem. 1985, 89, 2253. Ho, Y_P.; Dunbar, R. C.; Lifshitz, C. J. Am. Chem. Soc. 1995, 117, 6504. Dunbar, R. C.J. Chem. Phys. 1989, 91, 6080. So, H. Y.; Dunbar, R. C.J. Am. Chem. Soc. 1988, 110, 3080. Dunbar, R. C. J. Phys. Chem. 1987, 91, 2801. Rosenstock, H. M.; Stockbauer, R.; Parr, A. C.J. Chem. Phys. 1980, 77, 745. Kuhlewind, H.; Kiermeier, A.; Neusser, H. J." Schlag, E. W. J. Chem. Phys. 1987, 87, 6488. Huang, F. S.; Dunbar, R. C.J. Am. Chem. Soc. 1990, 112, 8167. Lifshitz, C.Acc. Chem. Res. 1994, 27, 138. Faulk, J. D.; Dunbar, R. C.J. Phys. Chem. 1991, 95, 6932. Ho, Y_P." Dunbar, R. C.J. Phys. Chem. 1993, 97, 11474. Brand., W. A.; Baer, T. Int. J. Mass Spectrom. Ion Phys. 1983, 49, 103. Faulk, J. D.; Dunbar, R. C. J. Am. Chem. Soc. 1992, 114, 8596. Lin, C. Y.; Dunbar, R. C. J. Phys. Chem. 1995, 99, 1754. Klippenstein, S. J.; Faulk, J. D.; Dunbar, R. C. J. Chem. Phys. 1993, 98, 243. Ahmed, M. S.; So, H. Y.; Dunbar, R. C. Chem. Phys. Lett. 1988, 151, 128. Ahmed, M. S.; Dunbar, R. C. J. Chem. Phys. 1988, 89, 4829. Malinovich, V.; Lifshitz, C. J. Phys. Chem. 1986, 90, 2200. Gotkis, Y.; Naor, M.; Laskin, J.; Lifshitz, C.; Faulk, J. D.; Dunbar, R. C. J. Am. Chem. Soc. 1993, 115, 7402. Lin, C. Y.; Dunbar, R. C.J. Phys. Chem. 1994, 98, 1369. Some confusion about toluene ion dissociation thermochemistry has arisen from the PEPICO rate--energy curve reported by Bombach, R.; Dannacher, J.; Stadelmann, J.--P. J. Am. Chem. Soc. 1983, 105, 4205, which is not in agreement with other observations and apparently suffered from an experimental artifact. The two-channel analysis offered in their paper was qualitatively but not quantitatively correct. See Refs. 5, 19. Dunbar, R. C. J. Phys. Chem. 1990, 94, 3283. Klots, C. E. J. Phys. Chem. 1992, 96, 1733. Faulk, J. D.; Dunbar, R. C.; Lifshitz, C. J. Am. Chem. Soc. 1990, 112, 7893. Weddle, G. H.; Dunbar, R. C.; Song, K.; Morton, T. H. J. Am. Chem. Soc. 1995, 117, 2573. Gerlich, D.; Homing, S. Chem. Rev. 1992, 92, 1509.

New Approaches to Ion Thermochemistry

123

35. Dunbar, R. C. In Unimolecular and Bimolecular Ion-Molecule Reaction Dynamics; Ng, C. Y.; Baer, T.; Powis, I., Eds.; Wiley: New York, 1994: Vol. 2, Chapter 5. 36. Kofel, P.; McMahon, T. B. J. Phys. Chem. 1988, 92, 6174. 37. Dunbar, R. C. Int. J. Mass Spectrom. Ion Proc. 1990, 100, 423. 38. Herbst, E.; Dunbar, R. C. Mon. Not. R. Astr. Soc. 1991, 253, 341. 39. Dunbar, R. C.; Klippenstein, S. J.; Hrusak, J.; St0ckigt, D.: Schwarz, H., manuscript in preparation. 40. Bates, D. R.; Herbst, E. In Rate Coefficients in Astrochemistry; Millar, T. J.: Williams, D. A., Eds.; Kluwer Academic: Norwell, MA, 1988; p 17. 41. Fisher, J. J.; McMahon, T. B. Int. J. Mass Spectrom. Ion Proc. 1990, 100, 701. 42. Th61marm, D.; McCormick, A.; McMahon, T. B. J. Phys. Chem. 1994, 98, 1156. 43. Lin, Y.; Ridge, D. P.; Munson, B. Org. Mass Spectrom. 1991, 26, 550. 44. McEwan, M. J.; Denison, A. B., Jr.; Huntress, W. T.; Anicich, V. G.; Snodgrass, J.; Bowers, M. T. J. Chem. Phys. 1989, 93, 4064. 45. Anicich, V. G.; Sen, A. T., Jr.; Huntress, W. T.; McEwan, M. J. J. Chem. Phys. 1990, 93, 7163. 46. Sen, A. T., Jr.; Huntress, W. T.; Anicich, V. G.; McEwan, M. J.; Denison, A. B.J. Chem. Phys. 1991, 94, 5462. 47. Weddle, G. H.; Dunbar, R. C. Int. J. Mass Spectrom. Ion Proc. 1994, 134, 73. 48. Dunbar, R. C.; Faulk, J. D. Chem. Phys. Lett. 1993, 214, 5. 49. Dunbar, R. C.; Uechi, G. T.; Solooki, D.; Tessier, C. A.; Youngs, W.; Asamoto, B. J. Am. Chem. Soc. 1993, 115, 12477. 50. Weddle, G. H.; Dunbar, R. C. Int. J. Mass Spectrom. Ion Proc. 1994, 134, 73. 51. Dunbar, R. C.; Uechi, G. T.; Asamoto, B.J. Am. Chem. Soc. 1994, 116, 2466. 52. St0ckigt, D.; Hrusak, J.; Schwarz, H. Int. J. Mass Spectrom. Ion Proc., in press. 53. Ho, Y.-P.; Dunbar, R. C., to be published. 54. Cheng, Y_W.; Dunbar, R. C. J. Phys. Chem. 1995, 99, 10802. 55. Mautner, M.; Hamlet, P.; Hunter, E. P.; Field, F. H.J. Am. Chem. Soc. 1978, 100, 5466. 56. Meot-ner, M.; Field, E H. J. Phys. Chem. 1976, 80, 2865. Sieck, L. W.; Meot-ner, M. J. Phys. Chem. 1984, 88, 5324. Sieck, L. W.; Meot-ner, M. J. Phys. Chem. 1984, 88, 5328. Meot-ner, M.; Sieck, L. W. Int. J. Mass Spectrom. Ion Proc. 1989, 92, 123. Stone, J. A.; Wytenberg, W. J. Int. J. Mass Spectrom. Ion Proc. 1991, 104, 95. Mason, R. S.; Parry, A. Int. J. Mass Spectrom. Ion Proc. 1991, 108, 241. 57. Th61mann, D.; Tonner, D. S.; McMahon, T. B. J. Phys. Chem. 1994, 98, 2002. 58. Tonner, D. S. M.Sc. Thesis, University of Waterloo, 1993. 59. Dunbar, R. C.; Zaniewski, R. C. ,I. Chem. Phys. 1992, 96, 5069. 60. Uechi, G. T.; Dunbar, R. C. J. Chem. Phys. 1993, 98, 7888. 61. Ho, Y.-P.; Dunbar, R. C.J. Phys. Chem. 1993,97, 11474. 62. Dunbar, R. C.: McMahon, T. B.; Th61mann, D.; Tonner, D. S.; Salahub, D. R.; Wei, D. J. Am. Chem. Soc., in press. 63. Dunbar, R. C. J. Phys. Chem. 1994, 98, 8705. 64. Dunbar, R. C. s Chem. Phys. 1991, 95, 2537. 65. Hiraoka, K.; Misuze, S. Chem. Phys. 1987, 118, 457. 66. Lin, Y. C.; Dunbar, R. C. J. Phys. Chem., in press. 67. Pozniak, B. Ph.D. Thesis, Case Western Reserve University, 1995. 68. Wardlaw, D. M.; Marcus, R. A. Chem. Phys. Lett. 1984, 110, 230. Wardlaw, D. M.; Marcus, R. A. J. Chem. Phys. 1985, 83, 3462. Wardlaw, D. M.; Marcus, R. A. J. Phys. Chem. 1986, 90, 5383. Klippenstein, S. J. Chem. Phys. Lett. 1990, 170, 71. Klippenstein, S. J.J. Chem. Phys. 1991, 94, 6469. 69. Quack, M.; Troe, J. Int. Rev. Phys. Chem. 1981, 1, 97. 70. Bass, L. M.; Chesnavich, W. J.; Bowers, M. T. d. Am. Chem. Soc. 1979, 101, 5493. Bass, L. M.; Bowers, M. T. Lecture Notes Chem. 1982, 31,432. Chesnavich, W. A.; Bowers, M. T. Prog. React. Kinet. 1982, 11, 137.

124

ROBERT C. DUNBAR

71. Lifshitz, C.; Louage, E; Aviyente, V.; Song, K. J. Phys. Chem. 1991, 95, 9298. 72. Robinson, E J.; Holbrook, K. A. Unimolecular Reactions; Wiley-Interscience: New York, 1972. Forst, W. Theory of Unimolecular Reactions; Academic: New York, 1973. 73. Rosenstock, H. M.; Stockbauer, R.; Parr, A. C.J. Chem. Phys. 1979, 71, 3708. 74. Lifshitz, C. Adv. Mass Spectrom. 1989, 11,713. 75. A recent example of the continuing use of this equation for data fitting is Bouyer, R.; Roussel, F.; Monchicourt, E; Perdrix, M.; Pradel, E J. Chem. Phys. 1994, 100, 8912. 76. Note that the useful empirical functional form discussed in Ref. 7 differs from the unsatisfactory Equation (29) in having the additional adjustable constant or, which can be adjusted to make this a useful equation. 77. The classical RRK expression, similar to Equation (29) but with the E z terms omitted, is similarly inaccurate and useless. By making an empirical adjustment of s, or by adjusting E z, these RRK functions were forced to fit experimental data in older literature, but such procedures have been largely outmoded by the success of the more satisfactory RRKM formulation.

ALKYL CATION-DIHYDROGEN COMPLEXES; SILONIUM AND GERMONIUM CATIONS" THEORETICAL CONSIDERATIONS

Peter R. Schreiner, Henry F. Schaefer !ii, and Paul v. Ragu~ Schleyer

Abstract

I. II.

III.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Introduction

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Theoretical Approach

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A.

B a s i s Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B.

B a s i s Set S u p e r p o s i t i o n E r r o r ( B S S E )

. . . . . . . . . . . . . . . . . . .

C.

C h a r a c t e r i z a t i o n o f S t a t i o n a r y Points

. . . . . . . . . . . . . . . . . . .

Selected S y s t e m s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.

A l k o n i u m Cations

B.

Silonium Cations

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C.

G e r m o n i u m Cations

D.

Neutral Analogues

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Advances in Gas Phase Ion Chemistry Volume 2, pages 125--160. Copyright 9 1996 by JAI Press Inc. All rights of reproduction in any form reserved. ISBN: 1-55938-703-3

125

126 126 127 128 129 130 130 130 142 147 153

126

SCHREINER, SCHAEFER III, and SCHLEYER

IV. Some Systematic Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . V. ConcludingRemarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

154 157 158 158

ABSTRACT The analyses of the electronic and geometric structure of Group IV cation dihydrogen complexes and some of their neutral analogues are presented. The choice of most suitable basis sets and methods is outlined with respect to the reproduction and prediction of structures, relative energies, dissociation limits, hydrogen scrambling barriers, rotational constants, and vibrational frequencies. Systematic trends within the Group are examined, and comparisons are made between the charged and neutral complexes. A simple relationship between the dihydrogen stretching frequency and the dissociation barrier is derived to aid experimental work.

!. I N T R O D U C T I O N Ab initio electronic structure theory has become a powerful tool for the determination of molecular structures and properties. The theory is particularly useful where experimental data are difficult to obtain, such as when the system under examination is very weakly bound, highly unstable, or very short lived. Computations are able to reproduce experimental findings very accurately for small molecules with only a few heavy (non-hydrogen) atoms. For larger systems, qualitative features usually agree very well with experiment. The real advantage of quantum chemical calculations lies in the very detailed, sometimes experimentally inaccessible, information on molecular properties (energies, dipole moments, polarizabilities, charges, vibrational frequencies, rotational constants, etc.) afforded by the scrutiny of the solutions of the electronic Schrrdinger equation. However, weakly bound systems, which constitute the majority of all species presented in this chapter, also are challenging theoretically. The time required to converge to a stationary structure and the quality of geometry optimizations depends upon the force constants for the individual bonds. For weakly associated systems, where the "bonds" holding the two fragments together are not well defined (i.e., they have very small force constants), geometry optimizations may be difficult and time consuming. Large changes in geometry very often result in only small changes of the total electronic energy, and many iterations are needed until the minimum is found. The forces holding the weakly associated subunits together consist of electrostatic, inductive, exchange (including charge transfer), and van der Waals interactions. Covalent contributions are generally negligible. Because the exchange energies are very small and the bond distances can be quite long (up to a few angstroms), the inclusion of electron correlation and the use of large, flexible basis sets are prerequisites to obtain reliable results. Otherwise small errors

Cation-Dihydrogen Complexes: Theoretical Considerations

127

due to computational limitations such as the basis set superposition error (BSSE) become apparent when small energies are being dealt with (see discussion). Theoretical studies of dihydrogen-cation complexes in the gas phase serve several purposes. First, the limited size of the system reduces the computational problem. Second, the simplicity of the resulting structures allow various electronic and geometrical effects to be differentiated. Finally, the findings serve as a simple model to understand the various explicit (i.e., not depending upon the bulk properties) molecular interactions between charged species and neutral molecules during the transition from the gas phase into solution. In other words, the direct effect (e.g., hydrogen bonding, polarization, etc.) of solvent molecules can be examined. There is considerable interest in neutral dihydrogen complexes of transition metals, 1'2but charged and main group systems have received less attention. Hydrogen-complexed organic cations (R§ are involved during the hydrogen evolution in reactions of protic superacids and branched hydrocarbons. 3'4 The intermediates involved are particularly interesting because of their pentacoordinate carbons and electron-deficient three-center, two-electron (3c/2e) bonds. An understanding of this nonclassical binding in detail is important for chemistry. Are there general trends for binding molecular hydrogen within a group, and how do these compare with uncharged analogues? When does the dihydrogen subunit remain intact, and when is the H-H bond cleaved? What are the barriers for hydrogen scrambling? These and other chemical questions are discussed in the present chapter, which reports theoretical studies on prototype Group IV cation-dihydrogen complexes (CH~,CH~, C2H~, SiI-I~, SiH~, Gelid, Gelid) and some of their neutral analogues of Group III (BH 5 and A1Hs).

I!. THEORETICAL A P P R O A C H We have used the supermolecular method to compute the total energy of the system: the interaction (complexation) energy is obtained by subtraction of the energies of the constituent molecular fragments. This method is theoretically straightforward and can be improved successively by an increase in the theoretical sophistication. The wavefunction used in this procedure gives the molecular properties directly. The most important "weak" many-body interactions, such as exchange repulsion, polarization, and dispersion of a complex-like molecular system, are not equally well described by all theoretical methods. In the simplest self-consistent-field (SCF) 5 or Hartree---Fock (HF) methods, only zeroth- and first-order perturbations are taken into account, i.e., only many-body exchange repulsion and classical polarization terms. 6 All computations of higher order perturbations contain the higher order dispersion terms already present in the SCF energy components. Therefore, perturbation expansion and size-consistent methods are superior. Moller---Plesset7 perturbation theory of the nth order (MPn) and the coupled cluster method (CC) 8 belong in this category, whereas tnmcated configuration interaction (CI) techniques 9 are disadvantageous because of their size inconsistency.

128

SCHREINER, SCHAEFER III, and SCHLEYER

In the present chapter, geometries for all stationary points were optimized with analytic gradients by employment of SCF, 5 CISD (configuration interaction with single and double substitutions with respect to the HF reference determinant), 9 and CCSD (coupled cluster including all single and double excitations) methods. 8 The effect ofunlinked quadruple excitations on the CISD energies was estimated by the Davidson correction, l~ denoted as CISD+Q. In order to circumvent the size consistency problem, a supermolecule consisting of the two molecular fragments separated by about 500 * was used to determine dissociation energies at the CISD levels. The effect of connected triple excitations on the CCSD wavefunction was included perturbatively [CCSD(T)]. ll For C2H~, MP2-optimized (full) geometries were used for MP4SDTQ (frozen core, including single, double, triple, and quadruple excitations) single point energies. Generally, the heavy atom core orbitals were kept frozen and the highest lying virtual orbitals were deleted in the correlation procedures. Corrections to the basis set superposition error (BSSE, discussed below) were computed without frozen core orbitals. Residual cartesian gradient and internal coordinates were always < 10-6 atomic units. The d-and f-functions in the augmented basis sets were the six- and ten-component, respectively. All computations were carried out with the program suite PSI2.0.8,12 except for the MPn calculations, which were done with GAUSSIAN 92.13 A. Basis Sets

In general, large basis sets are needed to reproduce weak interactions involving large separations (up to 3 ,~) properly. For increased flexibility, it is essential to augment the basis with multiple sets of polarization and/or diffuse functions, as both have small exponents to help describe long-range interactions. We decided to use energy-minimized polarization functions for comparison with published research or studies in progress. To obtain state-of-the-art results for the reproduction of geometries, energies, and vibrational frequencies, it is necessary to use a balance between theoretical method and basis set. The combination of the CCSD(T) method with the TZ (plus element-specific polarization functions) basis sets usually achieves these goals. 14-16

Hydrogen A TZ basis set for hydrogen (5s/3s) was expanded with appropriate sets of polarization functions to balance the heavy atom basis. The polarization function exponents were ap (H) = 1.50, 0.375 and txd (H) = 1.00.

Carbon For the qualitative analysis of basis set effects in the CH~+ systems (e.g, CH~ ), we used Huzinaga--Dunning tfiple-~ basis sets,17---designated C(10s6p/5s3p) and H(5s/3s)--with two sets of polarization functions (TZ2P) on all the nuclei. The p o l a r i z a t i o n function exponents were Ctd(C) = 1.50, 0.375. The

Cation-Dihydrogen Complexes: TheoreticalConsiderations

129

C(10s6p2dlfl5s3p2dl J) basis set [uj(C) = 0.80] is referred to as TZ2P +f, whereas TZ2P(fd) corresponds to a C(10s6p2dlfl5s3p2dlf) and H(5s2p 1d/3s2p 1d) basis. For protonated ethane complexes, standard 6-31G(dp) and 6-311G(dp) basis sets were employed. 18

Silicon Two basis sets were utilized: TZ2P for SiH~ [consisting of (12s9p2d/6s5p2d) for silicon 19with polarization function orbital exponents ofud(Si) = 1.00, 0.25] and a basis set of TZ2P(s quatity for SiH~, [Si(12s9p2dlfl6s5p2dlf), with an f-polarization function orbital exponent of uf(Si) = 0.32].

Germanium The largest basis set was of triple-~ plus polarization plus f-functions (TZP + f ) quality, which consisted of a TZP basis set flexibly contracted to Ge(14sllp3dlfllOsSp3dlf). 2~This basis set was augmented with a set of d- and f-like polarization functions [ud(Ge ) = 0.25 and uf(Ge) = 0.45; Up(H) = 0,75]. Only the valence electrons were correlated; the 14 lowest occupied molecular orbitals for GeH~ and GeH~ (Ge ls, 2s, 2p, 3s, 3p, 3d) were frozen, and the six highest virtual molecular orbitals (Gels*, 2s*, 2p*, 3s*) were deleted in the CI and CC procedures.

Boron The largest boron basis set used for geometry optimizations was of TZ2P quality, 17~1 augmented with a third set of d-type polarization functions [u d (B) = 0.145] and one set off-type functions [uf(B) = 0.882]. This basis set is denoted as TZ(3dlf,2pld). Final energies were evaluated by adding a set of boron g-type functions [af(B) = 0.673, 15-component] to give TZ(3dlflg,2p ld).

Aluminum The McLean-Chandler triple-~ basis set employed for aluminum was

(12s9p/6s5p), expanded with two sets of polarization functions with exponents u d - 0 . 8 and 0.2. 22

B. Basis Set Superposition Error (BSSE) BSSE arises from the intrinsic problem that finite basis sets do not describe the monomer and complex forms equally well. For instance, the energy of two monomers calculated in the full dimer basis is not the same as for the dimer.23'24A simple evaluation of the interaction energy (AE) of the two fragments [Equation (1)] is incorrect. This problem is especially serious with small basis sets. Hence, the magnitude of the BSSE can be used as a measure of the basis set incompleteness. AE = EAB - E A - E B

(I)

130

SCHREINER, SCHAEFER III, and SCHLEYER

Several methods have been suggested to estimate the BSSE and to correct Equation (1). The widely utilized full counterpoise correction 25 suggests the computation of the interaction energy (AE ep) as the difference of the dimer (AB) and monomer energies evaluated with the basis of the dimer: AE cp = EAB -- EA{AB}-- EB{AB}

(2)

The BSSE correction is then: BSSE = EA{AB} + EB{AB}- E A - E B

(3)

Some argue that Equations (2) and (3) lead to an overcorrection of the BSSE, and, indeed, this is still under considerable discussion. 26 Sufficiently large basis sets, usually with multiple sets of polarization functions, seem to overcome most of the B S S E . 27 Therefore, we computed the magnitude of the BSSE for the dissociation energies separately to evaluate our "basis set error margins" approximately.

C. Characterization of Stationary Points Vibrational frequencies were computed in order to characterize stationary structures. Mimima have no imaginary frequencies; transition structures have exactly one. More than one imaginary mode indicates a higher order saddle point, usually without chemical relevance. The force constants were determined by computation of the second derivatives of the energy with respect to all nuclear coordinates. At the SCF level of theory, harmonic vibrational frequencies were obtained from analytic second derivative methods, 2s whereas at correlated levels of theory they were computed by finite central differences of analytic gradients. SCF level zero-point vibrational energies (ZPVE) and vibrational frequencies were scaled by a factor of 0.91 to account for anharmonicity and electron correlation. 29At the CISD and CCSD levels, the scaling factor was 0.95 to correct primarily for anharmonicity. 3~All relative energies are corrected for ZPVE.

II!.

SELECTED SYSTEMS A. Alkonium Cations

Protonated alkanes are important highly reactive intermediates in the acid-catalyzed transformations of hydrocarbons. 3 However, the simplest protonated alkane, the methonium ion, CH~, 31 which exemplifies the entire family of nonclassical ions, is a well-conceived but experimentally not well characterized species. Known in the gas phase since the 1950s, 32 it is now a very common reagent for chemical ionization mass spectrometry, 33 but its infrared and microwave spectra remain elusive. In contrast, protonated methane has been studied extensively theoretically, owing to its small size. 31,34-40 Most studies suggest that the C s (I) form (1, A = C,

,

~

,

0 0

m

j

,/\

,

r~

~

I

..%

r..)

\

/ \

2: ~

o ~

L_

"1< l-

$,~ -r" < "1<

e-

o i

~

t-

m e-

~.---

~

e.i,

~

o

~

~

~

~

~"o

0

II

0

+

e{a0 .~..,

8~

E 0~-

9~_. ~

<

u

u

t~

132

SCHREINER, SCHAEFER ill, and SCHLEYER

Figure 1), a tightly bound (by about 40 kcal mo1-1) complex of CH~ and H2, is the global minimum, but more recent investigations show that this picture is not entirely correct.31,34,40 Although other isomers (2-5, A = C, Figure 1) have also been thought plausible candidates, only I is a true minimum. Structures 4 (A = C) and 5 (A = C) are higher order saddle points (with two imaginary frequencies) without chemical relevance. Both 2 (A = C) and 3 (A = C) serve as transition structures for hydrogen .....

1 A"

....y:. :.:..................... ............: -..:..

"'~: ...............

...... ~:ii::: ...............

...........

:;J'~/"::'""

. ........

...

..

.: :' ..7

. ..... ...."...:2

4A'

.

i

3A'

