Molecular Orbitals and Organic Chemical Reactions: Reference Edition

Molecular Orbitals and Organic Chemical Reactions

Molecular Orbitals and Organic Chemical Reactions Reference Edition

Ian Fleming Department of Chemistry, University of Cambridge, UK

A John Wiley and Sons, Ltd., Publication

This edition first published 2010 Ó 2010 John Wiley & Sons, Ltd Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com. The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. The publisher and the author make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of fitness for a particular purpose. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for every situation. In view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of experimental reagents, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each chemical, piece of equipment, reagent, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions. The fact that an organization or Website is referred to in this work as a citation and/or a potential source of further information does not mean that the author or the publisher endorses the information the organization or Website may provide or recommendations it may make. Further, readers should be aware that Internet Websites listed in this work may have changed or disappeared between when this work was written and when it is read. No warranty may be created or extended by any promotional statements for this work. Neither the publisher nor the author shall be liable for any damages arising herefrom. Library of Congress Cataloging-in-Publication Data Fleming, Ian, 1935– Molecular orbitals and organic chemical reactions / Ian Fleming. — Reference ed. p. cm. Includes bibliographical references and index. ISBN 978-0-470-74658-5 1. Molecular orbitals. 2. Chemical bonds. 3. Physical organic chemistry. I. Title. QD461.F533 2010 5470 .2—dc22 2009041770 A catalogue record for this book is available from the British Library. 978-0-470-74658-5 Set in 10/12pt Times by Integra Software Services Pvt. Ltd, Pondicherry, India Printed and bound in Great Britain by CPI Antony Rowe, Chippenham, Wiltshire.

Contents

Preface 1

Molecular Orbital Theory 1.1 The Atomic Orbitals of a Hydrogen Atom 1.2 Molecules Made from Hydrogen Atoms 1.2.1 The H2 Molecule 1.2.2 The H3 Molecule 1.2.3 The H4 ‘Molecule’ 1.3 C—H and C—C Bonds 1.3.1 The Atomic Orbitals of a Carbon Atom 1.3.2 Methane 1.3.3 Methylene 1.3.4 Hybridisation 1.3.5 C—C  Bonds and  Bonds: Ethane 1.3.6 C¼C  Bonds: Ethylene 1.4 Conjugation—Hu¨ckel Theory 1.4.1 The Allyl System 1.4.2 Butadiene 1.4.3 Longer Conjugated Systems 1.5 Aromaticity 1.5.1 Aromatic Systems 1.5.2 Antiaromatic Systems 1.5.3 The Cyclopentadienyl Anion and Cation 1.5.4 Homoaromaticity 1.5.5 Spiro Conjugation 1.6 Strained  Bonds—Cyclopropanes and Cyclobutanes 1.6.1 Cyclopropanes 1.6.2 Cyclobutanes 1.7 Heteronuclear Bonds, C—M, C—X and C=O 1.7.1 Atomic Orbital Energies and Electronegativity 1.7.2 C—X  Bonds 1.7.3 C—M  Bonds 1.7.4 C¼O  Bonds 1.7.5 Heterocyclic Aromatic Systems 1.8 The Tau Bond Model 1.9 Spectroscopic Methods 1.9.1 Ultraviolet Spectroscopy 1.9.2 Nuclear Magnetic Resonance Spectroscopy

ix 1 1 2 2 7 9 10 10 12 13 15 18 20 23 23 29 32 34 34 37 41 42 44 46 46 48 49 49 50 56 57 59 61 61 61 62

vi

CONTENTS

1.9.3 1.9.4 2

Photoelectron Spectroscopy Electron Spin Resonance Spectroscopy

65 66

Molecular Orbitals and the Structures of Organic Molecules 2.1 The Effects of  Conjugation 2.1.1 A Notation for Substituents 2.1.2 Alkene-Stabilising Groups 2.1.3 Cation-Stabilising and Destabilising Groups 2.1.4 Anion-Stabilising and Destabilising Groups 2.1.5 Radical-Stabilising Groups 2.1.6 Energy-Raising Conjugation 2.2 Hyperconjugation— Conjugation 2.2.1 C—H and C—C Hyperconjugation 2.2.2 C—M Hyperconjugation 2.2.3 Negative Hyperconjugation 2.3 The Configurations and Conformations of Molecules 2.3.1 Restricted Rotation in -Conjugated Systems 2.3.2 Preferred Conformations from Conjugation in the  Framework 2.4 The Effect of Conjugation on Electron Distribution 2.5 Other Noncovalent Interactions 2.5.1 Inversion of Configuration in Pyramidal Structures 2.5.2 The Hydrogen Bond 2.5.3 Hypervalency 2.5.4 Polar Interactions, and van der Waals and other Weak Interactions

69 69 69 70 76 78 81 83 85 85 92 95 100 101

122

3

Chemical Reactions—How Far and How Fast 3.1 Factors Affecting the Position of an Equilibrium 3.2 The Principle of Hard and Soft Acids and Bases (HSAB) 3.3 Transition Structures 3.4 The Perturbation Theory of Reactivity 3.5 The Salem-Klopman Equation 3.6 Hard and Soft Nucleophiles and Electrophiles 3.7 Other Factors Affecting Chemical Reactivity

127 127 128 135 136 138 141 143

4

Ionic Reactions—Reactivity 4.1 Single Electron Transfer (SET) in Ionic Reactions 4.2 Nucleophilicity 4.2.1 Heteroatom Nucleophiles 4.2.2 Solvent Effects 4.2.3 Alkene Nucleophiles 4.2.4 The -Effect 4.3 Ambident Nucleophiles 4.3.1 Thiocyanate Ion, Cyanide Ion and Nitrite Ion (and the Nitronium Cation) 4.3.2 Enolate Ions 4.3.3 Allyl Anions 4.3.4 Aromatic Electrophilic Substitution

145 145 149 149 152 152 155 157

111 113 115 115 118 121

157 160 161 167

CONTENTS

4.4

4.5

4.6

5

6

Electrophilicity 4.4.1 Trigonal Electrophiles 4.4.2 Tetrahedral Electrophiles 4.4.3 Hard and Soft Electrophiles Ambident Electrophiles 4.5.1 Aromatic Electrophiles 4.5.2 Aliphatic Electrophiles Carbenes 4.6.1 Nucleophilic Carbenes 4.6.2 Electrophilic Carbenes 4.6.3 Aromatic Carbenes 4.6.4 Ambiphilic Carbenes

Ionic Reactions—Stereochemistry 5.1 The Stereochemistry of the Fundamental Organic Reactions 5.1.1 Substitution at a Saturated Carbon 5.1.2 Elimination Reactions 5.1.3 Nucleophilic and Electrophilic Attack on a  Bond 5.1.4 The Stereochemistry of Substitution at Trigonal Carbon 5.2 Diastereoselectivity 5.2.1 Nucleophilic Attack on a Double Bond with Diastereotopic Faces 5.2.2 Nucleophilic and Electrophilic Attack on Cycloalkenes 5.2.3 Electrophilic Attack on Open-Chain Double Bonds with Diastereotopic Faces 5.2.4 Diastereoselective Nucleophilic and Electrophilic Attack on Double Bonds Free of Steric Effects Thermal Pericyclic Reactions 6.1 The Four Classes of Pericyclic Reactions 6.2 Evidence for the Concertedness of Bond Making and Breaking 6.3 Symmetry-allowed and Symmetry-forbidden Reactions 6.3.1 The Woodward-Hoffmann Rules—Class by Class 6.3.2 The Generalised Woodward-Hoffmann Rule 6.4 Explanations for the Woodward-Hoffmann Rules 6.4.1 The Aromatic Transition Structure 6.4.2 Frontier Orbitals 6.4.3 Correlation Diagrams 6.5 Secondary Effects 6.5.1 The Energies and Coefficients of the Frontier Orbitals of Alkenes and Dienes 6.5.2 Diels-Alder Reactions 6.5.3 1,3-Dipolar Cycloadditions 6.5.4 Other Cycloadditions 6.5.5 Other Pericyclic Reactions 6.5.6 Periselectivity 6.5.7 Torquoselectivity

vii

178 178 180 182 183 183 186 199 199 200 201 203 205 207 207 210 214 222 225 226 238 241 250 253 254 256 258 258 271 286 286 287 288 295 295 298 322 338 349 355 362

viii

CONTENTS

7

Radical Reactions 7.1 Nucleophilic and Electrophilic Radicals 7.2 The Abstraction of Hydrogen and Halogen Atoms 7.2.1 The Effect of the Structure of the Radical 7.2.2 The Effect of the Structure of the Hydrogen or Halogen Source 7.3 The Addition of Radicals to  Bonds 7.3.1 Attack on Substituted Alkenes 7.3.2 Attack on Substituted Aromatic Rings 7.4 Synthetic Applications of the Chemoselectivity of Radicals 7.5 Stereochemistry in some Radical Reactions 7.6 Ambident Radicals 7.6.1 Neutral Ambident Radicals 7.6.2 Charged Ambident Radicals 7.7 Radical Coupling

369 369 371 371 373 376 376 381 384 386 390 390 393 398

8

Photochemical Reactions 8.1 Photochemical Reactions in General 8.2 Photochemical Ionic Reactions 8.2.1 Aromatic Nucleophilic Substitution 8.2.2 Aromatic Electrophilic Substitution 8.2.3 Aromatic Side-chain Reactivity 8.3 Photochemical Pericyclic Reactions and Related Stepwise Reactions 8.3.1 The Photochemical Woodward-Hoffmann Rule 8.3.2 Regioselectivity of Photocycloadditions 8.3.3 Other Kinds of Selectivity in Pericyclic and Related Photochemical Reactions 8.4 Photochemically Induced Radical Reactions 8.5 Chemiluminescence

401 401 403 403 405 406 408 408 411 430 432 437

References

439

Index

475

Preface

Molecular orbital theory is used by chemists to describe the arrangement of electrons in chemical structures. It provides a basis for explaining the ground-state shapes of molecules and their many other properties. As a theory of bonding it has largely replaced valence bond theory,1 but organic chemists still implicitly use valence bond theory whenever they draw resonance structures. Unfortunately, misuse of valence bond theory is not uncommon as this approach remains in the hands largely of the less sophisticated. Organic chemists with a serious interest in understanding and explaining their work usually express their ideas in molecular orbital terms, so much so that it is now an essential component of every organic chemist’s skills to have some acquaintance with molecular orbital theory. The problem is to find a level to suit everyone. At one extreme, a few organic chemists with high levels of mathematical skill are happy to use molecular orbital theory, and its computationally more amenable offshoot density functional theory, much as theoreticians do. At the other extreme are the many organic chemists with lower mathematical inclinations, who nevertheless want to understand their reactions at some kind of physical level. It is for these people that I have written this book. In between there are more and more experimental organic chemists carrying out calculations to support their observations, and these people need to know some of the physical basis for what their calculations are doing.2 I have presented molecular orbital theory in a much simplified and entirely nonmathematical language. I have simplified the treatment in order to make it accessible to every organic chemist, whether student or research worker, whether mathematically competent or not. In order to reach such a wide audience, I have frequently used oversimplified arguments. I trust that every student who has the aptitude will look beyond this book for a better understanding than can be found here. Accordingly, I have provided over 1800 references to the theoretical treatments and experimental evidence, to make it possible for every reader to go further into the subject. Molecular orbital theory is not only a theory of bonding, it is also a theory capable of giving some insight into the forces involved in the making and breaking of chemical bonds—the chemical reactions that are often the focus of an organic chemist’s interest. Calculations on transition structures can be carried out with a bewildering array of techniques requiring more or less skill, more or fewer assumptions, and greater or smaller contributions from empirical input, but many of these fail to provide the organic chemist with insight. He or she wants to know what the physical forces are that give the various kinds of selectivity that are so precious in learning how to control organic reactions. The most accessible theory to give this kind of insight is frontier orbital theory, which is based on the perturbation treatment of molecular orbital theory, introduced by Coulson and Longuet-Higgins,3 and developed and named as frontier orbital theory by Fukui.4 Earlier theories of reactivity concentrated on the product-like character of transition structures—the concept of localisation energy in aromatic electrophilic substitution is a well-known example. The perturbation theory concentrates instead on the other side of the reaction coordinate. It looks at how the interaction of the molecular orbitals of the starting materials influences the transition structure. Both influences are obviously important, and it is therefore helpful to know about both if we want a better understanding of what factors affect a transition structure, and hence affect chemical reactivity. Frontier orbital theory is now widely used, with more or less appropriateness, especially by organic chemists, not least because of the success of the predecessor to this book, Frontier Orbitals and Organic Chemical Reactions, which survived for more than thirty years as an introduction to the subject for a high proportion of the organic chemists trained in this period. However, there is a problem—computations show

x

PREFACE

that the frontier orbitals do not make a significantly larger contribution than the sum of all the orbitals. One theoretician put it to me as: ‘It has no right to work as well as it does.’ The difficulty is that it works as an explanation in many situations where nothing else is immediately compelling. In writing this book, I have therefore emphasised more the molecular orbital basis for understanding organic chemistry, about which there is less disquiet. Thus I have completely rewritten the earlier book, enlarging especially the chapters on molecular orbital theory itself. I have added a chapter on the effect of orbital interactions on the structures of organic molecules, a section on the theoretical basis for the principle of hard and soft acids and bases, and a chapter on the stereochemistry of the fundamental organic reactions. I have introduced correlation diagrams into the discussion of pericyclic chemistry, and a great deal more in that, the largest chapter. I have also added a number of topics, both omissions from the earlier book and new work that has taken place in the intervening years. I have used more words of caution in discussing frontier orbital theory itself, making it less polemical in furthering that subject, and hoping that it might lead people to be more cautious themselves before applying the ideas uncritically in their own work. For all their faults and limitations, frontier orbital theory and the principle of hard and soft acids and bases remain the most accessible approaches to understanding many aspects of reactivity. Since they fill a gap between the chemist’s experimental results and a state of the art theoretical description of his or her observations, they will continue to be used, until something better comes along. In this book, there is much detailed and not always convincing material, making it less suitable as a textbook for a lecture course; in consequence I have also written a second and shorter book on molecular orbital theory designed specifically for students of organic chemistry, Molecular Orbitals and Organic Chemistry—The Student Edition,5 which serves in a sense as a long awaited second edition to my earlier book. The shorter book uses a selection of the same material as in this volume, with appropriately revised text, but dispenses with most of the references, which can all be found here. The shorter book also has problem sets at the ends of the chapters, whereas this book has the answers to most of them in appropriate places in the text. I hope that everyone can use whichever volume suits them, and that even theoreticians might find unresolved problems in one or another of them. As in the earlier book, I begin by presenting some experimental observations that chemists have wanted to explain. None of the questions raised by these observations has a simple answer without reference to the orbitals involved. (i) Why does methyl tetrahydropyranyl ether largely adopt the conformation P.1, with the methoxy group axial, whereas methoxycyclohexane adopts largely the conformation P.2 with the methoxy group equatorial? OMe O

OMe O

OMe

OMe

P.1

P.2

(ii) Reduction of butadiene P.3 with sodium in liquid ammonia gives more cis-2-butene P.4 than trans-2butene P.5, even though the trans isomer is the more stable product. Na, NH3 P.3

+ P.4

60%

P.5

40%

(iii) Why is the inversion of configuration at nitrogen made slower if the nitrogen is in a small ring, and slower still if it has an electronegative substituent attached to it, so that, with the benefit of both features, an N-chloroaziridine can be separated into a pair of diastereoisomers P.6 and P.7?

PREFACE

xi

Cl

slow N

N

Cl

P.6

P.7

(iv) Why do enolate ions P.8 react more rapidly with protons on oxygen, but with primary alkyl halides on carbon?

H

sl ow

H O

OH

f ast

O

OH

P.8 f ast I

Me

Me

sl ow

O

O

OMe

P.8

(v) Hydroperoxide ion P.9 is much less basic than hydroxide ion P.10. Why, then, is it so much more nucleophilic? N HOO–

C

P.9

Ph

N 105 times f aster than

HO–

C

P10

Ph

(vi) Why does butadiene P.11 react with maleic anhydride P.12, but ethylene P.13 does not? O O P.11

O

O O

O P.12

O

O P.13

O

O

O P.12

O

(vii) Why do Diels-Alder reactions of butadiene P.11 go so much faster when there is an electronwithdrawing group on the dienophile, as with maleic anhydride P.12, than they do with ethylene P.13? O

O f ast

O P.11

P.12 O

sl ow O O

P.11 P.13

(viii) Why does diazomethane P.15 add to methyl acrylate P.16 to give the isomer P.17 in which the nitrogen end of the dipole is bonded to the carbon atom bearing the methoxycarbonyl group, and not the other way round P.14?

xii

PREFACE

N

N

N

N

CO2Me

N

CO2Me N

CH2

CO2Me P.14

P.15

P.16

P.17

(ix) When methyl fumarate P.18 and vinyl acetate P.19 are copolymerised with a radical initiator, why does the polymer P.20 consist largely of alternating units?

OAc

CO2Me

CO2Me CO2Me CO2Me OAc OAc OAc

R

+ MeO2C P.18

CO2Me

P.19

CO2Me

CO2Me

P.20

(x) Why does the Paterno-Bu¨chi reaction between acetone and acrylonitrile give only the isomer P.21 in which the two ‘electrophilic’ carbon atoms become bonded?

O (+)

CN +

h

CN O

(+) P.21

In the following chapters, each of these questions, and many others, receives a simple answer. Other books commend themselves to anyone able and willing to go further up the mathematical slopes towards a more acceptable level of explanation—a few introductory texts take the next step up,6,7 and several others8–11 take the story further. I have been greatly helped by a number of chemists: first and foremost Professor Christopher LonguetHiggins, whose inspiring lectures persuaded me to take the subject seriously at a time when most organic chemists who, like me, had little mathematics, had abandoned any hope of making sense of the subject; secondly, and more particularly those who gave me advice for the earlier book, and who therefore made their mark on this, namely Dr W. Carruthers, Professor R. F. Hudson, Professor A. R. Katritzky and Professor A. J. Stone. In addition, for this book, I am indebted to Dr Jonathan Goodman for help with computer programs, to Professor Wes Borden for some helpful discussions and collaboration on one topic, and to Professor A. D. Buckingham for several important corrections. More than usually, I must absolve all of them for any errors left in the book.

1

1.1

Molecular Orbital Theory

The Atomic Orbitals of a Hydrogen Atom

To understand the nature of the simplest chemical bond, that between two hydrogen atoms, we look at the effect on the electron distribution when two atoms are held within bonding distance, but first we need a picture of the hydrogen atoms themselves. Since a hydrogen atom consists of a proton and a single electron, we only need a description of the spatial distribution of that electron. This is usually expressed as a wave function , where 2dt is the probability of finding the electron in the volume dt, and the integral of 2dt over the whole of space is 1. The wave function is the underlying mathematical description, and it may be positive or negative; it can even be complex with a real and an imaginary part, but this will not be needed in any of the discussion in this book. Only when squared does it correspond to anything with physical reality— the probability of finding an electron in any given space. Quantum theory12 gives us a number of permitted wave equations, but the only one that matters here is the lowest in energy, in which the distribution of the electron is described as being in a 1s orbital. This is spherically symmetrical about the nucleus, with a maximum at the centre, and falling off rapidly, so that the probability of finding the electron within a sphere ˚ is 90 % and within 2 A ˚ better than 99%. This orbital is calculated to be 13.60 eV lower in of radius 1.4 A energy than a completely separated electron and proton. We need pictures to illustrate the electron distribution, and the most common is simply to draw a circle, Fig. 1.1a, which can be thought of as a section through a spherical contour, within which the electron would be found, say, 90 % of the time. This picture will suffice for most of what we need in this book, but it might be worth looking at some others, because the circle alone disguises some features that are worth appreciating. Thus a section showing more contours, Fig. 1.1b, has more detail. Another picture, even less amenable to a quick drawing, is to plot the electron distribution as a section through a cloud, Fig. 1.1c, where one imagines blinking one’s eyes a very large number of times, and plotting the points at which the electron was at each blink. This picture contributes to the language often used, in which the electron population in a given volume of space is referred to as the electron density.

H

0

90

1Å

(a) One contour

80 40

20 60

99

2Å

(b) Several contours

(c) An electron cloud

Fig. 1.1 The 1s atomic orbital of a hydrogen atom

Molecular Orbitals and Organic Chemical Reactions: Reference Edition  2010 John Wiley & Sons, Ltd

Ian Fleming

2

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS a0

1.0 0.8

4 r 2 (r)

P 0.6

van der Waals radius

0.4 0.2

1Å 2Å r (a) Fraction of charge-cloud outside a sphere of radius r

Fig. 1.2

1Å 2Å r (b) Radial density f or the ground state hydrogen atom

Radial probability plots for the 1s orbital of a hydrogen atom

Taking advantage of the spherical symmetry, we can also plot the fraction of the electron population outside a radius r against r, as in Fig. 1.2a, showing the rapid fall off of electron population with distance. The ˚ has no theoretical significance—it is an empirical measurement from solidvan der Waals radius at 1.2 A state structures, being one-half of the distance apart of the hydrogen atom in a C—H bond and the hydrogen atom in the C—H bond of an adjacent molecule.13 It does not even have a fixed value, but is an average of several measurements. Yet another way to appreciate the electron distribution is to look at the radial density, where we plot the probability of finding the electron between one sphere of radius r and another of radius ˚ from the nucleus, showing that, in spite r þ dr. This has a revealing form, Fig. 1.2b, with a maximum 0.529 A of the wave function being at a maximum at the nucleus, the chance of finding an electron precisely there is ˚ proves to be the same as the radius calculated for the orbit of an electron in very small. The distance 0.529 A the early but untenable planetary model of a hydrogen atom. It is called the Bohr radius a0, and is often used as a unit of length in molecular orbital calculations.

1.2

Molecules Made from Hydrogen Atoms

1.2.1 The H2 Molecule To understand the bonding in a hydrogen molecule, we have to see what happens when two hydrogen atoms are close enough for their atomic orbitals to interact. We now have two protons and two nuclei, and even with this small a molecule we cannot expect theory to give us complete solutions. We need a description of the electron distribution over the whole molecule—a molecular orbital. The way the problem is handled is to accept that a first approximation has the two atoms remaining more or less unchanged, so that the description of the molecule will resemble the sum of the two isolated atoms. Thus we combine the two atomic orbitals in a linear combination expressed in Equation 1.1, where the function which describes the new electron distribution, the molecular orbital, is called  and 1 and 2 are the atomic 1s wave functions on atoms 1 and 2.  ¼ c1 1 þ c2 2

1:1

The coefficients, c1 and c2, are a measure of the contribution which the atomic orbital is making to the molecular orbital. They are of course equal in magnitude in this case, since the two atoms are the same, but they may be positive or negative. To obtain the electron distribution, we square the function in Equation 1.1, which is written in two ways in Equation 1.2. 2 ¼ ðc1 1 þ c2 2 Þ2 ¼ ðc1 1 Þ2 þ ðc2 2 Þ2 þ 2c1 1 c2 2

1:2

1 MOLECULAR ORBITAL THEORY

3

Taking the expanded version, we can see that the molecular orbital 2 differs from the superposition of the two atomic orbitals (c11)2þ(c22)2 by the term 2c11c22. Thus we have two solutions (Fig. 1.3). In the first, both c1 and c2 are positive, with orbitals of the same sign placed next to each other; the electron population between the two atoms is increased (shaded area), and hence the negative charge which these electrons carry attracts the two positively charged nuclei. This results in a lowering in energy and is illustrated in Fig. 1.3, where the horizontal line next to the drawing of this orbital is placed low on the diagram. In the second way in which the orbitals can combine, c1 and c2 are of opposite sign, and, if there were any electrons in this orbital, there would be a low electron population in the space between the nuclei, since the function is changing sign. We represent the sign change by shading one of the orbitals, and we call the plane which divides the function at the sign change a node. If there were any electrons in this orbital, the reduced electron population between the nuclei would lead to repulsion between them; thus, if we wanted to have electrons in this orbital and still keep the nuclei reasonably close, energy would have to be put into the system. In summary, by making a bond between two hydrogen atoms, we create two new orbitals,  and *, which we call the molecular orbitals; the former is bonding and the latter antibonding (an asterisk generally signifies an antibonding orbital). In the ground state of the molecule, the two electrons will be in the orbital labelled . There is, therefore, when we make a bond, a lowering of energy equal to twice the value of E in Fig. 1.3 (twice the value, because there are two electrons in the bonding orbital).

*H—H

Energy E

H

H

1 node

*

1sH

1sH E

H—H

Fig. 1.3

HH

0 nodes

The molecular orbitals of hydrogen

The force holding the two atoms together is obviously dependent upon the extent of the overlap in the bonding orbital. If we bring the two 1s orbitals from a position where there is essentially no overlap ˚ through the bonding arrangement to superimposition, the extent of overlap steadily increases. at 3 A The mathematical description of the overlap is an integral S12 (Equation 1.3) called the overlap integral, which, for a pair of 1s orbitals, rises from 0 at infinite separation to 1 at superimposition (Fig. 1.4). ð S12 ¼ 1 2 dt 1:3

The mathematical description of the effect of overlap on the electronic energy is complex, but some of the terminology is worth recognising, and will be used from time to time in the rest of this book. The energy E of

4

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS +1

S 0.5

HH

H H 1Å

H 2Å

r H-H

H 3Å

Fig. 1.4 The overlap integral S for two 1sH orbitals as a function of internuclear distance

an electron in a bonding molecular orbital is given by Equation 1.4 and for the antibonding molecular orbital is given by Equation 1.5: E¼

þ 1þS

1:4

E¼

 1S

1:5

in which the symbol  represents the energy of an electron in an isolated atomic orbital, and is called a Coulomb integral. The function represented by the symbol  contributes to the energy of an electron in the field of both nuclei, and is called the resonance integral. It is roughly proportional to S, and so the overlap integral appears in the equations twice. It is important to realise that the use of the word resonance does not imply an oscillation, nor is it exactly the same as the ‘resonance’ of valence bond theory. In both cases the word is used because the mathematical form of the function is similar to that for the mechanical coupling of oscillators. We also use the words delocalised and delocalisation to describe the electron distribution enshrined in the  function—unlike the words resonating and resonance, these are not misleading, and are the better words to use. The function  is a negative number, lowering the value of E in Equation 1.4 and raising it in Equation 1.5. In this book,  will not be given a sign on the diagrams on which it is used, because the sign can be misleading. The symbol  should be interpreted as ||, the positive absolute value of . Since the diagrams are always plotted with energy upwards and almost always with the  value visible, it should be obvious which  values refer to a lowering of the energy below the  level, and which to raising the energy above it. The overall effect on the energy of the hydrogen molecule relative to that of two separate hydrogen atoms as a function of the internuclear distance is given in Fig. 1.5. If the bonding orbital is filled (Fig. 1.5a), the energy derived from the electronic contribution (Equation 1.4) steadily falls as the two hydrogen atoms are moved from infinity towards one another (curve A). At the same time the nuclei repel each other ever more strongly, and the nuclear contribution to the energy goes steadily up (curve B). The sum of these two is the familiar Morse plot (curve C) for the relationship between internuclear distance and energy, with a minimum at the bond length. If we had filled the antibonding orbital instead (Fig. 1.5b), there would have been no change to curve B. The electronic energy would be given by Equation 1.5 which provides only a little shielding between the separated nuclei giving at first a small curve down for curve A, and even that would change to a repulsion earlier than in the Morse curve. The resultant curve, C, is a steady increase in energy as the nuclei are pushed together. The characteristic of a bonding orbital is that the nuclei are held together, whereas the characteristic of an antibonding orbital, if it were to be filled, is that the nuclei would fly apart unless there are enough compensating filled bonding orbitals. In hydrogen, having both orbitals occupied is overall antibonding, and there is no possibility of compensating for a filled antibonding orbital.

1 MOLECULAR ORBITAL THEORY

5

B nuclear Coulombic repulsion

C overall energy

E

E B nuclear Coulombic repulsion

0

C overall energy 0.75Å HH

A electronic energy A electronic energy

H H 1Å

H 2Å

r H-H

H 3Å

(a) -Bonding orbital f illed

Fig. 1.5

H

H 1Å

2Å

H

H

r H-H

3Å

(b) -Antibonding orbital f illed

Electronic attraction, nuclear repulsion and the overall effect as a function of internuclear distance for two 1sH atoms

We can see from the form of Equations 1.4 and 1.5 that the term  relates to the energy levels of the isolated atoms labelled 1sH in Fig. 1.3, and the term  to the drop in energy labelled E (and the rise labelled E*). Equations 1.4 and 1.5 show that, since the denominator in the bonding combination is 1 þ S and the denominator in the antibonding combination is 1 – S, the bonding orbital is not as much lowered in energy as the antibonding is raised. In addition, putting two electrons into a bonding orbital does not achieve exactly twice the energy-lowering of putting one electron into it. We are allowed to put two electrons into the one orbital if they have opposite spins, but they still repel each other, because they have to share the same space; consequently, in forcing a second electron into the  orbital, we lose some of the bonding we might otherwise have gained. For this reason too, the value of E in Fig. 1.3 is smaller than that of E*. This is why two helium atoms do not combine to form an He2 molecule. There are four electrons in two helium atoms, two of which would go into the -bonding orbital in an He2 molecule and two into the *-antibonding orbital. Since 2E* is greater than 2E, we would need extra energy to keep the two helium atoms together. Two electrons in the same orbital can keep out of each other’s way, with one electron on one side of the orbital, while the other is on the other side most of the time, and so the energetic penalty for having a second electron in the orbital is not large. This synchronisation of the electrons’ movements is referred to as electron correlation. The energy-raising effect of the repulsion of one electron by the other is automatically included in calculations based on Equations 1.4 and 1.5, but each electron is treated as having an average distribution with respect to the other. The effect of electron correlation is often not included, without much penalty in accuracy, but when it is included the calculation is described as being with configuration interaction, a bit of fine tuning sometimes added to a careful calculation. The detailed form that  and  take is where the mathematical complexity appears. They come from the Schro¨dinger equation, and they are integrals over all coordinates, represented here simply by dt, in the form of Equations 1.6 and 1.7: ð 1:6  ¼ 1 H1 dt ð

 ¼ 1 H2 dt

1:7

6

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

where H is the energy operator known as a Hamiltonian. Even without going into this in more detail, it is clear how the term  relates to the atom, and the term  to the interaction of one atom with another. As with atomic orbitals, we need pictures to illustrate the electron distribution in the molecular orbitals. For most purposes, the conventional drawings of the bonding and antibonding orbitals in Fig. 1.3 are clear enough—we simply make mental reservations about what they represent. In order to be sure that we do understand enough detail, we can look at a slice through the two atoms showing the contours (Fig. 1.6). Here we see in the bonding orbital that the electron population close in to the nucleus is pulled in to the midpoint between the nuclei (Fig. 1.6a), but that further out the contours are an elliptical envelope with the nuclei as the foci. The antibonding orbital, however, still has some dense contours between the nuclei, but further out the electron population is pushed out on the back side of each nucleus. The node is half way between the nuclei, with the change of sign in the wave function symbolised by the shaded contours on the one side. If there were electrons in this orbital, their distribution on the outside would pull the nuclei apart—the closer the atoms get, the more the electrons are pushed to the outside, explaining the rise in energy of curve A in Fig. 1.5b.

(a) The σ-bonding orbital

(b) The σ*-antibonding orbital

Fig. 1.6 Contours of the wave function of the molecular orbitals of H2

We can take away the sign changes in the wave function by plotting 2 along the internuclear axis, as in Fig. 1.7. The solid lines are the plots for the molecular orbitals, and the dashed lines are plots, for comparison, of the undisturbed atomic orbitals 2. The electron population in the bonding orbital (Fig. 1.7a) can be seen to be slightly contracted relative to the sum of the squares of the atomic orbitals, and the electron population

2 1

* 2H-H

2 2

2 H-H

2 1

H2

H1 (a)

bonding

H1

2 2

H2

(b) * antibonding

Fig. 1.7 Plots of the square of the wave function for the molecular orbitals of H2 (solid lines) and its component atomic orbitals (dashed lines). [The atomic orbital plot is scaled down by a factor of 2 to allow us to compare 2 with the sum of the atomic densities (12þ22)/2]

1 MOLECULAR ORBITAL THEORY

7

between the nuclei is increased relative to that sum, as we saw when we considered Equation 1.2. In the antibonding orbital (Fig. 1.7b) it is the other way round, if there were electrons in the molecular orbital, the electron population would be slightly expanded relative to a simple addition of the squares of the atomic orbitals, and the electron population between the nuclei is correspondingly decreased. Let us return to the coefficients c1 and c2 of Equation 1.1, which are a measure of the contribution which each atomic orbital is making to the molecular orbital (equal in this case). When there are electrons in the orbital, the squares of the c-values are a measure of the electron population in the neighbourhood of the atom in question. Thus in each orbital the sum of the squares of all the c-values must equal one, since only one electron in each spin state can be in the orbital. Since |c1| must equal |c2| in a homonuclear p diatomic like H2, we have defined what the values of c1 and c2 in the bonding orbital must be, namely 1/ 2 ¼ 0.707: c1

c2

σ*

0.707

–0.707

Σc 2 = 1.000

σ

0.707

0.707

Σc 2 = 1.000

Σc 2 = 1.000

Σc 2 = 1.000

If all molecular orbitals were filled, then there would have to be one electron in each spin state on each atom, and this gives rise to a second criterion for c-values, namely that the sum of the squares of all the cvalues on any one atom in all the molecular orbitals must also equal one. Thus the *-antibonding orbital of hydrogen will have c-values of 0.707 and –0.707, because these values make the whole set fit both criteria. Of course, we could have taken c1 and c2 in the antibonding orbital the other way round, giving c1 the negative sign and c2 the positive. This derivation of the coefficients is not strictly accurate—a proper normalisation involves the overlap integral S, which is present with opposite sign in the bonding and the antibonding orbitals (see Equations 1.4 and 1.5). As a result the coefficients in the antibonding orbitals are actually slightly larger than those in the bonding orbital. This subtlety need not exercise us at the level of molecular orbital theory used in this book, and it is not a problem at all in Hu¨ckel theory, which is what we shall be using for p systems. We can, however, recognise its importance when we see that it is another way of explaining that the degree of antibonding from the antibonding orbital (E* in Fig. 1.3) is greater than the degree of bonding from the bonding orbital (E). 1.2.2 The H3 Molecule We might ask whether we can join more than two hydrogen atoms together. We shall consider first the possibility of joining three atoms together in a triangular arrangement. It presents us for the first time with the problem of how to account for three atoms forming bonds to each other. With three atomic orbitals to combine, we can no longer simply draw an interaction diagram as we did in Fig. 1.3, where there were only two atomic orbitals. One way of dealing with the problem is first to take two of them together. In this case, we take two of the hydrogen atoms, and allow them to interact to form a hydrogen molecule, and then we combine the  and * orbitals, on the right of Fig. 1.8, with the 1s orbital of the third hydrogen atom on the left. We now meet an important rule: we are only allowed to combine those orbitals that have the same symmetry with respect to all the symmetry elements present in the structure of the product and in the orbitals of the components we are combining. This problem did not arise in forming a bond between two identical hydrogen atoms, because they have inherently the same symmetry, but now we are combining different sets

8

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

H A

H H

1sH

H H z

H

A

*

*

H

H

1 node

H

0 nodes

2

S

H yz

H S H

y

H 1

x

H

H

Fig. 1.8

yz

Interacting orbitals for H3

of orbitals with each other. The need to match, and to maintain, symmetry will become a constant refrain as the molecules get more complex. The first task is to identify the symmetry elements, and to classify the orbitals with respect to them. Because all the orbitals are s orbitals, there is a trivial symmetry plane in the plane of the page, which we shall label throughout this book as the xz plane. We can ignore it, and other similar symmetry elements, in this case. The only symmetry element that is not trivial is the plane in what we shall call the yz plane, running from top to bottom of the page and rising vertically from it. The  orbital and the 1s orbital are symmetric with respect to this plane, but the * orbital is antisymmetric, because the component atomic orbitals are out of phase. We therefore label the orbitals as S (symmetric) or A (antisymmetric). The  orbital and the 1s orbital are both S and they can interact in the same way as we saw in Fig. 1.3, to create a new pair of molecular orbitals labelled 1 and 2*. The former is lowered in energy, because all the s orbitals are of the same sign, and the latter is raised in energy, because there is a node between the top hydrogen atom and the two bottom ones. The latter orbital is antibonding overall, because there are two antibonding interactions between hydrogen atoms and only one bonding interaction. As it happens, its energy is the same as that of the * orbital, but we cannot justify that fully now. In any case, the other orbital * remains unchanged in the H3 molecule, because there is no orbital of the correct symmetry to interact with it. Thus we have three molecular orbitals, just as we had three atomic orbitals to make them from. Whether we have a stable ‘molecule’ now depends upon how many electrons we have. If we have two in H3þ, in other words a protonated hydrogen molecule, they would both go into the 1 orbital, and the molecule would have a lower electronic energy than the separate proton and H2 molecule. If we had three electrons H3• from combining three hydrogen atoms, we would also have a stable ‘molecule’, with two electrons in 1 and only one in 2*, making the combination overall more bonding than antibonding. Only with four electrons in H3– is the overall result of the interaction antibonding, because the energy-raising interaction is, as usual, greater than the energy-lowering interaction. This device of building up the orbitals and only then feeding the electrons in is known as the aufbau method. We could have combined the three atoms in a straight line, pulling the two lower hydrogen atoms in Fig. 1.8 out to lay one on each side of the upper atom. Since the symmetries do not change, the result would have been similar (Fig. 1.9). There would be less bonding in 1 and 2*, because the overlap between the two lower hydrogen atoms would be removed. There would also be less antibonding from the * orbital, since it would revert to having the same energy as the two more or less independent 1s orbitals.

1 MOLECULAR ORBITAL THEORY

9

H

*

2

S

H

S

H H

*

*

H

H

H

2

H

H

H

*

H

H

H

1

A

H

A

H

S H

S

1

H

Fig. 1.9

H

Relative energies for the orbitals of triangular and linear H3

1.2.3 The H4 ‘Molecule’ There are even more possible ways of arranging four hydrogen atoms, but we shall limit ourselves to tetrahedral, since we shall be using these orbitals later. This time, we combine them in pairs, as in Fig. 1.3, to create two hydrogen molecules, and then we ask ourselves what happens to the energy when the two hydrogen molecules are held within bonding distance, one at right angles to the other. We can keep one pair of hydrogen atoms aligned along the x axis, on the right in Fig. 1.10, and orient the other along the y axis, on the left of Fig. 1.10. The symmetry elements present are then the xz and yz planes. The bonding orbital x on the right is symmetric with respect to both planes, and is labelled SS. The antibonding orbital x* is symmetric with respect to the xz plane but antisymmetric with respect to the yz plane, and is accordingly labelled SA. The bonding orbital y on the left is symmetric with respect to both planes, and is also labelled SS. The antibonding orbital y* is antisymmetric with respect to the xz plane but symmetric with respect to the yz plane, and is labelled AS. The only orbitals with the same symmetry are therefore the two bonding orbitals, and they can interact to give a bonding combination 1 and an antibonding combination 2*. As it happens, the latter has the same energy as the unchanged orbitals x* and y*. This is not too difficult to understand: in the new orbitals 1 and 2*, the coefficients c, will be (ignoring the full

HH

*

*

y

H

AS

*

H

y

x

H

H

H SA

H

*

H

H

x

H

H

x

H

*

2

H

H

SS z

y

SS

H

y

H 1

x

H

Fig. 1.10

H

The orbitals of tetrahedral H4

10

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

treatment of normalisation) 0.5 instead of 0.707, in order that the sum of their squares shall be 1. In the antibonding combination 2*, there are two bonding relationships between hydrogen atoms, and four antibonding relationships, giving a net value of two antibonding combinations, compared with the one in each of theporbitals x* and y*. However the antibonding in the orbital 2* is between s orbitals with p coefficients of 1/ 4, and two such interactions is the same as one between orbitals with coefficients of 1/ 2 (see Equation 1.3, and remember that the change in electronic energy is roughly proportional to the overlap integral S). We now have four molecular orbitals, 1, 2*, x* and y*, one lowered in energy and one raised relative to the energy of the orbitals of the pair of hydrogen molecules. If we have four electrons in the system, the net result is repulsion, as usual when two filled orbitals combine with each other. Thus two H2 molecules do not combine to form an H4 molecule. This is an important conclusion, and is true no matter what geometry we use in the combination. It is important, because it shows us in the simplest possible case why molecules exist, and why they largely retain their identity—when two molecules approach each other, the interaction of their molecular orbitals usually leads to this repulsion. Overcoming the repulsion is a prerequisite for chemical reaction and the energy needed is a major part of the activation energy.

1.3

C—H and C—C Bonds

1.3.1 The Atomic Orbitals of a Carbon Atom Carbon has s and p orbitals, but we can immediately discount the 1s orbital as contributing to bonding, because the two electrons in it are held so tightly in to the nucleus that there is no possibility of significant overlap with this orbital—the electrons simply shield the nucleus, effectively giving it less of a positive charge. We are left with four electrons in 2s and 2p orbitals to use for bonding. The 2s orbital is like the 1s orbital in being spherically symmetrical, but it has a spherical node, with a wave function like that shown in Fig. 1.11a, and a contour plot like that in Fig. 1.11b. The node is close to the nucleus, and overlap with the inner sphere is never important, making the 2s orbital effectively similar to a 1s orbital. Accordingly, a 2s orbital is usually drawn simply as a circle, as in Fig. 1.11c. The overlap integral S of a 1s orbital on hydrogen with the outer part of the 2s orbital on carbon has a similar form to the overlap integral for two 1s orbitals in Fig. 1.4 (except that it does not rise as high, is at a maximum at greater atomic separation, and would not reach unity at superimposition). The 2s orbital on carbon, at –19.5 eV, is 5.9 eV lower in energy than the 1s orbital in hydrogen. The attractive force on the 2s electrons is high because the nucleus has six protons, even though this is offset by the greater average distance of the electrons from the nucleus and by the shielding from the other electrons. Slater’s rules suggest that the two 1s electrons reduce the nuclear charge by 0.85 atomic charges each, and the other 2s and the two 2p electrons reduce it by 3  0.35 atomic charges, giving the nucleus an effective charge of 3.25.

r 2Å

1

1

2Å

C 2s

(a) Wave f unction of a 2s orbital on carbon

Fig. 1.11

(b) Contours f or the wave f unction

(c) Conventional representation

The 2s atomic orbital on carbon

1 MOLECULAR ORBITAL THEORY

11

The 2p orbitals on carbon also have one node each, but they have a completely different shape. They point mutually at right angles, one each along the three axes, x, y and z. A plot of the wave function for the 2px orbital along the x axis is shown in Fig. 1.12a, and a contour plot of a slice through the orbital is shown in Fig. 1.12b. Scale drawings of p orbitals based on the shapes defined by these functions would clutter up any attempt to analyse their contribution to bonding, and so it is conventional to draw much narrower lobes, as in Fig. 1.12c, and we make a mental reservation about their true size and shape. The 2p orbitals, at –10.7 eV, are higher in energy than the 2s, because they are held on average further from the nucleus. When wave functions for all three p orbitals, px, py and pz, are squared and added together, the overall electron probability has spherical symmetry, just like that in the corresponding s orbital, but concentrated further from the nucleus. Bonds to carbon will be made by overlap of s orbitals with each other, as they are in the hydrogen molecule, of s orbitals with p orbitals, and of p orbitals with each other. The overlap integrals S between a p orbital and an s or p orbital are dependent upon the angles at which they approach each other. The overlap integral for a head on approach of an s orbital on hydrogen along the axis of a p orbital on carbon with a lobe of the same sign in the wave function (Fig. 1.13a), leading to a  bond, grows as the orbitals begin to overlap ˚ apart (C), falls fast as some of the s (D), goes through a maximum when the nuclei are a little over 0.9 A orbital overlaps with the back lobe of the p orbital (B), and goes to zero when the s orbital is centred on the carbon atom (A). In the last configuration, whatever bonding there would be from the overlap with the lobe of the same sign (unshaded lobes are conventionally used to represent a positive sign in the wave function) is exactly cancelled by overlap with the lobe (shaded) of opposite sign in the wave function. Of course this

2p

2Å

0.5

1

1Å

1

2Å

1.5Å

1.5Å

r x-axis

1Å

–0.5

(a) Wave f unction of a 2px orbital on carbon

(b) Contours f or the wave f unction

(c) Conventional representation

Fig. 1.12 A 2px atomic orbital on carbon

0.5

0.5

C

S

S

F

E

D

G

B A 1Å

2Å

r C-H

(a) Overlap integral f or overlap of a p orbital on C with an s orbital on H

Fig. 1.13

3Å

1Å

2Å

r C-C

(b) Overlap integral f or overlap of two p orbitals on C

Overlap integrals for  overlap with a p orbital on carbon

3Å

12

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

configuration is never reached, in chemistry at least, since the nuclei cannot coincide. The overlap integral for two p orbitals approaching head-on in the bonding mode with matching signs (Fig. 1.13b) begins to grow ˚ apart (F), falls to zero as when the nuclei approach (G), rises to a maximum when they are about 1.5 A overlap of the front lobes with each other is cancelled by overlap of the front lobes with the back lobes (E), and would fall eventually to –1 at superimposition. The signs of the wave functions for the individual s and p atomic orbitals can get confusing, which is why we adopt the convention of shaded and unshaded. The signs will not be used in this book, except in Figs. 1.17 and 1.18, where they are effectively in equations. In both cases, s overlapping with p and p overlapping with p, the overlap need not be perfectly head-on for some contribution to bonding to be still possible. For imperfectly aligned orbitals, the integral is inevitably less, because the build up of electron population between the nuclei, which is responsible for holding the nuclei together, is correspondingly less; furthermore, since the overlapping region will also be off centre, the nuclei are less shielded from each other. The overlap integral for a 1s orbital on hydrogen and a 2p orbital on carbon is actually proportional to the cosine of the angle of approach , where  is 0 for head-on approach and 90 if the hydrogen atom is in the nodal plane of the p orbital. 1.3.2 Methane In methane, there are eight valence electrons, four from the carbon and one each from the hydrogen atoms, for which we need four molecular orbitals. We can begin by combining two hydrogen molecules into a composite H4 unit, and then combine the orbitals of that species (Fig. 1.10) with the orbitals of the carbon atom. It is not perhaps obvious where in space to put the four hydrogen atoms. They will repel each other, and the furthest apart they can get is a tetrahedral arrangement. In this arrangement, it is still possible to retain bonding interactions between the hydrogen atoms and the carbon atoms in all four orbitals, as we shall see, and the maximum amount of total bonding is obtained with this arrangement. We begin by classifying the orbitals with respect to the two symmetry elements, the xz plane and the yz plane. The symmetries of the molecular orbitals of the H4 ‘molecule’ taken from Fig. 1.10 are placed on the left in Fig. 1.14, but the energies of each are now close to the energy of an isolated 1s orbital on hydrogen, because the four hydrogen atoms are now further apart than we imagined them to be in Fig. 1.10. The s and p

HH

*

x

H

H H H

H H C

C H

H H

H H

C H

H

H

H y

H

SA AS H SS H SS

H

H

* *

2

SA AS SS

C

2py

C 2pz

H

SS

1

H

2px

C

C

2s

H

z H H y

C x

Fig. 1.14

H

H

The molecular orbitals of methane constructed from the interaction of the orbitals of tetrahedral H4 and a carbon atom

1 MOLECULAR ORBITAL THEORY

13

orbitals on the single carbon atom are shown on the right. There are two SS orbitals on each side, but the overlap integral for the interaction of the 2s orbital on carbon with the 2* orbital is zero—there is as much bonding with the lower lobes as there is antibonding with the upper lobes. This interaction leads nowhere. We therefore have four interactions, leading to four bonding molecular orbitals (shown in Fig. 1.14) and four antibonding (not shown). One is lower in energy than the others, because it uses overlap from the 2s orbital on carbon, which is lower in energy than the 2p orbitals. The other three orbitals are actually equal in energy, just like the component orbitals on each side, and the four orbitals are all we need to accommodate the eight valence electrons. There will be, higher in energy, a corresponding set of antibonding orbitals, which we shall not be concerned with for now. In this picture, the force holding any one of the hydrogen atoms bonded to the carbon is derived from more than one molecular orbital. The two hydrogen atoms drawn below the carbon atom in Fig. 1.14 have bonding from the low energy orbital made up of the overlap of all the s orbitals, and further bonding from the orbitals, drawn on the upper left and upper right, made up from overlap of the 1s orbital on the hydrogen with the 2pz and 2px orbitals on carbon. These two hydrogen atoms are in the node of the 2py orbital, and there is no bonding to them from the molecular orbital in the centre of the top row. However, the hydrogens drawn above the carbon atom, one in front of the plane of the page and one behind, are bonded by contributions from the overlap of their 1s orbitals with the 2s, 2py and 2pz orbitals of the carbon atom, but not with the 2px orbital. Fig. 1.14 uses the conventional representations of the atomic orbitals, revealing which atomic orbitals contribute to each of the molecular orbitals, but they do not give an accurate picture of the resulting electron distribution. A better picture can be found in Jorgensen’s and Salem’s pioneering book, The Organic Chemist’s Book of Orbitals,14 which is also available as a CD.15 There are also several computer programs which allow you easily to construct more realistic pictures. The pictures in Fig. 1.15 come from one of these, Jaguar, and show the four filled orbitals of methane. The wire mesh drawn to represent the outline of each molecular orbital shows one of the contours of the wave function, with the signs symbolised by light and heavier shading. It is easy to see what the component s and p orbitals must have been, and for comparison the four orbitals are laid out here in the same way as those in Fig. 1.14.

Fig. 1.15

One contour of the wave function for the four filled molecular orbitals of methane

1.3.3 Methylene Methylene, CH2, is not a molecule that we can isolate, but it is a well known reactive intermediate with a bent H—C—H structure, and in that sense is a ‘stable’ molecule. Although more simple than methane, it brings us for the first time to another feature of orbital interactions which we need to understand. We take the orbitals

14

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

of a hydrogen molecule from Fig. 1.3 and place them on the left of Fig. 1.16, except that again the atoms are further apart, so that the bonding and antibonding combination have relatively little difference in energy. On the right are the atomic orbitals of carbon. In this case we have three symmetry elements: (i) the xz plane, bisecting all three atoms; (ii) the yz plane, bisecting the carbon atom, and through which the hydrogen atoms reflect each other; and (iii) a two-fold rotation axis along the z coordinate, bisecting the H—C—H angle. The two orbitals, HH and *HH in Fig. 1.16, are SSS and SAA with respect to these symmetry elements, and the atomic orbitals of carbon are SSS, SSS, ASA and SAA. Thus there are two orbitals on the right and one on the left with SSS symmetry, and the overlap integral is positive for the interactions of the HH and both the 2s and 2pz orbitals, so that we cannot have as simple a way of creating a picture as we did with methane, where one of the possible interactions had a zero overlap integral. In more detail, we have three molecular orbitals to create from three atomic orbitals, and the linear combination is Equation 1.8, like Equation 1.1 but with three terms:  ¼ c1 1 þ c2 2 þ c3 3

1:8

Because of symmetry, |c1| must equal |c3|, but |c2| can be different. On account of the energy difference, it only makes a small contribution to the lowest-energy orbital, as shown in Fig. 1.17, where there is a small p lobe, in phase, buried inside the s orbital s. It would show in a full contour diagram, but does not intrude in a simple picture like that in Fig. 1.16. The second molecular orbital up in energy created from this interaction, the z orbital, is a mix of the HH orbital, the 2s orbital on carbon, out of phase, and the 2pz orbital, in phase, which has the effect of boosting the upper lobe, and reducing the lower lobe. There is then a third orbital higher in energy, shown in Fig. 1.17 but not in Fig. 1.16, antibonding overall, with both the 2s and 2pz orbitals out of phase with the HH orbital. Thus, we have created three molecular orbitals from three atomic orbitals. Returning to Fig. 1.16, the other interaction, between the *HH orbital and its SAA counterpart, the 2px orbital, gives a bonding combination x and an antibonding combination (not shown). Finally, the remaining p orbital, 2py with no orbital of matching symmetry to interact with, remains unchanged, and, as it happens, unoccupied. If we had used the linear arrangement H—C—H, the x orbital would have had a lower energy, because the overlap integral, with perfect head-on overlap ( ¼ 0), would be larger, but the z orbital would have made no contribution to bonding, since the H atoms would have been in the node of the p orbital. This orbital would

C

2py

SAA ASA SSS

H

H

antibonding bonding *HH

H

H

HH

H

H

H

C

x

H

H SSS

y

C

2s

C

s

Fig. 1.16

2py

z

C H

x

C

C 2pz

SAA SSS

z

2px

C

H

H

The molecular orbitals of methylene constructed from the interaction of the orbitals of H2 and a carbon atom

1 MOLECULAR ORBITAL THEORY

H

H

15

+

C

+

H

H –2s

HH

H

H

+

–2s

HH

H HH

Fig. 1.17

C

H

+

C 2s

*z

C

C

2pz

+

C

–2pz

+

–2pz

z

C H

H

C

C H

s

H

Interactions of a 2s and 2pz orbital on carbon with the HH orbital with the same symmetry

simply have been a new orbital on carbon, half way between the s and p orbitals, making no contribution to bonding, and the overall lowering in energy would be less than for the bent structure. We do not actually need to combine the orbitals of the two hydrogen atoms before we start. All we need to see is that the combinations of all the available s and p orbitals leading to the picture in Fig. 1.16 will account for the bent configuration which has the lowest energy. Needless to say, a full calculation, optimising the bonding, comes to the same conclusion. Methylene is a bent molecule, with a filled orbital of p character, labelled z, bulging out in the same plane as the three atoms. The orbital s made up largely from the s orbitals is lowest in energy, both because the component atomic orbitals start off with lower energy, and because their combination is inherently head-on. An empty py orbital is left unused, and this will be the lowest in energy of the unfilled orbitals—it is nonbonding and therefore lower in energy than the various antibonding orbitals created, but not illustrated, by the orbital interactions shown in Fig. 1.16. 1.3.4 Hybridisation One difficulty with these pictures, explaining the bonding in methane and in methylene, is that there is no single orbital which we can associate with the C—H bond. To avoid this inconvenience, chemists often use Pauling’s idea of hybridisation; that is, they mix together the atomic orbitals of the carbon atom, adding the s and p orbitals together in various proportions, to produce a set of hybrids, before using them to make the molecular orbitals. We began to do this in the account of the orbitals of methylene, but the difference now is that we do all the mixing of the carbon-based orbitals first, before combining them with anything else. Thus one-half of the 2s orbital on carbon can be mixed with one-half of the 2px orbital on carbon, with its wave function in each of the two possible orientations, to create a degenerate pair of hybrid orbitals, called sp hybrids, leaving the 2py and 2pz orbitals unused (Fig. 1.18, top). The 2s orbital on carbon can also be mixed with the 2px and 2pz orbitals, taking one-third of the 2s orbital in each case successively with one-half of the 2px and one-sixth of the 2pz in two combinations to create two hybrids, and with the remaining two-thirds of the 2pz orbital to make the third hybrid. This set is called sp2 (Fig. 1.18, centre); it leaves the 2py orbital unused at right angles to the plane of the page. The three hybrid orbitals lie in the plane of the page at angles of 120 to each other, and are used to describe the bonding in trigonal carbon compounds. For tetrahedral carbon, the mixing is one-quarter of the 2s orbital with one-half of the 2px and one-quarter of the 2pz orbital, in two combinations, to make one pair of hybrids, and one quarter of the 2s orbital with one-half of the 2py and one-quarter of the 2pz orbital, also in two combinations, to make the other pair of hybrids, with the set of four called sp3 hybrids (Fig. 1.18, bottom).

16

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

√ 2 2s 1 √ 2 2s 1

+ +

√ 2 –2px 1 √ 2 2px 1

=

sp hybrid

=

sp hybrid

√ 3 2s

+

√ 2 –2px

+

√6 2pz

=

sp2 hybrid

√ 3 2s

+

√2 2px

+

√ 6 2pz 1

=

sp2 hybrid

+

√ 3 –2pz

=

sp2 hybrid

1

1

1

1

√13 2s

1

2

√ 4 2s 1

+

√2 –2px

+

√ 4 –2pz

=

sp3 hybrid

√ 14 2s

+

√21 2px

+

√ 4 –2pz

=

sp3 hybrid

√ 14 2s

+

√ 12 –2py

+

√ 14 2pz

=

(large lobe in front of the plane of the page, and small lobe behind)

√

+

√

+

√

=

(large lobe behind the plane of the page, and small lobe in front)

1 4 2s

1

1 2 2py

1

1

Fig. 1.18

1 4 2pz

sp3 hybrid

sp3 hybrid

Hybrid orbitals

The conventional representations of hybrid orbitals used in Fig. 1.18 are just as misleading as the conventional representations of the p orbitals from which they are derived. A more accurate picture of the sp3 hybrid is given by the contours of the wave function in Fig. 1.19. Because of the presence of the inner sphere in the 2s orbital (Fig. 1.11a), the nucleus is actually inside the back lobe, and a small proportion of the front lobe reaches behind the nucleus. This follows from the way a hybrid is constructed by adding one-quarter of the wave function of the s orbital (Fig. 1.11a) and three-quarters in total of the wave functions of the p orbitals (Fig. 1.12a). As usual, we draw the conventional hybrids relatively thin, and make the mental reservation that they are fatter than they are usually drawn.

=0.1 =0.2 =0.3 =0.4 2Å

Fig. 1.19

1

1

2Å

A section through an sp3 hybrid on carbon

1 MOLECULAR ORBITAL THEORY

17

The interaction of the 1s orbital of a hydrogen atom with an sp3 hybrid on carbon can be used in the usual way to create a CH bonding orbital and a *CH antibonding orbital (Fig. 1.20). Four of the bonding orbitals, each with two electrons in it, one from each of the four hybrids, point towards the corners of a regular tetrahedron, and give rise to the familiar picture for the bonds in methane shown in Fig. 1.21a.

*C—H

H

H

sp3C

1sH

C—H

Fig. 1.20

H

Bonding and antibonding orbitals of a C—H bond

H H H H

H H

(a) The sp3 hybrids on carbon overlapping with the s orbitals of hydrogen

Fig. 1.21

H

H

(b) Conventional bonds

Methane built up using sp3 hybridised orbitals

This picture has the advantage over that in Fig. 1.14 that the C—H bonds do have a direct relationship with the lines drawn on the conventional structure (Fig. 1.21b). The bonds drawn in Fig. 1.14 do not represent anything material but without them the picture would be hard to interpret. The two descriptions of the overall wave function for methane are in fact identical; hybridisation involves the same approximations, and the taking of s and p orbitals in various proportions and various combinations, as those used to arrive at the picture in Fig. 1.14. For many purposes it is wise to avoid localising the electrons in the bonds, and to use pictures like Fig. 1.14. This is what most theoreticians do when they deal with organic molecules, and it is what the computer programs will produce. It is also, in most respects, a more realistic model. Measurements of ionisation potentials, for example, show that there are two energy levels from which electrons may be removed; this is immediately easy to understand in Fig. 1.14, where there are filled orbitals of different energy, but the picture of four identical bonds from Fig. 1.20 hides this information. For other purposes, however, it is undoubtedly helpful to take advantage of the simple picture provided by the hybridisation model, even though hybridisation is an extra concept to learn. It immediately reveals, for example, that all four bonds are equal. It can be used whenever it offers a simplification to an argument as we shall find later in this book, but it is good practice to avoid it wherever possible. In particular, the common

18

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

practice of referring to a molecule or an atom as ‘rehybridising’ is not good usage—the rehybridisation in question is in our picture, not in the molecule. It is likewise poor (but unfortunately common) practice to refer to atoms as being sp3, sp2 or sp hybridised. Again the atoms themselves are not, in a sense, hybridised, it is we who have chosen to picture them that way. It is better in such circumstances to refer to the atoms as being tetrahedral, trigonal, or digonal, as appropriate, and allow for the fact that the bonds around carbon (and other) atoms may not have exactly any of those geometries. 1.3.5 C—C s Bonds and p Bonds: Ethane With a total of fourteen valence electrons to accommodate in molecular orbitals, ethane presents a more complicated picture, and we now meet a C—C bond. We will not go into the full picture—finding the symmetry elements and identifying which atomic orbitals mix to set up the molecular orbitals. It is easy enough to see the various combinations of the 1s orbitals on the hydrogen atoms and the 2s, 2px, 2py and 2pz orbitals on the two carbon atoms giving the set of seven bonding molecular orbitals in Fig. 1.22.

H

H

H C

H

*z′

C

H

H

H

bonding H H

H

H

H

H

H

H

H

H

H

H

C H

H C

C

z

H

2 nodes

H

H H

H

H

y′

x

H

C

C

H

C

H C

H

C

H H

H

z′

C

H

H

H

H

H

*x

C H

C

3 nodes

H

H

H

H

*y′

C

H C

antibonding

H

C

H

H

C

H

H

H C H

y

H

1 node

s′

H

H

H C

H

H C H

s

0 nodes

H

Fig. 1.22 The bonding orbitals and three antibonding orbitals of ethane

There is of course a corresponding picture using sp3 hybrids, but the following account shows how easy it is to avoid them. We shall concentrate for the moment on those orbitals which give rise to the force holding the two carbon atoms together; between them they make up the C—C bond. The molecular orbitals (s and s0 ), made up

1 MOLECULAR ORBITAL THEORY

19

largely from 2s orbitals on carbon, are very like the orbitals in hydrogen, in that the region of overlap is directly on a line between the carbon nuclei; as before, they are called  orbitals. The bonding in the lower one is very strong, but it is somewhat offset by the antibonding (as far as the C—C bond is concerned) in the upper one. They are both strongly bonding with respect to the C—H bonds. There is actually a little of the 2px orbital mixed in with this orbital, just as we saw in Fig. 1.17 with a 2pz orbital, but most of the 2px orbital contributes to the molecular orbital x, which is also  in character, and very strong as far as the C—C bond is concerned. This orbital has a little of the 2s orbital mixed in, resulting in the asymmetric extension of the lobes between the two carbon nuclei and a reduction in size of the outer lobes. This time, its antibonding counterpart (*x) is not involved in the total bonding of ethane, nor is it bonding overall. It is in fact the lowest-energy antibonding orbital. In the molecular orbitals using the 2py and 2pz orbitals of carbon, the lobes of the atomic orbitals overlap sideways on. This is the distinctive feature of what is called p bonding, although it may be unfamiliar to meet this type of bonding in ethane. Nevertheless, let us see where it takes us. The conventional way of drawing a p orbital (Fig. 1.12c) is designed to give elegant and uncluttered drawings, like those in Fig. 1.22, and is used throughout this book for that reason. A better picture as we have already seen, and which we keep as a mental reservation when confronted with the conventional drawings, is the contour diagram (Fig. 1.12b). With these pictures in mind, the overlap sideways-on can be seen to lead to an enhanced electron population between the nuclei. However, since it is no longer directly on a line between the nuclei, it does not hold the carbon nuclei together as strongly as a -bonding orbital. The overlap integral S for two p orbitals with a dihedral angle of zero has the form shown in Fig. 1.23, where it can be compared with the corresponding  overlap integral taken from Fig. 1.13b. Whereas the  overlap integral ˚ and then falls rapidly to a value of –1, the p overlap integral rises more goes through a maximum at about 1.5 A ˚ long, the overlap slowly but reaches unity at superimposition. Since C—C single bonds are typically about 1.54 A integral at this distance for p bonding is a little less than half that for  bonding. p Bonds are therefore much weaker. 1

pp

S 0.5

p p 1Å

2Å

r C-C

3Å

–0.5

–1

Fig. 1.23

Comparison of overlap integrals for p and  bonding of p orbitals on C

Returning to the molecular orbitals in ethane made from the 2py and 2pz orbitals, we see that they again fall in pairs, a bonding pair (py and pz) and (as far as C—C bonding is concerned, but not overall) an antibonding pair (py0 and pz0 ). These orbitals have the wrong symmetry to have any of the 2s orbital mixed in with them. The electron population in the four orbitals (py, pz, py0 and pz0 ) is higher in the vicinity of the hydrogen atoms than in the vicinity of the carbon atoms, and these orbitals mainly contribute to the strength of the C—H bonds, towards which all four orbitals are bonding. The amount both of bonding and antibonding that they contribute to the C—C bond is small, with the bonding and antibonding combinations more or less cancelling each other out. Thus the orbital (x) is the most important single orbital making up the C—C bond. We can construct for it an interaction diagram (Fig. 1.24), just as we did for the H—H bond in Fig. 1.3. The other major contribution to C—C bonding comes from the fact that s is more C—C bonding than s0 is C—C antibonding, as already mentioned.

20

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

*

x

E

*

px

px E

x

Fig. 1.24

A major part of the C—C  bond of ethane

Had we used the concept of hybridisation, the C—C bond would, of course, simply have been seen as coming from the bonding overlap of sp3 hybridised orbitals on carbon with each other, and the overall picture for the C—C bond would have looked very similar to x in Fig. 1.24, except that it would have used different proportions of s and p orbitals, and would have been labelled sp3. For simplicity, we shall often discuss the orbitals of  bonds as though they could be localised into bonding and antibonding orbitals like x and x*. We shall not often need to refer to the full set of orbitals, except when they become important for one reason or another. Any property we may in future attribute to the bonding and antibonding orbitals of a  bond, as though there were just one such pair, can always be found in the full set of all the bonding orbitals, or they can be found in the interaction of appropriately hybridised orbitals. 1.3.6 C=C p Bonds: Ethylene The orbitals of ethylene are made up from the 1s orbitals of the four hydrogen atoms and the 2s, 2px, 2py and 2pz orbitals of the two carbon atoms (Fig. 1.25). One group, made up from the 1s orbitals on hydrogen and the 2s, 2px and 2py orbitals on carbon, is substantially  bonding, which causes the orbitals to be relatively low in energy. These five orbitals with ten of the electrons make up what we call the  framework. Standing out, higher in energy than the -framework orbitals, is a filled orbital made up entirely from the 2pz orbitals of the carbon atom overlapping in a p bond. This time, the p orbital is localised on the carbon atoms with no mixing in of the 1s orbitals on the hydrogen atoms, which all sit in the nodal plane of the pz orbital. The bonding in this orbital gives greater strength to the C—C bonding in ethylene than the p orbitals give to the C—C bonding in ethane, which is one reason why we talk of ethylene as having a double bond. Nevertheless, the C—C  bonding in the  framework is greater than the p bonding from overlap of the two pz orbitals. This is because, other things being equal, p overlap is inherently less effective in lowering the energy than  overlap. Thus in the interaction diagram for a p bond (Fig. 1.26), the drop in energy Ep from p bonding is less than E in Fig. 1.24 for comparable  bonding, and this follows from the larger overlap integral for  approach than for p approach (Fig. 1.23). Similarly, Ep* in Fig. 1.26 is less than E* in Fig. 1.24. Another consequence of having an orbital localised on two atoms is that the equation for the linear combination of atomic orbitals contains only two terms (Equation 1.1), and the c-values are again 0.707 in the bonding orbital and 0.707 and –0.707 in the antibonding orbital. In simple Hu¨ckel theory, the energy of the p orbital on carbon is given the value , which is used as a reference point from which to measure rises and drops in energy, and will be especially useful when we come to deal with other elements. The value of Ep in Fig. 1.26 is given the symbol , and is also used as a reference with which to compare the degree of bonding in other p-bonding systems. To give a sense of scale, its value for ethylene is approximately 140 kJ mol–1 (¼ 1.45 eV ¼ 33 kcal mol–1). In other words the total p bonding in ethylene is 280 kJ mol–1, since there are two electrons in the bonding orbital.

1 MOLECULAR ORBITAL THEORY

21

H H

C

C

H H

z

H H

C

C

H H

z

*

antibonding bonding

C

C

H H

y'

H H H H

C

C

H H

x

y

H H

C

C

H H

s'

H H

Fig. 1.25

H H

C

C

the bonding orbitals of the framework

H H

C

C

H H

s

The bonding orbitals and one antibonding orbital of ethylene

* E

*

pz

pz E

Fig. 1.26

A C¼C p bond

This separation of the  framework and the p bond is the essence of Hu¨ckel theory. Because the p bond in ethylene in this treatment is self-contained, free of any complications from involvement with the hydrogen atoms, we may treat the electrons in it in the same way as we do for the fundamental quantum mechanical picture of an electron in a box. We look at each molecular wave function as one of a series of sine waves. In these simple molecules we only have the two energy levels, and so we only need to draw an analogy between them and the two lowest levels for the electron in the box. The convention is to draw the limits of the box one bond length out from the atoms at the end of the conjugated system, and then inscribe sine waves so that a node always comes at the edge of the box. With two orbitals to consider for the p bond of ethylene, we only need the 180 sine curve for p and the 360 sine curve for p*. These curves can be inscribed over the orbitals as they are on the left of Fig. 1.27, and we can see on the right how the vertical lines above and below the atoms duplicate the pattern of the coefficients, with both c1 and c2 positive in the p orbital, and c1 positive and c2 negative in p*. The drawings of the p orbitals in Figs. 1.26 and 1.27 have the usual problem of being schematic. A better picture as we have already seen, and which we keep as a mental reservation when confronted with the

22

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

*

c1 c2

c1

Fig. 1.27

c2

The p orbitals of ethylene and the electron in the box

conventional drawings, is the contour diagram (Fig. 1.12b). A better sense of the overlap from two side-byside p orbitals is given in Fig. 1.28, where we see more clearly that in the bonding combination, even sideways-on, there is enhanced electron population between the nuclei, but that it is no longer directly on a line between the nuclei. The wire-mesh diagrams in Fig. 1.29, illustrate the shapes of the p and p* orbitals even better, with some sense of their 3D character.

Fig. 1.28

Fig. 1.29

A section through the contours of the p and p* wave functions of ethylene

Wire-mesh outlines of one contour of the p and p* wave functions of ethylene

1 MOLECULAR ORBITAL THEORY

1.4

23

¨ ckel Theory16,17 Conjugation—Hu

The interaction of atomic orbitals giving rise to molecular orbitals is the simplest type of conjugation. Thus in ethylene the two p orbitals can be described as being conjugated with each other to make the p bond. The simplest extension to make longer conjugated systems is to add one p orbital at a time to the p bond to make successively the p components of the allyl system with three carbon atoms, of butadiene with four, of the pentadienyl system with five, and so on. Hu¨ckel theory applies, because in each case we separate completely the p system from the  framework, and we can continue to use the electron-in-the-box model. 1.4.1 The Allyl System The members of the allyl system are reactive intermediates rather than stable molecules, and there are three of them: the allyl cation 1.1, the allyl radical 1.2 and the allyl anion 1.3. They have the same  framework and the same p orbitals, but different numbers of electrons in the p system. 2 1

3

1.1

1.2

1.3

It is necessary to make a mental reservation about the diagrams 1.1–1.3, so commonly used by organic chemists. These diagrams are localised structures that seem to imply that C-1 has the positive charge (an empty p orbital), the odd electron (a half-filled p orbital) or the negative charge (a filled p orbital), respectively, and that C-2 and C-3 are in a double bond in each case. However, we could have drawn the cation 1.1, redrawn as 1.4a, equally well the other way round as 1.4b, and the curly arrow symbolism shows how the two drawings are interconvertible. This device is at the heart of valence bond theory. For now we need only to recognise that these two drawings are representations of the same species—there is no reaction connecting them, although many people sooner or later fall into the trap of thinking that ‘resonance’ like 1.4a ! 1.4b is a step in a reaction sequence. The double-headed arrow interconnecting them is a useful signal; this symbol should be used only for interconnecting ‘resonance structures’ and never to represent an equilibrium There are corresponding pairs of drawings for the radical 1.5a and 1.5b and for the anion 1.6a and 1.6b.

1.4a

1.4b

1.4c

1.5a

1.5b

1.5c

1.6a

1.6b

1.6c

One way of avoiding these misleading structures is to draw the allyl cation, radical or anion as in 1.4c, 1.5c and 1.6c, respectively, illustrating the delocalisation of the p orbitals with a dashed line, and placing the positive or negative charge in the middle. The trouble with these drawings is that they are hard to use clearly with curly arrows in mechanistic schemes, and they do not show that the positive charge in the cation, the odd electron in the radical or the negative charge in the anion are largely concentrated on C-1 and C-3, the very feature that the drawings 1.4a and 1.4b, 1.5a and 1.5b and 1.6a and 1.6b illustrate so well. We shall see that the drawings with

24

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

apparently localised charges 1.4a, 1.4b, 1.5a and 1.5b and 1.6a and 1.6b illustrate not only the overall p electron distribution but also the important frontier orbital. It is probably better in most situations to use one of the localised drawings rather than any of the ‘molecular orbital’ versions 1.4c, 1.5c or 1.6c, and then make the necessary mental reservation that each of the localised drawings implies the other. H H

C

H C

C H

H

1.7

The allyl cation, radical and anion have the same  framework 1.7, with 14 bonding molecular orbitals filled with 28 electrons made by mixing the 1s orbitals of the five hydrogen atoms either with the sp2 hybrids or with the 2s, 2px and 2py orbitals of the three carbon atoms. The allyl systems are bent not linear, but we shall treat them as linear to simplify the discussion. The x, y and z coordinates have to be redefined as local x, y and z coordinates, different at each atom, in order to make this simplification, but this leads to no complications in the general story. As with ethylene, we keep the  framework separate from the p system, which is made up from the three pz orbitals on the carbon atoms that were not used in making the  framework. The linear combination of these orbitals takes the form of Equation 1.9, with three terms, creating a pattern of three molecular orbitals, 1, 2 and 3*, that bear some resemblance to the set we saw in Section 1.3.3 for methylene. In the allyl cation there are two electrons left to go into the p system after filling the  framework (and in the radical, three, and in the anion, four). ¼c1 1 þ c2 2 þ c3 3

1:9

We can derive a picture of these orbitals using the electron in the box, recognising that we now have three orbitals and therefore three energy levels. If the lowest energy orbital is, as usual, to have no nodes (except the inevitable one in the plane of the molecule), and the next one up one node, we now need an orbital with two nodes. We therefore construct a diagram like that of Fig. 1.27, but with one more turn of the sine curve, to include that for 540, the next one up in energy that fulfils the criterion that there are nodes at the edges of the box, one bond length out, as well as the two inside (Fig. 1.30). The lowest-energy orbital, 1, has bonding across the whole conjugated system, with the electrons concentrated in the middle. Because of the bonding, this orbital will be lower in energy than an isolated p

*

c1

–0.707

3

0.500

c1

c2

c2

c3 0.500

–0.707

2

c3

0.707

c1

c2

c3

1 0.500

Fig. 1.30

0.707

The p orbitals of the allyl system

0.500

1 MOLECULAR ORBITAL THEORY

25

orbital. The next orbital up in energy 2, is different from those we have met so far. Its symmetry demands that the node be in the middle; but this time the centre of the conjugated system is occupied by an atom and not by a bond. Having a node in the middle meansphaving a zero coefficient c2 on C-2, and hence the coefficients on C-l and C-3 in this orbital must be –1/ 2, if, squared and summed, they are to equal one. The atomic orbitals in 2 are so far apart in space that their repulsive interaction does not, to a first approximation, raise the energy of this molecular orbital relative to that of an isolated p orbital. In consequence, whether filled or not, it does not contribute to the overall bonding. If the sum of the squares p of the three orbitals on C-2 is also to equal one, then the coefficients on C-2 in 1 and 3* must also be –1/ 2. Finally, since symmetry requires that the coefficients onpC-1 and C-3 in 1 and 3* have the same absolute magnitude, and the sum of their squares must equal 1–(1/ 2)2, we can deduce the unique set of c-values shown in Fig. 1.30. A pattern present in the allyl system because of its symmetry is seen with other symmetrical conjugated systems: the |c| values are reflected across a mirror plane placed horizontally, half way up the set of orbitals, between 1 and 3*, and also across a mirror plane placed vertically, through C-2. It is only necessary therefore to calculate four of the nine numbers in Fig. 1.30, and deduce the rest from the symmetry. In this picture of the bonding, we get no immediate appreciation of the energies of these orbitals relative to those of ethylene. The nonbonding orbital 2 is clearly on the  level, that of a p orbital on carbon, and 1 is lowered by the extra p bonding and 3* is raised. To assess the energies, there is a simple geometrical device that works for linear conjugated systems. The conjugated system, including the dummy atoms at the ends of the sine curves, is inscribed vertically inside a circle of radius 2, following the convention that one p bond in ethylene defines . This is shown for ethylene and the allyl system in Fig. 1.31, where the dummy atoms are marked as dots at the top and bottom of the circle. The energies E of the p orbitals can then be calculated using Equation 1.10: E ¼ 2 cos

kp nþ1

1:10

where k is the number of the atom along the sequence of n atoms. This is simply an expression based on the trigonometry of Fig. 1.31, where, for example, the p orbital of ethylene is placed on the first atom (k ¼ 1) of the sequence of two (n ¼ 2) reading anticlockwise from the bottom. Thus the energies of the p orbitals in the allyl system are 1.414 below the  level and 1.414 above the  level. 3

*

2

*

3

1.414 2

/3

1.414 1

1

0

ethylene

Fig. 1.31

the allyl system

Energies of p molecular orbitals in ethylene and the allyl system

We can gain further insight by building the picture of the p orbitals of the allyl system in another way. Instead of mixing together three p orbitals on carbon, we can combine two of them in a p bond first, as in Fig. 1.26, and then work out the consequences of having a third p orbital held within bonding distance of

26

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

the C¼C p bond. Although Fig. 1.26, and all the interaction diagrams for single bonds, illustrated the bonding orbital as less bonding than the antibonding orbital is antibonding, this detail confuses the simple picture for conjugated systems that we want to build up here, and is left out of the discussion. We have to consider the effect of the p orbital, on the right of Fig. 1.32 on both the p and p* orbitals of ethylene on the left. If we look only at the interaction with the p orbital, we can expect to create two new orbitals in much the same way as we saw when the two 2pz orbitals of carbon were allowed to interact in the formation of the p bond of Fig. 1.26. One orbital 1 will be lowered in energy and the other x raised. Similarly if we look only at its interaction with the p* orbital, we can expect to create two new orbitals, one lowered in energy y and one raised 3*. We cannot create four orbitals from three, because we cannot use the p orbital separately twice.

*

3

* x

pC

y

1

Fig. 1.32

A p orbital interacting independently with p and p* orbitals. (No attempt is made to represent the relative sizes of the atomic orbitals)

We can see in Fig. 1.32 that the orbital 1 has been created by mixing the p orbital with the p orbital in a bonding sense, with the signs of the wave function of the two adjacent atomic orbitals matching. We can also see that the orbital 3* has been created by mixing the p orbital with the p* orbital in an antibonding sense, with the signs of the wave functions unmatched. The third orbital that we are seeking, 2 in Fig. 1.33, is a combination created by mixing the p orbital with the p orbital in an antibonding sense and with the p* orbital in a bonding sense. We do not get the two orbitals, x and y in Fig. 1.32, but something half way between, namely 2 in Fig. 1.33. By adding x and y in this way, the atomic orbitals drawn to the left of the energy levels labelled x and y in Fig. 1.32 cancel each other out on C-2 and reinforce each other on C-1 and C-3, thereby creating the molecular orbital 2 in Fig. 1.33. We have of course arrived at the same picture for the molecular orbitals as that created from mixing the three separate p orbitals in Fig. 1.30. As before, the atomic orbitals in 2 are far enough apart in space for the molecular orbital 2 to have the same energy as the isolated p orbital in Fig. 1.33. It is a nonbonding molecular orbital (NBMO), as distinct from a bonding ( 1) or an antibonding ( 3*) orbital. Again we see for the allyl cation, radical and anion, that, as a result of the overlap in 1, the overall p energy of the allyl system has dropped relative to the sum of the energies of an isolated p orbital and of ethylene by 2E, which we know from Fig. 1.31 is 2  0.414 or something of the order of 116 kJ mol–1 of extra p bonding relative to that in

1 MOLECULAR ORBITAL THEORY

27

*

3

*

pC

2

E 1

Fig. 1.33

The allyl system by interaction of a p orbital with p and p* orbitals

ethylene. In the radical and anion, where 2 has either one or two electrons, and 3* is still empty, the energy drop is still 2E, because p and 2 are essentially on the same level. (It is not uncommon to express these drops in energy as a ‘gain’ in energy—in this sense, the gain is understood to be to us, or to the outside world, and hence means a loss of energy in the system and stronger bonding.) It is worth considering at this stage what the overall p electron distribution will be in this conjugated system. The electron population in any molecular orbital is derived from the square of the atomic orbital functions, so that the sine waves describing the coefficients in Fig. 1.34a are squared to describe the electron distribution in Fig. 1.34b. The p electron population in the molecule as a whole is then obtained by adding up the electron populations, allowing for the number of electrons in each orbital, for all the filled p molecular orbitals. Looking only at the p system, we can see that the overall p electron distribution for the cation is

–0.707

*

*2

3

3 0.500

0.500

–0.707 2

0.707

0.25

2 2

0.50

0.50

0

0.25

0.50

0.25

0.50

2 1

1 0.500

0.707

0.500

(a) Wave f unctions

Fig. 1.34

0.25

(b) Electron populations f or one electron

Wave functions and electron population for the allyl orbitals

28

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

derived from the squares of the coefficients in 1 alone, since this is the only populated p orbital. Roughly speaking, there is half an electron (2  0.52) on each of C-1 and C-3, and one electron (2  0.7072) on C-2. This is illustrated graphically in Fig. 1.35a. Since the nucleus has a charge of þ1, the excess charge on C-1 and C-3 is þ0.5, in other words the electron deficiency in the cation is concentrated at the two ends.

2

2 1

2 0.50

(a)

1.0

2 1

2 2

0.50

1.50

electron population in the allyl cation

Fig. 1.35

+2

(b)

1.0

1.50

electron population in the allyl anion

Total p electron populations in the allyl cation and anion

For the anion, the p electron population is derived by adding up the squares of the coefficients in both 1 and 2. Since there are two electrons in both orbitals, there are 1.5 electrons (2  0.52 þ 2  0.7072) roughly centred on each of C-1 and each of C-3, and one electron (2  0.7072) centred on C-2. This is illustrated graphically in Fig. 1.35b. Subtracting the charge of the nucleus then gives the excess charge as –0.5 on C-1 and C-3, in other words the electron excess in the anion is concentrated at the two ends. Thus the drawings of the allyl cation 1.4a and 1.4b illustrate the overall p electron population, and the corresponding drawings for the anion 1.6a and 1.6b do the same for that species. As we shall see later, the most important orbitals with respect to reactivity are the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). These are the frontier orbitals. For the allyl cation, the HOMO is 1, and the LUMO is 2. For the allyl anion, the HOMO is 2, and the LUMO is 3*. The drawings of the allyl cation 1.4a and 1.4b emphasise not only the overall p electron population but even better emphasise the electron distribution in the LUMO. Similarly, the drawings of the allyl anion 1.6a and 1.6b emphasise the HOMO for that species. It is significant that it is the LUMO of the cation and the HOMO of the anion that will prove to be the more important frontier orbital in each case. In radicals, the most important orbital is the singly occupied molecular orbital (SOMO). For the allyl radical this is the half-filled orbital 2. Once again, the drawings 1.5a and 1.5b emphasise the distribution of the odd electron in this orbital. One final detail with respect to this, the most important orbital, is that it is not quite perfectly nonbonding. Although C-1 and C-3 are separated in space, they do interact slightly in 2, as can be seen in the wire-mesh drawing of the nonlinear allyl system in Fig. 1.36, where the perspective allows one to see that the right hand

ψ1

ψ2 Fig. 1.36

ψ 3*

The p molecular orbitals of the allyl system

1 MOLECULAR ORBITAL THEORY

29

lobes, which are somewhat closer to the viewer, are just perceptibly repelled by the left hand lobes, and that neither of the atomic orbitals on C-1 and C-3 in 2 is a straightforwardly symmetrical p orbital. This orbital does not therefore have exactly the same energy as an isolated p orbital—it is slightly higher in energy. 1.4.2 Butadiene The next step up in complexity comes with four p orbitals conjugated together, with butadiene 1.8 as the parent member. As usual there is a  framework 1.9, which can be constructed from the 1s orbitals of the six hydrogen atoms and either the sp2 hybrids of the four carbon atoms or the separate 2s, 2px and 2py orbitals. The  framework has 18 bonding molecular orbitals filled with 36 electrons. Again we have two ways by which we may deduce the electron distribution in the p system, made up from the four pz orbitals and holding the remaining four electrons. Starting with the electron in the box with four p orbitals, we can construct Fig. 1.37, which shows the four wave functions, inside which the p orbitals are placed at the appropriate regular intervals. 4

2

H H

1 3

C

C H

1,

C

H H

1.9

1.8

We get a new set of orbitals,

H C

2,

3*,

and

4*,

each described by Equation 1.11 with four terms:

¼ c1 1 þ c2 2 þ c3 3 þ c4 4

0.371

3 nodes

1:11

–0.600 0.600 –0.371

*

4

0.600

0.600 –0.371 –0.371

2 nodes

*

LUMO

3

0.600

1 node

–0.600

HOMO

2

0.371

0 nodes

0.371 –0.371

0.600 0.600

0.371

1

Fig. 1.37

p Molecular orbitals of butadiene

30

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

The lowest-energy orbital 1 has all the c-values positive, and hence bonding is at its best. The nexthighest energy level has one node, between C-2 and C-3; in other words, c1 and c2 are positive and c3 and c4 are negative. There is therefore bonding between C-l and C-2 and between C-3 and C-4, but not between C-2 and C-3. With two bonding and one antibonding interaction, this orbital is also overall bonding. Thus the lowest-energy orbital of butadiene, 1, reasonably enough, has a high population of electrons in the middle, but in the next orbital up, 2, because of the repulsion between the wave functions of opposite sign on C-2 and C-3, the electron population is concentrated at the ends of the conjugated system. Overall, summing the squares of the coefficients of the filled orbitals, 1 and 2, the p electrons are, at this level of approximation, evenly spread over all four carbon atoms of the conjugated system. We can easily give numerical values to these coefficients, using the convention that the edge of the box is drawn one bond length out from the terminal carbon atoms. Treating the conjugated system as being linear, the coefficients are proportional to the sine of the angle, as defined by the position of the atom within the sine curve. The algebraic expression for this idea in the general case, and illustrated in Fig. 1.37 for the specific case of butadiene, with the atomic orbitals inscribed within the sine curves, is Equation 1.12: rffiffiffiffiffiffiffiffiffiffiffiffiffi 2 rjp sin 1:12 cjr ¼ nþ1 nþ1 giving the coefficient cjr for atom j in molecular orbital r of a conjugated system of n atoms (so that j and r ¼ 1, 2, 3, . . . , n). The expression in front of the sine function is the normalisation factor to make the squares of the coefficients add up to one. Thus, taking 2 for butadiene (r ¼ 2, n ¼ 4 and the sine curve is a full 2p): the normalisation factor for n ¼ 4 is 0.632, the angle for the first atom (j ¼ 1) is 2p/5, the sine of which is 0.951, and the coefficient c1 is the product 0.632  0.951 ¼ 0.600. Similarly, c2 is 0.371, c3 is –0.371 and c4 is –0.600. Large lists of coefficients for conjugated systems, some as easily calculated as butadiene above, some more complicated, have been published.18 As with the allyl system, other patterns are also present because of the symmetry of the molecule: for alternant conjugated systems (those having no odd-membered rings), the |c| values are reflected across a mirror plane placed horizontally, half way between 2 and 3*, and also across a mirror plane placed vertically, half way between C-2 and C-3. It is only necessary therefore to calculate four of the 16 numbers in Fig. 1.37, and deduce the rest from the symmetry. Alternatively, we can set up the conjugated system of butadiene by looking at the consequences of allowing two isolated p bonds to interact, as they will if they are held within bonding distance. It is perhaps a little easier to see on this diagram the pattern of raised and lowered energy levels relative to those of the p bonds from which they are derived. Let us first look at the consequence of allowing the orbitals close in energy to interact, which they will do strongly (Fig. 1.38). (For a brief account of how the energy difference between interacting orbitals affects the extent of their interaction, see the discussion of Equations 1.13 and 1.14 on p. 54.) The interactions of p with p and of p* with p* on the left create a new set of orbitals, a- d*. This is not the whole story, because we must also allow for the weaker interaction, shown on the right, of the orbitals further apart in energy, p with p*, which on their own would create another set of orbitals, w- z*. Mixing these two sets together, and allowing for the greater contribution from the stronger interactions, we get the set of orbitals (Fig. 1.39), matching those we saw in Fig. 1.37. Thus, to take just the filled orbitals, we see that 1 is derived by the interaction of p with p in a bonding sense ( a), lowering the energy of 1 below that of the p orbital, and by the interaction of p with p* in a bonding sense ( w), also lowering the energy below that of the p orbital. Since the former is a strong interaction and the latter weak, the net effect is to lower the energy of 1 below the p level, but by a little more than the amount ( in simple Hu¨ckel theory, illustrated as Ep in Fig. 1.26) that a p orbital is lowered below the p level (the dashed line  in Figs. 1.31, 1.32 and 1.33, called  in simple Hu¨ckel theory) in making the p bond of ethylene. However, 2 is derived from the interaction of p with p in an antibonding sense ( b), raising the energy above that of the p orbital, and by the interaction of p* with p in a bonding sense ( x), lowering it again. Since the former is a strong interaction

1 MOLECULAR ORBITAL THEORY

31

*

d

*

*

y

*

z

*

*

c

b

w

a

Fig. 1.38

x

Primary interactions of the p molecular orbitals of two molecules of ethylene. (No attempt is made to represent the relative sizes of the atomic orbitals)

and the latter weak, the net effect is to raise the energy of 2 above the p level, but not by as much as a p* orbital is raised above the p level in making the p bond of ethylene. Yet another way of looking at this system is to say that the orbitals 1 and 2 and the orbitals 3* and 4* mutually repel each other. We are now in a position to explain the well-known property that conjugated systems are often, but not always, lower in energy than unconjugated systems. It comes about because 1 is lowered in energy more than 2 is raised (E1 in Fig. 1.39 is larger than E2). The energy (E1) given out in forming 1 comes from the

*

4

*

* * LUMO

3

2

HOMO

E2 E1 1

Fig. 1.39

Energies of the p molecular orbitals of ethylene and butadiene by orbital interaction

32

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

overlap between the atomic orbitals on C-2 and C-3; this overlap did not exist in the isolated p bonds. It is particularly effective in lowering the energy of 1, because the coefficients on C-2 and C-3 are large. By contrast, the increase in energy of 2, caused by the repulsion between the orbitals on C-2 and C-3, is not as great, because the coefficients on these atoms are smaller in 2. Thus the energy lost from the system in forming 1 is greater than the energy needed to form 2, and the overall p energy of the ground state of the system ( 12 22) is lower. We can of course see the same pattern, and attach some very approximate numbers, using the geometrical analogy. This is illustrated in Fig. 1.40, which shows that 2 is raised above p by 0.382 and 1 is lowered below p by 0.618. The overall lowering in energy for the extra conjugation is therefore (2  0.618 þ 2  1.618) – 4 ¼ 0.472 or about 66 kJ mol–1.

*

4

* *

3

0.618 2

1.618 1

ethylene

Fig. 1.40

butadiene

Energies of the p molecular orbitals of ethylene and butadiene by geometry

Before we leave butadiene, it is instructive to look at the same p orbitals in wire-mesh diagrams (Fig. 1.41) to reveal more accurately what the electron distribution in the p molecular orbitals looks like. In the allyl system and in butadiene, we have seen more than one filled and more than one empty orbital in the same molecule. The  framework, of course, with its strong  bonds, has several other filled orbitals lying lower in energy than either 1 or 2, but we do not usually pay much attention to them when we are thinking of reactivity, simply because they lie so much lower in energy. In fact, we shall be paying special attention to the filled molecular orbital which is highest in energy ( 2, the HOMO) and to the unoccupied orbital of lowest energy ( 3*, the LUMO).

ψ1 Fig. 1.41

ψ2

ψ 3*

ψ 4*

The p molecular orbitals of butadiene in the s-trans conformation

1.4.3 Longer Conjugated Systems In extending our understanding to the longer linear conjugated systems, we need not go through all the arguments again. The methods are essentially the same. The energies and coefficients of the p molecular orbitals for all six systems from an isolated p orbital up to hexatriene are summarised in Fig. 1.42. The viewpoint in this drawing is directly above the p orbitals, which appear therefore to be circular. This is a common simplification, rarely likely to lead to confusion between a p orbital and an s orbital, and we shall use it through much of this book.

–0.500 –0.600

0.288 0.371

1.414 0.500

–0.418

0.600

0.418

0.500 0.600

–0.371

0.521

0.232

0.288

0.576

0.418

–0.521

0.500

1

0.232

–0.521

0.618

–0.500

0.500

0.521

–0.418

0.445

–0.371

0.600

–0.232

–0.521

0.232

1.247

–0.500

1

1.802

1.732

1.618

–0.707

–0.707 0.707

–0.371

–0.500

–0.232

0.418

0.232

0.418

–0.521

C

C

0.707

1.00

–0.576

0.576

–0.707

0.521

0.576

–0.418

0.445

–0.600

0.371

0.232

0.618 0.500 –0.371

0.600

1

–0.500

0.418 –0.500

0.500

0.707 0.707 1.414

0.600

0.500

0.600

–0.521

0.232

1.247

1.802 0.576

–0.232

0.521

0.500

1.732 0.288

0.521

0.232

–0.418

0.418

0.288 0.418

Fig. 1.42

0.521

0.371

0.500 1.618 0.371

–0.418

1

0.707

0.500

0.232

The energies and coefficients of the p molecular orbitals of the smaller conjugated systems

0.521

0.232

34

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

The longer the conjugated system, the lower the energy of 1, but each successive drop in energy is less than it was for the system with one fewer atoms, with a limit at infinite length of 2. Among the even-atom species, the longer the conjugated system, the higher the energy of the HOMO, and the lower the energy of the LUMO, with the energy gap becoming ever smaller. With a narrow HOMO—LUMO gap, polyenes allow the easy promotion of an electron from the HOMO to the LUMO, and the longer the conjugated system, the easier it is, making the absorption of UV and visible light ever less energetic. Most organic chemists will be happy with this picture, and most of the consequences in organic chemistry can be left at this level of understanding. At the extreme of an infinite polyene, however, simple Hu¨ckel theory reduces the HOMO—LUMO gap to zero, since the secants in diagrams like Fig. 1.40, would become infinitely small as they moved to the perimeter of the circle. Such a polyene would have equal bond lengths between each pair of carbon atoms, there would be no gap between the HOMO and the LUMO, and it would be a metallic conductor. This is not what happens— long polyenes, like polyacetylene, have alternating double (or triple) and single bonds, and their interconversion, which is the equivalent of the movement of current along the chain, requires energy. The theoretical description of this modification to simple Hu¨ckel theory is known by physicists as a Peierls distortion. It has its counterpart for chemists in the Jahn-Teller distortion seen, for example, in cyclobutadiene, which distorts to have alternating double and single bonds, avoiding the degenerate orbitals and equal bond lengths of square cyclobutadiene (see Section 1.5.2). The simple Hu¨ckel picture is evidently wrong at this extreme of very long conjugated systems. One way of appreciating what is happening is to think of the HOMO and the LUMO interacting more strongly when they are close in energy, just as the filled and unfilled orbitals of butadiene repel each other (Fig. 1.39), but more so. The residual gap, corresponding approximately to what is called by physicists the ‘band-gap energy’, is amenable to tuning, by attaching suitable substituents, just like any other HOMO—LUMO gap. Tailoring it has proved to be a basis for tuning the properties of optical devices.19 The process by which alternating double and single bonds might exchange places is strictly forbidden by symmetry, but occurs in practice, because the mismatch in symmetry of adjacent elements is disrupted by having an atom lacking an electron or carrying an extra electron in the chain.20 Thus an ‘infinite’ polyene can have long stretches of alternating single and double bonds interrupted by a length of conjugated p orbitals resembling a conjugated cation, radical or anion. Such ‘defects’ are chains of conjugated atoms, but like the chain of the polyene itself, the feature of equal bond lengths does not stretch infinitely along the whole ‘molecule’, as simple Hu¨ckel theory would suggest. It is limited in what physicists call ‘solitons’. In the soliton, there is no bond alternation at its centre, but bond alternation appears at greater distances out from its centre. Solitons provide a mechanism for electrical conduction along the chain, which is described as being ‘doped’. Unfortunately, the physicists’ nomenclature in the polymer area departs from that of the organic chemist, with expressions like ‘tight binding model’ meaning much the same as the LCAO approximation, ‘band structure’ for the stack of orbitals, ‘band gap’ for the HOMO—LUMO gap, ‘valence band’ for the HOMO, ‘Fermi energy’ meaning roughly the same as the energy of the HOMO, and the ‘conduction band’ meaning roughly the same as the LUMO. The physical events are of course similar, and the comparisons have been elegantly discussed.21 Such a breakdown in Hu¨ckel theory is not normally encountered in organic chemistry, where delocalisation can be expected to stretch undeterred by the length of the conjugated systems in what we might call ordinary molecules.

1.5

Aromaticity22

1.5.1 Aromatic Systems One of the most striking properties of conjugated organic molecules is the special stability found in the group of molecules called aromatic, with benzene 1.10 as the parent member and the longest established example. Hu¨ckel predicted that benzene was by no means alone, and that cyclic conjugated polyenes would have exceptionally low energy if the total number of p electrons could be described as a number of the form (4n þ 2), where n is an integer. Other 6p-electron cyclic systems such as the cyclopentadienyl anion 1.11 and the cycloheptatrienyl cation 1.12 belong in this category. The cyclopropenyl cation 1.13 (n ¼ 0),

1 MOLECULAR ORBITAL THEORY

35

[14]annulene 1.14 (n ¼ 3), [18]annulene 1.15 (n ¼ 4) and many other systems have been added over the years.23 Where does this special stability come from?

1.10

1.11

1.12

1.13 1.14

1.15

We can approach this question in much the same way as we approached the derivation of the molecular orbitals of conjugated systems. We begin with a  framework containing the C—C and C—H  bonds. We must then deduce the nodal properties of the p molecular orbitals created from six p orbitals in a ring. They are all shown both in elevation and in plan in Fig. 1.43. The lowest-energy orbital 1 has no node as usual, but because the conjugated system goes round the ring instead of spilling out at the ends of the molecule, as it did

–0.408

0.577

0.408

0.408

–0.408

–0.408

–0.289

–0.289

–0.289

–0.289

0.500

–0.500

–0.500

0.500

0.500

–0.500

0.500

–0.500

0.408

0.577

*

6

*

*

4

5

2

0.577

3

1

0.289

0.289

–0.289

–0.289 0.408 –0.577 0.408

0.408

0.408

0.408

0.408

Fig. 1.43

The p molecular orbitals of benzene

36

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

with the linear conjugated systems, the coefficients on all six atoms are equal. The other special feature is that there are two orbitals having the same energy with one node 2 and 3, because they can be created in two symmetrical ways, one with the node horizontal 2 and one with it vertical 3. Similarly, there are two orbitals, 4* and 5*, with the same energy having two nodes. Finally there is the one orbital, 6*, with three nodes. The size of the coefficients can be deduced from the position of the atoms within the sine curves, in the usual way. They support the assumption from symmetry that the amount of bonding in 2 equals that in 3. Thus the allyl-like overlap in the two halves of 2 has bonding between a large (–0.577) and two small (–0.289) lobes, whereas the antibonding interaction is between the two small lobes. The result is actually a lowering of energy for this orbital equal to that of the p bond in ethylene (). In 3 there is bonding between lobes of intermediate size (–0.500) and the interaction across the ring between the lobes of opposite sign is, like 2 in the allyl system, nonbonding rather than antibonding. Overlap between the p orbitals in ethylene (c ¼ 0.707) gives rise to a lowering of energy () worth one full p bond. Overlap between two lobes of the same sign in 3 with coefficients of –0.50 gives rise to half a p bond (0.7072 ¼ 0.500), and two such interactions comes again to one full p bond. The fully bonding overlap of the six orbitals (c ¼ 0.408) in 1 gives rise to two p bond’s worth of bonding. The total of p bonding is thus 2  4, which is two more  units than three isolated p bonds. Benzene is also lowered in p energy by more than the amount for three linearly conjugated p bonds: taking the numbers for hexatriene from Fig. 1.40, the total of p bonding is 2  (1.802 þ 1.247 þ 0.445) ¼ 7. The extra p bonding is the special feature of aromatic systems. The energies of the molecular orbitals can also be deduced by the same device, used for linear conjugated systems, of inscribing the conjugated system inside a circle of radius 2. There is no need for dummy atoms, since the sine curves go right round the ring, and the picture is therefore that shown in Fig. 1.44.

*

6

*

*

4

5

2 2

3

1

Fig. 1.44 The energies of the p molecular orbitals of benzene

It is also possible to find the source of aromatic stabilisation by looking at an interaction diagram. For benzene 1.10, one way is to start with hexatriene 1.16, and examine the effect of bringing the ends of the conjugated system, C-1 and C-6, within bonding distance (Fig. 1.45). Since we are only looking at the p energy, we ignore the C—H bonds, and the fact that to carry out this ‘reaction’ we would have to break two of them and make a C—C  bond in their place. In 1 and 3 the atomic orbitals on C-1 and C-6 have the same sign on the top surface. Bringing them within bonding distance will increase the amount of p bonding, and lower the energy of 1 and 3 in going from hexatriene to benzene. In 2 however, the signs of the atomic orbitals on C-1 and C-6 are opposite to each other on the top surface, and bringing them within bonding distance will be antibonding, raising the energy of 2 in going from hexatriene to benzene. The overall result is two drops in energy to one rise, and hence a lowering of p energy overall.

1 MOLECULAR ORBITAL THEORY

37 6 1

1.16

1.10

–0.521 3

0.445

–0.521

1

2

3

0.418

–0.418

0.232

0.232

Fig. 1.45

2

1

1.247

1.802 2

1

The drop in p energy in going from hexatriene to benzene

However, the ups and downs are not all equal as Fig. 1.45, which is drawn to scale, shows. The net lowering in p energy, relative to hexatriene, is actually only one  value, as we deduced above, not two. It is barely legitimate, but there is some accounting for this difference—the overlap raising the energy of 2 and lowering the energy of 3 is between orbitals with large coefficients, more or less cancelling one another out; however, the overlap between C-1 and C-6 in 1 is between orbitals with a small coefficient, making that drop close to 0.5 as shown in Fig. 1.45. One of the most striking artifacts of aromaticity, in addition to the lowering in energy, is the diamagnetic anisotropy, which is characteristic of these rings. Although known long before NMR spectroscopy was introduced into organic chemistry, its most obvious manifestation is in the downfield shift experienced by protons on aromatic rings, and perhaps even more vividly by the upfield shift of protons on the inside of the large aromatic annulenes. The theory24,25 is beyond the scope of this book, but it is associated with the system of p molecular orbitals, and can perhaps be most simply appreciated from the idea that the movement of electrons round aromatic rings is free, like that in a conducting wire, as epitomised by the equal C—C bond lengths. Like the conjugation in polyenes that we saw earlier, aromaticity does not stretch to infinitely conjugated cyclic systems, even when they do have (4nþ2) electrons. Just as long polyenes do not approach a state with equal bond lengths as the number of conjugated double bonds increases, the (4nþ2) rule of aromaticity breaks down, with bond alternation setting in when n reaches a large number. It is not yet clear what that number is with neither theory nor experiment having proved decisive. Early predictions26 that the largest possible aromatic system would be [22] or [26]annulene were too pessimistic, and aromaticity, using the ring-current criterion, probably peters out between [34] and [38]annulene.27 1.5.2 Antiaromatic Systems A molecule with 4n p electrons in the ring, with the molecular orbitals made up from 4n p orbitals, does not show this extra stabilisation. Molecules in this class that have been studied include cyclobutadiene 1.17

38

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

(n ¼ 1), the cyclopentadienyl cation 1.18, the cycloheptrienyl anion 1.19, cyclooctatetraene 1.20 and pentalene 1.21 (n ¼ 2), [12]annulene 1.22 (n ¼ 3) and [16]annulene 1.23 (n ¼ 4). We can see this most easily by looking at the molecular orbitals of square cyclobutadiene in Fig. 1.46. As usual, the lowest energy orbital 1 has no nodes, and, as with benzene and because of the symmetry, there are two exactly equivalent orbitals, 2 and 3, with one node. The bonding in 1 is between atomic orbitals with coefficients of 0.500, not only between C-1 and C-2, but also between C-2 and C-3, between C-3 and C-4 and between C-4 and C-1. If the overlap in 3 of benzene, which also has coefficients of 0.500, gives an energy-lowering of 1, then the overlap in 3 of cyclobutadiene should give twice as much energy-lowering, since there are twice as many bonding interactions (this makes an assumption that the p orbitals are held at the same distance by the  framework in both cases). In contrast, the bonding interactions both in 2 and 3 are exactly matched by the antibonding interactions, and there is no lowering of the energy below the line () representing the energy of a p atomic orbital on carbon. The molecular orbitals 2 and 3 are therefore nonbonding orbitals, and the net lowering in energy for the p bonding in cyclobutadiene is only 2  2. The energies of the four p orbitals are again those we could have deduced from the model inscribing the conjugated system in a circle, with the point of the square at the bottom. The total p stabilisation of 2  2 is no better than having two isolated p bonds—there is therefore no special extra stabilisation from the cyclic conjugation relative to two isolated p bonds. There is however less stabilisation than that found in a pair of conjugated double bonds—the overall p bonding in butadiene, taking values from Fig. 1.40, is 2  (1.618 þ 0.618) ¼ 4.472 and the overall p bonding in cyclobutadiene is only 2  2 making it less stable by 0.472.

0.500

–0.500

–0.500

0.500

*

4

2

3

2 0.500

0.500

–0.500

–0.500

Fig. 1.46

1

0.500

0.500

0.500

0.500

0.500

–0.500

0.500

–0.500

The p molecular orbitals of cyclobutadiene

1 MOLECULAR ORBITAL THEORY

1.17

1.18

39

1.19

1.20

1.21 1.22

1.23

We can reach a similar conclusion from an interaction diagram, by looking at the effect of changing butadiene 1.24 into cyclobutadiene 1.25 (Fig. 1.47). This time there is one drop in p energy and one rise, and no net stabilisation from the cyclic conjugation. As with benzene, we can see that the drop is actually less (from overlap of orbitals with a small coefficient) than the rise (from overlap of orbitals with a large coefficient). Thus cyclobutadiene is less stabilised than butadiene.

1.25

1.24

2 –0.600

2

0.618

1

1.618

0.600

0.371

0.371

Fig. 1.47

2

1

No change in p energy in going from butadiene to cyclobutadiene

There is much evidence that cyclic conjugated systems of 4n electrons show no special stability. Cyclobutadiene dimerises at extraordinarily low temperatures (>35K).28 Cyclooctatetraene is not planar, and behaves like an alkene and not at all like benzene.29 When it is forced to be planar, as in pentalene, it becomes unstable to dimerisation even at 0 C.30 [12]Annulene and [16]annulene are unstable with respect to electrocyclic reactions, which take place below 0 C.31 In fact, all these systems appear on the whole to be significantly higher in energy and more reactive than might be expected, and there has been much speculation that they are not only lacking in extra stabilisation, but are actually destabilised. They have been called ‘antiaromatic’32 as distinct from nonaromatic. The problem with this concept is what to make the comparisons with. We can see from the arguments above that we can account for the destabilisation

40

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

relative to conjugated p bonds—linear conjugation is more energy-lowering than the cyclic conjugation of 4n electrons, which goes some way to setting the concept of antiaromaticity on a physical basis. This argument applies to the thermodynamics of the system, which indirectly affects the reactivity. That 4n systems are unusually reactive is also explicable with an argument based on the frontier orbitals, as we shall see later—the HOMO is unusually high in energy for a neutral molecule, at the nonbonding  level for cyclobutadiene and the other uncharged cyclic hydrocarbons 1.18–1.23, significantly above the level of the HOMO of the linear conjugated hydrocarbons, and at the same time the LUMO is correspondingly low in energy. The prediction from the argument in Fig. 1.46 is that square cyclobutadiene ought to be a diradical with one electron in each of 2 and 3, on the grounds that putting a second electron into an occupied orbital is not as energy-lowering as putting the first electron into that orbital (see Section 1.2). This is not borne out by experiment, which has shown that cyclobutadiene is rectangular with alternating double and single bonds and shows no electron spin resonance (ESR) signal.33 We can easily explain why the rectangular structure is lower in energy than the square. So far, we have made all p bonds contribute equally one -value to every p bond. The difference in -values, and hence in the strengths of p bonds, as a function of how closely the p orbitals are held, can be dealt with by defining a standard  0 value for a C¼C double bond and applying a correction parameter k, just as we shall in Equation 1.16 for the effect of changing from a C¼C double bond to a C¼X double bond. Some values of k for different distances r can be seen in Table 1.1,34 which was calculated with 0 based on an aromatic double bond, rather than the double bond of ethylene, and by assuming that  is proportional to the overlap integral S.

Table 1.1 Variation of the correction factor k with distance r ˚) r (A

k

˚) r (A

k

1.20 1.33 1.35 1.397

1.38 1.11 1.09 1.00

1.45 1.48 1.54

0.91 0.87 0.78

In the rectangular structure of cyclobutadiene, the symmetry is lowered, and the molecular orbitals corresponding to 2 and 3 are no longer equal in energy (Fig. 1.48). The overall bonding in 1 is more or less the same as in the square structure—C-1 and C-2 (and C-3 and C-4) move closer together in 1, and the level of bonding is actually increased by about as much as the level of bonding is decreased in moving the

C-1

C-2

0.500

–0.500

0.500

–0.500

*

3 0.500

0.500 2

–0.500

–0.500 C-4

Fig. 1.48

C-3

0.500

0.500

0.500

0.500

1

The three lowest-energy p molecular orbitals of rectangular cyclobutadiene

1 MOLECULAR ORBITAL THEORY

41

other pairs apart. In the other filled orbital, 2, the same distortion, separating the pair (C-1 from C-4 and C-2 from C-3) will reduce the amount of p antibonding between them, and hence lower the energy. The corresponding argument on 3 will lead to its being raised in energy, and becoming an antibonding orbital. With one p orbital raised in energy and the other lowered, the overall p energy will be much the same, and the four electrons then go into the two bonding orbitals. This is known as a Jahn-Teller distortion, and can be expected to be a factor whenever a HOMO and a LUMO are very close in energy,35 as we have already seen with very long conjugated systems in Section 1.4.3. The square structure will be the transition structure for the interconversion of the one rectangular form into the other, a reaction that can be expected to be fairly easy, but to have a discernible energy barrier. Proper molecular orbital calculations support this conclusion.36 We must be careful in arguments like this, based only on the p system, not to get too carried away. We have not allowed for distortions in the  framework in going from the square to the rectangular structure, and this can have a substantial effect. 1.5.3 The Cyclopentadienyl Anion and Cation A slightly different case is provided by the cyclopentadienyl anion and cation. The device of inscribing the pentagon in a circle sets up the molecular orbitals in Fig. 1.49. The total of p bonding energy is 2  3.236 ¼ 6.472 for the anion, in which there are two electrons in 1, two electrons in 2, and two electrons in 3. The anion is clearly aromatic, since the open-chain analogue, the pentadienyl anion has only 2  2.732 ¼ 5.464 worth of p bonding (Fig. 1.40), the extra stabilisation being close to 1, and closely similar to the extent by which benzene is lower in energy than its open-chain analogue, hexatriene. The cyclopentadienyl anion 1.11, a 4nþ2 system, is well known to be exceptionally stabilised, with the pKa of cyclopentadiene at 16 being strikingly low for a hydrocarbon. The cation, however, has p-bonding energy of 2  2.618 ¼ 5.236, whereas its open-chain analogue, the pentadienyl cation, in which there are two electrons in 1 and two electrons in 2, has more p bonding, specifically 2  2.732 ¼ 5.464. The cyclopentadienyl cation 1.18, a 4n system, can be expected to be thermodynamically high in energy overall and therefore difficult to make, and so it is known to be. The cyclopentadienyl cation is not formed from its iodide by solvolysis under conditions where even the unconjugated cyclopentyl iodide ionises easily.37 In addition, the cyclopentadienyl cation ought to be especially electrophilic for kinetic reasons, since the energy of the LUMO is actually below the  level. It is also known to be a diradical in the ground state.38 The fluorenyl cation, the dibenz analogue of the cyclopentadienyl cation, however, does not appear to be significantly higher in energy than might be expected of a doubly benzylic cation held coplanar.39 0.60 4*

0.20

5* –0.51 –0.37 4*

1.618

0.63

*

5

0.37

–0.60

0.618 2

0.20

3

2 0.63

0.60 2 1

3 0.45 1

Fig. 1.49

The energies and coefficients of the p molecular orbitals of the cyclopentadienyl system

42

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

A striking difference between all the aromatic and all the antiaromatic systems is the energy difference between the HOMO and the LUMO. The aromatic systems have a substantial gap between the frontier orbitals, and the antiaromatic systems a zero gap in simple Hu¨ckel theory or a small gap if the Jahn-Teller distortion is allowed for. The difference in energy between the HOMO and the LUMO correlates with the hardness of these hydrocarbons as nucleophiles, and with some measures of aromaticity.40 For example, in antiaromatic rings with 4n electrons, there is a paramagnetic ring current, which is a manifestation of orbital effects, just like the diamagnetic ring currents from aromatic rings. The protons at the perimeter of a 4n annulene, when it is stable enough for measurements to be made, are at high field, and protons on the inside of the ring are at low field. The slow interconversion of the double and single bonds in antiaromatic systems means that there is no free movement of the electrons round the ring, and so any diamagnetic anisotropy is muted. At the same time, the near degeneracy of the HOMO and the LUMO in the 4n annulenes allows a low-energy one-electron transition between them with a magnetic moment perpendicular to the ring, whereas the aromatic systems, with a much larger energy gap between the highest filled and lowest unfilled orbitals do not have this pathway.41 Single electrons are associated with induced paramagnetic fields, as seen in the ESR spectra of odd electron systems. 1.5.4 Homoaromaticity42 The concept of aromaticity can be extended to systems in which the conjugated system is interrupted, by a methylene group, or other insulating structural feature, provided that the overlap between the p orbitals of the conjugated systems can still take place through space across the interruption. When such overlap has energy-lowering consequences, evident in the properties of the molecule, the phenomenon is called homoaromaticity. Examples are the homocyclopropenyl cation 1.26, the trishomocyclopropenyl cation 1.27, the bishomocyclopentadienyl anion 1.28 and the homocycloheptatrienyl cation 1.29. Each of these species shows evidence of transannular overlap, illustrated, and emphasised with a bold line on the orbitals, in the drawings 1.26b, 1.27b, 1.28b and 1.29b. The same species can be drawn without orbitals in localised structures 1.26a, 1.27a, 1.28a and 1.29a and with the drawings 1.26c, 1.27c, 1.28c and 1.29c showing the delocalisation. For simplicity, the orbital drawings do not illustrate the whole set of p molecular orbitals, which simply resemble in each case the p orbitals of the corresponding aromatic system. However, homoaromaticity appears to be absent in homobenzene (cycloheptatriene) 1.30a and in trishomobenzene (triquinacene) 1.31a, even though transannular overlap looks feasible. In both cases, the conventional structures 1.30a and 1.30c, and 1.31a and 1.31c are lower in energy than the homoaromatic structures 1.30b and 1.31b, which appear to be close to the transition structures for the interconversion.

H H H

H H 1.26a

1.26b

1.26c

1.27a

H

1.27b H

1.28a

1.28b

1.28c

1.29a

H

1.29b

1.27c H

1.29c

1 MOLECULAR ORBITAL THEORY

43

Homoantiaromaticity is even less commonly invoked. Homocyclobutadiene 1.32b and the homocyclopentadienyl cation 1.33b are close to the transition structures for the interconversion of cyclopentadiene 1.32a and bicyclo[2.1.0]pentene 1.32c and of the cyclohexatrienyl cation 1.33a and the bicyclo[3.1.0]hexenyl cation 1.33c. However, homoantiaromaticity does show up in these cases, in the sense that, unlike the interconversions in 1.30 and 1.31, neither of these interconversions is rapid. H H

1.30b

1.30a

1.30c

1.31b

1.31a

1.31c

H

H

H

H

1.32b

1.32a

1.33b

1.32c

1.33a

1.33c

We evidently have three situations, summarised in Fig. 1.50. In Fig. 1.50a, the homoaromatic structures 1.26c–1.29c, however they may be drawn, are at an energy minimum relative to the hypothetical localised structures 126a–129a, and there is an energy E associated with the cyclic delocalisation. In Fig. 1.50b, we have the localised structures 1.30a and c or 1.31a and c at minima, with the potentially homoaromatic systems 1.30b or 1.31b near or at the top of a shallow curve. Finally with the homoantiaromatic systems, the transition structures 1.32b or 1.33b are evidently high in energy with a greatly enlarged DE, the activation energy for the interconversion of the localised structures. We shall see this again in Chapter 6 with electrocyclic interconversions—those with aromatic transition structures like 1.30b and 1.31b are ‘allowed’, and those with antiaromatic transition structures like 1.32b and 1.33b are ‘forbidden’. The concept of homoaromaticity and homoantiaromaticity is sound. The nature of the overlap in the aromatic and antiaromatic systems is not dependent upon the atoms being directly bonded by the  framework. The  framework in an aromatic system has the effect of holding the p orbitals close,

44

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS 1.32b,1.33b

1.26a-1.29a

1.30b,1.31b

E

E

E

1.32c,1.33c

1.30c,1.31c 1.26c-1.29c (a) Homoaromatic systems

Fig. 1.50

1.32a,1.33a

1.30a,1.31a (b) Potentially homoaromatic systems

(c) Homoantiaromatic systems

Relative energies of some localised, homoaromatic and homoantiaromatic structures

making the p overlap strong in consequence. Separating the p orbitals by a methylene group, or any other insulating group, will usually weaken such overlap, and often cause it to be stronger on one surface than the other, but it does not necessarily remove it completely. In favourable cases it can be strong, and lead to noticeable effects. The factors affecting when it is and is not strong have been discussed.43 1.5.5 Spiro Conjugation In addition to  and p overlap, p orbitals can overlap in another way, even less effective in lowering the energy, but still detectable. If one conjugated system is held at right angles to another in a spiro structure, with the drawing 1.34 representing the general case and hydrocarbons 1.35 and 1.36 two representative examples, the p orbitals of one can overlap with the p orbitals of the other, as symbolised by the bold lines on the front lobes in the drawing 1.34. The overlap integral will be small, but if the symmetry matches, the interaction of the molecular orbitals can lead to new orbitals, raised or lowered in energy in the usual way. If the symmetry is not appropriate, the overlap will simply have no effect.

1.34

1.35

1.36

Take spiroheptatriene 1.35, with the unperturbed orbitals of each component shown on the left and right in Fig. 1.51. The only orbitals that can interact are 2 on the left and p* on the right; all the others having the wrong symmetry. For example, the interaction of the top lobes of 1 on the left and the upper p orbital of the p orbital on the right, one in front and one behind, have one in phase and one out of phase, exactly cancelling each other out; similarly with the front p lobes on the right and the upper and lower lobes of the front-right p orbital of 1 on the left. The two orbitals that do interact, 2 and p*, which have the same symmetry, create the usual pair of new orbitals, one raised and one lowered. Since there are only two electrons to go into the new orbitals, the overall energy of the conjugated system is lowered. The effect, DEs, is small, both because of the poor overlap, and because the two orbitals interacting are far apart in energy, which we shall see later is an important factor. Nevertheless, it is a general conclusion that if the total number of p electrons is a (4nþ2) number, the spiro system is stabilised, leading to the concept of spiroaromaticity.

1 MOLECULAR ORBITAL THEORY

45

*

4

* *

3

Es

2

1

1.35

Fig. 1.51

p Molecular orbitals of the ‘aromatic’ spiroheptatriene

There is equally a phenomenon of spiroantiaromaticity when the total number of p electrons is a 4n number, as in spirononatetraene 1.36 (Fig. 1.52). Here the only orbitals with the right symmetry to interact productively are the 2 orbitals on each side (ignoring the interaction of the unfilled 4* orbitals with each other, which has no effect on the energy because there are no electrons in these

*

4

*

*

3

4

*

3

Es* 2

2

Es

1

1

1.36

Fig. 1.52

p Molecular orbitals of the ‘antiaromatic’ spirononatetraene

46

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

orbitals). They lead to the usual two new orbitals, but since there are four electrons to go into them, the net effect is to raise the overall energy, with the bonding combination lowered in energy DEs less than the antibonding combination is raised DEs*. The splitting of the energy levels (DEs þ DEs*) has been measured to be 1.2 eV, and this molecule does show exceptional reactivity, in agreement with the increase in overall energy and the raising of the energy of the HOMO.44

1.6

Strained s Bonds—Cyclopropanes and Cyclobutanes

As we have just seen, it is possible to have some bonding even when the overlap is neither strictly head-on nor sideways-on. It is easily possible to retain much more of the bonding when the orbitals are rather better aligned than those in spiro-conjugated systems, as is the case in several strained molecules, epitomised by cyclopropane. 1.6.1 Cyclopropanes There are several ways to describe the  bonds in cyclopropane. The most simple is to identify the C—H bonds as coming from the straightforward sp3 hybrids on the carbon atoms and the 1s orbitals on the hydrogen atoms 1.37 in the usual way, and the C—C bonds as coming from the remaining sp3 hybrids imperfectly aligned 1.38. In more detail, these orbitals ought to be mixed in bonding and antibonding combinations to create the full set of molecular orbitals, but even without doing so we can see that C—C bonding is somewhere between  bonding (head-on overlap) and p bonding (sideways-on overlap). We can expect these bonds to have some of the character of each, which fits in with the general perception that cyclopropanes can be helpfully compared with alkenes in their reactivity and in their power to enter into conjugation. Thus cyclopropane 1.40 is much less reactive than ethylene 1.39 towards electrophiles like bromine, but it is much more reactive than ethane 1.41. Conjugation of a double bond or an aromatic ring with a cyclopropyl substituent is similar to conjugation with an alkene, but less effective in most cases. However, conjugation between a cyclopropane and an empty p orbital on carbon is more effective in stabilising the cyclopropylmethyl cation than conjugation with a double bond is in the allyl cation (see p. 88).

H

H

H

H

HH

H

H H

H

1.37

Br

1.39

f ast

1.38

Br

Br Br

H H

Br

Br

Br

Br

no reaction Br 1.40

slow

Br 1.41

Another way of understanding the C—C bonding, known as the Walsh description, emphasises the capacity of a cyclopropyl substituent to enter into p bonding. In this picture, which is like the picture of the bonding in ethane without using hybridisation (Fig. 1.22), the six C—H bonds are largely made up from the s orbitals on hydrogen and the s, px and pz orbitals on carbon, with the x, y and z axes redefined at each corner to be local x, y and z coordinates. The picture of C—H bonding can be simplified by choosing sp

1 MOLECULAR ORBITAL THEORY

47

hybridisation from the combination of the 2s and 2px orbitals, and using the three sp hybrids with the large lobes pointing outside the ring and the three pz orbitals to make up the CH bonding orbitals (Fig. 1.53). Some of these orbitals contribute to C—C bonding, notably the CH,pCC orbital, but the major contributors are the overlap of the three sp hybrids with the large lobes pointing into the ring, which produce one bonding combination CC, and the three py orbitals, which combine to produce a pair of bonding orbitals pCC, each with one node, and with coefficients to make the overall bonding between each of the C—C bonds equal.

H

H H

H

H

H CC

py

H H H H

CC

H

H

H

H

H

py

H

H H

CH

H H

CH

H

H

H

H H

H

H

CC

H

H

H H

H

H

CH, CC

H

H

H H H

H

H

H

H CH

H H

CH

H

H

H

H H

H

H CH

H H

Fig. 1.53

H

A simplified version of the occupied Walsh orbitals of cyclopropane

The advantage of this picture is that it shows directly the high degree of p bonding in the C—C bonds, and gives directly a high-energy filled p orbital, the pCC orbital at the top right, largely concentrated on C-1, and with the right symmetry for overlap with other conjugated systems, as we shall see in Section 2.2.1. A remarkable property of cyclopropanes is that they are magnetically anisotropic, rather like benzene— but with the protons coming into resonance in their NMR spectra at unusually high field, typically 1 ppm upfield of the protons of an open-chain methylene group. For 1H NMR spectroscopy, this is quite a large effect, and it is also strikingly in the opposite direction from that expected by the usual analogy drawn between a cyclopropane and an alkene. The anisotropy45 is most likely a consequence of the presence of overlap from three sets of orbitals having a total of six electrons in them. These could be seen as the 1s sp3 orbitals contributing to the C—H bonds 1.37, which we could have mixed to get a set of orbitals resembling

48

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

the p orbitals of benzene. Alternatively, turning to Fig. 1.53, the pair of CH orbitals just below the highest occupied orbitals, together with the CH,pCC orbital, clearly have the same nodal pattern as the filled p orbitals of benzene (Fig. 1.43), and the pattern is repeated in the three filled orbitals of lowest energy. This pattern of orbitals is associated, as with benzene, with the capacity to support a ring current, but, in contrast to benzene, the derived field places the protons in cyclopropanes in the region experiencing a reduced magnetic field 1.42. The same explanation, although we shall not show the molecular orbitals, has been advanced to account for the small difference in chemical shift between the axial and equatorial protons in cyclohexanes, detectable in cyclohexane itself by freezing out at –100 C the otherwise rapid interconversion of the two chair conformations.46 The axial protons come into resonance upfield at d1.1 and the equatorial protons downfield at d1.6. It is possible that the three axial C—H bonds on each side overlap in a p sense to create a trishomoaromatic system, with a diamagnetic ring current which places the axial protons in the reduced magnetic field 1.43, and the equatorial protons in the enhanced magnetic field 1.44. 0.3 applied field

H H

1.1

1.6

H

H H

H

H

H H

H

H

H

H

1.42

H

H

H

H

H 1.43

1.44

1.6.2 Cyclobutanes It is not necessary to go through the whole exercise of setting up the molecular orbitals of cyclobutanes, which show many of the same features as cyclopropanes, only less so. Cyclobutanes also show enhanced reactivity over simple alkanes, but they are less reactive towards electrophiles, and cyclobutyl groups are less effective as stabilising substituents on electron-deficient centres than cyclopropyl groups. The most striking difference, however, is that the protons in cyclobutanes come into resonance in their 1 H NMR spectra downfield of the protons from comparable methylene groups in open-chain compounds.47 The effect is not large, typically only about 0.5 ppm, with cyclobutane itself, for example, at d1.96 in contrast to the average of the cyclohexane signals at d1.44. In a cyclobutane, four sets of C—H bonds are conjugated, and the pattern of orbitals will be similar to those of cyclobutadiene (Fig. 1.46). Again there will be two sets, and the top two of each set will be degenerate. The ring current is therefore in the opposite direction, adding to the applied field at the centre of the ring, and the protons experience an enhanced field 1.45. The effect may be rather less in cyclobutanes than in cyclopropanes, because the cyclobutane ring is flexible, allowing the ring to buckle from the planar structure 1.45, and the C—H bonds thereby avoid the full eclipsing interactions inevitable in cyclopropanes, and compensated there by the aromaticity they create. applied field

H H

H

H H

H

H

1.45

H

1 MOLECULAR ORBITAL THEORY

1.7

49

Heteronuclear Bonds, C—M, C—X and C=O

So far, we have been concentrating on symmetrical bonds between identical atoms (homonuclear bonds) and on bonds between carbon and hydrogen. The important interaction diagrams were constructed by combining atomic orbitals of more or less equal energy, and the coefficients, c1 and c2, in the molecular orbitals were therefore more or less equal in magnitude. It is true that C—H bonds, both in the picture without hybridisation (Fig. 1.14) and in the picture with hybridisation (Fig. 1.20), involve the overlap of atomic orbitals of different elements, but the difference in electronegativity, and hence in the energy of the atomic orbitals of these two elements, was not significant at the level of discussion used in the earlier part of this chapter. In other cases where we have seen orbitals of different energy interacting, we have either ignored the consequences, because it did not make any significant difference to the discussion at that point, or we have deferred discussion until now. The interaction of orbitals of different energy is inescapable when we come to consider molecules, like methyl chloride and methyllithium, with single bonds to other elements, and molecules with double bonds to electronegative elements like oxygen. As we have mentioned in passing, atomic orbitals of different energy interact to lower (and raise) the energy of the resultant molecular orbitals less than orbitals of comparable energy. 1.7.1 Atomic Orbital Energies and Electronegativity There are two standard ways of assessing the relative energies of the orbitals of different elements. One is to use one or another of the empirical scales of electronegativity. Pauling’s, which is probably the most commonly used, is empirically derived from the differences in dissociation energy for the molecules XX, YY and XY. Several refinements of Pauling’s scale have been made since it first appeared in 1932, and other scales have been suggested too. A good recent one, similar to but improving upon Pauling’s, is Allen’s,48 drawn to scale in Fig. 1.54, along with values assigned by Mullay49 to the carbon atoms in methyl, vinyl and ethynyl groups. H and First Row 0.91

1.58 2.05 2.30 2.54

Hybrids on C

Li

Be B H C

3.07

N

3.61

O

4.19

F

Fig. 1.54

Second Row 0.87

Na

1.29

Mg

1.61

Al

1.92

Si

2.3

sp3

2.25

P

2.6

sp2

2.59

S

2.87

Cl

3.1

Third Row 0.73

K

1.03

Ca

1.76

Ga

1.99 2.21 2.42 2.69

Ge As Se Br

Fourth Row 0.71 0.96

Rb Sr

1.66 1.82 1.98 2.16 2.36

In Sn Sb Te I

sp

Allen electronegativity values and Pauling-based values for carbon hybrids

In spite of the widespread use of electronegativity as a unifying concept in organic chemistry, the electronegativity of an element is almost never included in the periodic table. Redressing this deficiency, Allen strikingly showed his electronegativity scale as the third dimension of the periodic table, and his vivid picture is adapted here as Fig. 1.55.