H

~~~

.."

/

2A'

tl

1A'

Figure 3. Pseudo-three-dimensional plots of the canonical orbitals for CH~, 1 (A =

C). The atom labels are only indicated for the lowest lying carbon 1 s orbital; otherwise they are left out for clarity.

Cation-Dihydrogen Complexes: Theoretical Considerations

133

Table 1. Geometrical Parameters of CH~, C's (I) (1, A = C) at Various Levels of Theory SCF TZ2P 1.090 1.230 1.230 1.078 0.872

CISD

CCSD

CCSD(T)

TZ2P +f

7Z2P

TZ2P +f

TZ2P

TZ2P +f

TZ2P

TZ2P +f

1.090 1,223 1.232 1.078 0,870

1.099 1.200 1.200 1.082 0.921

1.101 1.199 1.199 1.083 0.927

1.101 1.202 1.201 1.085 0.927

1.104 1.200 1.199 1.086 0.934

1.104 1.200 1.200 1.086 0.936

1.106 1.198 1.197 1.088 0.945

Parameter

C-H4 C-H 2 C-H 3 C-H5,6 H2-H3

scrambling. The optimized structures for 1-3 (A = C) are shown in Figure 2. The bonding type in 1 (A = C) is definitely covalent, as strong orbital overlaps demonstrate (Figure 3). Figure 3 depicts the pseudo-three-dimensional canonical orbitals at the highest level of theory, and, apart from the pure carbon ls orbital (la'), all interactions of the a' orbitals (a symmetry requirement for overlap with the in-plane dihydrogen) are very strong. The changes in geometry (Table 1) and vibrational frequencies (Table 2) of I (A = C), as well as the differences in relative energies (Table 3) of isomers 2 and 3 with an increase in the quality of the theoretical method, emphasize the importance of electron correlation and basis set. Although the geometry of the CH~ fragment does

Table 2. Vibrational Frequencies (cm -1) of CH~, Cs(I) (1, A = C) at Different Levels of Theory a Assignment Asym. CH3 deg. stretch (A") Sym. CH 3 deg. stretch (A') Sym. CH 3 breath. (A') H2 stretch (A') H2 rock (A') H2 center-of-mass motion (A') Asym. CH 3 bend (A") CH 3 rock/bend (A') CH 3 bend/rock (A') Asym. CH 3 rock (A") CH 3 deg. bend/rock (A') H2 torsional twist (A") Note:

TZ2P SCF 3062.7 2991.5 2923.4 2773.9 2103.9 1513.6 1450.9 1436.6 1257.9 1248.6 967.9 137.8

TZ2P +f SCF 3055.0 2985.9 2924.9 2783.9 2103.6 1511.9 1444.7 1431.5 1255.1 1243.4 969.4 137.7

TZ2P CISD 3108.1 3024.2 2922.5 2667.1 2280.3 1560.6 1447.5 1422.1 1253.8 1239.1 886.6 12.4

TZ2P +f CISD 3107.1 3021.3 2920.8 2666.6 2307.5 1563.2 1439.9 1414.7 1251.6 1244.8 874.5 147.0

a(SCFfrequencies scaled by 0.91" correlated frequencies scaled by 0.95).

TZ2P CCSD 3080.7 2996.1 2892.8 2633.3 2266.1 1545.7 1434.6 1408.1 1238.8 1228.1 870.0 45.5i

TZ2P +f CCSD 3079.0 2992.6 2890.5 2632.5 2295.0 1547.2 1426.8 1400.5 1236.0 1234.4 855.7 144.9

134

SCHREINER, SCHAEFER III, and SCHLEYER

Table 3. Relative Energies (in kcal mo1-1) of the CH~ Transition Structures for Hydrogen Scrambling, 2 and 3 (A = C), Relative to 1 (Energetic Reference Point) at Different Levels of Theory.

r

(I~, G, 2 CA=c)

TZ2P Rel. energy Rel. energy + ZPVE

0.04

0.01

0.00

0.00

0.00

-0.12

0.08

0.07

0.08

0.08 a

TZ2P + f Rel. energy

1.29

0.05

0.04

0.04

Rel. energy + ZPVE

1.13

0.14

0.13

-0.06

-0.05 b

0.05

0.09 0.18

0.08 ---0.02c'e'f

0.09 -0.01 d'e'f

TZZPq;,d) Rel. energy Rel. energy + ZPVE

0.04 -0.13 f

0.08 0.17

CI-I~5(I1), cs, a (A = C) TZ2P Rel. energy

3.48

1.64

1.44

1.51

1.30

Rel. energy + ZPVE

2.39

0.63

0.33

0.56

0.31 a

Rel. energy

3.55

1.49

1.27

1.35

1.13

Rel. energy + ZPVE

2.45

0.58

0.36

0.25

0.03 b

1.05 0.14

1.13 0.03 c'e

TZ2P + f

TZ2P~,d) Rel. energy Rel. energy + ZPVE

3.41 2.34

1.26 0.35

0.90 --0.20 d'e'f

Notes: aZPVEfrom the CCSD/TZ2P level. bZPVE from the CCSD/TZ2P +flevel. eSingle point at the CCSD/TZ2P +foptimized geometry. dSingle point at the CCSD(T)/TZ2P +foptimized geometry. eZPVE from the CCSDfrZ2P +flevel. fA negative relative energy arises from the differences in ZPVEs and does not mean that this species is a lower energy minimum than 1; instead, it indicates that these species interconvert without a barrier.

not change significantly (0.016 ./k for the bond lengths) at the various levels of theory, the H-H distance of the dihydrogen moiety lengthens considerably (0.075 .s with an increase of basis set and correlation treatment. This illustrates that correlated methods favor nonclassically bound structures with extensions of the basis set. 34 The trends in the vibrational frequencies from the SCF to the correlated levels (Table 3) also reflect the increased stabilization of such species due to correlation. The hydrogen stretching frequency for the H 2 subunit of I decreases from 2774 cm-I at SCF/TZ2P to 2633 cm-1 at the CCSD/TZ2P+flevel of theory, indicating a considerable H-H bond weakening. The "floppiness" of CH~ with respect to the rotation of the hydrogen subunit is revealed by the small values for

Cation-Dihydrogen Complexes: Theoretical Considerations

135

the lowest vibrational frequencies for I at all levels of theory. While the inclusion of carbon f-functions changes the values for the lowest frequencies of I at the correlated levels appreciably, the addition of d-functions on the hydrogen atoms does not influence the vibrational frequencies significantly. The variation in frequency for the torsional twist of the H 2 subunit of I shows this effect drastically; at the CCSD/TZ2P level, 1 even has a small imaginary vibrational frequency. We confirmed the correctness of our method for the determination of the vibrational frequencies by using a different set of coordinates to exclude a systematic error in the method employed. The deviations were in the range of 0.1 crn-l. However, it is known that small errors do arise in the numerical procedures, and they are of greater relative importance for small vibrational frequencies. In the conventional view, both C~ structures [1 and 2, A = C] are energetically almost perfectly degenerate, allowing virtually free rotation of the H 2 moiety, but the C2v form is about 1 kcal mol-l higher in energy. But why has CH~ not been observed in interstellar media, and why is its characterization by infrared spectroscopy so difficult? The only measurable experimental quantity, the dissociation energy D~ K [42.5 kcal mo1-1 Equation 4], 41 shows that the methonium ion is quite CH~ --~ CH~ + H 2

(4)

stable, and this value is very well reproduced by theory [42.0 kcal mol-l at QCISD(T)/6-311 ++G(3df,3pd)//MP2(fu)/6-311 ++G(2df,2pd)]. 4~ A closer examination of the relative energies of the three lowest lying isomers explains why CH~ has not been and may not soon be characterized by vibrational spectroscopy. At the highest levels of theory, the three structures are, after inclusion of the zero-point vibrational energy, almost identical in energy (within 0.2 kcal mol-l). That is, complete hydrogen scrambling occurs essentially without barriers even at 0 K! The latest gas phase experiments showing very rapid H/D scrambling may be reinterpreted on this basis. All five C-H bonds are effectively equivalent and exchange dynamically very rapidly. 42 The usual representation of CH~ (1, A = C) with three-center two-electron bonding is misleading. Rather than serving as the nonclassical carbocation prototype, CH~ is unique.

Recent experimental efforts by Yuan Lee's group have been focused on accessing the structure of CH~ indirectly by attachment of a neutral molecule like H 2 or CH4 .43 One may assume that the attachment mainly restricts the scrambling process but does not significantly alter the structure of CH~. Using the well-characterized structures for H~, CH 4 and H 2 as a reference for, e.g., the shitts in vibrational frequencies, one should be able to deduce the CH~ structure. On the basis of the present study, we will discuss the effect of molecular hydrogen attachment to

CH .

136

SCHREINER, SCHAEFER III, and SCHLEYER

Theoretical investigations on the structures and binding energies of CH~ (CH4) n clusters for n = 1-4 give information on clustering behavior. 44'45 An important feature is that the first two CH 4 ligands are attached to the two protons of the 3c-2e bond of 1 (A - C). This result is in qualitatively good agreement with the experimental observation of a large difference in A/~_l, n between n - 2 and n = 3. 46,47 The experimental and theoretical binding energies between CH~ and H 2 were found to be in the range of 1-2 kcal mo1-1 through a correlation of the H-H stretching vibrational frequency shifts and binding energies of hydrogen cluster ions H~ (n = 5,7,9,11,13,15). 48'49 In the work being presented, the primary goal is to discuss the structures, relative energies, and the dissociation energy of the CH~ (H2) complex, and whether or not the attachment actually does stabilize the methonium ion sufficiently to resolve its IR spectrum. There are many structural possibilities for attaching dihydrogen to the methonium ion, but, by analogy to the CH~ (CH4)n46'47 structures, the H 2 approach to one of the two protons involved in the 3c-2e bond of I ( A - C) is most favorable. The resulting four possible structures were optimized at various levels of theory and are shown in Figure 4. Only 9 and 11 are true minima, whereas 10 and 12 resemble the transition structures for rotation of the attached dihydrogen. Structure 13 interconnects 9 and 11. As noted before, electron correlation effects are important and change the geometrical parameters significantly. In going from the TZ2P SCF to the TZ2P CISD level, the bond distance between H-2 and the center of the H 2 moiety decreases from 2.086 to 1.890 A, whereas the H 2 bond length of the CH~ moiety increases from 0.878 to 0.928 ,~. The C-H-2 and C-H-3 bond distances decrease by about 0.02-0.03 ,~ at the same time. However, the geometries change very little from TZ2P CISD to TZ2P CCSD(T). The effect of d-functions on four (2, 3, 7, and 8) of the seven hydrogens is minimal at the SCF level, but it is significant at the CISD level, where the structure appears to become more compact (the bond lengths for hydrogens 2 and 3 decrease and the distance to the center of mass ofhydrogens 7 and 8 becomes shorter). Consequently, the dissociation energy (to be discussed below) for the loss ofH 2 from CH~ (H2) increases. Structure 10 is the transition state for the out-of-plane rotation of the H 2 moiety. A natural bond orbital analysis 5~ shows that structure 9 is more stable than structure 10 owing to (1) the smaller electron donor effect from the bonding H-7-H-8 ~-molecular orbital to the antibonding a*-CH-2 orbital, and (2) the larger p-donating character of the H-7-H-8 bonding a-orbital into the empty out-of-plane p orbitals of H-2 and H-3. Therefore, the distance between CH~ and H 2 of 9 (1.890 ,~) is shorter than that of 2 (1.915 A). The other geometrical parameters for structures 9 and 10 remain largely unaffected. Very similar arguments apply to 11 and 12. The only other minimum is 14, which is connected to the other stable structures via 15. All other optimization attempts led back to the minima already located or converged to higher order saddle points. To judge whether dihydrogen attachment would increase the barrier for complete hydrogen scrambling, we also examined structures that contain the CEvisomer of

H

H~...0.744

96.8~(~.744

Hs

Hs

0.928 ~ 14.,,3,...... :H 2 ~ 164.4 o

1.18~:

',, "'~78.2 o !.082...-Cs/'~1.097 9

..,......-'"(

HSII 8.

~

157.0~~

I"14

H5'fl'8~:'"L ~ H'

10, C,, [I]

II, C,, [01 \

1.198 \ 0.927 H~ ...... H2 ;

2.334

:. : !.199 ", :'-,~79.4 o

.~,~,.o~H4 Hffi'8,.0 1"'~2 C~ i~/"

I"14

12, Cs, [I]

0.924 H 3 ...... H 2 " ,

9

13, C s, [I]

!.082

". :' --~78.6o C t - ) ! 101

Hs i'i8

H7

"-.0.741

.C,.._) i noo 151"!~ / ~ c ~

!.082

H8

H4

H~ 178"9~

15, C s, [ 1] H7

-"'1 ~ o 14, Cs, [0]

:: i.198

H5 1187 ~ o Y ~ '!10.0 - " / ~o

2.212

~

:

... /

" ..:-.~78.4o

'.,, /

H

s~ ............ l l ~ ~ ~ 10.!o

H4

H~

.....: !.!96 . ",. . . . . ::. . 1.196 1.199 \

'. :'--,,~80.9o

1.082 ..... ci - ; 1 096

I..(~...2.%,C,./'~l.096

1 1 8 . ~ x i I0.i o S 5..........

H7 2.287

/

,,,4',./"94

".../.~ 8 i.0o

I"14

~ ( " H3 0:9!? H2

-0:9.19::H2

: 1.212",9 .'1.194

:: 1.211

0.742 ..Hs

.-.t

H / S'

', :'-~78.3 o 1.082.....C l_; 1 097 .-"

9, C,, [0]

",,,4

0.744/,~ 91.2 ~

H

H 0.927 H ~ ,3 ,. ...... ::'~-~! 63.8 o

1.189 ". :: 1.211

H?

..-H7

..."

.741

Hs

H3

................. .,121.2o(/CI /.~o~o 1.171 / " 1.080

H~

H2

1.851

H7 0.745

i

H8 H4

16, C2v, [1]

Figure 4. The most important structures on the CH~ (H2) potential hypersurface optimized at the TZ2P CISD

level of theory. The number of imaginary vibrational frequencies is given in square brackets. Bonds lengths are in/~, angles in degrees.

138

SCHREINER, SCHAEFER Iii, and SCHLEYER

Table 4. The Relative Energies in kcal mo1-1 of the CH~ (H2) structures (as Shown in Figure 4) at the TZ2P ClSD+Q + ZPVE(TZ2P SCF) Level of Theory. (The Number of Imaginary Frequencies is in Squared Brackets) Isomer

9 [0]

10 [1]

11 [0]

12 [1]

13 [1]

14 [0]

IS [1]

16 [1]

Ere I

0.00

-0.02

0.01

0.00

0.55

0.98

1.07

0.18

CH~ (3, A = C). The stationary point 16 is the transition structure for the interconversion of equivalent C s forms of CH~ (H2), being the C2v-CH~ form. As the relative energies (Table 4) for the eight chemically important structures are very similar, it is obvious that attachment of H 2 does not stabilize any single CH~ substructure preferentially. Moreover, the internal rotations and H 2 migrations among the lowest lying CH~ (H2) isomers (9-13) have essentially no barrier. From this particular point of view, it may be difficult to deduce the CH~ spectrum experimentally by H 2 attachment. Our best value [TZ2P + d CCSD(T)] for the ZPVE-corrected dissociation energy, D 0, is 1.46 kcal mol-~. This result compares favorably with the experimental AH0 of 1.88 kcal/mol, 48 and with the experimental estimate of 1-2 kcal mo1-1 from the correlation of the H-H frequency shift and the binding energy of the hydrogen (H~+ ) clusters. 47 CH~ (H2) -~ CH~ + H 2

(5)

For an explicit examination of the basis set superposition error on weakly bound cationic structures at various theoretical levels, we performed full counterpoise calculations as outlined in Section liB (Table 5). Table 5 demonstrates nicely that the magnitude of the BSSE is indirectly proportional to the size of the basis set: at TZ2P, the error is on the average only about a quarter of that at DZP. This effect becomes more apparent with increased incorporation of electron correlation. At our best theoretical level, the BSSE amounts to only 0.1 kcal mol-~ (Table 5), which is insignificant for the dissociation energy of about 1.5 kcal mol-~. The best [TZ2P CCSD(T)] set of rotational constants for the global minimum Cs structure 9 is Ae = 4.061, Be = 0.824, and Ce = 0.921 c m -1, in mediocre agreement with experiment. 43A very approximate but potentially useful approach is to a v e r a g e the rotational constants of the five low-lying stationary points (9-13). The average rotational constants for the five structures are Ae = 3.96, B e = 0.79, and Ce = 0.78 cm-I (TZ2P CISD). The experimentally determined rotational constants 43 (Ae = 4.2, B e - 0.74, and Ce = 0.74 cm-1) most likely result from a superposition of quickly interconverting isomers, owing to the small differences in relative energies. Our theoretical values compare only moderately well with experiment. The proper theoretical approach to the prediction of the rotational constants A0, B0, and COis clear but presently impossible. One should use the 18-dimensional ab initio potential energy hypersurface to solve the Schr6dinger equation for the motion of

Cation-Dihydrogen Complexes: TheoreticalConsiderations

139

Table 5. The Basis Set Superposition Error (BSSE)for CHs(H2). The Monomers in Parentheses are Ghost Molecules. a AE Indicates the Difference between the Energy of the Monomer within the Monomer vs. the Dimer Basis (kcal moF 1) AE(C/~

AE(H2)

BSSE

DZ SCF

0.043

0.115

0.158

DZP SCF

0.070

0.107

0.177

TZ2P SCF

0.011

0.006

0.017

DZP CISD

0.152

0.260

0.412

TZ2P CISD DZP CISD + Q

0.066 0.158

0.039 0.267

0.105 0.425

TZ2P CISD + Q

0.071

0.036

0.107

DZP CCSD TZ2P CCSD

0.161 0.072

0.267 0.040

0.428 0.112

DZP CCSD(T) TZ2P CCSD(T)

0.174 0.080

0.275 0.043

0.449 0.123

Note: a"Ghostmolecule" means that the basis functions of this fragment have been added in the computation of the energy of the other fragment. AE(CI-I~ ) then implies that the energy of H2 was computed with the complete CI-I~(H2) basis set, occupied with only two electrons of H2.

the nuclei within the Born--Oppenheimer approximation. This would give rotational constants directly comparable with experiment. The number of nuclear degrees of freedom makes this task impractical at present, and the looseness of several degrees of freedom makes the situation even worse. A very approximate scheme that might provide somewhat better agreement with experiment would involve evaluation of the full cubic force field, followed by prediction of the r 0 structure from vibratiotr--rotation perturbation theory. The first and thus far only experimental IR spectrum of CH~ (H2) shows very broad C-H stretching bands of the CH~ moiety in the 2800-3150 crn-l region. 43 The H 2 stretching mode, on the other hand, is well resolved with the band origin at 4077.4 cm-~. This is red-shitted by 83.6 cm-~ from the vibrational origin (4161.0 cm-~) of the H 2 monomer. The theoretical H-H (TZ2P CCSD) stretching frequencies, 4107 crn-1 for the H2 moiety in CH~ (H2), and 4190 cm-1 for the H 2 monomer, demonstrate perfect agreement with the experimentally determined red shift (83 cm-~). With the application of an adjusted (through comparison of the H2 stretch) scaling factor of 0.94 to the TZ2P CCSD result, one can estimate the fundamentals for the C-H stretching frequencies to be 3048 cm-1, 2967 crn-l , and 2867 crn-l, and the H-H stretching frequency of the CH~ moiety to be 2573 cm-1. A comparison of the vibrational frequencies of 9 [CH~ (H2)] with those of CH~ shows that the H-H stretching and CH 2 asymmetric stretching frequencies of the CH~ moiety in CH~ (H2) are lower by 33 and 116 crn-1, respectively, than

140

SCHREINER, SCHAEFER III, and SCHLEYER

those of CH~ at the TZ2P CCSD level of theory. This result is consistent with the larger dihydrogen moiety distances of CH~ relative to those of CH~ (HE). For structure 9, there are two torsional H E twist frequencies (A"), which are strongly coupled with each other. This increases one torsional mode of 9 by 195 crn-~ and decreases the other by 87 crn-1 from that of CH~. The remaining frequencies of 9 are slightly larger than those of CH~. In conclusion, even though the binding energy of CH~ (HE) is small enough to uncouple the CH~ and H Emoieties, various energetically low-lying structures will make it difficult to extract precise structural information on CH~ experimentally. That is, dihydrogen attachment to the highly fluxional methonium ion does not seem to decrease the ease of hydrogen scrambling, delivering a very broad and featureless IR spectrum for the CH~ moiety.

C2H (H2) In alkane condensations in superacid media it is assumed, albeit never observed in solution, that reversible methane or ethane protonation is the first step. 4 Subsequent loss of dihydrogen, yielding the highly unstable methyl and ethyl cations, and reaction with excess alkane builds up higher hydrocarbons [Equation (6)]. CH~ + CH 4 ---) C2H ~ --> C2H~ + H 2

(6)

Protonated ethane, C2H~, the key intermediate in this mechanism, arises from protonation at the C-C or C-H bonds, 51 which react as o-electron donors to give three-center two-electron bonds. Many mechanistic implications have been discussed, 51 but we will concentrate here only on the most important structures in the context of dihydrogen-cation complexes. Deuterium-labeled methane and methyl cations were employed to examine the scrambling and dissociation mechanisms. The protonated ethane decomposition yields the ethyl cation and dihydrogen. Under the assumption that the extra proton is associated with one carbon only, a kinetic model was devised to explain the experimental findings, such as H/D scrambling. 52'42 The PES of protonated ethane is complex, as different species are observed depending upon temperature. 53 One isomer (18, Figure 5) was identified as a C-H-protonated ethane, whereas the more stable second isomer was considered to be the C-C-protonated form (17, Figure 5). Ethane prefers C-C over C-H protonation, making 17 the global minimum, but the newest theoretical results indicate that it is 19 and not 18 that is the second possible isomer. 51 At the MP4(fc, SDTQ)/6-311(dp)//MP2(fu)/6-31G(d) + ZPVE level, corrected to 298 K, the relative energies of 17-19 are 0.0, 6.6, and 5.1 kcal mo1-1, respectively. Only 17 and 18 have been considered experimentally, but we find 19 to be 2.1 kcal mo1-1 lower in energy than 18. However, 18 and 19 are very similar and have a low conversion barrier of only 0.1 kcal mo1-1, so that only 17 and 19 should be observed experimentally. The theoretical dissociation energy of 10.7 kcal mo1-1 [MP4(fc,

Cation-Dihydrogen Complexes: Theoretical Considerations H

H'"'/

,'"

H

"',

1.220 // H :.

0.902 H~ H ', . 1.215 ' 1.193

H

'C

C~>H

c'-i . . . . . . : : C - - H 1.940

..

H

H"/ H

H 17, C:

141

H

0.903 / ' H '!.208 ', .

1.564 ~

H'" .

H

H

11517 C'~IH \ H

18, Cs

19, C!

1. ~ 0 H

H

~ HH4 H

C

~ 1.527

:9

H ~ H '

1.151.'\d' 1.-~

H

~

HH

H

: C'~ H

1.542

H

H

20. C,~

0.736 /"

142

21, C s

H

1.294 , H

0736 H--r-H

H.

H

H/ 2.332

.... C

1.307 "', . .H " 'C '" ! .381 " > H

,'"

2.332

i

3.105 "

i i

9

,H, 1.302

H,

,

1.302 II

H

1.380

H

22, C2,.

H/'C

1.380

H.;.-H

H

23, C2v

0.735 2~, C s

Figure 5. The most important C2H~ structures optimized at the MP2(fu)/6-31G(dp) level. Bond lengths are in ,~,.

SDTQ)/6-3 l l(dp)//MP2(fu)/6-31G(d) + ZPVE, corrected to 298 K], probably arising through a 1,1-elimination from 19, agrees very well with experiment (10.5 + 254 and 13.0 kcal mol-1). 53 Whereas the reaction of methane with the methyl cation does not have an activation energy, the dihydrogen elimination from 19 requires 9.1 kcal mo1-1. The barrier for conversion (7.2 kcal mo1-1) of 17 via 21 into 19 is therefore lower than the various dissociation pathways. The dissociation energy for protonated ethane is much less than D Oof the methonium ion (40--42 kcal mo1-1) owing to the higher stability of the internally (through hyperconjugation) stabilized ethyl cation [26.6 kcal mo1-1, Equation (7)]. CH~ + CH 4 ---),C2H~ + H 2

(7)

The three experimentally known vibrational frequencies for the C-C protonated 17 (3128, 3082, and 2945 cm-1) 55 are very well reproduced by theory (3136, 3075, and 2936 cm-~, respectively), confirming the geometry of this isomer. However, there is n o agreement for the two possible C-H-protonated forms, 18 and 19. The

142

SCHREINER, SCHAEFER ili, and SCHLEYER

most characteristic dihydrogen mode lies at 3964 cm-~ experimentally, whereas the computed vibration occurs at 2770 cm-~. Clearly, this discrepancy must be due to two different structures. It may be possible that the experimental data arise from a weakly bound ethyl cation-xlihydrogen complex, whereas 18 and 19 are tightly bound species. Indeed, in contrast to the latter "inner" dihydrogen complexes, there are also several loose "outer" complexes (Figure 5) with binding energies of-0.9 (22),-1.0 (23), and-0.5 (24) kcal mol-l, which are much smaller than the energies for association of H 2 to the methonium ion (1, 1.5 kcal mol-l). Thus, these outer complexes appear to be too weakly bound to be observed experimentally. The comparison with the dihydrogen binding energy of the methonium ion is obvious: the more stable the cation, the smaller the binding energy to a hydrogen molecule. This applies to the inner and outer complexes. Thus, one can extrapolate that even more stable cations, like the isopropyl and t-butyl cations, do not benefit from an association with a neutral o-electron donor.

B. Silonium Cations

siu The structures of silonium cations are attractive both theoretically and experimentally. These hypercoordinate molecules provide insights into new structural features, and they are usually quite different from the analogous carbonium ion structures. The chemistry of silicon hydrides is closely related to the iotv-molecule reactions encountered in chemical vapor deposition processes, 56and silanes are also interesting from an organic chemist's point of view. For instance, silanes undergo electrophilic deuterium-hydrogen exchange even if the system does not contain transition-state stabilizing groups or lone pairs. 57 Therefore, a pentacoordinate silonium cation seems to play a major role in these reactions. For the silonium cation SiH~, ab initio theoretical methods 58'59have suggested a Cs structure that involves an H 2 subunit attached to the SiH~ cation. Thus, the silonium cation reveals H

H

1.460] 1.910 i 19.10("S.i=. . . . . . . . . .

-H 10.774

119.6~

1.458_[ 1.912 119.4~si ;
1"575/H H.,... ........ /1.571_

! 19.1~ 1 (A = Si), Cs (I)

2 (A = Si), Cs (II)

3 (A = Si), Cs

Figure 6. The optimized geometries for the three lowest lying Sill; structures at the TZ2P CCSD level of theory. Bond lengths are in ~,, angles in degrees.

Cation-Dihydrogen Complexes: Theoretical Considerations

143

Table 6. Relative Energies in kcal mo1-1 of the SiH~ Isomers (see Figure 1, A = Si) at the TZ2P CCSD Level of Theory. (The Number of Imaginary Frequencies is in Square Brackets) Isomer Ere I

I(A=Si)

2(A=Si)

3(A=Si)

4(A=Si)

5(A=Si)

6(A=Si)

C~(I) [0]

C~(II) [1]

C2v [1]

C3v [2]

C4v[2]

D3h [3]

0.0

0.0

26.9

8.8

60.6

82.6

nonclassical three-center two-electron (3c-2e) bonding as is also found in the methonium cation CH~ .31 However, a comparison of the detailed geometries (Figures 2 and 6) reveals that the dihydrogen moiety is much less disturbed in 1 (A = Si) than in I (A = C). The relative Si-H 2 bond length is considerably longer [by 3 1 % vs. 8 % compared to the Si-H (or C-H) bond length of the Sill 3 (or CH3) moiety], resulting in an almost perfectly planar (angle sum 357.8 ~ silyl cation moiety. At the same level of theory (TZ2P CCSD), the Si-H bond length of uncomplexed SiH~ is merely 0.001 A longer. As a consequence, the rotational barrier of the attached hydrogen molecule [via 2 (A = Si)] is negligible (Table 6), resulting in a very low value for the lowest vibrational frequency of only 24 crn-1 (Table 7). 59 In contrast to the methonium ion, however, the C2v form [3 (A = Si)] is high in energy, rendering complete hydrogen scrambling in SiH~ unlikely. 59 Complete hydrogen scrambling can also be excluded on the basis ofthe dissociation [Equation (8)] energy of only 10.3 kcal mo1-1 [TZ2P CCSD + ZPVE(TZ2P SCF)], which is just one fourth of that for CH~.

Table 7. The Vibrational Frequencies (in cm -1) and Intensities (in km mo1-1) of SiH~, 1 (A = Si), Cs (!), at the TZ2P CCSD Level (Scaled by 0.95) Mode H2 stretch (A') Sill3 deg. stretch (A') Sill3 sym. stretch (A') H2 rock (A') Sill3 deg. bend (A') Sill3 vs. H2 stretch (A') Sill3 + H2 rock (A') Sill3 + H2 rock (A') Sill 3 asym. stretch (A") Sill 3 asym. bend (A") Sill3 + H2 asym. rock (A") H2 torsional twist (A")

Frequency (Intensity) 3791 (169.2) 2252 (0.2) 2200 (0.0) 961 (18.3) 897 (68.2) 844 (83.7) 683 (99.0) 603 (2.5) 2259 (0.5) 890 (60.3) 620 (0.7) 24 (0.1)

144

SCHREINER, SCHAEFER III, and SCHLEYER

SiH~ --+ SiH~ + H2

(8)

It is difficult to compare this value to experiment because there are three values for the heat of formation for SiH~ .60--62Thus, with a heat of formation for SiH~ of 219 kcal mol-~, the experimental dissociation energy ranges from 10 to 20 kcal mo1-1, certainly too large to judge the quality of the theoretical D 0.

Sill; A major experimental breakthrough for the SiH~ system has very recently been made through the publication by Okumura's group 63 of the infrared spectrum for SiH~, displaying a single band centered around 3866 cm -1 in the 3500 to 4200 crn-1 region, which was assigned to a perturbed hydrogen-hydrogen stretching motion. The frequency shift of 295 cm-1 with respect to free hydrogen (H2) suggests that molecular hydrogen is a weakly bound subunit, an empirical estimate of the binding energy being 7 to 9 kcal mo1-1. The absence of a second band in the selected region furthermore indicates that the molecule must be symmetrical so that the two hydrogen subunits become symmetry equivalent, and a C2 as well a C2v structure was suggested. It was also concluded that the rotations of the hydrogen moieties occur with very low barriers. From the 2-.~ distance of the H 2 ligands from planar SiH~, the rotational constant B of 0.85 cm-1 was derived for this prolate-top molecule. How well are these experimental findings reproduced theoretically, and what else can be said about the chemistry of SiH~ ? Since the experimental results point to a structure where the dihydrogen moieties become equivalent, we have focused on structures of Ca and C2vsymmetry. The C2 structure of SiH~ is the lowest in energy at all levels of theory. However, the energy differences of the three structures [C2 (25), C2v(I) (26), and C2v(II) (27), Table 8] are less than 0.1 kcal mo1-1, resulting in essentially a zero barrier to rotation of the attached dihydrogens. 64 The geometries are very much basis-set-and method-dependent, as we find that all structures have at least one imaginary vibrational frequency at the DZP SCF level of theory. Optimization of 25 in the C 1 point group led to an only slightly distorted C2 structure, but the total energies differ only at the sixth decimal point. However, when the triple-~ basis sets were used, the number of imaginary frequencies for each structure decreased by one. The "missing" imaginary frequency in the change from the double-~ to the triple-~ basis sets corresponds to a motion that leads to non-equivalent Si-H 2 distances. Apparently, DZP is too small a basis set to describe SiH~ correctly, because the relatively tight single set of polarization functions in the DZP basis does not allow a proper description of the rather long silicon-hydrogen subunit bonds. The triple-~ basis sets also yield Si-H bonds (Figure 7) that are always longer than the ones obtained with the double-~ basis set. Inclusion off-functions on silicon does not alter the results significantly. The MP2 method used in another place 65 in conjunction with a TZ2P basis set, however, seems to underestimate the bond lengths and thus overestimates the general trend

Table 8. Relative Energies in kcal mo1-1 of the Three Examined SiH~ structures (see Figure 7) at the TZ2P CCSD(T) Level of Theory (The Number of Imaginary Vibrational Frequencies is in Squared Brackets) Isomer

25

26

27

Cs (I) [O]

C2v (I) [1]

C2v (lI) [1]

0.00

0.04

0.05

H2 82"5~ - - [ 1.457 2.080 (/ H5~ S i l , . : z = : H7 207i......... 9

[

2.080 H6 d.............. /- ~ H8/0"762 ]-1.457

/I.-,,\"~

25, C2

H4 \120.0 ~ H2 78.8~,,,,~.-~ 1.459 H~~ ! ~

2.078 S

i

~

26, C2v (I)

~

H6 10.762

H4 \120.30

H2

90.7~-., 1.456 2.08o .......... H,

H~ ........... ~

H7"~'-

-: 1.458 C2v II

-""Hs--

/'~H 3 H4 \ 1 1 9 . 7 ~

27, C2v (I)

Figure 7. The optimized geometries for the three lowest lying SiH~ structures at the TZ2P CCSD(T) level of theory. Bond lengths are in A, angles in degrees. 145

146

SCHREINER, SCHAEFER I!1, and SCHLEYER

of the vibrational frequencies (discussed below). The Si-H bond distances of the SiH~ counterpart in Sill 7 are slightly shorter than those of free SiH~ (see the discussion of SiH~ above). The H 2 bond length of SiH~ is only slightly shorter than the bond length of free H 2, indicating a small perturbation of the hydrogen subunits through the cation moiety. The o10 vibrational frequency (Table 9), which is the asymmetric combination of the two H 2 moieties, has been observed experimentally at 3866 c m - l , 63 whereas the theoretical frequency lies at 3944 cm-1. 64 The mode involving symmetric combination of the two H 2 vibrations does not change the dipole moment of the molecule, and thus has no IR intensity. The theoretical frequency shift of 259 cm -~ (compared to free hydrogen, 4161 crn-l) compares moderately well with the experimental hydrogen frequency shift of 295 crn-1. The previously determined 65 TZ2P MP2 frequencies give a shift of 328 crn-~. The computation of the rotational constants notwithstanding, the theoretical equilibrium rotational constants for the three stationary points (25-27) are remarkably similar. In particular, the theoretical value o f B e (0.84 cm -l, averaged for all three structures) agrees very well with the experimental B 0 = 0.85 cm -l. The best theoretical value for the dissociation energy D Oof SiH~ into SiH~ and H 2 is 4.6 kcal mol --1 at the TZ2P CCSD level, which is considerably lower than that estimated experimentally (7-9 kcal mo1-1) and also

Table 9. Harmonic Vibrational Frequencies (cm-1, CCSD and MP2, Scaled by 0.95 and 0.93, Respectively) and IR Intensities (km mo1-1, in Parentheses) for the SiH~ (C2, 25) Global Minimum Structure (see Figure 7) Mode

0)1 (A) 0)2 0)3 0)4 0)5 0)6

7"-Z2P CCSD

3963 (0) 2268 (1) 2214 (0) 882 (53) 772 (26) 704 (0)

TZ2P MP2

3949 (0) 2252 (1) 2200 (0) 879 (49) 799 (32) 701 (1)

0)7

558 (0)

548 (0)

0)8 0)9

336 (6) 74 (0)

338 (6) 72 (0)

0)13 0)14 0)15 0)16 0)17

3944 (366) 2267 (1) 883 (43) 853 (151) 772 (28) 705 (0) 363 (273) 332 (95)

3928 (358) 2252 (1) 879 (52) 845 (163) 800 (25) 702 (1) 355 (230) 333 (37)

0)18

73 (0)

18 (0)

0)10(B) toll COlE

Cation-Dihydrogen Complexes: Theoretical Considerations

147

less than half of the dissociation energy for the SiH~ ion (see discussion). The BSSE accounts for 0.4 kcal mol -~, favoring an even lower value for D 0. Certainly, a more accurate experimental determination is in order.

C. Germonium Cations

GeH~ Just as for the ions CH~ and SiH~, the structure of GeH~ has not been established experimentally. Surprisingly, there are only a few studies on this interesting species, namely, one experimental 66 and seven theoretical 67'68 investigations. Since chemical vapor deposition, 56 which uses the hydrides or the protonated hydrides of the desired metal, is one of the common methods to produce layered semiconductors, the knowledge of the structures of germane and its protonated form appears to be quite desirable. The early papers 67a favored D3h, Cav, and C4v structures [Figure 1, 7, 4, and 5 (A = Ge), respectively], concluding that the D3h form is the lowest in energy. The only experimental publication 66 merely reports on the proton affinity of monogermane (162.1-164.0 kcal mol-m). Much later, a C s (II) [Figure 1, 2 (A = Ge)] minimum structure for the germonium ion was suggested, 67b by use of a mixed basis set (double-~ for Ge, and 31G for hydrogen) in conjunction with the SCF method for geometry optimizations and the CI method for energy single points on the optimized structures. The computed 67a proton affinity of 161.4 kcal mo1-1 (164.2 kcal mol-l) 67b is in reasonable agreement with experimental results. 66 Protonated germane and silane are structurally and energetically very much alike. As for the other protonated Group IV tetrahydrides, the C4v [5, A = Ge)] and the D3h [6, A = Ge)] structures are high in energy {84 and 48 kcal mol -l, respectively, relative to the Cs(I) [1, (A = Ge)] structure, DZP SCF}, and those structures were not studied further. The D3h minimum energy structure suggested in the earlier literature 67a must be considered as an artifact of the insufficiency of the minimal basis set and their one-center integral method. The vibrational frequency analysis for this structure indicates that it is not a minimum (it has three imaginary frequencies). The C4v structure is also a higher order saddle point with two imaginary vibrational frequencies. Although the Cs(I) (1, A = Ge) form is the only

table 10. Relative Energies (in kcal mo1-1, including ZPVE) of the Optimized GeH~ Structures at the TZP + f CCSD Level of Theory. The BSSE at this Level Amounts to 0.1 kcal mo1-1 for 1 (A = Ge) Isomer

TZP +fCCSD

c, (/)

c, (T/)

c2, (1)

c2, (/1)

c2~ (~T/)

(1, A = Ge)

(2, A = Ge)

O, A = Ge)

(28)

(29)

0.0

0.0

33.5

9.8

10.2

SCHREINER, SCHAEFER Iil, and SCHLEYER

148 .93 ..0

H

o

H

,.01I

~'..GIe .~~,:::'y/'"

/

"\

, 2.026 . - //.. -/ H

i 0.772

40.5~ f( \ \ 1.511,,',,~ H H C~ .......)1367~

~.Ge 7-'-'.'" ) d 0.772

fill 1.521 H

H

1.522

H

Cs (II),2 A = Ge, [l]

Cs (I), 1 A = Ge, [0]

.58

C2v (I), 3 A = Ge, [ 1]

H

H

~1.522 1 1 9 . ~ G e 1.522

22.0~

.~176

H "" "-..

. . . . . . . "'~176 I "'n

H

0.745

~ H

.........

0.745

H ~ H

,522

,,

H

C2,., 28, [0]

C2v, 29, [2]

H

H 1.539

H T d.

30, [0]

[ 1.523

/~176 H D3h, 31, [2]

Figure O. The optimized geometries for the most important GeH~ structures at the CCSD TZP + f level of theory. Bond lengths are in A, angles in degrees. The number of imaginary vibrational frequencies is given in square brackets.

true minimum at all levels of theory, the Cs(II) (2, A = Ge) and the Czv(I) (3, A = Ge) structures are transition states for hydrogen scrambling, as is found for the carbon and silicon analogues. Again, the two Cs structures are very nearly energetically equivalent (Table 10, Figure 8), which results in a virtually free rotation of the hydrogen subunit. Also, the geometrical parameters of these two isomers differ by at most 0.002 ,~ (bond lengths) and 0.9 ~ (bond angles). Both C~ structures comprise an almost planar germyl cation (the dihedral angle of GeHZH5H6 is 167 ~ for both structures) with a weakly bound hydrogen molecule attached. The structural differences between the GeH~ moiety in protonated germane and the germyl cation (31) are small (Figure 8). The hydrogen--hydrogen bond length deviates only by 0.029 A from free hydrogen, optimized at TZP CCSD(T). There are two additional C2vs t r u c t u r e s (28 and 29, Figure 8) that were not located for the lighter elements. They are relatively low in energy (6.6 and 6.5 kcal mo1-1, respectively), but only the C2v (28) is a genuine minimum, which is best ascribed

Cation-Dihydrogen Complexes: Theoretical Considerations

149

Table 11. Vibrational Frequencies (cm -1) of GeH~, C5(I) (1, A = Ge) at the TZP + fLevel of Theory (Scaled by 0.95). Infrared Intensities in km mo1-1 Are Given in Parentheses. Assignment

H2 stretch (A') GeH3 asym. stretch (A") GeH3 sym. stretch (A') GeH3 sym. stretch (A') GeH3 rocking (A") GeH3 scissoring (A') H2 com.a motion (A') H2 rocking (A') H2 center-of-mass+ GeH3 wagging GeH3 twisting H2 center-of-mass+ GeH3 twisting H2 out-of-plane + GeH3 rocking free H2

TZP +f CCSD

3860 (195) 2176 (66) 2172 (546) 2135 (903) 925 (14) 816 (185) 815 (216) 794 (7) 605 (147) 549 (40) 546 (64) 23 (0) 4190

to a linear complex of the germyl cation and a hydrogen molecule. The C2v (29) structure is a transition state (with two imaginary frequencies due to degeneracy of the imaginary mode in this point group) for the H 2 rotation of the hydrogen subunit in 28. (There is another Cav transition structure for the out-of-plane rotation of the hydrogen molecule moiety in 28, but the barrier is zero at all levels of theory.) The C2v (3, A = Ge) structure is 33.5 kcal mo1-1 (TZP + f C C S D ) above the minimum, and complete hydrogen scrambling can therefore be excluded, as it also can be on the basis of the much lower dissociation barrier (to be discussed below). The vibrational frequencies (Table 11) for the minimum energy structure I (A = Ge) show some expected trends. The hydrogen stretching frequency, which can be used as an indication for the interaction of the germyl cation moiety with the hydrogen subunit, decreases with an increase in theoretical sophistication. The hydrogen frequency shift, which could be directly compared to experiment, is 330 c m -1 at TZP + f C C S D . This is similar to SiH~ (398 cm-~), but much less than for CH~ (1557 cm-1), indicating that the germyl cation has the weakest interaction with the hydrogen subunit among these species. The rotational constants for the two Cs structures are identical: A e = 2.322, B e = 1.489, and C e = 1.453, an observation that may assist in the experimental identification of GeH~. One of the theoretical problems with a highly nonrigid molecule such as GeH~ is the choice of which set of rotational constants (when there are essentially degenerate stationary points) should be observed. For GeH~ one has the fortuitous arrangement in which either of the two low-lying structures yields the same rotational constants.

150

SCHREINER, SCHAEFER III, and SCHLEYER

At the highest level of theory [TZP +fCCSD(T)], the dissociation energy (at 0 K, including ZPVE) D Ofor GeH~ is 10.0 kcal mol-l, which is, surprisingly, almost the same as D Ofor SiH~ (10.3 kcal mo1-1 at the TZ2P CCSD level, see Section IIIB), and about a fourth of that for CH~ (42.5 kcal mol-l). Gen~ ~ GeH~ + H2

(9)

However, if entropy is included, the free enthalpy change AGOfor Equation (9) is only 0.7 kcal mol-1 ! This is why it may be very difficult to observe and characterize protonated germane experimentally. One would expect a smaller dissociation energy for GeH~ because of a smaller charge on germanium in GeH~ (+0.84, NPA) compared to silicon in SiH~ (+1.01, NPA). This is due to the higher electronegativity of germanium (2.0) 69 versus silicon (1.7), 69 which makes germanium less capable of bearing a positive charge. Also, the long Ge--H bonds (2,031 and 2.034 A, TZP +fCCSD) are longer than the analogous Si-H bonds (1.910 and 1.915 A, TZ2P CCSD), which should additionally decrease the energy required to remove the hydrogen molecule from GeH~. But which interaction is responsible for the unexpectedly high Do? The binding between the AH~ and the H 2 part is mostly due to an interaction of the vacantp orbital (LUMO) on Aand the filled o H 2 orbital (HOMO), and the energy gap between those two orbitals will contribute to the magnitude of the interaction. The LUMG-HOMO gap is 0.495 eV for GeH~ and H 2, and 0.533 eV for SiH~ and H 2 (DZP SCF). Consequently, GeH~ is stabilized through a more favorable HOMO-LUMO orbital interaction. Another argument, which has been put forward for transition-metal hydrides, is that filled d orbitals tend to decrease the bond strength of the attached dihydrogen, leading to a stronger complexation to the cation. This question is addressed below (Section IV). Nevertheless, the germyl cation is more stable than the silyl cation by 18.8 kcal moV1 [DZP CCSD, Equation (10)], with respect to the tetrahydrides. Germane has the highest Gett 4 + SiH~ --~ GeH~ + Sill 4

(10)

proton affinity [PAo, 156.4 kcal tool-1 at TZP +fCCSD(T) + ZPVE(TZP + f SCF), [Equation (11)] of the first three tetrahydrides in Group IV [PAo(CH4)7~= 130.5 kcal tool-1, PAo(SiH4)71 = 153.3 kcal moV1]. Consequently, germane is able to abstract a proton from both CH~ and SiH~ [Equations (12), (13), and (14); DZP CCSD]. GeH4 + H + --~ GeH~

(11)

SiH~ + GeH4 --) Sill 4 + GeH~

(12)

AHo =-7.8 kcal mo1-1 SiH~ + C H 4 ~

Sill4 + C H ~

A H o = -26. I kcal m o V l

(13)

Cation-Dihydrogen Complexes: Theoretical Considerations

151

CH~ + GeH 4 ~ CH 4 + GeH~

(14)

AH0 =-33.5 kcal mo1-1 The experimental 66germane PA0 of 162.1 to 164.0 kcal mol-~ is somewhat higher than our best estimate. The assumption that the experimental PA0 is correct would lead to the conclusion that theory does a somewhat better job for germane than for protonated germane. However, the very recent study of Smith and Radom showed that the usual standard (PA0 of isobutene) for the experimental determination of proton affinities may have to be corrected downwards by 2.4 to 4.8 kcal mol-~, which brings the theoretical PAo close to the experimental value. 72 GeH + 7

Just as for protonated germane, the structure of GeH~ is experimentally not known. High-level ab initio studies thus can be a very useful guide and, when it is considered how well the theoretical methods reproduce the known experimental quantities, can also be used as a reference. 73 The investigation of the structm'al possibilities for GeH~ is therefore a timely effort. As mentioned before, the electronegativity of germanium lies between that of silicon and carbon. What is to be expected for the next higher dihydrogen complexes of germanium? Are the structures of GeH~ unique? Do they resemble'that of CH~ (i.e., GeH~ -H2) or are they isostructural to the SiH~ (i.e., HE-GeH~ -HE) isomers? The not surprising answer is that both GeH~ -HE-and HE-GeH~ -HE-like structures are found (Figure 9)! However, since Ge is even larger than Si, the latter structural type is energetically favored (Table 12) by some 4-5 kcal mol-l. As for the silicon analogues, the GeH~ C2 (32) and CEv (33 and 34) structures are virtually identical in energy, resulting in a free rotation of the dihydrogen moieties. The attachment hardly alters the geometry of the germyl cation fragment, as the difference in bond lengths is only 0.006 A. For future experimental comparisons, we calculated a vibrational frequency shii~ for the hydrogen molecule moieties of 216 cm-l [TZ(3dlf, lp) CCSD(T), scaled by 0.95] relative to free hydrogen (Table 13). This frequency corresponds to the asymmetric H-H stretching mode because the synunetric motion has zero oscillator o

Table 12. The Relative Energies in kcal mo1-1 of the GeH~ isomers (See Figure 9) at the TZ(3dl f,1 p) CISD + Q Level of Theory, Including ZPVE (The Number of Imaginary Frequencies is in Square Brackets) Isomer 32 33 34 35 a 36 a 37 a 38 a C2[0] Er~l

Note:

0.00

CEv(I) [1] CEv(lI) [21 -0.07

aZPVEat TZ(3dlf, lp) SCF.

-0.07

Cs [O]

Cs [1]

Cs fO]

Cs [1]

4.66

4.69

4.48

4.62

H2 [

2.189

I

"5\

H2

H2

. . . . . . . . . . . . .

H

Ho

5

[ I

I

~

I ~

2.198

.

H5............. [/ [

H6

2.261 ...............

H7 ""

.H6 .

H/

/ ",

/ H3

H4

H4

H4

33, C2v (I)

32, C2

34, C2v (Il) 0.742 ....H7

HZ. 0.742 2.486 0.768 J

0.767

H3 . . . . iH2 i i o

~'x~Ha

.3 .... ., Lrl r,,2

t

H7 ~/~.742

t

2.018 *i

i t

2.028", /2.022

2.486/

a i

"~i'1'93~"i~8~ ~ 84 86-35, C,, [0]

_o-L6sp2_ J

H~

Ha

i

/

1.515..Geb~1.517

H5"!'i91~"'i" "!'~193 ~ H,

i

2.026', / 2.018

0.742/

,, ,,

,2.026

Ha

H,

H7

~ 9

a, 0.768 .... 8~ ,

:

i

37, Cs, [0]

2.025'\

,'2.019

i

1.515. Geb,~l.516 H5........ i 1 9 ~(1 1~9 . 3 H4

H6

36, Cs, [1]

1.515... Gel.,,,~l.517 H5........ l l 9 y ( / 119.3 ~ 84 H6

38, Cs, [1]

Figure 9. The optimized geometries for the most important GeH~ structures at the CCSD TZP + flevel of theory. Bond lengths are in ,g,, angles in degrees. The number of imaginary vibrational frequencies is given in square brackets.

Cation-Dihydrogen Complexes: Theoretical Considerations

153

Table 13. Harmonic Vibrational Frequencies (cm-~, Scaled by 0.95), and IR Intensities (km mo1-1, in Parentheses) for the GeH~ (C2, 32) Global Minimum Structure Mode coI (A) 032 0)3

7Z(3dlf lp) CCSD(T) 3991 (0) 2173 (40) 2143 (0)

(04

804

(129)

(o5 (06 (O7 CO8

766 623 551 284

(20) (0) (0) (31 )

co9 col0 (B) coil col2 co13 col4 col5 (O16 col7 o)18

64 (0) 3974 (346) 2172 (40) 803 (128) 790 (147) 766 (20) 623 (0) 348 (595) 283 (33) 9 (0)

strength. As expected, the interaction of the second dihydrogen moiety is smaller than for the first (330-cm -1 frequency shift). 68 The hydrogen dissociation energy D O[Equation (15)] amounts to 3.1 kcal mo1-1 [TZ(3dlf, lp) CCSD(T) + ZPVE + BSSE], which is much less than for GeH~ (10 kcal mol-l). GeH~ ~ GeH~ + H 2