50

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS F

O

N Cl

H

Se

P B

I

As Si Al

Be

Br

S

C

Te

Ge

Sb Sn

Ga In

Mg Li Ca

Na

Sr

K Rb

Fig. 1.55

Electronegativity as the third dimension of the periodic table (adapted with permission from L. C. Allen, J. Am. Chem. Soc., 1989, 111, 9003. Copyright 1989 American Chemical Society)

An alternative and more direct way of getting a feel for the relative energies of atomic orbitals is to take them from calculations, reproduced to scale for the first and second row elements in Fig. 1.56.50 The soundness of these energies is backed up by measurements of the ionisation potentials (IPs), which measure the energy needed to remove an electron from the element. These calculations rank the elements in much the same order, although with a couple of explicable anomalies, which need not concern us here. This figure separates the s and the p orbitals, but we can easily calculate the relative energies of hybrid orbitals on any of the elements from group three to group eighteen. The ranking of the hybrids for carbon, nitrogen, oxygen and fluorine is given in Fig. 1.57 on the same scale and with the s and p orbital energies carried over for comparison. The two pictures, the empirical values of Fig. 1.54 and the calculated values of Fig. 1.56, show that the relative positions of the elements on these scales are essentially the same. However, the electronegativity scale shows the methyl, vinyl and ethynyl groups below that for the 1s orbital on hydrogen, whereas the atomic orbital energies place hydrogen in the middle of the range for the different kinds of carbon. This uncertainty provides fuel for debate about which way C—H bonds are polarised, and about whether a C—H bond or a C—C bond is the better electron donor, but the main conclusion is that the energies of the atomic orbitals for C and H are very comparable, and the bond between them is not strongly polarised. 1.7.2 C—X s Bonds We are now ready to construct an interaction diagram for a bond made by the overlap of atomic orbitals with different energies. Let us take a C—Cl  bond, in which the chlorine atom is the more electronegative element. Other things being equal, the energy of an electron in an atomic orbital on an electronegative element is lower than that of an electron on a less electronegative element (Fig. 1.56). As usual, we can tackle the problem with or without using the concept of hybridisation. The C—X bond in a molecule such as methyl chloride, like the C—C bond in ethane (Fig. 1.22), has several orbitals contributing

1 MOLECULAR ORBITAL THEORY

H

Li p s

51

B

Be

O

N

C

Na

F

–5.4 p

–6.0 p –5.7

s

–5.2 s

s

–9.4 p

s

Al

Mg

P

Si

S

Cl

–3.5

p

–12.9 p

p

–11.3

–15.9

–9.8 p

s p

–19.4

–7.8 p

s

–14.7

s

p –6.0

–10.7

–13.6 s

–7.6

p

–15.0

–18.6

s

–20.9

–25.6

s

s

–13.7

–18.4 s

s

–11.7

–25.3

–32.4

s

–40.1

Fig. 1.56 Valence atomic orbital energies in eV (1 eV ¼ 96.5 kJ mol–1 ¼ 23 kcal mol–1)

H

–13.6

C

1s

N

–10.7 –12.9 –13.6 –15.1

p sp3 sp2 sp

–19.4

s

O

–12.9

p

–16.1 –17.1 –19.3

sp3 sp2 sp

–25.6

s

–15.9

p

–20.0 –21.4

sp3 sp2

–24.2

sp

–32.4

Fig. 1.57

F

–18.6

p

–24.4 –25.8

sp3 sp2

–29.4

sp

–40.1

s

s

Atomic orbital energies for hybrid orbitals in eV

to the force which keeps the two atoms bonded to each other; but, just as we could abstract one of the important pair of atomic orbitals of ethane and make a typical interaction diagram for it (Fig. 1.24), so can we now take the corresponding pair of orbitals from the set making up a C—Cl  bond. The important thing for the moment is the comparison between the C—C orbitals and the corresponding C—Cl orbitals. What we learn about the properties of C—Cl bonds by looking at this one orbital will be the same as we would have learned, at much greater length, from the set as a whole. Alternatively, we can use an interaction diagram for an sp3 hybrid on carbon and an sp3 hybrid on chlorine, and compare the result with

52

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

the corresponding interaction of two sp3 hybrids on carbon. Both pictures will be very similar, and we can learn the same lesson from either. In making a covalent bond between carbon and chlorine from the 2px orbital on carbon and the 3px orbital on chlorine, we have an interaction (Fig. 1.58) between orbitals of unequal energy (–10.7 eV for C and –13.7 eV for Cl, from Fig. 1.56). The interaction diagram in Fig. 1.58 could equally have been drawn using sp3 hybrids on carbon and chlorine in place of the p orbitals. The hybrids have lower energies (–12.9 eV for carbon and –16.6 eV for chlorine), because they have some s character, and the difference in energy between them is greater, but the rest of the story and our conclusions will be unchanged. Alternatively we could use Allen’s electronegativities, which effectively take the involvement of s orbitals in hybrids into account.

*C—Cl

px EC

Cl

Ei Cl

px

ECl C—Cl

Cl

Fig. 1.58 A major part of the C—Cl  bond

On account of the loss of symmetry, the chlorine atom has a larger share of the total electron population. In other words, the coefficient on chlorine for the bonding orbital, CCl is larger than that on carbon. It follows from the requirement that the sum of the squares of all the c-values on any one atom in all the molecular orbitals must equal one, that the coefficients in the corresponding antibonding orbital, *CCl must reverse this situation: the one on carbon will have to be larger than the one on chlorine. What we have done in Fig. 1.58 is to take the lower-energy atomic orbital on the right and mix in with it, in a bonding sense, some of the character of the higher-energy orbital on the left. This creates the new bonding molecular orbital, which naturally resembles the atomic orbital nearer to it in energy more than the one further away. We have also taken the higher-energy orbital and mixed in with it, in an antibonding sense, some of the character of the lower-energy orbital. This produces the antibonding molecular orbital, which more resembles the atomic orbital nearer it in energy. When the coefficients are unequal, the overlap of a small lobe with a larger lobe does not lower the energy of the bonding molecular orbital as much as the overlap of two atomic orbitals of more equal size. ECl in Fig. 1.58, is not as large as E in Fig. 1.24. Using this interaction, and others taking account of the same factors, we can set up a set of filled orbitals for methyl chloride, represented schematically in Fig. 1.59a, along with the lowest of the unoccupied orbitals. As with other multi-atom molecules, several orbitals contribute to C—Cl bonding, with more bonding than antibonding from the overlap of the s orbitals, but probably nearly equal bonding and antibonding from the orbitals having p bonding between the carbon and the chlorine. The same degree of bonding can be arrived at by using the hybrid orbitals shown in Fig. 1.59b, where all of the C—Cl bonding comes from the sp3 hybrids. We might be tempted at this stage to say that we have a weaker bond than we had for a C—C bond, but we must be careful in defining what we mean by a weaker bond in this context. Tables of bond strengths give the C—Cl bond a strength, depending upon the rest of the structure, of something like 352 kJ mol–1 (84 kcal mol–1), whereas a comparable C—C bond strength is a little lower at 347 kJ mol–1 (83 kcal mol–1). Only part of the

1 MOLECULAR ORBITAL THEORY

53 H

H

LUMO

C

Cl

C

Cl

3

sp *CCl H H

H

*CCl

H H

Cl

C

LUMO

H C

Cl

C H

H H

H

C

Cl

H

H Cl

C H

H

H

CCl

H

H

Cl

C

H

Cl sp3CCl

H

H H

H

H

H

H C

C

H

Cl

Cl H (b) the sp3-hybridised orbitals of the C—Cl bond

H

(a) without using hybridisation

Fig. 1.59 The filled molecular orbitals and the lowest unfilled molecular orbital of methyl chloride

C—Cl bond strength represented by these numbers comes from the purely covalent bonding given by 2ECl in Fig. 1.58. The other part of the strength of the C—Cl bond comes from the electrostatic attraction between the high electron population on the chlorine atom and the relatively exposed carbon nucleus. We usually say that the bond is polarised, or that it has ionic character. This energy is related to the value Ei in Fig. 1.58, as we can readily see by using an extreme example: suppose that the energies of the interacting orbitals are very far apart (Fig. 1.60, where the isolated orbitals are the 3s orbital on Na and a 2p orbital on F, with energies of –5.2 and –18.6 eV); the overlap will be negligible, and the new molecule will now have almost entirely isolated orbitals in which the higher-energy orbital has given up its electron to the lowerenergy orbital. In other words, we shall have a pair of ions. There will be no covalent bonding to speak of, and Na

Na 3s

Ei

F

Fig. 1.60

2p F

A much oversimplified ionic bond

54

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

the drop in energy in going from the pair of radicals to the cation plus anion is now Ei in Fig. 1.60, which, we can see, is indeed related to Ei in Fig. 1.58. The C—Cl bond is strong, if we try to break it homolytically to get a pair of radicals, and a comparable — C C bond is marginally easier to break this way. This is what the numbers 352 and 347 kJ mol–1 refer to. In other words, EC þ ECl in Fig. 1.58 is evidently greater than 2E in Fig. 1.24. However, it is very much easier to break a C—Cl bond heterolytically to the cation (on carbon) and the anion (on chlorine) than to cleave a C—C bond this way. In other words, 2ECl in Fig. 1.58 is less than 2E in Fig. 1.24. The important thing to remember is that when two orbitals of unequal energy interact, the lowering in energy is less than when two orbitals of very similar energy interact. Conversely, when it comes to transferring an electron, the ideal situation has the electron in a high-energy orbital being delivered to the ‘hole’ in a low-energy orbital. In a little more detail, the extent of the energy lowering ECl is a function not only of the difference in energy Ei between the interacting orbitals, but also of the overlap integral S. The overlap integrals for forming a C—N, a C—O or a C—F bond are essentially, at least in the region for the normal internuclear distances and outwards, parallel to the overlap integral for the formation of a C—C bond (Figs. 1.13b and ˚ to shorter internuclear distances for each element. This is 1.23b), but displaced successively by about 0.2 A because the orbitals of the first-row elements have similar shapes, but the electrons are held more tightly in to the nucleus of the more electronegative elements, and the more electronegative they are the tighter they are held. This simply means that the atoms must be a little closer together to benefit from the overlap. We have already seen that when orbitals of identical energy interact, the energy lowering is roughly proportional to S (see p. 4). When they are significantly different in energy, however, it is roughly proportional to S2. They are also, as we have seen above, inversely proportional to the energy difference Ei. The equations for the energies of the lowered and raised orbitals in Fig. 1.58, ECCl and E*CCl, respectively, take the form shown in Equations 1.13 and 1.14. ECCl ¼ EpCl þ

ð CCl  EpCl SCCl Þ 2 EpCl –EpC

1:13

ECCl ¼ EpC þ

ð CCl  EpC SCCl Þ 2 EpC –EpCl

1:14

Clearly a full expression for the overall electronic energy is a complex one if it is to take account of the changes between these expressions and those in Equations 1.4 and 1.5 for the energies when the interacting orbitals are degenerate. A picture of the electron distribution in the  orbitals between carbon and chlorine is revealed in the wiremesh diagrams in Fig. 1.61, which show one contour of the CCl and *CCl orbitals of methyl chloride. Comparing these with the schematic version in Fig. 1.58, we can see better how the back lobe on carbon in CCl overlaps with the s orbitals on the hydrogen atoms, and that the front lobe in *CCl wraps back behind

σ CCl Fig. 1.61

σ *CCl

The major C—Cl bonding orbital and the LUMO for methyl chloride

1 MOLECULAR ORBITAL THEORY

55

the carbon atom to include a little overlap to the s orbitals of the hydrogen atoms. We need to remove an oversimplification and delve a little more into detail in order to see how this comes about. The pictures in Fig. 1.59a are shown as though the lowest-energy orbitals were made up from the interaction only of s orbitals with each other. Likewise the next higher orbitals are made up only of the interactions of p orbitals on the carbon and chlorine, and necessarily s orbitals on hydrogen. These interactions are certainly the most important, and the simplification works, because the s orbitals on carbon and chlorine are closer in energy to each other than they are to each other’s p orbitals, and vice versa, as shown in Fig. 1.62a. However, the direct interactions of s with s and p with p are only a first-order treatment, and a second-order treatment has to consider that the s orbital on carbon can interact quite strongly with the px orbital on chlorine, and there will even be a small interaction from the px orbital on carbon and the s orbital on chlorine. This complication is similar to something we saw earlier with methylene, with the allyl system and with butadiene (Figs. 1.16. 1.32 and 1.38), where we used the device for constructing molecular orbitals, first looking at the strong interaction of orbitals close in energy, and then modified the result by allowing for the weaker interactions of orbitals further apart in energy. The true mixing of orbitals for methyl chloride would still leave the lowest energy orbital looking largely like the mix of s with s, but there would be a contribution with some p character, in inverse proportion to the energy difference between the s and p orbitals. It is the presence of some p character in the orbitals contributing to the *CCl orbital in Fig. 1.61 that allows the outer counters to reach round behind the carbon atom. We saw the same feature earlier in the picture of an sp3 hybrid (Fig. 1.19), where the cause was essentially the same—the mixing of s and p orbitals in optimum proportions for lowering the overall energy. The problem of identifying sensible mixes of orbitals would have been much more acute had we used methyl fluoride instead of methyl chloride. With methyl fluoride, the 2s orbital on carbon is almost identical in energy with the 2p orbitals on fluorine, as shown in Fig. 1.62b. The 2px orbital from that element and the 2s orbital on carbon have the right symmetry, and their interaction would provide the single strongest contribution to C—F bonding. Continuing from here to make a full set of the molecular orbitals for methyl fluoride, mixing in a small contribution from the p orbital on carbon, for example, would not have made as tidy and understandable a picture as the one for methyl chloride in Fig. 1.59. Most strikingly, the lowestenergy orbital would be an almost pure, undisturbed s orbital on fluorine, and there would be correspondingly little of this orbital to mix in with the others.

–3.5 p Li –5.4 s

Li

pC –10.7

pC –10.7

pC –10.7

–13.7 p

Cl

sC –19.4

sC –19.4

–18.6 p F

sC –19.4

–25.3 s Cl

–40.1 s F

(a) Methyl chloride

(b) Methyl f luoride

(c) Methyllithium

Fig. 1.62 Some of the major interactions contributing to C—Cl bonding for MeCl, to C—F bonding for MeF, and to C—Li bonding for MeLi

56

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

1.7.3 C—M s Bonds When the bond from carbon is to a relatively electropositive element like lithium, the same problems can arise—with methyllithium the most strongly interacting orbitals contributing to the C—Li bond (Fig. 1.62c) are the 2s orbital on lithium and the 2px orbital on carbon. The pictorial set of molecular orbitals therefore is not one in which you can see immediately which atomic orbitals make the major contribution to which molecular orbitals. The interaction between a 2s orbital on lithium and a 2px orbital on carbon has the form shown in Fig. 1.63. The energy of the lithium 2s orbital is –5.4 eV, making the carbon atom, with a 2p orbital at –10.7 eV, the more electronegative atom. The bonding orbital LiC is polarised towards carbon, and the antibonding *LiC towards lithium. Organic chemists often refer to organolithium compounds as anions. Although there evidently is some justification for this way of thinking, it is as well to bear in mind that they are usually highly polarised covalent molecules. Furthermore, they are rarely monomeric, almost always existing as oligomers, in which the lithium is coordinated to more than one carbon atom, making the molecular orbital description below severely over-simplified

*LiC

Li

Li

sLi

px

LiC

Fig. 1.63

Li

A contributory part of the Li—C  bond

The filled and one of the unfilled orbitals for monomeric methyllithium are shown in Fig. 1.64. The lowest energy orbital is made up largely from the 2s orbital on carbon and the 1s orbitals on hydrogen, with only a little mixing in of the 2s orbital of lithium and even less of the 2p. The next two up in energy are largely p mixes of the 2pz and 2py orbitals on carbon with a little of the 2pz and 2py on lithium, and, as usual, the 1s orbitals on hydrogen. The 2pz and 2py orbitals on lithium have a zero overlap integral with the 2s orbital on carbon, and this interaction, although between orbitals close in energy (Fig. 1.62c), makes no contribution. Then come the two orbitals we have seen in Fig. 1.63: the 2px orbital on carbon interacting productively with the 2s orbital on lithium, giving rise to the highest of the occupied orbitals CLi, which has mixed in with it the usual 1s orbitals on hydrogen and a contribution from the 2px orbital on lithium, symbolised here by the displacement of the orbital on lithium towards the carbon. The next orbital up in energy, the lowest of the unfilled orbitals, is its counterpart *CLi, largely a mix of the 2s and the 2px orbital of lithium, symbolised again by the displacement of the orbital on lithium away from the carbon, with a little of the 2px orbital of carbon out of phase. A picture of the electron distribution in the frontier  orbitals between carbon and lithium is revealed in the wire-mesh diagrams in Fig. 1.65, which show one contour of the CLi and *CLi orbitals of methyllithium, unrealistically monomeric and in the gas phase. Comparing these with the schematic version in Fig. 1.64, we can see better how the s and px orbitals on lithium mix to boost the electron population between the nuclei in CLi, and to minimise it in *CLi. The HOMO, CLi, is used on the cover of this book.

1 MOLECULAR ORBITAL THEORY

57 H

H

H C

LUMO

H

*CLi

3

Li

C

sp *CLi

Li

H

H

H

H

H C

H H

Li CLi

H

C

H

H

H

HOMO

H C

Li

H

Li

sp3CLi

C

Li

H

H H C

Li

H (a) without using hybridisation

Fig. 1.64

(b) the sp3-hybridised orbitals of the C—Li bond

The filled and one of the unfilled molecular orbitals of methyllithium

σ CLi Fig. 1.65

σ *CLi The HOMO and LUMO for methyllithium

1.7.4 C=O p Bonds Setting up the molecular orbitals of a C¼O p bond is relatively straightforward, because the p orbitals in the p system in Hu¨ckel theory are free from the complicating effect of having to mix in contributions from s orbitals. The px orbital on oxygen is placed in Fig. 1.66 at a level somewhat more than 1 below that of the px orbital on carbon, although not to scale. The energy of a p orbital on oxygen is –15.9 eV and that on carbon –10.7 eV (Fig. 1.56). As with p bonds in general, the raising of the p* and lowering of the p orbitals above and below the atomic p orbitals is less than it was for a C—O  bond, and less than the corresponding p bond between two carbon atoms. Both the pC¼O and the p*C¼O orbitals are now lower in energy than the pC¼C and p*C¼C orbitals, respectively, of ethylene, which by definition are 1 above and 1 below the  level. The polarisation of the carbonyl group is away from carbon towards oxygen in the bonding orbital, and in the opposite direction in the antibonding orbital, as usual. The wire-mesh pictures in Fig. 1.67 show more realistically an outer contour of these two orbitals in formaldehyde, and the plots in Fig. 1.68 show the electron distribution in more detail. Note that in these pictures it appears that the p electron population in the bonding orbital is nearly equal on oxygen and on carbon. This is not the case, as shown by the extra contour around the oxygen atom in the plot in Fig. 1.68. The electron

58

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS 1 O

LUMO

*C=O

pC

1 pO O

HOMO

Fig. 1.66

π Fig. 1.67

C=O

A C¼O p bond

π*

Wire-mesh plot of the p and p* orbitals of formaldehyde

π Fig. 1.68

O

π*

Electron population contours for the p and p* orbitals of formaldehyde

1 MOLECULAR ORBITAL THEORY

59

distribution around the oxygen atom is simply more compact, as a consequence of the higher nuclear charge on that atom. This is another way in which the conventional lobes as drawn in Fig. 1.66 are misleading. There is no set of fundamentally sound values for  and  to use in Hu¨ckel calculations with heteroatoms. Everything is relative and approximate. The values for energies and coefficients that come from simple calculations on molecules with heteroatoms must be taken only as a guide and not as gospel. In simple Hu¨ckel theory, the value of  to use in a calculation is adjusted for the element in question X from the reference value for carbon 0 by Equation 1.15. Likewise, the  value for the C¼C bond in ethylene 0 is adjusted for C¼X by Equation 1.16. X ¼0 þ hX  0

1:15

 CX ¼kCX  0

1:16

The adjustment parameters h and k take into account the trends in Figs. 1.54–1.56 and the changes in the overlap integrals for making C—X bonds discussed on p. 54, but are not quantitatively related to those numbers. Instead, values of h for some common elements and of k for the corresponding C¼X p bonds (Table 1.2) have been recommended for use in Equations 1.15 and 1.16.51 They are only useful to see trends. Parameters for simple Hu¨ckel calculations for p bonds with heteroatoms

Table 1.2

Element B C N

C

N

N

O

C

N

h

k

Element

–0.45

0.73

0

1

Si

0.51

1.02

P

1.37

0.89

P

0.97

1.06

S

O

Si

P P

S

h

k

0

0.75

0.19

0.77

0.75

0.76

0.46

0.81

O

O

2.09

0.66

S

S

1.11

0.69

F

F

2.71

0.52

Cl

Cl

1.48

0.62

As with single bonds to electronegative heteroatoms, it is easier to break a C¼O bond heterolytically and a C¼C bond homolytically. Some reminders of a common pattern in chemical reactivity may perhaps bring a sense of reality to what must seem, so far, an abstract discussion: nucleophiles readily attack a carbonyl group but not an isolated C¼C double bond; however, radicals readily attack C¼C double bonds, and, although they can attack carbonyl groups, they do so less readily. 1.7.5 Heterocyclic Aromatic Systems The concept of aromaticity is not restricted to hydrocarbons. Heterocyclic systems, whether of the pyrrole type 1.46 with trigonal nitrogen in place of one of the C¼C double bonds, or of the pyridine type 1.47 with a

60

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

trigonal nitrogen in place of a carbon atom, are well known. The p orbitals of pyrrole are like those of the cyclopentadienyl anion, and those of pyridine like benzene, but skewed by the presence of the electronegative heteroatom. The energies and coefficients of heteroatom-containing systems like these cannot be worked out with the simple devices that work for linear and monocyclic conjugated hydrocarbons. The numbers in Fig. 1.69 are the results of simple Hu¨ckel calculations using parameters like those in Table 1.2 for equations like Equations 1.15 and 1.16, and some trends can be seen. The overall p energy is lowered by the cyclic conjugation. The lowest-energy orbital 1 is always polarised towards the electronegative atom, and the next orbital up in energy 2 (and the highest unoccupied orbital) is polarised the other way. This polarisation is more pronounced in the pyridinium cation 1.48, where the protonated nitrogen is effectively a more electronegative atom. In the pyridine orbitals, the HOMO is actually localised as the nonbonding lone pair of electrons on nitrogen, and the degeneracy of 2 and 3, and of the corresponding antibonding orbitals, is removed, but not by much. The orbitals with nodes through the heteroatoms are identical in energy and coefficients with those of the corresponding hydrocarbon. The orbitals 3 and 5* in pyrrole, with a node through the nitrogen atom, are identical to 2 and 4* in butadiene, and 3 and 5* in pyridine and its cation are identical to 3 and 5* in benzene.

N H

N 1.47

1.46

N H 1.48

–0.45

–0.48

0.45 0.44 –0.38 –0.60

*

6

*

5

4*

1.62

1.93

–0.39 0.32

–0.25

N H

*

5 0.57 –0.49

N

4*

1.00

0.57

1.00

N H

0.58

4*

3 2

0.5

N –0.50

0.50

1.00

N

1

2.30

1.32

N 0.65

0.41

2.11

N 0.34

0.43

H

0.63

2

1

0.33

N H

3

–0.19

H

N H

0.50

0.60

1.17

–0.56

0.42

1.00

N

N H 0.20

0.35 –0.58

1.00 0.70

–0.37

n 0.60

5

–0.24

0.55

0.62

*

N

0.37

N H

0.50

0.50

0.84

H

2

*

0.26

1.90

6

0.37

1.30

3

N

–0.08 –0.57

2.28 1

–0.52 0.26

0.36

N H

0.29

0.42

N 0.52

0.41 0.65

N H

Fig. 1.69 p Molecular orbitals of pyrrole, pyridine and the pyridinium ion. (Calculated using h¼1 and k¼1 for pyrrole, h¼0.5 and k¼1 for pyridine, and h¼1 and k¼1 for the pyridinium cation)

1 MOLECULAR ORBITAL THEORY

1.8

61

The Tau Bond Model

The Hu¨ckel version of molecular orbital theory, separating the  and p systems, is not the only way of accounting for the bonding in alkenes. Pauling showed that it is possible to explain the electron distribution in alkenes and conjugated polyenes using only sp3-hybridised carbon atoms. For ethylene, for example, instead of having sp2-hybridised carbons involved in full  bonding, and p orbitals involved in a pure p bond, two sp3 hybrids can overlap in something between  and p bonding 1.49. The overall distribution of electrons in this model is exactly the same as the combination of  and p bonding in the conventional Hu¨ckel picture (Fig. 1.25). In practice, this model, usually drawn with curved lines called t bonds 1.50,52 has found few adherents, and the insights it gives have not proved as useful as the Hu¨ckel model. For example, the t bonds between C-1 and C-2 and between C-3 and C-4 in butadiene 1.51 are not so obviously conjugated as the p bonds in the Hu¨ckel picture in Fig. 1.37. It is useful, however, to recognise that it is perfectly legitimate, and that on occasion it might have some virtues, not present in the Hu¨ckel model, especially in trying to explain some aspects of stereochemistry.

H

H

H

H

H H

H H 1.50

1.49 H H

1

H

3

2

H

4

H H

1.51

1.9

Spectroscopic Methods

A number of physical methods have found support in molecular orbital theory, or have provided evidence that the deductions of molecular orbital theory have some experimental basis. Electron affinities measured typically from polarographic reduction potentials correlate moderately well with the calculated energies of the LUMO of conjugated systems. Ionisation potentials can be measured in a number of ways, and the results correlate moderately well with the calculated energies of the HOMO of conjugated systems.53 Several other measurements, like the energies of conjugated systems, bond lengths, and energy barriers to rotation, can be explained by molecular orbital theory, and will appear in the normal course of events in the next chapter. A few other techniques, dealt with here, have helped directly in our understanding of molecular orbital theory, and we shall use evidence from them in the analysis of chemical structure and reactivity in later chapters. 1.9.1 Ultraviolet Spectroscopy When light of an appropriate energy interacts with an organic compound, an electron can be promoted from a low-lying orbital to a higher energy orbital, with the lowest-energy transition being from the HOMO to the LUMO. Selection rules govern which transitions are allowed and which are forbidden. One rule states that electron spin may not change, and another that the orbitals should not be orthogonal. The remaining selection rule is based on the symmetries of the pair of orbitals involved. In most cases, the rules are too complicated to be made simple here.54 Group theory is exceptionally powerful in identifying which transitions are allowed, and it is one of the first applications of group theory that a chemist pursuing a more thorough understanding comes across. One case, however, is easy—that for molecules which only have a centre of symmetry, like s-trans butadiene 1.8. The

62

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

allowed transitions for these molecules are between orbitals that are symmetric and antisymmetric with respect to the centre of symmetry. Thus the HOMO, 2, is symmetric with respect to the centre of symmetry half way between C-2 and C-3, and the LUMO, 3*, is antisymmetric (Fig. 1.37). Accordingly, this transition is allowed and is indeed strong, as is the corresponding transition for each of the longer linear polyenes. Data for this the longest wavelength p!p* transition are available for ethylene,55 where the problem is pulling out the true maximum from a broad band in the vacuum UV, and for a long list of the lower polyenes, where the maximum is easy to measure in the UV region when methyl or other alkyl groups are present at the termini to stabilise the polyenes against electrocyclisation and polymerisation. Fig. 1.70 is a plot of the experimentally determined56 values of lmax for the longest wavelength absorption for a range of such polyenes R(CH¼CH)nR, converted to frequency units, against (ELUMO – EHOMO) in  units calculated using Equation 1.17: DE¼4 sin

p 2ð2n þ 1Þ

1:17

which is simply derived from the geometry of figures like Figs. 1.31 and 1.39. The correlation is astonishingly good—in view of the simplifications made in Hu¨ckel theory, and in view of the fact that most transitions, following the Frank-Condon principle, are not even between states of comparable vibrational energy. Nevertheless, Fig. 1.70 is a reassuring indication that the simple picture we have been using is not without foundation, and that it works quite well for relative energies. Similarly impressive correlations can be made using aromatic systems, and even for ,-unsaturated carbonyl systems. It is not however a good measure of absolute energies, and the energy of the p!p* transition measured by UV cannot be used directly as a measure of the energy difference between the HOMO and the LUMO. This can be seen from that fact that the line in Fig. 1.70 does not go through the origin, as Hu¨ckel theory would predict, but intersects the ordinate at 15 500 cm–1, corresponding to an energy of 185 kJ mol–1 (44 kcal mol–1).

60,000

50,000

max

40,000

n 1 2 3 4 5 6 7 8 9

(nm) 162.5 227 274 310 342 380 401 411 426

max

max

(cm–1)

E( )

61, 500 44, 000 36, 400 32, 300 29, 200 26, 300 24, 900 24, 300 23, 500

2.00 1.24 0.89 0.69 0.57 0.48 0.42 0.37 0.33

0.6

0.8

30,000

20,000 0.2

0.4

1.0

1.2

1.4

1.6

1.8

2.0

E LUMO – E HOMO

Fig. 1.70

Frequency of first p!p* transitions of some representative polyenes R(CH¼CH)nR plotted against (ELUMO – EHOMO) calculated using Equation 1.17

1.9.2 Nuclear Magnetic Resonance Spectroscopy Chemical shift is substantially determined by the electron population surrounding the nucleus in question and shielding it from the applied field. Chemical shifts, and 13C chemical shifts in particular, are therefore used to probe the total electron population. The chemical shift range with protons is so small that aromatic ring currents and other anisotropic influences make such measurements using proton spectra unreliable.

1 MOLECULAR ORBITAL THEORY

63

Coupling constants J measure the efficiency with which spin information from one nucleus is transmitted to another. This is not usually mediated through space, but by interaction with the electrons in intervening orbitals. Transmission of information about the magnetic orientation of one nucleus to another is dependent upon how well the orbitals containing those electrons overlap, as well as by the number of intervening orbitals. In a crude approximation, the number of intervening orbital interactions affects both the sign and the magnitude of the coupling constant. Coupling constants can be either positive or negative. Although this does not affect the appearance of the 1HNMR spectrum, it does change the way in which structural variations affect the magnitude of the coupling constant. To understand why coupling constants can be positive or negative, we need to look into the energetics of coupling. In hydrogen itself, H2, there are three arrangements with different energies: the lowest energy with the nuclear spins of both nuclei H and H0 aligned, the highest with both opposed, and in between two ways equal in energy with the alignments opposite to each other (Fig. 1.71a, where upward-pointing arrows indicate nuclear magnets in their low-energy orientation with respect to the applied magnetic field, downward-pointing arrows indicate nuclear magnets in their high-energy orientation with respect to the magnetic field, and levels of higher energy are indicated by vertical upward displacement). The transitions which the instrument measures are those in which the alignment of one of the nuclei changes from the N state (the high-energy orientation, aligned with the applied magnetic field) to the N state (the low-energy orientation, aligned in opposition to the applied magnetic field). There are four such transitions labelled W in Fig. 1.71a, and all of them equal in magnitude. The receiving coils detect only the one signal, and the spectrum shows one line and hence no apparent coupling.

H H' W1

A X W A1

W 1'

H H'

A X

W X1

H H' W 2'

W2

H H'

A X

(a) H—H'

Fig. 1.71

W X2

A X W A2

(b) A—X not coupled

Energy levels of atomic nuclei showing no coupling

If now we look at two different atoms A and X, we have the same set-up, but this time the two energy levels in the middle are of different energy, one with A aligned and the other with X aligned (Fig. 1.71b). ‘A’ might be a 13C, and ‘X’ a 1H atom, but the general picture is the same for all AX systems. If there is no coupling (J ¼ 0), as when the nuclei are far apart, the AX energy level will be as much above the mid-point as the energy level for the AX nucleus is below it. There will again be four transitions, two equal for the A nucleus, labelled WA, and two equal for the X nucleus, labelled WX, giving rise to one line from each. If, however, the two nuclei are directly bonded, they will affect each other. The A spin will be opposed to the spin of one of the intervening electrons in an s orbital (only s orbitals have an electron population at the nucleus); that electron is paired with the other bonding s electron. In the lowest energy arrangement of the system, both the A and X nuclei are spin-paired with the bonding electrons with which they interact most strongly (as in Fig. 1.72c). As a result, the A and the X nuclei will be opposed in the lowest energy arrangement. Conversely, the system will be higher in energy when these spins are aligned. Thus, the two energy levels in which the A and X nuclei have parallel spins will be raised and the two energy levels in which they are opposed will be lowered (Fig. 1.72b). Thus, there are now four new energy levels, four different transitions, WA1 and WA2, and WX1 and WX2, and four lines in the AX spectrum. The A signal is a

64

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

doublet and the X signal is a doublet, with the same separation between the lines, because (WA1 – WA2) ¼ (WX1 – WX2) ¼ JAX. Thus, the extent of the raising and lowering of each of the energy levels is JAX/4. More complicated versions of this kind of diagram, more complicated than can be explained here, are needed to analyse spin interactions for nuclei with values of I 6¼ ½, for systems more complicated than AX, and even more complicated ones to make sense of those spectra that are not first order. J/4

A X

W A1 W X1

A X

J/4

A

X

W X2 A X A X

J/4

(a) A—X not coupled

Fig. 1.72

W A2

J/4

(b) A—X positively coupled

(c) Transmission of inf ormation about nuclear spin in directly bonded nuclei through the s electrons

Energy levels of atomic nuclei without (a) and with the capacity to show coupling (b)

If instead of being directly bonded, the A and X nuclei are separated by two bonds, the transmission of information through the s electrons leads the two nuclei to be parallel in the low-energy arrangement, in contrast to the high-energy arrangement of Fig. 1.72. The model that illustrates this point is given in Fig. 1.73c, and implies that the nuclei will be antiparallel in the high-energy arrangement. Now the energy levels will have the lowest and highest energy levels lowered by the interaction of the two spins, and the levels in between raised (Fig. 1.73b). If the coupling constant is the same as that in Fig. 1.72, the two transitions for the A nucleus, WA1 and WA2, are of the same magnitude as before but have changed places, and similarly for WX1 and WX2. The appearance of the spectrum will not have changed, but the coupling constant J is negative in sign. In general, although not always, one-bond couplings 1J and three-bond couplings 3J are positive in sign, and two- and four-bond couplings 2J and 4J are negative in sign. A X

J/4 J/4

A X

J/4 A X A X

C

W X1

A

W X2

X

W A2 J/4

(a) A—X not coupled

Fig. 1.73

W A1

(b) A—X negatively coupled

(c) Transmission of inf ormation about nuclear spin in geminally bonded nuclei through the s electrons

Energy levels of atomic nuclei with the capacity to show coupling through two bonds

The connection between spin-spin coupling and orbital involvement can be found in several familiar situations. Thus, the 1J values for 1H—13C coupling are correlated with the degree of s character at carbon 1.52–1.54. More subtly the 1H—13C coupling constant is a measure of the C—H bond length, with the axial protons in cyclohexanes having a slightly smaller value (122 Hz) than the equatorial protons (126 Hz),57 a phenomenon known as the Perlin effect.58 The explanation is found in the hyperconjugation of the antiperiplanar axial-to-axial C—H bonds on neighbouring atoms (see p. 85). The coupling between geminal

1 MOLECULAR ORBITAL THEORY

65

protons is negative but larger in absolute magnitude when both C—H bonds are conjugated to the same p bond 1.55 than when they are not 1.56. 1

J 125 Hz

H

H H

1

H

H

H 1.54

H

H H H

2

J –14.9 Hz

H

J 249 Hz

H

H 1.53

1.52

1

J 156 Hz

H

H

2

J –12 Hz

H

H 1.55

1.56

Strong coupling from anti-periplanar and syn-coplanar vicinal hydrogen atoms 1.57 and 1.59, and virtually zero coupling with orthogonal C—H bonds 1.58 (the Karplus equation), is a consequence of the conjugation of the bonds with each other.59 Coupling constants are usually larger when the intervening bond is a p bond, with the trans and cis 3J coupling in alkenes typically 15 and 10 Hz for the same 180 and 0 dihedral angles. Longer-range coupling is most noticeable when one or more of the intervening bonds is a p bond, most strikingly demonstrated by 5J values as high as 8–10 Hz in 1,4-cyclohexadienes 1.60. When there are no p bonds, the strongest long range coupling is found when the intervening  bonds are oriented and held rigidly for efficient conjugation with 4J W-coupling 1.61 and 1.62.

H

3J

9-13 Hz

3J

H

~0 Hz

H

H H

3

J ~10 Hz

H 1.57

H

1.58

H

5

J 9 Hz

1.59 J 1-2 Hz

H 1.60

1.61

5

J 1-1.5 Hz

H Ph

H

4

H

H 1.62

1.9.3 Photoelectron Spectroscopy Photoelectron spectroscopy60 (PES) measures, in a rather direct way, the energies of filled orbitals, and overcomes the problem that UV spectroscopy does not give good absolute values for the energies of molecular orbitals. The values obtained by this technique for the energies of the HOMO of some simple molecules are collected in Table 1.3. Here we can see how the change from a simple double bond (entry 6) to a conjugated double bond (entry 10) raises the energy of the HOMO. Similarly, we can see how the change from a simple carbonyl group (entry 8) to an amide (entry 14) also raises the HOMO energy, just as it ought to, by analogy with the allyl anion (Fig. 1.33), with which an amide is isoelectronic. We can also see that the interaction between a C¼C bond (p energy –10.5 eV) and a C¼O bond (p energy –14.1 eV) gives rise to a HOMO of lower energy (–10.9 eV, entry 16) than when two C¼C bonds are conjugated (–9.1 eV, entry 10). Finally, we can see that the more electronegative an atom, the lower is the energy of its HOMO (entries 1 to 5). All these observations confirm that the theoretical treatment we have been using, and will be extending in the following chapters, is supported by some experimental evidence.

66

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS Table 1.3 Energies of HOMOs of some simple molecules from PES (1 eV ¼ 96.5 kJ mol–1 ¼ 23 kcal mol–1)

Entry

Type of orbital

Energy (eV)

n n n n n π π n π ψ2 ψ1 ψ2 n π n π π

–9.9 –10.48 –10.85 –12.6 –12.8 –10.51 –11.4 –10.88 –14.09 –9.1 –11.4 or –12.2 –10.17 –10.13 –10.5 –10.1 –10.9 –8.9

18

π

–9.25

19

π

–9.3

n

–10.5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Molecule :PH3 :SH2 :NH3 :OH2 :ClH CH2=CH2 HC≡CH :O=CH2 CH2=CH-CH=CH2 HC≡C-C≡CH H2NCH=O: CH2=CH-CH=O

O

N

20

1.9.4 Electron Spin Resonance Spectroscopy A final technique which both confirms some of our deductions and provides useful quantitative data for frontier orbital analysis is ESR spectroscopy.61 This technique detects the odd electron in radicals; the interaction of the spin of the electron with the magnetic nuclei (1H, 13C, etc.) gives rise to splitting of the resonance signal, and the degree of splitting is proportional to the electron population at the nucleus. Since we already know that the coefficients of the atomic orbitals, c, are directly related to the electron population, we can expect there to be a simple relationship between these coefficients and the observed coupling constants. This proves to be quite a good approximation. The nucleus most often used is 1H, and the coefficient of the atomic orbital which is measured in this way is that on the carbon atom to which the hydrogen atom in question is bonded. The McConnell equation (Equation 1.18) expresses the relationship of the observed coupling constant (aH) to the unpaired spin population on the adjacent carbon atom (C) The constant Q is different from one situation to another, but when an electron in a pz orbital on a trigonal carbon atom couples to an adjacent hydrogen, it is about –24 G. Applied to aromatic hydrocarbons, where it is particularly easy to generate radical cations and anions, there proves to be a good correlation between coupling constants and the calculated coefficients in the HOMO and LUMO, respectively.62 a H ¼ QH CH C

1:18

1 MOLECULAR ORBITAL THEORY

67

However, the relationship between coupling constant and electron population is not quite as simple as this. Thus, although p orbitals on carbon have zero electron population at the nucleus, coupling is nevertheless observed; similarly, in the allyl radical 1.63, which ought to have zero odd-electron population at the central carbon atom, coupling to a neighbouring hydrogen nucleus is again observed. This latter coupling turns out to be opposite in sign to the usual coupling, and hence has given rise to the concept of ‘negative spin density’. Nevertheless the technique has provided some evidence that our deductions about the coefficients of certain molecular orbitals have some basis in fact as well as in theory: the allyl radical does have most of its odd-electron population at C-l and C-3; and several other examples will come up later in this book. We merely have to remember to be cautious with evidence of this kind; at the very least, the observation of negative spin density should remind us that the Hu¨ckel theory of conjugated systems (the theory we have been using) is a simplification of the truth. The standard ways of generating radicals for ESR measurements involve adding an electron to a molecule or taking one away. In the former case the odd electron is fed into what was the LUMO, and in the latter case the odd electron is left in the HOMO. Since these are the orbitals which appear to be the most important in determining chemical reactivity, it is particularly fortunate that ESR spectroscopy should occasionally give us access to their coefficients. Here is a selection of some of the more important conjugated radicals and radical ions, to some of which we shall refer in later chapters. They all show how the patterns of molecular orbitals deduced in this chapter are supported by ESR measurements. The numbers are the coupling constants |aH| in gauss. CH2 16.4

H 4.1 13.9 H 14.8 H

O

H 5.1

H H

H 6.7

H 1.8

1.63

H 1.9

H 6.1

H 10.2

1.64 H 3.75

H 6.9

CH3 0.8

CH3 5.1

H 5.5

H 1.5

1.8 H

1.68

H 5.3

H 5.0 H 1.8

H 3.5

CH3

H 1.1

1.69 6.5 H

H 1.9

1.72

CH3 2.0

H 6.9

H 7.7

1.67

1.71

NO2

H 5.1 H3C

H 0.6

1.66

1.65

H 3.9 1.70 5.3 H

H 3.1

H 1.5

H 1.4

1.73

H 2.7

1.74

2

Molecular Orbitals and the Structures of Organic Molecules

Chapter 1 established the fundamentals of molecular orbital theory, and especially of the Hu¨ckel method for handling conjugated systems. This chapter uses the language those ideas were presented in to explain some of the better known structural features of organic molecules. It is largely concerned with the ground state and the thermodynamic properties of molecules, not with kinetics and how molecules behave in chemical reactions, which is reserved for the rest of the book. It is important to realise that conjugation, for example, may, and usually does, make a molecule thermodynamically more stable than an unconjugated one, but it does not follow that conjugated systems are less reactive. Indeed, they are often more reactive or, we might say, kinetically less stable. Organic chemists use ‘stable’ and ‘stability’ without always identifying which meaning they are assuming. In this chapter we shall look at thermodynamic stability, and reserve reactivity for later chapters.

2.1

The Effects of p Conjugation

We saw in Chapter 1 that the p conjugation in the allyl system and in butadiene is energy-lowering, with the total p energy of a conjugated system lower than the sum of the energies of the isolated components. We have also seen even better energy lowering when the conjugation is within a ring of 4nþ2 p electrons. We must now look at the effect a substituent has on thermodynamic stability and polarisation when it is attached, and hence conjugated with, the p or p orbitals of simple systems like alkenes, carbocations, radicals and anions. The effects on energy can, of course, be estimated computationally using more or fewer assumptions and approximations, as we have already seen with some simple systems. Alternatively, in some cases, the information is available from an experimental measurement like the heat of combustion or of hydrogenation. However, these aids are not always to hand. Furthermore, a computation does not necessarily make immediate chemical sense, and an experimental measurement still needs an explanation. The discussion in the following pages shows that we can work out the effects of substituents in an easy, nonmathematical way, both on the overall energy, and on the energy and polarisation of the frontier orbitals. Although the procedure used is legitimate (and works), it is perhaps worth bearing in mind that it does not resemble the method used by theoreticians in proper calculations. 2.1.1 A Notation for Substituents Before we discuss the effects of substituents on the energies and coefficients of conjugated systems, it will be convenient to have at our disposal a notation for the various types of substituents which we shall come across. There are three common types, which we shall designate with the letters C-, Z- and X- (Fig. 2.1), each of

Molecular Orbitals and Organic Chemical Reactions: Reference Edition Ó 2010 John Wiley & Sons, Ltd

Ian Fleming

70

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

C

stands f or

or

OMe

R

Z

or stands f or

O

O

or

C

or

metal

OMe

X

donors or acceptors and neutral

etc.

N

or

stands f or or

Fig. 2.1

CH3

or

NO2

e.g.

NMe2

etc.

SiMe3

BR2

etc.

etc.

acceptors and acceptors acceptors but donors donors but acceptors donors but neutral

Definitions and character of substituents

which modifies the reactivity of conjugated systems in a different way. This classification, which was first introduced by Houk,63 is used throughout this book. C-Substituents are simple conjugated systems of carbon atoms, like vinyl or phenyl. They may be p donors or p acceptors, depending upon what they are conjugated with, responding to and stabilising electron demand or electron excess, as appropriate. Their effect on the  framework is small, because the point of attachment is a carbon atom, and C—C single bonds are not strongly polarised. Z-Substituents are conjugated systems which are also electron withdrawing, like formyl, acetyl, cyano, nitro, sulfonyl and carboxy. They withdraw electrons from double bonds that they are conjugated with, and, since most of them have electronegative heteroatoms, they are also weakly electron withdrawing by an inductive effect within the  framework. Such substituents are therefore strong p acceptors and usually weak, but occasionally, strong  acceptors, especially for substituents like nitro and sulfonyl, where an electronegative heteroatom is the point of attachment. There is another group of p electron-withdrawing substituents, which are slightly different from the Zsubstituents listed above. Metals, and metalloids like the silyl group, are p acceptors (Section 2.2.3.2) but, because metals are more electropositive than carbon, they are  donors. These substituents have not been given a separate symbol, but their effect on the p system is more often than not what we shall be interested in, and they are included among the group labelled Z. X-Substituents are typically electronegative heteroatoms like nitrogen, oxygen or sulfur which carry a lone pair of electrons. They donate their lone pairs to a p system, and those based on electronegative heteroatoms withdraw electrons from the  framework. They are therefore p donors and  acceptors, exactly the opposite of the metals and metalloids. We usually include simple alkyl groups in the category of X-substituents, because they are able, by overlap of the C —H (or C—C) bonds with the p system ( conjugation or hyperconjugation, Section 2.2) to supply electrons to a conjugated system. Alkyl groups are therefore p donors, but they are largely neutral with respect to the  framework. The electronegative halogen atoms are anomalous; technically they are X-substituents, but their effect in the p system is weak, because the lone pairs of electrons are so tightly held, and they are strong  acceptors.

2.1.2 Alkene-Stabilising Groups 2.1.2.1 C-Substituents. We saw in Chapter 1 with butadiene (Fig. 1.39) that a simple double bond, the most simple of the C-substituents, lowers the total p energy when it is conjugated to another double bond to

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

71

make butadiene. We can see the same thing with styrene, but the picture is a little more complicated, because we need to see how a substituent attached to a benzene ring affects the energies and coefficients of each of the p orbitals. We shall return to this problem later when we consider the effect of having Z- and X-substituents conjugated with the p orbitals of benzene. The filled and the lowest of the unfilled p molecular orbitals for styrene (actually calculated for simplicity for a hypothetical linear structure) are shown in Fig. 2.2. The lowest-energy orbital 1 is largely the same as 1 in benzene (Fig. 1.43) with a small addition from the p orbital of the ethylene component in phase and with a correspondingly small drop in energy, because the orbitals that we are mixing here are far apart in energy. With the ethylene attached to the large coefficient in 2 of benzene, the interaction in the bonding sense is strong because these two orbitals are similar in energy. The node shifts up, as drawn, to pass through the two ortho carbons, making this orbital close to the sum of two allyl fragments. As a result, it is significantly lowered in energy relative to 2 in benzene. The 4 orbital in styrene, higher in energy, is made up from the same two components, p in ethylene and 2 of benzene, combined in an antibonding sense. We see 2 lowered in energy and 4 raised in energy, in much the same way as 1 and 2 in butadiene are lowered and raised, respectively, relative to the energies of the p orbitals of ethylene. In contrast, the ethylene attached to the node in 3 in benzene has no effect, and the orbital 3 in linear styrene is identical to 3 in benzene. The net effect among the filled orbitals is to lift the degeneracy of 2 and 3 in benzene, lowering the energy of the one and leaving the other unchanged, and raising the energy and polarising the orbital 4 which most closely resembles the p orbital of ethylene. The total p stabilisation in styrene is 2  5.21, whereas the total p stabilisation for the separate components benzene and ethylene is 2  5.0. The lowest of the unfilled orbitals is largely made up from the p* orbital of ethylene combined in a bonding sense with the 4* orbital of benzene, lowering its energy. The p* orbital of ethylene can have no effect on the 5* orbital of benzene, because it would be at a node, and that orbital (not illustrated) would be the same as the 5* orbital of benzene. This exercise shows that the effect on the energy of the p molecular orbitals of adding simple conjugation in the form of a p bond or of a benzene ring is very similar—a C-substituent lowers the

–0.39

0.60

–0.33

LUMO

0.66

*

5

0.31 0.13 –0.39

0.39

0.60

–0.33

0.66 HOMO

4

–0.31 0.13

0.35

0.50

0

0

0.39

1.00 3

0.50

0.35

1.41

0

2

0.31

0

0.14

–0.35 0.51 –0.50

2.14

0.39

1 0.33 0.31

Fig. 2.2

The filled p molecular orbitals and the LUMO of styrene

72

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

overall p energy, it raises the energy of the HOMO (from 1 below the  level in ethylene to 0.62 below it in butadiene and 0.66 in styrene), and it lowers the energy of the LUMO (from 1 in ethylene to 0.62 in butadiene and 0.66 in styrene). Similarly with the coefficients—the terminal carbon atom in the sidechain, both in the HOMO and in the LUMO has a larger coefficient than the internal atom. Thus a benzene ring has a similar effect as a substituent to that of a simple double bond, but to a somewhat lesser degree. 2.1.2.2 Z-Substituents. As an example of the simplest possible Z-substituent, we need to work out the p molecular orbitals of acrolein 2.1. A simple Hu¨ckel calculation gives the picture in Fig. 2.3, which is what we want, but a derivation like this gives us no insight.

0.66

*

0.23

O

1.53

4

–0.43

O

–0.58 0.43

–0.23

2.1

LUMO

*

O

0.35

3

0.66

–0.58

–0.58

0.58

O HOMO

O

1.00 2

0

2.2

0.58 0.66

0.43

1.88

O

1 0.23

Fig. 2.3

0.58

The p molecular orbitals of acrolein. (These energies and coefficients were calculated using h ¼ 1 and k ¼ 1)

Dealing first with the energies, let us instead consider the p structure of acrolein. If we ignore the fact that one of the atoms is an oxygen atom and not a carbon atom, we shall simply have the orbitals of butadiene. Obviously we cannot ignore the oxygen atom. One way to take it into consideration is to regard the carbonyl group as a kind of carbonium ion, highly stabilised by an oxyanion substituent 2.2. Normally we do not draw it this way, because such good stabilisation is better expressed by drawing the molecule (as in 2.1) with a full p bond between the oxygen atom and the carbon atom. The truth is somewhere in between, and organic chemists usually make a mental reservation about the meaning of such drawings as 2.1 and 2.2. We make the mental reservation that the butadiene-like system, implied by the drawing of a localised structure 2.1, is only one extreme approximation of the true orbital picture for acrolein. The other extreme approximation is an allyl cation, substituted by a noninteracting oxyanion, as implied by the localised drawing 2.2. The energies for the molecular orbitals for these two extremes are shown in Fig. 2.4 with the allyl cation and the separate oxyanion on the left and butadiene on the right. The energies of the p* and p orbitals of ethylene are placed for reference as dashed lines 1 above and below, respectively. The true orbital energy for the orbitals of acrolein must be in between those of the corresponding orbitals of the allyl cation and

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

73

1.618

*

4

1.414

*

*

4

3

1 0.618 LUMO

*

3

LUMO

2

HOMO

*

3

LUMO

2

0.618

HOMO 1.414 HOMO

1

2

1.618

1

1 1

O

O =

O 2.2

Fig. 2.4

2.1

Z 2.3

The energies of the p orbitals of acrolein 2.1 as a weighted sum of the p orbitals of an oxyanion-substituted allyl cation 2.2 and butadiene 2.3

butadiene. We can perhaps expect the true structure to be more like the butadiene system than the allyl cation system (for the same reason that we prefer to draw it as 2.1 rather than 2.2). What we immediately learn from Fig. 2.4 is that the effect of mixing in some allyl cation like nature to the butadiene orbitals is to lower the energy of each of the molecular orbitals relative to those of butadiene. We can also see that the effect of having a Z-substituent conjugated with the double bond of ethylene is, as usual with conjugation, to lower the energy of the system overall, with 1 and 2 together having more p bonding than the separate orbitals of ethylene and a carbonyl group. The energy of the HOMO of acrolein, 2, is, however, little changed from that of the p orbital of ethylene. Also, because it is butadiene-like, the HOMO and the LUMO will be closer in energy than they are in ethylene—the LUMO will have been lowered in energy relative to that of ethylene and the HOMO will be very similar in energy. What we have done is to superimpose the orbitals of an allyl cation on those of butadiene, and, with suitable weighting, to add the two together. This device does not give us the whole picture of Fig. 2.3, but it does give us some sense of how the p orbitals can reasonably be expected to have the energies shown there. We can use the same ideas to deduce the pattern, but not the actual values, of the coefficients. We have again a contribution from the allyl-cation-like nature of acrolein and from its butadiene-like nature. The coefficients of the allyl cation orbitals and the oxyanion p orbital are on the left of Fig. 2.5, and the coefficients of the butadiene orbitals in the middle. The coefficients on each atom and in each molecular orbital of acrolein can then be expected to be somewhere in between the corresponding coefficients in the two components. The average of the two components is given on the right in Fig. 2.5, these representing a simple unweighted sum. These numbers are not coefficients, because they have not been arrived at with legitimate algebra, and, squared and summed, they do not, of course, add up either horizontally or vertically to one. They are however similar in their general pattern to those obtained by calculation in Fig. 2.3, and this

74

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS –0.707

–0.600

0.371

0.500

0.707

–0.371

0.500

–0.30

O

= 0.600

0.69

0.30

O

= 0.371

0.19

0.600

2

0.06

0.55

0.371

+

1.000

–0.54

0.54

–0.371

*

3

–0.600

0.600

O

O 0.65

+ 0.500

0.30

–0.19

0.371

HOMO

0.55

= 0.600

–0.707

*

4

0.600

+ 0.707

O 0.44

0.600 –0.371

LUMO

–0.19

=

+ 0.500

–0.65

–0.371

1

0.30 1

O

2.2

Fig. 2.5

=

+

2

Z

2.3

Crude estimates of the coefficients of the p orbitals of a Z-substituted alkene as an arbitrarily unweighted average of the coefficients of an allyl cation 2.2 and butadiene 2.3

similarity gives us some reason to believe that this way of deducing the relative magnitudes of the coefficients is legitimate. To take the LUMO of a Z-substituted alkene ( 3*) as an example, the carbon atom C-1 with the Z-substituent on it has a zero coefficient on the corresponding atom in the allyl cation and a small coefficient in butadiene (–0.371). The coefficient on C-1 in the LUMO of a Z-substituted alkene is therefore likely to be very small (–0.19 in Fig. 2.5, and –0.23 in Fig. 2.3). In contrast, the carbon atom C-2 has large coefficients both in the allyl cation (0.707) and in butadiene (0.60). The coefficient on C-2 in the LUMO of a Z-substituted alkene is therefore large (0.65 in Fig. 2.5, and 0.66 in Fig. 2.3). If we turn now to the HOMO of acrolein ( 2) and look at C-1, the allyl cation has a very large coefficient (0.707) on the central atom, but butadiene has a small coefficient on the corresponding atom (0.371). The two effects therefore act in opposite directions—the conjugation causing a reduction in the coefficient on the carbon atom carrying the formyl group, and the allyl-cation-like contribution causing an increase in this coefficient. The result is a medium-sized coefficient (0.54 in Fig. 2.5, and 0.58 in Fig. 2.3). For C-2, it is the allyl cation that has the smaller coefficient (0.500) and the butadiene the larger (0.600). The combination is again a medium-sized coefficient (0.55 in Fig. 2.5, and 0.58 in Fig. 2.3). We have already seen that acrolein is probably better represented by the drawing 2.1 than by the drawing 2.2, from which we may guess that it is the butadiene-like character which makes the greater contribution to the HOMO. If this is the case, acrolein will have its HOMO coefficients polarised in the same way as those of butadiene, but to a lesser extent (as indeed they are in Fig. 2.5). (Epiotis64 actually came to the opposite conclusion for acrylonitrile i.e. Z ¼ CN; his calculation was a legitimate one, not the crude approximation used here, but in effect it had evidently given greater weight to the allyl cation-like nature of the system. This shows that the situation is delicately balanced. It may well be that some Z-substituents do give the opposite polarisation in the HOMO to that shown in Fig. 2.5.)

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

75

2.1.2.3 X-Substituents. In an X-substituted alkene like methyl vinyl ether 2.4, we have a lone pair of electrons brought into conjugation with the double bond. We can deduce the pattern of molecular orbitals by an interaction diagram Fig. 2.6 resembling that for the allyl anion 1.6 in Fig. 1.33. The earliest example in which the idea of comparing a heteroatom-substituted system with the corresponding hydrocarbon anion as an extreme version, is found in Zimmerman’s use of the benzyl anion as a model for anisole.65 The difference is that the lone pair on oxygen, being on an electronegative element, is lower in energy than that on carbon. This lowers the energy of all the orbitals 1– 3* relative to their counterparts in the allyl system. However the orbital 1 is created by the interaction of the lone-pair orbital on the oxygen atom, labelled n, in a bonding sense with both p and p*, strongly with the former and weakly with the latter, because of the greater separation of energy of the interacting orbitals. In contrast, 2 is derived by the weak interaction of n with p* in a bonding sense, and strongly with p in an antibonding sense. As a result 1 is lowered in energy more than 2 is raised, and the overall energy is lowered relative to the energy of the separate orbitals of the p bond and the lone pair. We saw the same pattern in the interaction of the orbitals of butadiene from two separate p bonds (Fig. 1.39). As usual, conjugation has lowered the overall energy. The net p stabilisation has been measured crudely by comparing the heats of hydrogenation of ethylene and ethyl vinyl ether as 25 kJ mol1 (6 kcal mol1).66 We should also note that both the HOMO and the LUMO of an X-substituted alkene are raised in energy relative to the HOMO and LUMO of ethylene, with the HOMO raised more than the LUMO.

*

LUMO

1

*

LUMO

3

2

HOMO HOMO

n

1

1

OMe

=

X

OMe

2.4

Fig. 2.6

Energies of the p orbitals of an X-substituted alkene

In order to deduce the coefficients for an X-substituted alkene, we adopt the idea that at one extreme, the lone pair on the oxygen atom is fully and equally involved in the overlap with the p bond, so that the orbitals will be those of an allyl anion 2.5. At the other extreme, to make allowance for the fact that the lone pair on an electronegative atom like oxygen is not as effective a donor as a filled p orbital on carbon, it is an alkene with no participation from the lone pair on the oxygen atom, together with the isolated lone pair. Thus we add a bit of allyl anion-like character, on the left in Fig. 2.7, to the unperturbed alkene, in the centre of Fig. 2.7. The average of the two components is printed on the right in Fig. 2.7, these representing a simple unweighted sum. As with the Z-substituted alkene, these numbers are not coefficients, because they have not been arrived

76

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS –0.60

–0.707

LUMO

=

+ 0.500

*

3

0.25

0.50

0.500

0.500

X 0.25

=

+

HOMO 0.707

0.500

–0.707

X 0.60

0.707

0.35

+ 0.500

2

–0.35

O

=

X 0.25

0.500

1

0.75

1.000 1

=

+

2

X

—OMe 2.5

Fig. 2.7 Crude estimates of the coefficients of the p orbitals of an X-substituted alkene as an arbitrarily unweighted average of the coefficients of an allyl anion 2.5 and an alkene

at with legitimate algebra, and, squared and summed, they do not add up either horizontally or vertically to one. However illegitimate, they match the pattern of large, medium and small coefficients obtained from a simple Hu¨ckel calculation. The lowest-energy orbital 1 has a large contribution from the lone pair added to the lowest-energy orbital of the allyl anion, creating an orbital strongly polarised towards the X-substituent. For the HOMO, the unperturbed alkene has (necessarily) equal coefficients on each atom, and the allyl anion has a zero coefficient on the atom bearing the X-substituent. The result of mixing these two is 2, a relatively strongly polarised orbital as far as the coefficients on C-1 and C-2 are concerned. For the LUMO, the unperturbed alkene again has equal coefficients, but the allyl anion has a larger coefficient on the carbon atom carrying the X-substituent than on the other one. The result is 3*, an orbital mildly polarised in the opposite direction. Thus any of the three types of substituent, C, Z or X, is overall energy-lowering in the p orbitals of an alkene. Where pathways exist, we can therefore expect C¼C double bonds to move into conjugation with any of these substituents. We can also expect that there will be some regioselectivity to their reactions, because their frontier orbitals are polarised, a topic to which we shall return in later chapters. 2.1.3 Cation-Stabilising and Destabilising Groups67 2.1.3.1 C- and X-Substituents. A molecule having an empty p orbital on carbon, and therefore carrying a positive charge, will be lowered overall in energy by p conjugation with a C-substituent. We have seen this already, from the opposite direction, when we moved from the orbitals of an alkene to those of an allyl cation in Fig. 1.33. Similarly, the effect of an X-substituent is even more stabilising, as we saw in considering the orbitals of a carbonyl group in Fig. 1.66, which could equally well have been drawn with two electrons in the pO orbital and none in the pC. The weakest kind of X-substituent is an alkyl group, to which we shall return while discussing the stabilisation of cations by hyperconjugation in Section 2.2. Further manifestations of stabilisation by the overlap of a filled with an unfilled orbital are the effects of X-substituents on an empty p orbital on a metal. Thus trimethylborate 2.6 is much less Lewis acidic than boron halides 2.7, because the oxygen lone pairs overlap more efficiently with the empty p orbital on the

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

77

boron.68 When X is fluorine, the energy match with the empty orbital on the boron is worse than for oxygen, because fluorine is so much more electronegative, and when X is any of the other halogens, the p orbitals are spread too far out from the nucleus for good p overlap with a first-row element.

MeO

B

OMe OMe

X

2.6

B

X X

2.7

2.1.3.2 Z-Substituents. The effect of a Z-substituent on a neighbouring carbocation is not so straightforward. Fig. 2.8 shows the interaction between the orbitals of a carbonyl group and an empty p orbital on carbon. The set of p orbitals in the middle is quantitatively different but otherwise essentially the same as the set of orbitals in the middle of Fig. 2.6, which was arrived at by an alternative sequence. There are, however, two fewer electrons to go into the p system this time. We deduce that there is an overall lowering of p energy, because 1 is lower in energy than the pC¼O orbital as a result of the interaction with the empty p orbital, pC. However, this lowering is not large, because this interaction is between an orbital at the  level and a p orbital, pC¼O, low in energy (Fig. 1.66). The overall lowering in p energy is not therefore as great as the corresponding lowering in energy in 1 of the allyl cation (E in Fig. 1.33). We might notice at this stage that 2 is lowered in energy, whereas it was not lowered at all in the allyl cation. The reason is that this orbital is made up by interaction of the p orbital with the p orbital of the carbonyl group in an antibonding sense and with the p* orbital in a bonding sense, as with the allyl cation. Since both the p and p* orbitals are lower in energy in a carbonyl group than in an alkene, the antibonding contribution to 2 is weakened and the bonding contribution strengthened.

*

3

*C=O pC LUMO

2

C=O

HOMO

O

Fig. 2.8

1

O

The p orbitals of a carbocation conjugated to a Z-substituent

It is well known, however, that a carbonyl group does not appear to be a stabilising influence on a carbocation, and yet we have just deduced that it is stabilised in the p system. In the first place, much of

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MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

the evidence for its high energy comes from its high reactivity, that is its kinetic properties, and not its thermodynamic. Nevertheless there is evidence that it is thermodynamically destabilised. The most obvious factor that we have left out in the argument above is the Coulombic effect of the partially ionic character of both the  and the p bond of a carbonyl group. The polarisation of both bonds towards the oxygen atom (Fig. 1.66) places a significant positive charge on the carbonyl carbon atom, immediately adjacent to the full positive charge on the nucleus of the carbon atom carrying the empty p orbital. This is energy-raising, because the now relatively exposed nuclei repel each other. We thus have a small energy-lowering contribution from the p overlap, but an energy-raising contribution from an adverse Coulombic effect.69 Evidently the latter wins. For the first time, we see that conjugation cannot always be relied upon to lower the overall energy. 2.1.4 Anion-Stabilising and Destabilising Groups70 Organic chemists use the word anion, and especially the word carbanion, loosely, as mentioned already on p. 56. The ‘anions’ are either trigonal carbons carrying substantial excess negative charge, such as enolate ions, or compounds with carbon-metal (C—M) bonds. In enolate ions, the orbital of what we are calling an anion would correspond to the p orbital on the terminal carbon in 2 of an X-substituted alkene (Section 2.1.2.3), which has a large coefficient on C-2 (Fig. 2.7). In compounds containing a C—M bond, the orbital of the anion is the bonding orbital LiC in Fig. 1.63, which also has a large coefficient on carbon. Thus, C-2 of an enolate and a C—M bond have similar features to a genuine carbanion, and it is not altogether unreasonable to call them carbanions. 2.1.4.1 C-Substituents. The orbitals for the interactions of C-, Z- and X-substituents with a filled p orbital on carbon are the same as those we have just used for their interaction with an empty p orbital, but with two more electrons to feed into the resultant p orbitals. The interaction of a C-substituent with a filled p orbital gives us the orbitals of an allyl anion, and these are just as p-stabilised as the allyl cation (Fig 1.33). The p stabilisation by a C-substituent of an enolate ion or of a C—M bond would be similar, but made a little more complicated by having to bring in more orbitals. 2.1.4.2 Z-Substituents. Even better, conjugation of a filled p orbital with a Z-substituent gives us the same orbitals as in Fig. 2.8, but now 2 is filled, and, since it is lowered in energy by the interaction below the level of 2 of the allyl anion, the  level, the overall p energy is lower still. The extra pair of electrons means that a partial positive charge is no longer adjacent to an unshielded nucleus, and the nuclei are no longer as exposed to Coulombic repulsion. This is the p system for an enolate ion, to which we shall return when we consider the polarisation of the orbitals, and again for the ambident nucleophilicity of this important system. The special kind of Z-substituent (see p. 70) that is seen with metals is even more straightforwardly stabilising of an anion. The orbital interaction is that of an empty p orbital on the metal with the filled p orbital of the anion. It is the same story, but looked at from the opposite direction, as the overlap of an X-substituent with the empty p orbital of a metal as seen in the boron compounds 2.6 and 2.7. An example of anion stabilisation is the ease with which 9-methyl-9-BBN 2.8 can be deprotonated to give the organolithium compound 2.10.71 The special feature of this system is that the base 2.9 is strong enough to remove a proton, but too hindered to bond directly as a ligand on the metal, which would otherwise be the preferred reaction. As usual the ‘anion’ is in fact a LiC bond but the polarisation of the filled orbital is towards carbon, making it anion-like.

+ B 2.8

N Li 2.9

B 2.10

Li

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

79

A related explanation applies to the well known stabilisation of carbanions by a neighbouring sulfur, phosphorus or silicon group. Using a filled orbital on carbon as the generalised picture for such ‘anions’ as C—M bonds or enolate ions, the main stabilisation comes from overlap of the filled orbital of the anion with the *YR orbital 2.11,72 and is at a maximum when the orbitals are anti-periplanar, accounting for the exceptional ease with which the anion 2.12 can be prepared by removing the bridgehead proton.73 The effect in the p system is strong enough, even for a  donor like a trimethylsilyl group, counter-intuitively to be stabilising of an anion. In the simplest case, trimethylsilylmethyllithium 2.13 can be prepared from tetramethylsilane and butyl-lithium, showing that the silyl substituent is more stabilising than the propyl substituent in butyllithium. Li R S

*YR

S S

Si Li

Y 2.11 Y = Si, P or S

2.12

2.13

The interaction diagram is that in Fig. 2.9, illustrating overlap between a  bond and a p orbital, which is called  conjugation, and to which we shall return in Section 2.2. The bonding interaction between a first-row atom R and a second-row atom Y is inherently less energy-lowering for the YR orbital and less energyraising for the *YR orbital than it would be if Y were the corresponding first-row element—the overlap integrals are smaller because of the long bond lengths.74 Consequently, the energy of the YR orbital is relatively high, and the *YR orbital is relatively low. The overall stabilisation represented by E is substantial, because of the strong bonding interaction of the high level YR orbital and the pC orbital. However, in a sense more important, the relatively low energy of the *YR orbital makes the interaction between it and the pC orbital keep the energy of the 2 orbital relatively low. It may be above or below the  level, depending upon the element Y, and the nature of the substituents R, but it will not be raised high in energy overcoming the lowering in energy E. The sulfur and the phosphorus have the added advantage of being (mild) -withdrawing groups. The silicon, however, even though it is a  donor, has the advantage

*

3

R

R

*YR Y

Y R

Y

pC

2

R R YR

Y

E Y 1

Fig. 2.9

The stabilisation of an anion by adjacent sulfur, phosphorus and silicon groups

80

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

of having the Si—R bonds more polarised from silicon towards the R group. If R is hydrogen or a carbon group, they are the electronegative elements in this context, making the coefficient on silicon large in the antibonding orbital *SiH and therefore more effective in lowering the energy of the 2 orbital. Anion stabilisation by second-row elements has hitherto, and most simply, been accounted for by invoking overlap of the filled p orbital of the anion with an empty d orbital on the sulfur, phosphorus or silicon. This is unmistakably stabilising, as usual with the overlap of a filled with an unfilled orbital of any kind, but the contribution it makes is unlikely to be significant, because the 3d orbitals on these second-row elements and a 2p orbital on carbon are much too far apart in energy75 and too ill-matched in size to have a significant interaction. Anion stabilisation by sulfur, phosphorus and silicon appears to be better accounted for by the arguments expressed in Fig. 2.9, which has largely, but not entirely,76 replaced that using the overlap with the empty d orbitals. A lone pair on an electronegative element can take the place of the carbanion in this argument, and overlap with an appropriately electron-withdrawing  bond can be similarly p-stabilising. Trisilylamine 2.14, unlike trimethylamine, is planar,77 with a trigonal nitrogen atom, probably largely as a result of the overlap of the nitrogen lone pair with the Si—H orbitals, which are polarised from silicon towards the hydrogen. As a result of the involvement of the lone pair in this conjugation, silylamines are much weaker bases than ammonia.78 Silyl ethers 2.15 are similarly less effective as Lewis bases than other ethers,79 and they show wide angles  for the two bonds to the oxygen atom. The extent of the interaction of the oxygen lone pair with *SiX in a range of silyl ethers 2.15, detected by a shortening of the Si—O bond length d, correlates with the extent to which the Si—O—C bond approaches linearity, reaching 180° for hexaphenyldisiloxane 2.16, and the explanation can be found in orbital interactions related to those described above. 80,81 d

H

*SiH Si

N

H H 2.14

SiH3 SiH3

X3Si

O R 2.15

Ph3Si

O

SiPh3

2.16

2.1.4.3 X-Substituents. We have seen that sulfur- and phosphorus-based groups like phenylthio or diphenylphosphinyl are X-substituents that are anion-stabilising, but they are exceptional. X-Substituents are usually p-destabilising rather than stabilising. The interaction of a lone pair of electrons on an oxygen atom, as a model for an X-substituent, and a filled p orbital on carbon create the p orbitals of the carbonyl group (Fig. 1.66) but with two electrons in p*CO. Since this interaction is the interaction only of atomic orbitals, the overall effect is a rise in energy, because p*CO is raised more in energy than pCO is lowered. In practice, although this effect in the p system must be present, electronegative elements usually stabilise an adjacent ‘anionic’ carbon. The reason is two-fold. In the first place, there is a Coulombic effect working in the  framework against the effect in the p system. The Coulombic effect is energy-lowering for an anion, because X-substituents based on electronegative heteroatoms are  acceptors. We see this conspicuously in the ease with which a base can remove the proton from chloroform. In the second place, we do not usually have an anion—what we have is a C—M bond. The repulsive interaction of a lone pair on an X-substituent and the  orbital is energy-raising. However, when the atom is a metal, it changes the story, because it has empty orbitals that can accept coordination from the lone pairs of the electronegative heteroatom. This coordination may be directly within the molecule, but is more often present in an aggregate, and it is always powerfully energy-lowering, making any effect on the p overlap much less important. The one X-substituent that probably does destabilise an anion is an alkyl group. An alkyl group, although classified as an X-substituent, is not a  acceptor, nor does it have much of a capacity to coordinate to a metal. Its destabilising effect is by  conjugation, which is discussed in Section 2.2.1.

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

81

2.1.5 Radical-Stabilising Groups82 2.1.5.1 C-, Z- and X-Substituents. All three kinds of substituent stabilise radicals. A C-substituent gives the orbitals of the allyl radical, which is just as stabilised as it was for the cation and anion (Fig. 1.33). A Z-substituent gives the same orbitals as those in Fig. 2.8, but with one electron in 2, leading to an overall drop in p energy and a reduction in the amount of Coulombic repulsion that destabilised cations. Finally an X-substituent gives the orbitals of the carbonyl group (Fig. 1.66) but with one electron in p*CO. With two drops in energy from the doubly filled orbital pCO matched by only one rise in energy from the singly occupied p*CO, the overall effect is a drop in energy. The three types of radical are summarised and placed on the same energy scale in Fig. 2.10, which also draws attention to the singly occupied molecular orbital (SOMO), the frontier orbital of a radical.

*

3

*

O

3

1

1

*C=O

O SOMO

SOMO

2

O SOMO

2

1

1

1

O

O

O

C

Fig. 2.10

O

C=O 1

Z

X

Energies and coefficients of the p orbitals of C-, Z- and X-substituted radicals

The overall stabilisation by an X-substituent83 accounts for the ease with which such radicals as 2.17 and 2.18 are generated in the peroxidation of amines and ethers, and why such radicals as 2.19 are long-lived. O N

2.17

N O

O

2.18

2.19

Since both electron-donating and electron-withdrawing groups stabilise radicals, Hammett plots for radicalforming reactions using ,  ands þ values are poor, because these parameters emphasise the capacity to

82

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

stabilise charge. To solve this problem, independent of the polar character of radical reactions (Chapter 7), a special  scale has been constructed using hyperfine coupling constants with the benzylic hydrogens in substituted benzyl radicals to establish the values. The numbers are all small, but all kinds of parasubstituents give positive values, denoting stabilisation, with the unusual exception of fluorine (–0.11). Some examples are: Ac 0.066, CN 0.043, tBu 0.036, MeO 0.034, Cl 0.017, Me 0.015, SOMe 0.006, OAc 0.001, CF3 0.001 and, by definition, H 0.84 2.1.5.2 Captodative Stabilisation.85 A special case is a radical that has both an X- and a Z-substituent, either directly attached to a radical centre as in the radical 2.20 or conjugated to it through a p system, as in the long-lived radicals 2.21–2.24. Radicals with this feature are called captodative,86 the capto referring to the Z-substituent (electron capture) and the dative to the X-substituent. Such systems have also been called merostabilised.87 Since both types of substituent can stabilise a radical, it is reasonable that both together can continue to stabilise a radical. We can see how this might be in Fig. 2.11, where the filled orbitals of a Z-substituted radical on the right are taken from Fig. 2.10 and an arbitrary lone pair is placed on the left. The interaction of these two systems creates the set of orbitals in the centre. O– Me

CO2Me

CN

t

N

SBut

BuS

N Me

CN O 2.20

CN

N Et

2.21

2.22

CN

2.23

O2N

NPh2

NO2 2.24

There is a rise in energy in creating 3, but there is only one electron in this orbital. There is a small drop in energy in creating 2 and a more significant drop in energy in creating 1, both of which have two electrons in them. Overall the energy has dropped, and the radical as a whole is lower in p energy than the separate components. Another way of looking at the whole set of orbitals is to recognise that the captodative system consists minimally of four atoms, each with a p orbital, with the two at each end electronegative, and with a total of five electrons in the p system. An O—C—C—O arrangement is the paradigm. We can set up such a system in a different way from that in Fig. 2.11 by joining two carbonyl groups together by their carbon atoms, and feeding five electrons into the resultant p orbitals, which would resemble the p orbitals of butadiene, but all 3

2

1 2

1

X

1

X

Fig. 2.11

Z

Z

The effect of bringing an X-substituent into conjugation with a Z-substituted radical

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

83

lower in energy because of the presence of the electronegative atoms and with one electron in 3*. The result is of course the same as in Fig. 2.11, with 3 coming out as an essentially nonbonding orbital somewhere near the  level. Yet another way to appreciate this outcome is to think of the ultimate captodative system as being a radical flanked on one side by the simplest possible donor, a filled p orbital on carbon, and on the other by the simplest possible acceptor, an empty p orbital on carbon. This system is of course the allyl radical, which has its SOMO, 2 in this case, precisely at the  level. However, it is not obvious whether captodative substitution is actually better at lowering the overall energy than having two Z- or two X-substituents. Several calculations have been carried out and much experimental evidence has been accumulated, but the point has still not been resolved. What is clear is that captodative substitution is not inherently worse in stabilising a radical than two like substituents, and if there is a specific captodative effect, it is small, never more than about 25 kJ mol1 (6 kcal mol1). The kind of experimental evidence that seems to imply special stabilisation to captodative radicals is the ease of the reversible C—C fragmentation of the diaminosuccinate 2.25, in which the rate implies that the captodative radical 2.26 is some 17 kJ mol1 (4 kcal mol1) lower in energy than might be expected by adding together the stabilising effects of each of the substituents.88 Me2N

NMe2

Me2N

NMe2

+ EtO2C

CO2Et

EtO2C

2.25

CO2Et

2.26

Another piece of evidence comes from measurements of the rate of rotation about the C-2 to C-3 bond of a range of allyl radicals 2.27. At the point of highest energy in the rotation, the radical will lose its allylic character (Section 2.3.1.5), and be stabilised only by the substituents R1 and R2. The captodative radical with R1 ¼ OMe and R2 ¼ CN had the lowest activation energy, some 12 kJ mol1 (2.9 kcal mol1) lower than the sum of the substituent effects would have suggested, and with the radicals with R1 ¼ R2 ¼ OMe and R1 ¼ R2 ¼ CN having activation energies some 24 kJ mol1 (5.7 kcal mol1) higher in energy.89 R2 R1 2.27a

R1 R2 2.27b

What does seem to be clear is that neither two donors nor two acceptors have quite twice the stabilising effect on a radical of one, but one of each does have something close to an additive effect. In this formulation at least, the captodative effect does appear to be real. 2.1.6 Energy-Raising Conjugation We saw above that not all conjugation is energy-lowering—an empty p orbital conjugated to a Z-substituent (Section 2.1.3), and a filled p orbital conjugated with an X-substituent (Section 2.1.4) were both energyraising. In the former case, the system is usually stabilised in the p system, but Coulombic effects make it overall destabilising. In the latter, the repulsive effect of two filled orbitals inherently destabilise the p system (E2 > E1 in Fig. 2.12), but other factors such as coordination within dimers, sometimes lead to overall stabilisation. Examples of the repulsive interaction of two filled p orbitals where there are no mitigating factors are the conformations adopted by hydrogen peroxide 2.28 and hydrazine 2.29. The

84

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS 2

HOMO

E2 X

X E1 1

X

X

X

X

The p interaction of two X-substituents

Fig. 2.12

overlap is avoided by twisting about the X—X bond, so that the two lone pairs are as little in conjugation as possible.

O

H

H N

O

H N

H

H

2.28

2.29

H

Two further examples of energy-raising conjugation are related to the orbitals we saw in Fig. 2.11. Two carbonyl groups in conjugation can be viewed as a carbocation conjugated to a Z-substituent. We used the idea earlier of a carbonyl group as having some of the character of a carbocation, since the p bond is polarised towards the oxygen atom. If such a group is conjugated to a carbonyl group, the p molecular orbitals will be those of Fig. 2.11, but with no electrons in 3. As with a carbocation in Fig. 2.8, the presence of the Z-substituent is probably p-stabilising, with 1 in Fig. 2.11 falling in energy more than 2 rises, but there will be a Coulombic repulsion between the two carbon atoms, both of which bear a partial positive charge. Evidence for the consequent high energy comes from the extent to which -diketones like 1,2-cyclohexanedione 2.30 have the enol 2.31 as the stable tautomer, and evidence for the p stabilisation can be found in such molecules as glyoxal 2.32, where the carbonyl groups stay in conjugation rather than twisting. Twisting would do nothing to relieve the Coulombic repulsion, but it would remove the p conjugation. The s-trans conformation is favoured, because the relatively large partial negative charges on the oxygen atoms repel each other. O

O O

OH

H

O

2.32 2.30

O O

H

O 2.33

2.31

A second system is essentially the same, but with two more electrons—the enediolate ion 2.33 has the p molecular orbitals of butadiene, lowered by the presence of the two electronegative atoms, but with two electrons in 3*. However one thinks of it, it is a p system higher in energy than the separated components. We have seen therefore that both the diketone and the enediolate are destabilised systems, but that the

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

85

radical, with one electron more than the diketone and one fewer than the dienolate, may even be especially well stabilised. A manifestation of this situation is the use of enediolates and related systems like metol anion 2.34 as photographic developers, where their role is to transfer one electron to the silver cation.90 Another familiar example is the ease with which hydroquinone anions 2.35 are oxidised to the captodative quinhydrone radical anion 2.21, and quinones 2.36 are reduced to the same species. O

NHMe 2.34

2.2

O

O

O

–e, –H+

–e

+e, +H+

+e

OH

O

O

2.35

2.21

2.36

Hyperconjugation—s Conjugation91

Conjugation has largely been discussed so far as taking place between p orbitals in a p system. However, it is just as reasonable to consider the conjugation of  bonds with each other or of  bonds with p orbitals. It is usual to look at hybridised orbitals for the  bonds. In the simplest possible case, ethane, the p bonding from the pz components in Fig. 1.22 would be subsumed into the sp3 hybrids of the  C—H bonds and into their conjugation with each other. The overlap of  bonds with  bonds or p orbitals is called hyperconjugation, a serious misnomer, because hyperconjugation, far from being especially strong, as the prefix hyper implies, is usually a feeble level of conjugation compared with the kind of p conjugation that we have seen so far. Another term that is sometimes used is  conjugation, on the grounds that it is conjugation of a  bond with something else, but this is not satisfactory either, since the overlap is p in nature not . Yet another term that is used is vertical stabilisation,92 which is not a misnomer, but is not usefully specific about its nature. Perhaps for these reasons, the word hyperconjugation appears to survive, and probably cannot be dislodged. Although present in all compounds having interacting  bonds, it is most significant when it is energy-lowering. 2.2.1 C—H and C—C Hyperconjugation 2.2.1.1 Hyperconjugation of C—H Bonds with C—H Bonds. Using hybridised orbitals for C—H bonds, and mixing them in the usual way to show conjugation, creates the molecular orbitals of Fig. 2.13, which is set up for the anti-periplanar interaction. There is an equivalent set of orbitals interacting in a syn-coplanar arrangement, the relative merits of which are discussed on pp. 98–100. The major interactions are between the C—H orbitals close in energy, namely  with , and * with *. The  and * orbitals of the C—H bond are so far apart in energy that the effect of mixing in the interaction of  with * will be small, and the overall result can reasonably be expected to be energy-raising overall (E2 > E1). This is a useful lesson. The interaction of two filled orbitals is only energy lowering when there is an additional contribution from a bonding interaction with an empty orbital close enough in energy and with the right symmetry, as in the lowering in energy of both 1 and 2 in butadiene by the bonding contribution from the p with p* interactions (Figs. 1.38 and 1.39), in contrast to the situation here, where the  orbitals are too far apart in energy. The interactions of all the -bond orbitals with each other in larger molecules than ethane affect the overall electron distribution and energy, but sometimes a particularly strong interaction stands out, and can be invoked to explain a molecular property. This is the explanation93 for the Perlin effect mentioned on p. 64, in which the 1H-13C coupling constants reveal that the axial C—H bonds in cyclohexanes are slight longer than the equatorial C—H bonds. Of all the -bond interactions, that between the anti-periplanar axial C—Hs on

86

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS H (

1– 2)

* H

H

*

*

H

1

2

H

*

(

1+ 2)

(

1– 2)

H H

H

E2

H 1

2

H

E1

H (

1+ 2)

H

Fig. 2.13

Hyperconjugation of one C—H bond with another

adjacent atoms, the bold lines in the drawing 2.37, are the most powerful. As we can see in Fig. 2.13, this is overall energy-raising, and the effect is to stretch these C—H bonds as a result of their overall weakening. Evidently the geometrically similar anti-periplanar overlap of the equatorial C—H bonds with the neighbouring C—C bonds, the bold lines in the drawing 2.38, is less powerful, a feature that contributes to the idea that C—H hyperconjugation is stronger than C—C hyperconjugation. 2.2.1.2 Hyperconjugation of C—H Bonds with Lone Pairs. Overlap between a filled p orbital and the orbitals of a  C—H bond is similarly energy-raising overall. A C—H bond anti-periplanar to a filled p orbital is weakened 2.39, and the bond length increased. The hydrogen atom is potentially a hydride leaving group, and -hydride delivery is well known with alkyl Grignard and lithium reagents, which are often called anions. The same overlap explains94 the weakening of C—H bonds conjugated to anti-periplanar nitrogen lone pairs, as seen in the lower C—H stretching frequency in the infrared spectra for compounds like the amine 2.40, which gives what are called Bohlmann bands, typically at 2700–2800 cm1, instead of at the more usual frequency 2800–2900 cm1 for a more tightly held C—H bond.95

H

H H

H

N

H

H

H

H

H 2.37

2.38

2.39

H 2.40

H

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

87

2.2.1.3 Stabilisation of Alkyl Cations by Hyperconjugation. The effects of conjugation of one  bond with another are buried in the  framework, and their consequences, being the sums of several such interactions, are not particularly obvious except in minor features of bonding such as those discussed above. Hyperconjugation is much more evident in the stabilisation given to an empty p orbital on carbon by a neighbouring alkyl group, and to which the word is most frequently applied. It is well known that alkyl substituents stabilise carbocations. Fig. 2.14 shows the interaction of the  orbitals of the C—H bond on the left with the empty p orbital on the right. The net result is the lowering of the overall energy by an amount 2E. The interaction in Fig. 2.14 is similar to that shown in Fig. 1.33 for the allyl cation, except that it is a  bond instead of a p bond interacting with the empty p orbital. Because the CH orbital in Fig. 2.14 is lower in energy than the p orbital in Fig. 1.33, the hyperconjugative interaction with the empty p orbital is less effective, and the overall drop in energy 2E is less than it was for simple p conjugation.

*

H

3

H

*

CH

2

H

pC

H CH

E

H 1

Fig. 2.14 Interaction of the orbitals of a  C—H bond with an empty p orbital on carbon

As usual, hybridisation, although a convenient device, is unnecessary—the energy-lowering could equally well have been explained using the pz orbital on carbon, with the most significant interaction illustrated on the left in Fig. 2.15. Indeed, this provides a more simple way to appreciate that the lowest-energy conformation of the cation is not overwhelmingly that in which one of the  bonds is aligned to overlap with the empty p orbital. Because the two p-type orbitals, pz and py, have the same energy, the interactions in the two conformations shown in Fig. 2.15 are, to a first approximation, equal (EA ¼ EB). We can expect that the barrier to rotation about the C—C bond of the ethyl cation will be small. Although intuitively reasonable, it is not so easy to set up an interaction diagram using hybridisation to show that the energy-lowering effect of the imperfectly lined up overlap of two C—H  orbitals with the empty p orbital is the same as the perfectly lined up overlap of one. Whereas the interaction of a  C—H bond with another C—H bond is energy-raising (Fig. 2.13), the interaction of a  C—H bond with a  bond to an electronegative element is energy-lowering. The shift in electron population towards the electronegative element gives the carbon atom of the bond some of the character of a carbocation. As a result the hyperconjugation is more like the interaction of a C—H bond with an empty p orbital, and is both energy-lowering and more powerful. The effect can be seen in the lengthening of C—H bonds involved in such hyperconjugation, as in the 1,3-dioxan 2.41. In contrast to cyclohexanes,

88

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS H H

H

H H

C

H

C

C

H

pz

pyH

C

H H z

EA

H

H

y

C

C

EB

H

H

H H

C

H

H

(a) Conf ormation A

(b) Conf ormation B

Fig. 2.15

H C H

Orbital interactions stabilising two conformations of the ethyl cation

which have the axial C—H bonds longer than the equatorial, the equatorial C—H bond at C-5 in 1,3-dioxan is longer than the axial C—H bond. The reason is that the conjugation between the equatorial bond and the C—O bond anti-periplanar to it, emphasised with the bold lines, is now stronger.93 This is known as the reverse Perlin effect. H

lengthened

5

O O

H

2.41

The overlap and its consequences, as illustrated in Figs. 2.14 and 2.15, could equally well have been drawn with C—C bonds in place of the C—H bonds. The energies of C—C and C—H bonding and antibonding orbitals are similar to each other, and the value of E will be similar. Indeed it is still a matter of debate, both in theory and in interpreting experimental results, whether C—H or C—C bonds are more effective as p-donor substituents, a topic we shall return to in Chapter 5. What is clear is that alkyl groups in general are effectively p-electron donors, in much the same way as, but to a lesser extent than, a double bond or a lone pair. We have already used this fact in classifying an alkyl group as an X-substituent (Fig. 2.1). One case where C—C bonds are exceptionally effective in hyperconjugation is in the stabilisation provided by a cyclopropyl substituent to an empty p orbital. The cyclopropylmethyl cation is actually better stabilised than an allyl cation, as judged by the 41 times more rapid solvolysis in a good ionising solvent of cyclopropylmethyl chloride 2.42 than of crotyl chloride 2.43.96 Cl

H2O, EtOH

OEt Cl

50° 2.42

k1 (rel) 41

H2O, EtOH

OEt

50° 2.43

k1 (rel) 1

In this case, hyperconjugation appears, unusually, to be better than p conjugation. This can be explained using the Walsh orbitals of a cyclopropane (Fig. 1.53), where one of the degenerate pair of highest occupied orbitals is a py orbital with a large coefficient on carbon which can orient itself in such a way as to stabilise an empty p orbital on a neighbouring atom 2.44a, seen from a different perspective in 2.44b. This is like

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

89

conjugation with a full p orbital, and is therefore more effective in lowering the p energy than conjugation with a p bond is in the allyl cation (Fig. 1.33). The other high-energy filled orbital in the Walsh diagram has the wrong symmetry for overlap with the neighbouring p orbital, and has no effect on its energy one way or the other. If the carbonyl group is thought of as a highly stabilised carbocation, this picture 2.44 is supported experimentally by the preferred conformation in many systems,97 as can be seen in the two most populated conformations adopted by cyclopropane carboxaldehyde 2.45a and 2.45b.98 H H

H H

= H

H

H H

H

H O

H

O H

H

H 2.44a

2.44b

2.45a

2.45b

As usually defined, hyperconjugation implies no change in the shape of the molecule caused by the extra overlap, as illustrated in Fig. 2.14. However, the extra bonding in 1 between the  C—H bond and the p orbital ought to have the effect of shortening the C—C bond and lengthening the C—H bond (or C—C bond if that is involved), and there is experimental evidence from X-ray crystal structures that this does indeed happen.99 Thus the bicyclo[2.2.1]heptyl cation 2.46 shows shortening of the three C—C bonds to ˚ ), and the cationic centre relative to a typical bond between a tetrahedral and a trigonal carbon (1.522 A lengthening of the bond between C-1 and C-6 relative to a typical bond between two tetrahedral carbons ˚ ).100 This shows the effects expected from the hyperconjugative overlap shown with bold lines on (1.538 A the drawing 2.47.

H

–0.011Å 6

1 2

H

+0.172Å –0.113Å

–0.046Å 2.46

2.47

Hyperconjugation has had a chequered history. The valence-bond representation of it has misled many people. It was proposed in the 1930s, although not named as such, as an explanation for the BakerNathan order (Me > Et > Pri > But) of apparent electron-releasing ability of alkyl groups.101 Today, the Baker-Nathan order is almost always better explained by steric hindrance to solvation rather than by C—H hyperconjugation being more effective than C—C hyperconjugation: tert-butyl compounds are not as well solvated as methyl, and the device of placing the alkyl group para to the site of reaction does not, as it was supposed to, remove it from solvation sites. For this reason, hyperconjugation was quite widely discredited in the 1950s.102 Today, it enjoys a more soundly based popularity. Formulated in molecular orbital terms, as Mulliken did when he first used the word,103 and especially as used to explain the electron-donating effects of alkyl groups, hyperconjugation is widely accepted. It is better to think of an alkyl group as contributing its electrons by hyperconjugative p overlap than by an inductive effect in the  framework. An alkyl group is not a  donor, unless the atom to which it is bonded is significantly more electronegative than tetrahedral carbon, and, in any case,  donation is not obviously able to influence the thermodynamic and kinetic properties of a p system. The capacity of a methyl group to be either a donor or an acceptor, 104 depending upon what it is bonded to, has been a source of much unnecessary confusion.

90

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

attraction narrows the angle H

attraction shortens the C—C bond

2.48

H

H

H

2.49a

2.49b

2.49c

2.2.1.4 Bridging in Carbocations. Hyperconjugative overlap ought also to reduce the H—C—C angle , because there is now extra bonding between the hydrogen atom and the empty p orbital 2.48. Since 1 resembles more the CH orbital that it is close to in energy, the p orbital will have a small coefficient, and this effect may not be large. However, there is the possibility that the attraction builds up, until the hydrogen atom sits halfway between the two carbon atoms 2.49. The bonding in this structure 2.49a can be represented with hybridisation as two half filled orbitals made up from sp3 hybrids and the 1s orbital of hydrogen 2.49b, or without hybridisation as largely made up by the interaction of the empty 1s orbital of an isolated proton with both lobes of the p bond of ethylene 2.49c. The bonding, however it is described, is the same, and similar in nature to that of other two-electron, two-bond bridged systems, such as those in diborane. This structure may be the minimum in the energy profile, as it is in diborane, or it may be a maximum, in which case it is the transition structure for the [1,2]-shift of the hydrogen or carbon atom from one carbon to the next. Although tertiary cations like 2.46 are well established not to have bridged structures, it is not easy to discover whether hyperconjugation, with the minimum movement of the atoms, or the full bridged structure is the lower in energy for secondary cations. In the 1960s, a large amount of effort went into trying to solve experimentally the problem of the nonclassical ion, as it was called, using more complex systems than the ethyl cation, and with carbon as the bridging group.105 No easy answers were forthcoming, and theoretical calculations also gave conflicting or ambiguous answers, one of many problems being that calculations on ions in the gas phase inherently favour bridged structures, because bridged structures spread the charge more effectively when there is no solvent to help. The present state of opinion probably favours structures like 2.48 without bridging for almost every alkyl cation except the most simple, the ethyl cation itself, which is only found in the gas phase.106 The bridged structure 2.49 is therefore a low-energy transition structure for a [1,2]hydride shift, and, with carbon in the bridge, the transition structure for the Wagner-Meerwein type of cationic rearrangement. Successive [1,2]-shifts of this kind are so easy in cyclopropylmethyl cations 2.50 ! 2.51 ! 2.52 ! 2.53, etc., that each of the three carbons carrying two hydrogen atoms can take up the place of the others, and experimentally each has been found to have an equal probability of capturing whatever nucleophile is supplied.97 The other carbon, carrying just one hydrogen, is the only one that is different, but it too can capture a nucleophile to give cyclobutyl products 2.56. This has led to much conjecture about the low-energy structure of such cations, suggesting that the picture 2.44 is inadequate. Another aspect of this intriguing system is the possibility occasionally seen in substituted examples, in which the nucleophile is captured at one of the bridging methylene carbons to give 3-butenyl products 2.55 rather than cyclopropylmethyl products like 2.54 and 2.57. It is tempting to identify the bridged structure 2.51, which may or may not be a minimum, as the source of these products, since the picture 2.51 is the structure of a 3-butenyl cation with the empty p orbital coordinated to the p bond. However, this picture lacks the right symmetry to make all the methylenes identical, and an alternative 2.58, with the single carbon sitting above the middle of a trimethylene fragment is needed to do that. This picture is not, in fact, supported by any evidence, and a better structure, as judged by subtle NMR experiments, resembles a carbene sitting above the p orbitals of an allyl

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

91

cation 2.59.107 This picture is not far from that shown in 2.44, as long as we allow for the incompleteness of that picture, which only illustrates the major source of stabilisation for the carbocation, and accept that rapid interconversions make all the methylene carbons equivalent.

H H

H

H

2.50

2.51

2.52

2.53

Nu

Nu

Nu Nu 2.54

2.55

2.56

H

H C H

C H

CH C H H

2.57

C H

H

H H

C C

C

H

H

H

2.58

2.59

2.2.1.5 Stabilisation of a p Bond by Hyperconjugation. Hyperconjugation has also been used to explain another well-known thermodynamic property—that alkenes prefer to be more rather than less substituted by alkyl groups. An alkene like 2-methyl-1-butene 2.60 undergoes easy protonation in acid to give the t-amyl cation 2.61, which can lose a proton to give 2-methyl-2-butene 2.62. The ease of the reaction is explained by the hyperconjugative stabilisation given to the intermediate tertiary cation 2.61, as discussed in Section 2.2.1.3 above. What is not so obvious is why the more-substituted alkene 2.62 is lower in energy then the less-substituted alkene 2.60, which it certainly is, because the equilibrium lies well to the right. Heats of hydrogenation of alkenes provide quantitative evidence of the greater thermodynamic stability of the more substituted alkenes, with the attachment of one or more alkyl group more or less additively increasing the heat of hydrogenation of an alkene by about 10 kJ mol1 (2.4 kcal mol1).108 H

2.60

–H

2.61

2.62

One factor appears to be the hyperconjugative stabilisation of the C¼C p bond by the alkyl groups. Fig. 2.16 shows the interaction of the orbitals of a  bond with the orbitals of a p bond. Two p bonds interacting are overall energy-lowering, as we saw in Fig. 1.39 for butadiene. However, two  bonds interacting are overall energy-raising, as we saw in Fig. 2.13 for ethane. Hyperconjugation of a  bond with a p bond could go either way, and evidently it falls on the side of being energy-lowering. The -bonding orbital and the

92

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS H H

*

4

* H

* *

3

H 2

E2

H H E1

Fig. 2.16

1

Hyperconjugative stabilisation of a C¼C p bond

p*-antibonding orbital are perhaps just close enough for them to mix in a bonding sense effectively to lower the energies of 1 and 2, and thereby to make the drop in energy E1 a little greater than the rise in energy E2. 2.2.2 C—M Hyperconjugation In Fig. 2.14, the stabilising effect of the hyperconjugation was quite small, because the energy gap between the -bonding orbital and the empty p orbital on carbon was large. A  bond closer in energy to the empty p orbital should have a larger interaction and be more stabilising. This is the case when the  bond is between a metal and carbon. A metal is inherently more electropositive than carbon (to an organic chemist anything more electropositive than carbon can be regarded as a metal). A metal and a carbon atom will have an interaction diagram like that of the C—O  bond in Fig. 1.35, except that the carbon will be the electronegative atom and the metal will take the place of the carbon. Fig. 2.17 shows the energies of the bonding and antibonding orbitals from carbon to an electropositive element M on the left and to an electronegative element X on the right. Transferring the orbitals for a C—M bond on the left in Fig. 2.17 to an interaction diagram like that of Fig. 2.14, leads to Fig. 2.18 as a description of a -metalloethyl cation 2.63. With the CM bonding orbital higher in energy than the bonding CH orbital, the interaction with the empty p orbital on carbon will be stronger than it was for C—H, and the drop in energy E will be greater. Such cations are well stabilised by hyperconjugation. Metal-stabilised cations can be expected to adopt and retain the conformation 2.63. The alternative conformation 2.64, with the empty p orbital at right angles to the M—C bond, is not stabilised any better than it is by an alkyl group, because the M—C bond is in the node of the empty p orbital and there will be no interaction between them. Since rotation would have to go through this conformation, there must be a barrier. The stabilisation seen in Fig. 2.18 is enhanced by the polarisation of the M—C bond. The coefficients in the CM orbital are large on the carbon atom and small on the metal atom, just as the coefficients of the C—X (or C—O) bonding orbital are large on the X (or O) atom and small on the carbon atom (Figs. 1.59 and 2.19). The bonding interaction of the CM orbital with the empty p orbital will therefore be greater than it was for the corresponding overlap of the CH orbital in Fig. 2.14, where the coefficient on the carbon atom was smaller, being more or less equal on both atoms. Thus we have a more favourable energy match and a more favourable coefficient for the overlap of the M—C bond than for the H—C bond.

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

M

M

2.63

M

93

C

2.64

*CM *CX

C

X

pM

M

pC

C

pX M

C

CM

CX

Fig. 2.17

X

X

C

-Bonding and antibonding orbitals from carbon to an electropositive element M and to an electronegative element X

M

M

*

3

*CM C

C M

C 2

pC

M M

CM

C

E 1

Fig. 2.18

C

Interaction of the orbitals of a carbon-metal bond with an empty p orbital on carbon

94

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

The degree of this stabilisation is of course dependent upon what the metal is.109 In practice, cations with this general structure have been investigated using barely metallic metals, like silicon, because the more familiar and substantially metallic elements are too reactive. Even a trimethylsilyl group as the atom M in a cation 2.65 is lost too easily for the cation itself to be studied directly,110,111 with essentially only one sighting, and that in a heavily hindered case.112 Nevertheless, it is clear from much evidence that silyl groups are substantially stabilising of  cations.113 The Si—C bond is aligned with the empty p orbital,114,115 and rotation about the C—C bond is dramatically slowed down so that cations of the general structure 2.65 are configurationally stable during most reactions. Me3 Si

Me3Si

2.65

2.66

The question of bridging also arises here, since the lowest energy structure might be the bridged cation 2.66. Experimental evidence on -silylethyl cations is somewhat inconclusive,116 but is perhaps moving towards the belief that the hyperconjugation model is more likely to be true than the bridging model for most cations.112 Calculations in simple systems indicate that only the least substituted cation, the trimethylsilylethyl cation itself, might be bridged, and that applies only to the vapour phase, which is likely to emphasise bridging, since no solvent influences can provide stabilisation to the localised cation.117 The structure 2.65 with hyperconjugation is probably the better description of all the more substituted -silicon-stabilised cations. A complementary observation is seen when a silyl group is conjugated to a carbonyl group in an acylsilane 2.69, which is yellow in colour because of the exceptionally long wavelength of the n!p* transition in the UV spectrum. The n!p* transition is the promotion of one of the electrons of the lone pair on the carbonyl oxygen, labelled nO into the p* orbital of the carbonyl group (Fig. 2.19). Two effects contribute to the long wavelength of this transition in the acylsilane. The Si—C bond from the silicon atom to the carbonyl carbon is conjugated with the anti-periplanar lone pair on the oxygen atom. This conjugation is like that in Fig. 2.18,

1 *C=O

*C=O

*C=O n→ * max

n→ * 270 nm

max

n→ * 298 nm

max

380 nm nO

1

nO

nO

C=O

C=O

O

O

C=O

O SiMe3

2.67

2.68

Fig. 2.19

n!p* transitions of ketones

2.69

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

95

but with pC replaced by the lower-energy nO orbital of the lone pair. Thus the lone pair is raised in energy, just as 2 is raised, but this time it is filled. At the same time the Si—C bonds between the silicon atom and the methyl substituents are polarised as in Fig. 2.18 with the electron distribution moved away from the silicon and spread out into the methyl groups. A trimethylsilyl group is a Z-substituent, as we saw on pp. 78–80 of that special kind that does not include a contribution from having a p bond, and it lowers the energy of the p* orbital. The combination of the raised nO orbital and the lowered p* orbital decreases the frequency and hence increases the wavelength of the transition from 270 nm for acetone 2.67 to 380 nm for acetyltrimethylsilane 2.69. The conjugation from a C-substituent, as with the ,-unsaturated ketone 2.68, lowers the p* orbital more than the conjugation with the silyl group lowers it, but leaves the energy of the nO orbital essentially unchanged. The n!p* wavelength is raised relative to that of acetone, but the effect is smaller.118 2.2.3 Negative Hyperconjugation119 2.2.3.1 Negative Hyperconjugation with a Cation. If instead of a metal, the carbon is bonded to an electronegative element, the interaction diagram corresponding to Fig. 2.18 changes to that of Fig. 2.20. The orbitals of the X—C bond, taken from Fig. 2.17, are now lower in energy than the corresponding C—H orbitals. The interaction of CX with the p orbital will now have little energy-lowering effect on 1, because the orbitals are so far apart in energy. There is therefore little p stabilisation afforded to a cation in the conformation 2.70, and in addition there will be the usual strong inductive electron withdrawal destabilising it in the  framework. The alternative conformation 2.71 possesses the greater degree of hyperconjugative stabilisation, as long as the other substituents on the carbon atom are not as electronegative as X, and will be preferred, but the inductive withdrawal will still make it a relatively high-energy cation. A trifluoromethyl group, for which the two conformations would be essentially equivalent, is well known to be a powerful destabilising influence on a carbocation.69 X

X

2.70

2.71

X

*

3

X

*CX C

C X

pC

E C

2

X

X CX

C

Fig. 2.20

1

C

Interaction of the orbitals of a bond between carbon and an electronegative element X with a p orbital on carbon

96

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

2.2.3.2 Negative Hyperconjugation with an Anion. However, if it is a carbanion that is conjugated to the X—C bond, the p orbital is filled. The orbital 2 in Fig. 2.19 is lowered in energy significantly by an amount E as a consequence of the orbital *CX being so much closer in energy to the p orbital than either of the orbitals *CM in Fig. 2.18 or *CH in Fig. 2.14. Since 2 is filled, there is a drop in energy E, which the cation does not benefit from. As a consequence of the hyperconjugation, the conformation 2.72 is now stabilised more than the alternative 2.73. Furthermore, the large coefficient on carbon in the *CX orbital makes its overlap with the filled p orbital even more bonding than without the electronegative element X, and the small coefficient on carbon in the CX orbital makes its overlap with the filled p orbital even less antibonding, both factors further contributing to E, the lowering in energy of the 2 orbital. This type of hyperconjugation is sometimes called ‘negative’ hyperconjugation, because it is conjugation with a negative charge, but it is another serious misnomer, since energy-lowering is usually regarded as a positive outcome. X

X

2.72

2.73

This phenomenon is not usually seen with carbanions themselves. Even if it were, simple carbanions would not be trigonal as they are shown in Fig. 2.20 and in the drawings 2.72 and 2.73. The picture in Fig. 2.20 is simply the paradigm for the more general structures, like organolithium compounds, which are called anions. The well-known electron-withdrawing power of the trifluoromethyl group is at least partly, and perhaps wholly, explained by negative hyperconjugation,120 as is the capacity of an o-fluoro group to induce metallation of a benzene ring.121 Another manifestation of negative hyperconjugation is the capacity of neighbouring silicon-, phosphorus- and sulfur-based groups to stabilise anions, already covered in Section 2.1.4.2. 2.2.3.3 The Anomeric Effect.122 A lone pair on an electronegative element conjugated to a C—X bond, in which X is an electronegative element, is a special category of negative hyperconjugation. The bestknown illustration of this anomeric effect, as it is called,123 is in the equilibrium position for the methyl glucosides 2.74 and 2.75, where it has long been known that, when equilibration is possible, as it is here, the diastereoisomer with the axial methoxy group 2.75 is the lower in energy, in spite of the usual observation that the lowest-energy conformation of six-membered rings has substituents equatorial.124 HO HO HO

HCl, MeOH

O OMe OH 2.74

HO HO HO

O HO

OMe

2.75

Although several factors are at work, the generally accepted explanation for this phenomenon is principally associated with negative hyperconjugation, similar to the stabilisation of a carbanion discussed in the preceding section, but with the lone pair on the ring oxygen atom taking the place of pC. Lone pairs are given the letter n as a distinctive label. Thus the anomeric effect is a consequence of the overlap of the nonbonding lone pair nO with the low-lying * orbitals of the exocyclic C—O bond 2.76, superimposed, of course, on all the usual interactions of filled orbitals with filled orbitals.125 The lone pairs on oxygen can be described as being in two sp3 hybrids. Only when the exocyclic C—O bond is axial are its orbitals able to overlap well with the axial sp3 hybrid lone pair on the ring oxygen 2.76. Alternatively, without using hybridisation, it is the nonbonding pz lone pair that overlaps better with an axial C—O bond.

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

97

nO O H

* OMe 2.76

At the same time, the methyl group on the exocyclic oxygen adopts a conformation in which it sits gauche to the ring oxygen atom, as a consequence of the lone pair on the exocyclic oxygen atom being conjugated antiperiplanar with the * orbital of the endocyclic C—O bond 2.77. This is perhaps a little clearer in the Newman projection from above 2.78. The preference for the gauche orientation is called the exo anomeric effect. The exo anomeric effect operates even with those tetrahydropyrans that have equatorial substituents at the anomeric centre—although the endocyclic oxygen cannot indulge in an anomeric interaction, the exocyclic oxygen can 2.79 (¼ 2.80). O

O

* H

=

Me

O

*

O O

H H

O Me 2.78

=

O

H

nO

nO 2.77

Me

Me

2.79

2.80

The anomeric effect can be seen in many systems with the features RO—C—X, most of which adopt a conformation with the R group gauche to the X group rather than anti, as one might have expected. This is the generalised anomeric effect, and it has many manifestations, such as the preferred conformations for fluoromethanol 2.81 and methoxymethyl chloride 2.82. Nor is it confined to oxygen lone pairs. The preferred conformation for the diazaacetal 2.83 has one of the alkyl groups axial in order that the lone pair on that nitrogen can be conjugated with the C—N bond. The optimum anomeric effect in this system would have both alkyl groups axial, but this conformation would have a 1,3-diaxial interaction between the alkyl groups, and this steric repulsion, not surprisingly, overrides the anomeric effect. H

H F

N

O

H 2.81

R

H

Me Cl

O

N

H 2.82

2.83

R

Bond lengths are also affected, just as they are in the other examples of conjugation involving  bonds. When the two heteroatoms are different 2.84, with one lone pair on a less electronegative atom like oxygen and the other on a more electronegative element like a halogen, bond shortening is more noticeable in the O—C bond, and the C—X bond is increased in length. The anomeric effect between nO and *CX increases the p bonding in the C—O bond but, because it mixes in an antibonding orbital between the C atom and the halogen, that bond is weakened and made longer. The anomeric effect of nX with *CO is less, because *CX is lower in energy than *CO and nO is higher in energy than nX, making the energy match better between nO and *CX. Thus the consequence of a lop-sided anomeric effect is overall to weaken the C—X bond—as the electron population is increased on the carbon atom, the X atom moves away.

98

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

increased bonding, bond-shortening

decreased bonding, bond-lengthening

1.382Å

1.394Å 4

nO

O

*CX

O

3

O

1

X

1.819Å

Cl

O

Cl

O

2

1.425Å

1.781Å

1.432Å

2.85

2.84

2.86

This is dependent upon the geometry, as seen in the structure of cis-1,1-dichlorodioxan 2.85.126 The length of the equatorial C—Cl bond is the same as that in methyl chloride, because it is oriented at an angle giving little conjugation with the lone pairs on the neighbouring O-1. In contrast, the axial C—Cl bond is lined up for an anomeric effect with the axial lone pair on O-4, and it is longer. At the same time, the bond between O-4 and C-3 is shortened, whereas the bond between O-1 and C-2 is close to that for the C—O bond in a normal ether. In symmetrical systems, anomeric effects are acting in both directions, but it is clear that bond-shortening from the anomeric effect in the one direction is stronger than the bond-lengthening in the other, in line with the overall stabilisation provided by the anomeric effect. Thus, with dimethoxymethane 2.86,127 the central pair of C—O bonds are equal in length and both are shorter than normal because of the anomeric effects, while the other pair of C—O bonds, the O—Me groups, have normal C—O bond lengths. 1.326Å

1.358Å

1.385Å

HH F

F H

2.87

1.317Å

HH

FH F

F 2.88

FF F

F 2.89

F 2.90

Similarly, the fluoromethanes have F—C bonds that shorten128 as the number of fluorines increases from one in 2.87 to four in 2.90, and the number of generalised anomeric effects accumulates. The bond-strengthening represented by these bond-shortenings contributes to the reduced reactivity towards nucleophilic substitution seen in polyhalogenated alkanes. If the axial exocyclic oxygen-based group in a tetrahydropyran 2.76 is a better leaving group than methoxy, the anomeric effect between the ring oxygen and the substituent is increased. A better leaving group like phenoxy effectively has a more electronegative oxygen. The anomeric effect shortens the endocyclic bond, and lengthens the exocyclic bond. Using X-ray crystallographic data, Kirby has shown that there is a linear correlation between the pKa of a range of exocyclic groups OR and the length of either the endocyclic or the exocyclic C—O bond. He finds that the better the leaving group (the lower the pKa of RO–), the shorter the endocyclic and the longer the exocyclic bond, providing a quantitative demonstration of the anomeric effect. Since the pKas also correlate with the rates with which the acetals undergo solvolytic cleavage of the exocyclic bond, he has produced a true structure–reactivity correlation, and a series of stills from a movie for the early stages of the reaction.129 2.2.3.4 Syn-coplanar and Anti-periplanar Overlap. In the discussion about the anomeric effect, the lone pair has been oriented, without comment, anti to the C—X bond. The lone pair and the C—X bond are able to overlap in this orientation 2.91 since they are coplanar, but at first sight they could equally easily have overlapped had they been syn 2.92. Undoubtedly, coplanarity is the single most important constraint for good overlap, but what about the choice between syn and anti? One answer, immediately apparent even in these simplified drawings, is that the syn arrangement 2.92 carries with it at least one eclipsing

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

99

interaction with the substituent R, whereas the anti arrangement 2.91 has all substituents and lone pairs staggered. The eclipsed arrangement is not even a minimum, but a transition structure for rotation about the O—C bond. gauche

nO

*

=

O

=

O

*

R

X

X

nO R

R

R X

X

eclipsed eclipsed

2.91

2.92

This simple difference alone accounts for why anti arrangements, both in anomeric effects and in -eliminations (to be discussed in Chapter 4), are so common. However, this is not the whole story, because there are systems where this factor is not present, and yet there is still a preference for anti anomeric effects (and anti eliminations). Thus the tricyclic skeleton of the acetal 2.93 rigidly locks the exocyclic group OR syn to one oxygen lone pair in the ring and more or less orthogonal to the other. As a result it still shows an anomeric effect, but it is smaller than the corresponding anti anomeric effect found in simple tetrahydropyrans—the reactivity towards exocyclic bond cleavage and the bond length of the exocyclic C—O bond still correlate with the pKa of the OR group, but the slopes are not as steep.130 OR O

=

O

H

H OR 2.93

A tempting way to explain the inherent preference for anti over syn arrangements is to picture the antibonding hybridised orbitals with the large lobes behind the bond instead of between the atoms. Thus we might redraw the *CX orbital in 2.91 as 2.94, and 2.92 as 2.95. Intuitively, this seems to make sense—the orbitals of opposite sign in their atomic wave functions will repel each other. Many organic chemists succumb to this temptation, for, having chosen this picture, we see that there appears to be much better overlap with the nO orbital in the anti arrangement 2.94—the large lobes are close and on the same side. In the corresponding syn arrangement with this way of drawing the antibonding orbital 2.95, the large lobes are on opposite sides and the overlap is ‘obviously’ less.

nO

X

nO O

ant i

*

R

* O

syn R

X 2.94

2.95

Unfortunately it is illegitimate. When we mix two atomic orbitals, the bonding orbital with an attendant drop in energy is paired with an antibonding orbital with its corresponding rise in energy, and a mathematical formulation determines the sizes of the lobes in each. One cannot arbitrarily move the lobes in and out,

100

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

however commonly you may come across this device in your reading. A truer picture can be seen in the wiremesh drawing of the LUMO of methyl chloride in Fig. 1.61, where the *CCl orbital shows that both the inside lobe and the outside are large, and not at all like the lobes in the drawings 2.94 and 2.95, where the difference between them is much too exaggerated. We are left therefore with the problem of accounting for the preference for anti overlap. The confusion is partly an artifact of the use of hybridisation. Various attempts by theoretical chemists show how buried in subtle balances, and how far from straightforward, the preference for anti overlap may be.131,132 Perhaps the most simple explanation is a more careful use of pictures like those in 2.94 and 2.95, but drawing them 2.96 and 2.97 with somewhat more realistic hybrid orbitals. The anti arrangement still has good bonding overlap, but in the syn arrangement, there are both attractions and repulsions between the nO orbital and *CX orbital.133 Furthermore, the anti arrangement keeps the centres of negative charge as far apart as they can be. There is more discussion on this topic in the section on -elimination in Chapter 5. repulsion nO

X

nO O

ant i

*

R

* O

syn R

X 2.96

2.3

2.97

The Configurations and Conformations of Molecules

Defining the terms configuration and conformation poses a problem, because there is no sharp boundary between them. Eliel discusses this point authoritatively,134 but all we need here is some sense that conformational changes are usually those that can take place rapidly at room temperature or below, making the isolation of separate conformers difficult, and configurational changes have energy barriers high enough to make it possible to isolate configurational isomers. In the discussion that follows we shall cross the borderline from time to time—conformational barriers can rise above those that can be crossed at room temperature, and configurational barriers like double bond geometries can become so low that they are easily crossed, but the ambiguity is usually not serious. Although it is good practice to keep the two words distinct in your mind, it is wise not to get too fixated on which word is being used. Conjugation, whether it is in the p system or in the  system, is one of the factors responsible both for the configurations that molecules preserve and the conformations that molecules adopt. The energy-lowering induced by p conjugation usually has the effect of making the planar arrangement with the maximum of p overlap the lowest in energy, and imparting a barrier to rotation about any single bonds separating the elements of conjugation. At one extreme is benzene with its perfectly flat ring and no C—C single bonds. At the other extreme, is the preferred conformation for dimethoxymethane 2.86 stemming from the anomeric effect, a p effect embedded in a molecule with nothing but single bonds. Energy-raising conjugation has the opposite effect, as we have already seen in such examples as the orthogonal relationships of the lone pairs in hydrogen peroxide 2.28 and hydrazine 2.29, to which we could add two other examples. The twisted conformation 2.98 for a sulfonium ylid simultaneously stabilises the carbanion by negative hyperconjugation with the neighbouring S—Me bonds and avoids the overlap with the lone pair on sulfur.135 The buckling of cyclooctatetraene 2.99, with a clear separation into double and single bonds, allows it, amongst other things, to avoid the consequences of an antiaromatic conjugated system. We shall now look at some more general examples.

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

S

= Ar

S

101

Ar

2.98

2.99

2.3.1 Restricted Rotation in p-Conjugated Systems 2.3.1.1 One p Bond. It hardly needs saying that a p bond is not usually free to rotate. The p energy 2Ep that we saw in Fig 1.26 (˜280 kJ mol1) would be lost at the transition structure for rotation about the C—C bond, which would have the two p orbitals orthogonal. This value is higher than the energy normally available for a chemical reaction. For rotation about a p bond to become easy in the ground state, either the transition structures like diradical 2.101 or the zwitterion 2.102 must be stabilised or the planar structure 2.100 must be destabilised. A D C B B A

2.101

D C 2.100

A B

D C 2.103

A D C B 2.102

An experimental value for the activation barrier for the isomerisation of cis-2-butene 2.104 is 259 kJ mol1 (62 kcal mol1). Phenyl groups stabilise radical centres, and the barrier to rotation in stilbenes 2.105 is correspondingly reduced from that in 2-butene to 179 kJ mol1 (43 kcal mol1). Steric interaction between the cis-vicinal substituents raises the energy of the planar structure, and contributes to lowering the barrier to rotation. In a fairly extreme example, the bifluorenylidene 2.106 benefits from both effects, and the barrier falls to 95 kJ mol1 (23 kcal mol1).136 259 kJ mol–1

179 kJ mol–1

Ph 2.104

95 kJ mol–1

Ph 2.105

Pri Pri 2.106

Alternatively, the substituents A and B may stabilise a cationic centre on one side and the substituents C and D an anionic centre on the other 2.102. Alkenes having donor substituents at one end and acceptors at the other are called ‘push-pull’ alkenes, and the barriers to rotation are indeed lowered,137 with the enamine system of the alkene 2.107 having a barrier of 66 kJ mol1 (16 kcal mol1).138 More subtly, the substituents in the allene 2.108 enable the phenyl and the methyl groups to exchange places rapidly, with coalescence of

102

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

the signals from the trimethylsilyl groups in the 1H-NMR spectrum at –90 °C.139 The two trimethylsilyl groups stabilise a cation on the central carbon atom (see p. 94) of the allene, and the empty orbitals on the boron atoms stabilise an anion on the carbon atom adjacent to them (p. 78). There are more examples on pp. 109–111. 66 kJ mol–1

36 kJ mol–1 Ar

CO2Me Me2N

CO2Me 2.107

B

Me3Si Me3Si

B

Me Ph

Ar

2.108

Photochemical excitation, however, takes one electron from the p orbital and promotes it to the p*. The p energy now is (Ep – Ep*), removing the energetic benefit of conjugation, and making the conformation 2.101, with the two p orbitals orthogonal, the lowest in energy. Initially, the excited state must be in the high energy, planar conformation 2.100, but if the photochemically excited molecule has a long enough lifetime, the conformation will change to that with the lower energy 2.101. Later, when the electron in the p* orbital returns to the p orbital, the molecule will return to the planar arrangement 2.100 or 2.103. This is the pathway for cis–trans isomerisation of alkenes induced by irradiation. 2.3.1.2 Allyl and Related Systems. It is not quite so obvious that the allyl conjugated system is also more or less configurationally stable, whether it is the cation, the radical or the anion. The drawing of a  bond in the localised structure 2.109a disguises the p bonding present between C-1 and C-2. The pair of structures 2.109a and 2.109b, of course, reveal that this is not the case, and C-1 and C-2 are just as strongly p-bonded as C-2 and C-3. 2 3

2 1

2.109a

3

1

2.109b

It is even more impressively evident in the molecular orbitals of the allyl system (Fig. 1.33), where the lowest filled orbital, 1, has p bonding across the whole conjugated system, and the only other orbital, the nonbonding 2, makes no contribution to p bonding whether it is empty or filled. The total p-bonding energy for all three allyl systems (Fig. 1.31) is 2  1.414. If rotation were to take place about the bond between C-1 and C-2, the transition structure would have a full p bond between C-2 and C-3 and an orthogonal p orbital on C-1. The difference in p energy between the conjugated allyl system (2  1.414) and this transition structure with a full p bond (2) is therefore 2  0.414, or about 116 kJ mol1 (28 kcal mol1), making the p bond strength between C-1 and C-2 nearly half that of a simple p bond, quite large enough to restrict rotation under normal conditions. This is of course a very approximate calculation, which has been stigmatised as ‘little more than a mnemonic’.140 Nevertheless, higher levels of calculation show that a substantial barrier is present, but reveal that the cation, radical and anion are not in detail the same—the unsubstituted cation is calculated to have a rotation barrier in the gas phase of 140 kJ mol1 (33.5 kcal mol1), the radical a barrier of 63 kJ mol1 (15 kcal mol1) and the anion a barrier of 85 kJ mol1 (20 kcal mol1).140 The lower barrier in the radical may be associated with the difficulty of localising charge on a carbon atom in the transition structure for rotation in either of the ions. In solution, solvation by a notional polar solvent lowers the numbers for the cation and anion to 115 and 70 kJ mol1 (27.5 and 17 kcal mol1), still large enough to retain configurational identity under normal conditions. 1,3-Disubstituted

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

103

allyl systems therefore have three configurations, usually called W-shaped 2.110, sickle-shaped 2.111, and U-shaped 2.112, which do not easily interconvert by rotation about the C—C bonds.

W-shaped

sickle-shaped

U-shaped

2.110

2.111

2.112

Alternatively, interconversion between the stereoisomeric allyl cations can take place by capture of a nucleophile at either end, followed by rotation about the more or less normal single bond, and then regeneration of the cation by ionisation. Interconversion between the corresponding anions can take place similarly by  coordination (1) to a metal at one end or the other. Because of the availability of these pathways, experimental measurements of the barrier to rotation have confirmed that it is less than the very approximate theoretical value of 116 kJ mol1 (28 kcal mol1). Furthermore, measurements have generally been made on significantly more substituted systems. Such substitution can stabilise the filled, half-filled or empty p orbital, or the double bond, even when these components are no longer conjugated, and so appropriate substituents lower the barrier to rotation. In one of the most simple cases, with a methyl group at C-1 and C-3, the U-shaped cation 2.112 generated in a superacid medium was converted into the sickle-shaped cation 2.111 with a half-life of about 10 min at 10 °C, and the cation 2.111 into the W-shaped cation 2.110 with the same half-life at 35 °C. These correspond to enthalpies of activation of 74 and 101 kJ mol1 (18 and 24 kcal mol1), respectively. This measurement only sets lower limits to the rotation barrier of an allyl cation, because it is not known whether rotation takes place in the cations themselves or in the corresponding allyl chlorides with which they could be in equilibrium.141 The barrier in cations is also much affected by solvation and by the degree of substitution at the termini, since the transition structure for rotation draws on such stabilisation more strongly than the delocalised allyl cation does. R R 2.113

2.114

Allyl radicals like 2.113 can also retain their configuration before being trapped by a reagent, but rotation giving the isomer 2.114 can take place. Free energies of activation of 66 kJ mol1 (16 kcal mol1) (R ¼ D)142 and 60 kJ mol1 (14 kcal mol1) (R ¼ Me)143 have been measured for this process, close to the calculated value. For the allyl anion itself, a good measurement is not really possible, because the free anion is not an accessible intermediate in solution—it is usually coordinated to a metal. If the coordination to the metal is 1 it will weaken the p bonding relative to the free anion, and if it is 3 it will strengthen it. The measured barrier is therefore dependent upon the metal counterion, but values of 45, 70, and 76 kJ mol1 (11, 17, and 18 kcal mol1) have been measured for allyl-lithium, potassium and caesium, respectively, with the last of these presumably a lower limit for the true barrier in a free allyl anion.144 One system free of this complication has been thoroughly studied: the azomethine ylids 2.115 and 2.116 are isoelectronic with an allyl anion, but do not have metal counterions. The free energy barrier to the conversion of the isomer 2.115 into the isomer 2.116 is 85 kJ mol1 (20.3 kcal mol1) and for the reverse reaction it is 84 kJ mol1 (20.1 kcal mol1), there being little difference in energy (1 kJ mol1) between the two isomers.145 Note that the ester groups greatly stabilise the anionic charge at C-1 and C-3, making rotation about the bond between C-1 and C-2 (or between C-2 and C-3) much easier than it would be in the free allyl anion.

104

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

CO2Me

Ar N MeO2C

120°

MeO2C Ar N MeO2C

Ar = p-MeOC6H4-

2.115

2.116

A number of related conjugated systems of three p orbitals show the same restricted rotation, although not to the same degree. Amides 2.117 typically have a barrier to rotation about the C—N bond of 80–90 kJ mol1 (19–21.5 kcal mol1), they have nearly trigonal nitrogen atoms, in contrast to amines, which have nearly tetrahedral nitrogen atoms, and the C—N bond is shortened because of the extra bonding provided by the p overlap between the nitrogen lone pair and the p bond of the carbonyl group.146 The barrier to rotation is particularly easy to measure in this case, because rotation can be detected in the NMR spectra. The two methyl groups of an N,N-dimethylamide show separate N-methyl signals at room temperature, and heating causes the two signals to coalesce. The comparatively rigid and planar conformation present in the amide system has profound consequences on the conformations of peptides and proteins. The other systems, esters 2.118, 147 enamines 2.119,148 and enol ethers 2.120,149,150 similarly have restricted rotation about the bond drawn as a single bond but the barrier is successively lower in each as the degree of p bonding becomes less and less, and the degree of p bonding localised at the double bond increases. This localisation also affects the lone pair, so that enamines, unlike amides, do not have a trigonal nitrogen atom, but a somewhat pyramidalised one,151 with the lone pair tilted slightly away from the vertical, relieving some of the eclipsing suffered by the alkyl substituents on the nitrogen atom. 80-90 kJ mol–1

N

O

2.117

40-50 kJ mol–1

O

2.118

O

15-25 kJ mol–1

N

10-16 kJ mol–1

O

2.119

2.120

The asymmetry in these systems explains why the degree of p bonding differs on each side of the central atom. The allyl anion, with a plane of symmetry through the central atom, has a node at that atom in 2, and this orbital makes no contribution to p bonding. Amides, esters, enamines, enol ethers and enolate ions do not have a node precisely on the central atom, and so 2 does make a contribution to p bonding. Taking planar N,N-dimethylvinylamine and the enolate of acetaldehyde as examples, simple Hu¨ckel calculations give the p orbitals in Fig. 2.21, which includes the allyl anion for comparison. These are specific cases of X-substituted alkenes that we saw earlier in Figs. 2.6 and 2.7, and the enolate ion is also a specific example with the same set of orbitals as the more generalised cation shown in Fig. 2.8. While the overlap between the atomic orbitals on the N or the O and the adjacent C are strongly bonding in 1, they are antibonding in 2. However, both 1 and 2 contribute to p bonding between the two carbon atoms, and enamines and enolate ions have very restricted rotation there. This is one reason why it is usually wise to draw enolate ions with the charge on oxygen 2.121a rather than as carbonylstabilised carbanions 2.121b—not only is more of the total charge on oxygen, but the degree of

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES 0.500

–0.707

0.500

–0.70

0.65 –0.70

200

0.21

3*

170

*

N

3

0.69

0.19

140

O

*

3

–0.707

0.707

0

2

0.64 –0.61

0.500

105

0.707

0.37

88

–0.41

N

0.500

0.59

0.70

120

2

O 200

0.54

1

0.56

2

0.90

0.38

280

0.41

N

0.17

1

O

330 1

N O

Fig. 2.21 p Orbital energies and coefficients from simple Hu¨ckel calculations of the allyl anion, enamine and enolate ion (orbital energies in kJ mol1 relative to )

p bonding is better illustrated this way. As we shall see later, the carbanion drawing 2.121b reveals the nature of the HOMO ( 2).

O 2.121a

O 2.121b

One remaining detail to be explained is the relative energy of the two planar conformations available in some of these systems. Thus monosubstituted amides adopt the s-trans (Z) conformation 2.122a rather than the s-cis (E) 2.122b,152 esters similarly adopt the conformation 2.123a rather than 2.123b,153 and even enol ethers adopt the conformation 2.124a rather than 2.124b. Within each pair, the difference in energy [5–25 kJ mol1 (1.2 6 kcal mol1) at room temperature] is usually too large to detect the minor conformer directly, but the energy needed to interconvert them is low, making it impossible to isolate the conformers. The explanation for the conformational preference is most straightforward in the case of esters. The s-trans conformation 2.123a benefits from the anti orientation of the carbon chains R 1 and R2. In other words, the alkyl chain R1 is effectively a larger substituent than the carbonyl oxygen, and the ester alkyl group R2 prefers to be anti to it. This is certainly not the whole story, because formate esters, with R1 only a hydrogen atom, ought to be the other way round, and they are not. There must be a stereoelectronic component as well, which is identifiable as the generalised anomeric effect (Section 2.2.3.3) involving energy-lowering overlap of a p orbital on one electronegative atom with * for a bond from carbon to another electronegative atom. In the s-trans conformation 2.123a, a lone pair on the oxygen atom is oriented anti to the C—O single bond of the carbonyl group, but in the s-cis conformation 2.123b it is syn.154 This is partly responsible for the relatively high reactivity of the smaller-ring lactones compared with open-chain esters, since these lactones are forced to adopt the high-energy s-cis conformation.