(15)

D. Neutral Analogues

B~ Although beyond the main focus of this chapter, it is interesting to compare some of the properties of the cationic complexes to isovalent or isoelectronic neutral analogues, such as boron or aluminum pentahydride. Both BH 3 and A1H 3 are electron deficient, and their stable forms are B2H 6 and A12H6. But how much do they benefit from complexation with a hydrogen molecule? Are there chemical bonds or are the neutrals held together merely by induced dipole moments or van der Waals interactions?

154

SCHREINER, SCHAEFER III, and SCHLEYER

The existence of a monoborane--dihydrogen complex (BHs) was uncertain for a long time. Thus, this interesting species was often the subject of theoretical investigations, 74 but its existence was only very recently definitively theoretically suggested 75 and confirmed experimentally.76 The qualitative features of the possible stationary (not implying dynamic processes) BH 5 structures (Figure 1, A = B) are very similar to the methonium ion (Figure 1, A = C), i.e., the global minimum of Cs symmetry (1, A = B) comprises monoborane complexed to a hydrogen subunit. The dihydrogen rotation is virtually unrestricted, as 2 (A = B) has the same energy as 1 (A = B). However, in marked contrast to the methonium ion, total scrambling does not occur in BH 5 because the C2v structure 3 (A = B) has a dissociation energy D OK of 0.9 kcal mol-l [TZ(3dlflg,2p ld) CCSD(T)//TZ(3dlf, 2p 1d) CCSD(T) + ZPVE], at least 3.3 kcal mo1-1 below the energy of the C2visomer. The dissociation energy is very sensitive to basis set size and inclusion of electron correlation, as the I (A = B) is unstable at all noncorrelated levels. All structures of higher symmetry are much higher in energy [5 (A = B): 22.8; 6 (A = B): 45.3 kcal mo1-1] or dissociate [4 (A = B)]. Although the dihydrogen moiety is weakly bound in I (A = B), an analysis of the Weinhold natural charges [natural bond order (NBO) analysis] 77 indicates a considerable donation of electrori density from the H 2 moiety (H2:0.25 e; H3:0.23 e) into the empty p orbital on boron (-0.60 e). These induced dipole-dipole interactions play an important role in stabilizing BH 5. The Wiberg bond index 18 also indicates considerable binding between BH 3 and H 2 (B1-H 2 = 0.447; B1-H 3 = 0.457; B~-H 4 = 0.870; B1-H 5 = 0.927). According to this analysis, it is justified to assume chemical bonding between BH 3 and H 2, and not merely the product of van der Waals interactions.

atu As expected, AIH 5 behaves very similarly, but it is even less stable [Do = 0.1 kcal mol-l, TZ2P CCSD(T) + ZPVE]. 78 Here also, only the free rotation of the dihydrogen moiety occurs with no barrier, and total hydrogen scrambling via 3 (A = A1) is very unlikely (25.5 kcal mol-1). However, the C3vstructure 4 (A = A1) remains stable with respect to dissociation. It resembles the in-plane transition structure (with a pair of degenerate imaginary vibrational modes) for the hydrogen molecule rotation. Again, both the Car 5 (A = A1) and the D3h 6 (A = A1) isomers are chemically irrelevant (72 and 84 kcal mol-l above 1, A = A1, respectively).

IV. SOME SYSTEMATIC COMPARISONS An important question concerns the kind of relationships that exist between the dissociation energy, Do, and various other molecular properties. What are the main factors responsible for the chemical bonding? How does D Odepend upon the charge on the heavy atom? Does the HOMO-LUMO interaction of the fragments determine the magnitude of Do? And what is the role of d orbitals on higher elements?

CationADihydrogen Complexes: Theoretical Considerations

155

5000 E o ._=

CH7 + I GeHv +

H2

+

4OO0

Sill, § "

_' ~ ~ Sills+

3000

"''''..<

I 2000

" 0

.' ,o

'

"

"

,o

"

D i s s o c i a t i o n e n e r g y , Do, kcal m o l l

Figure 10. Correlation of the dihydrogen stretching frequency and the dissociation energy Do for charged dihydrogen complexes. Do the bonding principles found for dihydrogen-transition metal complexes apply to main group cations? As expected, there is a linear relationship between the dihydrogen stretching frequency and the binding energy of the cationic species (Figure 10). The linearity is quite remarkable, as the regression coefficient is 0.995. Therefore, it is sensible to use the resulting Equation (16) as a tool to determine D O from the measured frequency of the dihydrogen moiety, which is normally well resolved, even in complex spectra. In the equation co(H2) is the stretching frequency of the dihydrogen moiety in cm-l. D O= [4158 cm-1 - co(H2)]/35.73 kcal mol-l

(16)

This correlation only holds if charged and uncharged species are treated separately. Apparently, there is no direct relationship between D Oand the charge on the heavy atom of an AH~§ molecule. It is expected that a more electronegative element is less likely to accommodate a positive charge, but AH~§ species do not necessarily bear apositive charge on A: CH~ (C = -0.13 e), SiH~ (Si = + 1.13 e), GeH~ (Ge = +0.51 e), BH 5 (B =-0.11 e), and AIH 5 (A1 = +0.75 e). What is the effect ofd orbitals on the binding energy? It is known that transition metals bind hydrogen in two different ways: (1) as an intact molecule (39) or (2) as the insertion product (40). The common explanation is that the type of binding depends upon the nature of M, i.e., its ability to "back-donate" electrons from filled H M'~ ...........

/H M

J

H 39

H 40

156

SCHREINER, SCHAEFER III, and SCHLEYER 2.8-

AIHs n

r

~" 9

."r'

2.7

9

2.6

r,.,. ,.,=,

< ,~ 9

2.5

--]

2.4

"~GeH5

§

Sill5+ ,,, C H s ~ . ~ =_ 2.3

9

.,

.

;

'

~

"

-4

In D o

Figure 11. Double logarithmic correlation between the HOMO-LUMO separation of the AH(3§ fragment and dihydrogen and the dissociation energy Do for all pentacoordinated complexes.

d orbitals into the antibonding o* H 2 orbital, which subsequently leads to H-H bond cleavage, yielding 40. It is expected that a cationic charge will reduce the backbonding and lead to structures of type 39. But how does this apply to main group elements with occupied (e.g., germanium) or unoccupied (e.g., silicon) d orbitals? The effect of d orbitals, unoccupied or occupied, on the heavier atoms (Si, Ge) is generally negligible. The contributions to the binding of the dihydrogen moiety through electron transfer via r --~ d(Si) for SiH~ or d(Ge) ~ r are in the range of 0.2--0.3 % (NBO analysis). This is due to the size incompatibility of the hydrogen o and the metal d orbitals, which make a significant orbital overlap impossible. Another important factor for the magnitude of D O is the orbital energy gap between the AH~+) LUMO and the o H 2 orbital (HOMO), comprising the 3a' orbital (Figure 3). This relationship determines how much electron density is allowed to be transferred from the dihydrogen moiety to the electron-deficient AH~+) fragment. A double logarithmic representation of the orbital energy difference and D O supports this trend (Figure 11). What are the chemical consequences of these observations? Table 14 summarizes the relative energies for the various structural isomers depicted in Figure 1. With the exception of CH~, all ions prefer structures where the H 2 subunit remains intact. The energy required to break the hydrogen-qaydrogen bond (104 kcal mo1-1) is not compensated by the two newly formed A-H (A = Si, Ge, B, or A1) bonds. Thus, only for the methonium ion are the Cnv and D3h isomers not much higher in energy than C~(I)(I, A = C), which also contributes to the fluxional nature of CH~. Conversely, all AH~+) C3v isomers (except CH~ C3v) are low in energy. In a first approximation, the proton affinity (PA0) and the dissociation energy D O are in-

Cation-Dihydrogen Complexes: Theoretical Considerations

157

Table 14. Comparison of the Relative Energies (in kcal mo1-1, Including ZPVE), H 2 Dissociation Energies (Do), and Proton Affinities (PA0) of AH(5§ Species

Geometry

CI-~ a

SiI-I~5b

GeH~5

BH5 h

AIH5 h

G(])

o.o

o.o

o.o

o.o

Cs(II )

0.1

0.0

0.0

0.0

0.0

C2v(I)

0.6 31.5

26.9 8.8

32.7 7.5

11.6 0.22 i

26.0 0.1 i

3.5

60.6

83.8 f

22.8

71.9

11.5 42.0 g

82.6 10.3

48.3 f 10.0

45.3 0.9 j

84.0 0.07 k

C3v C4v D3h Do d

PAoe Notes:

130.5

153.2

156.4

345.8 j

o.o

328.3 k

aDZp CCSD. bTZ2P CCSD, unless otherwise specified. CTZP +fCCSD, unless otherwise specified. dAI-~+)--), AH(3+)+ H 2. eAH(4-) + H+ __>(AH)(+). fDZP SCF. gQCISD(T)/6-311 ++G(3df,3pd)llMP2(fu)16-311++G(2df,2pd). Experimental D o = 45.3 kcal mol-I" AHfof CH~ = 216.0 kcal tool-l (Ref. 79); bHfofCI-~3 = 261.3 kcal tool- (Ref. 41b). hDZp CCSD. iDissociates at higher levels. JTZ(3dlflg,2p l d) CCSD(T)ttTZ(3dlf,2pl d) CCSD(T). kTZ2P CCSD(T).

versely proportional, as CH~ has the highest D Obut the lowest PA0 and both BH 5 and A1H5 have small dissociation energies and high proton affinities.

V. C O N C L U D I N G REMARKS We conclude that all AH~+) species are held together by chemical bonds and not merely by van der Waals interactions. The bonding of the second hydrogen molecule, e.g., in the AH~ (H2) and (H2)AH ~ (H 2) complexes, is mostly electrostatic. With the exception of the unique, highly fluxional methonium ion (which undergoes complete hydrogen scrambling even at 0 K), the dihydrogen moieties are well separated from the cationic fragments, allowing virtually free H 2 rotation. The binding arises both from charge transfer (H 2 ~ AH~+)) and suitable orbital overlap [o (H2) ~ p (AH~+))]. The participation of d orbitals is unimportant. The linear correlation between the dihydrogen stretching frequency and the dissociation energy can be used conveniently to estimate D o from experimental IR data. BSSE corrections to D o are important as they can account for up to 0.5 kcal mo1-1, even when good basis sets are used. Overall, the available experimental results are very well reproduced by theory.

158

SCHREINER, SCHAEFER Iii, and SCHLEYER

ACKNOWLEDGMENTS The work in Erlangen was supported by the Deutsche Forschungsgemeinschafi, the Fonds der Chemischen Industrie, and the Convex Computer Corporation. The work in Georgia was supported by the U.S. Department of Energy, the U.S. National Science Foundation, and the U.S. Air Force Office of Scientific Research.

REFERENCES AND NOTES 1. Chatasifiski, G.; Szcz~niak, M. M. Chem. Rev. 1994, 94, 1723. 2. Crabtree, R. H. Acc. Chem. Res. 1990, 23, 95. 3. Olah, G. A.; Prakash, G. K. S.; Williams, R. E.; Field, L. D.; Wade, K. Hypercarbon Chemistry; Wiley-Interscience: New York, 1987; p 1. 4. Olah, G. A.; Prakash, G. K. S.; Summer, J. Superacids; Wiley-Interscience: New York, 1985; p 1. 5. Purvis, G. D.; Bartlett, R. J. J. Chem. Phys. 1982, 76, 1910. Urban, M.; Noga, J.; Cole, S. J.; Bartlett, R. J. J. Chem. Phys. 1985, 83, 4041. 6. Szczesniak, M. M.; Chalasinski, G. J. MoL Struct. (Theochem.) 1992, 261, 37. 7. Moller, C.; Plesset, M. S. Phys. Rev. 1934, 46, 618. Binkley, J. S.; Pople, J. A. Int. J. Quant. Chem. 1975, 9, 229. Pople, J. A.; Binkley, J. S.; Seeger, R. Int. J. Quant. Chem. 1976, S1 O, 1. 8. Scheiner, A. C.; Scuseria, G. E.; Lee, T. J.; Rice, J. E.; Schaefer, H. F. J. Chem. Phys. 1987, 87, 5391. 9. Brooks, B. R.; Laidig, W. D.; Saxe, P.; Goddard, J. D.; Yamaguchi, Y.; Schaefer, H. E J. Chem. Phys. 1980, 72, 4625. Rice, J. E.; Amos, R. D.; Handy, N. C.; Lee, T. J.; Schaefer, H. F.J. Chem. Phys. 1986, 85, 963. 10. Langhoff, S. R.; Davidson, E. R. Int. J. Quantum Chem. 1974, 8, 61. 11. Scuseria, G. E. Chem. Phys. Lett. 1991, ! 76, 27. 12. Janssen, C. L.; Seidl, E. T., Scuseria, G. E.; Hamilton, T. P. Yarnaguchi, Y.; Remington, R. B.; Xie, Y.; Vacek, G.; Sherrill, C. D.; Crawford, T. D.; Fermann, J. T.; Allen, W. D.; Brooks, B. R.; Fitzgerald, G. B.; Fox, D. J.; Gaw, J. F.; Handy, N. C.; Laidig, W. D.; Lee, T. J.; Pitzer, R. M.; Rice, J. E.; Saxe, P.; Scheiner, A. C.; Schaefer, H. E PSITECH, Inc.: Watkinsville, GA 30677, USA; 1994. 13. Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomperts, R.; Andres, J. L; Raghavachari, K.; Binkley, J. S.; Gonzales, G.; Martin, R. L.; Fox, D. J.; DeFrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. GAUSSIAN 92; Gaussian, Inc.: Pittsburgh, PA; 1992. 14. Thomas, J. R.; DeLeeuw, B. J.; Vacek, G.; Schaefer, H. F.J. Chem. Phys. 1993, 98, 1336. 15. Thomas, J. R.; DeLeeuw, B. J.; Vacek, G.; Crawford, T. D.; Yamaguchi, Y.; Schaefer, H. E J. Chem. Phys. 1993, 99, 403. 16. Fermann, J. T.; Sherrill, C. D.; Crawford, T. D.; Schaefer, H. F.J. Chem. Phys. 1994, 100, 8132. 17. Dunning, T. H., Jr. J. Chem. Phys. 1971, 55, 716. Huzinaga, S.J. Chem. Phys. 1965, 42, 1923. 18. Hehre, W. J.; Radom, L.; Pople, J. A.; Schleyer, P. v. R. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. 19. Huzinaga, S. "Primitive Basis Sets for Silicon"; Department of Chemistry Report II, University of Alberta: Edmonton, Alberta, Canada, 1971. 20. Dunning, T. H. J. Chem. Phys. 1970, 53, 2823. The contraction of this primitive Ge basis set is due to R. S. Grev and H. E Schaefer, unpublished material. 21. Dunning, T. H.; Hay, E J. In Modern Theoretical Chemistry; Schaefer, H. E, Ed.; Plenum: New York, 1977; 3, pp 1-27. 22. McLean, A. D.; Chandler, G. S.J. Chem. Phys. 1980, 72, 5639.

C a t i o n - D i h y d r o g e n C o m p l e x e s : Theoretical Considerations

23. 24. 25. 26. 27. 28.

29. 30. 31.

32. 33. 34. 35. 36. 37. 38. 39. 40. 41.

42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59.

159

Hobza, P.; Zahradnik, R. Chem. Rev. 19118,88, 871. Chalasinski, G.; Gutowski, M. Chem. Rev. 1988, 88, 943. Boys, S. F.; Bemardi, F. Chem. Phys. Lett. 1969, 3, 140. Duijneveldt, E B. v.; Duijneveldt-v. d. Rijdt, J. G. C. M.; Lenthe, J. H. v. Chem. Rev. 1994, 94, 1873. Feller, D.J. Chem. Phys. 1992, 96, 6104. Pople, J. A.; Kilshnan, R.; Schlegel, H. B.; Binkley, J. S. Int. J. Quant. Chem. 1975, S13, 225. Saxe, E; Yamaguchi, Y.; Schaefer, H. E J. Chem. Phys. 1982, 77, 5647. Osamura, Y.; Yamaguchi, Y.; Saxe, P.; Vincent, M. A.; Gaw, J. F.; Schaefer, H. F. Chem. Phys. 1982, 72, 13 I. Grev, R. S.; Janssen, C. L.; Schaefer, H. F.J. Chem. Phys. 1991, 95, 5128. Besler, B. H.; Scuseria, G. E.; Scheiner, A. C.; Schaefer, H. F. J. Chem. Phys. 1988, 89, 360. Schreiner, E R.; Kim, S.-J.; Schaefer, H. E; Schleyer, E v. R.J. Chem. Phys. 1993, 99, 3716, and references cited therein; for a semipopular review of this work, see Scuseria, G. E. Nature 1993, 366, 512. Tal'roze, V. L.; Lyubimova, A. K. Dokl. Akad. Nauk. SSSR 1952, 86, 909. Jennings, K. R. Gas Phase Ion Chemistry; Bowers, M. T., Ed.; Academic: New York, 1979; Vol.2, p 123. Dyczmons, V.; Staemmler, V.; Kutzelnigg, W. Chem. Phys. Lett. 1970, 5, 361. Lathan, W. A.; Hehre, W. J.; Curtiss, L. A.; Pople, J. A.J. Am. Chem. Soc. 1971, 93, 6377. Dyczmons, V.; Kutzelnigg, W. Theor. Chim. Acta 1974, 33, 239. Ragavachari, K.; Whiteside, R. A.; Pople, J. A.; Schleyer, E v. R. J. Am. Chem. Soc. 1981, 103, 5649. Hirao, K.; Yamabe, S. Chem. Phys. 1984, 89, 237. Klopper, W.; Kutzelnigg, W. J. Phys. Chem. 1990, 94, 5625. Schleyer, P. v. R.; Carneiro, J. W. de M.J. Comput. Chem. 1992, 13, 997. (a) AHf(CH5+) = 218.8 kcal mol-l: Bohme, D. K.; Mackay, G. I.; Schiff, H. I.J. Chem. Phys. 1980, 73, 4976. (b) AHf(CH3+) = 261.3 kcal mol-l: Traeger, J. C.; McLoughlin, R. G.J. Am. Chem. Soc. 1981, 103, 3647. Heck, J. R. A.; de Koning, L. J.; Nibbering, N. M. M. J. Am. Soc. Mass. Spectrom.1991, 2, 453, and references cited therein. Boo, D. W.; Lee, Y. T. J. Chem. Phys. 1993, 211, 358. Yamabe, S.; Osamura, Y.; Minato, T. J. Am. Chem. Soc. 1980, 102, 2268. Fois, E.; Gamba, A.; Simonetta, M. Can. J. Chem. 1985, 63, 1468. Hiraoka, K.; Kebarle, P. J. Am. Chem. Soc. 1975, 97, 4179. Hiraoka, K.; Moil, T. Chem. Phys. Lett. 1989, 161, 111. Hiraoka, K.; Kudaka, I.; Yamabe, S. Chem. Phys. Lett. 1991, 184, 271. Okumura, M.; Yeh, L. I.; Lee, Y. T.J. Chem. Phys. 1988, 88, 79. Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. Rev. 1988, 88, 899. Carneiro, J. W. de M.; Schleyer, P. v. R.; Saunders, M.; Remington, R. B.; Schaefer, H. F.; Rauk, A.; Sorensen, T. J. Am. Chem. Soc. 1994, 116, 3483, and references cited therein. Weiner, J.; Smith, G. P. K.; Saunders, M.; Cross, R. J., Jr. dr. Am. Chem. Soc. 1973, 95, 4115. (a) Hiraoka, K.; Kebarle, P. dr. Am. Chem. Soc. 1976, 98, 6119. (b) Hiraoka, K.; Kebarle, P. Adv. Mass. Spectrom. 1978, 7b, 1408. French, M.; Kebarle, P. Can. J. Chem. 1975, 53, 2268. Yeh, L. I.; Price, J. M.; Lee, Y. T. dr. Am. Chem. Soc. 1989, 111, 5597. Powell, C. F. Vapor Deposition; Wiley: New York, 1966. Olah, G. A.; Heiliger, L.; Aniszfeld, R.; Prakash, G. K. S. New J. Chem. 1990, 877. Collins, J. B.; Schleyer, P. v. R.; Binkley, J. S.; Pople, J. A.; Radom, L. dr. Am. Chem. Soc. 1976, 98, 3436. Hu, C.-H.; Shen, M.; Schaefer, H. F. Chem. Phys. Lett. 1992, 190, 543

160

SCHREINER, SCHAEFER i11, and SCHLEYER

60. Rosenstock, H. M.; Draxl, K.; Steiner, B. W.; Herron, J. T. J. Phys. Chem. Ref. Data 1977, 6, Supplement 1. 61. Potzinger, P.; Ritter, A.; Krause, J. Z. Naturforsch. 1975, 30A, 347. 62. Dyke, J. M.; Jonathan, N.; Morris, A.; Ridha, A.; Winter, M. J. Chem. Phys. 1983, 81,481. 63. Cao, Y.; Choi, J.-H.; Haas, B.-M.; Johnson, M. S.; Okumura, M. J. Phys. Chem. 1993, 97, 5215. 64. Hu, C.-H.; Schreiner, P. R.; Schleyer, P. v. R.; Schaefer, H. F. J. Phys. Chem. 1994, 98, 5040. 65. Liu, R.; Zhou, X.J.J. Phys. Chem. 1993, 97, 9555. 66. Senzer, S. R.; Abernathy, R. N.; Lampe, F. W. J. Phys. Chem. 1980, 84, 3068. 67. (a) Hartmann, H.; Papula, L.; Strehl, W. Theor. Chim. Acta 1970, 19, 155. (b) Kohda--Sudoh, S.; Ikuta, S.; Nomura, O.; Katagiri, S.; Imamura, M. J. Phys. B: At. MoL Phys. 1983, 16, L529. (c) Kohda-Sudoh, S.; Ikuta, S.; Nomura, O.; Katagiri, S. Nippon Kagaku Kaishi 1984, 10, 1625 (through CA). (d) Sudoh, S.; Nomura, O.; Ikuta, S.; Katagiri, S. Rikagaku Kenkyusho Hokoku 1983, 59, 65. (e) Sudoh, S.; Nomura, O.; Ikuta, S.; Katagiri, S. Rikagaku Kenkyusho Hokoku 1983, 59, 71. (f) Sudoh, S.; Nomura, O.; Ikuta, S.; Katagiri, S. Rikagaku Kenkyusho Hokoku 1983, 59, 123. 68. Schreiner, P. R." Schaefer, H. F.; Schleyer, P. v. R.J. Chem. Phys. 1994, 101, 2141. 69. Allred, A. L.; Rochow, E. G. J. Inorg. NucL Chem. 1958, 5, 264. 70. Bohme, D. K.; Mackay, G. I.; Schiff, H. I.J. Chem. Phys. 1980, 73, 4978. 71. Cheng, T. M. H.; Lampe, F. W. Chem. Phys. Lett. 1973, 19, 532. 72. Smith, B. J.; Radom, L.J. Am. Chem. Soc. 1993, 115, 4885. 73. Archibong, E. F.; Schreiner, P. R.; Leszczynski, J.; Schleyer, P. v. R.; Schaefer, H. F.; Sullivan, R. J. Chem. Phys. 1995, 102, 3667. 74. (a) Olah, G. A.; Westerman, P. W.; Mo, Y. K.; Klopman, G. J. Am. Chem. Soc. 1972, 94, 7859. (b) Hoheisel, C.; Kutzelnigg, W. J. Am. Chem. Soc. 1975, 97, 6970. (c) Collins, J. B.; Schleyer, P. v. R.; Binkley, J. S.; Pople, J. A.; Radom, L. J. Am. Chem. Soc. 1975, 98, 3436. (d) Pepperberg, I. M.; Halgren, T. A.; Lipscomb, W. N. J. Am. Chem. Soc. 1975, 98, 3442. 75. (a) Stanton, J. F.; Lipscomb, W. N.; Bartlett, R. J.J. Am. Chem. Soc. 1988,111, 5273. (b) Schreiner, P. R.; Schaefer, H. F.; Schleyer, P. v. R J. Chem. Phys. 1994, 101, 7625. (c) Watts, J. D.; Bartlett, R. J. J. Am. Chem. Soc. 1995, 117, 825. 76. Tague, T. J., Jr.; Andrews, L. J. Am. Chem. Soc. 1994, 116, 4970. 77. Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 18, 553. 78. Schreiner, P. R.; Schaefer, H. F.; Schleyer, P. v. R.J. Chem. Phys. 1995, 103, 5565. 79. Lias, S. G.; Bartmess, J. E.; Liebmann, J. F.; Holmes, J. L.; Levin, R. D.; Mallard, W. G. J. Phys. Chem. Ref. Data 1988, 17, 1.

SYMMETRY-INDUCED KINETIC ISOTOPE EFFECTS IN ION-MOLECULE REACTIONS

Gregory i. Gellene

Io II. III. IV. V. VI. VII. VIII.

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theory Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . He~ Formation: An Illustrative Example . . . . . . . . . . . . . . . . . . . . H~- Formation: Insight into the Approximations . . . . . . . . . . . . . . . . O~ Formation: The Effect of Electronic Degeneracy . . . . . . . . . . . . . (CO2)~ Formation: Separation of the Degeneracies . . . . . . . . . . . . . . . Ar.CO~ Formation: Isolation of the Electronic Degeneracy . . . . . . . . . . Concluding Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

161 162 163 165 171 174 181 186 188 189 189

ABSTRACT Symmetry-induced kinetic isotope effects cause changes in the rate of a chemical process involving identical nuclei when the nuclear symmetry of the system is altered

Advances in Gas Phase Ion Chemistry Volume 2, pages 161-191. Copyright 9 1996 by JAI Press Inc. All rights of reproduction in any form reserved. ISBN: 1-55938-703-3

161

GREGORY I. GELLENE

162

by isotopic substitution. A recently proposed theory of the phenomenon is briefly presented and applied to several ion--molecule reaction systems where order-of-magnitude kinetic isotope effects have been observed. The specific examples discussed are chosen to illustrate various aspects of the theory and are presented in order of increasing complexity beginning with simple atom/atom collisions (He+/He), followed by diatomic/diatomic (H~/H2 and O~/O2) and triatomic/triatomic (CO~/CO2) collisions, and ending with an atom/triatomic system (CO~/Ar). The final system is particularly unique because it represents the first example of symmetry-induced kinetic isotope effects in a system where the reactants have no atoms in common.

I. I N T R O D U C T I O N Nearly all kinetic isotope effects (KIE) have their origin in the difference of isotopic mass due to the explicit occurrence of nuclear mass in the SchrOdinger equation. In the nonrelativistic Born-Oppenheimer approximation, isotopic substitution affects only the nuclear part of the Hamiltonian and causes shit, s in the rotational, vibrational, and translational eigenvalues and eigenfunctions. In general, reasonable predictions of the effects of these shit, s on various kinetic processes can be made from fairly elementary considerations using simple dynamical models. Over the past decade, evidence has been mounting for a kinetic isotope effect in systems containing identical nuclei that has its origin in symmetry rather than mass considerations. It is thus qualitatively and quantitatively different from those usually considered in chemical dynamics. In particular, these symmetry-induced kinetic isotope effects (SIKIE) can, in principle, occur with significant magnitude (factors of ten or more will be discussed) for all the elements of the periodic table. For elements having three or more isotopes, equivalent SIKIE are expected for the different ways the system can be made isotopically heteronuclear. This second characteristic is particularly important because it can be considered as the signature of SIK/E. One of the first chemical reactions for which SIKIE was identified was the association reaction ofO 2 and O to produce ozone. The initial key observation 1was that stratospheric ozone was enriched in 180 at levels up to 40% above natural abundance. Following laboratory experiments, 2'3 which showed that the enhancement occurred independently of isotopic mass (i.e., 490 3 and 500 3 were equivalently enhanced) under a variety of temperature and pressure conditions, stratospheric measurements 4'5 of 490 3 demonstrated that the enhancement occurring in the atmosphere was also independent of isotopic mass. However, despite more than ten years of study,6"-1~neither the fundamental role of symmetry nor the details of isotopic fractionation in this important atmospheric reaction are presently understood. Although SIKIE have been observed in additional systems (e.g., the formation Of SEF10from SF 5+ SF 5 and CO 2 from CO + O and the photodissociation ofO3), ll-13

Symmetry-Induced Kinetic Isotope Effects

163

this is a largely unexplored area of chemical kinetics and reaction dynamics. Our own interest in the problem was motivated by the observation of SIKIE in the formation of O~ from O~ and 02 with a magnitude considerably greater (SIK/E up to 100) than those previously reported for other systems. This result could not be rationalized by any existing theory, and a new theoretical approach ~4 was developed. Guided by the predictive capability of this theory, SIKIE were subsequently observed in the formation of He~, (CO2)~, and Ar-CO~. Each of these systems illustrates a different aspect of SIKIE and will be discussed in detail, following an overview of the theory as it is presently understood.

II. THEORY OVERVIEW The importance of symmetry considerations in chemical dynamics has long been recognized and is embodied in such correlation schemes as the Wigner-Witmar rules 15 for atomic reactants, and Schuler's rules 16 and the Woodward--Hoffmann rules 17 for molecular reactants. These rules have been found to be very useful in the prediction and understanding of the nature of the products in many chemical systems. For example, because the Woodward--Hoffmann rules correlate the electronic orbital symmetry of reactants and a specified transition state, they can be used to make qualitative kinetic predictions. However, the treatment of only the electronic degrees of freedom precludes consideration of the symmetry-breaking effects of nuclear motion or isotopic substitution. The effect of nuclear symmetry in chemical dynamics has been considered by Quack. 18 Because the nuclear configuration of reactants, products, and the intervening transition state generally cannot be related to a single reference geometry, point group operations were not suitable for this symmetry analysis. Instead, Quack used permutation inversion (PI) symmetry groups where the operations are defined by permutation of identical nuclei with and without coordinate inversion. (For a particularly complete treatment of PI symmetry groups and their application to the classification of molecular symmetry properties, the .reader is referred to Ref. 19). Neglecting only coupling to nuclear spin, Quack showed that the invariance of the system Hamiltonian to PI symmetry operations implied that only certain rovibronic states of reactants and products are connected in reactions involving identical nuclei, regardless of the details of the chemical transformation. Ironically, the independence of Quack's correlation scheme from transition-state consideration is both the origin of its power and generality (because details of the Hamiltonian in the interaction region are frequently unknown) and the reason why the scheme cannot be used to estimate the likelihood of a particular allowed reaction. A symmetry correlation scheme that is capable of addressing SIKIE must combine the geometry-independent treatment of all the molecular degrees of freedom characteristic of Quack's approach with the connection of reactant and transition-state symmetries characteristic of a Woodward-Hoffmann-type analysis. To make the problem somewhat less abstract, consider the cartoon in Figure 1

164

GREGORY I. GELLENE

depicting two diatomic molecules faced with "deciding" between a reactive and a nonreactive potential energy surface (PES) on which to interact. At infinite reactant separation, the symmetry properties of the nuclear-rotational-vibrational-electronic-translational wavefunction (~I/nrvet) for the supermolecular system (i.e., the two reactants treated as a single molecule) can be determined from PI symmetry considerations. 19 In general, the symmetry properties will be found to depend on the evenness or oddness of various angular momentum quantum numbers such as J (the total angular momentum of a molecule exclusive of nuclear spin) and l (the relative orbital angular momentum of the two molecules) emphasized in Figure 1. Determination of the symmetry properties of the asymptotic wavefunction, however, is not sufficient to treat SIKIE, because the critical question is whether the symmetry of a particular ~IJnrvet affects the propensity to connect with a particular PES. Usually, the symmetries of the electronic states (~e) of the reactants are known so that the actual question being asked is whether reactivity can depend on the symmetry of the nuclear motional states (~nrvt)" For a completely general collision between diatomic molecules (e.g., AB + CD), the symmetries of qbe and ~nrvt are uncorrelated and no symmetry-based restrictions on the reactivity of different ~nrvt would be expected. However, if the system contains identical nuclei, the symmetries of ~e and ~nrvtare correlated by restrictions placed on the symmetry of the total wavefunction by the Pauli principle. In this case, symmetry-based restrictions on the reactivity of different ~nrvt states can occur. We have recently developed a new symmetry correlation scheme 14that connects symmetry-distinct rovibronic states of the isolated reactants with distinct electronic symmetries of the system in the interaction region independent of the detailed geometry of the collision complex. Briefly, the approach can be logically divided into four steps. First, the appropriate PI group for describing the isolatedreactants is chosen. Second, ~nrvet for the reactant supermolecule system and the electronic states of the collision complex are expressed in terms of an appropriate set of basis

!

O Figure 1. Cartoon depicting symmetry considerations of the asymptotic wavefunction that influences which potential energy surface is accessed. Representative angular momentum quantum numbers relevant to the process are the total molecular angular momentum exclusive of nuclear spin (J) and the relative orbital angular momentum (/).

Symmetry-Induced Kinetic Isotope Effects

165

functions having well-defined transformation properties under the operations of the PI group. Third, Pauli-allowed symmetry-adapted ~nrvet'S are projected out of the set of basis functions. Finally, possible symmetry restrictions are identified by correlation of the symmetry-adapted ~Pnrvetwith the electronic states of the collision complex. Following this approach it is possible to identify two general ways in which a symmetry restriction may arise: (1) the two reactants are identical, but in different electronic states, or (2) at least one of the reactants is in a degenerate electronic state. It is important to emphasize that this theory of SIKIE should be considered as a work in progress and that the symmetry restrictions identified by this approach are generally best thought of as propensities. The approximations in the theory lie not in the symmetry assignments of tPnrvet (which can always be accomplished), 19 but rather in the use of a correlation scheme based on asymptotic states of the reactants that can be mixed by neglected PES coupling terms. For example, suppose the two molecules in Figure 1 are initially in an l = even state. As the molecules approach each other, long-range anisotropy in the interaction potential can mix some l = odd character into the initial l = even state. With increasing mixing, both the usefulness ofl as a good quantum number for describing the supermolecule and the likelihood of realizing a symmetry restriction based on l decrease. In other words, the extent to which the macroscopic kinetics of a system containing identical nuclei will be affected by a predicted symmetry restriction can be thought of as depending on the "goodness" of the relevant asymptotic quantum number at separations where the dynamics can be thought of as occurring on one PES or the other. Unfortunately, the a priori prediction of the magnitude of relevant PES coupling terms is a difficult proposition. Thus, further understanding of SIKIE requires a strong interplay between experiment and the developing theory. In the sections that follow, several examples of SIKIE (chosen to illustrate various aspects of the theory) will be discussed. These examples come from work in this laboratory and concentrate on ion-molecule reactions because the theoretical requirement of an asymptotic PES degeneracy can be readily satisfied. Also, by use of the ion source as the reaction vessel, SIKIE can be determined directly by mass spectrometric measurements without the need for separation or purification of the reaction products.

!11. He~ FORMATION" AN ILLUSTRATIVE EXAMPLE The concepts introduced in the previous section can be made more concrete by consideration of the termolecular formation of He~ according to the energy transfer mechanism,

k He + + He ~ - (He~)* k~

(1)

166

GREGORY I. GELLENE

ks (He~)* + He ~ He; + He

(2)

where (He~)* represents a collision complex and ka, kd, and ks are the phenomenological association, dissociation, and stabilization rate constants, respectively. This case will be treated in some detail because the atomic nature of the reactants leads to a relatively simple symmetry analysis and a straightforward understanding of the ensuing SIKIE. It is intended that this treatment will provide a working appreciation of how the theory is applied and, in the more complicated cases subsequently considered, only a summary of the results of the symmetry analysis

.•He•

1

+ HeB

0

HeA + He~

2T-,u

-1

R (A)

b

3He+ + 4He @

E

3He

o

+ 4He+

i -1"

2T__,+ -2"

-3

3

s

R (A)

8

~

Figure 2. Potential energy curves relevant to He+(251/2) and He(15) collisions of (a) identical and (b) nonidentical isotopes.

Symmetry-Induced Kinetic Isotope Effects

167

will be given. For a full treatment, 2~the interested reader is referred to the original literature cited. Ordinarily, termolecular association is thought of as occurring on a single Born--Oppenheimer surface corresponding to electronic ground state species. However, significant symmetry restrictions exist that prevent this from always being so for reaction (1) with identical nuclei. The potential energy curves 2~'22 relevant to reaction (1) are shown in Figure 2. For identical nuclei (Figure 2a), an asymptotic electronic degeneracy arises from the quantum mechanical inability to specify which atom is the He(IS) neutral and which is the He+(2S1/2) ion. A decrease in the internuclear separation removes the degeneracy, giving rise to the 2E~ ground and 2E+_ excited Born-Oppenheimer electronic states. Figure 2b shows potential energy g curves 23 for the corresponding states of 7He~ that are fundamentally different from those of the h o m o n u c l e a r case because the different energy of the 4He+/3He and 3He+/4He asymptotes removes the degeneracy at large separation. The detailed symmetry analysis of reaction (i) begins with the selection of the appropriate PI group, which is D~h(M) and C~v(M ) for identical and non-identical nuclei, respectively. 19 Because of the very weak coupling of nuclear spin, electron spin, and rotation in this molecule, and the absence of electronic orbital angular momentum, good quantum numbers for this system are the total molecular nuclear spin (/), the individual atomic nuclear spins (I 1 and I2), the total electronic spin (S) and its projection on a space-fixed Z axis (Ms), and the relative orbital angular momentum of the two atoms (/). Consequently, it is appropriate to use Hund's case (b13)functions 24 as a basis for both the asymptotic He+/He and the (He~)* wavefunctions. In terms of these basis functions, zero-order wavefunctions for the S = 1/2, M s - 1/2 state of He+/He of any isotopic composition can be written as a linear combination of the product wavefunctions,

V a = IlsIlsIlsIIllSMs)lll(1)I2(2);IMi)llMtjl)

(3)

Wb = [lsI lslI lsII[[SMs>[II(2)I2(1)'IMl)[lMtjt)

(4)

where [.-.[ is a normalized Slater determinate of ls atomic orbitals with a bar indicating a B-electron spin and the roman numeral superscripts distinguishing between coordinates center on the two atoms; [SMs) is an electron spin wavefunction; [lMtit) is a relative translational wavefunction composed of a spherical Bessel function ([ Jr)) for the component along the line connecting the atoms and a spherical harmonic (I/Mr)) for the rotational component; and [/1(2)12(1);IMI) is a nuclear spin wavefunction. I 1 and I 2 couple to form the resultant molecular nuclear angular momentum I having a space-fixed Z component M I. ~a represents the case where atom 1 is the neutral and atom 2 is the ion, whereas ~I~b represents the opposite situation. 9 , and Wb have well-defined transformation properties under the operations of Dooh(M) and Coov(M), and it is found that they transform into +/- themselves or +/-

168

GREGORY I. GELLENE Table 1. Symmetry Analysis and CorrelationScheme for He§

lsotopomer 4He*./4He

3He+/3He

3,4He+/4,3He

l

I

Parity

even

even

odd

even

even even odd odd

--~ He~

tlfln,.vet

~e

(+)

q'Ja + q*b

~Pa + ~Pb

Yg(~P*)

(-)

~a - ~b

t~a - (~b

Y~+(t~gs)

even

(+)

odd

(+)

even odd

(-) (-)

~a + ~Pb ~I'ta -- ~I/b ~IJa - ~t/b q~a + ~I~b

~a + t~a t~a ~a +

Zg(~*) Y":(t~gs) Y~:(t~gs) Zg(~)*)

even

--

(+)

odd

--

(-)

~IJa -----~db ~'la - ~IJb

(~a + (~b ~a 4- (~b

~b {~b t~b ~)b

Coupling

I"(~e) a

+

l

J

l-(l I + 12+ s)

1 , l'(I1 + I2 + S)

+

Zg t~) Z u ~g t~ 5-'.+

Note: a~, and ~gs denote excited and ground electronic states respectively.

each other, depending on the evenness or oddness of the angular momentum quantum numbers l for Do~h(M) and C~v(M ), and on I - I 1 - 12 (i.e., the difference of the molecular nuclear spin and the sum of the atomic nuclear spins) for Do~h(M) only. These results are then used to produce symmetry-adapted Pauli-allowed ~Jnrvet'S f r o m which possible symmetry restrictions can be identified from the correlation scheme, ~a + ~ b ~ t~a + t~b = [lsIlsIlsII[ + [lsllslIlsI-~[; r'(t~e)= ~'g+

(5)

m

kI~a -- kPb ~ (~a -- (~b = I1sIlsllslI[

- [lsI1slIlslII;

1-'(r

= Eu+

(6)

where ~e transforms as l"(t~e) in D~h(M ) (i.e., the symmetry of the Coulombic potential regardless of isotopic composition). The result of this analysis and the ensuing symmetry restrictions for the various isotopomers are summarized in Table 1. Although these symmetry restrictions have been known for some time, 25'26 the kinetic implications appear not to have been recognized previously. For 4He+/4He collisions, the ground electronic state can be accessed only by collisions of odd l, which, except at extremely low temperature, account for 50% of the collisions. For 3He+/3He collisions, with the assumption that the coupling of the atomic spins occurs independently of l (valid when the average collisional kinetic energy is very much greater than spin-rotation interactions), a similar conclusion of 50% of the collisions accessing the ground electronic state is reached. Finally, for 4He+/3He or 3He+/4He collisions, no symmetry restrictions occur and 100% of the collisions can access the ground electronic state. Thus, this analysis predicts a SIKIE that favors production of 7He~ by a factor of two over 6'8He~, a result that was not anticipated by any previous theoretical treatment 27-29 of this reaction. Before leaving this analysis, it is worth making two additional points. First, the inferred symmetry restrictions are rigorous only in the case of 4He+/4He because the non-zero value of

Symmetry-Induced Kine6c Isotope Effects

169

nuclear spin for 3He allows coupling of the two electronic states through the spin--rotation interaction, !.(I 1 + 12 + S), which might become important at extremely low collision energies. Thus, even for this simple atomic reaction, the symmetry restrictions are best thought of as propensity rules. Second, no consideration has yet been given to conventional mass-dependent kinetic isotope effects nor to tunneling effects, which might not be insignificant given the relatively light masses of the reactants. Although a detailed analysis of these effects requires more mechanistic and rate constant information than is currently available, several approximate treatments 27-29 of reactions (1) and (2) predict a mass-dependent KIE of only about 15%, which is considerably smaller than the predicted SIKIE. Experimentally, the determination of KIE in the formation of He~ is a relatively straightforward mass spectrometric experiment, and the methodology described is common to all the subsequently discussed experimental SIKIE studies. He + ions were produced by electron ionization (El) of 3He/4He mixtures at total ion source inlet pressures of 10 to 1500 mtorr as measured by a capacitance manometer, accelerated through 5 keV, magnetically mass resolved, and detected by a channeltron electron multiplier operating in a single ion counting mode. KIE can be measured by the determination of relative ion intensities (I;/Ij where i andj are the m/z values of the He~ ion) as a function of ion source inlet pressure. To emphasize the kinetic isotope effects, it is convenient to express the isotopomer intensity measurements in terms of a statistically normalized enhancement factor, EF(i,j) = (Ii/Ij)~

(7)

(Ii/Ij)stat where m/z =j is taken as the high-symmetry isotopomer and will be omitted from the EF notation in cases where only one high-symmetry isotopomer is considered. With this definition, KIE can be identified by deviations from EF = 1. The experimentally determined EF(7,8) and EF(7,6) as a function of ion source inlet pressure are presented in Figures 3a and 3b respectively. On a qualitative level, both plots show a similar dramatic increase in EF at low pressure, indicating the 2. The apparent loss of EF occurrence of significant SIKIE in the formation of 7He + at increased pressure is best understood not as a loss of SIKtE but rather as an increase in the importance of reactions such as, 7He~ + 4He ~

8He +2 + 3He

(8)

that can scramble the nascent isotopic distribution of He~ ions and lead ultimately to an equilibrium distribution. The establishment of equilibrium in Figure 3b at lower inlet pressure than that in Figure 3a can be understood by a consideration of the reaction scheme:

6He k67[~e]7He~ k7613He]

k7~e] 8He~"

kaT[3He]

(9)

1 70

A

3! t

GREGORY I. GELLENE b

..

Stabilization with I~

<

Stabili.zation with

W

1

0 Inlet Pressure (mTorr)

0

100

200

300

400

Inlet Prelmure (mTorr)

+ + Figure 3. (a) Statistically normalized 7 He2/~He2 ion intensity ratio as a function of

ion source inlet pressure. The 3HeflHe ratio is 0.096 + 0.003. (b) Statistically normal+ + ion intensity ratio as a function of ion source inlet pressure. The ized 7He2/6He2

3HeflHe ratio is 1.09 + 0.02.

Because the system initially has excess 7 He +2 (relative to equilibrium value), the inlet pressure dependence of EF(7,6) is dominated by the left side of reaction (9) whereas the inlet pressure dependence of EF(7,8) is dominated by the fight side. Thus, EF(7,8) and EF(7,6) will approach equilibrium with effective rate constants k78 and kT~ respectively, given approximately by, /r ~ k7814He] + k8713He] = k78[He](7,~ + 2Z3)

(lOa)

k76 ~ k67[ 4He] + k76[ 3He] = k76[He](2Z4 + g3)

(lOb)

where [He] is the total He concentration, ~3 and Z4 are the mole fractions of 3He and 4He respectively, and advantage has been taken of the fact that statistical equilibrium requires that k67 = 2k76 and k87 = 2k78. Substitution of the mole fraction values appropriate for the data in Figures 3a and 3b into Equations (10a) and (10b), respectively, and approximation of k78/k76 by the ratio of their respective Langevin 3~collision rates, yields the prediction that k78/k7~r= 2/3. The results in Figures 3a and 3b also provide an interesting and unique insight into the nature of the stabilization step [reaction (2)]. The near independence of the low-pressure KIE on the 3He/4He composition ratio suggests that energy transfer without atom exchange dominates the stabilization step 2~and points to an important role for large impact parameter,/-changing collisions. This conclusion suggests an explanation for the near-zero inlet pressure EF being greater than the factor of two

Symmetry-Induced Kinetic Isotope Effects

171

predicted by the symmetry analysis of reaction (1): namely, an additional SIKIE would be expected for/-changing stabilization because AI = +1 is allowed for (THe~)* whereas Al = +_2 is the minimally allowed/-change for (6'SHe~)*. The lack of experimental evidence for atom exchange and the importance of angular momentum effects in the stabilization of the cluster are both unexpected conclusions of this study and illustrate how SIKIE measurements can provide unusual mechanistic information. Progress toward further establishment of the validity of these conclusions regarding the stabilization step is currently being made in this laboratory by theoretical dynamical studies of reactions (1) and (2) with use of a high quality ab initio global He~ PES.

IV.

+

H 3 F O R M A T I O N " I N S I G H T I N T O THE APPROXIMATIONS

The proton/atom transfer reaction,

(11)

H~ + H2 __>H~ + H

and its isotopic variants has been extensively studied by many workers 31-41 using a variety of techniques. Significant in the present context is the fact that the reaction satisfies the criterion of comprising identical reactants in different electronic states and is thus a candidate for SIKIE. The detailed application of the symmetry correlation scheme to reaction (11) has been published elsewhere, 14and the results are summarized in Table 2 where N ~ and N are the Hund's coupling case (b) rotational quantum numbers for the ion and the neutral, respectively. Similar to the result obtained for He+/He collisions, Table 2 indicates that, in the absence of Table 2. SymmetryAnalysis and Correlation Scheme for H~/H2 --> H: and its

Isotopic Variantsa

H~ID2 or D~/H2

I~/H2 or D~ID2 t

N

N+

even even odd

even

even

ovon even

ovon odd

odd odd odd

odd

odd

Parity

~e

(+) } (+)

r

odd

even

(+) } (+)

even odd

even odd even

(-) (-) (-)

even

odd

~*

~gs

Coupting

, 1

I.(N

+

N+)

1,(N + N +)

1

d:e

}

}

~gs

Note: aThe correlation table for HD+/HD is obtained from that for I-l~2/H2 by interchange of ~" and ~gs.

(~* +

~gs

~* + ~gs

GREGORY I. GELLENE

1 72

coupling between the electronic states, only half of the collisions of isotopically identical diatoms would access the ground state and undergo reaction, implying that the rate of reaction (11) for identical vs. nonidentical reactants might be as much as a factor of 2 slower. Although reaction (11) has been the subject of several multiple PES dynamics calculations, 42-46 the absence ofdetailednuclear symmetry considerations in the treatment of the PES couplings in those studies makes it difficult to apply the results to the question of SIKIE. Experimentally, there did appear to be some evidence for SIKIE in reaction (11). Table 3 lists experimentally determined thermal rates for reaction (11) and its isotopic variants. Although the reported increased rates of H~/D 2 and D~/H 2 relative to those ofH~/H 2, D~/D2, and HD+/HD are supportive of the existence of SIKIE in this reaction, there are reasons to be concerned that the rates of H~/D 2 and D~/H 2 may be too high. Because reaction (11) is significantly exoergic (1.7 eV) and is believed to proceed by a direct mechanism 4~ without any observable barrier, the thermal rate of reaction should be well approximated by the collision rate. Column 3 of Table 3 lists the classical collision rate constants calculated using the Langevin pure polarization model of Gioumousis and Stevenson (kL).3~A comparison of the values in Table 3 indicates that the reported rate constant of reaction (11) for identical reactants is in good agreement with predictions of this