106

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

H

R1 N

R1 O R2 N H

O R2

2.122a

2.122b

R1 O O R2

R1 R2 O

O

2.123b

2.123a R1 O R2

R1 R O 2

2.124b

2.124a

The explanation for the preferred conformation of enol ethers 2.120 is probably similar, with * for the C—C p bond lower in energy than * for the other C—C or C—H  bond leading to R1, making the p orbital on oxygen align itself anti to the p bond. This preference is much less than with esters—the difference in energy between the two conformations 2.124 is only about 5 kJ mol1 (1.2 kcal mol1),155 whereas with esters 2.123 it is probably 20 kJ mol1 (6 kcal mol1) or more.156 All these effects can be overridden by steric effects from large substituents, so that enol ethers with substituents cis to the oxygen atom no longer adopt the s-cis conformation. The explanation for why amides prefer to adopt the conformation 2.122a with the N—H bond anti to the carbonyl group is less certain. The carbon chains are still anti, and that may well be the major effect. In most proteins and peptides, the NH is involved in hydrogen bonding, and that will make some contribution. It is tempting to see in this system evidence for hyperconjugation from the H—N bond, anti to * for the C—O  bond, being better than hyperconjugation from the alkyl group R2, but this is probably quite a minor factor. 2.3.1.3 Dienes. In order to maintain the maximum level of p bonding, butadiene is planar, with the orbitals shown in Fig. 1.37. We estimated there that the conjugation between the two p bonds lowered the energy by about 66 kJ mol1 (16 kcal mol1). We can see it in another way by noting that the p bonding in 1 between the p orbitals on C-2 and C-3 is between large lobes (c2 ¼ c3 ¼ 0.600), and the antibonding interaction in 2 is between small lobes (|c1| ¼ |c2| ¼ 0.371). The planar conformations are called s-trans 2.125 and s-cis 2.126, where the letter s denotes a conformation about a single bond. Experimentally, the activation energy for rotation about the bond between C-2 and C-3 is approximately 28 kJ mol1 (6.7 kcal mol1) going from s-trans to s-cis, and 16 kJ mol1 (3.8 kcal mol1) going from s-cis to s-trans,157 low enough for rotation to take place rapidly at room temperature, but different enough to ensure that most of the molecules will be in the s-trans conformation. Since the difference in energy between these two conformations is 12 kJ mol1 (2.9 kcal mol1) in favour of the s-trans, making the population of the s-cis conformation at room temperature about 1%. s-trans

1

2

3

s-cis 4

100 1

2.125

1

4

H

H

2.126

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

107

There are two reasons for the preference for the s-trans conformation. The more obvious is that the hydrogen atoms at C-1 and C-4 which are cis to the other double bond are sterically quite close in the s-cis conformation 2.126, and repel each other. However, the difference in energy between cis- and trans-2butene, which have similar, although not the same, differences in steric compression, is only about 4 kJ mol1 (1 kcal mol1). Another reason can be found in the p system (exaggerated in Fig. 2.22), where the p orbitals on C-1 and C-4 are closer in space in the s-cis conformation than they are in the s-trans, and all the other orbital interactions, C-1 with C-2, C-1 with C-3, and their symmetry counterparts, are all equal in the two conformations. The lobes on C-1 and C-4 in 1 are small and bonding, but this attractive overlap is more than offset by the antibonding interaction between the large lobes in 2, making the overall interaction repulsive (DE2 > DE1).158

LUMO

*

3

Etrans

HOMO

Ecis

bonding

2

E2

antibonding

E1 1

bonding

Fig. 2.22

Differences in p orbital energies for s-trans and s-cis butadiene

This perception also provides a simple explanation for an otherwise puzzling observation in UV spectroscopy. Dienes constrained to adopt an s-cis conformation by being endocyclic in a six-membered ring, absorb UV light at a longer wavelength than open-chain dienes with a comparable degree of substitution. Woodward’s rules for UV absorption in dienes give a base value for s-trans dienes of 214 nm and for s-cis dienes of 253 nm. This absorption is a measure of the gap in energy between 2 and 3*. If we look again at Fig. 2.22, we can see that whereas 2 is raised in energy in the s-cis conformation relative to the s-trans, 3* will be lowered in energy, making the energy gap Ecis less than Etrans. Another otherwise puzzling result can be explained in a similar way. Reduction of butadiene with sodium in liquid ammonia159 or in an amine160 gives more cis-2-butene Z-2.131 than trans-2-butene E-2.131, typically in a ratio of about 60:40. Since the trans-2-butene is the lower in energy, by about 4 kJ mol1 (1 kcal mol1), this is certainly counterthermodynamic. To explain this result we first have to know at what stage the geometry became fixed, and then determine why the kinetics favoured the formation of the cis product. By looking at the orbitals of the starting materials and each of the likely intermediates 2.127 2.130, we can work out that the stereochemistry is probably determined in the first step, the addition of the first electron to the diene system. The diene conformations are present in a ratio of about 99:1. The first intermediate will be the radical anions 2.127, which will have the extra electron in 3*. This increases the degree of p bonding between C-2 and C-3, and so rotation is less likely at this stage than it was in the diene. The next step is either the addition of a second electron to give the dianions 2.128 or protonation to give the

108

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

allyl radicals 2.129, with the next step in either case being the formation of the allyl anions 2.130.161 With an extra electron in 3*, the dianions have even stronger bonding between C-2 and C-3, and so do the allyl radicals and anions, as already discussed in Section 2.3.1.2. Finally, protonation of the allyl anions is evidently selective for the terminus C-1, giving the 2-butenes 2.131, which no longer have any possibility of rotation between C-2 and C-3. Thus the degree of p bonding between C-2 and C-3 increases at each step as the reaction proceeds, and it seems likely that the excess of cis-2-butene Z-2.131 in the mixture is caused by the s-cis diene 2.126 accepting the first electron more easily than the more abundant s-trans diene 2.120. This is plausible, since we have already deduced that 3* in the diene which accepts this electron is lower in energy in the s-cis conformation. +H

+e +e

+H

E-2.128 +H

slow 2.125

+e E-2.130

E-2.127

E-2.131

E-2.129 1

99 +H

+e 2

+e fast 2.126

1

Z-2.128

3

+H

+H

+e Z-2.130

Z-2.127

Z-2.131

Z-2.129

The overall conclusion here is that cis-2-butene is formed selectively from the s-cis conformation of the diene, in spite of the mixture being rich in the s-trans. This shows that chemical reactions cannot safely be used, as they have been,162 to estimate the proportions of the conformations present at equilibrium. Although less plausible, there is one final observation that might be explained by the attractive interaction in 3* between the ends of a conjugated system of four p orbitals. 1-Substituted allyl-metal species are surprisingly a little more stable in the sickle-shaped configuration 2.132 than in the W-configuration 2.133,163 in contrast to butadiene, which is more stable in the s-trans conformation. The C—H bond of the cis methyl group is conjugated with the p orbitals of the allyl anion, and as such will have orbitals that resemble those of butadiene, but with two extra electrons. There could therefore be a net attractive force between the methyl group and C-3, in spite of the expected steric repulsion. This observation has received a lot of attention, and much more sophisticated theoretical treatment than this.164 1.7-13.4 kJ mol–1 R

3

2.132

1

R

2.133

2.3.1.4 Enones. Simple ,-unsaturated carbonyl compounds also show thermodynamically a preference for the s-trans conformation. Acrolein has a smaller difference in energy than butadiene between the s-trans 2.134a and s-cis 2.134b conformations of 7 kJ mol1 (1.7 kcal mol1), but a similar barrier to rotation of

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

109

about 28 and 21 kJ mol1 (6.7 and 5 kcal mol1), depending upon which direction the barrier is approached from.165 Methyl acrylate 2.135 has an even smaller difference in energy of 1.3 kJ mol1 (0.3 kcal mol1), and a somewhat smaller barrier to rotation [approximately 16 kJ mol1 (3.8 kcal mol1) from either direction].166 These successively smaller differences in energy look like steric effects, since the oxygen of the carbonyl group in acrolein is smaller than the methylene group in butadiene, and the methoxy substituent in methyl acrylate is larger than the hydrogen in acrolein. However, methyl vinyl ketone 2.136, with an energy difference of 2.4 kJ mol1 (0.6 kcal mol1) in favour of the s-trans conformation, is rather more s-trans 2.136a than methyl acrylate,167,168 yet the methyl group can usually be counted on to be more sterically demanding than a methoxy group. This implies that some conjugation effects are present that override the steric effects to some extent. However, steric effects do come into play when there are -substituents cis to the carbonyl group. Mesityl oxide 2.137 is variously estimated to be 95% or 72% in the s-cis form 2.137b,167,168 which obviously benefits from the smaller steric interaction from the cis C-3 methyl group with the oxygen atom in the s-cis conformation than with the methyl group of the ketone in the s-trans conformation 2.137a. Steric effects also come into play when there is a C-2 substituent, which increases the proportion of s-trans conformer. O

95 5

H 2.134a

OMe

O 2.134b

O

73 7

2.136a

O

H

28 or 5 72 or 95

2.137a

O 2.135b

O

O

OMe

37

2.135a

3

2.136b

63

3

O 2.137b

By analogy with butadiene, we might expect an aptitude kinetically for reaction in the s-cis conformation. This has barely been looked at; lithium in ammonia reduction of various ,-unsaturated ketones gives mixtures of the E- and Z-enolates possibly reflecting the proportions of the s-trans and s-cis conformers, respectively, in the starting material as well as their relative reactivity with respect to accepting an electron. There is, however, some evidence that the proportion of Z-enolate is a little higher than the proportion of s-cis conformer.169 2.3.1.5 Lowering the Energy of the Transition Structure for Rotation. With longer conjugated systems the p stabilisation increases in the usual way, but each increment makes a smaller and smaller difference. In the transition structure for rotation, the full p stabilisation is divided into two, with each part having a shorter conjugated system. As a result, the barrier to rotation about the internal double bonds goes down as conjugated systems get longer. With polyenes, the barrier does appear to drop, although there is always ambiguity about the mechanism of isomerisation with such reactive compounds. Carotenoids, for example, having eleven double bonds conjugated together, are notoriously susceptible to cis-trans isomerisation, but it does seem likely that some of them are simply thermally induced rotations.170 Moving on to the weaker p bonding in allyl systems, we deduced in Section 2.3.1.2 that the simple Hu¨ckel barrier to rotation is 0.828. By the same type of calculation we can estimate the barrier in the pentadienyl system: the full degree of p stabilisation (Fig. 1.42) is 2 þ (2  1.73) ¼ 5.46; the p stabilisation of the separate components for rotation between C-2 and C-3 is the sum of the energy of a p bond (2) and of an allyl system (2  1.414), which comes to 4.82, and so the difference is now only 0.64. The experimental

110

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

value in simple allyl systems is only a little above that which can be crossed at the normal temperatures of chemical reactions, and so we can expect that the longer conjugated systems with an odd number of atoms will rarely have stable configurations. This effect is supplemented by terminal electronegative substituents, which increase the overall electron population at the extremities of the conjugated system, and reduce the effectiveness of overlap in the carbon chain in between. Thus the system of five conjugated p orbitals present in an alkene with an X-substituent at one end and a Z-substituent at the other (a ‘push-pull’ alkene, see p. 101), will have molecular orbitals related to the pentadienyl anion (Fig. 1.42). The nitroenamine 2.138, which has one of the best donors and one of the best acceptors, although drawn with a full double bond between C-2 and C-3, has much weaker p bonding between these atoms than that drawing implies, just as the enamine 2.107 did. Rotation about this bond is actually fast enough to make isolation of individual geometrical isomers impossible.171 The individual isomers in systems like this can sometimes be detected in the NMR spectra, where another consequence of the reduced double bond character between C-2 and C-3 is seen in the low coupling constant (10.5 Hz) between the trans-disposed protons.172

<80 kJ mol–1

N

O

3

N 1

2

N

N

O

2.139

<40 kJ mol–1 NO2

N N

O 2.138

O

N

O O N H

2.141

H 2.140

Another way of looking at the ease of rotation between C-2 and C-3 and the restriction between N-1 and C-2 is with the resonance structure 2.139, which has the effect of expressing the reduction in double bond character and the stabilisation of the cationic and anionic components, at C-2 and C-3, respectively, in the transition structure for rotation. However, it is important to recognise the difference between the resonance structure 2.139 and the transition structure for rotation 2.140. The difference is that overlap of orbitals expressed as resonance cannot have any change in the position of the atoms, and it is correctly symbolised with the double-headed arrow. Rotation does have a change in the position of the atoms, and it is a ‘reaction’, symbolised with conventional reaction arrows. The cation-stabilising group at one end and the anionstabilising group at the other stabilise the intermediate components, which are no longer conjugated in the transition structure 2.140. Such contributions to lowering the energy barrier will come from any stabilisation of the intermediate components in the transition structure—cation-stabilising, radical-stabilising or anionstabilising, as appropriate—they will all lower the barrier, as we have seen for the radical in Section 2.2.5 and for the anion in Section 2.3.1.2. Increasing the stabilisation of the cationic centre in the transition structure, by having two donor substituents, as in the enediamine 2.141, causes the two N-methyl groups to be coincident in the NMR spectrum even at 63°C, because rotation about the formal C¼C double bond is fast on the NMR timescale.173 At the same time, rotation about the formally single bond between N-1 and C-2 in these compounds is more restricted than drawing a single bond implies, just as it was with amides and with the enamine 2.107. The two N-methyl groups in both enamines 2.107 and 2.138 have different chemical shifts and coalescence measurements show that the free energy of activation for rotation is 56 kJ mol1 (13 kcal mol1) for the former and 69 kJ mol1 (16.5 kcal mol1) for the latter, which indicates that the degree of p bonding there

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

111

and between C-2 and C-3 must be comparable in both cases.174 Decreasing the stabilisation of the anionic centre in the transition structure with a less powerful acceptor than a nitro group, as in the ester 2.142, lowers the barrier to rotation about the N—C bond from 69 kJ mol1 to 58 kJ mol1 (14 kcal mol1). 69 kJ mol–1

56 kJ mol–1

58 kJ mol–1

67 kJ mol–1

CO2Me N

CO2Me

N

N

O

O

N

O 2.107

OMe

2.138

O

N

OMe

2.142

2.143

Extended conjugation through double bonds illustrates the principle of vinylogy, a word made up by combining vinyl and analogy. Vinylogous conjugated systems often have similar properties, both in the ground state and in reactivity, to the parent systems. The conjugated system of 2.142, for example, is that of a vinylogous carbamate, in which the restricted rotation about the N—C bond, 58 kJ mol1 (14 kcal mol1) is similar to but smaller than that of the corresponding carbamate 2.143, 67 kJ mol1 (16 kcal mol1).175 This illustrates again the lowering in the degree of p bonding between neighbouring atoms as the conjugated system gets longer. Another way in which the barrier to rotation about a single bond is lowered is when conjugation is not energy lowering (Section 2.1.6). Whereas the barrier to rotation about the C—O bond of anisole 2.144 is close to 25 kJ mol1 (6 kcal mol1), because the lone pair on the oxygen has net p bonding with the benzene ring in the same way as it has with ethylene in methyl vinyl ether 2.124, the barrier disappears in p-dimethoxybenzene 2.145. Conjugation between the lone pairs on the two oxygen atoms is not energy lowering.176 In contrast, the barrier substantially increases when the lone pair is conjugated through the benzene ring to an empty p orbital 2.146.177 25 kJ mol–1

O

~0 kJ mol–1

O

2.144

44 kJ mol–1

O

O

2.145

2.146

2.3.2 Preferred Conformations from Conjugation in the s Framework We have already seen in Section 2.2.3.3 how conformation can be affected by anomeric interactions, which can lead electronegative substituents to be axial at the 2-position in tetrahydropyranyl rings, and sometimes cause a chain of atoms to adopt a seemingly more hindered gauche conformation 2.81–2.83, 2.85 and 2.86 rather than the more usual zigzag arrangement. Similar hyperconjugative interactions in neutral molecules between two  bonds, one a  donor and the other a  acceptor, can lead them to adopt conformations in which the stereoelectronic effect overrides the purely steric effect. 1,2-Difluoroethane might be expected to adopt the zigzag conformation 2.147, both because the dipoles from the C—F bonds will be opposed, and because the two larger groups will be further apart. However, it does not—it adopts the conformation 2.148 instead, with an enthalpy advantage of 2.5–3.8 kJ mol1 (0.6–0.9 kcal mol1) as well as a small favourable entropy factor, since there are two gauche conformations and only one anti.178 The enthalpy advantage in this conformation stems from the anti-periplanar conjugation of the

112

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

C—H bonds with the vicinal C—F bonds. Hyperconjugation will be energy-lowering with an interaction diagram like that in Fig. 2.14, but with the low-lying antibonding orbital *CF taking the place of the empty pC orbital. It is the same interaction of orbitals that we saw in the C—H bond lengthening in the 1,3-dioxan 2.41. A similar explanation accounts for the fact that cis-difluoroethene 2.150 is lower in energy than its trans isomer 2.149, in contrast to most other alkenes.179 Although less powerful, the effect is still evident in other dihaloethanes, in other 1,2-disubstituted alkanes like dimethoxyethane, and in the helical conformation of polyoxyethylene -(CH2CH2O)n-, which contrasts with the zigzag conformation of polyethylene. HH

F

HH

H

H

F

H

H

F

HH

F

FH

F

H

F

F

2.148

2.147

2.149

2.150

The same type of overlap can take place through a double bond to give a vinylogous version. In the conformation 2.151 of an allylic ether, the C—O bond is conjugated with the p bond, but in the conformation 2.152 the C—H bond is conjugated with the p bond and the C—O bond is not. Which of these is preferred is dependent upon the electronic nature of the substituent Y at the other end of the double bond. When the substituent Y is an alkyl group (a p donor by hyperconjugation) the preferred conformation is 2.151, because there is then an energy-lowering interaction, conjugated through the double bond, with the C—O bond (a p acceptor). When the substituent Y is a carbonyl or nitrile group (a p acceptor), the preferred conformation is 2.152, because this avoids the energy raising conjugation through the double bond of one p acceptor with another.180,181 This type of allylic ether is one of the most important examples of a stereogenic centre adjacent to a double bond affecting which surface of the double bond is the less hindered, and hence the more reactive. R

Y

H

H

Y OR

RO

R 2.151

2.152

preferred for Y = alkyl

preferred for Y = CO2Et or C≡ N

With a more powerful donor like an Si—C bond, the preference for the donor and the acceptor bonds to be anti can be seen in cyclohexyl esters carrying a  silyl group. The equilibrium proportion of the alcohol is in favour of the normal diequatorial isomer 2.153 (R ¼ H), but with esters (R ¼ acyl) the equilibrium shifts to favour the diaxial conformation 2.154. Furthermore, the equilibrium constant correlates with how good the carboxylate ion is as a leaving group (pKa of RO drops).182 OR OR SiMe3 SiMe3 2.153

2.154

preferred for R = H

preferred for R = acyl

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

2.4

113

The Effect of Conjugation on Electron Distribution

Conjugation affects not only the energies and conformations of organic molecules but also the distribution of the electrons. This has consequences on where the sites of highest charge are located, and on the polarities of molecules as manifest in such properties as the sites of ambident reactivity, dipole moments and the patterns in which they stack in crystals. We are already familiar with the stabilising effect of an electronegative substituent conjugated with an empty p orbital (see p. 58). The carbonyl group is polarised so that the carbon atom carries substantial positive charge, as symbolised in Fig. 1.66 by the small p orbital on the carbon atom in the HOMO. Conversely, the oxygen atom carries a substantial negative charge, and carbonyl compounds have a strong dipole. This shift in the electron population is often illustrated with resonance structures like 2.155 and 2.156 which show the oxygen carrying negative charge. An imine shows a similar polarity to that in a carbonyl group, but reduced because nitrogen is less electronegative than oxygen. However, in an iminium ion, in which the molecule as a whole carries a positive charge, the effect is enhanced, and iminium ions are more reactive electrophiles than the corresponding aldehyde or ketone. However, expressing this idea with resonance structures like 2.157 and 2.158 can be misleading. The impression is given that the nitrogen atom is positively charged in the one, and not carrying charge in the other, in contrast to the negative charge inoffensively written on the corresponding resonance structure 2.156 for a ketone. The nitrogen atom in the imminium ion is negatively charged throughout, not only in the p system but in the  framework as well.

O

2.155

O

2.156

N

2.157

N

2.158

Organic chemists, using resonance structures, are meticulous about keeping track of charge, illustrating it with strict adherence to Lewis structures and carefully placing a formal charge on an atom whenever appropriate. The convention has the charge on the nitrogen in this case, because of the consumption of the lone pair on the nitrogen in forming the fourth bond when an imine is changed into an iminium ion. The positive charge is drawn on the nitrogen atom as a formality —it is a kind of bookkeeping. In fact, the electron deficiency is spread elsewhere —to the adjacent carbon atom, as illustrated in the resonance structure 2.158, and relayed by conjugation onto the hydrogen and carbon atoms joined to that carbon and to the nitrogen atom itself. The electron population on the electronegative atom is high, and not low as the drawing 2.157 implies. The sum of the coefficients in the filled p orbitals on the nitrogen atom in pyridine 1.47 in Fig. 1.69 is smaller than the sum of the coefficients on the nitrogen atom in the pyridinium ion 1.48, in which the nitrogen is drawn, as usual, with a positive charge which it does not carry. There is nothing wrong with this formalism —drawing these structures is unavoidable if curly arrows are to be used to show where the electrons are coming from and moving to in the course of a reaction—but it can certainly be misleading about the actual electron distribution. If the carbonyl group is conjugated with a p bond, as in ,-unsaturated ketones, the fraction of positive charge on the carbon atom is shared with the p bond, and the  carbon becomes partly cationic in nature, as symbolised in Figs. 2.3 and 2.4 by the relatively small p orbitals on the  carbon atom in 1 and 2 of acrolein as a model for a Z-substituted alkene. Looking again at those pictures, it is clear that the sum of the coefficients of the filled p orbitals on the carbonyl carbon is smaller than the sum at the  carbon, and that

114

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

the p electron deficiency is therefore greater at the carbonyl carbon. We shall return to this picture when we discuss ambident electrophilicity in Chapter 4 in Section 4.5.2. Enol ethers, and even more powerfully enolate ions, have an oxygen lone pair conjugated to a p bond, with the result that the total p electron population at C-2 is high, as illustrated in Fig. 2.7 for an enol ether and in Fig. 2.21 for an enolate ion. It is not, however, higher than the total p electron population on the oxygen atoms, which remain the sites of highest electron population. This sharing of the electrons is often illustrated with resonance structures such as 2.121 for an enolate ion and 2.159 for an enol ether. The drawings 2.121a and 2.159a remind us that there is a substantial p bond from C-1 to C-2, but the drawings 2.121b and 2.159b illustrate the increase in the electron population on C-2. Nevertheless, the oxygen atom is not positively charged in an enol ether as the drawing 2.159b seems to imply. The electron deficiency is taken up by the substituents on C-1 and on the oxygen atom. Although an increase in electron population is spread to C-2, the electrons remain substantially on the oxygen atom itself, as befits an electronegative element. We shall return to the enolate ion when we discuss ambident nucleophilicity in Chapter 4 in Section 4.3.2.

MeO

MeO

2

2.159a

1 2

2.159b

Experimental evidence for the shift in electron population when an X-substituent is attached to a double bond is found in the chemical shifts of protons on C-2 in enol ethers, and even more conspicuously in the NMR spectra of enamines. Thus, the proton on C-3 in the enamine 2.161 comes into resonance at higher field than the corresponding proton in phenalene 2.160, because the increased electron population on C-3 shields the adjacent proton. The corresponding proton in the ammonium salt 2.162 is at unusually low field, first of all because there is no lone pair conjugated with the double bond, but also because the ammonium ion inductively withdraws the electrons from the p bond, demonstrably leaving H-3 relatively exposed.183 Again, the ammonium ion, although positively charged overall has most of the charge on the p-bonded carbons, on their substituents, and especially on the hydrogen atoms of the methyl groups, not on the nitrogen atom, on which it is formally placed. H

H

3

6.49

3

5.70

2.160

H

NMe

3

NMe2

7.10

2.161

2.162

A striking illustration of how misleading it is to place the positive charge on the electronegative atom in drawings like 2.159b, 2.157 and 2.162, is provided by the standard explanation found in many textbooks for why the dipole of pyrrole 2.163 points from the nitrogen atom towards the carbon atoms of the ring, whereas the dipole for furan 2.164 is in the other direction. The standard explanation is that the overlap illustrated by the resonance structures 2.163b and 2.163c moves the electron population onto the carbon atoms and leaves the nitrogen positively charged. Furan with a more electronegative heteroatom is not so strongly polarised. This cannot be the reason, because the resonance structures 2.163b and 2.163c illustrate the electron distribution in only one of the p orbitals, the highest in energy 3 in Fig. 1.69. The overall negative charge

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

115

on the nitrogen is higher than on carbon if we sum the coefficients for the three filled p orbitals, and the same pattern must hold in the  framework. It is not permissible when explaining a physical property of a whole molecule to use only one of the orbitals—it is like confusing thermodynamic with kinetic effects—that one orbital, the HOMO, appears to have a profound effect on the kinetics, but is not adequate to explain a thermodynamic property.

N

N H

N H

O

2.163b

2.163c

2.164

H 2.163a

The explanation for the unexpected direction of the dipole is that pyrrole has an N —H bond, strongly polarised towards the nitrogen and furan does not have a substituent on the oxygen atom. Calculations support this picture, and reveal that the dipole moments in these systems are all lower than their saturated counterparts as a result of the overlap in the p system.184 The overlap illustrated by the curly arrows does move charge towards the carbon atoms, but not powerfully enough to overcome the usual pattern, that the electronegative atom carries more of the negative charge than the carbon and hydrogen atoms.

2.5

Other Noncovalent Interactions185

We began in Chapter 1 by considering the strongest forces involved in bonding, the covalent bonds themselves, and worked our way down from the strongest  bonds to the weakest p bonds. In this Chapter, we have looked at the weaker p interactions of covalent bonds with each other and with p orbitals, and have come down to a level at which they provide only a delicate balance affecting the shapes molecules choose to adopt. There are a few other forces at work, both within a molecule and affecting how one molecule can interact with another, which also stem from the electron distribution. Weak though some of them are, these forces have profound consequences not only on the shape a molecule adopts, but also on the degree and sites of solvation, on intermolecular forces affecting the bulk properties of polymers and controlling crystal packing, on intramolecular forces affecting protein folding, and on molecular recognition in such important pairings as those between an enzyme and its substrate, and between a receptor and its agonist. 2.5.1 Inversion of Configuration in Pyramidal Structures Amines are pyramidal in structure, but if the nitrogen atom carries three different substituents it cannot be resolved into a pair of enantiomers, because of the rapid inversion of configuration 2.165a ! 2.165b, which has an energy barrier of the order of 24 kJ mol1 (6 kcal mol1).186 In contrast, the corresponding phosphines are easily resolved, and are configurationally highly stable with respect to the inversion 2.166a ! 2.166b, which probably has a barrier of at least 140 kJ mol 1 (34 kcal mol1).187 The inversion of configuration at nitrogen is made slower if the nitrogen is in a small ring, and slower still if it has an electronegative substituent attached to it. With the benefit of both features, an N-chloroaziridine can be separated into a pair of diastereoisomers 2.167a and 2.167b.188 In contrast to amines, imines, which have trigonal nitrogen atoms, are configurationally stable with respect to cis–trans isomerisation 2.168a ! 2.168b by way of inversion at nitrogen, as well as by restricted rotation about the p bond.

116

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

fast N

slow P

N

P

24 kJ mol–1 2.165a

140 kJ mol–1 2.165b

2.166a

2.166b

Cl N

Cl

slow

N N

N >100 kJ mol–1

2.167a

2.167b

2.168a

2.168b

All these properties can be understood by considering the molecular orbitals involved in the inversion process.189 The method is to start with the orbitals of the planar arrangement, and look for interactions that encourage pyramidalisation. For ammonia and phosphine the three occupied orbitals and the lowest unoccupied orbital are shown in Fig. 2.23. In both cases, the pyramidal arrangement, which keeps the electron populations as far apart as possible, is the stable conformation. The HOMO and the LUMO are orthogonal in the planar arrangement, and there is no Jahn-Teller distortion (see pp. 34 and 41). In the pyramidal arrangement, with the hydrogen atoms moved down (or up), the HOMO and LUMO are no longer orthogonal, and Jahn-Teller distortion occurs, lowering the energy of the HOMO and raising the energy of the LUMO. The lower energy of the HOMO lowers the overall energy of the molecule from that of the planar arrangement. The closer in energy the HOMO and the LUMO, the more strongly they interact. The HOMO energy is largely that of a p orbital on nitrogen or phosphorus, and the latter is higher in energy, since nitrogen is the more electronegative. Bonding between one of these elements and hydrogen will lead to a larger split between the  and the * orbital with nitrogen than with phosphorus, because the energy match is closer. In consequence the LUMO, which is a * orbital, is relatively lower in energy for phosphine than for ammonia. With the HOMO higher in energy and the LUMO lower in energy for phosphorus than for nitrogen, the Jahn-Teller distortion is stronger in phosphines. It follows that losing that stabilisation by passing through the planar arrangement is energetically more costly for phosphorus than for nitrogen. The larger the HOMO–LUMO interaction in the planar configuration the more favourable is it for the hydrogen atoms to be out of the plane, and phosphines do indeed have a smaller H—P—H bond angle than the H—N—H angle in ammonia. Carbanions are tetrahedral, and inversion of configuration can be expected to be easy—since the LUMOs, the *CH orbitals, are high in energy, the HOMO–LUMO gap is not small as it is in a phosphine. However, carbanions in the form of compounds containing C—Li bonds can often be configurationally stable by virtue of the  bond, which would have to be broken to allow inversion. If two of the hydrogen atoms in Fig. 2.23a are brought closer together, in imitation of having the atom A in a small ring, the LUMO energy will be lowered as the bonding between the hydrogen atoms increases. There will be no effect on the HOMO, which does not involve the hydrogen atoms, and so the HOMO–LUMO gap will be reduced, thus explaining why a small ring stabilises the tetrahedral geometry. Similarly, replacing one of the hydrogen atoms with an electronegative element will lower the energy of the LUMO, and leave the HOMO largely unaffected. Any p contribution from the lone pair on the electronegative element will be small, and will raise the energy of the HOMO a little. Aziridines like 2.167 and cyclopropyl lithium reagents are notably more configurationally stable than their open-chain counterparts. The highest filled and the two lowest unfilled molecular orbitals of a linear methyleneimine are shown in Fig. 2.24. The HOMO is largely the lone pair, but the LUMO p*CN offers no opportunity for bending at the nitrogen atom to have any effect. However, the next orbital up in energy *CN, called the NLUMO, while orthogonal to the HOMO in the linear structure, can mix with it if the N—H bond bends. Mixing in the NLUMO with the HOMO lowers the energy of the latter, and therefore lowers the energy overall. The vinyl

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES A H

H

H

H H

A

H

H H

A

HOMO

H

H

A

A H

H H

A

* LUMO

H H

A

A

H H

LUMO

H H

HOMO

A H

A H

(a) planar

Fig. 2.23

H H

H H

H

117

H H

H H (b) pyramidal

Filled molecular orbitals and the lowest unfilled of planar ammonia and phosphine

H H H H

N

Fig. 2.24

N

H

NLUMO

LUMO

H

H H

H H

N

N

H

HOMO

H

Highest filled and lowest unfilled orbitals of linear methyleneimine

anion and protonated formaldehyde are isoelectronic with this system, but the HOMO–NLUMO gap will be larger the more electronegative the element carrying the lone pair. Vinyl anions can be expected to be configurationally stable, as indeed vinyl Grignard and lithium reagents are, but protonated carbonyl groups will be less so. When the nitrogen of the imine carries another electronegative atom, as it does in oximes and hydrazones, a kind of  effect comes into play, the HOMO–NLUMO gap is reduced, the interaction is made stronger on bending, and the bent structure is even lower in energy relative to the linear than it was for the simple imine. The same considerations apply to radicals,190 except that inversion is more favourable than it was with anions and lone-pair bearing atoms, because pyramidalisation with one electron in the HOMO only contributes half the stabilisation imparted by having two electrons. EPR spectroscopy allows the rates of inversion to be measured, and it has been found that, although the methyl radical itself is essentially planar, any substitution, but especially with electronegative elements or by incorporation into a small ring, increases the degree of pyramidalisation, and the barrier to inversion. In general, even though most substituted

118

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

carbon-based radicals are pyramidal, their configurations are rapidly lost by inversion through a planar transition structure. The methyl groups in the tert-butyl radical, for example, are 10° out of plane, and the barrier for inversion is only about 2 kJ mol1 (0.5 kcal mol1). However, as with anions and lone-pair bearing systems, a radical based on an element lower in the periodic table, like phosphorus, silicon or tin, can be stable enough to retain its configuration through a chemical reaction, as the radical 2.170 does in the halogenation of the enantiomerically enriched silane 2.169. The product is the enantiomerically enriched chloride 2.171 with retention of configuration.191 A comparable reaction on carbon would have given racemic product. Me

(PhCOO)2 Si H

Np Ph

Me Np Ph

2.169

Me

CCl4 Si

Si Cl Np Ph

2.170

2.171

2.5.2 The Hydrogen Bond192 2.5.2.1 X—H . . . X Bonds. The traditional hydrogen bond is found when a hydrogen atom bonded to one electronegative atom is close to another electronegative atom. It is found at its strongest and most simple in the HF2 ion, which has been estimated to have in the gas phase an energy below that of the separate components of no less than 167 kJ mol 1 (39 kcal mol1), and at its most famous in the strong AT and GC pairing of bases in the double helical structure of DNA. The pattern of filled molecular orbitals in the HF2 system, shown in Fig. 2.25, resembles that of the allyl anion—a low-energy orbital with no nodes, and a nonbonding orbital with a node at the central atom. The node at the hydrogen atom leaves it with no interactions with the two fluorine atoms, which are far enough apart to be essentially nonbonding. For this arrangement to be stabilised, 1 and 2 must together be lower in energy than the corresponding orbitals in the separate components HF and F. Electronegative elements will lead to high electron populations on the atoms at the two ends of the three-atom system, incidentally making it exceptionally difficult to locate the hydrogen atoms by X-ray crystallography, and leading to the very low field at which they come into resonance in 1H-NMR spectra. More importantly, with respect to the energy of the system, electronegative elements have compact orbitals in 2, making residual repulsion between them lower. This orbital picture also explains why a linear array is best; any bending decreases the bonding in 1 and increases the antibonding in 2. With other atoms, inherently less electronegative than fluorine, hydrogen bonding becomes weaker: in water it is estimated to be 22 kJ mol1 (5 kcal mol1) and the intramolecular hydrogen bond in the enol of a -dicarbonyl compound is in the range 33–57 kJ mol1 (8–14 kcal mol1).

Fig. 2.25

F

H

F

3

F

H

F

2

F

H

F

1

*

The molecular orbitals of the symmetrical hydrogen bonds in HF2

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

119

The same set of orbitals applies to such other forms of strong hydrogen bonding as the bridged B—H—B bonds in diborane 2.172193 and the bridged C—H—C bond in the cyclodecyl cation 2.173,194 except that in these systems there are only two electrons to be fed into the three-atom orbitals, leaving 2 empty. Since high electronegativity for the two atoms at the ends principally exerts its effect in keeping 2 as little antibonding as possible, high electronegativity is no longer a requirement when 2 is empty.

H B H

H H B H

H H

H

2.172

2.173

An alternative perception for the nature of conventional hydrogen bonding, not in conflict with the molecular orbital picture, is that it stems from a Coulombic attraction between the negative charge of the lone pairs of the one electronegative element, and the partial positive charge left on the hydrogen atom by the polarisation of the bond towards the other electronegative element. In this picture, we also see that a hydrogen bond resembles the transition structure for proton transfer between basic sites. This is perhaps the best way to explain why hydrogen bonding towards the fluorine atom of an F—C bond is extraordinarily weak.195 Although highly charged, the fluorine atoms are not basic, and are not available for attracting a proton. 2.5.2.2 C—H. . .X Bonds. When the hydrogen atom is attached to carbon, it still has an attractive interaction with lone pairs on electronegative elements, but the degree of hydrogen bonding is much smaller than with conventional hydrogen bonds, probably never more than about 17 kJ mol1 (4 kcal mol1), and usually much less. These kinds of hydrogen bonds manifest themselves in small shifts in spectroscopic properties,196,197 such as a lowering by anything up to 100 cm1 in the C—H stretching frequency in their infrared spectra,198 in small downfield shifts of protons when the 1H-NMR spectra are taken in oxygen-containing solvents, and in preferred conformations, such as that for propanal 2.187a, and as seen within many structures derived from X-ray crystallographic data.199 The strength of this kind of hydrogen bond correlates with the acidity of the C—H bond,197,200 in line with the picture of hydrogen bonding as a model for proton transfer. Thus the hydrogen atoms on haloforms, on acetylenes, on methylene groups between two electron-withdrawing groups, on aldehydes and on alkenes are the ones most often involved in C—H. . .O hydrogen bonds. Knowledge of when these hydrogen bonds might be strong has made it possible to design pairs of compounds that crystallise together, like the 2:1 combination 2.174 of trinitrobenzene and dibenzylidenecyclo-pentanone, and has provided a basis for crystal engineering and supramolecular design.

O N

O

O

H

O

H H

H

O

H

N O

H N

H

O

H

H

O

N

H

O N O

O

N O2S

B

O O

O

O H H

N O

2.175 2.174

H

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MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

One of the most striking manifestations of the importance of C—H. . .X hydrogen bonds is in the way they affect the conformations adopted in transition structures, where small energy differences can have a large effect. Conspicuously, the capacity of the hydrogen atom in an aldehyde to be a relatively good hydrogenbond donor, considering that it is attached to a carbon atom, has played a major role in understanding how chiral catalysts work.201 One example is the structure deduced for the complex 2.175 between benzaldehyde and Kiyooka’s oxazaborolidine, which induces high enantiocontrol in Mukaiyama aldol reactions. The carbonyl oxygen is coordinated to the boron, and the weak hydrogen bond—the dashed line—is just strong enough to hold the si face of the aldehyde, the front face as drawn here, exposed to the attack of nucleophiles. 2.5.2.3 X—H . . . p Bonds. Similarly weak hydrogen bonds can also be formed from protons bound to electronegative elements coordinating to the p orbitals of C¼C p bonds. The strength, estimated to be anything up 17 kJ mol 1 (4 kcal mol1), is clearly strong enough to be important in interactions like that of a drug with its receptor in biological systems.202 The effect is seen in lower frequency O—H stretching in the infrared spectra of alcohols, correlating with how closely the hydrogen atom sits to a double bond or an aromatic ring,203 and most dramatically in the upfield shift of 1.5 ppm for the phenolic OH proton when the spectrum is taken for a solution approaching infinite dilution in benzene rather than in carbon tetrachloride.204 The large shift is not so much a measure of the strength of the O—H. . .p hydrogen bond, as a consequence of the proton sitting in the shielding region of the ring current 2.176. 2.5.2.4 C—H . . . p Bonds. Even weaker hydrogen bonds, rarely responsible for stabilisation of more than 4 kJ mol 1 (1 kcal mol1), can be detected between C—H bonds and C¼C p bonds. 205 These interactions are again seen in some packing arrangements in X-ray crystal structures, in small changes in infrared stretching frequencies, and most dramatically in some noticeable upfield shifts in the 1 H-NMR spectra when changing the solvent from carbon tetrachloride or chloroform to benzene or toluene. On the whole, the larger shifts in the NMR spectra are seen with the more acidic C —H bonds, with chloroform for example showing a shift of 1.35 ppm at infinite dilution, because of the formation of a bond to the centre of the p system 2.177.206 It has been suggested that an ammonium salt can interact with aromatic rings 2.178 by C —H. . .p hydrogen bonding, and thereby explain how the charged ammonium neurotransmitter from acetylcholine can be recognised at its aromatic-rich receptor site, in spite of the ionic nature of the one component and the hydrophobic nature of the other. 207

Ph

O

1.5 ppm upfield

Cl

Cl 1.35 ppm C Cl upfield

H

H

2.176

2.177

N H

H H

2.178

It might perhaps be argued that hydrogen bonding may not be the best way to describe this attraction. Because H—C bonds made up from the 1s orbitals on hydrogen and the 2px and 2py orbitals on carbon are overall polarised towards carbon, the hydrogen atoms on the periphery of p systems are overall positively charged, and the centre of the p system is negatively charged. The attraction of the one for the other is then seen as simply electrostatic. One might equally argue that all kinds of hydrogen bonding can best be thought of as simply electrostatic, and that arguments over what to call the attraction are only about what to call it and not about its fundamental nature.

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

121

Weak C—H. . .p interactions may also be responsible for such unexpected observations as the preference for a gauche interaction between the tert-butyl and phenyl groups in the sulfoxide 2.179a rather than the more obvious anti-periplanar arrangement 2.179b of the two largest groups,208 for the cyclohexanone 2.180 to have the phenyl group axial,209 where it can bond to the hydrogen atoms of the methyl group, rather than equatorial, as would be expected for a group with a higher A-value (2.8) than that of a methyl group (1.7), and for the frequent occurrence in crystal structures and in host–guest interactions of arrangements of aromatic rings in which the C—Hs of one aromatic ring point at the plane of the ring of another 2.181,210 in contrast to p stacking that is so often invoked (Section 2.5.4).

H-bonded?

H-bonded? Me

H O

S

S

H

O

H H

H

H-bonded? O

H

H

Me

2.179a

2.179b

2.180

2.181

It might be thought that feeble hydrogen bonding of this kind was of little significance, but its effect is magnified when it contributes to small energy differences in transition structures, where arguments about preferred conformations influenced even by such small effects as C—H. . .p hydrogen bonding and other weak interactions are often called upon.211 An energy difference of 4 kJ mol1 (1 kcal mol1) in two transition structures derived from the same starting materials gives a product ratio of 83:17 at room temperature. Ratios of this kind are commonplace in organic reactions, where small energy differences determine the sense and degree of stereo and other kinds of selectivity. 2.5.3 Hypervalency There are many well known molecules which clearly have more than the complete octet of electrons found in traditional Lewis structures. These include such molecules as PF5, SF4, PhICl2 , and XeF2, such ions as SiF5 and PCl 6, and transition structures like those involved in S N2 reactions at carbon and silicon, and any of the elements below them and to the right of them in the periodic table. Such molecules have been called hypervalent, 212 and have been said to have expanded valence shells. Hypervalent molecules almost always have a high proportion of electronegative elements among their ligands. The standard method of explaining how such molecules can be stable is to invoke the interaction of a filled p or hybrid orbital on one of the ligands with an empty d orbital on the central element. This immediately explains why the stable hypervalent molecules are all found with elements in the second row or below, where d orbitals are available, and not in the first, where they are not. The d orbitals can be combined with the s and p orbitals in any combination to give a bewildering array of hybrid orbitals to use for this kind of bonding. Like any interaction of filled with unfilled orbitals, interactions with empty d orbitals are bound to be stabilising. The problem, as we have already seen earlier in explaining why a silyl, phosphenyl, or sulfenyl group is p-withdrawing, is that d orbitals are too high in energy relative to the p orbitals for their interaction to have much effect. It is better to see hypervalent bonding as the consequence of orbital interactions like those involved in hydrogen bonding.213 Essentially, the central atom Y is seen as involved in normal bonding to n2 of its ligands. In addition, a p orbital on each of the two remaining ligands X together with an unused p orbital on the central element Y interact to create a set of three molecular

122

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

*

X

Y

X

3

X

Y

X

2

X

Y

X

1

Fig. 2.26 The key molecular orbitals of hypervalent bonding

orbitals as shown in Fig. 2.26. For the system to be overall bonding, it is necessary for 2 to be largely nonbonding, which it will be if the ligands are kept well apart, and are electronegative elements, just as they are in hydrogen bonding. Thus a pentacovalent phosphorus compound will have the three least electronegative ligands in the plane of a trigonal bipyramid 2.182, with bonds formed from the 3s and the 3px and 3py orbitals, and the two most electronegative ligands disposed linearly at the apices, with bonds formed from the two lower orbitals in Fig. 2.26. Furthermore, the more electronegative ligands will also carry more negative charge, and will repel each other most thoroughly if they are both apical. In consequence of both orbital and charge effects, the apical bonds are weaker than the basal, and these are well known214 to be the ones that break during reactions. It follows that they are also the ones that are formed most easily in the reverse of those reactions, and apical attack is indeed normally observed. Nu (–)

X R

P X 2.182

R R

R

C R R X (–) 2.183

Nu R

Si R R X 2.184

The same pattern is seen in the transition structures 2.183 for the SN2 reaction at carbon, which will have five ligands around the central atom. Apical entry of a nucleophile and apical departure will give the lowestenergy transition structure, and hence explain the overall inversion of configuration. Changing to silicon, what was a transition structure with carbon can be an intermediate with a lifetime 2.184, because the bonds are so much longer and 2 is that much less antibonding. We shall return to this subject when we discuss the stereochemistry of nucleophilic substitution in Chapter 5. 2.5.4 Polar Interactions, and van der Waals and other Weak Interactions 2.5.4.1 Coulombic Forces. If two molecules, or two parts of one molecule, have charges or dipoles, the sites of opposite charge can attract each other, and sites with the same charge can repel each other. These forces can be large and have a conspicuous influence on molecular properties, and especially on reactivity, as we shall see in later chapters. One way of looking at hydrogen bonding is to see it as primarily Coulombic. The same electrostatic forces also come into play in a less direct way in a number of weaker interactions. For example the axial lone pairs in the 1,3-dioxan 2.185 can sense the electron deficiency at the para position of the nitrobenzene ring, and make the conformation with the aryl group axial lower in energy than the conformation when it is equatorial. The usual pattern is seen in the 1,3-dioxan 2.186 with a benzene ring in place of the nitrobenzene.215

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

123

NO2 H

H Me

H

H

H

O

H

O

O

H

Me

O

H

Preferred conformation (71:29)

H Preferred conformation (79:21)

2.185

2.186

Furthermore, polar attractions from one polar molecule to another, or from one strongly hydrogen-bonding molecule to another, lead such molecules to aggregate, and to exclude nonpolar molecules. This is the basis for the well-known hydrophobic effect, in which nonpolar molecules stick together to avoid being in water. 2.5.4.2 Dipole-Dipole Attraction. If only one of the molecules is charged or a dipole, it can still respond to weak polar forces in molecules not traditionally thought of as being polar. Two related examples of weak but significant dipolar interactions are seen in propanal 2.187216 and propanol 2.188,217 in which the lowerenergy conformations, 2.187a and 2.188a, have the methyl groups close to the oxygen atom. The small degree of polarisation of the H—C bonds in the methyl groups leaves a weak positive charge on the outside, and this is attracted to the partial negative charge on the oxygen atoms, making these conformations slightly lower in energy than the less sterically hindered conformations 2.187b and 2.188b. This phenomenon is essentially the same as that of hydrogen bonding at the weaker end of its range (Section 2.4.2.2, where the conformation of propanal was mentioned). We return to this conformational preference in Chapter 5, where it contributes to our understanding of the Felkin-Anh rule. H

8 kJ mol–1 Me

H Me

H

O

OH H H

H 2.187a

2.187b

O

Me

H

H

H

4 kJ mol–1

OH H

H

H

H

H

Me

2.188a

2.188b

There is a somewhat similar phenomenon in which the presence of a dipole within a molecule induces a temporary dipole, either elsewhere in the molecule or in another molecule. The induced dipole is then attracted to the inducing charge or dipole, and another small attractive force comes into play that is not included in the molecular orbital picture at the most simple level of calculation, but is included when larger basis sets are used. Weak dipolar attractions like these, both the static and the induced, are not strong, and so nonpolar molecules are not well solvated by polar molecules—the polar solvent molecules would rather solvate each other and the nonpolar molecules are left to their own devices. As it happens they do not repel each other as much as one might expect. 2.5.4.3 van der Waals Attraction. In addition to forces directly associated with charge, two molecules repel each other, because the interaction of the filled orbitals of one with the filled orbitals of the other is inherently energy-raising. This is the basis for steric hindrance of all kinds. The repulsion is countered by a small attractive force from the interactions of filled orbitals with unfilled orbitals, which are inherently energy-lowering. Both forces fall off exponentially with distance, but they are not the only interactions between nonpolar molecules. If we look at two electrons, one in each of two nonpolar molecules, the electron in one molecule will repel the electron in the other. At any given moment, if the first electron is on the side of the molecule facing the other molecule, it will cause its opposite number to spend more of its time on the far

124

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

side of the second molecule. The electrons are said to be correlated. As the two electrons spend, on average, more of their time far away from each, the two molecules experience a small attractive dipolar electrostatic attraction. This only comes into play at short distances, with the energy falling off as the inverse sixth power of the distance apart. The resultant attractive force, countering the simple repulsion, is known as a dispersion force, or more commonly as the van der Waals attraction. It is responsible, for example, for the weak force that keeps liquid hydrocarbons in the liquid state, and that helps them to aggregate in polar solvents. In liquid helium, at very low temperatures, the only attractions holding the atoms together are van der Waals forces. We saw correlation earlier on p. 5, when we learned that two electrons can be placed into one orbital, provided, of course, that their spins are opposed. The correlated movement of the electrons within that orbital keeps them, on average, far apart but there is an energetic penalty from putting a second electron into an orbital already singly occupied. The electron correlation reduces the severity of the penalty, and is often needed in calculations to get the right answers. In the same way, van der Waals interactions often have to be invoked when calculations based on molecular orbitals and dipolar effects do not explain all the attractions or repulsions found in practice. 2.5.4.4 p-p Interactions and p Stacking.218 Aromatic rings show an aptitude to aggregate that is not simply explained by van der Waals attractions. The phenomenon shows up in such important areas of molecular recognition as the stacked interactions between bases within the DNA double helix, in intercalation by drugs and carcinogens into the DNA stack,219 in the aggregation of the chlorin rings in the chloroplast, in the tertiary structure of proteins, and in many host–guest supramolecules. We have already seen one way in which they aggregate, edge-to-face 2.181, but a face-to-face stacking arrangement is not uncommon. However, a stack of nonpolar aromatic rings perfectly lined up directly on top of each other is straightforwardly repulsive (Fig. 2.27a)—one p system repels the other, whether one sees it as the interactions of filled orbitals with other filled orbitals, or as one negatively charged p cloud repelling another. The van der Waals attractions are not powerful enough on their own to stabilise this arrangement, but aromatic rings stacked above one another do find a stable arrangement when one p system is offset relative to the other (Fig. 2.27b). With the p system of one molecule lying over the edge of the one below, there is an electrostatic attraction from the positively charged  framework with the negatively charged p cloud, especially since the positive charge is largely on the peripheral and therefore exposed hydrogen atoms.220 This electrostatic attraction can only come into play in a stack if the rings are offset. The van der Waals forces are proportional to the area of contact and are weakened by the offset, so a balance is struck by a degree of offset that can be estimated using an electrostatic model. p Stacking is more common with the larger aromatic systems like porphyrins, probably because of the greater area for the van der Waals forces to work on, than they are with simple benzenes, where the arrangement 2.181 and the offset p stack are close in energy.221 negative charge

H

H (C C C C)n H

positive charge

negative charge

H

H

negative charge

repulsion

≡

positive charge

repulsion H

positive charge

negative charge

H

H

negative charge

(a) Face-to-f ace

attraction

attraction

negative charge

H (C C C C)n H

H

negative charge

stacks

positive charge

H

negative charge

(b) Of f set

stacks

Fig. 2.27 p Stacking

A simple example is found in the crystal packing of [18]annulene 2.189, where the p system of one molecule lies over the cavity of the molecule below it.222 In the other dimension, not shown, the hydrogen atoms at the

2 MOLECULAR ORBITALS AND THE STRUCTURES OF ORGANIC MOLECULES

125

edge of one ring point at the p system of another, as in 2.181. Electron-donating or electron-withdrawing substituents, or heteroatoms in the aromatic rings, shift the electron distribution, introducing stronger or opposing electrostatic effects. This can be seen in the crystal packing of tetramethyl-benzoquinone 2.190,223 and in the 1:1 complex 2.191 between 1,2,4,5-tetracyanobenzene and naphthalene.224 In these stacks, areas of electron deficiency lie above areas of electron excess, achieved in the one case 2.190 by the uneven distribution of electrons within the one molecule, and in the other case 2.191 by alternating electron-rich and electron-deficient rings in the stack. In extreme cases like these, the offset is no longer needed for electrostatic attractions to hold the two planes together, but an offset is still common with many systems, including those with donor and acceptor substituents like the 1:1 complex between 1,2,4,5-tetracyanobenzene and N,N,N0 ,N0 -tetramethyl-1,4-diaminobenzene.225 No one has looked at the crystal packing in 1,3,5triazene 2.192, but it is a fair guess that it would stack one ring above the other, but with the nitrogen atoms, carrying an excess of negative charge, directly above the carbon atoms, carrying an excess of positive charge.

O NC

N CN

O O

NC

N

N

CN O 2.189

2.190

2.191

2.192

Probably the most striking example of a stack of alternating electron-rich and electron-poor benzene rings is in a 1:1 mixture of benzene and hexafluorobenzene.226 Each of these compounds on its own lines up edge to face, as in 2.181 and Fig. 2.28a, but the 1:1 mixture stacks face to face with alternating benzene and hexafluorobenzene rings as in Fig. 2.28b. The simple electrostatic model for the stack explains how the negatively charged benzene ring is directly above and below the positively charged hexafluorobenzene ring, and the negatively charged fluorine atoms are above and below the positively charged hydrogen atoms. Neither compound has a dipole moment, and yet they attract one another electrostatically because of their high electric quadrupole moments of opposite sign. There is no need to think of them as charge transfer complexes. The mixture melts 20 °C higher than either of the pure compounds, which is not what usually happens with a mixture.

(a) Edge-to-f ace stacks seen in the crystal structures of benzene and hexaf luorobenzene

Fig. 2.28

(b) Face-to-f ace stacks seen in the crystal structure of a 1:1 mixture of benzene and hexaf luorobenzene

Edge-to-face stacking and face-to-face stacking

3

3.1

Chemical Reactions—How Far and How Fast

Factors Affecting the Position of an Equilibrium

All the attractive and repulsive forces discussed at the end of the preceding chapter, from van der Waals forces, through hydrogen bonding and other electrostatic effects, to the interactions of the molecular orbitals, affect not only the shape a molecule adopts within itself but also how favourably it can interact with another molecule, as indeed we saw in the stacking of aromatic rings in the last few examples. Most of these interactions, the repulsive forces that help molecules to retain their identity, and the attractive forces, like the van der Waals forces and hydrogen bonding, that allow them to come close, do not necessarily lead to reaction. They are important in determining a favourable alignment of two molecules, and hence the stereochemistry of approach, but for insight into the nature of the events leading to reaction and to the sources of reactivity, we need to look further, first to find whether two molecules colliding can possibly create one or more molecules lower in energy than the starting materials—the thermodynamics—and then whether there is an energetically accessible pathway between the starting materials and the products—the kinetics. We shall now examine the interactions that lead beyond mere association to chemical reaction, and begin to find out what factors influence chemical reactivity. Straightforwardly, a reaction may take place if the total free energy of the starting materials is higher than the total free energy of the products. There may or may not be a barrier to such a reaction, but that we shall come to later. As far as feasibility is concerned, we can simply measure experimentally the energy content of both sides of the reaction, and this will give us the answer. This is useful in all sorts of ways, but what we want now is some understanding of why the numbers come out the way they do. Thus we can understand easily enough that the reaction between bromine and ethylene giving dibromoethane is exothermic—it replaces one p bond (C¼C) with two  bonds (C—Br) at the expense of a weak  bond (Br—Br). Organic chemists deduce from this that bromine is a reactive molecule, and allow their knowledge of this and hundreds of other reactions to inform their sense of which reactions are likely to be feasible and which are less likely. Factors such as cancellation of charge, improved solvation, the creation of conjugation, in all its manifestations, and especially aromaticity, and relief of steric repulsions can all be handled in this empirical way to make sense of the direction reactions are seen to go in. However, it is not always obvious how strong the bond will be when one molecule combines with another to form a single new molecule, or what happens to the energy if we exchange parts of one molecule with parts of another. A useful addition to understanding this sort of problem has been Pearson’s concept of hard and soft acids and bases (HSAB). It does not replace other perceptions, or conflict with them, but in several systems it has provided useful extra insight.

Molecular Orbitals and Organic Chemical Reactions: Reference Edition  2010 John Wiley & Sons, Ltd

Ian Fleming

128

3.2

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

The Principle of Hard and Soft Acids and Bases (HSAB)227

Lewis acids and bases (including Hþ and OH) can be classified as belonging, more or less, to one of two groups, one called hard and the other called soft. The striking observation is, and this is the basis of the classification, that hard acids form stronger bonds with hard bases, and soft acids form stronger bonds with soft bases. For example, a hard acid like the proton is a stronger acid than the silver cation, Agþ, when a hard base like a hydroxide ion is used as the reference point; but if a softer base like iodide ion had been used, we would have come to the opposite conclusion. This situation is summarised in the rule: hard-likes-hard and softlikes-soft, introduced, at first into inorganic chemistry,228 but later into organic chemistry as well.229 What it amounts to is that the equilibrium in Equation 3.1 lies to the right, where H equals hard and S equals soft. H-Acid : S-Base þ S-Acid : H-Base Ð H-Acid : H-Base þ S-Acid : S-Base

3:1

Pearson’s classification and rank ordering of acids and bases was intended to simplify and illuminate the problem but it did not, and at that stage was not intended to explain it or give it a quantitative basis. It has proved to be a durable idea, and furthermore has now been placed, first by Klopman,230,231 and more thoroughly by Pearson and by Parr,232,233 on a sounder theoretical basis. At its most simple,231 we look at the equilibrium between a Lewis acid and a Lewis base and the salt they form. The position of the equilibrium is affected both by charge and by orbital interactions. In outline, it seems that a hard acid bonds strongly to a hard base by electrostatic interactions. Hard acids and bases have the HOMO of the base and the LUMO of the acid far apart in energy. This leads, as we saw in Fig. 1.60, to an ionic bond with little overlap, and we can associate the strength of the bond with the value Ei on that diagram (see p. 53). Also, the smaller the ion or molecule, the harder it is, because the charges can get closer in the ionic bond, which is Coulombic in nature. A high positive charge on the acid and a high negative charge on the base will also contribute to the strength of the ionic bond. However, a soft acid bonds strongly to a soft base because the orbitals involved are close in energy. As we saw in Figs. 1.3 and 1.20, we get the maximum overlap for covalent bonding when the interaction is between orbitals of similar energy, and we can associate the strength of the bond with the value E in Fig. 1.3. We can also see that in practice we shall not often have pure hardness and pure softness in our acids and bases; rather, there is a continuum, and the C—Cl bond in Fig. 1.58 is a case where the bond strength comes from both types of interaction. In summary, a hard acid is small, has a high positive charge and a high-energy LUMO, and a hard base is small, has a high negative charge and a low-energy HOMO. The smaller the ion, the higher the charge and the higher the energy of the LUMO of an acid, the harder it is as an acid. Similarly, the smaller the ion, the higher the charge and the lower the energy of the HOMO of a base, the harder it is as a base. Thus a proton is a hard acid and the silver cation is soft; a fluoride ion is a hard base and an iodide ion is soft. To go into this idea in more detail, and quantitatively,232 we need definitions of hardness and softness, and we shall want to rank acids and bases on scales of hardness. This has been done in two ways: one related to ideas we have already used in molecular orbital theory; and the other based on density functional theory. The former is perhaps the more accessible, but both provide useful insights. We define two parameters. One is called the absolute electronegativity, w, and is approximately the same as electronegativity as Mulliken originally defined it for atoms, namely the average of the ionisation potential I and the electron affinity A (Equation 3.2). The other is called the absolute hardness, ,234 which is identified with the difference in energy between the ionisation potential I and the electron affinity A (Equation 3.3). [In earlier versions of Equation 3.3 the term (I – A) was divided by 2 to make the two equations similar, but it is best left out.] ðI þ A Þ 2

3:2

 ¼ ðI  AÞ

3:3

¼

3 CHEMICAL REACTIONS—HOW FAR AND HOW FAST

129

Hardness in this definition is therefore identical to the energy change for the reaction in Equation 3.4. The species R has zero hardness when this disproportionation has no change in energy. This also identifies the maximum degree of softness, which is therefore defined as the reciprocal of hardness. This definition fits the earlier qualitative approach to explaining hardness and softness as being associated with polarisability— those species with a large difference between I and A were the ones that were not easily polarised. R  þ R  ! Rþ þ R

3:4

The relationship between the two parameters  and w is expressed graphically in Fig. 3.1, using Koopman’s theorem that the ionisation potential is the negative of the energy of the HOMO and the electron affinity is the negative of the energy of the LUMO. The figure shows the starting materials and products of two reactions: the combination of a methyl radical with a fluorine atom on the left and with an iodine atom on the right. The ionisation potential and electron affinity data, which are taken from Table 3.1, are the negatives of the energies used in an orbital energy graph like that in Fig. 3.1.