Table 3. 300-K Thermal Rate Constants a for H~ + H 2 --> H~ + H and Its Isotopic Analogues Isotopomer

kexptb

kl, c

kc d

I-I~2/H2

2.02, e 1.85,f2.11, g 2.0 + 0.1 h 2.08 + 0.03, i 2.12 +_0.14j

2.11

2.19 + 0.02

D~/D 2

1.4, k 1.44, e 1.44,1 1.60, g 1.6 + 0.1, h 1.54 + 0.15 j

1.49

1.58 + 0.02

1.66, e 1.80, g 1.66, l 1.8 + 0.1 h

1.72

1.82 + 0.02

/D 2

3.2 _+ 0.6 h

1.83

1.95 +_ 0.03

D~/HE

3.0 +_ 0.6 h

1.83

1.92 _ 0.02

HD+/HD

Notes: aRate constants are in units of 10--9 cm3s-1. bMost experimental rates are for ions in a vibrational state distribution given approximately by H2(v" = 0)/H~(v') Franck-Condon factors. CLangevin collision rate calculated by the method of Ref. 30. dCollision rate calculated by the method of classical trajectories in Ref. 48. eRef. 32. fRef. 33. gRef. 35. hRef. 37. iRef. 38. JRef. 39. kRef. 31. IRef. 36.

Symmetry-Induced Kinetic Isotope Effects

173

classical theory, whereas the reported rate constants for reaction (11) with nonidentical reactants are approximately 70% larger than the classical theoretical predictions. Thus, either the contribution of the quadrupole of H E to the collision rate is much larger than is normally expected, 47 or the reported rate constants for H~/D 2 and D~/H 2 reactants are too high. This question was addressed by use of classical trajectory techniques 48 with an ion-quadrupole plus anisotropic polarizability potential to determine the collision rate constant (kc). Over one million trajectories with initial conditions coveting a range of translational temperature, neutral rotor state, and isotopic composition were calculated. The results for the thermally average 300 K values for kc are listed in the last column of Table 3 and indicate that reaction (11) for H~/H E, D~/DE, and HD§ proceeds at essentially the classical collision rate, whereas the reported experimental rates for H~/D 2 and D~/H 2 reactions seem to be in error as they are significantly larger'than kc. This conclusion raises two questions" ( 1) If the symmetry restrictions outlined in Table 2 apply, how are they essentially completely overcome at 300 K? (2) Do conditions exist where the restriction would give rise to observable kinetic effects? Table 2 indicates that the strength of the symmetry restriction depends on the "goodness" of the asymptotic quantum number l, because mixing of the ground and excited H~ electronic states at large H~/H 2 separation is mediated by the coupling of orbital angular momentum with either H~ or H 2 rotational angular momentum. Some insight into the goodness of l as a quantum number can be gained from the trajectory calculations by examination of the extent to which its classical analogue (L) is preserved. This point was addressed by determination of the distribution of AL2 (defined as the change from the asymptotic value of L 2) as a function of H~/H2(J= 0,1) separation (denoted R) at translational temperatures of 300 and 10 K. Some idea of the AL2 distributions can be obtained from the plots of (AL2) and (AL2) + o~2 as a function of R in Figure 4. Remarkably, the results show that the anisotropy ofion-quadrupole potential is sufficient to couple the angular momenta at separations as large as 50 au [i.e., ~Ar2(R = 50 au) is +_2.5 h 2 and +1.7 h 2 for J = 0 and J = 1, respectively]. If this efficient loss of L as a constant of the motion in the classical dynamics can be taken as an indicator of the loss of/as a good quantum number in the quantum (i.e., actual) dynamics, then a facile breaking of the symmetry restriction may be occurring at 300 K that would account for the near equivalence of the experimental and classical collision rates at this temperature. With this interpretation, the best conditions for observation of the effect of the symmetry restriction would be those for which L (as an indicator of/) is preserved. The plots in Figure 4 indicate that the experimental determination ofH~/H2(J= 0) reaction rate at T < 10 K may provide the best direct information on the importance of symmetry restrictions in this reaction. From a more general point of view, the trajectory calculations on the H~/H 2 system suggest that SIKIE predictions for ion-molecule reactions based solely on differing symmetry correlations for even and odd l may not be readily realized under

1 74

GREGORY I. GELLENE

E

J=l

J=O

10

T=300 K

40.

20-

4-t v -10

o-

&.-. -20

-20-

d-.ao 0

A

10 20

30 40 50 .

I

9

.

T=10K

-4o

0

9

10 20 30 40 50 |

r

!

20 ....

.

!

.

!

~

|

__ _.T =_'I0 I _~ K

10

+i A

o "O

m

C A

-2

-3

-lO

0

9,

10 20

30 40 50

-20

0

R (au)

10 20 30 40 50 R (au)

Figure 4. The average change in the squared value of the classical orbital angular momentum ((AL2)) and the standard deviation of the AL 2 distribution (AL 2) + aaL2as a function of R for H~/H2(J = 0,1 ) collisions at translational temperatures of 300 and 10 K. In each case the bold curve represents (AL 2) and the lighter curves represent (AL 2) + cat 2. Note the different scales used in the four plots.

typical thermal reaction conditions. The He+/He system is an obvious exception to this generalization, where SIKIE based on even and odd l was nevertheless observed because the goodness of l could be lost only by the relatively weak coupling of l to spin, rather than rotational, angular momentum.

V. 0 4 FORMATION" THE EFFECT OF ELECTRONIC DEGENERACY The two cases considered thus far have involved reactants in spatially non-degenerate electronic states. A significant new level of complexity is introduced in the termolecular association reaction,

o (x2ri ) + o2(x3z ) + M

+M

(12)

Symmetry-Induced Kinetic Isotope Effects

175

by the degeneracy of the FI state of O~. However, long before reaction (12) was the subject of a SIKIE study,49 a number of experimental observations were reported suggesting unusual features for the reaction. In 1963, Curran 5~ investigated the effect of ionizing electron energy on the rate of reaction (12) with M = 0 2 and made the surprising observation that the appearance potential of O~ was 16.9 + 0.1 eV, a value almost 5 eV greater than that of ground-state O~. On the basis of this electronic state of observation, Curran suggested a role for the m e t a s t a b l e O~ in reaction (12), although no consideration was given to the unusual requirement of electronic excitation for the production of a relatively weakly bound cluster ion. Unfortunately, no notice of this result appears to have been taken by other workers in subsequent studies of O~ formation. The temperature dependence of reaction (12) was studied independently by Conway and Janik, 5~ Kebarle and co-workers, 52'53Brhringer et al., 54 Rowe et al., 55 and Randeniya et al. 56 Unique among these studies were the results of Brhringer et al., where a deviation from the expected T -n proportionality was observed below 80 K, which prompted speculation about the existence of energetic barriers 57'58and incomplete energy randomization 59 in association reactions. However, the subsequent studies by Rowe et al. near 20 K 55 and by Randeniya et al. over the temperature range of 4-20 K 56 failed to find any evidence for a deviation from a T -n proportionality and concluded that no barrier to association existed. With the exception of the work of Randeniya et al., these kinetic studies produced O~ by E1 electronic state would be readily produced and under conditions where t h e thus do not address the origin of the electronic energy requirement identified by Curran. However, Randeniya et al. produced O~ by a resonance-enhanced multiphoton ionization (REMPI), which is known to produce only electronic groundstate ions. 6~ Thus the results of Randeniya et al. can be compatible with those of Curran only if REMPI and near-threshold E1 produce ion state populations that differ in some critical aspect, affecting the kinetics of reaction (12). It will be shown subsequently that this critical aspect is intimately related to SIKIE in this reaction. Application of the symmetry correlation scheme to reaction (12) is summarized in Table 4 where N is the Hund's coupling case (b) rotational quantum number for 0 2 and J+ - S + is the difference of the Hund's coupling case (a) quantum numbers of total angular momentum and electron spin (S + = 1/2) angular momentum, respectively. To consider the high-symmetry isotopomer system first, the results in Table 4 indicate that only odd l collisions of 3202(J++ _ S + = odd) with 320 2 can lead without restriction to 64O +4. Although the results of the previous section argue against the realization of a restriction based solely on l, a restriction based on J§ - S § is a very different matter. The relaxation of this restriction involves various spin couplings (including spin--spin coupling between the ion and the neutral not listed in Table 4) that are expected to involve much shorter range forces than the ion-quadrupole interaction dominantly responsible for relaxing l restrictions. Thus, at an intermediate separation in the collision, J + - S + is expected to be a better

anI-Iu

aal-Iu

176

GREGORY I. GELLENE Table 4. Symmetry Analysis and Correlation Scheme for O~/O2 --, 04

Isotopomer

320~/3202

320~73'3402

33,340~/3202

N

J+-S +

1

Parity

d~e

odd odd odd odd

even odd even odd

odd odd even even

(+) (+) (-) (-)

~* ~gs ~* ~*

even odd even odd even odd even odd

even even odd odd even even odd odd

even odd even odd odd even odd even

(+) (+) (+) (+) (-) (-) (-)

l

(-)

I

odd odd odd odd

even odd even odd

even even odd odd

(• (• (• (•

J

Coupling t

+ - S+)*(N + i)

(J+-S+)*(N + i)

% }

~, (J+ - S+),(N + !)

1

~gs

~ ~*+~gs

J

quantum number than is l, and, consequently, restrictions based on J+ - S + are more likely to influence the kinetics than are restrictions based on l. It remains to consider the isotopically heteronuclear systems to complete the symmetry analysis of this system. Because the experiments are performed under natural abundance conditions, only systems containing a single rare isotope (170 or 180) need be considered. However, because the spatial degeneracy of the electronic state of the ion and the neutral differ, the case where either the neutral or the ion is isotopically heteronuclear must be considered separately. The results in Table 4 show that when the neutral is made isotopically heteronuclear the/-based restriction is removed, while that based on J+ - S § is preserved. Conversely, when the ion is made isotopically heteronuclear, all restrictions are removed. The comparison of these two cases makes clear that the J+ - S § restriction has its origin in the centrosymmetry of the ion whereas the l restriction has its origin in the asymptotic O~/O 2 indistinguishability symmetry. Unfortunately, because the experiment is not sensitive to the origin of the unique oxygen isotope in the termoleculer association, this interesting distinction between the two types of symmetry lowering could not be addressed in this system. With the prospect for realizing a symmetry restriction based on J § S § established, it is interesting to consider the possible magnitude of the effect. For 320~, J + - S § is a well-defined quantum number with odd and even values corresponding to e andfparity label states respectively. The e/fnotation 61 refers to the

Symmetry-Induced Kinetic Isotope Effects

177

11

J(6s)~(ss)
. . . . . . . . . . . . . . .

..o--

. . . . . . . . . . . . . . .

m. ..........

0.1

m c .E

i(66)/i(64)

0.01

m(es)n(e4) 0.001410

20

30

electron energy (eV)

40

Figure 5. Intensity ratios of isotopically substituted O~ ions as a function of ionizing electron energy. 1(64)corresponds to O: ions containing four 160 atoms and, because the experiments were performed under natural abundance conditions, 1(65) and 1(66) correspond to ions where one 160 atom is replaced with an 170 and laO, respectively. The dotted lines indicated the expected ratios based on natural abundance.

total parity, exclusive of rotation, 62 of the two A-doublet components of a spatially degenerate electronic state of a linear molecule (in this case the X21-Igstate of O~). In the limit of high rotation, it is possible to associate these A-doublet components with states where the half-filled orbital is either in, or perpendicular to, the plane of rotation. 63 If the ions are thermally equilibrated, the e and f parity label states would each represent 50% of the population, implying a possible SIKIE on the order of a factor of two. However, there is no fundamental reason why EI cannot have a propensity for producing a particular parity label state that could lead to SIKIE considerably larger (or smaller) than a factor of two. The experimentally determined 49 I65/I64 and I66/I64 for reaction (12) as functions of ionizing electron energy (Ee) are shown in Figure 5 where the dotted lines indicate the expected ratios based on natural abundance considerations. At low E e, a strong KIE is observed with the intensity of the mixed isotopic O~ ions approaching a 10-fold enhancement near threshold (E e ~ 12 eV). Most significant in the present context is the equivalent enhanced incorporation of 170 and 180 into the cluster (relative to natural abundance levels), shown clearly by the I65/I66 ratio having its natural abundance value independent of E e. This experimental result provides the strongest possible evidence that the KIE is indeed symmetry induced, which, in the context of the symmetry correlation scheme, implies that EI has a propensity for producing f parity label states of O~(2I-Ig). As E e is increased, the I65/I64 and I66/I64 ratios decrease continuously, and natural abundance values are observed for E e > 40 eV. The most dramatic changes in the I65/I64 and the I66/I64 ratios occur near the threshold for O~(a41"Iu) production (E e ~ 16 eV), suggesting

GREGORY I. GELLENE

1 78

that much of the SIKIE decrease observed with increasing E e may be due to increasing participation of O~(a4I-I_) in cluster formation. This conclusion is in agreement with the work of Curran ~~because a decreased SIKIE is interpreted in the context of the present theory as an increased production rate of the high-symmetry product (i. e., 640~). It is worth noting that the present observation of 640~ at E e < 16.9 eV is not necessarily incompatible with the appearance potential measurement of Curran because the present measurements do not distinguish between 640~ ions produced directly from 320~/320 2 clustering and those produced by the switching reaction: 65'660~ + 320 2 ----) 640 + 4 + 33,3402

(13)

Because the electronic energy of the a4rlu state is almost ten times the cluster binding energy, it is unlikely that termolecular formation of O~ proceeds directly from O~(a4I-Iu). A more likely role for the a4I-Iu state is the production of e parity label states of o~(2rlg) (i.e., J+ - S § = odd) from the energy transfer reaction, O~(a41Iu) + 02 --->O~(X2rXg) + 02

(14)

which is known to be very efficient. 64To further explore the importance of reactions (13) and (14) on the observed SIKIE in reaction (10), O~ was produced by the ionization ofvarious mixtures ofO 2 and rare gases (Rg = He, Ar, or Kr) at a constant total ion source pressure. Before the results of these experiments are examined, it is useful to consider the four distinct ways in which the presence of a rare gas can effect the observed SIKIE. 1. The importance of isotopic scrambling by reaction (13) is diminished because the partial pressure of 0 2 is reduced. 2. O~ can be produced by the two-step chaperone mechanism,

3.

O~ + Rg + M -+ O~.Rg + M

(15)

O~.Rg + 0 2 --), O~ + Rg,

(16)

which may have different symmetry restrictions than does reaction (12). When Rg = Ar or Kr, quenching of O~(a4IIu) can occur by, O~(a41-lu) + Rg -+ 02(X~Eg) + Rg +,

which diminishes the importance of O~ produced by reaction (14). 4. O~ can be produced by the charge-transfer reaction,

(17)

Symmetry-Induced Kinetic Isotope Effects

179

Rg + + 0 2 ~ Rg + O~

(18)

for which the O~ e/f parity label state distribution may differ from that produced by direct E1 or reaction (14). Results obtained for Rg = He, Ar, and Kr are shown in Figures 6, 7, and 8, respectively. Because He is ineffective in quenching O~(aal-Iu) and only weakly binds to O~, the most important effect of addition of He to the ion source is the decreased importance of the scrambling reaction (13). This consideration accounts for the increasing EF(66) with increasing He partial pressure at low E e and indicates that the initial SIKIE may be a factor of 100 or more. At higher E e, quartet states of O~ are produced by Penning ionization 65 (E e > 20 eV) and reaction (16) (E e > 24.58 eV). This enhanced production of quartet states could account for the EF(66) having its natural abundance at E e > 21 eV. In contrast to He, Ar is as effective as 0 2 in quenching O~(aaI-Iu)66 and has a substantial binding energy 67 with O~. At low E e, the chaperone mechanism appears to be the dominant effect, and an increase in Ar partial pressure decreases EF(66). However, at higher E e, reaction (17) becomes important, and an increase in Ar 7060. so.

~,

~'

- - 1:2 He:O 2 - - - - 2:1 He:O2

0. 0-

I"'

t

..... 3:1 He:O 2

20

.

.

.

.

.

.

e l e c t r o n e n e r g y (eV)

Figure 6. Isotopic enhancement factor for 180 in O: as a function of ionizing energy and O2/He ratio at a constant ion source inlet pressure of 0.75 torr.

50-

40

fill

--

1:1 Ar:O2

2:1 Ar:O 2

..... 3:1 Ar:O2 30

A

(D

LLI

20

,~~..

~ .....

10

l 0

..............................

%

m

Tl, m.o~o.mlo..~__.Jml......Pll.~mL-.m~

:--

~ ' " ' . . . . . . 2b. . . . ' . . . . 3~ ' ~ ' ' ' ' ' ~ ' ' ' ~

::::-:~-

.....

electron energy (eV)

Figure 7. Isotopic enhancement factor for 1BO in O~ as a function of ionizing energy and OJAr ratio at a constant ion source inlet pressure of 0.75 torr. .._ /

30

(o co in i.

A

v

1:1 Kr:,O2

/

20

/

/

S

/

/ 2:1 Kr:O2

1/

.... [ ...........

I I I

.

=o

= ' ' ' "

3:1 Kr:O2 9

.,

, ..-' 2" 9

t ~o

~

/

I

10

::

"

j

~

..........

"9 _, 0

. . . .

10

~w,=~l~_ (W}

' . . . " . . w ' . - . :

20

. . . . . .

, ~ . . . . . . . ~

30

.,e...

40

. . . . . .

,.,,,

. . . .

SO

:

electron energy (eV)

Figure 8. Isotopic enhancement factor for 180 in O~ as a function of ionizing energy and 02/Kr ratio at a constant ion source inlet pressure of 0.75 torr. 180

Symmetry-Induced Kinetic Isotope Effects

181

partial pressure increases EF(66). It is significant that the crossover point between these two effects occurs near the threshold for O~(a41-Iu) production. Also, with the effect of O~(aaI-Iu) diminished by reaction (15), significant SIKIE is observed up to at least E e = 100 eV (the highest energy investigated), indicating that the propensity to producefparity label states of O~(2I-lg) by El is not solely a threshold effect. The effect of adding Kr might be expected to be very similar to that of Ar addition because the ability of Kr to bind O~ and quench O~(aal-lu) is very similar. 66-69 The expectation that the chaperone mechanism would be important is indeed realized because an increase in Kr partial pressure decreases EF(66) at all E e investigated. However, the increase in EF(66) with E e for E e > 15.5 eV cannot be attributed solely to quenching of O~(aaI-Iu) because the effect begins below the appearance potential of the quartet. Alternatively, reaction (18) could account for this result if Kr+/O2 charge transfer had a propensity for producingfparity label states of O~. Although no direct information on the detailed angular momentum product states of reaction (18) is available, evidence for an analogous e/f propensity in Ar+/CO2 charge transfer reactions will be presented in Section VII.

Vl. (CO2) ~ FORMATION" SEPARATION OF THE DEGENERACIES A particularly interesting result of the symmetry analysis of the 0~/0 2 system was the prediction of different kinetic effects for the loss of molecular centrosymmetry of the ion and the loss of the asymptotic O~/O 2 degeneracy. Although the effects of these two conceptually different types of symmetry lowering could not be experimentally distinguished in the O~/O 2 system, they can be distinguished in the analogous CO~/CO 2 system. Like O~, CO~ has a 21-Igelectronic ground state that gives rise to the molecular centrosymmetry restriction. Unlike O~/O 2, however, the asymptotic degeneracy in the CO~/CO 2 can be lifted without the destruction of molecular centrosymmetry by isotopic substitution on the carbon. As originally developed, the symmetry correlation scheme addressed collisions of diatomic molecules, and an extension of the theory 7~ is required to treat the present case of linear triatomic molecules. In particular, triatomic molecules process non-totally symmetric vibrational modes that, upon excitation, can alter the overall symmetry of the wavefunction. Special care is required in the treatment of the bending mode, because excitation in this mode increases the asymptotic degeneracy of the wavefunction. Application of the appropriately extended theory to 44C0~/44C02 collisions reveals that, in general, only a restriction based on l is predicted, suggesting that an experimental distinction of the different effects of breaking molecular and asymptotic symmetry may not be possible. Further, because the H~/H 2 trajectory calculations 48 suggest that symmetry restrictions based solely on l are not expected to be very strong in ion-molecule reactions, the prospect of

182

GREGORY I. GELLENE

observation of any SIKIE in (CO2) ~ formation would seem low. However, if + attention is limited to 44CO2/44CO2 collisions where the vibrational angular momentum of the ion is zero, additional symmetry restrictions emerge. It is now found that a restriction based on the e (restricted) orf(allowed) parity label is predicted. Thus, if a dynamical reason exists for zero vibrational angular momentum states being favored in the clustering reaction, the desired distinction between molecular and asymptotic symmetry can be made. The physical origin of vibrational angular momentum can be understood by consideration of a two-dimensional isotropic oscillator 71 (e.g., the v 2 bending mode of a linear triatomic). In a harmonic approximation, the energy levels and associated wavefunctions are labeled by two quantum numbers. If the problem is solved by use of rectilinear coordinates (e.g., x andy), these quantum numbers are the familiar ones of two independent one-dimensional oscillators, VEa and VEb, with no restrictions on their relative magnitudes. However, if the problem is solved by use of curvilinear coordinates (e.g., a magnitude, r, and a polar angle, ~), the quantum numbers are v 2 and/2, where l2 is the quantum number of vibrational angular momentum and is restricted to the values l2 - v 2, v 2 - 2,..., 0 or 1. It being noted that (CO2) ~ is a relatively weakly bound complex, 72 a plausible origin for a dynamical constraint favoring l2 - 0 ions in complex formation arises from energetic considerations that suggest that ground vibrational state reactants, for which only zero vibrational angular momentum states are allowed, will be most efficient for complex formation. A summary of the symmetry analysis for the various isotopomers is presented in Table 5 where, in keeping with the conclusions of the general analysis, only ground vibrational states of the reactants are considered. Inspection of Table 5 indicates that isotopic substitution that preserves the CO~ centrosymmetry lifts the restriction based on l while preserving the restriction based on the e/fparity label state. Because 13C substitution will always preserve molecular centrosymmetry, the symmetry analysis predicts that 89(CO2)~ clusters containing a 13C isotope could show at most a formation-rate enhancement of a factor of two above that of 88(CO2)~. Also, because this symmetry restriction is independent of the detailed nature of the quantum states of the CO~ ions, the lac SIKIE is predicted to be independent of the way in which the ion is prepared (i.e., Ee). Conversely, Table 5 indicates that when the CO~ centrosymmetry is removed, there are no symmetry restrictions to )+ containing a cluster formation. The extent to which the formation of 89'9~ 22 17'18OCO+ ion will be enhanced above that of 88(CO2)~ depends on the e/fparity label state distribution of the CO~ ions, which, as was demonstrated in the O~/O 2 study,49 can depend on E e. In the context of the symmetry correlation schemes in Table 5, the experimental determination of enhancement factors for the individual elements, EF(13C) and EF(180), are more relevant than the directly measured EF(89) and EF(90). Because the experiment is done under natural abundance conditions, EF(90) can be taken

Symmetry-Induced Kinetic Isotope Effects

Table5.

SymmetryAnalysis and Correlation Scheme for CO~/CO2 --~ (CO2)~,

Isotopomer

44C0.~/44C02

13C0~/C02 or C0~/13C02 or CO~/17'18OCO

17'18OCO+/~O2

Note:

183

N

J+- S +

I

Parity

dpe

eveneven even odd

odd odd

(+) (+)

~gs](j%.S+)e(N+l )

even even

even odd

even even

(-) (-)

~" ~"

even od~ even odda even odda even odda

even even odd odd even even odd odd

even even even even

even odd even odd

r

odd

(+) I]

~gs

even odd even even

(+) (+) (+) (-)

(

odd

(-)

even odd

(-) (-)

I

(•

1

even even odd odd

(•

Coupling

;

} (J% S+).(N + !)

1 I }

~gs

J

1

(J~ S+).(N +l)

~* +~gs

(• (•

aN= odd is allowedonlyfor CO~/17a8OCO.

as a direct measure of EF(180). With this interpretation, EF(13C) can be determined from the expression, 7~ EF(13C) = EF(89) + [EF(89) - EF(170)]

(~70fractionof m/z= 891(19) 3C fraction of m/z = 89 tat

where, in keeping with the symmetry analysis, EF(170) is taken to be equal to EF(180). The experimentally determined values of EF(13C) and EF(180) are plotted in Figure 9 as a function of inlet pressure for three different values o f E e. The solid curve in each plot is a fit of the data to the integrated rate expressions describing the isotope exchange reactions, 7~ ,

(co2)2

+ k~[c~

~ (co2)~ k_l['CO2]

(20)

that scramble the nascent isotopic distribution of (CO2) ~ and ultimately establish equilibrium. In reaction (20), the asterisk used as a prefix denotes a molecule containing a ~3C, ~70, or ~80 isotope. This kinetic analysis allows a quantitative determination of the zero-pressure enhancement factor (ZPEF) for a particular isotope. Figure 9 shows that ZPEF(~3C) is relatively independent of E e, in agreement with the requirements of the symmetry analysis; however, its value of 5.1 + 1 warrants

184

GREGORY I. GELLENE 30

A

Ee= 100oV

Ee = 50 oV

Eo = 25 eV

20

00

I

I

100 Inlet P (mTorr)

0

I

100 Inlet P (mTorr)

~'

l ~7~

100 Inlet P (mTorr)

10

U. UJ

0

L 0

100 Inlet P (mTorr)

0

l,

~

e

~

I

100

Inlet P (mTorr)

0

I

C

I

....

100

Inlet P (mTorr)

Figure 9. Isotopic enhancement factors for 180 and 13C in (C02)~ as a function of ionizing energy and ion source inlet pressure.

further consideration because it is larger than the maximum value of 2 that can be accommodated solely by the syn~netry analysis of the CO~/CO 2 association reaction. Thus, the possibility of SIKIE in the (CO2)~* complex dissociation or stabilization step of the termolecular mechanism must be considered. In this context, it can be noted that the symmetry lowering of the molecular system caused by isotopic substitution has the effect of increasing the Pauli-allowed density of states. At first thought it might be argued that such an increase in the density of states of the complex might decrease the dissociation rate and thereby contribute to the increased rate of low-symmetry cluster formation. However, this density of cluster states effect will be at least partially (if not completely) offset by a corresponding increase in the number of allowed dissociation channels for the complex. Thus, it would seem unlikely that symmetry effects could alter the dissociation rate by the required factor of 2-5. Conversely, the stabilization step is an energy-transfer step for which the efficiency would be expected to increase with increasing density of states, and this is exactly the type of SIKIE suggested 2~ by the enhancements of greater than a factor of 2 observed for He+/He. Further, the

Symmetry-Induced Kinetic Isotope Effects

185

possibility that the stabilization step could be subject to SIKIE may have important implications for the SIKIE observed in the formation of 0 3 by termolecular association ofO 2 + O. All previous proposed explanations of SIKIE in 0 3 formation have focused only on the association and dissociation steps of the mechanism 73-77 with no consideration being given to the final stabilization step of the mechanism. Both the He+/He and the CO~/CO 2 results suggest that the neglect of the stabilization step in a theoretical model of SIKiE for termolecular association may not be justified. Similar to the results obtained in the O~/O 2 study, Figure 9 shows that EF(180) decreases with increasing E e, suggesting that CO~(e)-state production is favored at low E e and that this propensity decreases with increasing E e. Some insight into the mechanism of E e dependence of the e/fpropensity is provided by examination of the (CO2) ~ cluster formation efficiency (i.e., I88/144) as a function of Ee. Over the range of E e where SIKIE was measured (25-100 eV), CO~ cluster formation efficiency increases by about a factor of four, in quantitative agreement with the measured decrease in SIKIE over the same range of E e. (Recall that a decrease in SIKIE arises from an increased formation efficiency of the high-symmetry species). This quantitative agreement provides a valuable independent check on the internal consistency of the kinetic analysis. More instructive, however, was the observation that the cluster formation efficiency increased by about a factor of four over the narrow range of E e = 17-19 eV. When it is considered that the threshold for formation of the excited A2I-lu state of CO~ is 17.32 eV,78 this result strongly suggests a role for this excited electronic state in the increased cluster formation efficiency and the corresponding decrease in SIKIE. The A2Hu state is known to efficiently radiate to the X2I-lg ground state, 79 which, as a 21-Iu~ 2Hg transition, is dominated by P and R branches 8~ obeying the parity label selection rules e 4-~ e,f+--~fe +/..),f62 Thus, if the near-fourfold increase in I88/I44 observed between E e = 17 and 19 eV is attributed to an increase in CO-~(XZFIg,u) production by participation of the AZl-Iu state in the ionization process, the inference is that EI favors production o f f levels in the 2IIu electronic state and e levels in the 21-'[g electronic level. Although such an inference is somewhat speculative in the absence of a specific theory of the process, it does not seem unreasonable that the propensity could change from e tofas the final electronic state changes from 2IIg to 21-Iu.When these EI propensities are included with the one inferred from SIKIE in the O~ + 0 2 --+ O~ reaction, the emerging pattern can be tentatively summarized as" (n 2) 3E~ + e- --~ (n~) 2FIgOCfavored) + 2e(e favored) + 2e-

(22)

3 Eg+ + e - - ~ (n.) 2I-[u (ffavored) + 2e-.

(23)

Zg + e---~ 1

(21)

186

GREGORY I. GELLENE

VII. Ar.CO~ FORMATION" ISOLATION OF THE ELECTRONIC DEGENERACY An interesting consequence of the C O ~ / C O 2 symmetry analysis is that the e/f symmetry restriction depends only on the symmetry properties of the CO~ ion. This result raises the intriguing possibility that symmetry restrictions may still exist if CO 2 is replaced with other closed-shell species. In other words, the symmetry correlation scheme predicts that the H-electronic degeneracy of CO~ alone is sufficient to give rise to SIKIE, and the reactants are not required necessarily to have identical atoms in common. This possibility was explored by examination of isotope effects in the formation of Ar.CO~ by the association of Ar and CO~. Application of the symmetry correlation scheme to Ar/CO~ collisions is very analogous to that for CO~/CO 2 collisions, with symmetry restrictions based on the e/f parity label states of CO~ being predicted only for ground vibrational state reactants. Restriction of the analysis to this subset of all possible reactant states is again justified on energetic groun .ds81because the binding energy of Ar.CO~ is only about one third that of (CO2)~. Two important conclusions can be drawn from the summary of the symmetry analysis of Ar/CO~ collisions in Table 6. First, no SIKIE is predicted for ~3C substitution because the symmetry of the system is independent of the isotope of carbon involved. Second, because the predicted e/f-based symmetry restrictions for Ar.CO~ cluster formation are identical to those predicted for (CO2) ~, a dependence of the magnitude of observed 17'180 SIKIE on the conditions of CO~ formation is expected. However, the e/f parity label state propensities for El-produced CO~, inferred from 180 SIKIE in (CO2)~ formation, are not sufficient to predict the magnitude of 180 SIKIE in Ar.CO~ formation because, for E e above the threshold for Ar § formation, CO~ ions are also produced by the charge-transfer reaction, (24)

Ar + + CO 2 --~ Ar + CO~

Table 6. Symmetry Analysis and Correlation Scheme for CO~/Ar -> ArCO~

Isotopomer

J+- S+

1

Parity

CO~/Ar or 13CO~/Ar

even odd even odd even odd even odd

odd odd even even even even odd odd

(+) (+) (-) (-) (+) (+) (+) (+_)

17:8OCO+/Ar

1 ~

J

t~e

Coupling

dPgsl

(jL_ S+).!

~gs l ~* J

(j+- S+).l

~, + ~gs

5ymmetry-lnduced Kinetic Isotope Effects

187

for which no information is available regarding e/fproduct state distribution for CO~. Although, in principle, it is possible to study the formation of Ar.CO~ without the complication of reaction (24) if E e = 13.8-15.7 eV, in practice, higher E e is required to obtain reliable cluster ion intensity measurements. Therefore, a SIKIE study of Ar.CO~ formation was performed with E e = 21 eV, which ensured that the primary E1 products were only Ar § and CO~ (i.e., no CO § O § etc. were produced). 82 However, the practical inability to eliminate reaction (24) does not preclude the obtaining of information regarding its effect on SIKIE because the relative importance of CO~ produced by EI and reaction (24) could be experimentally adjusted by a change in the Ar/CO 2 ratio in the ion source. EF(85) and EF(86) as a function of total ion source inlet pressure were measured for three Ar/CO 2 mixtures from which the EF(13C) and EF(180) shown in Figure 10 were determined by the method used in the CO~/CO 2 study. The most significant results are that, as required by the symmetry analysis, EF(13C) = 1 under all conditions investigated and, at low inlet pressure, EF(~80) >> 1, providing the first example of SIKIE for reactants with no atoms in common. Closer inspection of EF(180) shows that the low inlet pressure value depends strongly on the Ar/CO 2 mixture ratio, decreasing from EF(~80) = 20 at low Ar/CO 2 (1/15) to EF(180) = 5 at high Ar/CO 2 (1/0.58). Although a detailed kinetic analysis of these results has not yet been performed, the decreasing 180 SIKIE with increasing mole fraction of Ar clearly indicates that reaction (24) favors Ar:CO2 1:15

Ar:CO2 1".2

Ar:CO2 1:0.58

l

20.

20.

~i 10.

10~

A

H

C..

t~

H 0

o . . . . . . !

-~--O--Q-C -

I

0 100200300 Inlet Pressure (mTorr)

0

"--

___~ !

9

o__,o_! 9

!

0 10O200300 Inlet Pressure (mTorr)

o _-%,o..o..-?-..~

0 lo02O03X] Inlet Pressure (rnTorr)

2

2

2.

1--]-~-~-~L--D--]~-~,

1--~]~-~-~--,I--'

1. - - ~ w 1 6 7

0

0

0

A

~,

. , . , . , 0 100 200 300 Inlet Pressure (mTorr)

. , . , . , 0 100 200 300 Inlet Pressure (mTorr)

-

!

-

!

-

i

0 1O02003O0 Inlet Pres~Jm (reTort)

Figure 10. Isotopic enhancement factors for 180 and 13C in Ar.CO~ as a function of ion source inlet pressure and Ar/C02 ratio.

188

GREGORY I. GELLENE

production of CO~ ions that have no symmetry restrictions for producing Ar.CO~ (i.e., the f parity label states). When this charge-transfer propensity is combined with one inferred from the O~/O 2 SIKE study, the emerging pattern can be summarized as,

O2(X3y~;) + Kr+(283/2) ---} O~(21-Ig~ffavored)+ Kr(1S) CO2(XlZg) + ar+(2P3/2) --~ CO~(2yIgffavored)

+ Aft'S)

(25) (26)

where specification of the lower spin-orbit state is justified on the basis of its much higher reactivity s3,s4 for these charge-transfer reactions compared to that of the upper spin-orbit state. Reaction (26) may prove to be a valuable starting point for a theoretical understanding of these charge-transfer propensities because the presence of only one open-shell species on each side of the reaction greatly simplifies the symmetry considerations.

VIII.

CONCLUDING

COMMENTS

Although SIKIE may well occur in neutral chemistry (e.g., 0 3 formation), gas phase ion chemistry has shown itself to be a valuable arena for exploring the phenomenon and evaluating emerging theories. For example, one theory of non-mass-dependent KIE indicated that isotopic fractionation cannot ensue directly from symmetry alone. 76 However, such a conclusion would appear to be incorrect, because that is exactly what is happening in the several cases discussed. The error in that analysis arises in the statistical thermodynamic treatment of the reversible association reaction: A + B ~ - (AB)'.

(27)

In the development of various equilibrium expressions, it was assumed implicitly that every internal energy state of the reactants (A + B) would have an equal probability of interacting on the particular Born-Oppenheimer PES relevant to the chemical process of interest. The work described here clearly demonstrates that the validity of such an assumption can depend directly on symmetry considerations. Indeed, it is the propensity of reactants in motional states of a particular symmetry to preferentially interact on a Born-Oppenheimer PES of a complementary symmetry when identical nuclei are present that is at the heart of the present theoretical description of SIKIE. Much of the success in the use of ion-molecule reactions to study SIKIE stems from the relative ease with which the theoretically identified requirement of there being identical reactants in different electronic states, or at least one of the reactants being in a degenerate electronic state, can be experimentally realized. Thus, it is natural to consider possible future directions in which ion-molecule studies might extend the current understanding of SIKIE. Presently, all known systems exhibiting

5ymmetry-lnduced Kinetic Isotope Effects

189

SIKIE are association- or photodissociation-type reactions. However, there is no fundamental reason why SIKIE must be limited to such reactions. An important question, therefore, is whether the effect could be observed in a more general reaction under thermal conditions where the chemistry involves a substantial rearrangement of atoms in going from reactants to products. The H~/H 2 proton/atom transfer reaction at low temperatures has been suggested already as a possible example where SIKIE may be observed in a more general reaction, and kinetic measurements of this reaction below 10 K would be very interesting. Additional attractive possibilities include bimolecular reactions of O~ and CO~ because of the extraordinarily large SIKIE these ions have demonstrated in termolecular reactions. A final comment should be made about the inferred e / f p a r i t y label state propensities in the ionic products of EI and charge-transfer reactions, which are two of the more intriguing insights that have emerged from these SIKIE studies. Such remarkable propensities were completely unexpected, and the SIKIE studies have opened a window on a level of detail in reaction dynamics where previously it might have been thought that there was nothing interesting to see. Currently, there is no detailed understanding of the origin of these propensities, and it is hoped that results such as those presented here will motivate additional theoretical research in this area.

ACKNOWLEDGMENTS It is a pleasure to acknowledge the contributions of Drs. K. S. Griffith and R. K. Yoo and Mr. C. A. Picconatto to the experimental studies of SIKIE in this laboratory. Also acknowledged is Dr. C. A. Williams for many helpful discussions during the development of the symmetry correlation theory. Finally, the financial support of NSF (Grant No. CHE9024091) and the Donors of the Petroleum Research Fund administered by the American Chemical Society is gratefully acknowledged.

REFERENCES 1. 2. 3. 4. 5.

Mauersberger,K. Geophys. Res. Lett. 1981, 8, 935. Heidenreich, J. E., III; Thiemens, M. H.J. Chem. Phys. 1983, 78, 892. Heidenreich, J. E., III; Thiemens, M. H. J. Chem. Phys. 1986, 84, 2129. Mauersberger,K. Geophys. Res. Lett. 1987, 14, 80. Abbas, M. M.; Guo, J.; Carli, B.; Mencaraglia, F.; Carlotti, M.; Nolt, I. G. Geophys. Res. 1987, 92, 13231. 6. Thiemens, M. H.; Jackson, T. Geophys. Res. Lett. 1987, 14, 624. 7. Thiemens, M. H.; Jackson, T. Geophys. Res. Lett. 1988, 15, 639. 8. Morton, J.; Schuler, B.; Mauersberger, K. Chem. Phys. Lett. 1989, 154, 143. 9. Anderson, S. M.; Morton, J.; Mauersberger, K. Chem. Phys. Lett. 1989, 156, 175. 10. Morton, J.; Barnes, J.; Schueler, B.; Mauersberger, K.J. Geophys. Res. 1990, 95, 901. 11. Bains-Sahota, S. K.; Thiemens, M. H. J. Chem. Phys. 1989, 90, 6099. 12. Battacharya, S. K.; Thiemens, M. H. Z. Naturforsch. A 1989, 44, 435. 13. Valentini, J. J.; Gerrity, D. P.; Phillips, D. L.; Nieh, J. C.; Tabor, K. D. J. Chem. Phys. 1987, 86, 6745.

190

GREGORY I. GELLENE

14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24.

Gellene, G. I.J. Chem. Phys. 1992, 96, 4387. Wigner, E.; Witmar, E. E. Z. Physics 1928, 51,859. Schuler, K. E.J. Chem. Phys. 1953,21, 624. Woodward, R. B.; Hoffmann, R. Angew. Chem., Int. Ed. Engl. 1969, 8, 781. Quack, M. Mol. Phys. 1977, 34, 21. Bunker, P. R. Molecular Symmetry and Spectroscopy; Academic: New York, 1979. Gellene, G. I. J. Phys. Chem. 1993, 97, 34. Balasubramanian, K.; Liao, M. Z.; Lin, S. H. Chem. Phys. Lett. 1987, 142, 349. Metropoulos, A.; Nicolaides, C. A.; Buenker, R. J. Chem. Phys. 1987, 114, 1. Griffith, K. S.; Gellene, G. I., unpublished results. Dunn, T. M. In Molecular Spectroscopy: Modern Research; Rao, K. N.; Mathews, C. W., Eds.; Academic: New York, 1972; pp 231-257. Geltman, S. Topics in Atomic Collision Theory; Academic: New York, 1969; p. 183--191. Stebbings, R. E Adv. At. 11401.Phys. 1988, 73, 1717. Mahan, B. H.J. Chem. Phys. 1965, 43, 3080. Dickinson, A. S.; Roberts, R. E.; Bernstein, R. B. J. Phys. B. 1972, 5, 355. Chatterjee, B. K.; Johnsen, R. aT. Chem. Phys. 1990, 93, 5681. Gioumousis, G.; Stevenson, D. P.J. Chem. Phys. 1958, 29, 294. Stevenson, D. P.; Schissler, D. O.J. Chem. Phys. 1955, 23, 1353. Reuben, B. G.; Friedman, L.J. Chem. Phys. 1962, 37, 1636. Warneck, P.J. Chem. Phys. 1967, 46, 502. Chupka, W. A.; Russel, M. E.; Refaev, K.J. Chem. Phys. 1968, 48, 1518. Bowers, M. T.; Elleman, D. D.; King, J., Jr. J. Chem Phys. 1969, 50, 4748. Huntress, W. T., Jr.; Elleman, D. D.; Bowers, M. T. J. Chem. Phys. 1971, 55, 5413. Clow, R. T.; Futrell, J. H. Int. J. Mass Spectrom. Ion Phys. 1972, 8, 119. Threard, L. P.; Huntress. W. T., Jr. J. Chem. Phys. 1974, 60, 2840. Drewits, H. J. Int. J. Mass Spectrom. Ion Phys. 1976, 19, 313. Borkman, R. F.; Cobb, M.J. Chem. Phys. 1981, 74, 2920. Anderson, S. L.; Houle, F. A.; Gerlich, D.; Lee, Y. T.J. Chem. Phys. 1981, 75, 2153. Stine, J. R.; Muckerman, J. T.J. Chem. Phys. 1976, 65, 3975. Eaker, C. W.; Schatz, G. C.J. Phys. Chem. 1985, 89, 2612. Stine, J. R.; Muckerman, J. T. J. Phys. Chem. 1987, 91,459. Baer, M.; Ng, C. Y.J. Chem. Phys. 1990, 93, 7787. Pollard, J. E.; Johnson, L. K.; Cohen, R. B.J. Chem. Phys. 1991, 95, 4877. Su, T.; Bowers, M. T. Int. J. Mass Spectrom. Ion Phys. 1975, 17, 309. Picconatto, C. A.; Gellene, G. I.J. Phys. Chem. 1993, 97, 13629. Griffith, K. S.; Gellene, G. I. J. Chem. Phys. 1992, 96, 4403. Curran, R. K.J. Chem. Phys. 1963, 38, 2974. Conway, D. C.; Janik, G. S. J. Chem. Phys. 1970, 53, 1859. Durden, D. A.; Kerbarle, P.; Good, A. J. Chem. Phys. 1969, 50, 805. Payzant, J. D.; Cunningham, A. J.; Kerbarle, P. J. Chem. Phys. 1973, 59, 5615. B6hringer, H.; Arnold, F.; Smith, D.; Adams, N. G. Int. J. Mass Spectrom. Ion Phys. 1983, 52, 25. Rowe, B. G.; Dupeyrat, G.; Marquette, J. B." Gaucherel, P.J. Chem. Phys. 1984, 80, 4915. Randeniya, L. K.; Zeng, X. K.; Smith, R. S.; Smith, M. A. J. Phys. Chem. 1989, 93, 8031. Mickens, R. E. aT. Chem. Phys. 1983, 79, 1102. Ferguson, E. E. Chem. Phys. Lett. 1983, 101, 141. Bates, D. R. J. Chem. Phys. 1984, 81,298. Sur, A.; Ramana, C. V.; Colson, S. D. J. Chem. Phys. 1985, 83, 904. Brown. J. M.; Hougen, J. T.; Huber, K. P.; Johns, J. W. C.; Kopp, I.; Lefebvre--Brion, H.; Merer, A. J.; Ramsey, D. A.; Rostas, J.; Zare, R. N. J. Mol. Spectrosc. 1975, 55, 500.

25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61.

Symmetry-lnduced Kinetic Isotope Effects

191

62. Lefebvre---Brion, H.; Fields, R. W. Pertubations in the Spectra of Diatomic Molecules; Academic: New York, 1986. 63. Alexander, M. H.; Andresen, P.; Bacis, R.; Bersohn, R.; Comes, F. J.; Dagdigian, J.; Dixon, R. N.; Field, R. W.; Flynn, G. W.; Gericke, K.-H.; Grant, E. R.; Howard, B. J.; Huber, J. R.; King, D. S.; Kinsey, J. L.; Kleinermanns, K.; Kuchitsu, K.; Luntz, A. C.; McCaffery, A. J.; Pouilly, B.; Reisler, H.; Rosenwaks, S.; Rothe, E. W.; Shapiro, M.; Simons, J. P.; Vasudev, R.; Wiensenfeld, J. R.; Wittig, C.; Zare, R. N. J. Chem. Phys. 19811, 89, 1749. 64. Lindinger, W.; Albritton, D. L.; McFarland, M.; Fehsenfeld, F. C.; Schmeltekopf, A. L.; Ferguson, E. E. J. Chem. Phys. 1975, 62, 4101. 65. Richardson, W. C.; Setser, D. W. J. Chem. Phys. 1973, 58, 1809. 66. Glosik, J.; Rakshit, A. B.; Twiddy, N. D.; Adams, N. G.; Smith, D. J. Phys. B 1978, 11, 3365. 67. B6hringer, H.; Duruo-Ferguson, M.; Fahey, D. W.; Fehsenfeld, F. C.; Ferguson, E. E. J. Chem. Phys. 1983, 79, 4201. 68. Jarrold, M. F.; Misev, L.; Bowers, M. T.J. Chem. Phys. 1984, 81, 4369. 69. Ferguson, E. E.; Smith, D.; Adams, N. G. Int. J. Mass Spectrom. Ion Phys. 1984, 57, 243. 70. Yoo, R. K.; Gellene, G. I.J. Chem. Phys. 1995, 102, 3227. 71. Pauling, L.; Wilson, E. B., Jr. Introduction to Quantum Mechanics; Dover: New York, 1963; pp 100-111. 72. Keesee, R. G.; Castleman, A. W.J. Phys. Chem. Ref. Data 1986, 15, 1011. 73. Kaye, J. A.J. Geophys. Res. 19116, 91, 7865. 74. Bates, D. R. Geophys. Res. Lett. 1981, 15, 13. 75. Bates, D. R.J. Chem. Phys. 1990, 93, 2158. 76. Bates, D. R. J. Chem. Phys. 1990, 93, 8739. 77. Chajia, M.; Jacon, M.d. Chem. Phys. 1994,.101,271. 78. Rosenstock, H. M.; Draxel, K.; Steiner, B. W." Herron, J. T. J. Phys. Chem. Ref. Data 1977, 6, 268. 79. Johnson, M. A.; Zare, R. N. J. Chem. Phys. 1984, 80, 2407. 80. Herzberg, G. Spectra of Diatomic Molecules; Van Nostrand Reinhold: New York, 1950; p 268. 81. Pratt, S. T.; Dehmer, P. M. J. Chem. Phys. 1983, 78, 6336. 82. Crowe, A.; McConkey, J. W. J. Phys. B 1974, 7, 349. 83. Adams, N. G.; Smith, D.; Alge, E.J. Phys. B 1980, 13, 3235. 84. Rakshit, A. B.; Warneck, P.J. Chem. Phys. 1980, 73, 2673.

This Page Intentionally Left Blank

ION-MOLECULE CHEMISTRY" THE ROLES OF INTRINSIC STRUCTURE, SOLVATION, AND COUNTERIONS