–6.2

6

CH3F

4 2 0

0.08

CH3

0.08

–2

F

CH3I

0.20

– 3.2

3.40

–4

CH3 3.06

– 4.96

I – 4.9

– 4.96

–6

– 6.76 9.74

–8 –10

9.74

9.82

– 10.41

–12

18.7

9.82

9.50

10.45

CH3

12.5

+

9.30

7.39 I

CH3I

–14 14.02

–16 eV

Fig. 3.1

17.42

CH3

+

F

CH3F

Orbital energies for the reaction of a methyl radical with fluorine and iodine atoms

It is not yet a well established concept in organic chemistry, but it appears that there is a principle of maximum hardness,235 which says that reactions take place in the direction that increases hardness. We can use the two reactions in Fig. 3.1 to see how this works. The hardness of a pair of starting materials is measured by taking the smaller value of I and the more positive value of A, and using Equation 3.3. The combination of a methyl radical and a fluorine atom has a change from  ¼ 9.82  3.40 ¼ 6.42 to  ¼ 18.7, whereas the combination of a methyl radical with an iodine atom has a change from  ¼ 9.82  3.06 ¼ 6.76 to  ¼ 9.30. Thus the former is the reaction with the greater increase in hardness, with methyl fluoride a very hard molecule, and is the more exothermic reaction. The second approach to defining the absolute hardness  has a companion parameter taken from density functional theory, called the electronic chemical potential m. The value of m is essentially the same as the negative of w, as defined in Equation 3.2, and the value of  is essentially the same as in the more approximate definition in Equation 3.3 but both are defined differently. If the total electronic energy of an atom or molecule is plotted as a function of the total number of electrons N, the graph takes the form of Fig. 3.2 in which the only experimental points are at integral values of N but between them it is convenient to

130

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS Table 3.1 Absolute hardness  (in eV) for some radicals232

Radical F H OH NH2 HO2 CN CHO Me Cl NO Et PH2 Br SH Ph

I 17.42 13.59 13.17 11.40 11.53 14.02 9.90 9.82 13.01 9.25 8.38 9.83 11.84 10.41 8.95

A 3.40 0.74 1.83 0.74 1.19 3.82 0.17 0.08 3.62 0.02 0.39 1.25 3.36 2.30 0.10

w



10.41 7.17 7.50 6.07 6.36 8.92 5.04 4.96 8.31 4.63 4.00 5.54 7.60 6.40 5.20

14.02 12.85 11.34 10.66 10.34 10.2 9.73 9.74 9.39 9.23 8.77 8.58 8.48 8.11 8.85

Radical CH2¼CH CF3 Pri NO2 MeCO SeH I But CCl3 PhCH2 SiH3 PhO PhS SiCl3 Li

I 8.95 9.25 7.57 >10.10 8.05 9.80 10.45 6.93 8.78 7.63 8.14 8.85 8.63 7.92 5.39

A 0.74 >1.10 0.48 2.30 0.30 2.20 3.06 0.30 1.90 0.88 1.41 2.35 2.47 2.50 0.62

w 4.85 >5.18 3.55 >6.20 4.18 6.00 6.76 3.31 5.35 4.26 4.78 5.60 5.50 5.20 3.00

 8.21 <8.15 8.05 >7.80 7.75 7.60 7.39 7.23 6.88 6.75 6.73 6.50 6.16 5.42 4.77

draw a smooth curve. Starting at the neutral point, the addition of an electron can only lower the energy by a small amount, if anything, and further additions of electrons will probably not be possible, so the curve flattens out. Taking an electron out of the system will cause a large rise in energy, and it will be harder still to take more electrons out, so the curve will rise steeply. This picture matches ordinary chemical experience. The absolute electronegativity is now defined by Equation 3.5, which is the negative of the slope of the E vs. N curve. This is a continuous function, which allows for nonintegral electron populations, a familiar concept in organic chemistry. The absolute hardness is then defined as the second integral of the same curve in Equation 3.6, which is therefore the curvature.   qE 3:5 ¼ qN ¼

1 2



q2 E qN 2

 3:6

Table 3.1 gives experimental ionisation potentials and electron affinities for a range of radicals, together with the absolute hardness and electronegativity calculated from them using Equations 3.2 and 3.3. Table 3.2 does the same for some molecules. A useful perception revealed in these tables is that a soft ligand on a hard atom will soften it. (Compare CF3 with CCl3 in Table 3.1, or BF3 and BCl3 in Table 3.2.) The soft ligand will be effective in transferring electrons to the central atom, moving it down the curve of Fig. 3.2, and flattening the curvature. This is very much in line with experience. Lewis acids with electronegative ligands like fluoride and chloride are strong Lewis acids towards hard bases, because they are themselves harder. It had not been obvious before why substituents have such a profound effect on the hardness of the reacting atom. When we come to bases we meet a difficulty—many bases are anions, and are therefore at the foot of the graph in Fig. 3.2, with a slope and curvature too close to zero to be useful. As a base acts, electrons are transferred and the curvature becomes larger, so we must choose a point on the graph to reflect this feature. The choice used to create the data in Table 3.3 is to take the point where one electron has been transferred from the base, defining the I and A values as those for the base minus one electron. This gives the elemental

3 CHEMICAL REACTIONS—HOW FAR AND HOW FAST

131

Table 3.2 Absolute hardness  (in eV) for some molecules232 Molecule

I

A

w



HF CH4 BF3 H2O MeF N2 CO2 H2 NH3 HCN HCl Me2O CO MeCN MeCl MeNH2 HCCH SiH4 PF3 HCO2Me Me3N CH2¼CH2 H2S AsH3 Me2S PH3 O2 CH2¼O

16.0 12.7 15.8 12.6 12.5 15.58 13.8 15.4 10.7 13.6 12.7 10.0 14.0 12.2 11.2 9.0 11.4 11.7 12.3 11.0 7.8 10.5 10.5 10.0 8.7 10.0 12.2 10.9

6.0 7.8 3.5 6.4 6.2 2.2 3.8 2.0 5.6 2.3 3.3 6.0 1.8 2.8 3.7 5.3 2.6 2.0 1.0 1.8 4.8 1.8 2.1 2.1 3.3 1.9 0.4 0.9

5.0 2.5 6.2 3.1 3.2 6.70 5.0 6.7 2.6 5.7 4.7 2.0 6.1 4.7 3.8 1.9 4.4 4.8 5.7 4.6 1.5 4.4 4.2 4.0 2.7 4.1 6.3 5.0

22.0 20.5 19.3 19.0 18.7 17.8 17.6 17.4 16.3 15.9 16.0 16.0 15.8 15.0 14.9 14.3 14.0 13.7 13.3 12.8 12.6 12.3 12.6 12.1 12.0 11.9 11.8 11.8

Molecule Me3P MeBr Me2NCHO MeCHO Me3As BCl3 SO2 CCl4 Me2CO CH2¼CHCN SO3 O3 MeNO2 HI benzene HNO3 pyridine butadiene CS2 PCl3 :CH2 MeI Cl2 PhCH¼CH2 PBr3 Br2 S2 I2

E

I

A

w



8.6 10.6 9.1 10.2 8.7 11.6 12.3 11.5 9.7 10.91 12.7 12.8 11.13 10.5 9.3 11.03 9.3 9.1 10.08 10.2 10.0 9.5 11.6 8.47 9.9 10.56 9.36 9.4

3.1 1.0 2.4 1.2 2.7 0.33 1.1 ~0.3 1.5 0.21 1.7 2.1 0.45 0.0 1.2 0.57 0.6 0.6 0.62 0.8 0.6 0.2 2.4 0.25 1.6 2.6 1.66 2.6

2.8 4.8 3.4 4.5 3.0 5.97 6.7 5.9 4.1 5.35 7.2 7.5 5.79 5.3 4.1 5.80 4.4 4.3 5.35 5.5 5.3 4.9 7.0 4.11 5.6 6.6 5.51 6.0

11.7 11.6 11.5 11.4 11.4 11.3 11.2 11.2 11.2 11.1 11.0 10.7 10.7 10.5 10.5 10.5 9.9 9.7 9.5 9.4 9.4 9.3 9.2 8.7 8.3 8.0 7.7 6.8

neutral

N

Fig. 3.2

The electronic energy E as a function of the total number of electrons N

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MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS Table 3.3

Absolute hardness (in eV) for some bases232

Base

IB þ

ABþ



Base

IBþ

ABþ

B

F H2O NH3 H CO OH NH2 CN H2S

17.42 26.6 24.0 13.59 26.0 13.0 11.3 14.2 21§

3.40 12.6 10.2 0.75 14.0 1.83 0.74 3.6 10.5

14.02 14.0 13.8 12.84 12.0 11.17 10.56 10.6 10.5

PH3 N3 Cl NO2 ClO Br SH Me I

20.0 11.6 13.01 12.9 11.1 11.84 10.4 9.82 10.45

10.0 1.8 3.62 3.99 2.2 3.36 2.3 1.8 3.06

10.0 9.8 9.39 8.91 8.9 8.48 8.1 8.02 7.39

Table 3.4 Absolute hardness (in eV) for some acids232 Acid

IA

AA

wA

A

Acid

IA

AA

wA

A

Hþ Al3þ Liþ Mg2þ Naþ Ca2þ Fe3þ Rbþ Zn2þ Tl3þ Cu2þ

1 120.0 75.6 80.1 47.3 51.2 56.8 27.5 39.7 50.7 36.8

13.59 28.4 5.39 15.03 5.14 11.87 30.6 4.18 17.96 29.8 20.29

1 74.2 40.5 47.6 26.2 31.6 43.7 15.8 28.8 40.3 28.6

1 91.6 70.21 65.07 42.16 39.33 26.2 23.32 21.74 20.9 16.51

Hg2þ Agþ CO2 Pd2þ Cuþ AlCl3 SO2 Brþ Cl2 Iþ I2

34.2 21.5 13.8 32.9 20.3 12.8 12.3 21.6 11.4 19.1 9.3

18.75 7.57 0.0 19.42 7.72 ~1 1.1 11.8 2.4 10.5 2.6

26.5 14.6 6.9 26.2 14.0 6.9 6.7 16.7 6.9 14.8 6.0

15.45 13.93 13.8 13.48 12.58 11.8 11.2 9.8 9.0 8.6 6.7

anions like fluoride ion the same values as the fluorine atoms in Table 3.1. The same problem does not arise for acids in Table 3.4, because they start off further up the curve, and the normal definition works. These tables give a sense of the large trends, and match the simple version in that the small, charged and electronegative fluoride ion can be seen to be hard, while the large, uncharged and not strongly electronegative hydrogen sulfide is soft. Similarly, the small, charged proton or the lithium cation can be seen to be hard, while the large silver cation and the uncharged sulfur dioxide are soft. A problem interpreting the numbers in Tables 3.3. and 3.4, which are for the gas phase, is that ions in practice are solvated—heavily so in polar solvents. Thus ions are not carrying their full charge but substantially sharing it with solvent. The same goes especially for the infinitely hard bare proton, which is never involved in solution chemistry. In fact, all the data for H, the radical, anion and cation, are unreliable— hydrogen is a special case. To overcome the problem with the charges on acids and bases, we can be less ambitious, and make more restricted comparisons of acidity and basicity.233 To obtain a useful quantitative measure of the hardness of acids and bases, we apply the concept in Equation 3.1 to the acid:base exchange reaction in Equation 3.7, which will take place from left to right if A1 and B1 are the harder acids and bases relative to A2 and B2. A1 : B2 þ A2 : B1 Ð A1 : B1 þ A2 : B2

3:7

3 CHEMICAL REACTIONS—HOW FAR AND HOW FAST

133

We would like to know the bond strengths of A:B with respect to separation into the free acid and the free base. This only takes us back to the same problem, so we avoid it, since only comparisons will be made, by using the better documented gas-phase bond dissociations D for separation into the pair of radicals A and B. For monovalent Lewis acids, we can then take a pair of reference monovalent bases, such as fluoride ion and iodide ion, one hard and one soft, and for which there are plenty of data. We use the reaction in Equation 3.8 to define the scale of local hardness at the atom in the bond we are using by the difference DFI using Equation 3.9. A1 —I þ A2 —F Ð A1 —F þ A2 —I

3:8

DFI ¼DAF – DAI

3:9

The results of these calculations give the scale of local hardness for a range of cations in Table 3.5—the larger the value of DFI the harder the acid. These numbers allow us to calculate the equilibrium energy for the competition in Equation 3.8. Thus an extreme case is the equilibrium in Equation 3.10, which is exothermic by 335 kJ mol1 (80 kcal mol1). The products can be seen as more stable than the starting materials, not because of any special bonding, but because of the correct matching of hard-with-hard and soft-with-soft. 335kJmol—1

H3 Si—I þ HO—F Ð H3 Si—F þ HO—I

Table 3.5 Acid CF3þ SiH3þ

MeCOþ CHOþ Hþ Phþ Butþ CH2¼CHþ Liþ Naþ Priþ Etþ

DAF 543 619 502 510 568 518 451 497 573 514 447 447

3:10

Empirical hardness (in kJ mol1) for some cationic acids233 DAI 226 301 209 217 297 268 209 263 343 288 222 222

DFI 318 318 293 293 272 251 242 234 230 226 226 226

Acid CH2¼CHCH2 Meþ c-C3H5þ Tlþ CNþ NOþ Csþ Iþ Cuþ Agþ HOþ

þ

DAF

DAI

DFI

410 456 464 439 468 234 493 280 426 351 217

184 234 247 268 305 84 343 150 314 251 234

226 222 217 171 163 150 150 130 113 100 -17

There appears to be an anomalous order for the alkyl cations, which have decreasing hardness in the order But > Pri > Et > Me. With the charge expected to be more spread out in the more-substituted cation, one would have expected the reverse order. The problem is that this applies only to the p energy, delocalised by hyperconjugation. With the carbon 2s orbital being more electronegative than a hydrogen 1s orbital (Section 1.7.1), the lowest energy molecular orbital for a methyl group has the higher electron population on the carbon atom, and replacing the hydrogen atoms with alkyl groups actually moves the total electron population away from the central carbon atom. The reference acids that Pearson used to estimate the local hardness of bases are the hard proton and the soft methyl cation. They do not have as large a spread of hardness as the fluoride ion and iodide ion, but the

134

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS Table 3.6

Empirical hardness (in kJ mol1) for some anionic bases233

Base

DHB

DMeB

DHMe

Base

F OH AcO PhO NH2 NO3 MeO HO2 NCS Cl Br ONO SH O2N PhNH PhCH2 I PrnS Me PhS

568 497 443 364 447 426 435 368 401 431 368 326 380 <326 368 368 297 364 439 347

456 385 347 268 355 334 347 288 322 355 293 251 309 255 297 301 234 301 376 288

113 113 96 96 92 92 88 79 79 75 75 75 71 <71 71 67 63 63 63 59

Et SeH AsH2 NCCH2 MeCOCH2 CH2¼CHCH2 NC PH2 Ph Pri CH2¼CH But HCC SiH3 MeCO CF3 GeH3 CN H

DHB

DMeB

DHMe

410 330 314 389 410 359 460 364 464 397 481 385 543 380 401 443 364 518 435

355 280 263 339 359 309 410 318 418 351 439 343 510 355 380 422 347 510 439

54 50 50 50 50 50 50 46 46 46 42 42 33 25 21 21 17 8 4

data are abundant, allowing Equations 3.11 and 3.12 to create the scale in Table 3.6. A few of the anions are ambident, a topic that we shall return to in the next chapter. They are the nitrite ion and cyanide ion, for which two values are given, a harder value for bonding to the more electronegative element and a softer value for bonding to the less. Me—B1 þ H—B2 Ð H—B1 þ Me—B2

3:11

DHMe ¼ DHB – DMeB

3:12

The trends in these tables are useful, although the numbers may be less so, because there are situations where the principle of HSAB does not work well. Some of these are easily recognisable:236 1. When both the acid and the base are intrinsically very strong, the strength can overcome the contribution of hardness and softness to an equation like Equation 3.7. 2. When some form of bonding is possible in one of the combinations but not the other. Thus, p bonding is possible from a methyl group (by hyperconjugation) but not from a proton, exaggerating the softness of those anions, like cyanide, trifluoromethyl, phenyl, vinyl and acetyl, able to indulge in it. 3. There is a significant entropy change. 4. When solvation in one of the combinations is exceptionally better than the other. 5. When there are multiple sites of bonding, as with chelating (bidentate) ligands. We shall return to the concepts of hardness and softness when we come to discuss kinetics, since it is there that we shall use them most tellingly.

3 CHEMICAL REACTIONS—HOW FAR AND HOW FAST

3.3

135

Transition Structures

In order to approach the problem of chemical reactivity, let us imagine two molecules which are about to combine with each other in a simple, one-step, exothermic reaction leading to two possible products A and B (Fig. 3.3a). We shall assume that we know the energies of the starting materials and the two products. Chemists have long appreciated that the more exothermic reaction, that leading to the product B, is usually the faster—it has been called the rate-equilibrium relationship, and is related to the reactivity-selectivity principle.237 The explanation is easy enough—whatever features lead the product B to be lower in energy than the product A will have developed in the transition structure to some extent. Thermodynamics does affect kinetics—a source of endless confusion. Because it is not always true, nor is it enough, we need to know more about what else affects the energy of the transition structure. We bear in mind that influences from both sides of the reaction coordinate affect the transition structure. Perturbation theory238 gives us one way to learn something about the reactant side—we treat the interaction of the molecular orbitals of the two components as a perturbation on each other. The perturbation is similar to that which leads to bonding and antibonding orbitals in interaction diagrams like those in Chapter 1, where two separate orbitals interact to create molecular orbitals. However, as the perturbation increases, it ceases to be merely a perturbation, and the mathematical basis of the theory fails to be able to accommodate so large a change. We do not, therefore, have direct access to a good picture of the transition structure in this way; nevertheless, we do get an estimate of the slope of an early part of the path along the reaction coordinate leading up to the transition structure (labelled path A and path B in Fig. 3.3a). Unless something unusual happens nearer the transition structure, the slopes will probably predict which of the two transition structures is the easier to get to—on the whole, the steeper path is likely to lead to the higher-energy transition structure. Transition structure A Transition structure B Path A Path B

Transition structure B Path A Path B

Transition structure A Curve crossing

Starting materials

Starting materials

Product A

Product A

Product B

Product B

(a) Thermodynamics and kinetics in concert

(b) Thermodynamics and kinetics in opposition

Fig. 3.3 The energy along two possible reaction coordinates

The situation shown in Fig. 3.3a is the common one: the higher-energy transition structure leads to the higher-energy product, and the better orbital interaction matches it. However, there are some situations where this is not so, where there is a crossing of the curves (Fig. 3.3b). Some of the most interesting mechanistic problems arise when the more exothermic reaction is not the faster—in other words, when

136

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

the thermodynamics and the kinetics do not go together. In these reactions, perturbation theory, which looks at the reactant side of the reaction coordinate, offers some insight. If the orbital interaction for path A is stronger than that for path B, as in Fig. 3.3b, it can help to explain the anomalous order of the two transition structures. Hitherto organic chemists have more often concentrated on the product side, but we now have a useful, and in some situations unique, tool for examining the reactant side of the reaction coordinate. The Hammond postulate says that the transition structure for an exothermic reaction (Fig. 3.4a) is closer in energy to the energy of the starting materials, and so it has more of the character of the starting materials, or, looking at the distances along the reaction coordinate, A
Starting materials

Products A

B

Products B

Starting materials

(a) An exothermic reaction, with a reactant-like transition structure

Fig. 3.4

3.4

A

(b) An endothermic reaction, with a product-like transition structure

The Hammond postulate

The Perturbation Theory of Reactivity

Now let us look at the perturbation which the reacting molecules exert upon each other’s orbitals. Let the two reacting molecules have orbitals, filled and unfilled, as shown in Fig. 3.5. As the two molecules approach each other, the orbitals interact, assuming that they have the right symmetry. Thus we can take, let us say, the highest occupied orbital (HOMO) of the molecule on the left and the highest occupied orbital of the molecule on the right and combine them in a bonding and an antibonding sense, just as we did when making a p bond from two isolated p orbitals. The new molecular orbitals, in the centre of Fig. 3.5 will then be a first approximation to two of the orbitals of the transition structure. The formation of the bonding orbital is, as usual, exothermic (El), but the formation of the antibonding orbital is endothermic (E2), because there are two electrons which must go into it. As in the attempt to form a helium molecule from two helium atoms, the energy needed to force the molecules together in an antibonding combination is greater than that released from the bonding combination. This situation will be true for all combinations of fully occupied orbitals, which all contribute to the normal repulsion experienced by one molecule when it is brought close to another. This is a major contributor to the activation energy of any

3 CHEMICAL REACTIONS—HOW FAR AND HOW FAST

137

E2 HOMO HOMO

E1

Fig. 3.5 The interaction of the HOMO of one molecule with the HOMO of another

reaction, and it is the basis for steric hindrance. Combinations of unfilled orbitals with other unfilled orbitals will have no effect on the energy of the system, because without any electrons in them there is no energy to gain or lose. The interactions which do have an important energy-lowering effect are the combinations of filled orbitals with unfilled ones. Thus, in Fig. 3.6a and Fig. 3.6b, we have such combinations, and in each case we see the usual drop in energy in the bonding combination, and a rise in energy in the antibonding combination but without effect on the actual energy of the system, because there are no electrons to go into that orbital. We can also see in Fig. 3.6a that it is the interaction of the HOMO of the left-hand molecule and the lowest unoccupied orbital (LUMO) of the right-hand molecule that leads to the largest drop in energy (2EA > 2EB). The interaction of other occupied orbitals with other unoccupied orbitals, as in Fig. 3.6b, is less effective, because the closer the interacting orbitals are in energy, the greater is the splitting of the levels (see p. 52). Now we can see why it is the HOMO/LUMO interaction which we look at, and why these orbitals, the frontier orbitals, are so important. The other occupied orbital/unoccupied orbital interactions contribute to the energy of the interaction and hence to lowering the energy of the transition structure, but the effect is usually less than that of the HOMO/LUMO interactions.

LUMO

HOMO EA EB

(a) The interaction of the HOMO with the LUMO

(b) The interaction of a lower f illed MO with a higher unf illed MO

Fig. 3.6 The interaction of occupied orbitals of one molecule with unoccupied orbitals of another

138

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

The HOMO/HOMO interactions (Fig. 3.5) are large compared with the HOMO/LUMO interactions (Fig. 3.6a)—both El and E2 in Fig. 3.5 are much larger than EA in Fig. 3.6. This is because HOMO/HOMO interactions will usually be between orbitals of comparable energy, whereas the HOMO of one molecule and the LUMO of another are usually well separated in energy. (In the mathematical form of perturbation theory, the former are first-order interactions, whereas the latter are usually second order.) This will also be true of many of the interactions of the other occupied orbitals on one compound with the occupied orbitals on the other. Although the bonding (El) and antibonding (E2) interactions cancel one another out to some extent, the net antibonding interaction between two molecules will be large—many such orbitals interact in this way, and their interactions are first order. These interactions give rise to a large part of the activation energy for many reactions. The second-order interactions, like those of Fig. 3.6, even though they are entirely bonding in character and reduce the activation energy, are relatively small. The HOMO/LUMO interaction is merely the largest of a lot of small interactions. We shall discuss this matter further in the next section, where we meet a formidable looking equation, from which the strength of these interactions can be estimated quantitatively. We might note that the separation of the interactions into pure filled-with-filled and pure filled-withunfilled, is similar to the way we examined how the orbitals interacted in setting up conjugated systems. We saw on p. 31 that we could explain the stabilisation from having two p bonds conjugated in butadiene, by first taking the filled-with-filled interactions, p with p, and p* with p*, and then modifying this large, and overall energy-raising, effect with the smaller, but energy-lowering, effect from the interactions of filled-withunfilled orbitals, p with p*. There, where we were not talking about reactions, we used the language of ‘mixing in’ the character of one set of orbitals with another in a bonding or antibonding sense. Here we are talking about reactions, and that language is inappropriate, even though the way we are using the idea is similar.

3.5

The Salem-Klopman Equation

Using perturbation theory, Klopman230 and Salem241 derived an expression for the energy (DE) gained and lost when the orbitals of one reactant overlap with those of another. Their equation has the following form:

X DE ¼ –

ðqa þ qb Þ ab Sab

ab

|{z} first term

þ

X

Qk Ql

k
"Rkl

|{z}

second term

þ

occ: unocc: occ: unocc: X X X X –

r

s

s

2ðSab cra csb ab Þ 2

r

E r – Es

|{z}

3:13

third term

qa and qb are the electron populations (often loosely called electron densities) in the atomic orbitals a and b,  and S Qk and Ql " Rkl cra Er Es

are the resonance and overlap integrals in Equations 1.5 1.7, are the total charges on atoms k and l, is the local dielectric constant, is the distance between the atoms k and l, is the coefficient of atomic orbital a in molecular orbital r, where r refers to the molecular orbitals on one molecule and s refers to those on the other is the energy of molecular orbital r and is the energy of molecular orbital s.

The derivation of this equation involves, as one might expect, many approximations and assumptions, which we shall not go into. It is valid only because S will always be small for the overlap of orbitals of p character. The integral S has the form shown in Figs. 1.13 and 1.23: for a C—C bond being formed by p orbitals overlapping in ˚ and then rapidly falls off. Thus, any a  sense, it reaches a maximum value of 0.27 at a distance of 1.74 A

3 CHEMICAL REACTIONS—HOW FAR AND HOW FAST

139

reasonable estimate of the distance apart of the atoms in the transition structure cannot fail to make S small. The integral  is roughly proportional to S, so the third term of Equation 3.13 above is the second-order term. With S always small, the higher-order terms are naturally very small indeed, and we neglect them. This is why a second-order perturbation treatment works. Let us now look at each of the three terms of Equation 3.13. (i) The first term is the first-order, closed-shell repulsion term, and comes from the interaction of the filled orbitals of the one molecule with the filled orbitals of the other (as in Fig. 3.5). It is always antibonding in effect. This term will usually be large relative to the other two terms—it represents a good deal of the enthalpy of activation for many reactions. Apart from this, its main effect on chemical reactivity can probably be identified with the well known observation that, on the whole, the smaller the number of bonds to be made or broken at a time, in a chemical reaction, the better. If a reaction can take place in several, not too difficult stages, it will probably go in stages, rather than in one concerted process. The concerted process, whatever it is, must involve the making (or breaking) of more than one bond, and for every bond to be made (or broken), we must have an energy-raising contribution from the first term of Equation 3.13. Another important reason for the general preference for stepwise reactions is, of course, the much more favourable entropy term when a relatively small number of events happen at once. The interaction of a filled orbital with a filled orbital, as in Fig. 3.5, leads to a small antibonding effect, but there are many filled orbitals interacting strongly with many filled orbitals, and the total effect is the sum of many small ones. The overall effect of the first term of Equation 3.13 is, therefore, rather unpredictable, but it seems that adding up a lot of small items very often averages out the total effect. Thus, if a molecule can be attacked at two possible sites, we can hope that the first term will be nearly the same for attack at each site. Similarly, if there are two possible orientations in a cycloaddition, the first term may not be very different in the two orientations. This appears not to be the case for the other two terms, and it is therefore with them that we shall mainly be concerned in explaining differential reactivity of this kind. In practice it is not obvious that we can rely on a benign first term, but we often do, and we seem to be able to get away with it. We shall, therefore, be largely ignoring the first term from now on, because frontier orbital theory is mainly used to explain features of differential reactivity. We are on weak ground in doing so, and we should not forget it. (ii) The second term is simply the Coulombic repulsion or attraction. This term, which contains the products of the total charges, Q, on each atom, is obviously important when ions or polar molecules are reacting together. Its contribution to the energy is inversely proportional both to the dielectric constant and to the distance apart of the two charges. (iii) The third term represents the interaction of all the filled orbitals with all the unfilled of correct symmetry (Fig. 3.6). It is the second-order perturbation term, and is only true if Er 6¼ Es. (When Er ¼ Es, the interaction is better described in charge-transfer terms, and the perturbation is then first order of the form Sab2cracsb ab.) Here we can see again, this time in simple arithmetical terms, that it is the HOMO and the LUMO which are most important—they are the orbitals with the smallest value of Er  Es, and hence they make a disproportionately large contribution to the third term of Equation 3.13.

In summary: As two molecules collide, three major forces operate. (i) The occupied orbitals of one repel the occupied orbitals of the other. (ii) Any positive charge on one attracts any negative charge on the other (and repels any positive). (iii) The occupied orbitals (especially the HOMOs) of each interact with the unoccupied orbitals (especially the LUMOs) of the other, causing an attraction between the molecules.

140

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

*

*

3

3

LUMO

2

2

E1

HOMO

LUMO

E2

1

1

HOMO (+) (–) allyl anion

interaction leading to the transition structure

allyl cation

Fig. 3.7 Orbital interactions in the reaction of the allyl anion with the allyl cation

We are now in a position to apply these ideas to the components of a chemical reaction. Let us begin with a negatively charged, conjugated system, like the allyl anion 3.1, reacting with a positively charged, conjugated system, like the allyl cation 3.2. In this imaginary242 reaction, the major contributions to bond-making will be the very powerful charge-charge interaction (the second term of Equation 3.13) and the very strong interaction from the HOMO of the anion and the LUMO of the cation (E1 in Fig. 3.7). By contrast, the interaction of the HOMO of the cation and the LUMO of the anion is much less effective (E2 in Fig. 3.7), because Er  Es is relatively so large. The allyl anion þ allyl cation reaction is most unusual because Er  Es for the important interaction of the HOMO of the anion with the LUMO of the cation. For this reason, the important frontier orbital interaction is not typical—it is both very strong and first order, not second order like the third term of Equation 3.13. Nevertheless, it provides a simple illustration of how the ideas behind Equation 3.13 work, and it also shows how it comes about that in general the important frontier orbitals for a nucleophile reacting with an electrophile are HOMO(nucleophile)/LUMO(electrophile) and not the other way round. 2 3

1

3

1 2

3.1

3.2

Having identified the causes for the ease of a reaction like this one, we must next use the ideas behind Equation 3.13 to identify the sites of reactivity in each of the reacting species. To find the contribution of the Coulombic forces, we need the total electron population on each atom, which we have already seen in Fig. 1.35. For the allyl anion, the excess charge is concentrated on C-1 and C-3, and it is therefore here that positively charged electrophiles will attack. For the allyl cation, the overall electron deficiency is

3 CHEMICAL REACTIONS—HOW FAR AND HOW FAST

141

concentrated on C-1 and C-3, where the electron population is lowest, and it is therefore here that a negatively charged nucleophile will attack. Thus when the reaction takes place, the charge-charge attraction represented by the second term of Equation 3.13 will lead C-1 (¼ C-3) of the allyl anion to react with C-1 (¼ C-3) of the allyl cation, and C-2 will have little nucleophilic or electrophilic character. When we add the contribution from the frontier orbitals, the picture is even more striking. The HOMO of the anion has coefficients at C-1 and C-3 of – 0.707, and similarly the LUMO of the cation has coefficients at C-1 and C-3 of þ0.707. In both frontier orbitals the coefficient on C-2 is zero. Thus the frontier orbital term is overwhelmingly in favour of reaction of C-1 (C-3) of the anion with C-1 (C-3) of the cation. Only the relatively ineffectual HOMO(cation)/LUMO(anion) interaction shows any profit in bonding at C-2 of either component. We have now seen how the attraction of charges and the interaction of frontier orbitals combine to make a reaction between two such species as the allyl anion and allyl cation both fast and highly regioselective. We should remind ourselves that this is not the whole story: another reason for both observations is that the reaction is very exothermic when a bond is made between C-1 and C-1: the energy of a full  bond is released with cancellation of charge, which we could not easily do if reaction were to take place at C-2 on either component. In other words, we find, as we often shall, that we are in the situation of Fig. 3.3a—the Coulombic forces and the frontier orbital interaction on one side, and the stability of the product on the other, combine to lower the energy of the transition structure. Indeed, you may well feel that there was little point in looking at the frontier orbitals in a reaction like this, where bonding between C-2 of the anion and C-2 of the cation to give an intermediate 3.3 would be absurd:243

or 3.1

3.2

3.3

The purpose of doing so was two-fold: in the first place, it did show that we get the same answer by considering the frontier orbitals as we do from the product development argument; and secondly, it showed how the allyl anion and allyl cation are nucleophilic and electrophilic, respectively, at both C-1 and C-3 without our having to draw canonical structures. One of the arguments for retaining valence bond theory has been the ease with which things like the nucleophilicity of the allyl anion at C-1 and C-3 are explained by drawing the canonical structures. Even as simple a version of molecular orbital theory as the one presented here does the job just as well. The drawings chemists use for their structures will inevitably be crude representations—we shall always have to make some kind of localised drawing, whether it is of a benzene ring, or an enolate ion, or whatever. At the same time, we shall continue to make, as we already do, considerable mental reservations about how accurately such drawings represent the truth. If our mental reservations are made within the framework of the molecular orbital theory, we shall have a better and more reliable picture of organic chemistry at our disposal.

3.6

Hard and Soft Nucleophiles and Electrophiles

The principle of HSAB has also been applied to kinetic phenomena.244,245 In this connection, organic chemistry has provided most of the examples, because reactions in organic chemistry are often slow enough for rates to be easily measured. In organic chemistry, and in ionic organic chemistry in particular, we are generally interested in the reactions of electrophiles with nucleophiles. These reactions are a particular kind

142

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

of the general acid-with-base type of reaction, and so the principle of HSAB applies equally to the reactions of electrophiles with nucleophiles. Hard and soft acid and base theory gives access to an early part of the slope in a reaction profile like that in Fig. 3.3, just as perturbation molecular orbital theory does. Using the definitions of absolute electronegativity and absolute hardness derived in Equations 3.5 and 3.6, the (fractional) number of electrons DN transferred is given by Equation 3.14. DN ¼

El  Nu 2ðEl þ Nu Þ

3:14

This says that reaction will take place in the direction in which electrons flow from the species of lower electronegativity w to the species with higher electronegativity, and the sum of the hardness values  in the denominator holds the reaction back. A large value of N implies a low energy barrier ahead, with the change in energy given by Equation 3.15. DE ¼

ðEl  Nu Þ 2 4ðEl þ Nu Þ

3:15

This is because the harder a reagent, the less it will give its electrons up to covalent bond formation. A pure hard-hard interaction, being Coulombic in nature, should offer no barrier to the association of the two reagents. The barriers that do exist between oppositely charged (or partially charged) hard reagents are more probably associated with the need to remove solvation, which is inevitably stronger with hard reagents than with soft.246 The rates with which nucleophiles attack one electrophile are not necessarily a good guide to the rates with which the same nucleophiles will attack other electrophiles, just as there is no single measure of thermodynamic acidity or basicity. Following the principle of HSAB, we categorise nucleophiles (bases) and electrophiles (acids) as being hard or soft. Other things being equal, hard nucleophiles react faster with hard electrophiles, and soft nucleophiles with soft electrophiles. We can now return to Equation 3.13, which deals with the application of Coulombic effects and molecular orbital interactions to reaction rates. Essentially, the second term of Equation 3.13 represents the attraction between the two molecules from a hard-hard interaction, and the third term represents the contribution to bonding from a soft-soft interaction. We saw from our consideration of the imaginary reaction of the allyl anion (the base or nucleophile) with the allyl cation (the acid or electrophile) that the important frontier orbital of a nucleophile is the relatively high-energy HOMO, and the important frontier orbital of an electrophile is the relatively low-energy LUMO. Since hard reagents are characterised by having a large separation between the HOMO and the LUMO, hard nucleophiles (Tables 3.2, 3.3 and 3.6) are generally those which are negatively charged and have relatively low-energy HOMOs—typically the anions centred on the electronegative elements. Likewise, hard electrophiles (Tables 3.2, 3.4 and 3.5) are generally those which are positively charged and have relatively highenergy LUMOs, typically the cations of the more electropositive elements. Thus their reactions with each other are fast because each makes a large contribution to the second term of Equation 3.13. However, soft nucleophiles have high-energy HOMOs and soft electrophiles have low-energy LUMOs, and their reactions with each other are fast because each makes a large contribution to the third term of Equation 3.13. To take a simple example, the hydroxide ion 3.4 is a hard nucleophile, at least partly because it has a charge, and because oxygen is a small, electronegative element. Accordingly, it reacts faster with a hard electrophile like the solvated proton 3.5 than with a soft electrophile like bromine 3.6. However, an alkene 3.7 is a soft nucleophile, at least partly because it is uncharged and has a high-energy HOMO. Thus it reacts faster with an electrophile which has a low-energy LUMO, like bromine or the silver cation, than it does with a proton.

3 CHEMICAL REACTIONS—HOW FAR AND HOW FAST

HO

H

3.4

OH2 3.5

Br 3.7

is f aster than

143

HO

Br

3.4

Br

3.6

H

is f aster than

3.6

Br

3.7

OH2 3.5

The rates of most reactions are affected by contributions from both terms of Equation 3.13, with one often being more important than the other. It is important to realise, for example, that a hard nucleophile may react faster with a soft electrophile than a soft nucleophile with the same soft electrophile. Thus the hydroxide ion almost certainly reacts faster with the silver ion than ethylene does. This is because the hydroxide ion is, for several reasons, more generally reactive than ethylene. Hardness and softness are most useful when they are used to differentiate finer grades of reactivity.

In summary: Hard nucleophiles have a low-energy HOMO and usually have a negative charge. Soft nucleophiles have a high-energy HOMO but do not necessarily have a negative charge. Hard electrophiles have a high-energy LUMO and usually have a positive charge. Soft electrophiles have a low-energy LUMO but do not necessarily have a positive charge. (i) A hard-hard reaction is fast because of a large Coulombic attraction. (ii) A soft-soft reaction is fast because of a large interaction between the HOMO of the nucleophile and the LUMO of the electrophile. (iii) The larger the coefficient in the appropriate frontier orbital (of the atomic orbital at the reaction centre), the softer the reagent.

3.7

Other Factors Affecting Chemical Reactivity

Of the many factors controlling chemical reactivity some are obviously involved in the derivation of Equation 3.13, but some are not. Thus we are including the Coulombic factors which lead ions to react faster with polar or oppositely charged molecules than with nonpolar or uncharged ones. We are also, at least in part, including factors such as the strength of the bond being made (it affects ) and the strength of any bond being broken (it affects Er and/or Es). The Woodward-Hoffmann rules are included in a sense, in that we have to evaluate whether the overlap integral (S and hence ) is bonding or antibonding; however, it would be easy to overlook this in a calculation. The loss of conjugation—for example, the loss of aromaticity in the first step of aromatic electrophilic substitution—is partly taken account of. Thus, the low energy of 1 in benzene leads the value of Er – Es for that orbital to be much larger than if the aromaticity were not present. The simpler HOMO/LUMO approach, however, makes no such allowance. A number of other factors are either being ignored in this treatment or at least being underestimated. Strain in the  framework, whether gained or lost, is not included, except insofar as it affects the energies of those orbitals which are involved. Factors which affect the entropy of activation are not included. Finally, steric effects are ignored, because we are not using the first term of Equation 3.13. Fortunately, although chemists in the 1950s had to be persuaded that steric effects were important in organic chemistry,247 that is hardly a problem today—steric effects are more likely to be overemphasised than ignored.

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MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

We cannot, then, expect this approach to understanding chemical reactivity to explain everything. We should bear in mind its limitations, particularly when dealing with reactions in which steric effects are likely to be important, and in which solvent effects are involved. Solvent effects are well known, for example, to be a large part of the explanation of ambident reactivity and other manifestations of the principal of HSAB.246 Some mention of all these factors will be made again in the course of this book. Arguments based on the interaction of frontier orbitals are powerful, as we shall see, but they must not be taken so far that we forget these important limitations. Even more serious is the problem that most attempts to check the validity of frontier orbital theory by calculation strongly indicate that the sum of all the interactions of the filled with the unfilled orbitals swamp that from the frontier orbitals alone. Even though the third term of the Salem-Klopman equation is weighted in favour of the frontier orbitals, quantitatively they do not account for the many features of chemical reactions for which they seem to provide an uncannily compelling explanation. This problem has exercised theoretical chemists mightily, with some success.248,249 Organic chemists, with a theory that they can handle easily, have fallen on frontier orbital theory with relief, and comfort themselves with the suspicion that something deep in the patterns of molecular orbitals must be reflected in the frontier orbitals in some disproportionate way. As an example of how seductive following the orbitals can be, let us look at a -elimination (Fig. 3.8). To keep the orbitals simple, we use ethane, and the imaginary removal of a proton from one atom with a hydride ion as the base and with (unrealistically) a hydride ion as a leaving group from the other to give ethylene. Since both hydrogen atoms are actually leaving groups, we need words to describe which group leaves with the electrons and which without—the proton is called the electrofuge, and the hydride the nucleofuge. The appropriate frontier orbitals will be the HOMO of the nucleophile, the 1sH orbital of the hydride ion, and an unoccupied molecular orbital of ethane (Fig. 1.22), but not in this case the LUMO, *X, because it has the wrong symmetry to have anything to do with the formation of a p bond. The next orbitals up in energy are a degenerate pair, with one of the pair (p*y0 ) having a node through the reaction centres, which means that it cannot be involved. The other low-lying antibonding orbital (p*z0 ) is the unoccupied orbital that is most suggestive of a -elimination, since it has antibonding C—H relationships, and a p-bonding relationship between the two carbon atoms. The attacking hydride ion will move electrons into this orbital, ‘carrying the system along the E2 reaction coordinate’.132 As the hydride nucleofuge leaves, the p bond of ethylene pz is filled, reducing all the C—H bonding to zero and fully instating the C¼C p bond. In the face of such an ‘obviously’ important orbital, with the C—H bonds ready to break and the C¼C bond already visible, it is difficult not to believe that it must play a large part in driving the reaction smoothly on. In practice, of course, it needs a better nucleofuge than the hydride ion.

LUMO

H

H C

HOMO

H 1sH

Fig. 3.8

H

H H H

C

H

H

*z'

H

C

C

H H

H H z

The p*z0 of ethane as a model for the -elimination of hydrogen

4

Ionic Reactions—Reactivity

Ionic reactions are the core of organic chemistry. Trying to understand them in electronic terms challenged organic chemists from the 1920s onwards, beginning with Lapworth’s and Robinson’s brilliant early perceptions, and crowned in the 1950s by R. B. Woodward, who, more than anyone else, showed how mechanistic understanding could shape the thinking leading to a total synthesis of a complex molecule, and illuminate the reactions used to investigate the structures of natural products. The task is never over—how many times have you read that something is not yet fully understood? Nothing is ever fully understood. However, the general outline of understanding has been in place for some time, guided by the principles that pairs of electrons, illustrated with curly arrows, would flow from the less electronegative elements towards the more electronegative, that p bonds would be more reactive than  bonds, and that conjugation was energy-lowering, especially if it was aromatic. More recently, a fundamental re-evaluation is in progress. The problem is that it seems inherently unlikely that pairs of electrons would act in concert: a pair of electrons in a single orbital spend as much time as far away from each other as possible—the electrons are described as correlated.—so why would a pair of electrons act together to move from one bond into another? It seems, somehow, more reasonable for them to move one at a time. The transfer of one electron from one molecule to another is well known—it is the basis for one-electron oxidation and one-electron reduction, with many examples in electrochemistry, in sodiumin-ammonia reductions, and in inorganic redox reactions—but is it a common pathway in ionic organic chemistry, or something that only happens in favourable circumstances?

4.1

Single Electron Transfer (SET) in Ionic Reactions250

Let us look at the key steps in three of the most fundamental reaction types in ionic organic chemistry—the SN2 reaction 4.1 ! 4.2, nucleophilic attack on an X¼Y double bond 4.3 ! 4.4, where X and Y may be any combination of C, N, O or S, and electrophilic attack on a C¼C double bond 4.5 ! 4.6. A high proportion of ionic organic chemistry is covered by these three reactions or their reverse. The standard formulation for the first has the electron pairs moving in concert from the nucleophile into the Nu—C bond and the simultaneous movement of the electrons in the C—X bond onto the leaving group. For nucleophilic attack on a p bond, a lone pair or a p bond provides the electrons for a new  bond Nu—X, and a pair of electrons from the p bond move onto the atom Y which is the more electronegative, or the one better able to stabilise a negative charge. The subsequent fate of the anion 4.4 will depend upon the rest of the structure. For electrophilic attack by a p bond 4.5, the pair of electrons moves to make a  bond to the electrophile, and leaves behind a carbocation centre 4.6. The fate of this cation also depends upon the rest of the structure—the two most common fates being the loss of a proton, when the p bond is part of an aromatic ring, or the capture of a nucleophile, when it

Molecular Orbitals and Organic Chemical Reactions: Reference Edition  2010 John Wiley & Sons, Ltd

Ian Fleming

146

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

is isolated. For now, we are concerned with the first steps, the attack of the nucleophile or electrophile, because, more often than not, these are rate-determining. Nu

X

+

Nu

4.1

X

4.2 Nu

Nu

X

Y

X

4.3

Y 4.4 E

E 4.5

4.6

In the most simple alternative mechanism involving single electron transfer (SET), the two reagents in each case, which may or may not come together in a loose association called a charge-transfer complex 4.7, 4.10 and 4.12, transfer one electron from the partner with the lower ionisation potential (higher-energy HOMO) to the one with the higher electron affinity (lower-energy LUMO). In all three types of reaction, this creates a pair of radicals 4.8, 4.11 and 4.13, which may or may not be charged, depending upon the charge carried by each of the original reagents. In the SN2 case, the radical anion 4.8 can lose the halide ion X– to give the radical 4.9. In all three cases, the radical pairs 4.9, 4.11 and 4.13 can be expected to combine together very fast. Radical-radical couplings are rare, because radicals, usually created in low concentration, do not live long enough to meet another radical but in this case two radicals are created as a pair within a solvent cage, effectively in high concentration. With the concentration problem overcome, radical-radical couplings are inherently fast, because they are so exothermic. It therefore follows that the rate-determining step is likely to have been the transfer of the electron. At this stage the product 4.2, and the intermediates 4.4 and 4.6, are the same as those in the conventional mechanism. Occasionally, an even slower step may be involved later on, but, whatever the overall rate-determining step is, the radical coupling can be expected to be faster than the electron transfer. e-transfer Nu

+

X

Nu

4.1

Nu

X 4.7

X 4.8 radical X

Nu

Nu coupling

4.9

4.2

e-transfer Nu

+ X

Y

Nu

X

radical Nu

Y

X

Y

Nu X

Y

coupling 4.3

4.10

4.11

4.4

e-transfer + E 4.5

E coupling

4.12

E

radical

E 4.13

4.6

4 IONIC REACTIONS—REACTIVITY

147

There is good evidence that some nucleophilic substitution reactions do involve a single electron transfer, but the best established use a slightly different mechanism. These are the SRN1 reactions, with the subscript RN standing for radical nucleophilic. Examples are the reaction of the nitronate anion 4.14 with pnitrobenzyl chloride 4.15, 251 and the reaction of the pinacolone enolate 4.16 with bromobenzene.252 The former might have been a straightforward SN2 reaction, but actually takes the SRN1 pathway because the nitro groups make the electron transfer exceptionally easy. The latter cannot take place by a conventional SN2 reaction, because aryl (and vinyl) halides are not susceptible to direct displacement, and the SRN1 pathway overcomes this difficulty.

O

N

O

NO2 +

NO2

NO2

Cl

4.14

+

Cl

+

Br

4.15

O

O

+ Br 4.16

In more detail, SRN1 reactions begin with an initiation step in which an electron is transferred to the electrophile R-X to give a radical anion R-X•–, which breaks apart to give the radical R• and the anion X–. The radical R• combines with the nucleophile Nu– to give a radical anion R-Nu•–, and this transfers its electron to the electrophile R-X, giving the product R-Nu and the radical anion R-X•–, making the sequence cyclic and self sustaining. There is a further subtlety in which the departure of the nucleofugal group X– is concerted with the electron transfer, in which case the radical anion R-X•– is no longer an intermediate but a transition structure.

R-X

R-X

R

R-Nu

R-Nu

+

X

Nu

There is equally good evidence that some examples of nucleophilic and of electrophilic attack on a double bond are preceded by charge-transfer complexation, with bonding resembling that of a Lewis acid-base interaction, and that either heat or irradiation of the charge transfer complex can provide the energy needed to transfer the electron from the donor to the acceptor. A charge-transfer species like 4.17 or 4.20 may or may not be on the direct line for the reaction, but solvation effects, and selectivities in the coupling steps like 4.18 ! 4.19 and 4.21! 4.22 are powerfully supportive of SET pathways in at least some reactions like these.253

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MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

Me Me NC

CN

Me Me

e-transfer

Me Sn

Me

Me NC

Me

CN

4.17

NC

CN

NC

CN

Sn

Me Me Sn Me Me

NC

CN

NC

CN

radical coupling

NC

CN

Me

CN CN

4.18

4.19

e-transfer Hg(O2CCF3)2

Hg(O2CCF3)2

4.20

H

HgO2CCF3

radical HgO2CCF3 coupling O2CCF3

O2CCF3 4.21

4.22

Given then that SET pathways are almost certainly involved in some nucleophile-electrophile combinations, ought we to consider that they are the most likely pathway in all of them? This is a seductive proposition, because a unified mechanism for a wide range of reactions has an instant appeal. Most of the well established SET pathways have been found with reagents conspicuously carrying radical-stabilising substituents like the nitro group or for substrates like bromobenzene incapable of following the traditional mechanism. Consequently, the feeling has grown that SET pathways may well be followed in those substrates well adapted to SET, but that the rest probably retain the more conventional mechanisms. This may be right, but it is not a good argument. If the radicals inside the cage are well stabilised, they are more likely to live long enough to escape, and to give us opportunities to detect them, but if the radicals in the cage are not well stabilised, their coupling is likely to be so fast that they can evade the radical probes with which we try to detect them. We shall not be able to come to a firm conclusion here. The debate continues.254,255 Nevertheless, we do need to address the problem of how to use molecular orbital theory, and the principle of HSAB, to explain all the examples of reactivity and selectivity to be discussed in the rest of this chapter. The traditional two-electron mechanism and the SET mechanisms will need different wording, and maybe a different explanation. Fortunately, this is not a great problem. The aspects of molecular orbital theory that we shall invoke, and of frontier orbital theory in particular, work in much the same way in both families of mechanism. Thus, a nucleophile will be more nucleophilic if its available pair of electrons is in a high energy orbital, whether those electrons are used directly to make a bond or one of them is transferred on its own. Electrophilicity, likewise, will be greater if the reagent has a low-energy LUMO, whether this is encouraging direct attack by a pair of electrons or the acquisition of a single electron. For this parallel to work, the electron transfer must be slower than the coupling of the radicals, which it usually is. Regioselectivity in product formation, however, may need different explanations, since the new bond is formed in the conventional mechanism in the first step, but in the SET mechanism it is formed in the radical coupling step or, in SRN1 reactions, the step in which a radical attacks the nucleophile.

4 IONIC REACTIONS—REACTIVITY

149

The discussion in the rest of this chapter will be phrased using the conventional two-electron mechanism—that mechanism has yet to be displaced from most discourse about most reactions. If an illuminating point can be made with the SET mechanism it will be.

4.2

Nucleophilicity

4.2.1 Heteroatom Nucleophiles In the last chapter we saw that there is no single measure of acidity and basicity. Similarly, there is no single measure of nucleophilicity and electrophilicity—the rank order of nucleophiles is totally upset when the reference electrophile is changed. A hard nucleophile like a fluoride ion reacts fast with a silyl ether in an SN2 reaction at the silicon atom, which is relatively hard, but a soft nucleophile like triethylamine does not. In contrast, triethylamine reacts with methyl iodide in an SN2 reaction at a carbon atom but fluoride ion does not. These examples, which are all equilibria, are governed by thermodynamics, but there are similar examples illustrating divergent patterns of nucleophilicity in the rates of reactions. Hard-hard:

Sof t-hard: Et3N

F Me3Si

O

Me3Si

O F

O Et3N

Soft-soft: Et3N

O

SiMe3 +

SiMe3 +

Hard-soft: Me

I

Et3N Me

+

I

F

Me

I

F

Me

+ I

A scale of nucleophilicity, therefore, requires at least two parameters, and these were first provided empirically by Edwards with Equation 4.1.256 log

k Nu ¼ EN þ H k0

4:1

where kNu is the rate constant (or equilibrium constant) for a reaction, k0 is the rate constant (or equilibrium constant) for water as the nucleophile, and EN and H are the two scales of nucleophilicity. The EN scale is measured by the rate of reaction with methyl bromide, and the H scale is the (pKa þ 1.74), where the 1.74 is a correction for the pKa of H3Oþ. Thus the two scales reflect both softness (EN) and hardness (H), although these terms were not in use when Edwards formulated his equation. The extent to which the hard or soft character of the electrophile contributes will affect the relative sizes of  and , which will be different for each reaction, a high value of / implying a soft electrophile. Another way of looking at the same problem uses the Salem-Klopman equation that we saw in the last chapter, and hence follows from the concept of HSAB, instead of preceding it, and is based on theory rather than experiment. Using only the HOMO of a nucleophile and the LUMO of an electrophile, Klopman simplified Equation 3.13 to Equation 4.2: DE ¼

QNu QEl 2ðcNu cEl  Þ 2 þ "R EHOMOðNuÞ – ELUMOðElÞ

4:2

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MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

As we have seen earlier, using only the frontier orbitals is a risky approximation because the interactions of the other orbitals will all have an effect, but they all have larger values of Er – Es and thus make a smaller contribution to the third term of Equation 3.13. Starting with this simplification, Klopman worked out the contribution of the frontier orbital terms to the nucleophilicities and electrophilicities of a range of inorganic bases and acids.230 From the known ionisation potentials and electron affinities, and correcting for the effect of solvation, he calculated values (E‡, Table 4.1, listed with hardness at the top and softness at the bottom) for the effective energy of the HOMO of the nucleophiles and the LUMO of the electrophiles. The results agree well with Pearson’s original, empirically derived order of softness, and, if allowance is made for the absence of solvation, with his more theoretically derived order in Tables 3.3 and 3.4. The higher the value of E‡ for the HOMO of a nucleophile, the softer it is, and the higher the value of E‡ for the LUMO of an electrophile, the harder it is. Table 4.1 is therefore a useful practical list.

Table 4.1 bottom) Nucleophile F– H2O HO– Cl– Br– CN– HS– I– H–

Calculated softness character for inorganic nucleophiles and electrophiles (hard at the top and soft at the Effective HOMO E‡ (eV)

Electrophile

Effective LUMO E‡ (eV)

–12.18 –10.73 –10.45 –9.94 –9.22 –8.78 –8.59 –8.31 –7.37

Al3þ La3þ Ti4þ Mg2þ Ca2þ Fe3þ Cr3þ Ba2þ Cr2þ Fe2þ Liþ Hþ Ni2þ Naþ Cu2þ Tlþ Cuþ Agþ Tl3þ Hg2þ

6.01 4.51 4.35 2.42 2.33 2.22 2.06 1.89 0.91 0.69 0.49 0.42 0.29 0 –0.25 –1.88 –2.30 –2.82 –3.37 –4.64

Klopman then used Equation 4.2 to estimate the relative nucleophilicities of a range of anionic nucleophiles: I–, Br–, Cl–, F–, HS–, CN– and HO– towards a small range of different electrophiles.230 He assumed unit charges and unit values for the coefficients, c. For the EHOMO(Nu) term, he used the values of E‡ from Table 4.1. Since it is roughly proportional to the overlap integral S, the value of  changes, depending on which elements are forming the new bond, but it can readily be calculated.257 This left only the energy of the LUMO of the electrophile, ELUMO(El), as an unknown on the right-hand side of the equation. Klopman therefore calculated DE values for a series of imaginary electrophiles with different values for the energy of the lowest unoccupied orbital ELUMO. His striking results are given in Table 4.2.

4 IONIC REACTIONS—REACTIVITY Table 4.2 230

151

Nucleophilicity of inorganic ions towards electrophiles as a function of EHOMO – ELUMO DE calculated for:

Found:

Nucleophile

EHOMO

ELUMO –7 eV

ELUMO –5 eV

ELUMO þ1 eV

k  104 Equation 4.3

Edwards’ E Equation 4.4

pKa Equation 4.5

F– HO– Cl– Br– CN– HS– I–

–12.18 –10.45 –9.94 –9.22 –8.78 –8.59 –8.31

1.06 1.49 1.54 1.75 2.30 2.64 2.52

0.82 1.01 0.97 0.98 1.17 1.25 1.07

0.54 0.58 0.52 0.48 0.56 0.55 0.45

0 0 0.001 0.23 10 too fast 6900

1.0 1.65 1.24 1.51 2.79 too fast 2.06

3.2 15.7  –4.3 9.1 7.1 –7.3

(i) Setting ELUMO(El) at –7 eV (a low value) made the EHOMO – ELUMO term small, and hence the frontier orbital term, the second term of Equation 4.2, made a large contribution to DE. The order of the values DE was HS– > I– > CN– > Br– > Cl– > HO– > F–, which is the order of nucleophilicities which has been observed for the attack of these ions on peroxide oxygen (Equation 4.3).258

Nu

HO

OH

Nu

OH

+

4.3

OH

(ii) Setting ELUMO(El) at –5 eV, the order of nucleophilicities is slightly changed, because the frontier orbital term makes a slightly smaller contribution to DE. The order of DE values is now HS– > CN– > I– > HO– > Br– > Cl– > F–, which parallels the Edwards E values256 for the nucleophilicities of these ions towards saturated carbon (Equation 4.4).

Nu

X

+

Nu

X

4.4

(iii) Finally, setting ELUMO(El) very high at þ1 eV, the frontier orbital term is made relatively very unimportant, and the order of DE values is governed almost entirely by the Coulombic term of Equation 4.2: HO– > CN– > HS– > F– > Cl– > Br– > I–. This is the order of the pKas of these ions, in other words, of the extent to which the equilibrium lies to the right in Equation 4.5.

Nu

H

OH2

Nu

H

+

H2O

4.5

Thus, simply by adjusting the relative importance of the two terms of Equation 4.2, we can duplicate the otherwise puzzling changes of nucleophilic orders as the electrophile is changed. The solvated proton is a very hard electrophile because it is charged, and especially because it is small. Hence, a nucleophile can get close to it in the transition structure and R in Equation 4.2 is made small. The oxygen-oxygen bond, however, has no charge, and, being both weak and between electronegative atoms, it has a conspicuously low-lying * LUMO for a  bond. It is therefore a very soft electrophile. Similarly, with nucleophiles such as F–, Cl–, Br– and I–, the energy of the HOMO will rise as we go down the periodic table, and with nucleophiles like Cl–,

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MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

HS– and R2P–, the energy of the HOMO will rise as we move to the left in the periodic table. This explains, therefore, the observations in the reactions above, and in many others, that the ‘softness’ of a nucleophile increases in these two directions. Quantitative support for the importance of orbital energies comes from studies259 of the SN2 reaction between 41 thiocarbonyl compounds 4.23 with methyl iodide and other methylating agents, in which the Coulombic term was kept small and relatively constant. The rates correlated well with the ionisation potential of the lone pair on the sulfur atom, measured by photoelectron spectroscopy and a direct measure of the energy of the HOMO. The lone pair, however, was not always the HOMO. With some donor substituents R, the bonding p electrons were actually the HOMO but the correlation worked better with the lone-pair energy. Evidently developing overlap with a nonbonding pair of electrons is more effective, even when they are lower in energy, than with a bonding pair. The effect would be taken care of by the value of  in Equation 4.2. R1

Me

I

R1

S R2

Me S

I

R2 4.23

4.2.2 Solvent Effects Solvents have long been implicated in the divergent scales of nucleophilicity and electrophilicity because small, charged nucleophiles and electrophiles are often highly solvated. Empirically, gas phase SN2 reactions, where there is no solvent, are very different from their solution counterparts.260,261 Nevertheless, gas phase reactions do show a pattern in which matching the nucleophile to the leaving group can lead to higher rates, reminiscent of hard-hard and soft-soft pairings, and so it seems that solvent effects are not the whole story. How important solvent effects are in explaining relative nucleophilicities is still an open question, to which we shall return from time to time, as we saw that Klopman did by correcting for it. The orbitals of a solvent interacting with those of the nucleophile and the electrophile are responsible for some of the energy of solvation, and should be amenable to treatment by perturbation theory. If the orbitals are close enough in energy for a first-order treatment to be appropriate, reaction would occur; so solvation is a second-order interaction. The second term of Equation 4.2 will therefore be a good approximation, and the major interactions will be between the HOMO of the solvent and the LUMO of an electrophile, and between the LUMO of the solvent and the HOMO of a nucleophile. Using this idea (and hence the second term of Equation 4.2), and using ionisation potentials and electron affinities as measures of the energies of the HOMO and the LUMO of a range of solvents, Dougherty262 has been able to explain some otherwise puzzling changes of solvating power. Thus no single scale of solvating power works for all reactions, just as there is no single scale of nucleophilicity. We can now see that—amongst other things, no doubt—a balance between both sets of frontier orbital interactions (HOMOsolvent/LUMOreagent and LUMOsolvent/HOMOreagent) may help to account for this. 4.2.3 Alkene Nucleophiles Alkenes 4.24, with a p orbital as the HOMO and no charge, are inherently soft nucleophiles, and their nucleophilicity ought to have some relationship to the energy of their HOMOs. The relative rates of attack by different alkenes have been measured for such electrophiles as bromine, peracids, sulfenyl halides, electrophilic 1,3-dipoles (Chapter 6), metal cations (Hg2þ, Agþ) and boranes. These electrophiles fall into two groups: those like bromine, peracid and sulfenyl halides that show a correlation between the rate and the ionisation potential of the alkene, and those like 1,3-dipoles, metal cations and boranes, that show significant discrepancies.263 The first group show little sign of steric effects, since the more substituted alkenes, with the

4 IONIC REACTIONS—REACTIVITY

153

higher energy HOMOs, generally react faster than the less substituted. These reactions have a ratedetermining first step, the electrophiles have a modest steric demand, and they form bridged intermediates 4.25, or, in the case of epoxidation, products. The second group show steric effects, with the more-substituted alkenes reacting more slowly than expected for their relatively high energy HOMOs. The explanation264,265 for electrophilic 1,3-dipoles is probably steric effects on the first (and only) step, since 1,3-dipoles are relatively large compared with the first group of electrophiles. The explanation with the metal electrophiles is that they rapidly and reversibly form an intermediate, but the rate-determining step is the opening of that intermediate, in a reaction that evidently responds to steric effects.

E

E+

Nu

Nu–

or E

E

4.24

RDS correlates with IP of alkene (Br2, RCO3H, PhSCl)

RDS affected by steric effects (Hg2+, Ag+, R2BH)

4.25

Mayr has measured the nucleophilicity of a wide range of alkenes 4.26 being attacked by a family of diarylmethyl cations 4.27, which, being highly delocalised, are relatively soft for cations.266 These reactions are like those with metal cations and boranes in having the first step rate-determining, but they are different, because the formation of the intermediate 4.28 is endothermic. R2 R1 4.26

Ar Ar 4.27

R2

RDS R1

Ar Ar

4.28

The order of nucleophilicity, graphically illustrated in Fig. 4.1, matches well with expectation—the better donor substituents are the more effective at increasing the rate of reaction. For alkenes having a terminal methylene group, an extra methyl group increases the reactivity by four orders of magnitude (compare propene with isobutylene). A trimethylsilylmethyl group (R 1 ¼ Me3SiCH2, R2 ¼ H) and a tributylstannylmethyl group (R1 ¼ Bu3SnCH2, R2 ¼ H) further increase the nucleophilicity (relative to R1 ¼ Me, R2 ¼ H) by five and nine orders of magnitude, respectively. An alkoxy group (R1 ¼ EtO, R2 ¼ H) increases the nucleophilicity by five to six orders of magnitude more than an alkyl group. Since this is an endothermic reaction, the transition structures are product-like (Fig. 3.4b), estimated in this case to have something like two-thirds of the charge transferred to the alkene component. As a consequence, the rates correlate well with the stabilities of the carbocations produced 4.28, but not well with the ionisation potential (and hence the HOMO energy) of the alkene.267 Donor substituents R1 and R2, of course, stabilise the cation 4.28 (see pp. 77–78, 87–90 and 92–94), and can be expected to lower the energy of the transition structure. The situation changes somewhat for those alkenes 4.29 having substituents on the carbon atom under attack. Alkyl substituents R2 do not contribute much to the stabilisation of the cation 4.30, but they do contribute to raising the energy of the HOMO of the alkene 4.29. On the whole, a substituent on the carbon atom under attack () does increase the rate of attack, with 2-butene about one order of magnitude more reactive than propene. A large effect from having substituents on the  position and a small effect from having them on the  position identifies a transition structure leading to an unbridged intermediate 4.30

154

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

Bu3Sn

1010 109

Bu3Sn Me3Si

108

EtOH

107 106

k rel

105

Me3Si

EtO MeO

H2O EtO

Me3Si

104 103 102 10 1

Fig. 4.1

Relative nucleophilicities of alkenes towards carbocations

268

(see pp. 90–91). In agreement with this, the difference in rates for 2-butene and propene is not as large as having the extra methyl group on the  carbon, as in isobutylene. Most remarkably, the effect of a  substituent is more powerful with enol ethers than the effect of an  substituent: 1-ethoxypropene is nearly twice as reactive as 2-methoxypropene. Furthermore, the relative rates for enol ethers correlate well with the HOMO energy as measured by the ionisation potentials.269 In these reactions, the starting material is reactive (high in energy), the product cation is stabilised (low in energy) and it is appropriate that the transition structure should be earlier (Fig. 3.4a) and more responsive to orbital effects in the starting material. Ar

Ar R

R1

2

Ar 4.29

4.27

R1

Ar R2 4.30

It is worth emphasising now that the effects of C-, X-, and Z-substituents on the nucleophilicity of an alkene often match their effects on the energy of the HOMO. Following the arguments developed in Chapter 2:

C- and X-substituents raise the energy of the HOMO and increase nucleophilicity. Z-substituents lower the energy of the HOMO and decrease nucleophilicity.

4 IONIC REACTIONS—REACTIVITY

155

4.2.4 The a-Effect270 The solvated proton is a hard electrophile, little affected by frontier orbital interactions. For this reason, the pKa of the conjugate acid of a nucleophile is a good measure of the rate at which that nucleophile will attack other hard electrophiles. We shall see that carbonyl groups are fairly hard, but somewhat responsive to frontier orbital effects, more so, anyway, than solvated protons. Thus a thioxide ion, RS–, is more nucleophilic towards a carbonyl group than one would expect from its pKa: a plot, known as a Brønsted plot, of the log of the rate constant for nucleophilic attack on a carbonyl group against the pKa of the nucleophile is a good straight line only when the nucleophilic atom is the same. In other words, there is a series of straight lines, one for oxygen nucleophiles, one for sulfur nucleophiles, and yet another for nitrogen nucleophiles. Some nucleophiles, HO2–, ClO–, HONH2, N2H4 and R2S2, stand out because they do not fit on Brønsted plots: they are more nucleophilic towards such electrophiles as carbonyl groups than one would expect from their pKa values.271 These nucleophiles all have a nucleophilic site which is flanked by a heteroatom bearing a lone pair of electrons (an X-substituent, in other words). The orbital containing the electrons on the nucleophilic atom overlaps with the orbital of the lone pair of the X-substituent (Fig. 2.12), raising the energy of the HOMO relative to its position in the unsubstituted nucleophile, as usual with an X-substituent. Consequently, the denominator of the third term of Equation 3.13 is reduced, and the importance of this term is increased. The result is an increase in nucleophilicity, called the -effect, which can sometimes be quite dramatic (Table 4.3). The order of the effect appears to be right: the LUMO of the triple bond of the nitrile will be lower than that of the double bond of the carbonyl group, which will be lower than that of the  bond of the bromide. Hence the frontier orbital term is most enhanced in the case of benzonitrile, and least enhanced for benzyl bromide and methyl arenesulfonates.272 The -effect is sometimes increased when reactions are carried out in dipolar aprotic solvents.273 As these solvents do not stabilise anions by solvating them, orbital effects become more noticeable.

Table 4.3 Electrophile PhCN p-O2NC6H4CO2Me PhCH2Br

Relative nucleophilicity of hydroperoxide ion and hydroxide ion kHOO–/kHO–

Electrophile

kHOO–/kMeO–

105 103 50

ArSO2OMe

6–11 kHOO–/kHO– 10–4

H3Oþ

However, the energy of the HOMO in a range of -nucleophiles does not actually correlate well enough with their nucleophilicity274 for this explanation of the effect to be satisfactorily settled. For all that the LUMO energy is lower for carbonyl groups than for alkyl halides, the latter are conspicuously softer electrophiles, yet show a much smaller -effect, and do not show it at all in the gas phase.275 Even more puzzling, although the -effect appears to follow the order digonal>trigonal>tetrahedral, ethynyl methyl ketone, another digonal electrophile, only has an -effect of about 10. Furthermore, -effect nucleophiles like hydrazine, unlike ordinary nucleophiles, show a kinetic isotope effect kH/kD of 2.3, indicating that the mechanistic details are different.276 The problem raised by the small -effect in reactions with alkyl halides, where the LUMO energy is not conspicuously low, and yet they are soft electrophiles, raises the question of what happens when both charge and frontier orbital terms are small, and what happens when they are both large? Prediction is not simple in this situation, but Hudson has suggested the two rules in the box, which are usually but not invariably observed. In the case of the p-nitrobenzoate and benzyl bromide, we have a 20-fold increase in

156

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

nucleophilicity towards a carbonyl group, accompanied by a 10 000-fold decrease in basicity. It serves to alert us that carbonyl groups, although mainly responsive, as we shall see, to basicity (charge control), are not unresponsive to frontier orbital effects.

(i) When both charge and orbital terms are small: nucleophiles and electrophiles will be soft (that is, orbital control is more important). (ii) When both charge and orbital terms are large: nucleophiles and electrophiles will be hard (that is, charge control is more important).

The raised energy of the HOMO also provides an explanation with an SET mechanism, since it allows an electron to be transferred more easily to the LUMO of the electrophile, and the radical pair then couple, as usual. A single electron removed from one of the two pairs will leave behind a stabilised radical, and so the rate constant of a reaction of an -effect nucleophile ought to be more sensitive to the ionisation potential (LUMO energy) of the electrophile than the rate constant with a normal lonepair nucleophile. 277 This proved to be the case in the rates of N-methylation of a series of Nphenylhydroxylamines compared with the rates in some comparable anilines. 278 Further support for an SET mechanism is provided by superoxide anions, RO 2•–, which are exceptionally powerful nucleophiles benefiting simultaneously from an -effect and from the availability of an unpaired electron. 279 The -effect is observed not only as a kinetic effect but also as a thermodynamic -effect, as seen in the equilibrium constants for the removal of acetyl groups from N-acetylimidazole with hydroxylamine derivatives, which parallel their kinetics.280 For an explanation, we may compare an amide 4.31 with a hydroxamic acid 4.32. The overlap of a lone pair with the p* orbital of a carbonyl group (4.31, arrows, see also pp. 104–106) is an important part of the reason why amides are stabilised relative to ketones. The effect of another lone pair is to raise the energy of the first lone pair (Fig. 2.12) and hence to make the overlap with the p* orbital more energy-lowering.

O

N 4.31

O

N

OH

4.32

The -effect with oximes and hydrazones contributes to making them less electrophilic than other imines. The overlap of the lone pair on the second heteroatom with the developing lone pair on the nitrogen atom of the imine is destabilising. This is only part of the explanation, since the same lone pairs will be conjugated to the C¼N p bond of the starting materials, raising the energy of the HOMO and LUMO, and stabilising the system. The energy of the HOMO can, in principle, be raised by through-space interactions 281 as well as by conjugation in the sense seen with the -effect. A series of amines which might have shown such an effect were disappointing: the nucleophilicity towards an ester carbonyl group was very similar for the simple amine 4.33 and the g-methoxyamine 4.34. 282 The inductive effect through the bonds reduces the nucleophilicity of the amine 4.34, and this will be in force in any of the conformations that it adopts. The through-space effect can only show up in the U-shaped conformation that may rarely be adopted.