John E. Bartmess

Abstract

I. II. III.

IV.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Introduction

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

196

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

198

T e c h n i q u e s a n d Tools Chemistry

194 194

A.

E q u i l i b r i u m Acidities . . . . . . . . . . . . . . . . . . . . . . . . . . . .

198

B. C.

Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Effect o f Solvation on Reactivity . . . . . . . . . . . . . . . . . . .

202

D.

The Effect o f C o u n t e r i o n s on Reactivity . . . . . . . . . . . . . . . . . .

209

E.

Structures o f Ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

212

Conclusions

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

205

214

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

214

R e f e r e n c e s and N o t e s

215

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Advances in Gas Phase Ion Chemistry Volume 2, pages 193-217. Copyright 9 1996 by JAI Press Inc. All rights of reproduction in any form reserved. ISBN: 1-55938-703-3

193

194

JOHN E. BARTMESS

ABSTRACT A comparison is made between the gas phase and solution phase reaction pathways for a wide range of organic reactions. Examples are presented in which the gas phase and solution phase mechanisms are the same for a given set of reactants; in which they differ, but attachment of the first molecule of solvent to the bare gas phase ionic reactant results in the solution phase products; and in which the bare, monosolvated, and bulk-solvated reactions proceed by three different pathways for the same reactants. The various tools available to the gas phase ion chemist are discussed, and examples of their use in the probing of ionic structures and mechanisms are reported.

I. I N T R O D U C T I O N What aspects of chemical structure control the rate and mechanism by which a chemical reaction takes place? Chemists have long sought good answers to this question, in terms of structure--reactivity correlations, both qualitative and quantitative. When chemists have analyzed the factors that affect reactivity, however, almost invariably the solvent has been, at first, regarded as a minor perturbation in the analysis. Unless there is some overwhelming effect, for example, the millionfold rate increase seen for some SN2 reactions such as: C1- + MeBr ~ Br- + MeC1

(1)

on going from protic to aprotic solvents, ~the solvent is regarded as something that is merely holding the reactants off the bottom of the flask. This simple view is clearly true for some reactions, e.g., the Diels-Alder dimerization of cyclopentadiene, where the rate constant in ethanol is the same as in hexane, and only a factor of three larger than in the gas phase. 2 In contrast, for the example mentioned above of the SN2 reaction (1), the reaction proceedsfifteen orders of magnitude faster in the gas phase than in methanol. 3 For the SN1 reaction of tert-butyl iodide, however, the gas phase rate constant can be estimated to be about 86 orders of magnitude slower than the solution phase rate constant. 4-6 It is thus for ionic reactions that the tremendous changes in the rate constant upon solvation are seen. We are therefore specifically interested in those gas phase iotr-molecule reactions that are the counterparts to the "well-known" solution phase reactions. A rationale for why iotv--molecule reactions exhibit major solvation effects is available based on the solvation energies, gas phase to solution, of the species of interest. Neutral molecules typically have aqueous solvation energies of 5 to 20 kcal/mol, as given in Table 1. In contrast, ions have solvation energies an order of magnitude greater. Even a poorly solvated ion, like perchlorate, is solvated by an amount greater than most solution phase activation energies. Historically, the discovery by Brauman and Blair of (1) the reversal in the order of the acidities of the aliphatic alcohols, on going from solution to the gas phase, 7

Intrinsic Structure, Solvation, and Counterions

195

Table 1. Solvation Energetics of Ions and Neutrals Ion

-Ansolv a'b

H§

(269) d

H3O+ K+

114 87 e

NH~ Cs+

87 76 66 55 116 118 92 89 87 80 70 60 51

pyridinium

Me4N+ F-HOMeCO 2 CH2=NO 2 PhOC1HC(CN)~ IC104

Neutral CH2(CN)2 PhOH MeCO2H pyridine

H20 MeNO 2 NH 3 Me3N MeOH Me2CO

-lMr-Isolvb'c 17.5 13.8 12.6 11.9 10.5 8.4 8.4 7.9 7.2 5.1

Notes: aFromFigure 1. See also Ref. 17 bkcal/mol, for transfer from the gas phase into H20. CAH~ p - AH~ from Refs. 17 and 32. dAll ionic values are anchored relative to this, based on the extrathermodynamic assumption in Ref. 73.

eRef. 73.

and (2) the fact that toluene is intrinsically a stronger acid than water, 8 were key starting points for development of this field. This alerted chemists to the fact that the mental pictures commonly used for visualizing structure-reactivity correlations might be too simplistic. Polarizability effects were shown to be just as important as the usual triumvirate of polar, resonance, and steric effects in the determination of structure-reactivity correlations. Solvation could play a major role, involving energetics far larger than most activation energies, in determining reactivity in solution. Unfortunately, these early examples led to a belief among many solution phase chemists that "everything is different in the gas phase" and therefore of little use to solution phase work. This was perhaps due to the way that the original articles 7,s were phrased, understandably emphasizing the differences between reactivity in the two phases. Nevertheless, the complex nature of the instrumentation involved, the relatively primitive capabilities of that instrumentation in the late 1960s and in the 1970s for handling molecules of even moderate size, plus the early debate about the attainment of thermal equilibrium 9'1~led to some disinterest by solution phase chemists in the developments occurring in gas phase ion-molecule chemistry. It is the goal of this review to set out some of the principles that can be derived from

196

JOHN E. BARTMESS

gas phase chemistry that help the understanding of structure--reactivity correlations in the solution phase. The focus here will be on the gas phase ion chemistry of negative ions, owing both to the author's interest, and to some bias toward the use of these in solution as reactive species, relative to cationic reagents.

II.

TECHNIQUES AND TOOLS

When ions in the gas phase are being dealt with, mass spectrometry is the technique that immediately comes to mind. Unfortunately, in conventional mass spectrometry, analytical chemists have spent the better part of this century getting rid of exactly the bimolecular chemical processes of interest here. In conventional mass spectrometry, if an ion encounters a neutral species at any point during its flight between the acceleration region and the detector, it is deflected from its path, resulting in at least decreased resolution and probably a decreased signal-to-noise ratio as well. Conventional mass spectrometers have thus been designed to minimize such occurrences. Under the typical conditions of low neutral gas pressure (ca. 10-6 torr) and short residence times (1-10 microseconds) for ions in such instruments, the chance of an ion colliding with a neutral molecule, so that a bimolecular reaction might occur, is less than 0.1%. The analogy in solution phase chemistry is one of running a synthetic reaction for too short a time with too low a concentration of reagents, resulting in a 0% yield of bimolecular product. To overcome this, instrumental techniques such as pulsed high-pressure mass spectrometry (PHPMS), 11the flowing afterglow (FA) and allied techniques like the selected-ion flow tube (SIFT), 12and ion cyclotron resonance (ICR) spectrometry 13 and its modem variant, Fourier transform mass spectrometry (FTMS), 14have been developed. These extend either the reaction time (ICR) or the concentration of species (PHPMS, FA), so that bimolecular chemistry occurs. The difference in the effect of increasing the pressure versus increasing the time, in order to achieve bimolecular reactivity, results in some variation in the chemistry observed with the techniques, and these will be addressed in this review as needed. Solution phase chemists have developed a tremendous variety of tools to elucidate mechanisms. Spectroscopy, kinetics, isotopic labeling, and many more are all in the chemical mechanic's tool kit, for use in mapping out reaction pathways. 15 In contrast, the tool kit for the gas phase reaction mechanic is far more limited. The low concentration and short lifetime of gas phase reaction intermediates and products severely limits the use of many of the conventional tools. Gas phase ion-molecule chemists have therefore both adapted solution phase tools to their unique needs and developed many new ones. Although thermochemistry, in the form of PKa'S, redox potentials, and so forth, is important in the analysis of solution phase reactivity, it is a critical tool when gas phase ion-molecule chemistry is being dealt with. This is because of a serious limitation in all current instrumentation utilized in the study of such reactions: all the flasks leak. None of the current techniques are perfect in trapping the ions, with

Intrinsic Structure, Solvation, and Counterions

197

these always being lost to the walls of the~vacuum systems. This limits the range ofbimolecular rate constants that can be measured in the ICR spectrometer: no rate constant slower than the ion loss rate constant can be measured accurately. ~6 At present, most instrumentation has ion loss rate constants on the order of 10-3 to 10-5 of the collision rate constant. 11'12'14As a result, no reaction that is more endothermic than about 3 - 5 kcal/mol, or has an energy of activation of that order of magnitude, can be observed to proceed with current instrumentation. This would appear to be a serious limitation to the examination of the gas phase counterparts of solution phase reactions, because many of the most common condensed-phase reactions have energies of activation much larger than this. There are two factors, however, that greatly mitigate this problem. First, if one considers the source of the energies of activation in solution, an appreciable part of this must be due not to the intrinsic structure of the reactants, but to the necessary desolvation of the reactants before reaction can proceed. For reaction (1), some of the energy of the activation barrier must arise from intrinsic factors such as the partial breaking of the carbon-bromine bond in the transition state, and possibly the rehybridization of carbon and delocalization of electron density away from electronegative chlorine. Solvation energetics must also be examined, however. Based on its heat of vaporization and of solution into water, l bromomethane is solvated by about 5 kcal/mol in aqueous solution. In contrast, chloride is solvated by about 80 kcal/mol, based on the thermochemical cycle shown in Figure 1, involving the gas phase and solution phase acidities, and heats of vaporization and solution of the conjugate neutral acid. 17 A similar scheme can be written for basicity reactions to obtain solvation energetics for cations. Typical solvation enthalpies for a variety of other ions are given in Table 1. Note that even those ions considered to be poorly solvated due to highly dispersed charge, such as the conjugate bases of malononitrile and perchlorate, still have enthalpies of solvation that are larger than the enthalpies of activation for most solution phase reactions. Although not all of this energetic price must be paid to desolvate the reactive sites of each molecule, some of it must contribute to the activation energy.

(g)

AH

Anacid

~

A-

+ H+

A/'~vap (1)

AH 9

(aq)

~soln

AH

AH~aq(H*)

AHg~(A-) ~

9

~

A-

9

+

H+

Figure 1. Thermochemical cycle for the solvation of ions from the gas phase into aqueous solution.

198

JOHN E. BARTMESS

It is thus expected that the barrier to reaction in the gas phase is likely to be smaller than that in solution. Secondly, as illustrated in Table 1, the energy gained by solvation for ions is so great that a gas phase ion will accept essentially any species as a solvent, including the neutral molecule with which it is reacting. When an ion approaches a neutral reactant, an ion-molecule complex is formed. This is typically about 7 to 35 kcal/mol more stable than the reactants. 18 For any activation barrier to rise above the energy of the reactants (i.e., for the reaction to have a positive Eact), it must be at least as large as the bonding energy of the complex. As a result of this combination of reduced barriers and stabilized reactants, the energy of the transition state for many ion--molecule reactions is less than the reactants' energy, resulting in a negative energy of activation. Such reactions are expected to proceed at the collision rate, or nearly so. This picture of the reaction coordinate is that of the "double minimum" potential of Kebarle and of Brauman. 19 There appear, however, to be additional dynamic aspects to ion--molecule reactions that proceed at less than collision rate, due to what might loosely be called steric effects. 2~ The limitation noted above, whereby reactions that are more than slightly endothermic do not occur owing to ion loss (hereatter referred to as the tool of"no endothermic reactions"), can be used as an important mechanistic tool in the gas phase. If a reaction that is expected to be endothermic is observed to yield a product ion, then the structure of that product ion may not be as expected. An alternative use of this tool involves the employment of a series of structurally similar reactants for a given reaction. The structure of these can be varied in such a way as to make a given step in a suspected mechanism pass from exothermic to endothermic. If the observed product ion ceases to be produced for a situation where that step is expected to become endothermic, then this can be taken as evidence supporting the occurrence of the proposed mechanism.

iil.

CHEMISTRY

A. Equilibrium Acidities Where do the thermochemical data that are used to determine the energetics of a reaction come from? For closed-shell species that can be generated chemically via proton transfer, gas phase acidities (reaction [2]) and basicities (reaction [3]) are the principal sources. If the acidity or basicity for a reaction leading to a given ion is known, then the heat of formation for that ion can be calculated via Equations (4) and (5). This latter point is important, because this is the source for much of the ionic thermochemical data that are used for application of the "no endothermic reactions" tool. AH ~

A-+H +

(2)

Intrinsic Structure, Solvation, and Counterions BH + ~ AfH(A-) = AfH~ AfH(BH +) = AfH~

B + H+

+ AfHacid(AH) - AfH(H +) - AfHbasc(BH) + AfH(H +)

199

(3) (4)

(5)

Because of the author's interests, this review will focus on the acidities at this point, but the various techniques that follow are equally applicable to basicities. Gas phase acidities for more than 1000 Bronsted acids are known at present. 6 These include data from direct equilibrium measurements, 9'~ bracketing measurements, ~~ and from a kinetic method involving the dissociation of acid--conjugate base cluster anions. 21 For the equilibrium method, considered to be the most accurate in general, there is agreement 22 between acidities from data obtained at microtorr pressures, room temperature, and on a millisecond to second timescale, l~ and acidities from data obtained at" high pressure" (tort), higher temperatures (up to 600 K), and on a microsecond timescale. 9 This agreement, over such a wide range of conditions, indicates that thermal equilibrium must have been attained and that the thermochemical data derived from this are valid. The reader should note, however, that some acidity values have changed since first reported, owing both to changes in the absolute acidities used to anchor the relative acidity scale, and to the correction of a significant error in the 1979 ICR acidity scale. 1~The current data compilation reflects these changes. 6 In spite of the original reports cited above, 7'8 the bulk of the known gas phase acidities do parallel the solution phase acidities. Very early, it was reported that the substituted benzoic acids, the defining system for the Hammer sigma constants, 23 have gas phase and solution phase acidities that are linearly correlated. A plot of the solution phase versus the gas phase acidities in this series yields a near-straight line. 24 The slope of this plot, representing the Hammett p value in the gas phase, is l0 times the size of the p value in aqueous solution. This indicates that, in the absence of the solvent, reactivity centers are much more sensitive to structural changes due to "distant" substituents. The solvent, by stabilizing part of the charge of the reactive site, reduces the effect of the substiment on the charge. There have been many confirmations of this general principle. 25 Although there are some substiments that exhibit minor solvent-dependent substiment effects, 26 most free energy relationships comparing gas phase and solution phase data are reasonably linear, as long as the reactive site remains unchanged. Likewise, for the elemental hydrides, the expected acidity orders of CH 4 < NH 3 < H20 < HF, and HF < HCI < HBr < HI are observed in the gas phase, just as in solution. 27 When different types of reactive sites are compared, however, there can be dramatic inversions of acidity order. 8 Fluoride is a relatively weak base in solution, with PKa(HF ) = 3.2 in aqueous solution. 28 In contrast, in the gas phase, fluoride is strong enough to exothermically deprotonate acetone, which has a pK a of about 20

200

JOHN E. BARTMESS

in aqueous solution. 29 Fluoride will also deprotonate other carbon acids such as acetonitfile, aniline, esters, and many acetylenes. 1~ These carbon acids have PKa's greater than 20 in DMSO solvent. 27 This contrast is because fluoride is the best hydrogen bond acceptor known, 3~ owing to its high electronegativity and concentrated charge. It is very well solvated in water, 17compared to other anions, as shown in Table 1. Its intrinsic reactivity is inhibited by its solvation, therefore, and it becomes weakly reactive in solution. It may be expected that acids that have conjugate bases with the negative charge residing primarily on oxygen, and to a lesser extent nitrogen, will have those anions better solvated by protic solvents, and thus be more acidic in solution, relative to the general run of gas phase acids. Likewise, oxyacids that are good hydrogen bond donors in their acid form will have some reduced acidity in solution, owing to favored solvation of the acid. The effect of the solvent on the acidity of various functional groups was pointed out several decades ago, and is shown in Figure 2. 31 From more current data, 1~ a comparison of gas phase acidities with those in water, 32 as shown in Figure 3, reveals a general trend, but with some intriguing deviations from that trend. The straight line represents the acidities of several primary alcohols, as an arbitrary standard set of acids. Points above that line represent species that are more acidic in water than in the gas phase, relative to these primary alcohols. It is noted that all Bronsted acids are more acidic in water than in the gas phase, in an absolute sense, owing to the solvation energetics of the ions. The weakest Bronsted acid in solution is probably methane, at a pK a of about 60, or about 82 kcal/mol endoergonic. 27 The

.///

6o

56 52 "

CH3COCH

4s-

i

/

c.3c~

CH2 (CN) 2

~o ~'4 1'a 2'2 2'a 3'o 3'. 3'a .'2 4'6 ~'o

EcluiliDPium

Acidities

in

DMSO

Figure 2. Gas phase acidities versus equilibrium acidities in DMSO from Ref. 31.

Both axes in kcal/mol. CpH = cyclopentadiene. The lines are least squares fits for the ketones (upper line) and nitriles (lower line).

Intrinsic Structure, Solvation, and Counterions 390

-

380

-

370

-

360

-

201

9H20

/

MeOH 9

to I~

9H F

Me2C"NOH m /

.ocl 9 350

9

9H2Sa

9H2S

/EtOH t Bu O_H /eOCH2CH20H 9 / 9HOCH2CH20H

/,'C~aCH20H

-

"13 "~ U tO (.9 <3

9HOOH

9u p s / "

~

9CpH

9

340-

330

~

-

=

all

O o -~ 9_0 o ~ 9 ~_ ~ll ,,-H2T~ . /

/ V

/

~."

"

~IB~ ~IB~ V V

"~'

9CH2 CH2 (CN) (CN) 2 2

320

o CF3CO2H 3'10

0

4

B 12 AGac i d (H20)

16

20

24

2'8

Figure 3. Gas phase acidities versus aqueous acidities. Data from Refs. 6 and 32.

Both axes in kcal/mol. Open squares = carboxylic acids. Open triangles -- phenols. The straight line is a least-squares fit to primary alcohol acidities. CpH = cyclopentadiene.

strongest gas phase neutral acid is probably perchloric acid, at about 281 kcal/mol endoergonic. 33 This >200 kcal/mol difference, closer to 300 kcal/mol if the comparison is made for the same acid in water versus the gas phase, represents the solvation energetics of any pair of charges, regardless of structure. As noted above, hydrogen fluoride is by far the most extreme case for differential solvent effects on acidities, though Figure 3 reveals that some inorganic oxyacids with localized anions also fall in this category, as well as the thiols. Points below the line represent species that are less acidic in water, relative to their gas phase acidities, than the alcohols. These are acids with delocalized, poorly solvated conjugate bases such as cyclopentadiene and malononitrile. Such anions are very poor hydrogen bond acceptors, owing to the low charge density at any one atom plus the low electronegativity of the atoms bearing negative charge. The phenols, indicated by the open triangles, fall slightly below this line, consistent with the lower electron density on the oxyanion compared to the alkoxides, which is due to charge delocalization to the aromatic ring. Carboxylic acids, represented by the open squares, are stronger acids in water, relative to their intrinsic acidity, presumably owing to their increased number of hydrogen bond acceptor atoms. Figure 4 reveals a similar pattern for acidities in DMSO solvent versus the gas phase.31,10,27 Once again, the small, localized anions result in solution acidities that are relatively stronger than the gas phase counterparts. The acids with large

JOHN E. BARTMESS

202 390

-

380

MeOHm

370

-

y 9HF

,-% {/] I1] c~

"13 .,-4 U II] <:1

360

~ m

-

7-

350

9

r

OMSO

~nm ,"

-

HCN NeCOaH *

340-

.o.o. 330

9H C l

.0 320

9HEIr"

o

Me sm03H 310

.

9 9 am

A ~

7/

CH:~C N

9

.-

/m.mm

/

x'~ EtOH 9 9

o

9

;

..

9

m

an/I-~ *

ao

v

9

~

~III~" ~ ~ " .,1 9~' 9

.- .,,~,,t'~,.,"

~

mill& = -" 9 aaLa

-

-"

"9. "

.,~'~v_ |

a5 20 AGac •

u

!

25 30 (DMSO)

!

u

!

35

4o

45

5o

Figure 4. Gas phase acidities versus acidities in DMSO solvent. Data from Refs. 6, 27, and 64. Both axes in kcal/mol. Open squares = carboxylic acids. Open triangles = phenols. The straight line is a least-squares fit to primary alcohol acidities. CpH cyclopentadiene.

delocalized conjugate bases, such as cyclopentadiene, do not lie below the primary alcohol line as in the aqueous case, but rather above it. The soft, polarizable DMSO solvent solvates such species somewhat better than oxyanions such as alkoxides and enolates, thus enhancing their acidity. 27 In both of these solvents, there are several examples of a trend in which the elaboration of a alkyl group on an acidic site, in the usual series of methyl, ethyl, isopropyl, and t-butyl, results in a decrease in the solution phase acidity and an increase in the gas phase acidity. First noted for the alcohol acidities, 7 this trend has been observed for a wide variety of acids since then. 34 B.

Mechanisms

As a starting point for an examination of the mechanisms of gas phase reactions, the Claisen condensation is a multistep reaction that appears to proceed by essentially the same mechanism in the gas phase as in solution, as illustrated in Figure 5. 35 In the gas phase, in cases where this reaction occurs, all that is observed is a disappearance of the enolate reactant and the appearance of 13-carbonyl enolate product. The intermediate ions in the mechanism react too rapidly to exist long enough for detection. In the ICR spectrometer, unless an ion exists for at least a millisecond or longer, there are not enough cyclotron cycles to create a detectable signal. Intermediates such as the ones postulated for this reaction, with 10-50

Intrinsic Structure, Solvation, and Counterions

203 o

I

+

O

RCX

R/~R 3

1

0

"

+ XH

o-

1

0

R/'~~~R + 2

X-

Figure 5. The mechanistic steps of the Claisen condensation.

kcal/mol of internal energy, will exist for microseconds at most before further reaction. Therefore, no direct evidence for these intermediates exists in the mass spectrum. The individual steps of this reaction can be probed, however, using the tool of"no appreciably endothermic reactions." The substituents were varied in a pattern designed to gradually vary the energy of intermediates I and 2, through the points where each became endothermic for production from the original reactants. Although the exact thermochemistry for these intermediates is not known, knowledge of the effect ofsubstituents on acidities allows prediction of acidities and thus heats of formation to within 2-4 kcal/mol, which is accurate enough for use with this tool. At the point where production of intermediate I from the reactants became endothermic, product 3 ceased to be formed. Likewise, X was varied to make X - a poorer leaving group thermochemically, and production of 3 stopped when its loss from I became endothermic. Finally, when X-became too weak a base to deprotonate the 13-carbonyl intermediate, only free X-was observed as a product. It was concluded that for the Claisen condensation, the mechanism in the gas phase closely mimics the condensed-phase one. 35 Another example of a reaction where the gas phase and solution phase mechanisms appear to be the same is the anionic oxy-Cope rearrangement, shown in Figure 6. 36 Rearrangements are particularly difficult to follow in the gas phase, because mass spectrometry inherently does not supply structural information, only mass-to-charge data. The latter are, of course, invariant in a rearrangement. Various supplementary methods must be used to detect a rearrangement process, usually involving specific reactivity of one isomer versus the other with a specialized neutral reagent. Examples of such probe reactions include deuterium exchange 37 and reaction with reagents such as methyl nitrite, 38 dimethyl disulfide, 39 and hexafluorobenzene, 4~ among others. By a comparison of the types of ion--molecule reactions that occur with ions of fairly well known structure, such as those produced by simple deprotonation, with the reactivity of an unknown product ion, numerous possibilities for the structure of that ion can be ruled out. For the

204

JOHN E. BARTMESS R

4

"~,~e 0 D, MeONO

eONO'~eOD

R~OH rl,r.

~~L

R

o-.... HORt

NO

D

_

o R

O

Ra

Figure 6. The anionic oxy-Cope rearrangement in the gas phase.

above-mentioned Cope rearrangement, it was found that, for the tertiary alkoxide 4b (R = Me) in Figure 6, the reactivity of the ion at long reaction times resembled that of a model ketone enolate: up to four deuteria exchanged into the ion on reaction with MeOD, and the ion reacted with methyl nitrite ester to produced Claisen-type products. 36 In contrast, the secondary alkoxide 4a (R = H) did not exchange any hydrogens for deuteria, and no reactivity with methyl nitrite was observed. This parallels the solution phase results, where the tertiary alkoxide underwent the Cope rearrangement, as determined by NMR spectroscopy, while the secondary alkoxide apparently fell apart into a polymeric mixture, at a rate of about 0.001 times that of the tertiary alkoxide. Subsequently, Lee and Grabowski 42 reexamined this reaction in the flowing afterglow and found that dimethyl disulfide was a more rapidly reacting structural probe than methyl nitrite and indicated that both 4a and 4b rearrange to the enolate structure. They found no deuterium exchange with MeOD of either 4a or 4b and slow reactivity of both with methyl nitrite. This difference in observed reactivity may reflect differences in the internal energy of the ions used in the various techniques. Owing to the many nonreactive collisions with the helium bath gas in the flowing afterglow, ions there are assumed to be fully thermalized, and it is possible for excess energy in reactive intermediates in some cases to be bled off to the bath gas. This results in frequent formation of ion-neutral clusters in the FA, a process rarely observed in the low pressures of the ICR spectrometer. (However, see below in Section IIIC, regarding radiative emission). In ICR spectrometry, the lack of a bath gas, other than the neutral reagent gas itself, results in the primary ions retaining any excess energy deposited in them upon formation. This energy should be passed to the neutral gas during collisions on a time-scale comparable to the reaction timescale. Therefore, the ions become thermalized, but slowly. The ion--molecule complexes created as intermediates during bimolecular reactions are not thermalized. Thus, it would not be surprising to find that, at short reaction times, reactions might occur with ions in the ICR spectrometer that do not occur in the flowing afterglow, owing to excess internal

Intrinsic Structure, Solvation, and Counterions

205

energy. However, this is the opposite of what is being observed in this example, where reactions happen in the FA and not in the ICR cell. A possible rationale is that the high-energy fraction of the molecules in the ICR spectrometer react quickly, but the rest are relatively inert to reaction because that high-energy population is not replaced by thermalizing collisions, as in the flowing afterglow. This difference in reactivity has not been systematically addressed yet.

C. The Effect of Solvation on Reactivity The Michael-type conjugate addition of an alkoxide such as methoxide to an a,13-unsaturated nitrile or aldehyde proceeds in solution quite readily, being complete in 5-10 minutes. In the gas phase however, it was found that reaction (6a) does not occur; 43 there is no evidence of the addition product even at the longest trapping times, nor in the unquenched mode. ~6 Rather, the sole product observed is due to proton loss from the nitrile, to form a nominal vinyl anion, reaction (6b). f

MeO-+CH2=CH-C=N ~-~ MeOCH2CH=C--N-

AHrxn=-22kcal/mol (6a)

--~ MeOH+CH2--C=C=N- AHrxn=-10kcal/mol (6b) Similar reactivity is observed for acrolein and for nitroethylene. Although such vinyl anions are not unknown in solution, 44 they are almost invariably formed via a redox process from a vinyl halide. Any base strong enough to deprotonate the vinyl position is also a good enough nucleophile to add in the conjugate fashion, and the latter reactivity is apparently preferred kinetically. The vinyl anion is a reasonable product energetically: the acidity of that site in acrylonitrile is 2.0 kcal/mol stronger than that of the a-cyano site in propionitrile, as expected for the greater electronegativity of the sp 2 carbon, compared to sp 3. Why is no addition product observed in the gas phase, in contrast to solution? This is not a case of"no endothermic reactions"; both the proton transfer reaction (6b) and the alkoxide addition reaction (6a) are exothermic pathways. 3 When an exothermic reaction occurs in solution, the excess energy is passed to the solvent. In the gas phase, with no solvent available, the excess energy remains in the intermediate. This can result in an effective internal temperature for that intermediate of hundreds to thousands of degrees. If there is some other bond that can be broken to yield a product ion plus a neutral in a pathway that is exothermic with respect to the reactants, the intermediate will fragment by that method, and the observed product will be that fragment ion. This internal temperature is the reason for the very short lifetime of the intermediates mentioned above. At the higher pressures of other ion-molecule techniques, such as flowing afterglow 12 or pulsed high-pressure mass spectrometry, ll both of which operate with a bath gas pressure of about 1 torr, collisions of such an excited intermediate with the bath gas occur on a nanosecond to microsecond time-scale, in competition with the unimolecular dissociation rate. For these techniques, ions that are the

206

JOHN E. BARTMESS

product of the simple addition or clustering of an ion with a neutral are often observed in competition with the fragmentation pathways of the intermediate. At the pressure used in ICR spectrometry (microtorr or less), collision times of ions with neutrals are on the order of many milliseconds, far slower than is needed for this collisional stabilization of the intermediate. Simple ion-molecule addition products are thus generally not observed, unless radiative stabilization (see below) is efficient. However, if there is no other exothermic pathway available, all the intermediate can do is revert to reactants. In such a situation, the more favorable the addition process is, the more internal energy is in the intermediate and the faster the reverse dissociation will occur. The better the addition is thermochemically, the worse it is kinetically. For the proton transfer pathway (6b), the neutral methanol product can carry off the excess energy as translational energy (and capture some of it in the newly formed OH bond) and the reaction proceeds. There is an alternative mechanism, radiative emission, that can lead to stabilized addition products at low pressures (see Chapters 2 and 3). The excited intermediate can radiate an IR photon to lose sufficient excess energy (though not necessarily all the excess energy) to stabilize itself with respect to dissociation. This process typically has a rate of 5-1000 s-l, so normally is not competitive with dissociation, 46 but there are cases known where certain structural features enhance radiative emission and it can become an important competitor to other chemistry. 45-48 For methoxide addition to acrylonitrile, nevertheless, it is unlikely to be an operating mechanism. 46 We can, however, form alkoxide ions that are monosolvated by a single alcohol group, via the Riveros reaction [Equation (7)]. 49 When the monosolvated methoxide is reacted with acrylonitrile, the addition process reaction (8a), is the major pathway, because there is a molecule of solvent available to carry off the excess energy. The proton transfer pathway, reaction (8b), becomes endothermic, because the methoxide-methanol hydrogen bond, at about 29 kcal/mol, 5~ must be broken in order to yield the products. Thus, one can observe either the unique gas phase mechanism in the gas phase, reaction (6b), or the solution phase mechanism in the gas phase, reaction (8a), and the only difference is in the presence of the first molecule of solvent. MeO- + HCO2Me ~ MeOH-..-OMe + CO MeOH...-OMe

f

]-~ MeOCH2CH=C--N- + MeOH

+ CH2--CH-C--N l~-~ 2MeOH + CH2=C=C=N-

(7) (8a) (8b)

An even more extreme case is the reaction of hydroxide with acetonitrile. 51 In the ICR spectrometer, the bare hydroxide ion yields a simple proton transfer product, by way of reaction (9). In contrast, in aqueous solution the bulk-solvated hydroxide ion reacts to hydrolyze the nitrile group to give the carboxylate ion plus

Intrinsic Structure, Solvation, and Counterions

207

ammonia. 52 The monosolvated hydroxide, prepared in the ICR spectrometer by the multistep variant of the Riveros reaction shown as reactions (10) and (11), yields neither the gas phase proton transfer product, nor the solution phase hydrolysis product, but rather the nucleophilic displacement product methanol, still hydrogenbonded to the cyanide leaving group, as shown in reaction (12). The latter ion is isobaric with the expected proton transfer/solvated ion CH2--C=N-... HOH, so structural evaluation was necessary. The product ion in this case was probed by being allowed to undergo solvent-switching reactions, of the type in reaction (13). Only products attributable to the original MeOH .-.-CN structure were observed, with a variety of alcohols, as shown, and also with CO 2. It appears that this is a system where the bare, monosolvated and bulk-solvated ions react by three different mechanisms. HO- + CH3C~N --) H20 + C H 2 = C = N -

(9)

H O - + HCONMe 2 -+ HOH-..-NMe 2 + CO

(10)

HOH..--NMe 2 + H20 -~ HOH..--OH + HNMe 2

(11)

CH3CN + HO--..HOH ~ CH3OH--.-CN + HOH

(12)

CH3OH...-CN

+

EtOH

f---~ EtOH...-CN + CH3OH

(13)

1

[---) EtOH...-OCH 3 + HCN

Such monosolvated ions are of interest themselves, for thermochemical reasons. The solvent-switching reactions just described can be carried out in an equilibrium fashion, as shown in reactions (14) and (15). MeO-...HOMe + EtOH ~

MeO--..HOEt + MeOH

MeO----HOEt + EtOH ~- EtO---.HOEt + MeOH

(14) (15)

If both MeOH and EtOH are present in the spectrometer vacuum system, then the reactions come to equilibrium, and the equilibrium constant can be determined, exactly as for proton transfer equilibria. 9'1~Via a thermochemical cycle, the relative hydrogen bond strengths of the two ions present can be determined from that equilibrium constant and the conjugate acidities of the two bare ions involved, according to Equation (16), AGHB (MeO-..-HOMe) - AGHB (EtO-...HOMe) = AGeq(14) + AGacid(MeOH) - AGacid(EtOH)

(16)

208

JOHN E. BARTMESS 24-

MeOH.F-t 22-

MeOH.MeO--

20 I

o rr

18-

r 121 Ol

LIii]

16-

MeOHO . htlalIn

14-

12 374

a~2

a~o

a;a

~ G a c i d (ROH)

a;6

MeOH.PhCC-

a;4

I a;2

Figure 7. Free energies of attachment of anions to methanol, versus the conjugate gas phase acidity. All data in kcal/mol, from Refs. 54 and 53, as reanchored to data in Ref. 49. The line is a least-squares fit to the MeOH.RO- points.

where the subscript HB represents the energetics of the breaking of the hydrogen bond. 53 These relative hydrogen bond strengths can then be converted to absolute hydrogen bond strengths, if any one of these is known in an absolute sense. 49 A variety of alcohol-alkoxide and alcohol-carbanion species of this type have been examined, and a good correlation between gas phase acid/base character and hydrogen bond donor/acceptor ability was found, for a constant structure of donor and acceptor, i.e., XOH ...-OY. 53 As shown in Figure 7, the hydrogen bond acceptor ability of a series ofalkoxide ions varies at about half the sensitivity of their anionic basicity, consistent with the simple picture of a hydrogen bond being a half-transferred proton. An sp-hybridized carbanion, from PhC~C-, is a weaker hydrogen bond acceptor than an alkoxide of equal basicity, by 3.5 kcal/mol, and a n sp 3 carbanion, from 5,5-dimethyl- 1,3-dithiane is a little weaker yet. Fluoride, based on other literature values, 54is about 5 kcal/mol stronger as an acceptor than an alkoxide of equal basicity. It is intriguing that such a trend, of hydrogen bonding ability tracking electronegativity, is commonly taught in beginning college chemistry, but very few quantitative data to support this exist in the solution phase literature. 3~ It should be noted that the absolute values assigned to these alcohol-alkoxide and related hydrogen bonds were originally based on a single experiment. 53 The absolute values have been revised since then, to all being about 7 kcal/mol stronger than in the original article, based on more recent data. 49 The values in the standard data compilation reflect these revised values. 6

Intrinsic Structure, Solvation, and Counterions

209

D. The Effectof Counterions on Reactivity It is evident from the preceding discussion that some, but not all, reaction mechanisms are sensitive to the level of solvation present. What of the counterion, the. oppositely charged ion in solution often regarded merely as a "spectator"? In ICR spectrometry, only one type of ion, positive or negative, is normally trapped in the cell at a time. The chemistry of ions independent of any counterion can thus be examined. An example where the presence of a counterion makes a difference between the gas phase and solution phase pathways involves the intriguing carbanion produced on deprotonation of 1,3-dithiane at C-2. In solution, this species, almost invariably produced by reaction of the dithiane with butyllithium, 55 is widely used as an acyl anion equivalent in synthetic chemistry. Its importance for the present work is that this is a configurationally stable lithiated species in solution: the carbanion stays sp3-hybridized, and the lithium prefers the equatorial position, even to the extem of driving a tert-butyl group on the same acidic C-2 carbanion to the axial position in the lithiocarbon species. 56 The carbanion is thought to be stabilized primarily by orbital overlap with the C-S amibonding orbitals, as opposed to more conventional polar and n-resonance stabilization. 57 During an attempt to measure the acidity of this interesting molecule in the gas phase, it was found that although an (M-H)- ion can be prepared by reaction of 1,3-dithiane with several alkoxides, an acceptable equilibrium could not be established between that (M-H)- ion and a wide variety of standard acids. 58 Deuterium labeling of the precursor 1,3-dithiane revealed that the original (M-H)- ion population consisted of two structures as shown in Figure 8. Although deprotonation did occur, it was accompanied by an E2-type elimination reaction, starting with the proton on C-5. As evidence for this, 2,2-d 2-1, 3-dithiane gave both ( M - H ) , from

X"

,

"~

-I- CH2=S

Figure 8. Reactions of 1,3-dithiane on proton abstraction in the gas phase.

210

JOHN E. BARTMESS

elimination starting at C-5, and ( M - D ) , from deprotonation at C-2. Further evidence for the elimination process was a second elimination as shown, when the attacking base was sufficiently strong to make both elimination steps exothermic. The elimination reaction was blocked by replacement of the C-5 hydrogens with gem-dimethyl groups. This resulted in a good equilibrium measurement of the gas phase acidity, consistent with a bracketing experiment for the threshold of (M-D)production from the labeled species. The distant dimethyl substituents should have a negligible (<0.3 kcal/mol) effect on the acidity. The acidity obtained is in good agreement with recent high-level ab initio calculations. 57 The elimination reaction is reasonable, based on a large body of data for such reactions. 59 The question arises as to why the elimination pathway does not occur in solution: the deprotonation product is typically produced almost quantitatively, 55 even though the elimination product should be more favored thermochemically. It is suggested here that this is a counterion-controlled mechanism. 58 The lithium counterion of the butyllithium species is likely to coordinate with the two sulfurs of the dithiane, in the weakly polar ethereal solvents typically used for such reactions. This places the carbanionic carbon of the attacking base close to the equatorial C-2 hydrogen. One could conceive of the carbanionic carbon swinging around to access the axial C-5 hydrogen, but that is the wrong hydrogen; the favored antiperiplanar geometry for an E 2 elimination requires that the equatorial hydrogen be removed, and that particular hydrogen is not accessible as long as the lithium is chelated to the sulfur atoms. It is noteworthy that, although other counterions have been used with 1,3-dithiane carbanions, 55they have always become associated with the carbanion by exchange with a lithium counterion, atter carbanion formation, rather than being associated with the original attacking base. It appears, based on the lack of contrary information in the literature, that there is something special about lithium as a eounterion for efficient production of this carbanion in solution. In the gas phase, with no counterion present, attack by an anionic base that is strong enough to carry out both reactions results in approximately equal amount of elimination and deprotonation. A second type of system where counterions appear to play a critical role in the determination of the nature of the solution phase pathway involves the relative gas phase anionic basieities of a variety of species commonly used in solution as strong bases. As shown in Figure 9, a plot of the gas phase versus solution phase enthalpies of reaction for a number of such species follows a general trend. 6~ Even very disparate functional groups, such as alkyl r nitranions, and alkoxides, fall on the same general pattern. Although a more precise analysis does indicate some functional group trends, 3~ the major deviations here appear to be two in number. The first is the situation mentioned previously, where larger alkyl groups on the functional center in question decrease the gas phase basieity by the expected polarizability effect 7,61and increase the solution phase basicity by what is normally explained as steric hindrance to solvation. 7'17 The second deviation is for a single compound that is notably off the trend: hexamethyldisilazide anion, (Me3Si)2N-.

Intrinsic Structure, Solvation, and Counterions 425

-

415

-

405

-

211

ICH4

01

395

-

~

9

9

9Et 2NH t P P 2 N H I m TMP

385

-

131 13 -H U

tBuH

mbenzene

W rn

inBuH

tPPOH 9 BtBuOH

375-

ItBuCOCH3

365 355

I H N (SINe3) 2

-.

6

; -AHrxn:

~'o I'~ do ds do ds go g. ~o s', do A L l

+

iPPOH/Et2

~

Figure 9. Gas phase enthalpies of acidity versus solution phase enthalpies of proton transfer. Data are from Refs. 60 and 62. Both axes in kcal/mol.

In solution, lithium hexamethyldisilazide (LiHMDS) is a strong enough base to deprotonate esters, ketones, and alcohols, 62'63 with a pK a of about 27 in DMSO solvent. 64 In the gas phase, the bare anion is too weak to deprotonate methanethiol, much less the ketones, esters, and comparable carbon acids. 6~The change in relative anionic basicity is on the order of 14 kcal/mol. Molecular orbital calculations, both at the semiempirical 6~ and the ab initio level, 65 indicate that the lithiated hexamethyldisilazide remains in a trigonal planar geometry, like the neutral amine itself, in agreement with electron diffraction structures. 66 The calculations at all levels indicate that, in contrast, the free anion undergoes rehybridization to a linear Si-N-Si geometry, with a shortening of the S i N bond by 0.13 A, relative to the neutral acid. This decrease in bond length on proton loss can be explained as being due to the rehybridization to an sp state at nitrogen and resultant bond shortening. The Mulliken charge populations do not appear to reflect a major charge increase on silicon, nor does expansion of the basis set to include d orbitals have much of an effect on geometry or energies. The calculated acidities (6-31G + / / 6 - 3 1 G + ) put HN(SiH3) 2 as 44.0 kcal/mol (l~Eacid) more acidic than HN(CH3)2; experimentally, HN(SiMe3) 2 is 39.3 keal/mol more acidic in terms of AGacid than HN(CH3) 2. Based on existing gas phase acidity data, 6 replacement ofhydrogens on silicon by methyls is expected to have very little effect on the acidity of adjacent sites. In solution, Amett and Moe 62 have found that LiN(SiMe3) 2 is 17 kcal/mol more basic than LiNMe2; the ab initio calculations yield a relative basicity for the lithiated species of 16.0 kcal/mol.

212

JOHN E. BARTMESS

As an experimental proof of the prediction of the calculations, the cyclic disilazane 1,1,3,3-hexamethyl-1, 3-disila-2-aza-cyclopentane was synthesized and its gas phase acidity determined. 65 With the disilazide moiety constrained to a bent geometry within the five-membered ring, the acidity is weakened by 11.5 kcal/mol relative to the acyclic hexamethydisilazane. This places the cyclic disilazane's acidity as essentially within the general trend of gas versus solution phase acidities in Figure 9, and validates the concept that the counterion's locking of the geometry of the anion is the controlling factor in the solution phase acidity of the acyclic form. Another example of the counterion being the controlling factor for the chemistry observed in solution involves equilibrium isotope effects (EIE) on an electron transfer reaction. 67 For reaction (17), in THF solution, the equilibrium favors the light ion (AG~ = 0.092 kcal/mol, NH 3 solution, K § counterion, 208 K). In the gas phase for the equilibrium shown in reaction (17), but with no counterions present, AG = 0.191 kcal/mol, indicating that this EIE is intrinsic to the radical anion. In contrast, for reaction (18) with the isotopic substitution at the nitrogen, the gas phase EIE is experimentally not distinguishable from unity (0.0 + 0.05 kcal/mol). In solution, however, AG = + 0.307 kcal/mol in ammonia solvent at 208 K with K § the counterion, and AG~ = - 0.379 with an Na + counterion. It is evident that ion association is the reason for the latter EIE in solution; there is no intrinsic EIE at all, and the observed value in solution is completely dependent on the type of counterion present. This difference between the effects of isotopic replacement of hydrogen versus nitrogen was rationalized based on the changes in bonding in the organic structure upon electron attachment. 67 C6HsNO2.K + + C6DsNO 2 ~

C6DsNO2.K § + C6HsNO 2

C6H~4NO2.K+ + C6H~5NO2 ~- C6H~SNO2.K+ + C6H~4NO2

(17) (18)

E. Structures of Ions A major limitation in the investigation of gas phase ion chemistry is the lack of structural information provided by mass spectrometry. The structures of ions produced in ion--molecule reactions are not always as expected. This has been discussed previously, in several examples such as the 1,3-dithiane (M-H)- ion (Section IIID), 58 the CH2=C--N-... HOH versus CN---. HOCH 3 problem (Section IIIC), 51 and the hexamethyldisilizane anion (Section IIID). 6~ An additional example, where a critical technique was not available at the time of the investigation, involves the stabilities of isomeric allylic anions. 68 Based on the measured relative acidities of cis- and trans-2-butene, and with the difference in stability of cis- and trans-2-butene being factored in, it was originally believed that the trans-2-buten1-ide anion was more stable than the cis isomer. These anionic stabilities were in the opposite order to that observed in solution, 69 and that difference was originally ascribed to a counterion effect. 68 It was explicitly assumed that the ions did not undergo isomerization and reprotonated solely to give the original isomer of the

Intrinsic Structure, Solvation, and Counterions

213

2-butene. Soon thereafter, the technique of gas phase deuterium exchange was introduced. 37 Reexamination of these ions revealed that they undergo exchange of all available hydrogens with D20 , under reaction conditions similar to those used to measure the equilibrium acidity. This requires that the butenide reprotonate to yield both 1- and 2-butenes, and thus the population ofbutenide anions could be a mixture of cis- and trans-isomers, invalidating the results. Here, the use of an auxiliary tool to verify structure was critical. Another such case, where the use of an auxiliary tool revealed important details about ion structure, dealt with generation of the nominally antiaromatic triphenylcyclopropenide anion, y~ This was formed by dissociative attachment of electrons to 3-trimethylsilyl- 1,2,3-triphenylcyclopropene. The basicity of the resulting anion was bracketed as being a stronger base than benzyl anion, but weaker than phenylcyclopropanide anion. When it is considered that the phenyl groups should stabilize the carbanion by polarizability effects, regardless of any resonance interactions, this basicity implies some destabilized character for the triphenylcyclopropenide anion. Owing to the rather wide bracketing limits, a quantitative statement as to how much destabilization was present could not be made. An

CH3~~_ ~CH3 , + DOCH3

~

CH3~CH3 "p/:"'-OCH 3

Ph

H

\

-i// Ph D

H CH3~_ Ph

Ph D

+

DOCH3

Figure 10. Reaction of 1,2-dimethyl-3-phenylcyclopropanide anion with MeOD in the gas phase.

214

JOHN E. BARTMESS

attempt at deuterium exchange revealed no exchangeable hydrogens, consistent with the predicted cyclopropenide structure. When 1,2-dimethyl-3-phenylcyclopropenide anion was formed similarly, however, it was found to be less basic (more stable) than the triphenyl analogue by about 16 kcal/mol. This is surprising, because normal structural effects would imply that the phenyl groups, for resonance, polar, and polarizability reasons, should stabilize the cyclopropenide anion, relative to methyl groups. It was postulated that the dimethylphenylcyclopropenide anion was isomerizing to a structure with an exomethylene group that would yield an anion stabilized by both vinyl and phenyl groups, without any antiaromatic character. The only reasonable mechanism for this isomerization involves a series of proton transfers between the cyclopropenide anion and the alcohol used as a bracketing acid, as shown in Figure 10. If the alcohol is labeled as an ROD species, then the mechanism shown in the Figure predicts that the label will not be left in the isomerized anion; but rather must leave with the alcohol. In practice, no deuterium incorporation was observed. It could be argued that the allylic anion 5 in Figure 10 could exchange the exomethylene hydrogens with an ROD species. However, the thermochemistry of such an exchange, estimated both from the bracketed acidities plus group additivity estimates71 of the neutrals' heats of formation and from MNDO calculations, 72should be at least 10 kcal/mol endothermic from the reactants. Thus, this is a case where the lack of reactivity can be used to yield structural information.

IV. CONCLUSIONS Although we are still far from being able to predict with accuracy the effect of solvent and counterion on reactivity, there are some general principles emerging from the studies presently available. In the gas phase at low pressures, energy disposal is a problem when there is no departing species to carry away the excess energy. Simple addition reactions can be carried out in the gas phase, at the higher bath gas pressures used in FA or PHPMS, but the factors that hinder them in the ICR spectrometer allow access to other interesting pathways. Areaction mechanism that involves localized anions as intermediates will be favored in protic solvents relative to the gas phase, where delocalization of charge is the best means of stabilizing intermediates. The thermodynamics of ionic reactions in the gas phase appears to be a well-established field; the thermodynamics of the solvation of such species is still an area of investigation, especially when dealing with the effect of counterions.

ACKNOWLEDGMENTS The author thanks the National Science Foundation, National Institutes of Health, the Petroleum Research Fund, and especially the National Institute for Standards and Technology for funding of the part of the research discussed here that was carried out in his research group. I am immensely grateful to my co-workers, including Dr. Gary Caldwell, Dr. Jeff

Intrinsic Structure, Solvation, and Counterions

215

Kiplinger, Dr. Terry Sumpter, Mr. Robert Hays, Ms. Cathy Crowder, Mr. Burton Wilson, Dr. Deborah Grimm, and Ms. Priscilla Higgins who carried out most of the research.

REFERENCES AND NOTES 1. 2. 3. 4. 5.

6.

7. 8. 9. 10. 11.

12.

13.

14.

15. 16. 17. 18. 19.

20. 21.

Parker, A. J. Chem. Rev. 1969, 69, 1 Sauer, J.; Sustman, R. Angew. Chem., Int. Ed. Engl. 1980, 19, 779. Mclver, R. T., Jr. Sci. Amer. 1981, 186. From the enthalpy for heterolytic cleavage of t-Bul to iodide plus the carbocation, with thermochemical data from Refs. 5 and 6. Lias, S. G.; Liebman, J. L.; Levin, R. D.; Kafafi, S. A.; Stein, S. E. NISTPositive Ion Energetics Data Base, Office of Standard Reference Data, National Institute for Standards and Technology: Gaithersburg, MD, 1993; SRD Database 19A, Version 2.0. Bartmess, J. E. NIST Negative Ion Energetics Database; Office of Standard Reference Data, National Institute for Standards and Technology: Gaithersburg, MD, 1993; SRD Database 19B, Version 3.0. Brauman, J. I.; Blair, L. K. J. Am. Chem. Soc. 1968, 90, 5636. Brauman, J. I.; Blair, L. K. J. Am. Chem. Soc. 1970, 92, 5986. Brauman, J. I.; Blair, L. K. J. Am. Chem. Soc. 1968, 90, 6561. Cumming, J. B.; Kebarle, P. Can. J. Chem. 1978, 78, 1. Bartmess, J. E.; Scott, J. A.; McIver, R. T., Jr. J. Am. Chem. Soc. 1979, 101, 6046. Bartmess, J. E.; Scott, J. A.; McIver, R. T., Jr J. Am. Chem. Soc. 1979, 101, 6056. Kebarle, P. In Interactions Between Ions and Molecules; Ausloos, P., Ed.; NATO-ASI Series C; Plenum: New York, 1974. Kebarle, P. In Techniques for the Study of Ion Molecule Reactions; Farrar, J. M ; Saunders, W. H., Jr. Eds.; Techniques of Chemistry Vol. 20; Wiley: New York, 1988; Chapter 5. Graul, S. T.; Squires, R. R. Mass Spectrom. Rev. 1988, 7, 263. Adams, N. G., Smith, D. In Techniques for the Study of Ion Molecule Reactions; Farrar, J. M.; Saunders, W. H., Jr., Eds.; Techniques of Chemistry Vol. 20; Wiley: New York, 1988; Chapter 4. Lehman, T.; Bursey, M. M. Ion Cyclotron Resonance Spectrometry; Wiley: New York, 1976. Kemper, P. R., Bowers, M. T. In Techniques for the Study oflon Molecule Reactions; Farrar, J. M.; Saunders, W. H., Jr. Eds.; Techniques of Chemistry, Vol. 20, Wiley: NY, 1988; Chapter 1. Fourier Transform Mass Spectrometry; Buchanan, M. V., Ed.; ACS Symposium Series 359; American Chemical Society: Washington DC, 1987. A. G. Marshall. Acc. Chem. Res. 1985, 18, 316. Lowry, T. H., Richardson, K .S. Mechanism and Theory in Organic Chemistry, 3rd. ed.; Harper and Row: New York, 1987. Hunter, R. L.; McIver, R. T., Jr. Anal. Chem. 1979, 51, 699. Bartmess, J. E.; Caldwell, G. Int. J. Mass Spectrom. Ion Phys. 1981, 41, 125. Wilson, B.; Bartmess, J. E.J. Am. Chem. Soc., 1991, 113, 1762. Keesee, R. G.; Castleman, A. W., Jr. J. Phys. Chem. Ref. Data 1986, 15, 101. Kebarle, P. In Interactions between Ions and Molecules, NATO-ASI proceedings of the Biarritz Conference; Plenum: New York, 1974; pp 459-487. Brauman, J. In Kinetics orlon-Molecule Reactions; Ausloos, P., Ed.; Plenum: New York, 1978; pp 153-163. Farneth, W. E.; Brauman, J. I.J. Am. Chem. Soc. 1976, 98, 7891. Pellerite, M. J.; Brauman, J. I.J. Am. Chem. Soc. 1980, 102, 5993. Lira, K. E; Brauman, J. I. J. Chem. Phys. 1991 94, 7164. Hinde, R. J.; Ezra, G. S.; Chem. Phys. Lett. 1994, 228, 333. Cooks, R. G.; Kruger, T. L. J. Am. Chem. Soc. 1977, 99, 1279. McLuckey, S. A.; Cameron, D.; Cooks, R. G.J. Am. Chem. Soc. 1981, 103, 1313.

216 22. 23. 24. 25. 26. 27. 28.

JOHN E. BARTMESS

Bartmess, J. E. Mass Spectrom. Rev. 1989, 8, 297. Jaff6, H. H. Chem. Rev. 1953, 53, 191. Kebarle, P.; McMahon, T. B. J. Am. Chem. Soc. 1977, 99, 2222. Taft, R. W. Prog. Phys. Org. Chem. 1983, 14, 248. Taft, R. W.; Topsom, R. D. Prog. Phys. Org. Chem. 1987, 16, 1. Bordwell, F. G. Acc. Chem. Res. 1988, 21,456. Christensen, J. J.; Hansen, L. D.; Izatt, R. M. Handbook of Proton Ionization Heats and Related Thermodynamic Quantities; Wiley: New York, 1976. 29. Chiang, Y.; Kresge, A. J.; Schepp, N. P. J. Am. Chem. Soc. 1989, 111, 3977. 30. Pimentel, G. C.; McClellan, A. L. Ann. Rev. Phys. Chem. 1971, 21, 346. Pimentel, G. C. The Hydrogen Bond, Freeman: New York, 1960. 31. Bordwell, E G.; Bartmess, J. E.; Drucker, G. D.; Margolin, Z.; Matthews, W. S. J. Am. Chem. Soc. 1975, 97, 3226. 32. A comprehensive data base, a collection of all literature data pertinent to Figure 1, to obtain solvation energetics for ions is in preparation in the author's laboratory. 33. Marcus, u J. Chem. Soc., Faraday Trans. 11987, 83, 339. 34. Bartmess, J. E.; Mclver, R. T., Jr. In Gas Phase Ion Chemistry; M. T. Bowers, Ed., Academic: New York, 1979, Vol. 2, Chapter 11. 35. Bartmess, J. E.; Hays, R. L.; Caldwell, G.J. Am. Chem. Soc. 1981, 103, 1338. 36. Rozeboom, M. D.; Kiplinger, J. P.; Bartmess, J. E. J. Am. Chem. Soc. 1984, 106, 1025. 37. Stewart, J. H.; Shapiro, R. H.; DePuy, C. H.; Bierbaum, V. M. J. Am. Chem. Soc. 1977, 99, 7650. DePuy, C. H.; Bierbaum, V. M.; King, G. K.; Shapiro, R. H.J. Am. Chem. Soc. 1978, 100, 2921. Hunt, D. F.; Sethi, S. K.J. Am. Chem. Sac. 1980, 102, 6953. Lloyd, J. R.; Agosta, W. C.; Field, F. H.J. Org. Chem. 45, 3483. 38. King, G. K.; Maricq, M. M.; Bierbaum, V. M.; DePuy, C. H.J. Am. Chem. Soc. 1981, 103, 7133. 39. Grabowski, J. J.; Zhang, L.J. Am. Chem. Soc. 1989, 111, 1193. 40. Ingemann, S.; Nibbering, N. M. M.; Sullivan, S. A.; DePuy, C.H.J. Am. Chem. Soc. 1982, 104, 5620. 41. Thomas, D. A.; Bloor, J. E.; Bartmess, J. E. J. Am. Soc. Mass Spectrom. 1990, 1,295. 42. Lee, J.; Grabowski, J. J. Proceedings, 42nd Annual Conference on Mass Spectrometry, Chicago, IL, May 29--June 3, 1994; p 573. 43. Bartmess, J. E. J. Am. Chem. Soc. 1980, 102, 2483. 44. Dreiding, A. S.; Pratt, R. J.J. Am. Chem. Soc. 1954, 76, 1902. 45. Woodin, R. L.; Beauchamp, J. L. Chem. Phys. 1979, 41, 1. Bomse, D. S; Beauchamp, J. L.J. Am. Chem. Soc. 1980, 102, 3967. 46. Caldwell, G.; Bartmess, J. E. J. Phys. Chem. 1981, 85, 3571. 47. Kiplinger, J. P.; Crowder, C. A.; Sorensen, D. N.; Bartmess, J. E.J. Am. Soc. Mass Spectrom. 1994, 5, 169. 48. Dunbar, R. C.Mass Spectrom. Rev. 1992,11,309. Weddle, G.; Dunbar, R. C.Int. J. Mass Spectrom. Ion Proc. 1994, 134, 73. Faulk, J. D.; Dunbar, R. C. J. Phys. Chem. 1994, 98, 11737. 49. Blair, L. K.; Isolani, P. C.; Riveros, J. M. J. Am. Chem. Soc. 1973, 95, 1057. 50. Meot-ner, M.; Sieck, L. W. J. Phys. Chem. 1986, 90, 6687. 51. Caldwell, G.; Rozeboom, M. D.; Kiplinger, J. P.; Bartmess, J. E. J. Am. Chem. Soc. 1984, 106, 809. 52. Reitz, O. Z. Phys. Chem. 1939, A183, 371. Rabinovitch, B. S.; Winkler, C. A. Can. J. Res. 1942, 20B, 185. Wideqvist, S. Ar~'v Kemi 1956 10, 265. Schaefer, E C.; Peters, G. A. J. Orig. Chem. 1961, 26, 412. 53. Caldwell, G.; Rozeboom, M. D.; Kiplinger, J. P.; Bartmess, J. E. J. Am. Chem. Soc. 1984, 106, 4660. 54. Larson, J. W.; McMahon, T. B. J. Am. Chem. Soc. 1983, 105, 2944. 55. Seebach, D. Angew. Chem., Int. Ed. Engl. 1967, 6, 639. Seebach, D. Synthesis 1969, 1, 17.

Intrinsic Structure, Solvation, and Counterions

217

56. Eliel, E. L.; Hartmann, A. H.; Abatjoglu, A. G. J. Am. Chem. Soc. 1974, 96, 1807. 57. Wiberg, K. B.; Castejon, H. J. Am. Chem. Soc. 1994, 116, 10489. Bernardi, F.; Czismadia, I. G.; Mangini, A.; Schlegel, H. B.; Whangbo, M.-H.; Wolfe, S. J. Am. Chem. Soc. 1975, 97, 2209. 58. Bartmess, J. E.; Hays, R. L.; Khatri, H. N.; Misra, R. N.; Wilson, S. R. J. Am. Chem. Soc. 1981, 103, 4746. 59. Sullivan, S. A.; Beauchamp, J. L. J. Am. Chem. Soc. 1976, 98, 1160. Sullivan, S. A.; Beauchamp, J. L. J. Am. Chem. Soc. 1977, 99, 5017. DePuy, C.; Bierbaum, V. J. Am. Chem. Soc. 1981, 103, 5034. DePuy, C.; Jarrold, M.; Bowers, M. J. Am. Chem. Soc. 1985, 107, 2818. de Koning, L. J.; Nibbering, N. M. M.J. Am. Chem. Soc. 1987, 109, 1715. 60. Grimm, D. T.; Bartmess, J. E.J. Am. Chem. Soc. 1992, 114, 1227. 61. Taft, R. W.; Taagepera, M.; Abboud, J. L. M.; Wolf, J. F.; DeFrees, D. J.; Hehre, W. J.; Bartmess, J. E.; Mclver, R. T., Jr. J. Am. Chem. Soc. 1978, 100, 7765. 62. Arnett, E. M., Moe, K. D.J. Am Chem. Soc. 1991, 113, 7388. 63. C. R.; Rochow, E. G., Angew. Chem., Int. Ed. Engl. 1963, 2, 617. Davis, F. A.; Vishwakarma, L. C.; Billmers, J. M.; Finn, J.J. Org. Chem. 1984, 49, 3243. Martel, B.; Aly, E.J. Organomet. Chem. 1971, 29, 61. 64. Bordwell, F. G., personal communication. 65. Higgins, P. R.; Bloor, J. E.; Grimm, D. T.; Bartmess, J. E., submitted for publication in Organometallics.

66. Rankin, D. W. H.; Robiette, A. G.; Sheldrick, G. M.; Sheldrick, W. S.; Aylett, B. J.; Ellis, I. A.; Monaghan, J. J.J. Chem. Soc. (,4) 1969, 1224. Robiette A. G.; Sheldrick, G. M.; Sheldrick, W. S.; Beagley, B.; Cruickshank, D. W.; Monaghan, J. J.; Aylett, B. J.; Ellis, I. A.J. Chem. Soc., Chem. Commun. 1968, 909. 67. Stevenson, S. R.; Reiter, R. C.; Espe, M. E.; Bartmess, J. E.; Crowder, C. A. J. Am. Chem. Soc. 1987, 109, 3847. 68. Bartmess, J. E.; Hehre, W. J.; Mclver, R. T., Jr.; Overman, L. E. J. Am. Chem. Soc. 1977, 99, 1976 69. Schlosser, M.; Hartmann, J. J. Am. Chem. Soc. 1976, 98, 4674. 70. Bartmess, J. E.; Kester, J. E.; Borden, W. T.; K6ser, H. G. Tetrahedron Lett. 1986, 27, 5931. 71. Benson, S. W. Thermochemical Kinetics, 2nd ed.; Wiley: New York, 1976: Benson, S. W.; Cruickshank, F. R.; Golden, D. M.; Haugen, G. R.; O'Neal, H. E.; Rodgers, A. S.; Shaw, R.; Walsh, R. Chem. Rev. 1969, 69, 279. 72. Dewar, M. J. S.; Thiel, W. J. Am. Chem. Soc. 1977, 99, 4899. Dewar, M. J. S.; Rzepa, H. S. J. Am. Chem. Soc. 1978 100, 784. Program No. QCMP 004, Quantum Chemistry Program Exchange, Indiana University, Bloomington IN 47405, with extensive modifications by the present author for more efficient PC operation. 73. Randles, J. E. B. Trans. Faraday Soc. 1956, 52, 1573. Trasatti, S. In Modern Aspects of Electrochemistry, Conway, E.; Bockris, J., Eds.; Plenum: New York; 1979; Vol. 13B.

This Page Intentionally Left Blank

GAS PHASE ION CHEMISTRY UNDER CONDITIONS OF VERY HIGH PRESSURE

W. Berk Knighton and Eric P. Grimsrud

Io II.

III.

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General Motivations for Studies of Ionic Reactions at Elevated P r e s s u r e s . . . A. Support for Analytical Instruments . . . . . . . . . . . . . . . . . . . . . B. Physical Effects of the Buffer Gas . . . . . . . . . . . . . . . . . . . . . C. Chemical Effects of the Buffer Gas . . . . . ............... Instrumental Methods for Studies of Gas Phase Ion Chemistry at Very High Pressures . . . . . . . . . . . . . . . . . . . . . A. The Flowing Afterglow Mass Spectrometer (FAMS) . . . . . . . . . . . B. The Pulsed High-Pressure Mass Spectrometer (PHPMS) . . . . . . . . . C. The Time-Resolved Atmospheric Pressure Ionization Mass Spectrometer (TRAPI) . . . . . . . . . . . . . . . . . . D. Optical Spectroscopy in a Pulsed Electrical Discharge (OSPED) . . . . . E. The Photodetachment-Modulated Electron Capture Detector (PDM-ECD) . . . . . . . . . . . . . . . . . . . . . . . F. The Ion Mobility Spectrometer (IMS) . . . . . . . . . . . . . . . . . . .

Advances in Gas Phase Ion Chemistry Volume 2, pages 219-258. Copyright 9 1996 by JAI Press Inc. All rights of reproduction in any form reserved. ISBN: 1-55938-703-3

219

220 220 221 221 223 227 229 229 231 235 237 237 240

220

W. BERK KNIGHTON and ERIC P. GRIMSRUD

IV. Comparisons of Rate Constants Measured in the Very High Pressure and Lower Pressure Ranges . . . . . . . . . . . . . . . . V. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

254 255 256 256

ABSTRACT Fundamental and experimental aspects of gas phase ion chemistry (GPIC) in the very high pressure (VHP) range are reviewed. The VHP range is defined here to be between about 0.01 and 10 atm. Owing to instrumental deficiencies of the past, relatively little is presently known about the effects of the buffer gas on gas phase ionic reactions over this pressure range. Increased knowledge is needed in this area for several reasons. One is to support several powerful instrumental methods of analysis that are based on gas phase ion chemistry at atmospheric pressure. Another is so that fundamental aspects of gas phase ionic reactions can be more completely understood. Following a summary of several specific motivations for increased GPIC research in the VHP range, this article focuses on how kinetic measurements of ion-molecule (IM) reactions can be made in the VHP range. Six different instrumental approaches are considered with respect to their accomplishments, to date, and their potential for further development. Emphasis has been placed here on instrumental approaches that are being pursued in the authors' laboratory. These are based on the pulsed e-beam high-pressure mass spectrometer (PHPMS), the photodetachment-modulated electron capture detector (PDM-ECD), and the ion mobility spectrometer (IMS).

!.

INTRODUCTION

The field of gas phase ion chemistry (GPIC) has attracted a tremendous amount of attention during the last 3 decades in both the physical and biological sciences. 1-3 One reason for this is that fundamental information concerning the intrinsic properties and behavior of ions and molecules in the absence of solvent is provided. As impressive as these accomplishments have been, however, our present knowledge of GPIC is still limited to those conditions in which the buffer gas pressure is less than about 0.01 atm. This is clearly due to instrumental deficiencies of the past, rather than to a lack of interest. The present chapter focuses on the instrumental methods that are being developed for the detailed characterization of gas phase ionic reactions under conditions of high pressure, from about 0.01 to 10 atm. Some of the motivating forces for increased research in GPIC at elevated pressures will also be briefly discussed. For convenience, the term "very high pressure (VHP)" is used here to distinguish the relatively unexplored pressure range between 0.01 and 10 atm from that of the so called "high-pressure (HP)" range, between about 0.1 and 5 torr, and that of the "low pressure (LP)" range, between about 10-7 and 10-5 torr, where the gas phase

High-Pressure Gas Phase Ion Chemistry

221

ion chemistry of numerous reaction systems have been extensively explored. The pressure range between about 10-5 and 0.1 torr is also relatively unexplored.

II.

GENERAL MOTIVATIONS FOR STUDIES OF IONIC REACTIONS AT ELEVATED PRESSURES

To our knowledge, less than 20 papers exist in the literature in which the rate constant or equilibrium constant of a gas phase ion-molecule (IM) reaction has been determined by an instrumental method that uses buffer gas pressures in the VHP range. 4-18 This is in spite of the fact that thousands of papers havebeen written concerning the GPIC of systems operating within the HP or LP ranges. Therefore, the simple fact that a void of knowledge exists today concerning the behavior of ions at elevated pressures provides what might be considered the strongest motivating force for increased GPIC research in the VHP range. In addition, three specific points of interest for GPIC research in the VHP range are described below.

A. Support for Analytical Instruments Some of the most powerful instrumental methods currently available for the analysis of organic compounds and for the characterization of biological samples are based on gas phase ionic reactions that occur in buffer gases of relatively high pressure, often at the ambient condition of one atmosphere. These methods include the atmospheric pressure ionization mass spectrometer (APIMS), ~9the ion mobility spectrometer (IMS), 2~ and the electron capture detector (ECD) 21 for gas chromatography (GC). The responses of the electrospray mass spectrometer, 22 a variety of GC detectors, 23 and certain types of gas phase ion lasers 24 are also dependent on ionic reactions occurring under conditions of near-atmospheric pressure. All of these instruments have become widely used for both routine analytical and specialized research purposes. However, in an attempt to understand, modify, and improve the performance of such instruments, the massive literature conceming the reactions of ions in the gas phase is often inadequate for predicting the outcome of ionic reactions under very high pressure conditions. Within our laboratory, alone, we have often found that the literature of the LP and HP ranges has essentially nothing to say about the ion chemistry that has been found to be operative under the atmospheric pressure conditions of an APIMS, an IMS, or an ECD. An example of this is provided below. In Figure 1 are shown three negative ion APIMS spectra of perfluoromethylcyclohexane (C7F14) that were obtained under three different ion source conditions. 25 It is well known that perfluorinated molecules of this size attach thermal electrons very rapidly to form molecular anions by the resonance electron capture (EC) mechanism (e + M ~ M-), and this is what is observed in Figure 1a where pure nitrogen buffer gas has been used. In the use of certain analytical instruments for the detection of such compounds, however, protic molecules such as water or

222

W. BERK KNIGHTON and ERIC P. GRIMSRUD

MC7F14

>,, U3 E E

..~,,,.,

(M-F)-

>

.--,,.

_o

I .,-

4

C

rr

I II

I

,

I

.; 9 ,

'

,

5 3

i

F.Sn Z

7 8

b

1~9,,

m/z

360 ,4x:,

Figure 1. Electron capture APIMS spectra of C7F]4 in pure nitrogen buffer gas (a) at atmospheric pressure and 150 ~ (b) with 13 tort of methanol (S) added to the nitrogen buffer gas at 150 ~ and (c) with 13 tort of methanol added to nitrogen buffer gas at 40 ~ From Reference 25.

methanol may also be present in the buffer gas (as in direct whole air 26 or liquid chromatographic detection schemes, 27 for example). If APIMS is to be used for detection, the following question then should be considered: Will these protic molecules affect the EC-APIMS mass spectra of these compounds? Upon consulting the existing GPIC literature, one might expect that the answer to this question is negative. That is, water and methanol are not expected to interact with thermal electrons and, therefore, their presence in the buffer gas should not cause the reactant thermal electrons to be converted to negative ions. This expectation was, in fact, verified with our APIMS instrument when 13 torr of either water or methanol was made a permanent component of the buffer gas. However, when the buffer gas was altered in this way, the EC spectrum then observed for CTF 14 was drastically changed, as shown in Figures lb and 1c (the effect of water was the same as shown here for methanol). At 150 ~ a fragment ion resulting from the loss of one fluorine atom was dominant. At 40 ~ only the F- ion was observed [the highly solvated F-(S), ions in Figure l c are due to the combined effects of subsequent clustering reactions and a cooling effect within the sampling aperture of the APIMS ion source]. 28'29 In an attempt to identify the cause of these changes in the EC-APIMS spectra of C7F14 and other EC-active perfluorinated compounds (in-

High-Pressure Gas Phase Ion Chemistry

223

cluding SF6), the existing literature of GPIC did not provide much assistance, because the partial pressure of methanol used for the spectra in Figure 1b, c exceeds the total system pressures allowed by the methods of the HP and LP ranges. Based only on our APIMS observations, the general model shown in reaction (1) was tentatively proposed 25 to account for post-EC reactions of the molecular anion, M-. + nS ~

(MF,,v.1)- + F + nS

( 1 a)

F-(S). + MFm_~

(1 b)

[(MFm-1 " 9"F(S)n]-------~

With a high partial pressure of methanol (S), a large number, n, of methanol molecules will be available for clustering to the intermediate species shown, which is envisioned have a weakened C-F bond. The pathway by which this intermediate then dissociates depends on the extent of its solvation. At low temperature, where n is expected to be larger, the excess negative charge will tend to remain on the smaller F atom fragment, as shown by pathway (lb). At a higher temperature, where n is expected to be smaller, the excess charge will tend to remain with the larger MFm_1 fragment, as shown by pathway (1 a). This example illustrates how a process that has not been noticed in the HP or LP ranges can become dominant when very high partial pressures of reactants are used, as they commonly are in the analytical instruments. In order to characterize such processes, new kinetic methods that extend into the VHP region are clearly needed.

B. Physical Effects of the Buffer Gas At least three significant physical effects of the buffer gas can be envisioned to be potentially operative in the VHP region.

High-Pressure Limit of Kinetic Behavior The high-pressure limit (HPL) of kinetic behavior for any reaction is achieved when all species along the reaction coordinate undergo a sufficient number of collisions that they are brought into a state of thermal equilibrium with the buffer gas at all times. The addition of this experimental capability to the field of GPIC would be of great importance because, as Speranza 3~ has recently pointed out, the rate constants of ion-molecule (IM) reactions that are obtained by the well-established methods of the LP and HP range can be unduly complicated by the existence of excited intermediates along the reaction coordinate. Speranza argued that only by performing kinetic measurements under conditions within the HPL can the observed rate constants, kobs, of IM reactions be rigorously interpreted in terms of the candidate mechanisms and potential energy surfaces for that reaction. An excellent illustration of this point is provided by the extensively studied SN2 nucleophilic displacement reaction between chloride ion and methylbromide. 15'17'32-38This reaction will be frequently referred to in this article and is shown in Equation (2).

224

W. BERK KNIGHTON and ERIC P. GRIMSRUD

--"- (CF.CH 3Br)* CF + CHaBr ~ kb

X*

--~ x---- (CH 3 C1.Br-)* --~ ~ CH3C1 + Bry*

(2)

Reaction (2) is about 7 kcal/mol exothermic 37 in the forward direction and occurs with an efficiency, Eft, of about 1.5% (where Eft = kobs/k c, and the collision rate constant, kc = 1.4 • 10-9 cm 3 s-1, has been calculated from ADO theory). 39 This reaction is envisioned to proceed over a double-well potential energy surface on which the entrance channel ion complex, X*, and the exit channel ion complex, Y*, reside at the two energy minima. 33 Early measurements of this reaction by Olmstead and Brauman 33 were made under LP conditions where it was appropriate to assume that X* and Y* would not suffer collisions during their lifetimes on the reaction coordinate and would retain the relatively large amounts ofintemal energy imparted to them by their exothermic formation processes. At that time, it was suggested that the efficiency for this reaction could be interpreted in terms of the tendency of the entrance channel complex, X*, to move forward over an envisioned SN2 transition state rather than backward to reactants, in accordance with the relationship, Eff = kp/(k b + kp), where the relative magnitudes of kp and kb could be deduced from statistical reaction rate theories. An inherent assumption in the above "statistical" view of reaction (2) is that the internal energy of X* is very rapidly distributed throughout all of its vibrational and rotational modes. Although the application of statistical theories 4~ to IM reactions has gained widespread use during the last two decades, evidence has also been accumulating in recent years 3s'41-44 indicating that these theories are not actually applicable to some IM reactions, including the one shown in reaction (2). Consider, for example, the results of trajectory calculations recently reported by Wang et al. 45 for the species X* in reaction (2). They concluded that two distinct patterns of behavior for X* in reaction (2) can be anticipated depending on how excess internal energy is initially imparted to this species. If, upon formation, the low-frequency modes (those associated with the "intermolecular" C1-...CH3Br motions) of X* are excited, that energy will tend to remain in these intermolecular modes until X* back-dissociates to reactants. If, on the other hand, excess internal energy is initially placed into the high-frequency modes (those associated with the "intramolecular" motions within the CH3Br entity) of X*, that energy will tend to be trapped in these intramolecular modes until X* passes over the transition state to form the exit channel ion complex, Y*. Furthermore, once y* is formed in this way, its energy will also tend to remain in its intramolecular modes so that its back-isomerization to X* will be favored over its forward dissociation to the final products of reaction (2). In this way, several recrossings of the SN2 transition states, X* ~--- Y*, were envisioned to occur prior to a dissociation of either X* or y* . All of these curious

High-Pressure Gas Phase Ion Chemistry

225

predictions for reaction (2) under low-pressure conditions are made because, contrary to the assumptions required for statistical theories, the rates of energy transfer within the ion complexes, X* and Y*, are now thought to be relatively slow. The above "nonstatistical" view of reaction (2) has been reinforced by recent experiments made under LP conditions 38'43 and presents a great challenge to the GPIC community. It now appears that the LP rate constants obtained for any nonstatistical reaction of this type will be extremely difficult to interpret in terms of candidate mechanisms and potential energy surfaces envisioned for that reaction. An accurate prediction ofkob s for such reactions would have to include a set of very complex factors, some of which are not presently well understood. These factors would include the initial distributions of energy within the set of collision complexes, X*, formed under all possible collision impact conditions; the rates of energy transfer between all vibrational modes within the species, X* and Y*; and the mode-dependent rate constants for the motion of individual species within the sets of ion complexes, X* and Y*, in both directions on the reaction coordinate. The formidable problems that are associated with the interpretation of LP kinetic data for nonstatistical IM reactions can be entirely avoided if the reactions can be studied in the HPL of kinetic behavior. 3~ In the HPL, the energy content of the initially formed species, X* and Y*, in reaction (2) would be very rapidly changed by collisions with the buffer gas so that .the altered species, X and Y, would have normal Boltzmann distributions of energy. Furthermore, those Boltzmann energy distributions would be continuously refreshed as the most energetic X and Y within the distributions move forwards or backwards along the reaction coordinate. The interpretation of rate constants measured in the HPL is expected to be relatively straightforward because conventional transition-state theory can then be applied. The obvious question then is the following: How high must the pressure be in order to move a reaction system into the HPL of kinetic behavior? The answer depends on the specific reaction system under consideration and is expected to vary greatly. For reaction (2), the calculations of Wang et al. 45 indicate that some of the shortest lived species, X*, will back-dissociate very rapidly, in about 3 ps. In order to collisionally "catch" these, as well as the other longer lived X* and Y* species, prior to their motion along the reaction coordinate, a buffer gas pressure of approximately 10 atm would be required. In our laboratory, rate constants for reaction (2) have been determined at 1.0-atm pressure 17 by the method described in Section IIIE At this pressure, a small increase in the rate constant was noted relative to those measured under HP and LP conditions. With the assumption that the trajectory calculations of Wang et al. 45 are correct, a significantly larger increase in the rate constant for reaction (2) would be expected if the buffer gas pressure could be raised to 10 atm.

Termolecular Ion-Molecule (IM) Collisions Another physical effect of the buffer gas that has been suggested 4-8'46 to be important in the VHP range is the onset of a termolecular ion--molecule collision

226

W. BERK KNIGHTON and ERIC P. GRIMSRUD

process by which the effective ion--molecule collision rate would be increased with increased buffer gas pressure. This effect on IM reactions has been previously demonstrated by Collins and co-workers, 4-8 who determined the rate constants of charge-transfer reactions between the ions, He~, Ne~, and Ar~, and a large number of small molecules, including H2, 02, N2, NO, CO, CO 2, CH4, HC1, HBr, H20, N20, NO2, C3H8, and CC12F2. Their experimental method, which allowed pressures as high as 2 atm, is described in Section IIID. They found, for example, that the pseudo-second-order rate constant for the reaction of He~ with HBr at room temperature in He buffer gas is given by kobs = k2 + k3[He ], where k2 = 2.7 x 10-9 cm 3 s-1 is the second-order rate constant for the bimolecular component of this reaction and k3 = 1.37 x 10-28 cm 6 s--l is the third-order rate constant for its termolecular component. Therefore, whereas this fast reaction is known to occur at the collision frequency throughout the LP and HP ranges, its kobs will be additionally increased in the VHP range. In He buffer gas at a pressure of 2.0 atm, Collins and Lee 5 observed kobs = 1.0 x 10-8 cm 3 s-1 for this reaction, a value four times greater than the ADO collision limit. It should also be noted at this point, however, that Matsuoka and co-workers, 1~ using the TRAPI method for studies of GPIC at 1-atm pressure (described in Section IIIC), did not observe rate constants for fast reactions that significantly exceeded the ADO collision limit. The mechanism for a nonassociative IM termolecular reaction is thought 46 to be similar to that of ion-ion recombination reactions. At low pressures, ion-ion recombination reactions occur without assistance from the buffer gas. However, as the buffer gas pressure is increased beyond about 10 torr, the apparent rate constant increases with increasing pressure. This occurs because an ion--buffer gas collision can remove energy from the interacting species and change what might have been a mere glancing interaction of that ion with a counterion into an inwardly spiralling orbit, if that ion--buffer gas collision occurs while the ion is within the Coulombic attractive force of the counterion. 47 For IM reactions, an ion-dipole attraction can be envisioned to provide the driving force for the analogous termolecular process. 46 A strong correlation of k3 with the dipole moment of the neutral reaction partner was, in fact, observed by Collins and co-workers. 4-7 Because an ion--dipole interaction is weaker and extends over a shorter range than do ion--ion interactions, the onset of a termolecular mechanism for IM collision would be expected to occur at much higher pressures than the onset for ion--ion recombination reactions. The results of Collins et al. suggest that this onset pressure is roughly one atmosphere for IM reactions at room temperature in He, Ne, or Ar buffer gases. In order to test the generality of this physical effect, the studies of Collins and co-workers should clearly be extended to include other types of IM reactions and a greater range of physical conditions, and to other instrumental methods of observation. If the termolecular collision process is further supported by such studies, this physical effect will clearly be important throughout much of the VHP range and will have to be quantitatively understood and accounted for in studies of other effects on IM reactions. For example, in future studies of the slow IM reaction (2) in the VHP

High-Pressure Gas Phase Ion Chemistry

227

range, it is conceivable that increased buffer gas pressure might cause kobs to change for two independent reasons: the effective collision constant, kc, would increase with increased pressure if the termolecular collision mechanism is operative, and the efficiency of the reaction would also be increased as the HPL of kinetic behavior is approached. In fact, Collins and Lee 6 have already pointed out that the pressure dependence of the slow charge-transfer reaction between Ar~ and NO can be explained in terms of these two simultaneous physical effects of the buffer gas.

Diffusion Effects As the pressure of the buffer gas is increased, the diffusion coefficients of ions and molecules will be proportionately decreased. At some point of increased pressure, the rate of an IM reaction will become affected by and then limited by the decreased diffusional rates. 48 In order to estimate the pressure at which diffusion effects might become important, the corresponding effect on ion-ion recombination reactions is, again, useful to consider. As indicated previously, an increase in the pseudo-second-order rate constants for ion-ion recombination reactions is observed as the pressure is increased above 10 torr. As the pressure is further increased to about 1 atm, a diffusion effect generally becomes noticeable and a maximum rate constant for ion-ion recombination is typically observed at about 2 atm. 47 As the pressure is further increased through the range of 3 to 10 atm, the recombination rate constant then decreases proportionately with increased pressure, indicating that this reaction has become diffusion limited over this pressure range. In the atmospheric pressure range, the pseudo-second-order rate constants for ion-ion recombinations are very large, about 2 x 10-6 cm 3 s-l. 47 Therefore, these extremely fast processes will be unusually sensitive to the rate-retarding effect of diffusion. Because IM collision rate constants will be about three orders of magnitude smaller than ion-ion collision rate constants at one atmosphere of pressure, the onset of diffusion effects on IM collisions would not be expected until the rates of diffusion were correspondingly decreased by about three orders of magnitude. 48 Therefore, diffusion effects will clearly not be important in IM reactions at one atmosphere and should not become important until the pressure is increased to levels significantly greater than 10 atm (assuming that the temperature is ambient or above). Since we have somewhat arbitrarily defined the VHP region of immediate interest here to include pressures up to 10 atm, it appears that diffusion effects do not need to be considered in this context and can be left for future considerations of GPIC under more extreme conditions of even higher pressure and lower temperature.

C. Chemical Effects of the Buffer Gas Because an important reason for studying ionic reactions in the gas phase, rather than in the condemed phase, is to eliminate the strong moderating effects of the solvent, it is generally desirable that the buffer gas serve only as a chemically inert physical medium in which the reactants are suspended and thermalized. In the VHP

228

W. BERK KNIGHTON and ERIC P. GRIMSRUD

region, however, it is appropriate to consider the possibility that weak chemical interactions between ions and buffer gas molecules might cause some alterations in both the potential energy surfaces and the rate constants of IM reactions. It is at present difficult to quantitatively predict the magnitude of these effects because the energetics of only a few of these weak interactions have been measured. However, the weak clustering interactions, Na § (N2)n_ 1 + N 2 ~ - Na + ('N2)n, where n = 1 and 2, are sufficiently strong to have been measured by a method of the HP region and can be used here to illustrate the potential importance of a chemical effect of the buffer gas. For these two reactions, Fehsenfeld and co-workers 49 reported ~ = -8.0 kcal/mol, ~ =-5.3 kcal/mol, A ~ = -18.6 cal/K mol, and A ~ = -18 cal/K mol by the FAMS method. These thermochemical values lead to the expectation that a chemical interaction between the Na + ion and nitrogen buffer gas would, indeed, be very important. For example, even if the temperature is elevated to 100 ~ in order to discourage clustering, the following relative equilibrium abundances of Na +, Na + (N2), and Na + (N2) 2 would be expected at 1.0 atm nitrogen pressure: 17%, 72%, and 11%, respectively. At 10 atm, these abundances would be 1%, 40%, and 59%, respectively (if higher order clustering is ignored). Only at much lower nitrogen pressures would an insignificant amount ofNa + clustering occur (at 1 torr, 99.5% of the Na § ions would be unclustered). From this example, it appears that careful attention should be given to this point when work is being done in the VHP range. However, more information concerning these weak interactions is needed in order to assess the general importance of such chemical effects for other classes of ions and other buffer gases. Hopefully, it will be found that these interactions are typically much weaker than for those ofNa § with N 2. In order to measure the magnitude of the chemical interactions between various ions and buffer gases, approaches that are based on the measurements of either equilibrium or rate constants for ionic processes can be envisioned. An example of a kinetic method is described in the following. The unimolecular kinetic process known as thermal electron detachment (TED) for negative ions (M- ~ M + e), should be particularly sensitive to a chemical effect of the buffer gas. This is because the rate of TED will be given by kTED = constant x e - E A / R T where the electron affinity (EA) of the detaching species will include the magnitude of the stabilizing ion-buffer gas chemical interaction. We have measured 5~ kTED for the molecular anion ofazulene (Az-; the method is described in Section IIIE) over the temperature range 130-190 ~ at a pressure of 2 atm (buffer gas was 10% methane-in-argon) and found that these rate constants were uniformly about one-third as great as those previously measured 5~ in methane buffer gas at 4 torr. In addition, we have recently studied the same TED reaction by another method (Section IIIF) using nitrogen buffer gas at a pressure of 1.0 atm and found these kTED values to be intermediate in magnitude between the previous 4-torr and 2-atm measurements. One reasonable explanation for an inverse pressure dependence of kTED for Az- is that a weak chemical interaction between Az- and the buffer gas lowers the potential energy of Az-slightly in the VHP range. An increase in the

High-Pressure Gas Phase Ion Chemistry

229

effective EA for the detaching species of only 1.0 kcal/mol would be sufficient to explain a one-third reduction in kTED for Az-. The magnitude of this chemical effect is, indeed, much lower than that of the Na + ion in nitrogen, described previously, where the expected additions of either one or two N 2 molecules to Na § would stabilize that ion by 8 and 13 kcal/mol, respectively.