4 IONIC REACTIONS—REACTIVITY

157

HH

HH

N

O O

MeO

relative rates 1.77:1

N

O O

Ar

Ar

4.33

4.3

4.34

Ambident Nucleophiles

Nucleophiles which have two sites at which an electrophile may attack are called ambident. The principle of HSAB often applies in these reactions, with hard electrophiles reacting at the harder nucleophilic site and soft electrophiles reacting at the softer site. Thus the disulfide 4.35 is cleaved by hydroxide ion to give the sulfenate ion 4.36, which is an ambident nucleophile. It reacts with the harder electrophile methyl fluorosulfonate at the oxygen atom, where most of the negative charge resides, to give the sulfenate ester 4.37. In contrast it reacts with the softer electrophile methyl iodide at the sulfur atom, the softer of the two nucleophilic sites, made more nucleophilic by an -effect, to give the sulfoxide 4.38.283

Ar

S

Me O

OSO2F Ar

4.36 Ar

S

S

Ar

S

O

Me

4.37

OH Me

4.35 Ar

S 4.36

O

I

Me Ar

S

O

4.38

4.3.1 Thiocyanate Ion, Cyanide Ion and Nitrite Ion (and the Nitronium Cation) Thiocyanate ions, cyanide ions and nitrite ions are well known ambident nucleophiles but the explanation for their behaviour is not so straightforward. Each can react with an electrophile Rþ, depending upon its nature and the conditions, to give either of two products: a thiocyanate 4.39 or an isothiocyanate 4.40 from the thiocyanate ion, an isonitrile 4.41 or a nitrile 4.42 from the cyanide ion, and an alkyl nitrite 4.43 or a nitroalkane 4.44 from the nitrite ion. The thiocyanate ion will be softer on the sulfur atom and harder on the nitrogen atom, the cyanide ion will be softer on the carbon atom and harder on the nitrogen atom, and the nitrite ion will be harder on the oxygen atom and softer on the nitrogen atom. We might expect that harder electrophiles will give the isothiocyanates 4.40, the isonitriles 4.41 and the nitrites 4.43. However, other factors are at work, and this pattern is unreliable. Earlier attempts to use these expectations to explain some of the patterns of reactivity in this area229,284 have been overtaken by more recent work. The thiocyanate 4.39 is the kinetically preferred product in alkylations by alkyl halides undergoing SN2 reactions285 and with carbocationic electrophiles in SN1 reactions,286 in spite of the fact that a carbocation, being charged, is a hard electrophile and the sulfur is the soft end of the nucleophile. This is partly explained by the relatively small change in bond lengths and in electronic reorganisation required in going from the thiocyanate ion to the thiocyanate product. Thiocyanates 4.39 more or less rapidly isomerise to isothiocyanates 4.40, which are the thermodynamically preferred products, the tertiary alkyl thiocyanates rearranging by an SN1 pathway,287 and primary alkyl thiocyanates by an SN2 pathway.288

158

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

R+ f ast R

S

C

R+ slow

N

R

N

S

N

4.39

R

N

R+

C

R+ C

R

N

C

N

4.42 R+

O

S

4.40

4.41

R

C

N

O

R+ O

O

N

R

O

N O

4.43 4.44

Cyanide ions react with the soft (see pp. 151–152) alkyl halides in SN2 reactions and with the hard carbocations in SN1 reactions to give, almost always, the nitrile 4.42, which is thermodynamically preferred.289 Isonitrile products are formed along with the nitrile products when the cation is so reactive that the rate has reached the diffusion-controlled limit, and the reversible reaction that would equilibrate the products is too slow.290 It is hardly surprising that reactions between a cyanide ion and a carbocation can be fast enough to reach the diffusion controlled limit, since they are ion-with-ion reactions, which are rather rare in organic chemistry. One consequence when reactions are as fast as this is that there is a barrierless combination of ions, and selectivity is not then controlled by the kinetic factors associated with the principle of HSAB. Other situations in which isonitrile products are formed have special features. Silver cyanide sometimes leads to isonitrile products291 whereas potassium cyanide gives nitriles. A telling example is the formation of the isonitrile 4.47 in the reaction with silver cyanide, whereas potassium cyanide gives the nitrile 4.46.292 Since both reactions take place with overall retention of configuration by way of an episulfonium ion 4.45, it cannot be that the silver ion induces an SN1 reaction. An explanation is that the relatively soft silver is attached to the carbon of the cyanide ion, leaving the nitrogen end free to be nucleophilic, whereas potassium is not so attached. Similarly, trimethylsilyl cyanide sometimes gives isonitrile products with carbocations stabilised only by alkyl groups,293 perhaps because the silyl group is attached to the carbon atom at the time of reaction, and the isonitriles rearrange too slowly. Nitrite ions generally give nitroalkanes 4.44 as the major products, which are also thermodynamically more stable than alkyl nitrites 4.43.294 Again, with carbocationic electrophiles, it is only when the reaction rate has reached the diffusion-controlled limit that alkyl nitrites can be detected or even be the major products. Nitrite ions also give mixtures of nitroalkanes and nitrites in SN2 reactions, even though the alkyl electrophiles are relatively soft. K+ N

C

H

H C

Ag

C

SMe H 4.46

4.45

SMe H

N

S Me

H Br

H

N H

H S Me 4.45

C

H N

SMe H 4.47

4 IONIC REACTIONS—REACTIVITY

159

A hint that the principle of HSAB might have some role in explaining ambident reactivity with nitrite ion comes from the SN2 reactions with methyl iodide (relatively soft), with the trimethyloxonium ion (harder) and with methyl triflate (hardest) giving mixtures of methyl nitrite and nitromethane in a pattern like the reactions of the sulfenate ion 4.36. There is an increase in the ratio of methyl nitrite to nitromethane with the harder electrophiles, rising from 30:70, through 50:50, to 59:41, respectively.294 A similar pattern is seen with the SN2 reaction of primary benzyl bromides with silver nitrite, where the ratio of nitrite to nitroalkane rises from 16:84 when the benzene ring has a p-nitro substituent, through 30:70 with no substituent to 61:39 with a p-methoxy substituent.295 These are small effects, and little weight can be placed on any explanation; nevertheless, we can see that the patterns in both series are in line with the different contributions made to Equation 4.2. The contribution from the first term is greater for the harder electrophiles because of the greater charge on the carbon atom in methyl triflate than in the less polarised methyl iodide, and in the greater degree of carbocationic character in the transition structure with the p-methoxybenzyl bromide. For the contribution from the second term of Equation 4.2, it is the HOMO of the nitrite ion that we need to look at. The p orbitals of the NO2 system are shown in Fig. 4.2, with the anion on the right and the cation on the left. Two of the p orbitals, an orthogonal pair, resemble 2 in the allyl system, with large coefficients on the oxygens and a node on the nitrogen but the next orbital above them, which is the HOMO in the nitrite anion, is an orbital resembling 3* in the allyl system, with a large coefficient on the nitrogen. The bent shape of the HOMO is another example of the HOMO-LUMO interaction (Jahn-Teller distortion) within a molecule that we saw in Section 2.4.1. The nitrogen will be the nucleophilic site when the second term of Equation 4.2 is the more important contributor to DE. Furthermore, S and hence  for N—C bond formation is higher than for O—C bond formation (see p. 54); when the frontier orbital term is dominant, this will enhance the propensity for bond formation to nitrogen, because it is in this term that  appears. An alternative or supplementary explanation is that the solvent gathers around the site of higher charge, the oxygen atoms in the case of nitrite, and that this hinders the reaction there, and the nitrogen, with so little of the charge, must be less crowded by solvent molecules.

LUMO O

N

O

O

N

O

n*

LUMO

HOMO

O

N

O

O

N

O

HOMO

N

O

n

linear NO2+

Fig. 4.2

O

bent NO2–

Frontier orbitals of the nitronium ion and the nitrite ion

In nitration, where we have an ambident cation, the important frontier orbital will be the LUMO of NO2þ, and this is a similar orbital to the HOMO of NO2–, except that the cation is linear. The nitronium ion, NO2þ, always reacts on nitrogen, both with soft nucleophiles like benzene and with hard ones like water. In the nitration of benzene, the solvent is often nonpolar; thus differential solvation is unlikely to be responsible for the fact that the nitrogen atom is the electrophilic site. ESR studies296 of nitrogen dioxide (NO2), which has one electron in the pn* orbital, confirm that the site of highest odd-electron population is indeed on nitrogen (about 53% of the electron, with the oxygens sharing the other 47%).

160

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

4.3.2 Enolate lons297 The most important ambident nucleophile is the enolate ion 4.48. Why does an enolate ion react with some electrophiles at carbon and with others at oxygen? We can now use the explanation based on the relative importance of the Coulombic and frontier orbital terms to account for this well-known observation.298 We have seen the p orbitals of an enolate ion calculated in Fig. 2.20, with the general pattern accounted for in the argument leading to Fig. 2.7. The size of the lobes can be taken as roughly representing the size of the c-values (or c2-values) of the atomic orbitals which make up the molecular orbitals. The system is closely related to that of the allyl anion in Fig. 1.33, but the effect of the oxygen atom is to polarise the electron distribution, with the lowest-energy orbital 1 strongly polarised towards oxygen, and the next orbital up in energy 2 polarised away from oxygen. The effective p charge on each atom in the ion is proportional to the sum of the squares of the c-values for the filled orbitals, namely 1 and 2. Using the values from Fig. 2.20, the total charge on the oxygen atom is 0.92 þ (–0.41)2 ¼ 0.98 and on the carbon atom it is 0.172 þ 0.72 ¼ 0.52. However, the c-values in the HOMO are the other way round, –0.41 on oxygen and 0.70 on carbon. With charged electrophiles, then, the site of attack will be oxygen, as is indeed the case, kinetically, with protons and carbocations. With electrophiles having little charge and relatively low-lying LUMOs, the reaction will take place at carbon. In other words, hard electrophiles react at oxygen and soft electrophiles at carbon. Once again, the fact that  values for bonds to carbon are usually higher than  values for bonds to oxygen enhances the tendency for the frontier orbital term to encourage reaction at carbon. Solvent, of course, also hinders reaction at the sites of highest solvation, which will generally be the atoms carrying the highest total charge. O

H

O MeI

Me

O

H

4.48

We can also explain why the nature of the leaving group on an alkylating agent affects the proportion of C- to O-alkylation in such enolates as the sodium salt 4.49 derived from ethyl acetoacetate. The observation is that the harder the leaving group (i.e. the more acidic the conjugate acid of the leaving group), the lower the proportion of C-alkylation (Table 4.4).299 The softer the leaving group, the lower will be the energy of the LUMO.300 In addition, the harder the leaving group, the more polarised is its bond to carbon, and hence the more charge there will be on carbon in the transition structure. This is the same phenomenon as the effect electronegative ligands have on the hardness of a Lewis acid (see pp. 77 and 130). As a result, the Coulombic term of Equation 4.2 will grow in importance with the hardness of the leaving group, making O-alkylation easier, and the frontier orbital term will grow with its softness, making C-alkylation easier.

Table 4.4 Nucleofugal group, X– kC/kO

The proportion of C- to O-alkylation as a function of the leaving group I–

Br–

TsO–

EtSO4–

CF3SO3–

>100

60

6.6

4.8

3.7

4 IONIC REACTIONS—REACTIVITY

161

O

O

O

kC

OEt

O + OEt

EtX

EtO

kO

Et

O

4.49

OEt

As before, we must not forget how much solvent effects may be the dominant influence in the regioselectivity. There is ample evidence that both the alkylation and the acylation of enolate ions in the gas phase take place, more often than not, on oxygen,301 the site that solvents protect. However, frontier orbital effects have been used to explain those gas phase reactions, and there are several, in which the enolate ion is attacked on carbon.302

4.3.3 Allyl Anions The allyl anion itself presents no problems: C-1 and C-3 are overwhelmingly the nucleophilic sites both for hard and soft electrophiles (Section 3.5). A substituent on C-1 makes the allyl anion 4.50 an ambident nucleophile, since attack can now take place at C-1, the  position, to give the alkene 4.51, or at C-3, the g position, to give what is usually the thermodynamically favoured product 4.52. The substituent can be C, Z or X, the geometry can be W-shaped or sickle-shaped, and the regioselectivity for each can be the same for hard and soft electrophiles, or different for each. There are further complications—allyl anions are not usually free anions, but can have a metal covalently bonded either to C-1 or C-3, and the nature of the metal and the position it is attached to, rather than any inherent selectivity in the free anion, may determine the regioselectivity. Steric interactions between a large substituent and a large electrophile can change selectivity from  attack to g attack. Allyl anions, especially those with Z-substituents, are well enough stabilised for the attack on some electrophiles to be reversible, especially with aldehydes and ketones, the halogens, and sulfenyl halides. Consequently, some results are thermodynamic and not kinetic, but it is not always easy to tell which, partly because proving which it is can be difficult. What is clear is that aldehydes and ketones often show different regioselectivity from other electrophiles, either because of reversibility or, more likely, because the metal coordinates to the carbonyl group delivering the electrophile in a six-membered ring transition structure to the allylic position relative to the metal. Finally, solvents, and leaving groups affect the ratio, and the presence of other substituents at C-1, C-2 and C-3 add even more variables. The outcome, not surprisingly, is that firm rules about regioselectivity are not yet in place, and the following brief discussion is far from a complete account.

E

C, Z or X 1 or

4. 50

3 or

C, Z or X

+ E 4. 51

C, Z or X

E

4. 52

4.3.3.1 X-substituted Allyl Anions. The allyl-lithium reagents 4.53–4.56 are relatively simple examples of X-substituted allyl anions. With oxygen303,304 or nitrogen305,306 substituents, 4.53 and 4.54, g alkylation is almost always the major pathway, but with sulfur, while g alkylation is known307 4.55,  alkylation is much more common 4.56.308,309

162

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

MeI

MeI

Li Et3SiO

Li PhNMe 4.54

Et3SiO 4.53

3:97

LiS

S

S

EtBr

MeI

Li

Li

PhNMe 6:94

EtS

S

4.55

S 4.56

23:77

only

These reactions are kinetically controlled, reasonably regular in their patterns, and explicable. The coefficients in the HOMO can be guessed at by using the simple arguments developed in Section 2.1.2.3, as illustrated in Fig. 4.3. The HOMO of an X-substituted allyl anion will have some of the character of 2 of the allyl anion, which is symmetrical but it will also have some of the character of a carbanion conjugated to an allyl anion, in other words 3* of butadiene, which has a larger coefficient on C-4, corresponding to the g position, than on C-2. This explains the g selectivity towards soft electrophiles like alkyl halides with the oxygen and nitrogen substituents. The total p-electron population is also greater at the g position (0.3712 þ 0.62 þ 0.62 > 0.62 þ 0.3712 þ 0.3712), which would suggest that this ought also to be the site of attack by hard electrophiles. There are a few examples where protonation is observed at this site with the oxygen310 and nitrogen substituents, including 4.54 itself,305 supporting this prediction. The anomalous results with the sulfur-containing anions can also be explained. The stabilisation of an anion adjacent to sulfur is by overlap with the neighbouring S—C bond (Section 2.2.3.2) and not by overlap with the lone pairs. If this is operating in the dithian-stabilised anion 4.56, it is no longer an X-substituent, but a Z-substituent, since the S—C bond is polarised away from the sulfur. Allyl anions with a Z-substituent are

0.600

–0.371

–0.19

X +

2 –0.707

3*

= HOMO –0.371

0.707

+

–0.54

0.600

=

0.65

X

Fig. 4.3 Estimating the coefficients of the HOMO of an X-substituted allyl anion

selective for reaction at the  position, and so that result is normal. The other sulfur-containing anion 4.55 does not have the possibility of this hyperconjugative overlap, and so it behaves as a normal X-substituted allyl anion. From this point on, the regioselectivity of substituted allyl anions is much less regular, and somewhat less explicable. For a start, X-substituted allyl anions react with carbonyl electrophiles with  selectivity. This is explicable, but it is determined by the site of coordination by the metal, not by the frontier orbitals. We can contrast the reaction of the oxygen-substituted lithium anion 4.57 with an alkyl halide, which is g selective, as usual, and the reaction of the zinc anion 4.58 with a ketone, which is  selective.304 The oxygen substituent coordinates to the zinc -bound at the g position, and the aldehyde is then delivered to the  position in a six-membered cyclic transition structure 4.59. The same reaction with the lithium reagent 4.57 gives a 50:50 mixture of  and g products, and so lithium is not so obviously coordinated in the way that the zinc is. This type of reaction is often brought under control in the sense 4.59 for synthetic purposes by

4 IONIC REACTIONS—REACTIVITY

163

changing the metal to a better Lewis acid,311 one that can simultaneously coordinate to the substituent and the carbonyl reagent. It is also possible to change the substituent to make it coordinate better when the metal is on C-1 (), and thereby make the allyl anion react with carbonyl compounds on C-3 (g).309

I Li EtO

EtO 4.57 O O

EtO

ZnCl

EtO 4.59

4.58

OH

Zn

OEt

Similarly, allyl anions with alkyl substituents almost always react with carbonyl electrophiles at the  position, as in the reaction of the prenyl Grignard reagent with aldehydes to give the product 4.61,312 presumably because the metal is attached to the less-substituted end and then delivers the electrophile in a six-membered transition structure 4.60. In contrast, alkylation of a similar anion with an alkyl halide gives mainly the product 4.62 of g attack,313 which might be counted as normal for an X-substituted allyl anion when a cyclic transition structure is not involved. Halogen substituents are anomalous. They are weak p donors and powerful  acceptors, which makes their contributions to regioselectivity difficult to predict. In practice, the dichloroallyl anion 4.63 reacts with all electrophiles to give products like 4.64 and 4.65 of attack at the  position.314 CHO

H

OH

Mg O

R = Me, M = MgBr R

4.61

4.60 M R

Br R = Me2C=CH(CH2)2

4.62

M = Li O

Li 4.63

OH

Cl Cl 4.64

Cl Cl

20:80

MeI Cl

Cl 4.65

4.3.3.2 C-Substituted Allyl Anions—Pentadienyl Anions.315 Allyl anions with C-substituents pose a different problem. Both  attack and g attack are known, as illustrated by the reactions of the open-chain C-substituted anions 4.66,316 and 4.67.317 The problem is not only that the regioselectivity is irregular, but explaining it is not straightforward either. Simple predictions based on the p orbitals suggest that the

164

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

C-substituted system should be equally reactive at the  and g carbons. Mixing any amount of 3 of the pentadienyl anion into the HOMO of the allyl anion will leave the HOMO coefficients at the  and g carbons equal. MeBr

Ph

Ph

Na 4.66

92:8

MeI 3

1

Li 4.67

+ C-3:C-5 35:65

5

Me3SiCl

SiMe3 C-3:C-5 1:99

The cyclohexadienyl anion 4.68 has been the focus of most interest because of its importance as the penultimate intermediate in Birch reduction. It is attacked almost exclusively at the central carbon atom, C-3, which corresponds to  attack on a C-substituted allyl anion. This gives the energetically less favourable product 4.69 with the two double bonds out of conjugation, and in spite of a 2:1 statistical preference for attack at C-1.318 This selectivity seems to be largely independent of the nature of the electrophile or of the metal, and the same pattern is found for cycloheptatrienyl systems too.319 The sums of the squares of the coefficients of the filled orbitals 1, 2 and 3 for the pentadienylsystem (Fig. 1.42) are equal on C-1 and on C-3 (and, of course, on C-5). The frontier orbital coefficients for the HOMO 3 are also equal on C-1, C-3 and C-5. However, the simple Hu¨ckel calculation which gives these values, neglects the fact that C-3 is flanked by two trigonal carbon atoms but that C-1 has only one trigonal carbon adjacent to it and one tetrahedral. Naturally, this perturbs the system. Total p-electron populations and HOMO coefficients have been calculated320 allowing for the overlap of the C—H bonds at C-6 with the p system (i.e. hyperconjugation), and these give the values shown in Fig. 4.4a and b, respectively. The presence of a larger coefficient on C-3 is supported by ESR measurements321 on the radical corresponding to this anion, which clearly show a larger coupling to the hydrogen on C-3 than to those on C-1 and C-5 (Fig. 4.4c). Thus both the experiment and the calculation imply that there is a larger coefficient and a higher total charge at C-3 than at C-1. It is, of course, a highly exothermic reaction—just the kind which should show the

H

H

H

H

1.294

Fig. 4.4

0.350

0.01 0.438

(a) Calculated total electron populations

H

0.318

0.964 1.438

H

(b) Calculated values f or c f or the HOMO

(–0.102) 0.506

(c) Spin densities obtained f rom ESR and converted to c values using the McConnell equation

Electron distribution in the cyclohexadienyl system

4 IONIC REACTIONS—REACTIVITY

165

influence from the interaction of the orbitals of the starting materials, rather than the influence from the relative energies of the two possible products.

H 1

H M

5

H

H

E

H

E

3

4.68

4.69

This adjustment to the simple Hu¨ckel calculations explains why the cyclic systems differ from the openchain pentadienyl anions, which have no alkyl groups at C-1 and C-5. These systems are evidently delicately balanced, so much so that quite minor perturbations can lead to high levels of attack at C-3,322 especially with the harder electrophiles like alkyl triflates.323

4.3.3.3 Z-Substituted Allyl Anions—Dienolate Ions. Electrophilic attack on Z-substituted allyl anions is almost always selective for attack at the  position. The problem is to explain it. A special group of Z-substituted allyl anions—the boron 4.70324 and 4.71,325 sulfur 4.72,309 and silicon 4.73326 groups have no double bond extending the conjugation but only an electron deficiency conjugated to the p system of the allyl anion. The boron has an empty p orbital, and the sulfoxide and silyl groups have negative hyperconjugation with neighbouring  bonds polarised from the sulfur and silicon atoms towards more electronegative atoms (Section 2.2.3.2). The coefficients in the HOMO of an allyl anion conjugated to an empty p orbital can be modelled by mixing in 2 of butadiene. This serves to increase the coefficient at the g carbon, where some of the reactions take place. The result with the hindered boron-substituted anion 4.71 is further explained by the steric repulsions from the mesityl groups. The -selectivity with the sulfoxide 4.72 may represent a contribution from coordination by the sulfoxide group stabilising an  lithium, and the same control can be forced on the silicon series by having a coordinating substituent on the silicon in place of the methyl groups.

sia2B

R

MeI sia2B

mes2B

Li

Li 4.70

R = n-C5H11

O Ph

Me2SO4

R mes2B

4.71

mes = 2,4,6-Me3C6H2

O MeI

S Li 4.72

Ph

S

PrnI

Me3Si

Prn

Me3Si

Li : 72:28

4.73

: 34:66

The more usual kind of Z-substituted allyl anions 4.74a have extra conjugation as well as the electron deficiency, and they are usually drawn as dienolate ions 4.74b. They almost always react faster at the  carbon than at the g carbon, both with soft and hard electrophiles,327 just like the more simple Z-substituted allyl anions 4.70 and 4.72.

166

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

OEt

OEt

OEt MeI

O

O 4.74a

O

4

2

Me

4.74b OLi excess

charge:

LiO –0.4 –0.2 4.75

Using a model like that in Section 2.1.2.3, the extra conjugation for this kind of Z-substituted allyl anion will mix 3 of the pentadienyl anion with 2 of butadiene (Fig. 4.5). This also suggests that the terminus, the g carbon, ought to be the more nucleophilic site. Clearly this is not borne out in practice, but measurements of the total electron population agree with this result. The excess p charge, calculated from the 13C-NMR chemical shifts of the lithium dienolate 4.75, show that the charge on C-2, the  carbon, is approximately twice that at C-4.328 The simple version of Hu¨ckel theory is inadequate for this problem.

–0.600

0.371

0.19

Z +

3 0.576

–0.576

= HOMO

2 –0.371

0.576

=

+

Fig. 4.5

–0.47

0.600

0.59

Z

Crude estimate of the coefficients of the p orbitals of a 1-Z-substituted allyl anion

Changing the conjugated system from a dienolate anion to a dienol ether changes the regioselectivity—the silyl enol ether 4.76 reacts mainly at the g position.329 The change from the oxyanion to the silyl ether effectively changes the orbitals from being best thought of as close to a pentadienyl anion to being closer to those for a 1-X-substituted diene. Using the usual arguments, we can predict that a 1-X-substituted diene will have some of the character of the pentadienyl anion, but also some of butadiene. Adding the frontier orbitals together gives the orbitals on the right of Fig. 4.6, where we see that the more butadiene character we add in, the more the coefficient at C-4 will increase relative to that at C-2.

Me3SiO Pri2CHO

O

Br ZnBr2 cat.

Pri2CHO

4.76

A calculation330 on a simple dienol ether 4.77, indicates that the total p-electron population remains higher at the - than at the g-carbon atom, but another calculation,331 on the same ether, gives HOMO coefficients 4.78, which match those in Fig. 4.6 but with a smaller difference. They support the conclusion that the g carbon ought to be the more nucleophilic site towards soft electrophiles.

4 IONIC REACTIONS—REACTIVITY –0.500

167

0.500

0.600

–0.371

*

+ 0.500

–0.500

–0.371

0.600

0.576

LUMO –0.191

0.550 –0.600

2

= 0.600

–0.371

HOMO –0.473

0.588 3

0.288 1

=

+

X 4

Fig. 4.6

–0.250

–0.300

0.191

+ –0.576

3

=

0.371

0.576

0.550

–0.435

2

Crude estimate of the coefficients of the p orbitals of a 1-X-substituted diene

OMe 1.053

OMe

1.071

0.498

-electron population 4.77

–0.492

HOMO coefficients 4.78

An oxyanion substituent on the diene is more powerfully electron donating than a methoxy substituent. It seems likely, therefore, that it is the model which is inadequate, not the idea of explaining the high nucleophilicity of the  position along these lines. Thus the reactivity at C-4 shown by silyl enol ethers is the expected behaviour—it is the reactivity at C-2 in the enolate anions that is hard to explain. Whatever the cause, the selectivity for the  position in a Z-substituted allyl anion is powerful enough to compete with the more or less reliable g-selectivity for an X-substituted allyl anion when both substituents are present 4.79.

MeI

NC Li NMe2 4.79

NC

NC + NMe2

NMe2 50:50

4.3.4 Aromatic Electrophilic Substitution Aromatic rings, except for highly symmetrical systems like benzene itself, are ambident nucleophiles. In electrophilic aromatic substitution, the rate-determining step is usually the attack of the electrophile on the p system, to create the Wheland intermediate332 having a tetrahedral carbon atom and a cyclohexadienyl cation (or other conjugated cation from nonbenzenoid rings). As with the closely similar reaction between an alkene and a carbocation (see p. 153), the first step is endothermic, and we can expect that the argument based on the product side of the reaction coordinate will be strong and satisfying, and so it is. The concept of ‘localisation energy’ has long been used to account for the rates, and sites, of electrophilic substitution. It is a calculated value of the endothermicity in a reaction and is therefore part of the argument based on product development control. The plot of localisation energy against rate constant is a good straight line.333

168

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

4.3.4.1 Molecular Orbitals of the Intermediates in Electrophilic Attack on Monosubstituted Benzenes. The standard explanation for the regioselectivity in aromatic electrophilic substitution of monosubstituted benzene rings, appropriately enough for an endothermic rate-determining step, assesses the relative stability of the possible cyclohexadienyl cations and assumes that the transition structures leading to them will be in the same order. With anisole 4.80, an X-substituted benzene, substitution takes place in the ortho and para positions, rather than in the meta position, because the intermediates produced by ortho and para attack 4.81 and 4.82 are lower in energy than the intermediate 4.83 produced by meta attack. The energies of the former intermediates are lower because of the coherent overlap of the lone pair of electrons on the oxygen atom with the conjugated cyclohexadienyl cation orbitals. This overlap is not possible with the meta intermediate. The overlap is easy to illustrate with curly arrows, and we can see that arrows cannot be drawn in the same way on the meta intermediate 4.83. OMe

OMe

OMe

OMe

H

+

E

E

+

+ H

4.80

E

E H 4.82

4.81

4.83

However, we ought to be clear that this valence bond description is a superficial argument (which fortunately works). Curly arrows, when used with a molecular orbital description of bonding, work as well as they do because they illustrate the electron distribution in the frontier orbital, and for reaction kinetics it is the frontier orbital that is most important. In the present case, we are using a thermodynamic argument, for which we need to know the energy of all of the filled orbitals, and not just one of them. To assess the energies of the three possible intermediates 4.81, 4.82 and 4.83, we can, for simplicity, ignore the fact that one of the atoms is an oxygen atom, and use instead the simple hydrocarbon-conjugated systems 4.85, 4.86 and 4.87 which are isoelectronic with them. We are using, in other words, the benzyl anion 4.84 as a model for an X-substituted benzene ring.

H

E+

E

+

+ H

4.84

4.85

E H 4.86

E 4.87

The calculated16 energies and coefficients of the p orbitals of these intermediates are shown in Fig. 4.7. Note that the larger the  value the greater the p-stabilisation and the lower the energy. Although the calculations do not give good absolute values for the energies, they get the relative energies right, which is all we need be concerned with. We can see in Fig. 4.7 that the main reason why the total p stabilisation of 4.85 (3.50) and 4.86 (3.45) is greater (3.08) than that of 4.87 is that the highest filled orbital, 3 in 4.87, is not lowered in energy (as 3 is in the intermediates 4.85 and 4.86) because there are no p-bonding interactions between any of the adjacent atoms—it is a nonbonding molecular orbital. This is, of course, the same point that the curly arrows were making but we ought to make sure that the two lower-energy orbitals do not compensate for the high energy of 3 in the intermediate 4.87. In fact, they do to some extent, but not much: we can see that 1 of 4.87 is

4 IONIC REACTIONS—REACTIVITY

169 –0.295 –0.431

0

0 0.730

3

0.521

0

0.436

–0.444 3

0.45

–0.418

0.232 –0.325

0.52 0.521

0.230

3

–0.418 0.444

0.232 0 0.418

0

1.0

2

1.25

1.18

0.500

0.521

0.232

0.316 0.500

2

0.372

–0.195

0.316

2 –0.418 –0.232

–0.512

–0.602 –0.521 0.232 0.316

1.80

0.521

0.325

0.418

1

1.93 0.232

1.90

0.628

0.512

0.602 0.316

1

1 0.500

0.521 0.418

0.230

0.372

0.195

Fig. 4.7 Coefficients and energies of the p molecular orbitals of the intermediates in the electrophilic substitution of the benzyl anion at the ortho, para, and meta positions

actually lower in energy (larger ) than 1 of 4.85, and 2 of 4.87 is lower than 2 of 4.86. Indeed, the sum of 1 and 2 for 4.87 is greater than ( 1 þ 2) for both 4.85 and 4.86. We can also see in Fig. 4.7 the reason for both of these results. The circles drawn round the atoms are very roughly in proportion to the c2-values—in other words, the electron population; the clear and darkened circles serve to identify changes of sign in the wave function. If we look at 1 of 4.87, we see four atoms with high coefficients (two of 0.316 and one of 0.512, each flanking one of 0.602) close together and all of the same sign. This leads to strong p-bonding and a low energy for this orbital. Such qualitative arguments can also be applied to 2 in each case, and they serve to give us some confidence in the general rightness of the calculated values of the energies of the orbitals in Fig. 4.7. These small effects on 1 and 2 clearly do not compensate for the effect of having no p-bonding in 3 in 4.87, but we do now have a more thorough version of the original explanation for ortho/para substitution in X-substituted benzenes.

H

E+

E

+

+ H E

4.88

4.89

E

H

4.90

4.91

In a similar way, we can use the benzyl cation 4.88 as a model for a benzene ring having a Z-substituent. Again we have three possible intermediates 4.89, 4.90 and 4.91. The p systems of these intermediates are the

170

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

same as the ones we have just been looking at, except that this time only 1 and 2 are filled in each case. We have already observed that the sum of the  values for 1 and 2 is greater for the intermediate 4.91 which is the result of attack in the meta position. This, then, is the product-development argument for meta substitution in Z-substituted benzenes. Furthermore, we can explain the relatively slow rate of such substitutions and the relatively fast rate of the ortho and para substitutions in X-substituted benzenes by using only the p energies of the orbitals together with the argument based on the contribution of product-like character to the transition structure. It is summarised in Fig. 4.8. The endothermicity of 1.28 on the right is not much greater than that for benzene (1.27); however, the presence of two positive charges in the intermediate on the right has not been allowed for, and this will obviously raise the energy of this intermediate above that shown.

H 2.73β

medium rate

E 3.08β H

4.0β 4.36β

Fig. 4.8

H

slow rate

fast rate

3.50β

E

E

4.36β

Relative rates of aromatic substitutions based on product-like character in the transition structure

This is an adequately satisfying explanation for the well known ortho/para and meta directing effects of aromatic substituents. For all that the argument from the starting material side of the reaction coordinate is inherently weak, frontier orbitals are often invoked,334 and so we should look at how well they cope. Arguments based on the starting material side of the reaction coordinate are worth looking at335 because they work quite well, as we shall see, in explaining many of the observations in this field. 4.3.4.2 The Frontier Orbitals of Monosubstituted Benzenes. The problem with using frontier orbital theory with simple aromatic compounds is that there are two or more high-energy molecular orbitals close in energy, and the HOMO itself is not of such overriding importance. In benzene itself, the HOMO is a degenerate pair 2 and 3 (Fig. 1.43), which, taken together with equal weight, make the frontier electron population on each atom equal. When a single substituent is attached, the degeneracy is lifted, with 3 unchanged in energy, because the substituent is in the node, and 2 either raised or lowered in energy depending upon what kind of substituent it is. For C-substituents, we have already seen the orbitals of styrene in Fig. 2.2, in which the orbital most resembling 2 is 4, raised in energy above 3. Using the same kind of arguments that we used earlier, in Section 2.1.2, we can estimate what the orbitals of X-substituted benzenes look like by mixing into the benzene orbitals a bit of the character of the corresponding orbitals of the benzyl anion. Similarly, for Z-substituted benzenes we need to mix together some of the character of the benzyl cation and some of the character of styrene. Thus we need a picture of the orbitals of the benzyl system. The three lowest-energy orbitals (Fig. 4.9)16 are, like those of styrene, and very similar to those of benzene. The HOMO of the anion (and the LUMO of the cation) is 4, and this, like the corresponding orbital in the allyl system, has nodes on the alternate atoms. For this reason, it is a nonbonding orbital, and its p energy is zero. Two simple rules3 enable us to work out the coefficients in such orbitals: (1) Place a zero on

4 IONIC REACTIONS—REACTIVITY

171 0.756

0

LUMO of the cation HOMO of the anion

–0.378 4

0.397

0.378

1

0.500 0.116

1.26

–0.500

3 –0.500

2 0.238

–0.354

0.500 –0.562

2.1

0.406 1 0.354 0.337

Fig. 4.9

The lower p orbitals of the benzyl system

the smaller number of alternate atoms, i.e. 4.92 rather than 4.93; this identifies the nodes; (2) the sum of the coefficients on all the unmarked atoms joined to any one of the marked atoms must be zero. Thus we can start at the para position in 4.94 and call the coefficient there a. The coefficients on the ortho positions must both be –a, in order that the second rule may be obeyed when applied to the meta positions marked by the zeros. Now we look at the ring carbon which has the exocyclic carbon atom joined to it. It has a total of three unmarked atoms next to it, two of which, we have deduced, have coefficients of –a. The exocyclic atom must therefore have a coefficient of 2a, in order that the second rule is obeyed. Thus the coefficients in 4 are those shown in the drawing 4.94. Since the sum of their squares must be one, we can give exact numbers to them, shown in the drawing 4.95. These are the numbers in Fig. 4.9. They are supported by ESR measurements on the benzyl radical 4.96 (¼ 1.64).61 0 0 0

0

2a

2/√7

0

0

–a

–a

–1/√7

16.4 gauss 5.1 gauss

–1/√7

and not 0

0

4.92

0

0

0

–1.8 gauss

0

0

a

1/√7

4.93

4.94

4.95

6.1 gauss

4.96

X-Substituents, like C-substituents, raise the energy of the HOMO to create 4, because we mixed in some of 4 of the benzyl anion, but they leave 3 unchanged. In contrast, Z-substituents lower the energy of 2, but also leave 3 unchanged, making it the HOMO by default. The result of lifting the degeneracy is to create definite HOMOs and, not far below them, next highest occupied molecular orbitals (NHMOs), as shown in Fig. 4.10. We can now see that the coefficients of the HOMO of the benzyl anion are high on the ortho and para positions, and zero on the meta positions. X-substituted benzenes can be expected to reflect this character, with calculations on phenol, for example, giving HOMO coefficients of 0.34 at the ortho positions, –0.496 at the para, and –0.22 at the meta.336 However, it is no longer a simple matter to use the HOMO to predict the nucleophilic sites because it is no longer safely the appropriate frontier orbital separable from all the others. For example, it is clear from the orbitals in Fig. 4.9 that the ortho and para positions are not strongly differentiated from the meta in Z-substituted benzenes. The ortho and meta positions are the most electron-rich in the HOMO, but the NHOMO, not much below the HOMO in energy, adds electron population to the para position. Fukui

172

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS X

C

Z 4

2

4

C

3

X

3

3

Z

3

2

Fig. 4.10 HOMOs and NHOMOs of monosubstituted benzenes

explicitly examined this problem,337 defining the frontier electron population, to combine with the HOMO any orbitals equal in energy to or just below it. He estimated the effective p-electron population (f) at any specific site in an aromatic ring using Equation 4.6: f ¼2

c23 þ c22 eDDl 1  eDDl

4:6

where c3 and c2 are the coefficients at that site in the two highest-energy p orbitals 3 and 2, respectively, with the one labelled 3 having arbitrarily the higher energy, Dl is the difference in energy between 3 and 2, and D is a constant (3 is used in fact) representing some kind of measure of the contribution of 2 to the overall effect. As it ought, this expression gives the higher-energy orbital 3 slightly greater weight. We can use Fukui’s frontier electron population f from Equation 4.6 to correct for the presence of the two highenergy filled orbitals contributing to the third term of Equation 3.13. For benzonitrile 4.98 and nitrobenzene 4.99, typical Z-substituted benzenes, more parameters were needed to cope with the presence of heteroatoms, but the f values for styrene 4.97 and these two compounds do show the right pattern, correcting for the presence of an awkward pair of frontier orbitals. 0.683

CN

0.259 0.264 0.170

NO2

0.247 0.318

0.098

0.181 0.212

0.335

0.219

0.259

0.246

0.181

4.97

4.98

4.99

Clearly the frontier orbital explanation for reactivity, and for ortho/para and meta selectivity, in the conventional mechanism for aromatic electrophilic substitution is less than compelling—the orbital effects are not opposing the standard pattern, but the original argument based on the stability of the intermediates remains more satisfying, just as it should for an endothermic reaction. If we turn to the SET mechanism, most of the same features return. The key step is the electron transfer within a charge-transfer complex, which is often detectable with the more nucleophilic aromatic rings or with highly conjugated or electron-deficient electrophiles by its long wave UV or visible absorption.338 High reactivity is encouraged by the formation of well-stabilised radicals, and by a small energy difference between the HOMO of the aromatic ring and the LUMO of the electrophile. The interesting feature with this mechanism is that the regioselectivityisdeterminedbytheeasewithwhichtheradicalcouplingtakes placeat each of thesitesinthebenzene ring.

4 IONIC REACTIONS—REACTIVITY

173

This is determined by the coefficients in the singly occupied molecular orbital (SOMO), which will be the orbital that had been the HOMO of the aromatic ring before the electron was transferred from it. However, we meet again the presence of another orbital close in energy, and the absence, in effect, of a straightforward SOMO, since a single electron transfer from the NHOMO to the HOMO (SOMO) does not have a high energy barrier. The explanation for the regioselectivity therefore uses the same orbitals in both the conventional and the SET mechanism. 4.3.4.3 Halogenobenzenes. It is well known that the halogenobenzenes are unusual in showing a mixture of the properties of the Z- and X-substituted benzenes. Like Z-substituted benzenes, they undergo electrophilic substitution more slowly than benzene, but, like X-substituted benzenes, they are ortho/para directing. On the ‘product’ side of the reaction coordinate, we are on weak ground. The intermediates 4.100 and 4.101 could be stabilised relative to the corresponding intermediate in benzene. The halogen is an X-substituent, with a lone pair of electrons, and there should be some p bonding gained by overlap of the kind shown by the benzyl anion. As the halogens are so much more electronegative and, below fluorine, so much larger than carbon, the overlap will be feeble. If the energy of the intermediates is lowered, then we have a problem in explaining the slower rate of attack by electrophiles. Alternatively, if the cationic centres are not stabilised, perhaps also because of electron withdrawal in the  framework, we have difficulty in explaining why the ortho and para intermediates 4.100 and 4.101 are selectively formed, rather than the product of meta attack 4.102. We shall find that there is no paradox in the frontier orbital explanation or in the SET mechanism—the factors affecting the overall rate are not the same as those affecting regioselectivity. Cl

Cl

Cl

H E H E 4.100

E

H

4.101

4102

We are however in difficulty, because the nonmathematical description of the orbitals we have been using is inadequate—even simple Hu¨ckel theory is not particularly good when there are strongly electronegative atoms present.Nevertheless,we havenodifficulty inseeingthat theperturbationtreatment leadingto Equation3.13makes it possible to have ortho/para substitution at a reduced rate: the o/p orientation is mainly dependent on the coefficients and overall charges at each of the atoms, and the reduced rate could be largely determined by the energies of the higher occupied orbitals. The same is true of the SET mechanism which draws on the same features. However, we are in difficulty in showing that this possibility is indeed true, unless we are prepared to do fairly elaborate calculations. 4.3.4.4 Frontier Orbitals of Polycyclic Aromatic Molecules. In the larger aromatic systems we sometimes have a clear HOMO to use for a frontier orbital treatment, but in many others we have the problem of more high energy orbitals than just the HOMO contributing to nucleophilicity. The numbers on the structures in Fig. 4.11 are either (for the first seven compounds) the coefficients of the HOMO of the molecule18,339 or (for the remaining five) the frontier electron population (f) calculated using an equation like Equation 4.6 modified to deal with the presence of electronegative heteroatoms. The preferred site of electrophilic attack in the nitration of all the aromatic molecules is indicated by an arrow pointing from it (or them, in some closely balanced cases).340 There are even more examples in Section 6.5.4.6, where they are introduced in connection with another problem. Except for the slightly anomalous pyrrocoline, the arrow does indeed come from the largest (or larger) number. Thus, in all these cases, we have the situation described in Fig. 3.3a, where the lower-energy product and the lower-energy approach to the transition structure are connected smoothly by what is evidently the lower-energy pathway. We can feel confident, in a situation like this, that we have a fairly good qualitative picture of the influences which bear on the transition structure.

174

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS 0.315

4%

0.233 0

0.440

0.425

–0.311

–0.042

0.174

–0.340

–0.220

0.263

0.163

0.091

27%

0.415

34% –0.38 0.543

–0.336

0.368

–0.164

0.371 0.296

0.259

0.600

0

0

N H NO2+ –0.38

0.345

0.47

0.595 0.218

0.058

–0.01 0.54 –0.38

0.219 0.217

O –0.23

0.031

N H

0.233

0.454

0.191

N

0.141 0.289

0.527

35% 0.214

0.492

all other electrophiles

0.177

0.454

0.220

0.157

0.364

0.115

0.013

0.394

N

0.534

N

0.362

0.072

0.300

N

0.201 47% 0.322

Fig. 4.11

0.057

Frontier electron populations and the sites (arrowed) of nitration

Fukui341 also suggested another parameter sr, defined in Equation 4.7: sr ¼

occ : c2 X j E j j

4:7

in which cj is the coefficient at the atom r in the filled orbital j, and Ej is the energy of that orbital. He called sr the superdelocalisability, both in unsubstituted and substituted benzene rings. This expression bears an obvious relation to the third term of Equation 3.13. Using a single electrophile—the nitronium ion—a plot of the rate constant for nitration at particular sites in a large range of aromatic hydrocarbons against sr gives a good correlation over several powers of ten in rate constant.270 4.3.4.5 ortho/para Ratios.244,299 The proportion of ortho to para substitution ought to be susceptible to molecular orbital treatment, but we should not be surprised to find that such treatment has had only a little success as yet. The changes in ortho/para ratios are relatively small, and steric effects are well known to be important in reducing the proportion of ortho product in many cases. Furthermore, the molecular orbital treatment we have been using is far from complete in identifying all the factors which contribute to transition structure energies. We can, however, see in the p molecular orbitals that product-like character in the transition structure favours ortho substitution over para for C-, Z- and X-substituted benzenes. When we look at the sum of the energies for the filled molecular orbitals of the intermediates 4.85 and 4.86, we see (Fig. 4.7) that the total p stabilisation of the former (3.50), which is linearly conjugated, is greater than the latter (3.45), which is cross-conjugated. Similarly with a Z-substituted benzene, the former gives a p stabilisation of 3.05 and the latter 2.93. The difference is greater in the Z-substituted case, and this is, in fact, the observed trend (Table 4.5): insofar as

4 IONIC REACTIONS—REACTIVITY

175

Table 4.5 o/2p ratios in aromatic nitration of PhR as a function of substituent R342 Type of substituent

R

%o

%m

%p

o/2p

XCZZ-

OMe Ph CO2Et NO2

17 53 28 6

— — 68 93

83 47 3 0.25

0.10 0.56 4.3 12.8

Z-substituted benzenes give any ortho and para products, the ortho/para ratio is greater than it is for C- and Xsubstituted benzenes, and the more powerfully the Z-substituent is electron withdrawing, the more marked is the effect. Turning to the frontier orbitals, we see that a C-substituted benzene ring has a higher coefficient (even allowing for the presence of two high-energy p orbitals) on the para than the ortho position 4.97. Soft electrophiles should give more substitution in the para position, which is what is observed with biphenyl (Table 4.6). Nitration involves a fairly hard electrophile (NO2þ), and so does protonation; the bromonium ion will be harder than the neutral halogens, and mercuration involves a very soft electrophile (Table 4.1). The o/2p ratios fall in this order. Table 4.6

o/2p ratios in aromatic substitution as a function of the electrophile343

Electrophilic substitution

o/2p for toluene (Ph-X)

o/2p for biphenyl (Ph-C)

Hydroxylation Chlorination with Clþ Bromination with Brþ Proton exchange Protodesilylation Nitration Chlorination with Cl2 Friedel-Crafts ethylation Sulfonation Mercuration Bromination with Br2 Friedel-Crafts acetylation

2.00 1.63 1.29 1.06–0.3 0.84 0.72 0.97–0.25 0.47 0.25 0.25 0.25–0.11 0.0006

— — 0.69 1.0–0.19 2.14 1.68 0.32 0.41 — 0.01 0.03 very small

For a Z-substituted benzene ring, the total electron population is usually calculated to be higher on the ortho than on the para position (and much higher on the meta, of course). The frontier electron population f is also higher on the ortho than on the para position in nitrobenzene 4.99, so again all three molecular orbital contributions, the low p energy of the intermediate, the relatively high charge and the frontier orbital coefficient, combine to explain the observation of high o/2p ratios for this compound in Table 4.5. For an X-substituted benzene, the total charge in the p system is larger on the ortho position, but the frontier electron population is larger on the para position (0.34 at the ortho positions, –0.496 at the para for phenol).336 We again expect the softer electrophiles to give more para substitution. This fits moderately well (Table 4.6) with some of the experimental observations. Nitration and bromination with Brþ give higher o/2p ratios with toluene than the softer electrophiles involved in halogenation with molecular halogen and in mercuration. Furthermore, the halogens, whether as Xþ or X2, are in the right order: chlorine is harder than

176

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

bromine and gives higher o/2p ratios. Friedel-Crafts acylation probably involves an acylium ion, but it seems likely that this species, although formally charged, will also have a low-energy LUMO and hence accept a high frontier orbital contribution. We cannot take this argument far. Steric effects are bound to be present, and there are striking anomalies. Thus hydroxylation (trifluoroperacetic acid), has a soft electrophile, but gives a high o/2p ratio, and sulfonation has a relatively hard electrophile (usually solvated SO3), but appears to have a rather low o/2p ratio. This latter observation is particularly likely to be a steric effect, because sulfonation, not unexpectedly, is unusually sensitive to steric effects, and it is also unusual in being reversible. There are even a few reactions in which it is the second step, the proton loss, which is rate-determining and hence product-determining.344 The proportion of ortho attack in any of these reactions is quite dependent upon the reaction conditions (thus the numbers in Table 4.5 are not the same as those in Table 4.6, the data coming from different sources). However, none is more sensitive than proton exchange. There is a steady decrease in the proportion of ortho attack as the acid strength is reduced (Table 4.7). The nearer the electrophile is to being a free proton, the harder it is, and the more ortho substitution there is. The changes in the o/2p ratio are unlikely to be all steric in origin, because the same trend is seen with toluene, with biphenyl and with tert-butylbenzene. Thus the frontier orbital theory is moderately successful in a field notoriously beset with confusing data and multifarious influences on the energies of the transition structures.

Table 4.7

o/2p ratios for proton exchange as a function of acid strength343

Conditions

o/2p for toluene (Ph-X)

o/2p for biphenyl (Ph-C)

1.06 1.00 0.98 0.60 0.49 0.50 0.28

— — — 0.63 0.60 0.25 0.19

75% H2SO4 71% H2SO4 65% H2SO4 CF3CO2H-H2O CF3CO2H Liquid HI Liquid HBr

4.3.4.6 Pyrrole, Furan and Thiophen. Electrophilic substitution in these three heterocyclic rings takes place faster at the 2-position than at the 3-position (Fig. 4.11). The p molecular orbitals of pyrrole are representative of all three—they are shown in Fig. 1.69, where 3 is the HOMO 4.103 (with a node running through the heteroatom, it is the same as 2 of butadiene). The larger coefficients in the HOMO are at C-2 and C-5, and the frontier orbitals explain the regioselectivity tellingly.345 The pattern is extendible to their benz analogues (Fig. 4.11). It is also effective in explaining a feature of gas-phase reactions in which most electrophiles attack C-2, but a few hard electrophiles attack the heteroatom or C-3.346 The total charge distribution in the p system 4.104 is calculated from the sums of the squares of the coefficients shown in Fig. 1.69. The heteroatom and C-3 carry more of the charge, and so hard electrophiles can attack there for the usual electrostatic reasons. 0.37

HOMO (

3)

0.58

charge ( c) N H 4.103

0.60

0.54

N H

0.76

4.104

4 IONIC REACTIONS—REACTIVITY

177

Since this is an endothermic reaction, a better explanation for attack at C-2 ought to reside in the relative energies of the intermediates 4.105 and 4.106. They both have conjugated systems of four p orbitals, with the heteroatom at the end in 4.105 and inside in 4.106. It is not obvious why the former should be lower in energy than the latter, although calculations agree that it is. Without the benefit of a calculation, one is reduced to saying that the conjugated system 4.105 is linearly conjugated, with the lone pair on the nitrogen atom overlapping with the p system of an allyl cation 4.105b, whereas the conjugated system 4.106 has the lone pair on the nitrogen atom overlapping with the p bond and an isolated cation 4.106b. This essentially valence-bond description hardly amounts to a satisfying explanation, although it does resemble the argument that a linearly conjugated system (like 4.85) is lower in energy than a cross-conjugated system (like 4.86). E H N H E+

3

E H

+ N H 4.106a

4.105a

2

E

N H

H N H

E H

4.105b

+ N H 4.106b

4.3.4.7 Pyridine N-oxide. A special case of aromatic electrophilic substitution is provided by the ambident reactivity of pyridine N-oxide 4.107. Klopman230 has used Equation 3.13 to calculate the relative reactivity (DE values) for electrophilic attack at the 2-, 3- and 4-positions as it is influenced by the energy of the LUMO of the electrophile. He obtained a graph (Fig. 4.12) which shows that each position in turn can be the most nucleophilic. At very high values of Er – Es (hard electrophiles), attack should take place at C-3; at lower values of Er – Es, it should take place at C-4; and, with the softest

2-position

3-position

4

4-position E

3

N O 4.107

E LUMO(electrophile)

Fig. 4.12

Electrophilic substitution of pyridine N-oxide

2

178

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

electrophiles, it should take place at C-2. Attack at each of these sites is certainly known: the hardest electrophile SO3 does attack the 3-position,347 the next hardest (NO2þ) the 4-position,348 and the softest (HgOAcþ) the 2-position.349 This time, without the complicating steric effect, sulfur trioxide is showing the expected behaviour. However, this reaction is really more complicated. The sulfonation, for example, almost certainly takes place on the O-protonated oxide rather than on the free N-oxide, and this must affect the relative reactivity of the 2-, 3- and 4-positions. The value of the exercise is not so much in the detail of this particular example as in the way in which it shows how a single nucleophile, such as pyridine N-oxide, can, in principle, be attacked at different sites, depending upon the energy of the LUMO of the electrophile.

4.4

Electrophilicity

Electrophiles in general are characterised by having a low-energy LUMO and electron deficiency, either as a full positive charge or as a polarised bond with a partial positive charge at one or more sites, but there is no single scale of electrophilicity, any more than there is for nucleophilicity. Simply from general experience, halogens, especially assisted by coordination to a Lewis acid, are powerful electrophiles, as is the nitronium ion. Among other heteroatom electrophiles, nitrosyl chloride, the diazonium ion, and metal halides like mercury(II) chloride are less electrophilic in approximately that order. Among carbon electrophiles, carbocations like tert-alkyl, the acylium ion, the trityl cation, protonated carbonyl groups, and iminium ions are less electrophilic, approximately in that order, following the order of the extent to which the carbocation is stabilised by conjugation with an X-substituent. Neutral carbon electrophiles like carbonyl compounds and alkyl halides are less electrophilic still, with the former, breaking a p bond, more electrophilic than the latter, breaking a  bond. 4.4.1 Trigonal Electrophiles Trigonal carbon electrophiles, other than simple carbocations, almost always react with nucleophiles with the formation of a tetrahedral intermediate or product, and this step, often rate-determining, may be followed by the expulsion of a nucleofugal group, if there is one. The direct displacement of a nucleofugal group from trigonal carbon is rare.350 Carbonyl groups, the most important trigonal electrophiles, are electrophilic in the order: acid chlorides > aldehydes > ketones > esters > amides > carboxylate ions. This list, where we are comparing like with like, is easily explained. Setting aside the acid chloride for the moment, the p energy of the conjugated system in the starting materials is lowered by the substituent X, with the oxyanion (X ¼ O–) most effective, a methyl group the least effective, and a hydrogen atom making no contribution at all. This allows us to rank the p energy of the starting materials in order on the left in Fig. 4.13. In the tetrahedral intermediate, this overlap is removed or rather it is reduced to an anomeric effect (see pp. 96–98) which, being in the  system, is less. This means that the energies of the intermediates, although probably in the same order, are closer together. The activation energy for disrupting the p stabilisation is therefore least for the aldehyde DEH and greatest for the carboxylate ion DEO-. This satisfying approach also works to explain why imines and thioketones are less electrophilic than ketones, and why ketenes are more electrophilic than isocyanates, which are more electrophilic than carbon dioxide. It is possible to account for the order of electrophilicity using only the energy of p*CO, which is the LUMO for each of the carbonyl compounds.351 While gratifying, this explanation is inherently less satisfactory, since it only looks at one side of the reaction coordinate, but, summarising the effects of C-, X- and Z-substituents on the energy of the LUMO of a reagent, following the arguments developed in Chapter 2, leads to the following generalisation:

4 IONIC REACTIONS—REACTIVITY

179

Nu–

X

X=H

Nu O

X

Nu O–

X

O–

EH

X = CH3 X = OR X = NR2 X = O– Fig. 4.13

E O–

Relative energies of starting materials, transition structures and tetrahedral intermediates for nucleophilic attack on carbonyl groups

C- Substituents lower the energy of the LUMO a little and may somewhat increase electrophilicity. X-Substituents raise the energy of the LUMO and decrease electrophilicity. Z-Substituents lower the energy of the LUMO and increase electrophilicity.