!!!. INSTRUMENTAL METHODS FOR STUDIES OF GAS PHASE ION CHEMISTRY AT VERY HIGH PRESSURES At the onset, it should be pointed out that noninstrumental, chemical methods have been used to study GPIC under VHP conditions during the last two decades, primarily by Cacace and his co-workers. 52-54 By two different ionization methods, one involving the radiolysis of reaction mixtures and the other utilizing the nuclear decay of tritium-labeled compounds, several chemical systems have been studied. A significant portion of the knowledge accumulated, to date, concerning GPIC at VHP has been produced through these efforts along with the associated theoretical contributions of Speranza. 3~ Thorough discussions of these chemical methods for GPIC at VHP can be found in several previous review articles. 3~ We have not included the chemical methods in this review, however, because they are not of the convenient, instrumental type that will facilitate future studies of GPIC in the VHP range. Most of our present knowledge concerning the interactions of ions and molecules in the gas phase has been generated by three basic mass spectrometric approaches. These are the Fourier transform mass spectrometer 55 (FTMS), which is closely related to its predecessor, the ion cyclotron resonance mass spectrometer ~6 (ICRMS); the flowing afterglow mass spectrometer 57 (FAMS), by which we mean to include the closely related selected ion flow tube 58 (SIFT); and the pulsed e-beam high-pressure mass spectrometer 59 (PHPMS), which evolved from the earlier technique known as the stationary afterglow mass spectrometer 6~ (SAMS). In a consideration of the extension of these methods to the VHP range, the FT- and ICR-based methods can be immediately eliminated from this discussion because the operational principles on which these methods depend cannot be sustained at total system pressures exceeding about 10-5 torr. 55 The other two MS-based approaches do have significant potential for extension into the VHP range and will be discussed in the following sections. Following these, other instrumental approaches that have shown promise for studies of GPIC in the VHP region will also be discussed.

A. The Flowing Afterglow Mass Spectrometer (FAMS) In the FA-based methods, 58 a buffer gas (usually He) is passed through a reaction tube of about 1.0-meter length and 8-cm diameter at a velocity of about 104 cm/s. Typically, a pressure of about 0.5 torr is maintained along the entire length of the tube. Reactant ions and neutrals are added at specific points in the upstream portion

230

W. BERK KNIGHTON and ERIC P. GRIMSRUD

of the tube and the change in the reactant ion density caused by the IM reaction of interest is measured at the end of the tube by aperture sampling to an associated mass spectrometer. High flow velocity is required because the rate at which ions are lost by radial diffusion to the walls is very fast at low pressure. Although the FAMS approach has not, to our knowledge, been extended into the VHP region, one can envision that this could be successfully accomplished. In order to preempt some of the major problems, as well as predict the benefits that might be expected in this effort, it is interesting to consider how the FAMS approach might be extended to 1.0-atm pressure. First, a practical consideration is that FAMS methods require relatively large amounts of buffer gas. Under the usual FAMS conditions described above, roughly one standard gas cylinder (T-size, 50 L, 2400 lb/in) is required for one day's (8 hours') operation. In order to establish a pressure of 1 atm in this flow tube while the same flow velocity is being maintained, a supply of buffer gas 1500 times greater would be required for one day's operation. Because this option is clearly not attractive, the diameter of the flow tube would undoubtedly be decreased so that the same flow velocity could be maintained with less gas. With the assumption that a reduced tube diameter of 1.0 cm would still be large enough to allow the placement of other required components within it, the buffer gas requirement would be reduced to only 23 times the normal FAMS requirement. In a reduction of the diameter of the tube to 1 cm, a change in the basic flow pattern might also occur, depending on what buffer gas is chosen. In the conventional FAMS experiment, the flow pattern is laminar, since the Reynolds number, 62 Re = dvp/e (where d is the tube diameter, v is the average linear velocity, p is the molecular density, and e is the coefficient of viscosity), will be about 50 for He and about 320 for N 2 or Ar under those conditions, and the requirement for laminar flow is Re < 1000. 62 With He buffer gas, the flow would still be laminar (Re - 850) in the 1-cm tube at atmospheric pressure. However, with N 2 or Ar buffer gas, the flow pattern would be turbulent (Re -~ 6000). In the choice between laminar versus turbulent flow, the strong recommendation for turbulent flow provided by Seeley et al. 63 is worthy of consideration. In their characterization of a high-pressure fast-flow apparatus for the study of fast gas phase neutral reactions at pressures up to 0.5 atm, they noted the following set of advantages under turbulent flow conditions. A turbulent "core" of gas will flow down the center of the flow tube with a relatively uniform velocity across the diameter of this core. A slower moving "laminar sublayer" of gas that is set up near the surfaces of the tube will protect the turbulent core from contact with the walls. Neutral reagents can be efficiently mixed into the turbulent core at any point along the tube by a simple injection device that increases turbulence at that point. In the planning of a FAMS for operation at 1.0-atm pressure, the advantages of turbulent flow as summarized above would be extremely useful. The radial mixing of neutrals added to the tube would be very fast, and ions within the turbulent core would be protected from contact with the wall. Under these conditions, ion-ion or ion-electron recombination reactions, alone, would provide the only physical

High-Pressure Gas Phase Ion Chemistry

231

means of total ion loss along the tube. In addition, the magnitude of ion losses by these second-order processes could be made almost negligible by the use of low, but still detectable, ion densities. For example, if the total ion density at the head of the flow tube was set to about 106 ions/cm 3, a typical ion-ion recombination reaction (krer ~ 2 x 10-6 cm 3 s-l) would destroy only 2% of the ions during the 10 ms required to travel the 1-m length of the tube at the standard flow velocity of 104 cm/s. The use of this and even lower ion densities might also allow the use of lower flow velocities, which, in turn, would provide a further reduction in buffer gas consumption. Since many of the issues concerning how to make and detect ions in an atmospheric pressure gas have already been addressed, 15 we presently believe that reliable kinetic methods for the study of GPIC in the VHP range could be developed using the FAMS approach.

B. The Pulsed High-Pressure Mass Spectrometer (PHPMS) A thorough description of the PHPMS technique, as it is normally configured in the HP range has been previously provided by Kebarle. 59 Typically, buffer gas pressures of 1 to 5 torr are used. A reaction volume (usually about 1 cm 3) is irradiated with an electron beam (about 3 kV energy) for several microseconds, thereby creating a population of secondary electrons and positive ions within the buffer gas. The beam is then turned off for several milliseconds, during which time the ions initially formed by the beam and by subsequent electron capture reactions will be further changed by succeeding IM reactions. Simultaneously, all ions will be lost by diffusion to the walls. A small slit or aperture located in one of the ion source walls allows the diffusional transport of a small portion of these ions out of the ion source and into an adjacent vacuum envelope where they are analyzed by an associated mass spectrometer. A multichannel scaler provides intensity versus time information for each detected ion by the accumulation of the ion signals over numerous (about 1000) pulse cycles. With respect to the practical considerations of gas flow and vacuum requirements, the PHPMS experiment might, upon cursory consideration, appear to be easily extended into the VHP region. That is, several MS-based analysis techniques routinely use ion source pressures of 1 atm. However, when an attempt to increase the pressure within a PHPMS ion source is made, the factors that do become problematic are those related to the subtle principles on which the method is based. Most importantly, the PHPMS method requires that the "fundamental mode of diffusion ''64 be quickly established within the ion source after each e-beam pulse, so that all ions are transported to the walls in accordance with a simple first-order rate law while the IM reactions of interest are occurring. 59 This ensures that a constant relationship exists between the ion density in the cell and the detected ion signal. The rates of the IM reactions can then be quantitatively determined from the observed time dependencies of the reactant ion signal because the contribution of diffusion to the time dependencies are well known and easily accounted for.

232

W. BERK KNIGHTON and ERIC P. GRIMSRUD

In the PHPMS experiment, it would be convenient if each e-beam pulse caused uniform ionization throughout the entire ion source volume. In that case, ion diffusion to the walls would very quickly occur by the desired fundamental mode, rather than by more complicated higher modes of diffusion. 64 In the PHPMS experiment, however, initial ionization is clearly not uniform throughout the ion source, since each pulse of electrons enters the source through a small aperture located at the center of one of the side walls and then penetrates less than a few millimeters into the interior volume. Fortunately, this initial nonuniformity of ionization does not cause a serious problem in the low-torr pressure range, as long as the ion source is designed so that the e-beam enters from the center of a side wall. Under these conditions, the undesirable higher modes of diffusion decay rapidly and are operative only in the very early portions of the period between pulses, quickly creating a relatively even distribution of ions throughout the source. After that point in time, the slower fundamental mode is dominant and first-order decay curves are observed. In the PHPMS experiment, one can then easily adjust the concentration of the neutral reactant so that the IM reaction of interest occurs during this long, well-behaved portion of the period between pulses. In our laboratory, we have intentionally made asymmetric PHPMS ion sources by moving the electron entrance aperture either forwards or backwards along the side wall. As expected, 64 a much longer time was then required for the complex higher modes of diffusion to decay and for the desired fundamental mode to be established. Clearly, a "well-behaved" PHPMS ion source is one in which the physical details of design and transport dynamics are delicately balanced. As the pressure within a PHPMS is gradually increased into the VHP range, additional complexities relating to the more subtle aspects of the PHPMS experiment can be easily envisioned. One of these is that, with higher pressure, the e-beam will penetrate progressively shorter distances into the ion source, thereby increasing the nonuniformity of initial ionization. Another is that the diffusional transport of ions becomes progressively slower with increased pressure so that ion-ion or iorv-electron recombination becomes progressively more important as a means of ion loss. Since recombination is a second-order process, its relative importance will also be enhanced by the higher local ion densities that will result from shorter e-beam penetration depths at high pressures. Under these more complex circumstances, the establishment of the desired fundamental mode of diffusion will undoubtedly be delayed to later portions of the period between pulses. In an effort to extend the PHPMS technique to pressures greater than those normally used, we have constructed the PHPMS ion source shown in Figure 2. This ion source is of the parallel plate design and has a very small active volume determined by a 2-mm thick copper gasket that separates the electron entrance and ion exit flanges shown. The pulsed e-beam enters the active volume of the ion source at a point directly opposite the ion exit aperture (50 ~m). With this ion source, some of the anticipated problems summarized above should be minimized. That is, by reduction of the size of the ion source, the relative importance of diffusion over recombination at a given

High-Pressure Gas Phase Ion Chemistry

233 ~ l,~t=,l/,,, ~ / =,

S

GLIS In s

S

e

f

9 s f

9

9

f

#

s

to Cluadrul3ole Mass F i l t e r

Ere

..... i

i

II

Figure 2. Pulsedelectron beam ion source for operation at elevated pressures. A 3-kV e-beam enters through a 50-1am aperture located at the center of one wall of the ion source. Ions are sampled through a 50-pm aperture located at the center of the other wall of the ion source. A 2-mm thick copper gasket determines the depth of the active source volume.

pressure should be greatly increased (because the rate coefficient, ka, for diffusion in any container of characteristic dimension, A, is given by k d = D/A2, where D is the ambipolar diffusion coefficient at that pressure). 64 In addition, the design shown in Figure 2 allows the e-beam to enter the active region of the ion source along its central axis. This is expected to produce a more even initial distribution of ions in a buffer gas of elevated pressure than can be obtained with the conventional design in which the e-beam enters from one side. Preliminary GPIC measurements with this ion source revealed some of the anticipated problems previously discussed with the use of increased pressure. For example, in Figure 3, PHPMS measurements of the reactant ion for the reaction of chloride ion with methyl bromide [reaction (2)] are shown. With no CH3Br added to the ion source, decay curve A indicates that the first-order fundamental diffusional mode becomes fully established only atter about 10 ms have passed following the e-beam pulse, at which time only about 1% of the original ion population remains. Unfortunately, this is too late, relative to the time over which the reaction of interest can be made to cause a significantly increased reactant ion decay rate, bythe addition of CH3Br to the buffer gas, as is shown in curves B and C. Therefore, rate constants of high accuracy probably cannot be obtained from these measurements. The problem illustrated in Figure 3 is thought to be caused by a combination of the factors discussed previously. In ongoing experiments, the individual effects of the relevant physical parameters (pressure, ion source width, e-beam intensity, e-beam penetration depth, and aperture sizes) are being characterized so that,

234

W. BERK KNIGHTON and ERIC P. GRIMSRUD 100000. q~

C

10000

C

,,m

C

0

looo~

A

om

"0 (g

m

1(X).

E 0 0

r

10=

1

0

C

2

4

6

8

10 12

14

16

18 20

time (ms) Figure 3. Chloride reactant ion decay curves obtained by the PHPMS ion source shown in Figure 2 for the SN2 nucleophilic displacement reaction, CI- + CH3Br CH3CI + Br-, in methane buffer gas at a pressure of 62 torr and a temperature of 125 ~ CI-is made by electron attachment to CCI4 (partial pressure = 0.06 mtorr). For curve A, no CH3Br was present so that the loss of CI- was determined only by the physical processes, diffusion and/or ion-ion recombination. For curves B and C, the concentration of CH3Br was 1.1 x 10 ~3 and 2.1 x 10 ~3 molecules/cm 3, respectively.

hopefully, PHPMS measurements can be successfully extended to pressures as high as about 100 torr. It is not likely that the PHPMS method could be extended to pressures as high as 1.0 atm. At atmospheric pressure, diffusion is so slow that ion-ion or ion--electron recombination will be the dominant means of ion loss throughout the source. 65 Therefore, the underlying principles of the PHPMS method would not apply to the signals observed at atmospheric pressure even if some means of creating a perfectly even initial distribution of ions were used. At atmospheric pressure, the transport of ions through the aperture would occur by convective flow with the buffer gas, rather than by diffusion through the buffer gas. 65 The appropriate analyses of such signals would require a fundamentally different understanding of those conditions. One additional point of concern in the extension of the PHPMS technique to elevated pressures is that the criteria normally considered to be necessary for accurate aperture sampling of a high-pressure ion source will probably be violated. A condition of"molecular" flow through the aperture is generally required 59'62'66 for accurate sampling. Molecular flow occurs when the critical dimension (such as the diameter of an orifice or the width of an exit slit) is equal to or smaller than the

High-Pressure Gas Phase Ion Chemistry

235

mean free path of the ions and molecules in the high-pressure region. The smallest slits and apertures that are typically used in MS ion sources have critical dimensions of about 10 to 20 ~tm. These distances are roughly equal to the mean free path of ions and molecules in the low-ton range. Therefore, as the pressure within an ion source is raised beyond this level, the flow condition moves progressively towards that of viscous flow. 62 Under viscous flow conditions, the ions being sampled will suffer numerous collisions in the immediate vicinity of the sampling aperture. Because the physical conditions existing in this region are likely to be significantly different from those of more interior regions of the ion source, perturbations of the ion abundances can occur as the ions pass through this region. In an atmospheric pressure ion source, the condition of flow through the aperture will definitely be viscous. 62 Therefore, it is not surprising that large sampling errors have been observed in measurements of fast IM clustering equilibria reactions by atmospheric pressure ionization mass spectrometry (APIMS). 28

C. The Time-Resolved Atmospheric Pressure Ionization Mass

Spectrometer (TRAPI)

The TRAPI was developed by Matsuoka and co-workers 1~ and has been used to determine the rate constants of about a dozen IM reactions at atmospheric pressure. As a first approximation, the TRAPI experiment might be described as an atmospheric pressure version of the PHPMS with initial ionization caused by a pulsed X-ray source. The X-rays cause relatively even ionization throughout the 6.4-cm 3 ion source volume by penetrating through thin sections of the ion source walls formed by 25-~m thick molybdenum foil. A 16-~tm ion-sampling aperture is located at the center of one of these thin walls. The ions that pass through this aperture are measured by an associated mass spectrometer as a function of time aider the X-ray pulse. In the TRAPI experiment, the new ions that are formed immediately aider each X-ray pulse are ot~en of greatest interest. Later in time, these relatively energetic ions will be converted to more stable "terminal" ions by unavoidable reactions with common buffer gas impurities (primarily water). Because ions are lost relatively slowly at atmospheric pressure, these terminal ions can persist in time over many pulse cycles (25 to 50 X-ray pulses are applied per second) while the fast decay curves of the more energetic ions are monitored aRer each pulse. In this way, for example, the rate of the reaction of N~ with added 0 2 was determined l~ from the observed time dependence of the N~ ion in nitrogen buffer gas at atmospheric pressure during the first 300 ~ts aRer each X-ray pulse. Even though the TRAPI and the PHPMS both involve a pulsed high-pressure ion source, they are fundamentally different methods in that they are based on different underlying principles. In the TRAPI method, ions are transported through the sampling aperture by convective flow with the buffer gas, rather than by diffusion through the buffer gas. Also, second-order ion--ion or iorr--electron recombination

236

W. BERK KNIGHTON and ERIC P. GRIMSRUD

will be the dominant means of ion destruction in all regions of the TRAPI ion source. As Matsuoka et al. 1~point out, however, with use of relatively low total ion densities, the fractional loss of ions by recombination can be made relatively small over the initial 300 laS following each pulse. Therefore, an IM reaction of interest can be made to dominate the changes in the reactant ion intensity observed during the initial 300-~ts portion of the period between pulses by appropriate choice of the concentration of the neutral reactant. From such measurements, the rate constant for the reaction of interest is obtained. In assessing the validity of kinetic measurements made by the TRAPI technique, the following question should be considered: Are the physical conditions within the region of observation being significantly perturbed by the aperture sampling process? In addressing this question, the following details of the TRAPI sampling process are relevant. The volumetric flow rate, F, of gas flowing through the 16-1am aperture is 2.3 cm 3 s-1. ~~During the critical measurement period (t = 0-300 laS after each X-ray pulse), a roughly hemispheric volume of gas immediately adjacent to the aperture will be swept through the aperture and its ionic components observed by the mass spectrometer. The radius of that hemisphere will be only 180 ~tm, because the radius = (3AtF/2x) t/3. 67 Because the dimensions of the ion source are 1.6 cm x 0.8 cm x 5 cm, only a very small fraction of the ion source volume, extending about a dozen "aperture lengths" from the aperture, is being used for the rate measurement. The diameter of the sampling aperture is about 200 times greater than the expected mean free path of the nitrogen molecules at atmospheric pressure, 62 and therefore the flow dynamics through the aperture will clearly be viscous, rather than molecular. With this microscopic view of the sampling process in mind, the original question might be rephrased in several more specific ways. 1. Are the buffer gas pressure and the partial pressure of the reactant neutral significantly lower in portions of the sampled volume than in the bulk of the ion source? 2. Is the effective temperature of the gas in this region being lowered by an adiabatic gas expansion? 3. Is the collision rate between the reactant ions and neutrals being lowered significantly by the increasingly directed flow that is being set up in this region? If any of these factors are of significance, the rate constants deduced from such measurements would probably be lower than those operative in the more interior regions of the TRAPI ion source. To our knowledge, these questions concerning the possible impact of viscous-flow ion sampling on TRAPI measurements have not been resolved.

High-Pressure Gas Phase Ion Chemistry

237

D. Optical Spectroscopy in a Pulsed Electrical Discharge (OSPED) In a series of articles, Collins and co-workers 4-9 have measured the charge-transfer reactions of He~, Ne~, and Ar~ with a variety of small molecules in He, Ne, or Ar buffer gas, respectively, over the pressure range 0.40-2.0 atm, using optical spectroscopic methods for reactant ion detection after an intense electron beam discharge. The relatively large ion source used in these studies has two quartz windows on opposing ends and a 25-~tm thick titanium window on one side wall. The 8-kA, 3-ns electron beam emitted by a Febetron 706 device was passed through the titanium window, thereby ionizing the gases within the source. In He, Ne, or Ar buffer gases, He~, Ne~, or Ar~ reactant ions, respectively, are first formed and, during the next microsecond, react with other compounds added to the buffer gas. The reactions of Ar~ were monitored by measurements of optical absorption by the Ar~ ion at 280 and 290 nm. 6 The reactions of He~ and Ne~ were monitored 4'5'7 by observation of the emission at 428 nm of the "indicator" ion, electronically excited N~* (the transition is B2Eu ~ X2Eg), which was formed in a competitive reaction of these two reactant ions with small amounts of added nitrogen. Because the spontaneous relaxation of excited N~* was thought to occur much faster than its formation, it was argued that the intensity of radiation emitted by N~* quantitatively tracks the concentrations of He~ and Ne~. The OSPED methods appear to offer one distinct advantage over all three of the MS-based methods discussed previously in this section. They should be less intrusive on the dynamic system being observed, because the transport of the reactant and product ions to some detection device is not required. Also, it appears that initial ionization by the discharge need not be uniform throughout the ion source. 9 A potential source of systematic error that might be suspected with use of the OSPED methods would be spectral interferences caused by species other than the reactant ions of interest. However, in the experiments of Collins and co-workers, 4-9 these potential sources of error were carefully considered and none were found in the reactions studied. A likely limitation of the OSPED approach is that it appears to be applicable only to a limited number of IM reactions. To our knowledge, OSPED has been applied only to the charge-transfer reactions of He~, Ne~, and Ar~ (see Section liB).

E. The Photodetachment-Modulated Electron Capture Detector (PDM-ECD) We have recently described 18 another spectroscopic method for observing IM reactions at atmospheric pressure that utilizes the photodetachment-modulated electron capture detector (PDM-ECD) 68'69 as a means of monitoring the negative ions either consumed or produced in an IM reaction. The reaction of interest is made to occur in a steady-state flow-through reactor in which ionization of the buffer gas is continuously caused by a 63Ni-on-Pt foil beta emitter. A chopped light beam of

238

W. BERK KNIGHTON and ERIC P. GRIMSRUD

selected wavelength is also passed through the ECD so that electron photodetachment (PD) of a small portion of either the reactant or the product negative ions occurs. The photodetachment-modulated component of the ECD signal thereby obtained is proportional to the concentration of the monitored ion. A very useful feature of the PDM-ECD technique is that the neutral reactant is introduced into the reactor in an unusually pure form by gas chromatography. This feature greatly facilitated an investigation in our laboratory of the reactions of the chloride ion with the series of 20 closely related alkyl bromides shown in Figure 4. In order to accurately determine the rate constants for these reactions (shown with each (4.1)

(1.4)

(3.2)

(0.66)

(1.7)

(0.036)

(0.11)

(2.8)

. (<0.01)

(0.097)

(<0.22)

(8.4)

~ (3.0)

/

(3.7)

r

(5.1)

~sr

Figure 4. Structure of a series of alkyl bromides and the rate constants (10-11 cm 3 s-1) for the IM reaction of each compound with the chloride ion, determined by the photodetachment-modulated electron capture detector (PDM-ECD) in 10% argon-inmethane buffer gas at atmospheric pressure and 125 ~

High-Pressure Gas Phase ion Chemistry

239

compound in Figure 4), it was essential that each compound be separated from its common alkyl bromide impurities at the time of the measurement. The rate constants indicated in Figure 4 were obtained in the following manner. The wavelength of light passing through the ECD was set to 365 nm. This light is sufficiently energetic to induce PD ofthe Br- ion, but not ofthe C1- ion. The detector gas was permanently doped with a small amount of CC14 so that about half of the thermal electrons within the ECD were converted to C1- ions. Known amounts of the alkyl bromides (RBr) were then introduced to the PDM-ECD by gas chromatography. For most of the alkyl bromides studied, normal ECD responses were not observed as they were passed through the ECD because their electron capture rate constants are very small. However, the PD-modulated component of the PDM-ECD did indicate the presence of each RBr, due to the IM reaction, C1- + RBr ~ RCI + Br-, and the PD reaction, Br- + hv ~ Br + e. By observation of the magnitudes of these PDM-ECD responses as a function of the concentration of each RBr introduced to the detector, the rate constants for the IM reactions were deduced. The PDM-ECD kinetic method demonstrated above is expected to be applicable to any IM reaction where (1) the reactant ion can be generated by a thermal electron capture reaction, (2) the neutral reactant does not react significantly with thermal electrons, and (3) either the reactant or the product negative ion possess a uniquely high PD cross section in some region of the UVNis/near-IR spectral range between 250 and 1200 r i m . 69 We have also shown 5~ that the PDM-ECD can be used to determine the rate constants of fast unimolecular reactions. In Figure 5, PD spectra for the azulene anion (Az-) determined at three different temperatures by the PDM-ECD are shown. 5~ It is seen that the apparent PD cross section of Az- is significantly decreased at all wavelengths by an increase in temperature. It was shown that this effect is caused by thermal electron detachment (TED) by Az-. The magnitude of kTED could be determined from a steady-state reaction model of the PDM-ECD, in which TED is envisioned to be in competition with ion--ion recombination as the dominant means of Az- destruction. From that model, the relationship, kTED = krn+(o/o'- 1), is obtained, where o and or' are the PD cross sections observed at low (50-100 ~ and elevated temperatures, respectively, kr is the ion--ion recombination rate constant, and n+ is the positive ion density. In the determination of kxED from the PD spectra shown in Figure 5, the measurements at 440 nm were used along with an independent determination of the product, ken§, for that reaction cell. 5~As previously described in Section IIC, TED reactions are of special interest in the VHP range because they are expected to be particularly sensitive to weak chemical interactions between the buffer gas and ions. By this general technique, it should also be possible to measure the first-order rate constants for other unimolecular decomposition processes involving negative ions that have large PD cross sections in the UV/Vis/near-IR region.

240

W. BERK KNIGHTON and ERIC R GRIMSRUD 0.3 0.2

o<~

0.0-1

C

0 U

130~

0.1

0.3"

9

Lr) U')

02-

150~

0.I-

0

L.

U

0.0 0.3-

I

i

i

T

I

-

]"

--

--

I

--

1

i

I

02-

0.1-

0.0

175~ 250

I

450

650

Wavelength

8~o

-

!

~o6o

.

.

.

.

~o

(nm )

Figure 5. The photodetachment spectra of Az- measured by the photodetachmentmodulated electron capture detector (PDM-ECD) in 10% argon-in-methane buffer gas at three different temperatures. F. The Ion Mobility Spectrometer (IMS)

We have recently explored the use of an ion mobility spectrometer (IMS) for the study of negative ion--molecule reactions at atmospheric pressure. 15-17 This instrument, shown in Figure 6, consists of three major components. They are an ion mobility spectrometer, a mass spectrometer, and a gas-handling plant (GHP). The walls of the IMS are defined by a Pyrex glass tube, 40 cm in length and 9 cm in diameter. The tube is terminated at both ends by glass-to-metal seals and

High-Pressure Gas Phase Ion Chemistry

241

z

,10ore'

Q

h

I 3

I .~ I

/( " 7 ' s nz I

-b

Figure 6. Diagram of our 1-atm ion mobility spectrometer (IMS) apparatus: (a) stainless steel source gas dilution volume, (b) septum inlet, (c) needle valve, (d) N2 source gas supply, (e) source and drift gas exhaust, (f) flow meter, (g) pressure transducer, (h) insulated box, (i) drift tube, (j) ion source, (k) Bradbury-Nielson gate, (I) Faraday plate/MS aperture, (m) drift gas inlet, (n) universal joint, (o) electrostatic lens element, (p) quadrupole mass filter, (q) 6"-diffusion pump, (r) first vacuum envelope, (s) channeltron electron multiplier, (t) second vacuum envelope, (u) 3"-diffusion pump, (v) N2 drift gas, (w) leak valve, (x) on/off valves, (y) fused silica capillary, (z) 4-liter stainless steel dilution volume, (aa) N2 gas supply.

stainless steel flanges. An electric field is generated along the length of the tube by application of a dc potential difference across 19 resistively coupled stainless steel rings that are strapped around the glass tube. The detector end of the resistor chain is grounded while the ion source and the ring closest to the ion source are biased to a potential of about - 4 kV. Ions are formed by a 15-mCi 63Ni-on-Pt radioactive foil that is located inside a movable ion source. Nitrogen gas flows continuously through the ion source from a 1-L dilution volume at a rate of about 25 mL/min. Following injection of a suitable compound into the dilution volume, the reagent negative ion of choice is formed by an electron capture reaction in the ion source. Some of the negative ions formed in the ion source will drit~ under the influence of the electric field toward the detection end of the IMS and will thereby enter a counterflowing current of nitrogen "drift gas." The drift gas enters the IMS tube

242

W. BERK KNIGHTON and ERIC P. GRIMSRUD

via two ports in the IMS-MS interface flange with a flow rate of about 500 mL/min. Both the source and drit~ gases exit through the ion source flange of the IMS tube. A movable Bradbury-Nielson (BN) ion gate is located about 0.5 cm in front of the ion source and consists of a set of 40 equally spaced, coplanar wires of 75-~tm diameter, glued between two ceramic disks of 1-in. internal diameter. Altemate wires are electrically connected so that a differential potential of about 15 V across the 0.52-mm distance between adjacent wires prevents the passage of all ions through the BN grid. In the pulsed mode of the IMS, the BN grid is "opened" for about 0.2 ms about 10 times per second. The principle means of ion detection is by a stainless steel Faraday plate and an associated fast operational amplifier set to a gain of 109 V/A. This signal is sent to a digital signal averager. At the center of the Faraday plate is a 50-~tm aperture that admits a small portion of the ions into the first vacuum stage of the mass spectrometer. The entire IMS is enclosed in an insulated box and is temperature-variable over a range from ambient to 175 ~ The GHP provides a means of accurately seeding the nitrogen drift gas with the neutral reactant of interest. The GHP has a 4-L stainless steel volume that is typically pressurized to about 2500 torr with nitrogen. Small quantities of the reactant compound are injected through a septum inlet into the GHP. The resulting mixture flows out of this volume through a fused silica capillary into a much larger flow of nitrogen drift gas, thereby providing a second stage of dilution. The ion cloud that enters the drift region has an initial radial diameter of about 1.0 cm and is expected to increase by only about 50% by diffusion as the ion cloud migrates to the far end of the tube. ~5Therefore, essentially all of the ions that enter the drift tube are expected to be collected on the 3.5-cm Faraday plate with use of drift fields in excess of about 100 V/cm. Even if lower drift fields are used, so that only a fraction of the ions arrive at the Faraday plate, the efficiency of ion collection by the plate is still expected to be the same for all ions, regardless of mass (that is, the ratio of the radial diffusion rate to the longitudinal drift rate will be the same for all ions). The kinetic energy imparted to the ions by the drift field of an atmospheric pressure buffer gas is negligible relative to the thermal energy of that ion at ambient or greater temperatures. 15 With the instrument shown in Figure 6, we have studied several SN2 nucleophilic displacement reactions, including reaction (2). For this reaction, C1- was formed in the ion source by electron capture to CC14, and CH3Br was made a permanent component of the drift gas. Typical signals then observed by the Faraday plate and MS detector are shown in Figure 7. The mass-analyzed ion mobility spectrum in Figure 7B unambiguously indicates the arrival time profiles of the CI- and Br- ions. Because C1- is made only in the ion source, it produces a normal, Gaussian-shaped IMS peak at about 24 ms. Because Br- is formed by the IM reaction of interest along the entire length of the reaction tube, it produces a skewed peak extending from 24 ms to about 27.5 ms. The relative sensitivity of the MS to the C1- and Brions is not known, and therefore the areas under the C1- and Br- peaks in the IMS/MS spectrum shown in Figure 7B cannot be used to determine the rate of the

High-Pressure Gas Phase Ion Chemistry

243

0.080.07-

*E 0.060.05-

o

0.04-

c

o

0.03-

S

0.020.01

|

O' 30~

ii

25O" B

o 15@ (D

CI"

100 9:) ,,,I,dL

G

2S

Drift Time (ms)

30

3S

Figure 7. (A) Reaction-modified IMS spectrum for the reaction of CI- with CH3Br in nitrogen buffer gas at atmospheric pressure and 125 ~ with 1.95 x 1012 molecules/cm ] of CH]Br in the drift gas.is (B) Mass-analyzed IMS spectra of the CI- and Brions under identical reaction conditions, is

IM reaction. Instead, the waveform simultaneously obtained by the Faraday plate shown in Figure 7A is used for this purpose, because the sensitivity of the Faraday plate to these two ions is identical. Also noted in Figure 7A are three small ion mobility peaks at drift times of about 28, 30 and 33 ms. These unwanted ions are formed in the ion source bythe clustering of the C1- ion to HCI, HCOOH, and CH3COOH. These impurities are not introduced with the buffer gas, but are formed by the 63Ni-induced radiation chemistry that is continuously occurring in the ion source. Because these ions do not interfere with the IM reaction of interest in Figure 7, their presence can be ignored as long as their

244

W. BERK KNIGHTON and ERIC P. GRIMSRUD 160 140120100" "i"

80" 60" 40" 20" 0

6

0

CH3Br Concentration (1012 molecules cm 4)

Figure 8. Plot of ot versus the concentration of CH3Br in the IMS drift tube, where ot = td-' In [(Acf + Aar-)/Acl-] is obtained from the analysis of IMS spectra such as the one shown in Figure 7A. The most accurate measurements are those for which ot is between 20 and 120 s-1, where both the reactant and product ions contribute significantly to the observed IMS spectra.

intensities are relatively low and their arrival times differ from those of the reactant and product ions of interest. For the IM reaction causing the IMS and MS waveforms shown in Figure 7, the pseudo-first-order reaction rate constant, ct = k2[CH3Br], is obtained from the relationship, ct = td-~ In [(Acl- + ABr-)/AcI-], where td is the drit~ time of the reactant C1- ion and Acv and ABr- are the respective areas of the reactant and product ions under the IMS waveform shown in Figure 7A. These areas are obtained ~5 from the IMS waveforms (7A) by application of an algorithm that accounts for the ion profiles indicated by the parallel MS measurements (7B). The concentration of CH3Br in the dritt gas is then varied and plots of ct versus [CH3Br ], such as illustrated in Figure 8, provide a large range of linearity for which the slope is expected to be equal to k2. Alternatively, the reaction time can be varied by a change in the strength of the drift field, as shown in Figure 9, where a greater extent of reaction with longer drift times is clearly indicated. A plot of In [(Acl + ABr)/Ac1 ] versus td for these data, as shown in Figure 10, also provides a straight line, as expected. From the slope of this line, the rate constant can also be determined (slope = k2[CH3Br]). A third method of obtaining k2 with this instrument has also been demonstrated. 15 By this method, the attenuation by reaction (2) of the steady-state MS signal observed for the reactant C1- ion was monitored while the BN grid was

[JS~HD]~>/o~, 9 ienba aq o~, pa]~adxa s! (s!sAleUe saJenbs4sea ! Aq pau!e~,qo) u~oqs aU!l aq:l .to adols a q l "6 aJn~!-! u! UAAO4S EJ:lE)gds SIAII PaL.t!pow-uo!},:)eaJ a4~. woJj pau!wJa:lap se aLu!}, ~!Jp -I~ snsJaA [-13~/(J8V + _13~)] Ul Jo },Old "Ol aArl~'./.4 ( s w ) o w ! 1 ~!JCI J O ge

~

.

.

~'8 .

.

oe

.

8~

a2

t,~ 8"I,

-9"I, o

-Z'l. + -g'l.

IXI -,,j

-6"1. 0

-I.'~

~lFtUolui "p!a~ N 8 poslnd tt ~u!sn sluotuoansttotu SIAII IOlF~ d s pou.tttuoJ,op _ID3O otup, 1J!..'p oql pu~ 'oqm ~l!ap oql u.t ~8~HDjO uo!ltmugouoo UA~OU" 4 oql '[~U~!S -ID oqlJo os~oaoop I~UO!lOe.tJpomosqo oql mo o poonpop uoql seta ,z? 'lu~lsuoo olea oq,L "po.LIgASeAxSe~ :l.J.up oql u.t aflSHD 3o lunotu~ oql pue uodo Xlsnonu!luoo goI

"Do ~ I. pue aJnssaJd 3!Jaqdsow~,e ~,e ua:8oJ~,!u s! se:8 ~!JC! st'W3/A 9E I. g.) '8# L (a) '6s t (P) 'LZ l (D) '~@ t (q) '#6t (E):scp,~uaJ~,s pla!j ~!jp ~u!MOllO J all}, ~uisn sE~ ~!Jp all}, u! saln~alow JS~HD ~t0l x 6~'t cI~,!M EJoads SWI pabt!pow-uo!pEa~l "6 aArl~!:l (sw) ew~ ~.0

m

o :3 0

St,?,

,41,~s!tuatt,9 UOl asettd se9 amssa.td-tt~

246

W. BERK KNIGHTON and ERIC P. GRIMSRUD

consistent determinations of k2 were obtained by all three of the above operational modes of the IMS instrument. We estimate that the accuracy of rate constants obtained by the IMS approach is typically about +20%, which is comparable to that obtained by the well-established methods of the LP and HP range. The rate constants obtained for the reaction of CI- with CH3Br at atmospheric pressure over the temperature range 35-150 ~ were found to be somewhat greater than those obtained in the LP and HP ranges, as discussed previously in Section liB. An interesting aspect of the IMS approach to reaction rate measurements is that fast equilibration in the reactions of an ion with an added clustering agent will be quantitatively reflected in the apparent drift time of the ion. 16For example, in Figure 11 is shown the observed dritt time of a partially clustered C1- ion packet as

o[ L

Odl%

Z

z,..15,.,

0 0

~r

i

'~ l.

.

.

.

f

.

g

__~h

o

S

1'o

~,~

drift time (msec) Figure 11. Ion mobility spectra obtained by the production of CI- by electron capture to CCI4 in the ion source with the following partial pressures of CHCI3 added to the drift gas: (a) none, (b) 1.61 x 104, (c) 3.2 x 10-~, (d) 6.5 x 10-6, (e) 1.29 x 10-s, (f) 2.6 x 10-s, (g) 5.2 x 10-s, and (h) 1.03 x 10-~ atm. 16 Drift gas is nitrogen at atmospheric pressure and 125 ~

High-Pressure Gas Phase/on Chemistry

247

increasing amounts ofCHC13 are added to the drift gas. These changes in drift time can be explained by a straightforward model that assumes that the observed driit time is the sum of drift times expected for the individual ions, CI-(CHCI3)n, where each term is weighted by the fraction of each ion present under equilibrium conditions. By a fit of the observed changes in drift times to this model, the two clustering equilibrium constants leading to the cluster ions, CI-(CHCI3) and C1(CHC13)2, were accurately determined. 16In addition, the single ion reduced mobili-

CI'(CHCl3) n

Br(CHC

0.02

0.01

< c

o

=m

b

o C

o

r :------ -'-

"

O.01

0.

=18

.

.

.

40

.

41

I10

m

drift time (msec) Figure 12. Reaction-modified IMS spectra of source-produced CI- ions with 2.22 x 10-s atm of the clustering agent, CHCI3, present in the drift gas along with the following

amounts ofthe reactant neutral, CH3Br: (a) none, (b) 2.6 x 1012, (c) 3.9 x 1012, and (d) 5.3 x 1012 molecules/cm3. ;6 Drift gas is nitrogen at atmospheric pressure and 125 ~

248

W. BERK KNIGHTON and ERIC P. GRIMSRUD

ties for the individual cluster ions were also provided by these measurements 16 for the first time. Analogous measurements for the Br-(CHC13) , reaction system were also performed by this technique. The IM reactions of any selected set of equilibrated cluster ions, such as that of CI-(CHC13)n ions with CH3Br, can also be determined by the IMS method from measurements such as those shown in Figure 12.16 It is interesting to note in Figure 12 that the reactant ion packet, CI-(CHC13)n, now has a greater drift time than the product ion packet, Br-(CHC13)m, because the clustering of C1- by CHC13 is more extensive than the clustering of Br- (that is, n > m). Only the bare C1- ion was shown to have significant reactivity with CH3Br in this study. In preliminary studies of other nucleophilic reactions by the IMS approach, interesting details of the reaction mechanism have been observed in the IMS spectrum. For example, in Figure 13, IMS spectra for the reactions of chloride ion with n-butylbromide and with i-propylbromide are shown under identical physical conditions. For the case ofn-butylbromide (Figure 13a), the rate constant (about 2 x 10-I~ cm 3 s-L) and the IMS waveforms are very similar to those discussed previously for the reaction of chloride with methylbromide. For the reaction involving i-propylbromide (Figure 13b), however, greater concentrations of this reactant must be added to the drift gas because the rate constant is significantly smaller than that of n-butylbromide. A significant difference in the IMS spectra is 0.050

0 "~'/

0.040

J

< r.. ~ c 11)

"0

0

3.9 X 1011

~ 1 . 5

1.2 X1012 , , , ~

x 1013

1.9 x 1012

0.030

0.020 0.010 0.000

0.045

0.05

0.055

I

0.045

0.05

0.055

t i m e (seconds)

Figure 13. Reaction-modified IMS spectra for the reactions of chloride ion with (A)

n-butylbromide and (B) i-propylbromide in nitrogen buffer gas at atmospheric pressure and 125 ~ The concentrations (molecules/era 3) of the alkylbromide added to the drift gas are indicated. The peaks at drift times greater than 0.050 seconds are due to impurities formed in the ion source and do not affect the kinetic measurements of interest.

High-Pressure Gas Phase Ion Chemistry

249

also noted in that the drift time of the apparent reactant ion, CI-, is smoothly increased by the addition ofi-propylbromide. This is thought to reflect the presence of a thermalized entrance channel complex, CI-(i-PrBr), where the C1- ion and the complex ion are maintained in a state of chemical equilibrium prior to passage over the transition state of this reaction. Since the magnitude of the shift in the reactant ion's drift time can be quantitatively related to the position of the preliminary equilibrium step, this additional source of information is expected to lead to a more detailed understanding of this reaction under high-pressure conditions. We expect that the IMS approach will be applicable to the study of most positive and negative IM reaction systems for which a stable reactant ion can be made in an atmospheric pressure buffer gas. However, the need for conditions in which the reactant ion is unaffected by side reactions with trace impurities can present a formidable problem in the IMS approach. This is because the timescale of the experiment is relatively long and the absolute concentration of impurities can be relatively high even though they are only minor components of the buffer gas. Consider, for example, ifa reactive impurity (with kiM = 2 x 10-9 cm 3 s-l) is present in an atmospheric pressure drift gas at a concentration of only 1 part per billion, that impurity will consume 80% of a set of reactant ions having a drift time of 30 ms. Therefore, very pure buffer gases and reagents are required. Since it is extremely difficult to reduce residual water to levels below 10 parts per billion, the IM reactions of ions that react readily with'water probably cannot be studied by the IMS method described here. As explained above, the continuous radioactive source used in our IMS also produces small, and sometimes troublesome, amounts of impurities within the ion source. In an effort to eliminate this problem, we are presently exploring the use of other source designs by which less radiation damage is done to the source gas. One of these alternative ionization methods is based on the photoemission of electrons from the back side of a gold foil. 7~ This ion source offers an attractive advantage for the study of negative IM reactions in that it can be shut off during most of the IMS duty cycle. There are no apparent reasons why the IMS approach cannot be extended to pressures both below and above atmospheric pressure, and two insmunents for these purposes are being constructed in our laboratory. Although an IMS-based instrument for operation in the 1- to 10-atm pressure range is presently only in the design stage, the construction of the other instrument, for the 0.01- to 1-atm pressure range, is near completion and is shown in Figure 14. As with the 1-atm IMS instrument described above, the drift tube of this instrument is also formed by a large glass tube with field-defining stainless rings placed on the outside of the drift gas manifold. Our experience with the 1-atm IMS has shown that the large glass drift tube design provides an excellent means of maintaining the purity and integrity of the drift gas mixture. Because the diameter of these glass tubes is large, ions are not allowed to contact and charge the glass walls. With this instrument, ionization will be initiated by a pulsed electron beam that has been designed after the PHPMS

250

W. BERK KNIGHTON and ERIC P. GRIMSRUD i

drift gas in & P gauge

._J~,..,.,_ r,_~,:~- Z ', -

i UP

I [ , [ [

5d

glus

oven

tube----[ [

r [ [ [

1

Z

Faxada I plate

J

I7

..- E-field rings ~---/)

J 1

i

[

\

\

\

,.

\

\

,

\

,,

I \

'~-

'

P guage

plate AI envelope

gas out

~,

\

\

\

\

"\

\

Ill/, ~,1 4

6" diff. pump

Figure 14. A pulsed electron beam ion mobility spectrometer for the study of GPIC over the pressure range of 0.01 to 1.0 atm. e-gun shown previously in Figure 2. An ionizer based on 63Ni would not be useful here because the penetration depths of the 63Ni beta particles (average ~nergy, 23 Kev) would be too great in the pressure range of 0.01 to 0.1 atm. 71 The penetration depth of the e-gun, however, will be very short and selectable through control of the e-gun voltage (0-5 KV). Operation of the e-gun in the pulsed mode is expected to be advantageous in IMS experiments for two reasons. One is that a pulsed e-gun

Table 1. Compilation of Rate Constants for Ion-Molecule Reactions Measured at

Atmospheric Pressure and at Lower Pressures

Reaction Rate Constant (cm 3 s-/)

Conditions

Method a

Ar~ + CO -4 products 7.8 x 10-1~ 8.5 x 10-l~

760 torr Ar, 300 K 1.2 torr Ar, 200 K

OSPED 6 FAMS 72

1.4 x 10- l ~ 8.0 x 10-1~

0.1-1 torr Ar, 300 K

SIFT 73 Langevin 39

Ar~ + H 2 -4 products 5.9 x 10-1~

760 torr Ar, 300 K

OSPED 6

4.9 x 10-1~

0.72 torr Ar, 200 K

FAMS TM

4.7 x 10-1~

0.1-1 torr Ar, 300 K

SIFT 75 Langevin 39

1.5 x 10-9 Ar~ + Kr -4 products 7.5 x 10-l~

760 torr Ar, 300 K

OSPED 6

7.5 x 10- l ~

1.3 torr Ar, 200 K

FAMS 72

5.3 x 10- l ~ 7.1 x 10-l~

0.1-1 torr Ar, 300 K

SIFT 73 Langevin 39

< 1.7 x 10-9

760 torr Ar, 300 K

OSPED 6

2.4 x 10-12 7.5 x 10-I0

0.004 torr Ar, 200K

FAMS 72 ADO 39

1.3 x 10-9

760 torr Ar, 300 K

OSPED 6

8.2 x 10-l~ 8.7 x 10-10

0.1-1 torr Ar, 300 K

SIFT 73 ADO 39

4.9 x 10-l~ 1.2 x 10-l~

760 torr Ar, 300 K 0.2 torr Ar, 200 K

OSPED 6 FAMS 72

7.4 x 10TM

0.1-1 torr Ar, 300 K

Ar~ + NO -4 products

Ar~+ N20 -4 products

Ar~ + 0 2 -4 products

SIFT 73 Langevin 39

7.0 x 10-l~ Ar~ + X e -4 products 1.6 x 10-9

760 torr Ar, 300 K

OSPED 6

2.3 x 10-l~ 8.5 x 10- l ~

0.1-1 ton" Ar, 300 K

SIFT 75 Langevin 39

8.1 x 10-1~

760 torr, 300 K

OSPED 4

2.0 x 10-1~ 1.6 x 10-9

0.2 torr He, 200 K

FAMS 72 Langevin 39

He~ + Ar -4 products

He~ + CO -4 products 2.0 x 10-9

760 torr, 300 K

OSPED 4

1.4 x 10-9 1.8 x 10-9

1.1 torr He, 200 K

FAMS 72 Langevin 39

(continued)

251

Table l. Reaction Rate Constant (cm 3 s-1)

(Continued) Conditions

Method a

He~ + CO 2 -~ products 3.2 x 10-9

760 torr, 300 K

OSPED 4

1.8 x 10-9

1.25 torr He, 200 K

FAMS 72 Langevin 39

2.1 x 10-9 He~ + H 2 --~ products 6.3 x 10-1~

760 torr, 300 K

5.3 x 10-10

0.93 torr He, 200 K

OSPED 5 FAMS 74 Langevin 39

1.6 x 10-9 He~ + NO ~ products 1.8 x 10-9

760 torr, 300 K

OSPED 5

1.3 x 10-9 1.2 x 10-9

1.1 torr He, 200 K

FAMS72 ADO 39

1.5 x 10-9

760 tort, 300 K

OSPED 4

1.3 x 10-9

1.0 torr He, 200 K

FAMS 72

He~ + N 2 --) products

Langevin 39

1.7 x 10-9 He~ + Ne ~ products 5.5 x 10- l ~

760 torr, 300 K

OSPED 4

6.0 x 10-l~

1.0 torr He, 200 K

FAMS 72 Langevin 39

8.1 x 10- l ~ He~ + 0 2 ~ products 1.9 x 10-9

760 torr, 300 K

1.05 x 10-9

1.0 torr He, 200 K

OSPED 5 FAMS 72 Langevin 39

1.2 x 10-9 Ne~ + N 2 -~ products 9.5 x 10-1~

760 torr, 300 K

9.1 x 10-10

1.2 torr Ar/Ne, 200 K

OSPED 7 FAMS 72 Langevin 39

7.6 x l0 - l ~ Ne~ + NO --~ products 1.1 x 10-9

760 torr, 300 K

OSPED 7

7.0 x 10- l ~ 7.5 • 10-10

1.0 torr Ar/Ne, 200 K

FAMS 72 ADO 39

Ne~ + 02 -~ products 8.1 x 10-10

760 tom 300 K

OSPED 7

7.1 x 10-10

1.0 torr Ar/Ne, 200 K

FAMS 72 Langevin 39

7.0 x l0 -1~ N~ + H 2 0 --~ H2 O+ + 2N 2 2.9 x 10-9

760 torr, 302 K

TRAP112

1.9 x 10-9

0.3 torr N2, 300 K

FAMS 76

3.0 x 10-9

0.5 torr He, 300 K

SIFT 77

1.9 • 10-9 1.9 • 10-9

1.2-3.2 torr N 2, 300 K

PHPMS 78 ADO 39

252

(continued)

Table 1. Reaction Rate Constant (cm 3 s-1) N~ + H 2 0 --~ H2NO + + N 2 1.5 x 10-9

(Continued)

Conditions

Method a

760 ton., 302 K

TRAP112

2.6 x 10-10

0.3 ton" N2, 300 K

FAMS 76

3.3 x 10-1~

0.5 ton" He, 300 K

SIFT 77 ADO 39

2 . 0 x 10-9 H20+N 2 + H 2 0 ~ H30+ + OH + N 2 2.8 x 10-9 2.8 x 10-9

760 ton", 302 K

TRAP112

3.4 torr Ar 300 K

Drift Tube 79 ADO 39

2 . 0 x 10-9 C2H~+ C3H 8 ~ sec-C3H ~ + n-C4Hlo 4.6 x 10-1~

760 ton., 302 K

TRAP113

6.2 x 10-1~

0.02-0.14 ton., 473 K

MS 8~

6.3 x 10-1~

low pressure

ICRMS 81 Langevin 39

1.4x 10-9 C3H ~ + n-C4Hlo ~ C4H]"0 + C3H 8 7.3 x 10-10 5.1 x 10- l ~ 1.4x 10-9

TRAP113 MS 82 Langevin 39

NO + + n-CsHI8 ~ CsH~ 7 + HNO 4.9 x 10-1~ 4.5 x 10- l ~ 1.9 x 10-1~

C V + CH3Br

760 tom 302 K 0.05-0.3 ton., 473 K

760 ton., 302 K

TRAP113

low pressure

ICRMS 81 Langevin 39

Br- + CH3C1

IMS 17

5.0 x 10TM

640 torr, 308 K

2.8 x 10TM

3 ton., 308 K

PHPMS 17

1.9 x 10TM

4 ton., 300 K

PHPMS 34

1.7 x 10TM

0.5 ton., 300 K

FAMS 36

2.7 x l0 TM

0.5 torr, 300 K

SIFT 83

2.4 x 10TM

SIFT 3s

1.7 x 10TM

0.5 torr, 300 K < 1 x 10-5 ton.

2.6 x 10TM

< 1 x 10-5 tort

FTMS 35 ADO 39

1.4x 10--9 C1- + C2H5Br -~ Br- + C2H5C1 8.6 x 10-12 8.1 x l0 -12 6.0 x l0 -12 5.0 x 10-12 1.6 x l 0 -9

ICRMS 33

640 ton., 308 K

IMS 17

3 tom 308 K

PHPMS 17

4 torr, 308 K

PHPMS 34

0.5 ton., 300 K

SIFT 83 ADO 39

C V + iso-C3H7Br --~ Br-- + iso-C3H7Cl 640 ton., 398 K 8.0 x 10-13 4 ton., 398 K 6.2 x 10-13 1.7 x l 0 -9

253

IMS 15 PHPMS 34 ADO 39

(continued)

254

W. BERK KNIGHTON and ERIC P. GRIMSRUD

Table 1. (Continued) Reaction Rate Constant (cm 3 s--1) C I - + n-C4H9Br --~ Br- + n-C4H9CI 2.6 x 10TM

Conditions

Method a

640 torr, 308 K

IMS 17

1.7 x 10TM

3 torr, 308 K

PHPMS 17

2.0 x 10TM 2.0 x 10-9

4 tom 308 K

PHPMS 34 ADO 39

Note: aTheacronyms used here are OSPED (optical spectroscopy in a pulsed electrical discharge), FAMS (flowing afterglow mass spectrometry), SIFT (selected ion flow tube), TRAPI (time-resolved atmospheric pressure ionization mass spectrometry), PHPMS (pulsed high-pressure ionization mass spectrometry), ICRMS (ion cyclotron resonance mass spectrometry), and ADO (averaged dipole orientation collision rate theory).

should provide a convenient means of gating the reactant ions into the drift region, and another is that fewer unwanted neutrals will be produced by radiation chemistry within this ion source because this radiation can be "shut off" during most of the IMS duty cycle. With this instrument, care must be taken to ensure that relatively low E/N (electric field strengths/buffer gas number density) values are used to direct ions towards the Faraday detector if thermal reaction rate constants are desired.

IV. COMPARISONS OF RATE CONSTANTS MEASURED IN THE VERY HIGH PRESSURE A N D LOWER PRESSURE RANGES In Table 1 (pp. 251-254), IM rate constants for reaction systems that have been measured at both atmospheric pressure and in the HP or LP range are listed. Also provided are the expected IM collision rate constants calculated from either Langevin or ADO theory. 39 (Note that the rate constants of several IM reactions that have been studied at atmospheric pressure 4-18 are not included in Table I because these systems have not been studied in the LP or HP ranges.) In general, it is noted that pressure-related differences in these data sets are not usually large. Where significant differences are noted, the suspected causes have been previously discussed in Section liB. These include the reactions of He~ and Ne~ with NO 5'7, for which pressure-enhanced reaction rates have been attributed to the onset of a termolecular collision mechanism at atmospheric pressure; and the reactions of Ar~ with NO 6 and C1- with CH3Br 17, for which pressure-enhanced rate constants have been attributed to the approach of the high-pressure limit of kinetic behavior for these reaction systems.

High-Pressure Gas Phase ion Chemistry

255

V. SUMMARY Several currently recognized motivations for increased GPIC research in the VHP range have been considered. One of these is to allow gas phase ionic reactions to be studied in what is known as their high-pressure limit of kinetic behavior. This addresses a central issue of GPIC that is directly linked to our basic understanding of gas phase ionic reactions, in general. Two other motivating forces are related to buffer gas effects that would be of importance only in the VHP range. These are (1) the potential onset ofa termolecular collision process and (2) the potential chemical effects of weak buffer gas-ion interactions. Another motivation for increased GPIC research in the VHP range is to support several powerful instrumental methods of analysis that are based on ionic reactions at atmospheric pressure. As more experimental measurements of ionic reactions in the VHP region are made, additional reasons for studying GPIC under these conditions will undoubtedly be identified. Six instrumental approaches to the study of GPIC in the VHP range were considered. One conclusion that can be drawn from these discussions is that the experimental segment of GPIC at VHP is, indeed, in its infancy. Each of the instrumental methods described has been explored, to date, by only a single research group---the one that developed it. In addition, the rate constants of only a few tens of ion-molecule (IM) reactions have been reported in the very high pressure (VHP) region so far, and very few of these reaction systems have been studied by two different experimental methods of the VHP range. The universal problem of unwanted side reactions caused by impurities in the reaction mixture is greatly magnified and can become overwhelming in the VHP range. Therefore, the emergence of two distinct classes of instrumental methods for the VHP range can be anticipated. One class, which will include the time-resolved atmospheric pressure ionization mass spectrometer (TRAPI) and optical spectroscopy in a pulsed electrical discharge (OSPED) methods described in Section III, will provide kinetic measurements over a very short timescale (less than one millisecond) aider an ionizing pulse. In this way, the slower reactions of buffer gas impurities with the reactant ion of interest can hopefully be ignored. Another class of instruments will include the flowing atterglow mass spectrometer (FAMS), pulsed high-pressure mass spectrometer (PHPMS), photodetachment-modulated electron capture detector (PDM-ECD), and ion mobility spectrometer (IMS) approaches described in Section III. These will allow the study of IM reactions involving relatively stable reactant ions that are unaffected by the presence of common buffer gas impurities, such as water. In spite of the considerable experimental difficulties associated with work in the VHP range, it is clear that progress is being made and that reliable methods for studies of GPIC in the VHP range can and will be developed by continued refinements of the general approaches discussed in this chapter.

256

W. BERK KNIGHTON and ERIC P. GRIMSRUD

ACKNOWLEDGMENT Our research in this area has been supported by a grant from the Chemistry Division of the National Science Foundation (Grant CHE-9211615).

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.

Bowers, M. T. Gas Phase Ion Chemistry; Academic: New York, 1979; Vol. 1. Bowers, M. T. Gas Phase Ion Chemistry; Academic: New York, 1979; Vol. 2. Bowers, M. T. Gas Phase Ion Chemistry; Academic: New York, 1984; Vol. 3. Lee, F. W.; Collins, C. B.; Waller, R. A.J. Chem. Phys. 1976, 65, 1605. Collins, C. B.; Lee, F. W.J. Chem. Phys. 1978, 68, 1391. Collins, C. B.; Lee, F. W.J. Chem. Phys. 1979, 71, 184. Collins, C. B.; Lee, F. W.J. Chem. Phys. 1980, 72, 5381. Collins, C. B.; Chen, Z.; Gylys, V. T.; Jahani, H. R.; Pouvesle, J. M.; Stevefelt, J. IEEEJ. Quantum Electron. 1986, 22, 38. 9. Gylys, V. T.; Jahani, H. R.; Collins, C. B.; Pouvesle, J. M.; Stevefelt, J. IEEEJ. Quantum Electron. 1986, 22, 47. 10. Matsuoka, S.; Nakamura, H.; Tamura, T.J. Chem. Phys. 1981, 75, 681. 11. Matsuoka, S.; Nakamura, H.; Takaaki, T. J. Chem. Phys. 1983, 79, 825. 12. Matsuoka, S.; Nakamura, H. J. Chem. Phys. 1988, 89, 5663. 13. Matsuoka, S.; Ikesoe, Y. J. Phys. Chem. 1988, 92, 1126. 14. Ikezoe, Y.; Shimizu, S.; Onuki, K.; Matsuoka, S.; Makamura, H.; Tagawa, S.; Tabata, Y. J. Phys. Chem. 1989, 93, 1193. 15. Giles, K.; Grimsrud, E.J. Phys. Chem. 1992, 96, 6680. 16. Giles, K.; Grimsrud, E. P. J. Phys. Chem. 1993, 97, 1318. 17. Knighton, W. B.; Bognar, J. A.; O'Connor, P. M.; Grimsrud, E. P. J. Am. Chem. Soc. 1993, 115, 12079. 18. Strode, K. S.; Grimsrud, E. P. Int. J. Mass Spectrom. Ion Proc. 1994, 130, 227. 19. Carroll, D. I.; Dzidic, I.; Homing, E. C.; Stillwell, R. N. Appl. Spectros. Rev. 1981, 17, 337. 20. Eiceman, G. A.; Karpas, Z. Ion Mobility Spectrometry; CRC Press: Boca Raton, FL, 1994. 21. Zlatkis, A.; Poole, C. F. Electron Capture, Theory and Practice in Chromatography; Elsevier: New York, 1981. 22. Fenn, J. B.; Mann, M.; Meng, C. K.; Wong, S. E; Whitehouse, C. Science 1989, 246, 64. 23. Dressier, M. Selective Gas Chromatographic Detectors; Elsevier: New York, 1986. 24. Silvast, W. T. In Encyclopedia of Lasers and Optical Technology; Duley, W. W., Ed.; Academic: New York, 1991; p 219. 25. Knighton, W. B.; Zook, D. R.; Grimsrud, E. P. J. Am. Soc. Mass Spectrom. 1990, 1,372. 26. Ketkar, S. N.; Dulak, J. G.; Fite, W. L.; Buchner, J. D.; Dheandhanoo, S. AnaL Chem. 1989, 61, 260. 27. Huang, S. K.; Klein, D. H.; McLoughlin, M. Biomed. Environ. Mass Spec. 1989, 18, 106. 28. Zook, D. R.; Grimsrud, E. P. J. Phys. Chem. 1988, 92, 6374. 29. Zook, D. R.; Grimsrud, E. P. Int. J. Mass Spectrom. Ion Proc. 1991, 107, 293. 30. Speranza, M. Mass Spectrom. Rev. 1992, 11, 73. 31. Speranza, M. Int. J. Mass Spectrom. Ion Proc. 1992, 118/119, 395. 32. Tanaka, K.; Mackay, G. I.; Payzant, J. D.; Bohme, D. K. Can. J. Chem. 1976, 54, 1643. 33. Olmstead, W. N.; Brauman, J. I.J. Am. Chem. Soc. 1977, 99, 4219. 34. Caldwell, G.; Magnera, T. F.; Kebarle, P. J. Am. Chem. Soc. 1984, 106, 959. 35. Ingemann, S.; Nibbering, N. M. M. Can. J. Chem. 1984, 62, 2273. 36. Bohme, D. K.; Raksit, A. B. Can. J. Chem. 1985, 63, 3007.

High-Pressure Gas Phase Ion Chemistry

257

37. Depuy, C. H.; Gronert, S.; Mullin, A.; Bierbaum, V. M. J. Am. Chem. Soc. 1990, 112, 8650. 38. Viggiano, A. A.; Morris, R. A.; Paschkewitz, J. S.; Paulson, J. F. aT. Am. Chem. Soc. 1992, 114, 10477. 39. Su, T.; Bowers, M. T. In Gas Phase Ion Chemistry; Bowers, M. T., Ed.; Academic: New York, 1979; Vol. 1, pp 83-118. 40. Chesnavich, W. J.; Bowers, M. T. In Gas Phase Ion Chemistry; Bowers, M. T., Ed.; Academic: New York, 1979; Vol. 1, pp 119-151. 41. Vande Linde, S. R.; Hase, W. L.J. Am. Chem. Soc. 1989, 111, 2349. 42. Vande Linde, S. R.; Hase, W. L. J. Phys. Chem. 1990, 94, 6148. 43. Graul, S. T.; Bowers, M. T. J. Am. Chem. Soc. 1991, 113, 9696. 44. Hase, W. L. Dynamics oflon--Molecule Complexes; JAI: London, 1994. 45. Wang, H.; Perlherbe, G. H.; Hase, W. L.,/. Am. Chem. Soc. 1994, 116, 9644. 46. Collins, C. B.; Lee, F. W.; Tepfenhart, W. M.; Stevefelt, J. J. Chem. Phys. 1983, 78, 6079. 47. Bates, D. R. In Advances in Atomic and Molecular Physics; Bates, D. R.; Bederson, B., Eds.; Academic: New York, 1985; Vol. 20, pp 1-40. 48. Berne, B. J.; Borkovec, M.; Straub, J. E../. Phys. Chem. 1988, 92, 3711. 49. Perry, R. A.; Rowe, B. R.; Viggiano, A. A.; Albritton, D. L.; Ferguson, E. E.; Fehsenfeld, F. C. ,/. Geophys. Res. 1980, 7, 693. 50. Mock, R. S.; Grimsrud, E. P. Int. J. of Mass Spectrom Ion Proc. 1989, 94, 293. 51. Grimsrud, E. P.; Chowdhury, S.; Kebarle, P. ,I. Chem. Phys. 1985, 83, 3983. 52. Cacace, F. Science 1990, 250, 392. 53. Cacace, F. Acc. Chem. Res. 1988, 21,215. 54. Cacace, F.; Speranza, M. In Techniques for the Study oflon Molecule Reactions; Farrar, J. M.; Saunders, W., Eds.; Wiley: New York, 1988; pp 287-323. 55. Comisarow, M. B. In Transform Techniques in'Chemistry; Griffiths, P. R., Ed.; Plenum: New York, 1978; p 282. 56. Lehman, T. A.; Bursey, M. M. In Ion Cyclotron Resonance Spectrometry; Wiley-Interscience: New York, 1976. 57. Ferguson, E. E.; Fehsenfeld, F. C.; Albritton, D. L. In Gas Phase Ion Chemistry; Bowers, M. T., Ed.; Academic: New York, 1979; Vol. 1, p 45. 58. Adams, N. G.; Smith, D. In Techniques for the Study of Ion Molecule Reactions; Farrar, J. M.; Saunders, W., Eds.; Wiley: New York, 1988; p 165. 59. Kebarle, P. In Techniques for the Study of Ion Molecule Reactions; Farrar, J. M.; Saunders, W., Eds.; Wiley: New York, 1988; pp 221-286. 60. Dickinson, P. H. G.; Sayers, J. Proc. R. Soc. London, Ser. A 1960, 76, 137. 61. Puckett, L. J.; Lineberger, W. C. Phys. Rev. A 1969, 186, 116. 62. Dushman, S. Scientific Foundations of Vacuum Technique; Wiley: New York, 1989; p 80. 63. Seeley, J. V.; Jayne, J. T.; Molina, M. J. Int. J. Chem. Kin. 1993, 25, 571. 64. McDaniel, E. W. Collision Phenomena in Ionized Gases; Wiley: New York, 1964; p 515. 65. Siegel, M. W.; Fite, W. L. J. Phys. Chem. 1976, 80, 2871. 66. Castleman, A. W.; Keesee, R. G. Chem. Rev. 1986, 86, 589. 67. Gobby, P. L.; Grimsrud, E. P.; Warden, S. W. Anal. Chem. 1980, 52, 473. 68. Mock, R. S.; Grimsrud, E. P. AnaL Chem. 1988, 60, 1684. 69. Mock, R. S.; Grimsrud, E. P. J. Am. Chem. Soc. 1989, 111, 2861. 70. Begley, P.; Corbin, R.; Foulger, B. E.; Simmonds, P. G. J. Chromatogr. 1991, 588, 239. 71. Grimsrud, E. P.; Connolly, M. J. J. Chromatogr. 1982, 239, 397. 72. Bohme, D. K.; Adams, N. G.; Mosesman, M.; Dunkin, D. B.; Ferguson, E. E.J. Chem. Phys. 1970, 52, 5094. 73. Shul, R. J.; Upschulte, B. L.; Passarella, R.; Keesee, R. G.; Castleman, A. W. J. Phys. Chem. 1987, 91,2556. 74. Adams, N. G.; Bohme, D. K.; Ferguson, E. E. J. Chem. Phys. 1970, 52, 5101.

258

W. BERK KNIGHTON and ERIC P. GRIMSRUD

75. Shul, R.J.; Passarella, R.; Upschulte, B. L.' Keesee, R. G.; Castleman, A. W.J. Chem. Phys. 1987, 86, 4446. 76. Bierbaum, V. M.; Kaufman, F. J. Chem. Phys. 1974, 61, 3804. 77. Smith, D.; Adams, N. G.; Miller, T. M.J. Chem. Phys. 1978, 69, 308. 78. Good, A,; Durden, D. A.; Kebarle, P. J. Chem. Phys. 1970, 52, 212. 79. Rakshit, A. B.; Wameck, P. J. Chem. Phys. 1981, 74, 2853. 80. Munson, M. S. B.; Franklin, J. L.; Field, F. H. J. Phys. Chem. 1964 68, 3098. 81. Lias, S. G.; Eyler, J. R.; Ausloos, P. Int. J. Mass Spectrom. Ion Phys. 1976, 19, 219. 82. Munson, M. S. B. J. Phys. Chem. 1967, 71, 3966. 83. Gronert, S.; DePuy, C.; Bierbaum, V. ,I. Am. Chem. Soc. 1991, 113, 4009.

INDEX

Ab initio calculations, 51,126 Acetone dimers, protonated, 61-64 Adiabatic crossing, 5 AI§ and relative association rate, 105 radiative association kinetic studies, 104 AIH 5 as neutral analogue, 153-154 dissociation energies, 157 relative energies of selected geometries, 157 Alkyl cation-dihydrogen complexes alkonium ions, 130 basis set superpostition error, 129-130 basis sets, 128--129 characterization of stationary points, 130 d orbital effect, 155 gas phase studies, 127 Hartree--Fock methods, 127 HOMO-LUMO separation correlations, 156 SCF studies, 127 systematic comparisons, 154-157 theoretical considerations, 116-121 APMIS (see Atmospheric pressure ionization mass spectrometer) Apparent threshold, 90 Appearance energy, 90 Appearance potential, 90 Ar.CO~ formation, 186-188 correlation scheme, 186

isotopic studies, 187 symmetry analysis, 186 Atmospheric pressure ionization mass spectrometer (APMIS), 221 BDE (see Bond dissociation energy) Be +, as ion target, 30 Benzene derivatives, time-resolved photodissociation studies of, 95 Benzyne ion, heat of formation of, 96 BH 5, as neutral analogue, 153-154 Blackbody radiation, 75 Boltzmann tail, 90 Bond dissociation energy (BDE), 89, 90 Bond strength determination, and rate--energy curves, 116-121 Bromobenzene, phase space theory studies, 117 Bromonaphthalene, time-resolved photoionization mass spectrometer studies, 99, 100 C2FI~5(H2), 140-142 and hyperconjugation, 141 Cation complexes, 125-160 CC12H§ electron impact ionization of, 29 CCI3H, theoretical treatment of, 33 Cd§ bond strength determination of, 106 CF3Br and dissociative electron attachment, 19 and steric factors, 15 heads of tails orientation of, 14 259

INDEX

260

hexapole transmission of, 10 molecular beam studies of, 12, 13 CF3CI hexapole transmission of, 10 molecular beam studies of, 12 CF3H hexapole transmission of, 10 molecular beam studies of, 12 CF3I, 17 and dissociative electron attachment, 19 and Rydberg states of, 21 molecular beam studies of, 12 CF3X, molecular beam studies of, 12 CH~ ion, 130 and hydrogen scrambling, 133 geometries of, 131, 133 orbitals geometries of, 132 relative energies of transition structures of, 134 vibrational frequencies of, 133 CH~(H2) complex, 135--142 basis set superposition errors for, 139 dissociation energy, 138 electron correlation effects, 136 geometries of, 137 global minimum of, 138 vibrational frequency shifts, 136 CH3+, electron impact ionization of, 29 CH3Br and dissociative electron attachment, 19 and steric factors, 15 heads or tails orientation of, 14 hexapole transmission of, 9, 10 molecular beam studies of, 12, 13 CH3Br+, electron impact ionization of, 29 CH3C1 and clustering reaction, 56 Coulomb potential plot of, 33 CH3C1§ electron impact ionization of, 29 CH3I and dissociative electron attachment, 19 molecular beam studies of, 12 CH3X CH3-end of, 33 H-end of, 33 theoretical treatment of, 33

Chemical reactivity and alkali metal atoms, 3 and alkyl halide molecules, 3 and entrance channel, 16 and exit channel, 16 and molecular shape, 2 and orientation, 20 and spatial orientation, 3 and the impulsive model, 20 Chlorobenzene, time-resolved photodissociation studies, 96 Claisen condensation, 202 Clustering reaction, 56 (CO2)~ formation, 181-185 and correlation scheme, 183 and parity label, 182 and symmetry analysis, 183 and trajectory calculations, 181 isotopic studies, 184 Collision theory, 2 Collision-induced dissociation, 116 Critical energy, 90 Cyanobenzene, time-resolved photodissociation studies, 96 Diabatic hop, 5 Diffusion effects, on ion-molecule reactions, 227 Dimethyl ether, and water complexes, 75 DIPR (see Direct interaction with product repulsion model) Direct interaction with product repulsion (DIPR) model, 17

1,3-Dithiane and equilibrium isotope effects, 212 and Mulliken charge populations, 211 fragmentation studies, 209-212 solvent effects, 211 Double-focusing mass spectrometer, 44-45 description of, 44 diagram of, 45 Durene, radiative association kinetics of, 106, 107, 108

EAv (see Vertical electron affinity) ECD (see Electron capture detector)

2 61

Index

Einstein coefficient, 111 Electron capture detector (ECD), 221 Electron impact ionization, 1-39 and broadside collisions, 33 and Coulomb forces, 30 and electron ionization, 28 and fragmentation pattern, 27 and G factor, 29 and harpoon mechanism, 37 and impact parameters, 30 and ion species ratio, 37 and ionization cross section, 27 and ionization potential, 31 and ionization probability, 28 and molecular polarizability, 35 and monochromatic electrons, 27 and orbital electrons, 31 and orientation dependence, 37 and polarizability volume, 35 and quantum model, 30 and random orientations, 34 and semiclassical model, 30 and semiempirical model, 30 and shape of molecular orbitals, 30 and spatial orientation, 37 and steric factor, 28, 29 and steric ratio, 28, 29 and transition-state species, 26 calculated and experiment maximum ionization cross sections for a range of species, 36 calculated and experimental steric ratios of selected species, 34 calculated versus experimental cross section plot, 34 description, 26-27 experimental technique, 27-28 model, 31-37 polarizability volume plots, 26 scattering region, 27, 28 scope of theory, 31 theoretical consideration, 30-31 Electron transfer, 1-39 and avoided crossing, 3 and electron affinity, 6

and entrance channel-electron transfer, 22-26 and ionic-covalent coupling, 3 and threshold behavior, 16 and uncertainty principle, 4 cross-beam experiment, 6-9 data acquisition, 11 experimental technique, 6-11 ion detection, 10 theoretical aspects, 3 Entrance channel-electron transfer, 22-26 and barriers, 25 and diabatic potentials, 25 and exit channel interactions, 23 and ion detection, 23 and repulsion, 25 and vertical electron affinity, EA v, 23 CF3Br studies, 23, 24 scope, 22, 23 Exit channel interaction, 17 and angular distribution, 17 and sideways orientation, 18 and thermal energy, 17 FA (see Flowing afterglow) FAMS (see Flowing afterglow mass spectrometer) Ferrocene ion, time-resolved photodissociation studies of, 95, 97 Flowing afterglow (FA), 196 Flowing afterglow mass spectrometer (FAMS), 229-231 experimental considerations, 230 scope, 230 Fourier transform ion cyclotron resonance spectrometer (FTICR), 46-47, 88, 93 and ion trapping, 89 description of, 46 diagram of, 47 use of in determining bond strengths, 89 FTICR (see Fourier transform ion cyclotron resonance spectrometer) G values, 15

262

Gas phase chemistry, 219-258 Ge~, 148 Ge~, 147-151 comparison with silyl cation, 150 optimized geometries, 148 physical properties of, 150 relative energies of selected geometries, 147 vibration frequencies of, 149 Ge~, 151-153 optimized geometries, 152 relative energies of selected geometries, 151 vibration frequencies of, 153 Germane, protonated, 148 Germonium cations, 125-160 +

H 3 formation, 171-174 and classical trajectory techniques, 173 potential energy surface dynamics calculations, 172 symmetry analysis, 171 thermal rate constants for isotopic analogues, 172 + H4 electronic states, 173 + He , as ~on target, 30 He~ formation, 165-171 and Pauli-allowed wave functions, 168 and Slater determination, 167 Born-Oppenheimer states, 167 correlation scheme, 168 experimental aspects, 169, 170 potential energy curves, 166, 167 symmetry analysis, 168 Hexapole characteristics, orientation distribution, 9 Hexapole field, description of, 8 High pressure gas phase chemistry, 219 and thermal electron detachment (TED), 228 azulene anion studies, 228 buffer gas, 223, 227-229 diffusion effects, 227 high pressure limit for kinetic behavior, 223-225 instrumental methods, 229

INDEX

termolecular ion--molecule collisions, 225-227 tools, 221 High-pressure mass spectrometers (HPMS), 44, 59 and species lifetimes, 59 HPMS (see High-pressure mass spectrometers) Hydrated chloride ion, zero pressure thermal-radiation-induced dissociation studies, 109, 110, 112, 115 ICR (see Ion cyclotron resonance) Impulsive model, 20 IMS (see Ion mobility spectrometer) Infrared-induced dissociation, 71-80 and Arrhenius dependence, 73 and chemical activation, 72 and deuterated acetone studies, 78 and deuterated benzene studies, 79 and deuterium isotope effect, 76, 77, 78 and Lindemann mechanism, 72 and radiation hypothesis, 73 and temperature dependence, 76 constant determination, 72 study of proton hydrate, 71, 74 Infrared-laser-induced thermal dissociation, 80 proton hydrate studies, 81, 82 Inhomogeneous hexapole electric field, 6 Iodotoluene, time-resolved photodissociation studies, 101 Ion cyclotron resonance, 64-70, 196 and ion loss rate constant, 197 experimental techniques, 65 scope, 64 Ion mobility spectrometer (IMS), 221 description of, 240, 242 diagram of insmmaent, 241 reaction-modified, 245 study of SN2 reactions, 243,246, 247, 248 Ion solvation, from gas to aqueous solution, 197 Ion-molecule chemistry, 193--217 1,3-dithiane, 209

Index and differential solvent effects on acidities, 201 and effect of counterions, 209-212 and free energies, 208 and the anionic oxy-Cope rearrangement, 203,204 and the Michael-type conjugate addition, 205 and the nonstatistical view, 225 and the Riverso reaction, 206 Claisen condensation, 202 equilibrium acidities, 198 gas phase acidities, 198--202 Hammer studies, 199 mechanisms, 202-205 techniques and tools, 196-198 Ion--molecule complex, 198 Ion--molecule reactions effect of pressure on rate constants, 254 rate constants of selected reactions, 251-254 Ions, structures of in gas phase, 212-214 Isotope effects, symmetry-induced, 161-191 Kinetic shift, 91, 116 conventional, 91 intrinsic, 91 Landau-Zener (LZ) relation, 4, 6, 19, 22 Lifetimes of chemically activated species, 59 and radiative fate, 61 and standard hydrocarbon model, 60 kinetics of, 59 rate constants of, 60 Lindermarm mechanism, 42, 71, 72 and collisional activation, 75 and steady-state approximation, 76 (LZ) (see Landau-Zener relation) Master equation modeling approach, 109, 111 Mesitylene, radiative association kinetics of, 106, 107, 108 Metal ion--benzene complexes, radiative association kinetic studies, 104

263 Metallocenes, time-resolved photodissociation studies of, 95 Metastable ion cyclotron resonance (MICR), 65 and elucidation of potential energy surfaces, 70 description of, 65 study of methoxymethyl cation with pivaldehyde, 68, 69 Methoxide-methanol dimer and deuterium isotope effect, 52 dissociation rate versus reciprocal temperature plot, 52 dissociation studies of, 48-54 potential energy surface, 53 Methoxymethyl cation, interaction with pivaldehyde, 67, 68 Methyl-substituted benzenes, radiative association kinetics of, 106, 107, 108 Methylnaphthalene, time-resolved photodissociation studies, 96 Mg 2§ as ion target,. 30 Michael-type conjugate addition, studies, 205,206 MICR (see Metastable ion cyclotron resonance) Molecular beam, 6 Molecular orientation, 1-39 and antiparallel orientation, 21 and neutralization, 21 and parallel orientation, 21 Na +, as ion target, 30 Naphthalene ion, time-resolved photodissociation studies of, 95 Naphthalene, time-resolved photodissociation studies, 93, 94 Natural bond order, 154 Nickelocene ion, time-resolved photodissociation studies of, 95, 97 +

O2 as reactant, 174 by charge-transfer reaction + 0 4 formation, 174-181 and ionization studies, 177 and isotopic enhancement studies, 179

INDEX

264

and parity labels, 176, 177 and the chaperone mechanism, 178, 180 appearance potential of, 175 mechanism of, 174 symmetry analysis of, 176 Optical spectroscopy in a pulsed electrical discharge (OSPED), 237 OSPED (see Optical spectroscopy in a pulsed electrical discharge) Oxy-Cope rearrangement, gas phase studies, 203,204 Oxygen, as reactant, 174 Ozone formation, 162 PDM-ECD (see Photodetachment-modulated electron capture detector) Penning ionization, 180 Perfluoromethylcyclohexane, APMIS studies of, 221,222 Phase space theory (PST), 104, 117 and bromobenzene, 117 Photodetachment-modulated electron capture detector (PDM-ECD), 237-240 description of, 237 explanation of experimental results, 238 scope, 239 Photoelectron photoionization technique (PEPICO), 43, 59, 92, 96 and quadrupolar excitation, 66 dynamics in cell, 66 study of methoxymethyl cation, 67 PHPMS (see Pulsed high-pressure mass spectrometry) Proton hydrate, infrared-induced dissociation studies of, 71, 74 Protonated ethane, 140 PST (see Phase space theory) Pulsed electron beam ion mobility spectrometer, diagram, 250 Pulsed high-pressure mass spectrometry (PHPMS), 196, 231-235 description of, 231 diagram, 233 experimental considerations, 232, 234 scope, 231

Quadrupolar excitation, 66 Radiation hypothesis, 73, 75 Radiative association, 59 and Boltzmann distributions, 92 and bond strength measurement, 92 and kinetic shift, 92 and thermal shifts, 92 Radiative association kinetics, 76, 88, 102-108 AI+C6H6 studies, 104 and ab initio calculations, 103 and binding energy, 106 and bond strength estimation, 102 and degrees of freedom, 106 and pressure dependence analysis, 102 and standard hydrocarbon estimation, 103, 106 benzene study, 103 description of, 102 determination of experimental rate constant, 105 metal ion-benzene complexes, 104 methyl-substituted benzenes, 106, 107, 108 Radiative lifetime of chemically activated ions, 59-64 Radiative mechanism, description, 75 Radiative rate, 61 and deuterium isotope effects, 61, 62 and hydrogen bonding, 62 and MIKES techniques, 63 studies of protonated acetone dimers, 61, 62, 63 van't Hoff plots of, 63 Radiative stabilization, 59 Random walk, 111 Rate-energy curves, and bond strength determination, 116-121 REMPI (see Resonance-enhanced multiphoton ionization) REMPI measurements, 96 Resonance-enhanced multiphoton ionization (REMPI), 175 Reverse activation barrier, 90, 96 Rittner-type potentials, 25 Riveros reaction, 206, 207

Index

RRKM theory, 42, 118-121 description of, 119 Rydberg electron, 22 $2F10 formation, 162 SiH~, 146 SiH~, 142-144 geometries of, 142 relative energies of isomers, 143 vibrational frequencies of, 143 SiH~ energies of selected isomers, 145 infrared studies of, 144 vibrational frequencies of, 146 SIKIE (see symmetry-induced kinetic isotope effects) Silonium cations, 142-147 Solvation energetics of ions and neutrals, 195 State selection, in inhomogeneous electric fields, 2 Styrene, time-resolved photodissociation studies, 101 Symmetry-induced kinetic isotope effects (SIKIE), 161-191 (CO2) ~ formation, 181-185 and ozone formation, 162 and S2FI0 formation, 162 and various oxygen species' formation, 163 Ar.CO~ formation, 186-188 + H 3 formation, 171-174 He~ formation, 165-171 + 04 formation, 174-181 TED (see Thermal electron detachment) Termolecular iotr--molecule collisions, 225-227 nonassociative, 226 Tetraethylsilane, zero pressure thermal -radiati on- in duced dissociation studies, 112, 113, 114 Thermal dissociation by ambient infrared radiation, 108-115 Thermal electron detachment (TED), 228, 239

265

Thermal radiation-induced dissociation, 89 Thermochemical threshold, 90, 98 Thermochemistry, 87-124 Time-resolved atmospheric pressure ionization mass spectrometer (TRAPI), 235-236 description of experiment, 235 results, 236 Time-resolved photodissociation (TRPD), 92-101 benzene studies, 95, 99 benzotropylium ion studies, 95 benzyl studies, 95 1-bromonaphthalene studies, 95, 99 chlorobenzene studies, 96 cyanobenzene studies, 96 ferrocene studies, 95 iodobenzene studies, 98 iodotoluene studies, 100 metallocene studies, 98 methylnaphthalene studies, 96 naphthalene ion studies, 93, 94, 95 nickelocene studies, 95 phenyl cation studies, 98 styrene studies, 100 toluene studies, 96 tri-t-butylbenzene studies, 95, 97 Time-resolved photoionization mass spectrometer (TPIMS), 93 bromonaphthalene studies, 99, 100 Tolman theorem approach, 110, 114 Toluene, time-resolved photodissociation studies, 96 TPIMS (see Time-resolved photoionization mass spectrometer) Transient SN2 intermediates, 54-59 and bimolecular rate constants, 58 and chloride isotope exchange, 55 and unimolecular rate constants, 58 and variation of relative ionic abundance studies, 57 Transition-state frequencies, 121 Transition-state theory, 42, 90

266

TRAPI (see Time-resolved atmospheric pressure ionization mass spectrometer) Tropylium intermediate, 97 TRPD (see Time-resolved photodissociation) True threshold, 90 Unimolecular dissociation lifetime of chemically activated ions, 59-64 Unimolecular dissociation of cluster ions, 48---82 and ADO model, 48 and bimolecular rate constant variation, 50 and collisional stabilization, 49 and energy surfaces, 49 and halide anion complexes, 51 and proton-bound methoxide dimer, 48 and thermal unimolecular dissociation, 48 and transition state, 50 kinetics of, 48 methoxide--methanol studies, 48 relationship between bimolecular clustering rate constant and ion source pressure, 58 transient SN2 intermediates, 54-59 van't Hoff plot, 56 Unimolecular dissociation of gaseous cluster ions, 41-85 Unimolecular dissociation of protonated acetone dimers, 64 Unimolecular rate constants, for ligand loss, 75 Unimolecular reactions, 42--44

INDEX

and chemical activation, 42, 43 and collision-induced decomposition, 43 and experimental techniques, 43, 44-47 and metastable dissociations, 43 and photoactivation, 43 and thermal activation, 42 classification of, 42, 43 van't Hoff plot, 56 Variational transition-state theory (VTST), 116 Vertical electron affinity, EA v, 23 VTST (see Variational transition-state theory) Water, and dimethyl ether complexes, 75 Xylene, radiative association kinetics of, 106, 107, 108 Zero pressure thermal-radiation-induced dissociation (ZTRID), 109 and bond dissociation energies, 111 determination of Arrhenius activation energy, 112 hydrated chloride studies, 109, 110, 112, 115 tetraethylsilane studies, 112 Zero-pressure enhancement factor (ZPEF), 183 ZPEF (see Zero-pressure enhancement factor) ZTRID (see Zero pressure thermal-radiati on- induced dissociation)

Advances in Gas Phase Ion Chemistry Edited by Nigel Adams, and Lucia M. Babcock,

Department of Chemistry, The University of Georgia

Advances in Gas Phase Ion Chemistry is different from other

ion chemistry series in that it focuses on reviews of the author's own work rather than give a general review of the research area. This allows for presentation of some current work in a timely fashion which marks the unique nature of this series. Emphasis is placed on gas phase ion chemistry in its broadest sense to include ion neutral, ion electron, and ion-ion reactions. These reaction processes span the various disciplines of chemistry and include some of those in physics. Within this scope, both experimental and theoretical contributions are included which deal with a wide variety of areas ranging from fundamental interactions to applications in real media such as interstellar gas clouds and plasmas used in the etching of semiconductors. The authors are scientists who are leaders in their fields and the series will therefore provide an up-to-date analysis of topics of current importance. This series is suitable for researchers and graduate students working in ion chemistry and related fields and will be an invaluable reference for years to come. The contributions to the series embody the wealth of molecular information that can be obtained by studying chemical reactions between ions, electrons and neutrals in the gas phase.

Volume 1, 1992, 329 pp. ISBN 1-55938-331-3

$97.50

CONTENTS: Preface, Nige/ Adams and Lucia M. Babcock. Flow Tube Studies of Small Isomeric Ions, Murray J. McEwan. Anion Molecule Experiments: Reactive Intermediates and Mechanistic Organic Chemistry, Joseph J. Grabowski. Thermochemical Measurements by Guided Ion Beam Mass Spectrometry, Peter W. Armentrout. Photoelectron Spectroscopy of Molecular Anions, Kent M. Ervin and W. Carl Lineberger. Ion Chemistry at Extremely Low Temperatures: A Free Jet Expansion Approach, Mark A. Smith and Michael Hawley. Theoretical Studies of Hypervalent Silicon Anions, Mark S. Gordon, Larry P. Davis and Larry W. Burggraf. Chemistry Initiated by Atomic Silicon Ions, Diethard K. Bohme. Spectroscopic Determination of the Products of Electron-Ion Recombination, Nige/ G. Adams. Index.

JAI PRESS INC.

55 Old Post Road # 2 - P.O. Box 1678 Greenwich, Connecticut 06836-1678 Tel: (203) 661- 7602 Fax: (203) 661-0792

.1 A l

P R E S S

.1 A l

Advances in Atomic Spectroscopy Edited by Joseph Sneddon, Department of Chemistry, McNeese State University This series describes selected advances in the area of atomic spectroscopy. It is primarily intended for the reader who has a background in atomic spectroscopy; suitable to the novice and expert. Although a widely used and accepted method for metal and nonmetal analysis in a variety of complex samples, Advances in Atomic Spectroscopy covers a wide range of materials. Each chapter will completely cover an area of atomic spectroscopy where rapid development has occurred. Volume 1, 1992, 238 pp. ISBN 1-55938-157-4

P R E S S

$97.50

Volume 1 consists of chapters covering the development, instrumentation, and results of a wide range of materials, including: background correction lasers, inductively coupled-mass spectroscopy; plasmas, electrothermal vaporizers, sample introduction, and Fourier transform atomic spectrocopy.

CONTENTS: Preface, Joseph Sneddon. Analyte Excitation

Mechanisms in the Inductively Coupled Plasma, Kuang-Pang Li and J.D. Winefordner. Laser-Induced Ionization Spectrometry, Robert B. Green and Michael D. Seltzer. Sample Introduction in Atomic Spectroscopy, Joseph Sneddon. Background Correction Techniques in Atomic Absorption Spectrometry, G. Dulude. Flow Injection Techniques for Atomic Spectrometry, Julian F. Tyson. Volume 2, 1995, 297 pp. ISBN 1-55938-701-7

$97.50

CONTENTS: Preface. Effect of Molecular Orientation on

Electron Transfer and Electron Impact Ionization, Phil R. Brooks and Peter W. Harland. Experimental Approaches to the Unimolecular Dissociation of Gaseous Cluster Ions, Terry B. McMahon. New Approaches to Ion Thermochemistry via Dissociation and Association, Robert C. Dunbar. Alkyl CationDihydrogen Complexes, Silonium and Germonium Cations: Theoretical Considerations, Peter R. Schreiner, H. Fritz and Paul v. R. Schleyer. Symmetry Induced Kinetic Isotope Effects in Ion-Molecule Reactions, Greg I. Gellene. Ion-Molecule Chemistry: The Roles of Intrinsic Structure, Solvation and Counterions, John E. Bartmess. Gas Phase Ion Chemistry under Conditions of Very High Pressure, IN. Burk Knighton and Eric P. Grimsrud. Index

Advances in Sonochemistry Edited by T i m o t h y J. M a s o n , School of Chemistry,

Coventry University, England

Over the past few years there has been a remarkable expansion in the uses of ultrasound as an energy source to promote or modify chemical reactivity. A new word has been coined to describe this area of scientific exploration and discovery n Sonochemistry. This new series has been designed to cater to both researchers and graduate students of the subject. In the first volume, contributions have been invited from some of the most prestigious workers from internationally famous centers of sonochemical research. A broad interpretation of the term sonochemistry has been taken, to encompass all aspects of chemistry which involve ultrasonic irradiation. Subsequent volumes will therefore include both the synthetic uses of power ultrasound (i.e. the kHz range) and diagnostic applications of high frequency sound (in the MHz range). REVIEWS: The book is very well produced and is written by leading experts in the field. The rapidly expanding subject of sonochemistry will be well served if future volumes in the series are of similar quality and all serious chemical libraries should consider a subscription to it. The first chapter of this book concludes with the statement that it is only a matter of time before sonochemistry takes its place along with photochemistry and radiochemistry in the chemical industry's armory. "[]me will tell whether this optimism in the technique is justified, but this volume, being the first in a new annual series, will be of interest to many chemists and should persuade them that the technique is worthy of their serious consideratione. Readers will find chapters on reactions with metals, carbonyl addition reactions (most of which involve organometallic reagents), and surfaces and solids of greatest interest. Those already familiar with the technique will find that the chapter by Margulis will give much food for thought as it describes a new electrical theory of cavitation phenomena.

Journal of Organometallic Chemistry. Volume 1, 1990, 275 pp. ISBN 1-55938-178-7

$97.50

CONTENTS: Introduction to Series: An Editor's Foreword, Albert Padwa. Introduction, Timothy J. Mason. Historical Introduction to Sonochemistry, D. Bremner. The Nature of Sonochemical Reactions and Sonoluminescence, M.A. Margull Influence of Ultrasound on Reactions with Metals, B. Pugin and A.T. Turner. Ultrasonically Promoted Carbonyl Addition Reactions, J.L. Luche. Effect of Ultrasonically Induced Cavitation on Corrosion, W.J. Tomlinson. The Effects

.1 A 1 P R E S S

J A 1

of Ultrasound on Surfaces.and Solids, Kenneth S. Suslick and Stephen J. Doktycz. The Use of Ultrasound for the Controlled Degradation of Polymer Solutions, G. Price. Volume 2, 1991, 322 pp. ISBN 1-55938-267-8

$97.50

CONTENTS: Sonochemical Initiation of Polymerization, P. Kruss. Free Radical Generation by Ultrasound in Acqueous Solutions of Volatile and Non-Volatile Solutes, P. Reisz. Ultrasonic Studies of Polymeric Solids and Solutions, R.A. Pethrick. The Action of Ultrasound on Solidifying Metals, O.V. Abramov. Ultrasound in Chemical Processing, N. Senapat. Ultrasonic Organic Synthesis Involving Non-Metal Solids, T. Ando. The Influence of Ultrasound on Oscillating Reaction, M.A. Margulis. The Manipulation of Particles in an Acoustic Field, C.J. Schram. Volume 3, 1993, 292 pp. ISBN 1-55938-476-X

P R E S S

$97.50

CONTENTS: Preface. Ultrasound and Colloid Science: The Early Years, David Gilling. Contributions to Various Aspects of Cavitation Chemistry, Arnheim Henglein. Sonochemistry: From Experiment to Theoretical Considerations, Jean-Louis Luche. Ultrasonic Agitation in Metal Finishing, Robert Walker. Ultrasonic Atomization, Andrew Morgan. Reations of Organosilicon Compounds in Acoustic Fields, 0.1. Zinovev and M.A. Margulis. Use of Ultrasound in the Identification of Biological Molecules, John A. Evans.. Initiation and Catalysis of Oxidation Proceses in an Acoustic Field, Evgen M. Mokry and Volodymyr L. Starchevsky. Index. Volume 4, In preparation, Summer 1996 ISBN 1-55938-793-9

Approx. $97.50

CONTENTS: Dosimetry for Power Ultrasound and Sonochemistry, J. Berlan (deceased) and T. J. Mason. Nuclear Magnetic Resonance Spectroscopy Combined with Ultrasound, J. Homer, Larysa Panynwyck and Stuart A. Palfreyman. Degassing, Filtration and Grain Refinement Processes of Light Alloys in an Acoustic Cavitation Field, Georgy Eskin. Sonochemistry in China, Yiyun Zhao, Jinlei Yin and Ruo Feng. Uses of Ultrasound in Food Processing, T. J. Mason and L. Paniwnyk. Sonoelectrochemistry, S. J. Phull and D. J. Walton.

JAI PRESS INC.

55 Old Post Road # 2 - P.O. Box 1678 Greenwich, Connecticut 06836-1678 Tel: (203) 661- 7602 Fax: (203) 661-0792