Thus an -diketone is unmistakably more electrophilic than an ordinary ketone—the energy of the starting material is raised by the conjugation of the two carbonyl groups (see p. 84), and the energy of the LUMO is lowered, since the extra carbonyl group is a Z-substituent. A simple conjugated ketone, however, has the LUMO energy lowered by conjugation, but so is the energy of the starting material lowered, and the two effects work in opposition. In practice ketones like acetophenone are usually less reactive towards nucleophiles than simple ketones like acetone. Acid chlorides are more electrophilic than aldehydes, even though there is a weak stabilising conjugation between the lone pair on the chlorine atom and the carbonyl p* orbital. There are three contributions to this anomaly: (i) the p stabilisation is small, because chlorine is electronegative, and consequently the energy match is poor; (ii) the p stabilisation is offset by strong inductive electron withdrawal along the C—Cl bond, raising the electrophilicity of the carbonyl group; and (iii) anomeric stabilisation (see pp. 96–98) in the tetrahedral intermediate is greater—conjugation of the oxyanion with the C—Cl * orbital pulls down the energy of the transition structure. Although these effects are also present with esters, they are too small to override the conjugation of the lone pair on the oxygen stabilising the starting material, but there is a more delicate balance with acid anhydrides, which are similar in electrophilicity to aldehydes. In one important case, stabilisation in the intermediate plays a larger role in determining electrophilicity than the differences in the energy of the starting materials. In contrast to the order of electrophilicity in alkyl halides in SN1, SN2, E1 and E2 reactions (I– > Br– > Cl–>> F–), aromatic

180

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

halides are electrophilic in the opposite order.352 2,4-Dinitrofluorobenzene (4.108, X ¼ F) reacts 600 times faster with methoxide ion than 2,4-dinitrochlorobenzene, and 3100 times faster than 2,4-dinitroiodobenzene. The explanation is that the anomeric effect between the methoxy oxygen and the C—halogen bond in the intermediate 4.110 combines with stabilisation from negative hyperconjugation between the C—halogen * orbital and the cyclohexadienyl anion p system. Both interactions lower the energy more for the C—F bond than for the other halogens, whereas the overlap of the lone pair on the halogens with the p system of the starting material 4.108 is relatively small. Thus the energy picture, Fig. 4.14, is like a mirror image of Fig. 4.13. The structure of the intermediate 4.110 significantly affects the energy of the transition structure 4.109, and the activation energy for the fluoride DEF is less than that for the iodide DEI. The normal order is restored when the second step becomes rate-determining, as it does with highly activated systems. MeO OMe O2N

X NO2

O2N

4.108

4.109

O2N X 4.110

EI

EF

Fig. 4.14

X

O2N

OMe O2N

X=I X = Br X = Cl X=F

Relative energies of starting materials, transition structures and tetrahedral intermediates for nucleophilic attack on aryl halides

A striking example of modified electrophilicity is provided by the imine 4.111.353 The conjugation of the Si—C bonds (Fig. 2.18) with the C¼N p system raises the energy of the LUMO, making it less electrophilic than an ordinary imine. Furthermore, since the Si—C bonds are X-substituents, they raise the coefficient on the imine carbon atom in the HOMO and reduce it in the LUMO (Fig. 2.7), further decreasing the electrophilicity, since that depends upon the coefficient of the atomic orbital as well as on the energy. The net result is that the imine 4.111 is a stable compound, unlike other methylene imines, which normally polymerise before they can be isolated. N

SiMe3 SiMe3

4.111

4.4.2 Tetrahedral Electrophiles Some of the same features affect the electrophilicity of tetrahedral electrophiles undergoing SN2 reactions. Thus some donor substituents on the carbon being attacked reduce the electrophilicity of alkyl halides, where the order of reactivity is methyl > ethyl > isopropyl > tert-butyl. This is usually explained, of course, as a

4 IONIC REACTIONS—REACTIVITY

181

consequence of steric hindrance to attack on the more substituted carbon atoms, but it has also been explained354 by making allowance for the change of the coefficient on the carbon atom. The same hyperconjugation which lowers the energy of the LUMO of the C—Br bond in tert-butyl bromide more than that in methyl bromide also reduces the coefficient on carbon (because the new orbital is now delocalised over more atoms), and at the same time lowers the overall energy of the starting material. These effects on the coefficients and the energy may contribute to the lower reactivity (in SN2 reactions) of tert-butyl bromide relative to methyl bromide. Z-Substituents and C-substituents conjugated to the site of attack increase the rates of SN2 reactions.355 The Z-substituent, as it does with -dicarbonyl systems, may partly operate by raising the energy of the starting material, but most probably both the C- and Z-substituents are primarily operating to lower the energy of the transition structures 4.112 and 4.113, respectively.356 The forming and breaking bonds have four electrons in total and any delocalisation of these in allylic overlap (see pp. 23–28 and 72) lowers the energy of the transition structure in a way that has no counterpart in the reactions on trigonal electrophiles. This explanation is dramatically supported by the difference in the rate of nucleophilic attack on the benzyl sulfonium salts 4.114 and 4.115, which react at relative rates of 8000:1. Whereas the open-chain system 4.114 can easily allow the forming and breaking bonds to overlap with the p system of the benzene ring, the cyclic sulfonium salt 4.115 cannot.357 Nu

Nu

Nu Et O

X

Bn

X 4.112

S

S

Nu

Et

4.113

4.114

Cl

4.115

N3

R

N3

R MeCN, H2O 4.116

4.117

X-Substituents can also accelerate SN2 reactions,358 even though the transition structure seems to have an excess of electrons at the site of substitution. The transition structures can adjust to take energetic advantage from more or less stretching of the C—X bond, with the extremes being the perfect SN2 and perfect SN1 reactions. For example a series of ring-substituted secondary benzyl chlorides 4.116 react with azide ion to give the azide 4.117 in an SN2 reaction, as shown by the first-order dependence upon the concentration of azide ion and inversion of configuration. The Hammett þ value of –2.9 indicates that electron-donating substituents R are speeding it up.359 Evidently, a feature that energetically helps the stretching of the C—X bond, such as an X-substituent on the carbon undergoing attack, or conjugated with it in a substrate like the chloride 4.116, lowers the energy of the transition structure, and speeds up the reaction. Thus we have the unusual feature that both X- and Z-substituents can accelerate reactions that are formally SN2.360 X-Substituents, of course, easily accelerate SN1 reactions like the solvolysis of the chloride 4.116 in aqueous acetonitrile, which has a larger Hammett þ value of –5.6, typical for an SN1 reaction with the formation of the cationic intermediate accelerated by X-substituents (see p. 76), while Z-substituents slow down their formation. The better the leaving group, the more electrophilic an alkyl halide or alkyl sulfonate, with alkyl iodides and trifluoromethanesulfonates exceptionally reactive. Several factors are at work here: the strength of the

182

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

C—X bond (weak for C—I), its degree of polarisation (high for C—OTf), the energy of the (solvated) nucleofugal group as measured by the pKa of its conjugate acid (low for HOTf, making triflate a good nucleofugal group), the LUMO energy (low for C—I), and the coefficient on carbon in the LUMO. Not surprisingly, a many-parameter equation would be needed to measure electrophilicity, and most important to measure change as the solvent and nucleophile changes, as we shall see. 4.4.3 Hard and Soft Electrophiles Except for the last paragraph, the discussion above has been about electrophilicity in general, or within a related group of electrophiles. However, the picture is not straightforward when we make comparisons from one group of electrophiles to an unrelated group, or when the nucleophile is changed. Electrophiles can be hard or soft—the hardest electrophiles are small, charged and have a relatively high-energy LUMO, and soft electrophiles are large, have little charge and have a conspicuously low-energy LUMO. The proton, because of its size and charge is very hard. Tables of acidity (pKa values) give a rank order of thermodynamic electrophilicity of protons attached to various ligands, but the only extensive tables related to electrophilicity for other electrophiles are the lists of hardness in Tables 3.2, 3.4 and 3.5, where we see that large metal cations like Hg2þ are relatively soft, in spite of their charge. p-Bonded species like C¼C double bonds conjugated to Z-substituents are inherently soft, with low-energy LUMOs, as are other uncharged reagents like methyl iodide, sulfenyl halides and iodine. It is not therefore possible to compare in any absolute sense the electrophilicity of a soft electrophile like iodine and a hard one like an acid chloride. There is a special problem in comparing the hardness and softness of alkyl halides and carbonyl compounds, the two most common carbon electrophiles. In SN2 reactions, the bond being broken is a  bond, with a LUMO higher in energy than that of a C¼O p bond, yet alkyl halides are generally softer than carbonyl compounds. One big difference is that S N2 reactions are exothermic (otherwise they would not take place) and the transition structure is early, resembling the starting materials more than the product, whereas addition to a carbonyl group is often endothermic, with a transition structure more like that of the tetrahedral intermediate. Arguments about the importance or otherwise of orbital interactions, and of hardness and softness, apply more effectively to SN2 reactions than to carbonyl additions, and so the anomaly may be illusory. When the halogen is low in the periodic table, like bromine or iodine, it is not very electronegative. The C—X bond is not strongly polarised, the overlap is poor, the LUMO energy low for a  bond and the charge on the carbon atom is small. With both frontier orbital and charge effects small (see p. 156), it is a soft electrophile. In attack on a carbonyl group, the electrophilic carbon has two bonds from carbon to an electronegative atom, and therefore has a greater electron deficiency on carbon. Since it is a p bond, it also has a relatively low-energy LUMO. With both charge and frontier orbital effects large (see p. 156), it is a hard electrophile. Carbonyl groups are well known to be hard relative to alkyl halides in spite of the lower energy of the LUMO—they are notably more responsive and better correlated to the basicity of the nucleophile. However, for all the endothermicity of their reactions, carbonyl groups are responsive to the frontier orbital terms; thus a sulfur nucleophile is about 100 times more nucleophilic towards a carbonyl group than is an oxygen nucleophile of the same basicity.361 Nevertheless, it remains seemingly anomalous that an alkyl halide undergoing nucleophilic displacement should be a soft electrophile, when a carbonyl group undergoing nucleophilic addition is relatively hard. The anomaly is made more disturbing if we are wedded to the idea of hybridisation (see pp. 15–17). An examination of the full set of lower-energy molecular orbitals of methyl chloride (Fig. 1.59) may make the anomaly less disturbing. Were we to use hybridised orbitals (Fig. 1.59b), we should have an antibonding orbital (sp3*CCl) which is at least as much antibonding as the bonding orbital (sp3CCl) is bonding. However, this antibonding orbital is no more the LUMO than CCl in Fig. 1.59a is the HOMO. The latter is only one of the bonding orbitals, and a proper measure of the total C—Cl bond strength would come much lower in

4 IONIC REACTIONS—REACTIVITY

183

energy than CCl, and would correspond to that of the bonding hybrid orbital (sp3CCl in Fig. 1.59b). There will be a complementary situation among the antibonding orbitals. This imbalance, in which the true LUMO (*CCl in Fig. 1.59a) is lower in energy than the antibonding hybrid orbital (sp3*CCl in Fig. 1.59b), is not found in the corresponding p bond of a carbonyl group, because that orbital is not made up of hybridised orbitals. Thus, in a comparison of alkyl halide chemistry with carbonyl chemistry, the use of hybridisation appears to exaggerate how high the energy of the LUMO of the carbon-halogen bond is. The energies of the LUMOs of the four methyl halides are also ranked in an order that might not at first sight be easy to guess. In setting up the orbitals CX and *CX like those in Fig. 1.59a, we would look at the interaction of the px orbitals on carbon and the px orbital on each of the halogens, since this is the major contribution to  bonding. Since the halogens are ordered with the most electronegative having the lowest energy, we might expect that the *CX orbitals would be in the same order. However, the overlap integral  between the px orbital on the halogens and the px orbital on carbon is much smaller for iodine than for the smaller fluorine. The net result, counter intuitively, is that the LUMO energies of the alkyl halides fall in the order MeF > MeCl > MeBr >MeI. The iodide is the most reactive and the most soft.362 Even within a group of very similar electrophiles, all soft like primary alkyl halides undergoing SN2 displacement, the scale of electrophilicity is not constant. Thus, in the relative rates of the two reactions 4.118 and 4.119, the iodide (X ¼ I) reacts 1674 times faster with the aniline than with ethanol (kArNH2 =kEtOH ), but the p-bromobenzenesulfonate 4.118 (X ¼ OBs) reacts only 184 times faster. The other alkyl halides fall in between.363 The amine is the softer nucleophile, since nitrogen is less electronegative than oxygen, and the iodide is the softest and the p-bromobenzenesulfonate the hardest of the electrophiles. These results could equally have been discussed as examples of the difficulty of setting up a single scale of nucleophilicity, since they are related to those for O- and C-alkylation of enolates (see p. 160), and to the whole discussion of ambident reactivity (see pp. 157–167)

X

X

k

/k

ArNH2

4.118

4.5

H2N

Cl

X=I X = Br X = Cl X = OBs

EtOH

1674 694 639 184

4.119

EtOH

Ambident Electrophiles

The attack of a nucleophile on a conjugated system is susceptible to the same kind of analysis that we gave to the attack of an electrophile on a conjugated system. In most cases, all the molecular orbital factors, both those affecting the product stability and those in the starting materials, point in the same direction. We use the LUMO of the conjugated system (and the HOMO of the nucleophile, of course) as the important frontier orbitals, as in Fig. 4.15, which shows electrophilic reactivity at the site (or sites) where the arrow points for a range of carbon electrophiles.364 In each case, there is a high coefficient of the LUMO at the site of attack; each of them also has a high total electron deficiency at this site; and, with the possible exception of pyridine 4.124, the tetrahedral intermediate obtained from such attack is lower in energy than attack at the alternative sites. 4.5.1 Aromatic Electrophiles365 4.5.1.1 The Pyridinium Cation. The pyridinium cation 4.126 is even more readily attacked by nucleophiles at C-2 and C-4 than pyridine 4.124. Looking at the product side of the reaction coordinate, the linearly

184

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

0.425 0

0.440

0.470

–0.311

0.102

–0.063

0.220

–0.263 –0.091

4.120

–0.290

–0.511

4.121

0.316

4.122 O

0.454 0.749 –0.190

0.521

–0.127

–0.351

–0.383

0.280

–0.232

N –0.418

0.684

4.123

4.124

4.125

Fig. 4.15 LUMOs of some carbon electrophiles and the sites of nucleophilic attack upon them

conjugated intermediate 4.127, which also benefits from an anomeric effect if the nucleophile is an electronegative heteroatom,366 is lower in energy than the cross-conjugated intermediate 4.129, and will therefore be the product of thermodynamic control. Since this step is neither strongly endothermic nor always reversible, the orbitals and the charge distribution in the starting material may be important when the reaction is kinetically controlled. The total p electron deficiency 4.126270 at C-2 of þ0.241 and at C-4 of þ0.165 indicates that charge control (in other words with hard nucleophiles) will lead to reaction at C-2. This is the case with such relatively hard nucleophiles as the hydroxide ion, amide ion, borohydride ion and Grignard reagents.367 (0.165+)

Nu–

4 3 2

products Nu

(0.241+)

N

N

Me

Me

4.126

4.127 H Nu

H

Nu– = OH–, NH2–, BH4–, R(MgBr)

Nu

–

H

products N

N

Me

Me

4.128

4.129

H

EtO2C

CO2Et

O

Nu– = CN–, S2O42–,

,

N Me

4.130

However, if we look at the LUMO (see p. 60), we find that it has the form 4.128, similar to 4* of benzene, but polarised by the nitrogen atom. The polarisation reduces the coefficient at C-3, and the coefficient at C-4 is larger than that at C-2, as can be seen from the simple Hu¨ckel calculation for pyridine itself 4.124,18 which gives LUMO coefficients of 0.454 and –0.383, respectively, and an energy of 0.56 (compare benzene with 1 for this orbital). Thus, soft nucleophiles should attack at C-4, where the frontier orbital term is largest. Again this is the case: cyanide ion, bisulfite, enolate ions, and hydride delivered from the carbon atom of the Hantsch ester 4.130 react faster at C-4 than at C-2.368

4 IONIC REACTIONS—REACTIVITY

185

4.5.1.2 ortho- and para-Halogenonitrobenzenes. It is well-known that ortho- and para-halogenonitrobenzenes are readily attacked by nucleophiles, as we saw in Fig. 4.14. The first step is usually ratedetermining. Product development control should therefore have ortho attack faster than para attack, because the intermediate 4.131 with the linear conjugated system will be lower in energy, other things being equal, than the intermediate 4.132 with the cross-conjugated system. The Coulombic term will also lead to faster reaction at the ortho than at the para position. The frontier orbital term, however, should favour attack at the para position. Thus the ESR spectrum of the benzyl radical (see p. 171), which has the odd electron in an orbital which ought to be a model for the LUMO of a Zsubstituted benzene, shows that there is a larger coefficient in the para position than in the ortho. Nu Cl O

Nu

Nu

Cl O

N O

O

N O 4.131

Nu Cl

Nu

Nu

Cl N

N O

O

N

O

O

N

O

O

O 4.132

There is some evidence which supports this analysis (Fig. 4.16).369 (a) With a charged activating group, as in the diazonium cations 4.133 and 4.134, attack at the ortho position is faster than attack at the para position HO

HO

F

F 10 times faster than

N

MeO Cl

4.135

N

N 4.134

4.133

MeO between 1 and Cl 4 times faster than Z Z Z = NO2, CN, 4.136 SO2Me and COMe

N

N

N

N

N

Cl

250 times Cl faster than NO2

O2N

4.137

Nu Y

Nu– = PhS– or MeO–

O2N

N 4.138

O

kPhS – kMeO –

increases F < Cl < Br < I

O

Fig. 4.16

Relative reactivity of halogenonitrobenzenes

186

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

because of the relatively large Coulombic contribution. With the uncharged activating groups in the compounds 4.135 and 4.136, the order is the other way round. (b) In the latter reaction with the nitro compound (Z ¼ NO2), with the neutral (and hence softer) nucleophile DABCO 4.137, the preference for para attack is enhanced. (c) The ratio of the rates at which PhS– and MeO– react with 2,4-dinitrohalogenobenzenes 4.138 is highest for the iodide and lowest for the fluoride. The former will make the Coulombic term less important, and the latter will make it more important.370 (d) When the rate of the second step is not rate-determining, the aryl fluoride is more readily attacked than the corresponding aryl chloride, bromide and iodide. As explained on p. 180, this can be explained by the anomeric stabilisation afforded to the intermediate, but we can add to it a Coulombic contribution from the electronegative halogen. The data in Table 4.8 show that the degree to which the fluoride is the more reactive, is greatest for the harder nucleophiles; but the story is complicated, because the second step of the reaction, the loss of the fluoride ion, does become rate-determining with some weak nucleophiles. Table 4.8 Effect of the nucleophile on the relative rates of attack on the fluoro and chlorodinitrobenzenes Nucleophile

N:

NO2

O

N

0.11

(H2N)2C=S:

Y

O

O2N

3.26

PhS– H3N: MeO–

33 460 890

O–

3160

hard soft

Nu

kF/kCl

4.138 NO2

Y = F or Cl

The ease with which fluorine can be displaced from benzene rings is such that it does not always need activating groups like nitro to stabilise the intermediate anions—oligofluorobenzenes can undergo substitution reactions. An attempt,371 using frontier orbital theory, to explain the selectivity with which one of several fluorine atoms is displaced has been contested in favour of a more general electrostatic analysis.372 4.5.2 Aliphatic Electrophiles 4.5.2.1 a,b-Unsaturated Carbonyl Compounds. Most nucleophiles attack ,-unsaturated ketones faster at the carbon atom of the carbonyl group (e.g. 4.140 ! 4.139) than at the  position. Attack at the  carbon (e.g. 4.140 ! 4.141) is commonly the result of a slower, but thermodynamically more favourable, reaction. For this mode of reaction to show up, the first step must be reversible. Conjugate attack is therefore most straightforward when the nucleophile is a well-stabilised anion, making the first step easily reversible, as it is when the nucleophile is a cyanide ion.373 HO

CN KCN, K2CO3, ≤15 °C

O

O

KCN, K2CO3, >15 °C NC

4.139

4.140

4.141

4 IONIC REACTIONS—REACTIVITY

187

Similarly, the simple lithium enolate 4.143 reacts with cyclohexenone at –78 C to give the product 4.142 of direct attack, but warming the reaction mixture to room temperature allows this step to revert to the starting materials, and they then form the thermodynamically more stable product 4.144 of conjugate attack.374 -Dicarbonyl enolates, commonly used in Michael reactions, usually do not allow the isolation of the product of direct attack, since the first step is even more easily reversible in such cases. O

CO2Me

O

–78 °C

O

OMe

O

MeO2C

+ > –78°C 4.142

4.143

4.144

Taking the most simple ,-unsaturated carbonyl compound, acrolein, even the simple Hu¨ckel calculation used in Fig. 2.3 shows that, while the total p-electron deficiency is greater at the carbon atom of the carbonyl group, the coefficient of the LUMO is larger at the  position. A better calculation than that used in Fig. 2.3 gives the frontier orbital coefficients and energies in Fig. 4.17.375 We can therefore expect that, if any nucleophile is going to attack directly at the -carbon atom, it will be a soft nucleophile, responsive to the frontier orbital term.376 This is borne out by the observation that radicals, which are inherently soft (Chapter 7), add at the  position, and that the relatively soft Grignard reagents are apt to give more conjugate addition than the relatively hard organolithium reagents.377 This simple analysis leaves out of consideration the fact that many additions to ,-unsaturated carbonyl compounds need or take advantage of coordination to the oxygen atom by a metal cation or a proton, or even just a hydrogen bond. This is especially true for hydride or carbon nucleophiles. The orbitals of the reactive species are therefore more like those of protonated acrolein, for which the LUMO has the larger coefficient on the carbonyl carbon, not the  position (Fig. 4.17). Thus even soft nucleophiles can be expected to attack directly at the carbonyl group when Lewis or protic acid catalysis is involved. It may be that the different degree of regioselectivity shown by Grignard and lithium reagents is largely a consequence of differences in the effectiveness of the coordination by the metal—with lithium the more powerful Lewis acid—than in differences in the hardness and softness of the nucleophiles. The effect of the Lewis acid on regioselectivity is seen with lithium aluminium hydride reacting with cyclohexenone—in ether, the ratio of direct to conjugate attack is 98:2 but if the lithium ion is sequestered by a cryptand, the selectivity changes to 23:77.378 0.51

–0.39

LUMO

*

O

2.5 eV

3

0.59

–0.48

0.48

HOMO

–0.58

LUMO

*

O

–7 eV

3

0.60

O

–14.5 eV 2 0.58

0.37

–0.09

0.65

–0.30

HOMO

–0.54

O

–23.5 eV 2

O

0.53

O

H

H

–0.70

H

–0.10

H

H

Fig. 4.17

Frontier orbital energies and coefficients for acrolein and protonated acrolein

188

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

Moving to ,-unsaturated esters, hydroxide ion379 and alkoxide ion380 (hard nucleophiles) react with ethyl acrylate 4.145 by direct attack at the carbonyl group to give ester hydrolysis and ester exchange, respectively, whereas the -dicarbonyl enolate ion 4.146 (a softer nucleophile) undergoes a Michael reaction.381 There is no certainty in this latter reaction that the attack of the enolate anion on the carbonyl group, in a Claisen-like condensation, is not a more rapid (and reversible) process.382 O

RO

O

O

(R = H, alkyl)

O

O

O

+H+

OEt 4.145

OEt

OEt

OR EtO

4.145

O

EtO

O

4.146

The ease with which sulfur nucleophiles add to ,-unsaturated esters 4.145 ! 4.147 is also ambiguous: thiolate anions do not react with esters to give thioesters 4.148, because the equilibrium lies in the other direction; so we cannot tell what are the relative rates of attack at the two sites of an ,-unsaturated ester, although it is likely that  attack is kinetically controlled. O PhS

O

PhS– OEt

OEt

4.147

O

EtO–

SPh

PhS–

4.145

O

4.148 O

NH3 OMe

H2N

4.149

OMe 4.150

4.149

MeO2C

N H

CO2Me

4.149

MeO2C

N

CO2Me CO2Me

4.151

4.152

One case, however, is clear—ammonia and amines do react with ordinary esters to give amides, and it is known383 that the attack at the carbonyl group is rate-determining and effectively irreversible above pH 7. Ammonia (neutral and therefore a relatively soft nucleophile) reacts in methanol with methyl acrylate 4.149 kinetically at the  position to give the primary amine 4.150, and reaction continues in the same sense to give successively the secondary and tertiary amines 4.151 and 4.152.384 The more a carbonyl group is like that of protonated acrolein (Fig. 4.17), the more likely is it that all nucleophiles will attack directly at the carbonyl carbon atom. In agreement with this perception, and in contrast to its behaviour with methyl acrylate, ammonia reacts with acryloyl chloride 4.153, which has a very electrophilic carbonyl group, at the carbonyl carbon atom to give acrylamide 4.154.385 O

NH3 Cl

4.153

O NH2 4.154

4 IONIC REACTIONS—REACTIVITY

189

We have just seen that making the carbonyl group more electrophilic increases the probability that reaction will take place directly at the carbonyl group. A corollary is that reducing the electrophilicity, as happens when we have an imine in place of the carbonyl group, increases the probability of getting conjugate attack. An example of the delicate balance possible with ,-unsaturated imines is seen in the two imines 4.155 and 4.156, which show conjugate and direct attack, respectively, simply by adjusting the degree of electron withdrawal from the substituent attached to the nitrogen atom. This pattern is seen with organolithium nucleophiles, with which direct attack at the imine carbon is most unlikely to be reversible, and the selectivity correlates with the calculated LUMO coefficients.386 N

C6H11-c

–0.593

0.514

0.531

4.155

Ph

N –0.426

4.156

The reduction of ,-unsaturated carbonyl compounds by metal hydrides, and the similar addition of organometallic carbon nucleophiles, is a complicated story.387 It is more common than not, in each case, to get direct attack at the carbonyl group, but delivery of hydride to the conjugate position is well known. The proportion of conjugate reduction of ,-unsaturated ketones by hydrides increases approximately in the order of increasing softness: aluminium hydrides less than boron hydrides less than the carbon hydride which is the active species 4.157 involved when lithium aluminium hydride is used in pyridine.388 Hydride delivered from carbon in the Meerwein-Ponndorf reduction is constrained by the six-membered ring transition structure 4.158 to give direct reduction.389 Conjugate reduction is avoided, however electronically favourable it might be, because it would involve an eight-membered ring. R Al

N

H

O

R Al

O

H H

O 4.157

4.158

These trends agree with the frontier orbital analysis. In particular, the delivery of hydride from carbon breaks a relatively unpolarised bond, making the hydride notably soft, as we saw earlier in its capacity to attack pyridinium salts preferentially at the 4-position. The metal hydrogen bond will be more polarised, and metal hydrides should therefore be harder. Similarly, the delivery of hydride from boron will make it softer than when it is delivered from the more electropositive metal, aluminium. It also seems that, among ,unsaturated carbonyl compounds, the susceptibility to conjugate reduction increases in the sequence: ketones < esters < acids < amides; but there are too few examples to be sure. With two activating substituents, as in the ester 4.159, conjugate reduction (and conjugate addition of carbon nucleophiles) is fast and almost always observed with any nucleophile.390 The stability of the conjugated enolate product 4.160, and Coulombic and frontier orbital factors, all readily explain this observation. Nu

CN OEt

Nu

CN

O 4.159

OEt O

4.160

190

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

4.5.2.2 Allyl Halides. The allyl halide system is related to that of , -unsaturated carbonyl compounds, but shows a number of differences. In bimolecular reactions, direct displacement of the halide ion (SN2) almost always occurs, and conjugate attack (SN20 ) is rare. Indeed, this is a contentious issue, for there is little evidence for any completely concerted SN20 -type of reaction.391 If an ion pair, such as 4.161, is the reactive species, we can see that charge control would strongly favour direct displacement, and we already know that the presence of the double bond stabilises the transition structure 4.112. However, attack at the ‘p bond’ may be preferred if frontier orbital control becomes more important, although it is hard to specify what exactly the orbitals are, in an allyl cation made unsymmetrical by ion pairing at one end of the conjugated system. It is perhaps significant that the few examples of conjugate reaction which have been observed are with strikingly soft nucleophiles such as phenylthioxide ion,392 cyanide ion, azide ion, and secondary amines,393 all in nonpolar solvents, and preferably with some steric hindrance at the  position. Cl

Nu–

Nu

SN2'

Cl (+)

(–)

Nu–

Nu

SN2

4.161

Organocuprates and a few other carbon nucleophiles sometimes react with allylic halides (or acetates) to give the product of what looks like an SN20 reaction. However, the mechanism is completely different— preliminary coordination by the copper or other transition metal to the C¼C p bond is the first step, and the coordination of the copper changes from -2 to -1 or -3 before a reductive elimination step establishes the C—C bond.394 Each of these steps affects the overall regiochemistry (and the stereochemistry discussed in the next chapter), which may look like an SN20 or an SN2 reaction, while mechanistically being neither. When the allylic system carries X-substituents, and the solvent is polar, the reaction may take a unimolecular path 4.162 ! 4.164, and the reactions are then SN1 and SN10 . The regioselectivity will be wholly determined by thermodynamic factors if the only available nucleophile is a good nucleofugal group, with the product 4.164 having the more-substituted double bond usually favoured. This selectivity will be enhanced by the greater steric hindrance usually present if the nucleophile is bonded to the more substituted site, and a corollary is that the thermodynamically less stable isomer 4.162 is the more reactive (by a factor of about 3 in ethanol at 25 C in this case).395 Cl

4.162

Cl

4.163

4.164

However, if the reaction is not under thermodynamic control, the regioselectivity will be determined by the coefficients and charges at the - and g-carbon atoms of the allyl cation. We can treat an Xsubstituted allyl cation as resembling an ,-unsaturated carbonyl compound. The orbitals of acrolein show us that a powerful donor substituent like an oxyanion conjugated to an allyl cation (on the left in Fig. 4.17) leads the -carbon atom (g in the allyl system) to have the higher coefficient. However, the

4 IONIC REACTIONS—REACTIVITY

191

donor substituent in protonated acrolein (on the right in Fig. 4.17) is a hydroxyl group, and it leads to a higher coefficient on the carbonyl carbon (equivalent to the  position in the allyl system). An allyl cation having a donor less effective than a hydroxyl ought therefore to have a larger coefficient in the LUMO at the carbon atom adjacent to it than at the other end. As it happens, the simple device we used (see pp. 70–86) to deduce the pattern of coefficients in substituted alkenes, does not work for substituted allyl cations. We would mix the orbitals of an allyl cation (equal on C and Cg) with those of 3* of butadiene (small on C and large on Cg). This covers the situation for a powerful donor, but no amount of mixing creates a LUMO with a larger coefficient on C than on Cg. In practice, kinetic control with a soft and not too large nucleophile leads to attack at the  carbon, especially as we are usually dealing with less powerful donor substituents than a hydroxyl. The methyl groups in the prenyl cation 4.163 are not powerful donors, and yet, when either of the chlorides 4.162 or 4.164 is solvolysed in water, under conditions that do not equilibrate the products, the major product (85:15) is the tertiary alcohol 4.165, showing that capture at the more sterically hindered site in the cation 4.163 is indeed faster than attack at the primary position giving the alcohol 4.166.395 OH

H2O

H2O

85 4.165

HO

15 4.163

4.166

A more extended version of the same idea accounts for the regioselectivity of attack by cyanide ion on the cation 4.168, derived from furylmethyl chloride 4.167, which leads, counter to the thermodynamics, to the product 4.169 of an SN100 reaction, and hence to the re-aromatised product 4.170.396

NC–

H2O Cl O 4.167

O 4.168

+H+ NC

O 4.169

–H+

NC

O 4.170

4.5.2.3 Unsymmetrical Anhydrides. Unsymmetrically substituted phthalic and maleic anhydrides show some curious selectivities. The selectivity for attack at one carbonyl group rather than the other is large enough to be useful to synthetic chemists, and it demands some kind of explanation. Nucleophilic attack on the carbonyl groups of the maleic anhydrides 4.171 by lithium aluminium hydride is completely selective for attack at C when R is a methoxy group, and still quite high (88:12) when R is a methyl group. Both methoxy and methyl are X-substituents conjugated to the  carbonyl, and ought to reduce the coefficient of the atomic orbital at the  site. This makes the  site the more electrophilic by default, in spite of the greater steric hindrance there. Calculations support this argument with larger coefficients at C in the LUMO for methoxy and methyl, and with the difference between them reduced for the less powerful X-substituent.397 However, when the attacking reagent is larger, as with a phosphorus ylid, the selectivity is in favour of attack at C when R is a methyl or phenyl group (: 6:94 and 0:100, respectively), although still in favour of attack at C when R is a methoxy group (: 100:0).398 It appears that the intrinsic (orbital controlled) reactivity at C is preserved with the better X substituent, but steric effects override it with the others. The fact that the methoxy group is quite as effective as it is may also be because it can help, by coordination, to deliver the reagent to the nearer carbonyl group.

192

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

R=MeO R=Me R=Ph

0.39 0.36 0.22

–0.34 –0.35 –0.25

O

O

LUMO coefficients c c

R

LUMO coefficients c c

O 4.171

O

R=MeO –0.26 –0.329 R=Me R=NO2 –0.21

O

0.30 0.328 0.08

O

R 4.172

This simple hope is not much supported by the results with the anhydride 4.172. The X-substituents, conjugated to the  carbonyl, ought to make the reaction intrinsically selective for attack at C , and the Z-substituent for attack at C. The coefficients in the LUMO match this expectation, except for R ¼ Me, when the values are barely different. In spite of the fact that C is still the sterically more hindered carbonyl group, attack is selectively at C for all three substituents (NaBH4, : 87:13, 57:43 and 83:17, respectively).399,400 The : ratio is suspiciously dependent upon the solvent, coordination may be playing a part here too, and there is a further complication in both series. For nucleophilic attack on a carbonyl to take place, coordination to the oxygen atom by a Lewis or protic acid is often necessary, as we have already seen with ,-unsaturated ketones. This means that there is a pre-equilibrium step between the bare carbonyl compound, used in the calculations, and the reactive species. There will be a higher concentration of the intermediate with the metal or other catalyst coordinated to the more basic of the two carbonyl groups, which will be the  carbonyl in 4.171. However, when the coordination is to the less basic carbonyl group, it will create a more reactive species. The balance of all these effects is hard to predict, and the overall story is too complicated for simple analysis. This is not an uncommon situation, and care must be taken in any analysis of subtle steric and electronic effects like those operating here and in much of the discussion about enones above. The story is even more remarkable for unsymmetrical succinic anhydrides 4.173, where hydride reduction takes place with surprising selectivity at the obviously more hindered carbonyl group, giving the lactones 4.174 and 4.175 in a ratio of 95:5.399,401 LUMO coefficients c

c

0.599

–0.591

LiAlH4 or NaBH4 O

O 4.173

O

+ O 4.174

O

O 95:5

O 4.175

The electronic difference between the two carbonyl groups is that C has a hyperconjugative interaction with a CMe 2 group, and C with a CH2 group. Which has the larger hyperconjugative effect is an ongoing debate—as mentioned already on p. 86—the hydrogen atom is more electropositive than carbon, and so the bond is more polarised, and better able to stabilise electron deficiency. On the other hand, the methyl group has a greater stock of electrons that can participate in delocalisation. The calculation in this case gave C  the larger coefficient in the LUMO, implying that C—H is the better at hyperconjugation, and agreeing with the experimental result. With Grignard reagents, when steric effects are more important, attack takes place unexceptionably at the less hindered site, C, and when the two substituents are chlorine atoms, effectively Z-substituents by negative hyperconjugation, attack is completely selective for C. 4.5.2.4 Unsymmetrical Epoxides. Epoxides are tetrahedral-carbon electrophiles like alkyl halides, except that the strain in the three-membered ring adjusts the bond angles further away from perfectly tetrahedral.

4 IONIC REACTIONS—REACTIVITY

193

Nevertheless, the factors that affect the electrophilicity of alkyl halides operate here, and lead to synthetically useful levels of selectivity. At one extreme, in the presence of Lewis or protic acid, the epoxide opens towards the side that gives the more stabilised cation, which is usually the more substituted side, leading to regioselectivity appropriate to an SN1 reaction. At the other extreme, in the absence of Lewis or protic acid, the reaction is SN2 in character, and takes place on the side best able to support an SN2 transition structure, which is usually the less substituted side. A simple example is the opening of 1-butene oxide 4.176 with chloride ion, which gives each of the chlorohydrins as the major product, 4.177 in acidic and 4.178 in neutral conditions.402 Cl

Cl–

O

OH OH

Cl

+

pH 4.5-7.0 4.176

4.177

77:23 at pH 4.5 16:84 at pH 7.0

4.178

In more detail in the acid-catalysed reactions, the cation is not always fully formed, but is instead captured by the nucleophile with overall inversion of configuration, appropriate to an SN2 reaction. Effectively the protonated oxygen shields the surface from which it departs, but the transition structure has, nevertheless, substantial cationic character at the carbon atom undergoing attack. If the epoxide has a Z-substituent, as in the amide 4.179, the Lewis acid catalysed opening avoids the formation of a destabilised cation adjacent to the carbonyl group (see pp. 77–78). In contrast, in the absence of Lewis acid, the Z-substituent encourages opening adjacent to itself (see p. 181).403 A particularly intriguing manifestation of the effect of a Z-substituent is the counter-steric opening of silyl epoxides like 4.180, which cleanly opens adjacent to the silyl group.404 A silyl group is a Z-substituent by virtue of the negative hyperconjugation of the Si—methyl bonds (see pp. 79–80) conjugated to the breaking and developing bonds. A C¼C double bond stabilises both the SN1 and SN2 transition structures, and a C-substituent encourages opening at the allylic or benzylic position, both with and without acid catalysis, as in the uncatalysed opening of styrene oxide 4.181.405 SPh

PhSH, Ti(OPri)4

O

NMe2

CH2Cl2

O

91:9

NMe2

OH OH

PhS–, THF

4.179

O

O NMe2

7:93

SiMe3

LiAlH4

N3

O

SiMe3 H

SPh

NaN3

OH

O Et2O 4.180

OH 4.181

In between the extremes, relatively weak Lewis acids like the surface of alumina,406 or trimethylsilyl chloride,407 accelerate the opening of an epoxide, without necessarily having it take place to the more

194

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

substituted side, and several organometallic nucleophiles also show this feature. Thus organoaluminium reagents are more likely to have the alkyl group attack at the more substituted side of propene epoxide 4.182,408 whereas Grignard reagents and cuprates attack at the less substituted side.409 The aluminium is the more powerful Lewis acid, and the transition structure adjusts to stretching the bond to the more substituted side in that case. Me3Al OH

EtMgCl O

OH

4.182

4.5.2.5 Arynes. o-, m- and p-Benzynes are all possible, all three have been implicated in various reactions, and all three have been studied at a high level of theory.410 The most commonly encountered, however, is obenzyne, which we shall call benzyne from now on. The two p orbitals are bent apart, making their interaction considerably less than the interaction of two p orbitals in forming the p bond of ethylene. The HOMO is therefore raised and the LUMO lowered in energy relative to the frontier orbitals of an alkene or a linear alkyne. The most common reactions of benzynes are cycloadditions, which will be dealt with in Chapter 6, and nucleophilic addition, made favourable by the low energy of the LUMO. Strikingly, arynes do not normally attack electrophiles, which ought also to be favourable because of the raised energy of the HOMO. Although this step is probably exothermic, the most likely explanation can be found on the product side of the reaction coordinate. The product of nucleophilic attack on a benzyne is a phenyl anion, and the product of electrophilic attack a phenyl cation. The former is well known—trigonal anions, having a more exposed nucleus, are stabilised relative to tetrahedral anions, and they are under no particular strain from being bent. This is one of the reasons why acetylenes in general react more readily than alkenes with nucleophiles.411 However, trigonal cations like the phenyl cation are high in energy, and the bending in them raises their energy even more above the already high energy of a digonal cation. The high energy of a digonal or trigonal cation is probably the main reason why acetylenes in general are less reactive than alkenes towards electrophiles. Looking at the starting material side of the reaction coordinate, it has also been suggested, both for benzyne reactions and for acetylene reactions in general, that bending an acetylene lowers the energy of the LUMO much more than it raises the energy of the HOMO because of bonding interactions between the p* and two * orbitals. Mixing these orbitals in lowers the energy of the LUMO, but there is no significant counterpart affecting the energy of the HOMO.412 The orbital referred to as the HOMO in the discussion above is not actually the HOMO in benzyne—it is so little raised in energy that one of the benzene p orbitals is the HOMO. To be ambident, a benzyne must be unsymmetrical, and the regioselectivity will be determined by the electronic and steric effects of the substituent. A major factor is the relative stability of the regioisomeric products, with the benzyne 4.183 giving the lithium intermediate 4.184,413 and the benzyne 4.185 giving the lithium intermediate 4.186.414 These two substituents are both excellent at stabilising the neighbouring C—Li bond, the former by coordination, and the latter by conjugation between the C—F bond and the C—Li bond. Looking at the starting material side of the reaction coordinate, which ought to be important, since it is an exothermic reaction, the C—F bond is a Z-substituent on the benzyne triple bond. Using the simple device we used to deduce the pattern of coefficients in substituted alkenes (see pp. 70–76), we can argue that the C—F bond has some of the character of a cation on carbon 4.187, in which the empty p orbital will be conjugated to the in-plane bent p bond. The LUMO will resemble that of an allyl cation, and will therefore have the larger coefficient on C-3 4.188. Finally, C-3 will also be the site with less steric hindrance, but it is clear from cycloaddition evidence415 that steric hindrance at C-2 is not the reason why nucleophiles attack at C-3.

4 IONIC REACTIONS—REACTIVITY

Et2N

O

195

Et2N 2

O

F

F

Li

PhSLi

3

3

SPh

4.183

Li

PhLi

2

4.184

Ph

4.185

4.186 F

F 2

has some of the character of

for which the LUMO is like that of an allyl cation 3

4.187

4.188

With an alkyl group as the substituent, the product anions are not substantially different, nor are the coefficients on C-2 and C-3. In practice, the benzyne 4.189 gives attack equally at C-2 and C-3, except when the nucleophile is larger.416 With an oxyanion substituent, and even more so with an amide anion 4.190, attack at C-2 becomes quite substantial, perhaps avoiding the formation of a C—Li bond adjacent to the anion.417 NH– 2

NH2

Li

KNH2

NH– 2

+

3

NH2

4.189

Li

KNH2

NH2

4.190

50:50

NH2 +

3

Li

NH–

Li

7:93

When the substituent is out of direct conjugation, the balance becomes more delicate, it no longer has a steric component, but it is still quite noticeable. The methyl substituent in the benzyne 4.191 slightly encourages attack by ethanol at C-3, and a chlorine in the benzyne 4.192 substantially encourages attack at C-4.418 The C—Me and C—Cl bonds are conjugated through the  bond between C-2 and C-3 to the p orbital on C-4, lowering and raising, respectively, the coefficient in the LUMO; the same conjugation destabilises and stabilises, respectively, the development of anionic charge on C-4. 61%

2 3

Cl

3

4

4.191

17%

2

4

39%

4.192

83%

Pyridynes are inherently unsymmetrical. Nucleophiles readily attack the 2,3-pyridyne 4.193 entirely at C-2.419 A calculation420 shows that the coefficient in the LUMO of 2,3-pyridyne 4.194 is larger at C-2 than at C-3. Also, the total charge distribution 4.195 is such that C-2 bears a partial positive charge. We can rationalise the polarisation of the LUMO by comparing the lobes of the p orbitals in the plane of the ring 4.194 with the p system of the allyl anion. The large coefficient in the LUMO of the allyl anion is on the central atom, just as it is here. The net result is that nucleophiles attack at C-2, because both Coulombic and frontier orbital forces favour attack at this site. They also react at the 2-position because the anion formed, a 3-pyridyl

196

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

anion, stabilised by negative hyperconjugation with the C—N bond, is more stable than the alternative 2-pyridyl anion. 2,3-Pyridyne is difficult to trap with a diene, because nucleophilic attack takes place much faster, even with relatively poor nucleophiles like acetic acid.421 For the reaction with a diene, Coulombic forces are small, and large coefficients on both C-2 and C-3 would help. Since, 2,3-pyridyne is quite strongly polarised, the ionic reaction is made easier than the cycloaddition.

Br

3

KNH2

N

N

NH3

2

N

NH2

4.193 3 –0.25

LUMO N

+0.23

N

2

total char ge distribution 4.194

4.195

Nucleophiles attack 3,4-pyridyne 4.196 at C-4 only slightly faster than at C-3, and both types of product 4.197 and 4.198 are formed.422 3,4-Pyridyne is much less polarised, because the p orbital on nitrogen is not directly conjugated with those on C-3 and C-4. It is weakly conjugated to the p orbital on C-4 through the  bond between C-2 and C-3, and the p orbital on C-3 is weakly conjugated by an anomeric effect with the bond between N-1 and C-2.420 The sum of these interactions make the coefficient on C-4 in the LUMO 4.199 slightly larger than the coefficient on C-3, and the total charge distribution 4.200 also makes C-4 the more electrophilic site. Since the polarisation is quite a bit smaller than that of 2,3-pyridyne, 3,4-pyridyne is less susceptible to nucleophilic attack and is comparatively easily trapped by a Diels-Alder reaction with dienes.421 NH2 Br

KNH2

NH2

NH3

N

+

N

N

N

4.196

4.197

4.198 +0.23

4 –0.25 3

LUMO N

N total char ge distribution

4.199

4.200

In spite of their high total energy, arynes in general are selective towards different nucleophiles; thus benzyne 4.201 selectively captures the anion of acetonitrile in the presence of an excess of dimethylamide ion.423 Nucleophilicity towards benzyne, determined by competition experiments, is in the order organolithium reagent  RS– > R2N–  RO– and I– > Br– > Cl–, which is an order of softness. The poor overlap of the p orbitals in the plane of the ring means that the LUMO of an aryne is low in energy, so much so that its

4 IONIC REACTIONS—REACTIVITY

197

interaction with the HOMO of a nucleophile may often be a first-order perturbation. This makes the aryne both electrophilic and responsive to the energy of the HOMO of the nucleophile. Since it is also uncharged, it will necessarily be a soft electrophile. NaNMe2 NMe2

NNa

slow

f ast

CN

4.201

4.5.2.6 Substitution versus Elimination. Alkyl halides react with nucleophiles by undergoing substitution or elimination, which are in competition with each other. The usual pattern is for the more substituted alkyl halides to undergo elimination more easily than substitution, and for the less substituted to undergo substitution more easily than elimination. A major factor in determining this pattern is the greater level of steric hindrance at the carbon atom of the more substituted alkyl halides, while at the same time the hydrogen atoms remain inherently unhindered on the periphery (and there are usually more of them). Other factors favouring elimination are the relief of steric compression as tetrahedral carbons become trigonal, and the lower energy of the more substituted alkenes. A more subtle factor affecting the ratio of substitution to elimination is the nature of the leaving group, and this is amenable to a treatment based on the molecular orbitals involved.424 The LUMO is the important frontier orbital for both SN2 and E2 reactions. We have already seen that this is largely localised as * for the C—Cl bond in methyl chloride (Fig. 1.59a), and we have also seen how well set up a low-lying unoccupied orbital is for elimination in ethane (Fig. 3.8). In a more realistic substrate for elimination like ethyl chloride, the LUMO is not localised on * for the C—X bond, where X is the electronegative group. We can try to deduce what the LUMO will look like from the interaction of the orbitals of a methyl group and the orbitals of a methyl group with an electronegative substituent. The orbitals of the methyl fragment are constructed from their component 2s and 2p orbitals on carbon and the 1s orbitals of hydrogen, mixed in appropriate proportions, and they make up the set in Fig. 4.18a, where we see a close similarity to the left-hand half of some of the orbitals of ethane (Fig. 1.22), except that now the drawing does not try to show the effect of mixing the 2s and 2px orbitals. We need to consider the antibonding orbitals, of which *3 and p*z have appropriate symmetry to mix with the relevant orbitals of an XCH2 group. The *3 orbital is a mix of the 2s and 2px orbitals, and the p*z orbital is purely a 2pz orbital, both being mixed with the 1s orbitals on hydrogen. When these are to interact with the orbitals of an XCH2 group, they mix with each other to some extent, because the symmetry has been broken. The *3 orbital acquires some 2pz character and the p*z orbital acquires some 2s character. Since they both have a 2pz component, these two orbitals can mix with the p* and * orbitals of the XCH2 group to create two orbitals labelled LUMO and LUMOþ1 in Fig. 4.18b, together with higher-energy orbitals that we need not consider. In this case, the LUMO is closer in energy to the *3 orbital, and so has more H—C antibonding character than C—X antibonding character. The two lower gauche hydrogens have opposite signs in *3 and p*z and nearly cancel, but the hydrogen atom anti-periplanar to the C—X bond has the same sign and is amplified.425 In addition, p bonding is already present, and elimination is therefore favoured by attack where the bold arrow approaches. The LUMOþ1 orbital, however, is closer in energy to the p*CX orbital, and it has much more C—X antibonding character. Because it has also mixed with the *CX orbital, which has a large 2s component, the upper lobe has been extended, and the lower reduced, making attack behind the C—X bond, where the bold arrow points, favourable. This argument suggests that, in the gas phase, and other things being equal, elimination is favoured in this substrate, because the LUMO is the lower energy of these two orbitals. Now let us take a different substrate with a leaving group Y, for which the energies of the p*CY and *CY orbitals are lower. A different picture emerges, in which the LUMO and the LUMOþ1 orbitals more or less

198

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS H H H H

H H

H *y *z

H H H

H H

H H

LUMO+1

H H

X

*z

*CX *CX

H

*3

X H H

H H H

*3

H H

X H

2

H H

X

(b) The interacting antibonding molecular orbitals of methyl and XCH2 f ragments H

H

H

LUMO

H H

H

H H

H H

H H y

H

*3

H H

H

*z

LUMO+1

H H

*CY

z

H H

H H

*CY H

H 1

H H (a) The molecular orbitals of the methyl f ragment

Fig. 4.18

H H

Y

H H

H H

LUMO

Y H H Y

Y

(c) The interacting antibonding molecular orbitals of methyl and YCH2 f ragments with YCH2 having lower-energy * and * orbitals than XCH2

The LUMO of EtX and EtY where Y is more electronegative than X

change places. In Fig. 4.18c, we see that the LUMO is now closer in energy to the p*CY orbital and has therefore more C—Y antibonding character, with the large lobe the site of attack for substitution. The LUMOþ1 orbital is now the one closer in energy to the *3 and p*z orbitals, and it has more of the character suitable for elimination. Thus with lower energy C—Y antibonding orbitals, substitution should be favoured, since the orbital pattern in the LUMO favours it. This picture allows us to see how the nature of the leaving group can affect whether substitution or elimination will be favoured. In practice, the more electronegative the leaving group the higher the SN2:E2 ratio (ROTs>RCl>RBr>RI>RNþMe3), in agreement with the analysis in Fig. 4.18, since the more electronegative the atom Y, the lower the energy of its antibonding orbitals.426 Superimposed on this pattern is the effect of changing the nucleophile, which is called a base if it is removing a proton in an elimination reaction. Hindered bases will inherently attack the more exposed hydrogen atoms, encouraging elimination. The hyperconjugation between the anti-periplanar C—H and C—Cl bonds that is manifest in the LUMO of ethyl chloride also removes charge from the hydrogen atom, which, because it is so small, will have a relatively concentrated partial positive charge. Hard nucleophiles, therefore, are more likely to induce an E2 reaction than an SN2 substitution, and soft nucleophiles to attack at

4 IONIC REACTIONS—REACTIVITY

199

carbon. This is the usual observation: the harder the nucleophile/base, the more elimination there is relative to substitution.427

4.6

Carbenes428

Carbenes are ambiphilic, having simultaneously both nucleophilic and electrophilic properties. We saw the lower-energy molecular orbitals of the parent singlet carbene CH2 in Fig. 1.16, which are redrawn in Fig. 4.19 from a better perspective for discussing their reactions. The HOMO is largely a filled p orbital (labelled n in Fig. 4.19, but z in Fig. 1.16) involved in some of the C—H bonding, but relatively high in energy, because of its closeness in energy to an isolated p orbital. (Using hybridisation, it would be a nonbonding filled sp2 hybrid.) The LUMO is an unfilled purely p orbital (pz in Fig. 4.19 and 2py in Fig. 1.16), which is therefore nonbonding. Thus the HOMO is high in energy, and the LUMO is low in energy, and, not surprisingly, carbenes are very reactive.

H H H H

HOMO

pz

LUMO

n H H

H H

CH2

CH2

Fig. 4.19 The filled and lowest unfilled molecular orbitals of methylene

Substituents have a profound effect on the reactivity of carbenes. Donor substituents lower the energy more if they are conjugated to the empty p orbital 4.202, and electron-withdrawing substituents lower the energy more if they are conjugated to the filled p orbital 4.203. Since these interactions leave the other frontier orbital more or less unchanged (it is orthogonal), the former still has a high-energy HOMO, and the latter still has a lowenergy LUMO. They become, therefore, relatively nucleophilic and electrophilic, respectively.429 filled filled

empty X X 4.202

empty empty

Z

filled

Z 4.203

4.6.1 Nucleophilic Carbenes In practice, donor substituents have the more remarkable effect, since they make it possible actually to isolate a range of carbenes 4.204.430 With somewhat less stabilisation, the carbene 4.205, although it is only found as a reactive intermediate, is exceptionally easy to form. It is the key intermediate in all the metabolic steps catalysed by thiamine coenzymes, and its reactions are characterised by nucleophilicity towards such substrates as aldehydes. Similarly, dimethoxycarbene 4.206 reacts with electrophiles like dimethyl maleate and benzoyl chloride to give the intermediates 4.207 and 4.209, and hence the products 4.208 and 4.210,431 typical of nucleophilic attack, but it does not insert into unactivated alkenes.

200

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

R

HO

N

OH P

O

O

OH P

OH

O

P

O

O

S

O

N

N

N R

N

4.204

4.205

H2N

CO2Me OMe

CO2Me

O

CO2Me

MeO MeO

MeO

OMe CO2Me

MeO

CO2Me

4.207

4.206

4.208

O

MeO Cl

Ph

Cl

Me

O

MeO

O

O

Ph

MeO

4.209

O Ph

4.210

The carbene 4.211 is a revealing case. In spite of having a neighbouring lone pair, it is only mildly nucleophilic in character, and, unlike strongly nucleophilic carbenes, it inserts into cis- and trans-2-butenes stereospecifically.432 This carbene has the lone pair and the empty orbital held more or less orthogonal, so that the orbital overlap which stabilises the carbene 4.202 is no longer possible.

N

N

4.211

The insertion of a carbene into an alkene, to be discussed again in the next chapter, can be viewed as the simultaneous interaction of the HOMO of the alkene with the LUMO of the carbene, and of the LUMO of the alkene with the HOMO of the carbene. Which interaction is the more important, and hence leads the bondforming process, depends upon the relative energies of the reacting partners. Nucleophilic carbenes will have a high-energy HOMO, which will interact strongly with a molecule having a low-energy LUMO (Fig. 4.20a).433 This is why they react well with electrophiles and electrophilic alkenes—in the case of the very nucleophilic dimethoxycarbene 4.206, bond formation is entirely dominated by the HOMO(carbene)LUMO(alkene) interaction, to the extent that it gives the zwitterionic intermediate 4.207, as shown by the loss of stereochemistry in going from a cis alkene to a trans cyclopropane, in contrast to the reaction of the less nucleophilic carbene 4.211, which shows the more usual behaviour for a carbene as a result of the more even balance of the frontier orbital interactions. 4.6.2 Electrophilic Carbenes Nucleophilic carbenes like dimethoxycarbene do not undergo cycloaddition reactions with simple alkenes, nor do they insert into C—H bonds. Electrophilic carbenes, on the other hand, like the bis(methoxycarbonyl)carbene 4.212, with a low-energy LUMO, react with molecules like alkenes that have a high-energy

4 IONIC REACTIONS—REACTIVITY

201

X X

LUMO

LUMO LUMO

HOMO

LUMO

X X

HOMO HOMO

HOMO Z Z

(a) Frontier orbital interactions f or a nucleophilic carbene and a good electrophile

Fig. 4.20

Z Z

(b) Frontier orbital interactions f or an electrophilic carbene and a good nucleophile

Frontier orbital interactions for carbenes with electrophilic and nucleophilic reagents

HOMO (Fig. 4.20b) stereospecifically to give cyclopropanes 4.213. They also insert into C—H bonds, especially tertiary C—H bonds, as in the highly selective formation of the malonate 4.214, even though there are only two tertiary C—H bonds and twelve primary.434 The selectivity for the tertiary C—H bond argues for a substantial degree of cationic charge on the carbon in the transition structure, characteristic of electrophilic attack on the H atom. Just as electrophiles in general react with alkenes and (less readily) with alkanes, and nucleophiles do neither, so the corresponding carbenes behave likewise.

MeO2C MeO2C

MeO2C

4.213 CO2Me

MeO2C 4.212

MeO2C

MeO2C +

4.214

MeO2C 93:7

4.215

Dihalocarbenes are characteristically electrophilic in character, inserting easily into the C¼C bonds of alkenes. As in other effects that halogens have, the inductive withdrawal along the C—halogen bond is decisive in lowering the electron population on the carbon, even though the chlorine atoms do have lone pairs that might conjugate in the p system. Calculations bear this out.435 4.6.3 Aromatic Carbenes Three special carbenes are the cyclopropenylidene 4.216,436 cycloheptatrienylidene 4.217437 and cyclopentadienylidene 4.218. The cyclopropenylidene 4.216 and cycloheptatrienylidene 4.217 have the empty p orbital conjugated with one and three p bonds, respectively, making them aromatic like the cyclopropenyl 1.13 and tropylium cations 1.12. The filled px orbital is unchanged as a source of nucleophilicity, and these carbenes are notably nucleophilic, reacting with electrophilic alkenes like fumarate but not with simple alkenes. Furthermore, cycloheptatrienylidene 4.217 reacts faster with styrenes having electron-withdrawing

202

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

substituents and slower with those having donor substituents, giving a  value of þ1.05, in contrast to the  value of –0.6 for the relatively electrophilic dichlorocarbene.438

empty

empty

Ph filled

filled

Ph 4.216

4.217

CO2Me Ph

Ph

CO2Me

+ Ph

CO2Me

CO2Me +

MeO2C

Ph

4.216 cis or tr ans

MeO2C

CO2Me

trans

4.217

cis and trans 50:50

CO2Me tr ans

Cyclopentadienylidene 4.218 is not quite so straightforward. It might change the normal configuration for a carbene 4.218a to that shown as 4.218b in order to allow the filled pz orbital to be conjugated with the two p bonds, making this an aromatic cyclopentadienyl anion 1.11, and the unfilled px orbital would have to take up the orthogonal role. However this is not without an energetic penalty,439 since it keeps the areas of high electron population close together on the left-hand side of 4.218b. This carbene is not notably electrophilic, at least in its reactions with alkenes, where the more-substituted alkenes react with it at much the same rate as the less-substituted,440 but it is somewhat electrophilic, reacting with dimethyl sulfide, for example, to give the ylid 4.219.441 filled

empty

empty

filled 4.218a

4.218b

+

S

S

4.218a

4.219

The superficially similar carbene 4.220, another carbene stable enough to be isolated, has the best of all worlds. With six electrons for the p system coming from the double bond and the two nitrogen lone pairs, it has an aromatic sextet without having to fill the pz orbital. Thus the px orbital remains filled, making this a nucleophilic carbene, which reacts with the electrophile carbon disulfide to give the zwitterion 4.221.442 empty S

N N N 4.220

+

filled N

N

S

N

S

C S

4.221

4 IONIC REACTIONS—REACTIVITY

203

4.6.4 Ambiphilic Carbenes A carbene carrying both a donor and an electron-withdrawing substituent presents a new pattern of reactivity, often called ambiphilic, since such species can show both nucleophilic and electrophilic properties. Thus chloro(methoxy)carbene 4.222 has a low enough energy LUMO, making it electrophilic towards simple alkenes, and yet a high enough HOMO to make it able to react with electrophilic alkenes like methyl acrylate.443 None of the carbenes discussed above is capable of both of these reactions.

Cl

OMe

Cl a nucleophilic alkene

MeO

CO2Me

Cl

an electrophilic alkene

OMe

CO2Me

4.222

The account given so far leaves no room for anomalies, and yet they abound. Some of the nucleophilic carbenes do not react with the common electrophilic probes, and some of the electrophilic carbenes do not react with the common nucleophilic probes. Furthermore, there is quite frequently only a poor correlation between the calculated frontier orbital energies and the patterns of reactivity. The usual qualifications have to be invoked—that the frontier orbital theory is not a complete account of all the forces at work. One of the more obvious of the other forces is steric hindrance, of course, and another is that some carbenes are unselective, because they are so reactive that they are diffusion controlled.444 Alternatively, the stabilisation given to carbenes by conjugation with either donor or withdrawing groups can also reduce their overall reactivity. An illustration of this factor is provided by the highly stabilised, potentially ambiphilic carbene 4.223. This carbene shows little in the way of carbene-like behaviour—it fragments, probably reversibly, into two molecules of HCN, and it dimerises to give the highly stabilised diamino dinitrile 4.224, and that is about all.445 These reactions are interesting because they might be involved in the primordial chemistry from which life evolved. H2N

H2N

CN

2HCN NC 4.223

NC

NH2 4.224

Triplet carbenes have a similar set of molecular orbitals to those shown in Fig. 4.19, but with one electron in each of the orbitals n and pz. The shape of a triplet carbene may be anywhere between tetrahedral, if the singly occupied orbitals are localised, and linear, if they are well delocalised by substituents. This is especially noticeable when the carbene has two C-substituents like phenyl groups, which can overlap one with each of the unpaired electrons.446 The reactions triplet carbenes undergo follow the patterns of radical chemistry (Chapter 7).

5

Ionic Reactions—Stereochemistry

The control of stereochemistry is often the most challenging and therefore interesting part of a synthesis. To achieve control, understanding is vital, and understanding requires a feeling for all the factors that influence the stereochemistry of organic reactions. We begin with two adjectives, stereoselective and stereospecific, which, with their derived adverbs, are much used and misused. They are used carefully in this book, and their meaning needs to be established firmly, since the distinction between them is important.447 A reaction is stereoselective when more of one stereoisomer is produced than of one or more others. Thus the reduction of camphor 5.1 takes place mainly with attack of the hydride reagent on the less-hindered face, avoiding the C-8 methyl group on the bridge, to give more isoborneol 5.2 than borneol 5.3.448 The degree of stereoselectivity is expressed as the diastereoisomer ratio, or dr, the ratio of isoborneol to borneol 5.2:5.3. It is helpful, in order to make comparisons easy, to normalise the numbers by presenting them as percentages adding up to 100, 90:10 in this case, without implying that the yield is 100%. 8

LiAlH4 OH H3Al

H

O

5.1

+

H 5.2

H OH

90 : 10

5.3

The less simple term stereospecific is used for those reactions where the configuration of the starting material and the configuration of the product are related in a mechanistically constrained way. Thus the diastereoisomeric bromides 5.4 and 5.6 give stereochemically different alkenes 5.5 and 5.7 by anti elimination. 449 Since each of these reactions produces more of one isomer than the other, they are also stereoselective, which is the more inclusive term. The characteristic feature of a stereospecific reaction is that one stereoisomer of the starting material gives one stereoisomer of the product, and a different stereoisomer of the starting material gives a different stereoisomer of the product.

Molecular Orbitals and Organic Chemical Reactions: Reference Edition  2010 John Wiley & Sons, Ltd

Ian Fleming

206

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

ButO H

H Ph

Ph Br

KOH, EtOH anti

Br

Ph Br

5.4

H Ph 5.5

ButO H

H Ph

Br Ph

KOH, EtOH anti

Br

Br Ph

5.6

H Ph 5.7

This particular reaction was studied when analytical methods were not available to measure the probably small degree to which each isomer gave some of the other alkene, either by a different mechanism or by incomplete stereospecificity in the E2 reaction itself. More recently, the E2 reactions of the tosylates 5.8 and 5.10, giving the trans- and cis-5-decenes 5.9 and 5.11, have been shown not to be 100% anti—each gives a little, depending upon the solvent, of the product of syn elimination (as well as the isomeric 4-decenes, which were separated off before the analysis, and the products of removal of the deuterium, which were allowed for).450 No matter how much stereochemical leakage of this kind there is, as long as the diastereoisomer ratio is greater than 50:50 (84:16 in both of these cases), the reactions are still stereospecific. It is thus quite acceptable, although not common, to have reactions that are measurably less than 100% stereospecific, as this one is. ButO H Bu

D

H Bu

KOBut, ButOH

OTs

anti 84 parts

5.8

syn

Bu D

H Bu 5.9

16 parts

t

Bu O H D Bu

H Bu OTs 5.10

KOBut, ButOH anti 84 parts

D Bu

H Bu 5.11

It is not helpful to use the word stereospecific to mean 100% stereoselective, as many people thoughtlessly do—a useful distinction is lost, and understanding suffers. Furthermore, it is arguable that there are no reactions that give not even a trace of the stereoisomer, and so all stereospecific reactions, when it is illdefined as those reactions which are completely stereoselective, are at risk of losing their status when a better analytical method comes along. Unfortunately, there is a grey area. There are reactions that are, in their fundamental nature, the same as those we call stereospecific, but for which it is not possible to have two stereoisomers either of the starting material or of the product. Thus the addition of bromine to an isolated double bond is well known to be stereospecifically anti, but the corresponding addition to an acetylene cannot be proved to be stereospecifically anti by the usual criterion because there is no possibility of having two stereoisomers of an acetylene. The same problem arises, of course, for reactions taking place in the opposite direction—in elimination reactions producing acetylenes, one vinyl bromide may react faster than the other, but they both produce the same acetylene. It is also possible, in spite of having two stereoisomers of the starting material and of the

5 IONIC REACTIONS—STEREOCHEMISTRY

207

product, to find that, whereas one stereoisomer of the starting material reacts to give one stereoisomer of the product, the other stereoisomer of the starting material undergoes a quite different reaction.451 Once again it is not possible to prove that such reactions are stereospecific, even though in their nature that is what they are. This chapter is divided into two sections, largely separating stereospecific reactions from the merely stereoselective. The first (Section 5.1) deals largely with stereospecific reactions, and the explanations based on molecular orbital theory for the sense of that stereospecificity. The second (Section 5.2) deals with stereoselective reactions, in which a new stereocentre is created selectively under the influence of one or more existing stereocentres or stereochemical features. The way in which a resident stereocentre controls which of two surfaces of a p bond is attacked is also sometimes a question of how the orbitals interact. The stereospecificity that is such a striking feature of pericyclic reactions is covered in the next chapter.

5.1

The Stereochemistry of the Fundamental Organic Reactions

5.1.1 Substitution at a Saturated Carbon 5.1.1.1 The SN2 Reaction.452 It is well known that bimolecular nucleophilic substitution (the SN2 reaction) takes place with inversion of configuration. This is a stereospecific reaction because one enantiomer of the starting material gives largely one enantiomer of the product. A number of factors contribute to this well nigh invariable result. The solvent is likely to be crowded round the electronegative element, blocking approach from that side. There will be a repulsion between any negative charge on the incoming nucleophile and the departing nucleofuge if they were both on the same side. The transition structure for inversion will be a trigonal bipyramid 5.12, with the electronegative elements in the apical positions. Having the sites of negative charge apical keeps them as far apart as possible. This is probably the single most powerful reason ensuring that the SN2 reaction takes place with inversion of configuration. (–) Nu

(–) X 5.12

This same explanation accounts for the stereochemistry of nucleophilic substitution at silicon and phosphorus centres, where the trigonal bipyramid may be an intermediate rather than a transition structure, since the larger nucleus allows more than four ligands to bond to the second row element with a significant lifetime. The rules for trigonal bipyramids on phosphorus214 (and presumably on silicon too)453 are: (i) that nucleophiles enter, and the nucleofugal groups leave, from apical positions, because they have the longer bonds; and (ii) electronegative substituents in the lowest energy configuration occupy the apical positions, because that keeps the negative charges as far apart as possible. When either or both the nucleophile and the nucleofugal group are electronegative, inversion of configuration is the normal observation, typified by the displacement of chloride by hydroxide ion in Sommer’s definitive work in the silicon series.454 The intermediate 5.13 has the formal charge on silicon, but the actual negative charge will be distributed largely to the two electronegative elements, and the silicon will carry a fraction of positive charge. The intermediate is unlikely to change its configuration, because it will remain in an energy well while the electronegative elements with their negative charge are apical. Np-1 HO

Si Ph Me 5.13

Cl

208

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

However, when the nucleofugal group is not electronegative, as in the silane 5.14 where it is a hydride ion,455 the initial attack is probably easiest if it takes place from the side opposite to the largest group. This leads to an intermediate 5.15 in which the hydrogen atom is not apical. Before the hydride can leave, a pseudorotation 5.15 ! 5.16 has to occur, in order to place it apical. The concept and word pseudorotation were first applied by Berry in the phosphorus series456 but apply equally here. In a pseudorotation (5.15, arrows), one basal substituent, the methyl group in this case, remains basal, and is called the pivot; the other two basal substituents, the phenyl and the hydride become apical, and the two apical substituents become basal. If the nucleofugal group departs before any further pseudorotations, the product 5.17 is that of retention of configuration, which is common when either the nucleophile or the nucleofuge is a hydride or carbon-based group. Another way of identifying this pattern is to note that hard nucleophiles and nucleofugal groups are apt to give rise to inversion of configuration and soft to retention of configuration. interchange

HO

Ph Si Me

Np-1

HO

Si Ph Me

interchange 5.14

H

H

H

5.15

Np-1 pivot

HO Si Np-1 Me

HO Me Si Np-1

Ph

Ph

5.16

5.17

The preference for electronegative elements to enter and to retain their apical positions ensures inversion of configuration when the nucleophile Nu and nucleofugal group X are both electronegative, and the other substituents are alkyl or aryl groups. When the nucleophile and the nucleofugal group are not both electronegative, and hence do not stabilise the arrangement in which they are both apical, apical attack may be followed by a pseudorotation to give a different intermediate, which explains the retention of configuration that is often seen in silicon chemistry when neither Nu nor X is conspicuously electronegative.454 Retention of configuration by way of pseudorotation also occurs when structural features, rather than orbital constraints, dictate an alternative to the simple story above. For example, if the methyl and the phenyl groups in the intermediate 5.15 were joined in a fivemembered ring, this configuration would be high in energy, because a small ring can only bridge from a basal to an apical position. In that case, even if the hydrogen were replaced by an electronegative element it would have to be in a basal position when the nucleophile attacks, in order that pseudorotation can give an intermediate like 5.16 with the small ring bridging a basal and an apical position throughout. The overall result would be retention of configuration even though both the nucleophilic and the nucleofugal groups are electronegative.453 Although the argument is inherently weaker, we can also explain inversion of configuration in the SN2 reaction by looking at the frontier orbitals, which will be the HOMO of the nucleophile and the LUMO of the electrophile.457 We saw the orbitals of methyl chloride in Fig. 1.56, from which we can abstract the LUMO for an alkyl halide in general—it is very largely associated with the C—halogen bond. We can view it, without hybridisation, as the *CX orbital. The overlap is bonding when the nucleophile approaches the electrophile from the rear (Fig. 5.1a), but is both bonding and antibonding when the nucleophile approaches from the front (Fig. 5.1b). The former is clearly preferred. We can see that there is no orbital impediment to approach from the rear, and we can add that repulsion between the HOMO of the incoming nucleophile and the higher-energy filled orbitals of the alkyl halide (Fig. 1.59) is also less from that side, where the carbon atom is left exposed. Nevertheless, the frontier orbital argument is a much weaker explanation for inversion of configuration in SN2 reactions than the explanation on p. 207. It is not absolutely impossible that retention of configuration might be found one day,458 and we can expect that one of the factors that might encourage it would be to have a low electronegativity for the nucleophile or for the atom being displaced. Full theoretical treatments have been carried out at many levels of theory, and they agree that the inversion pathway has the lower energy. The solvent, which is invariably present in everyday chemistry, is not

5 IONIC REACTIONS—STEREOCHEMISTRY

209 bonding Nu

bonding

H

H

Nu

H

C

*CX

*CX LUMO

(b) Retention of conf iguration

(a) Inversion of conf iguration

Fig. 5.1

X

H

LUMO

HOMO antibonding

C

X

H

HOMO

H

Frontier orbitals for the SN2 reaction

automatically included in calculations, and it makes a profound difference. In the absence of solvent, the gasphase SN2 reaction has, both experimentally260,261 and in calculations,459 a double well (Fig. 5.2): the nucleophile and the alkyl halide combine exothermically with no energy barrier to give an ion-molecule complex. In a sense the naked nucleophile is solvated by the only ‘solvent’ available, the alkyl halide. The SN2 reaction then takes place with a barrier and with many of the features of the solution phase SN2 reaction, such as inversion of stereochemistry, and a dependence on nucleophilicity and nucleofugal power; the product ion-molecule complex then dissociates endothermically to give the products. Calculations that include a few molecules of solvent have also been carried out,460 and they reduce the depth of the double well, approaching the normal pattern of solution-phase SN2 reactions, for which some of the barrier is the displacement of the solvent but some is the intrinsic component shared with the gas-phase reaction. H X

+ H

Y

H

H

H X

+

X H

Y

H

Y

H H H X

H Y

H

H

Fig. 5.2

Y

X HH

Energetics of the gas-phase SN2 reaction

5.1.1.2 The SE2 Reaction. In electrophilic substitution, the substrate is usually an organometallic reagent, for which we can use methyllithium as the simplest version. We saw the low-energy orbitals of methyllithium with and without hybridisation in Fig. 1.64. The frontier orbitals for the SE2 reaction will be the HOMO of the nucleophile (the CLi orbital strongly associated with C—M bonding) and the LUMO of the electrophile, modelled in Fig. 5.3 by an empty p orbital. In this case,457 the frontier orbital interaction (Fig. 5.3) can be bonding for attack on either side of the carbon atom. In agreement, electrophilic substitution at a saturated carbon atom sometimes takes place with retention of configuration 5.18 ! 5.19461 and 5.21 ! 5.22462,463 when it is called SE2ret,464 and sometimes, but more rarely, with inversion of configuration 5.18 ! 5.20 and 5.21 ! 5.23, when it is called SE2inv. Retention of configuration is the more usual pattern for electrophilic attack on a C—M bond, especially, but not invariably, for carbon electrophiles. This may simply be because electrophiles are attracted to the site of highest electron population, but explanations for changes from retention to inversion in going from one

210

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS bonding E bonding

H

E LUMO

H

H

C

C

Li

H

LUMO

H Li

H

HOMO

HOMO

(a) Inversion of conf iguration

Fig. 5.3

(b) Retention of conf iguration

Frontier orbitals for the SE2 reaction Ph Br

ClCO2Me CO2Me

retention H 5.19

Li H 5.18

ButO Br2

Br 5.20

O 5.22

Ph

O 5.21

H

inversion

ButO Li

N

CO2Me

N

retention

Ph Ar

CO2Me Ar

CHO

Ar

CHO

N

inversion ButO

O 5.23

electrophile to another, from one metal to another, and from one substrate to another are far from clear. It is not uncommon to find even one system in which the two pathways are delicately balanced.465 As it happens, it has only recently become possible for synthetic chemists to use the stereochemistry that this reaction possesses, as seen with the reagent 5.21 created using butyllithium and (–)-sparteine. The explanation offered in that case is that reactive electrophiles, those not requiring Lewis acid catalysis, are apt to react with inversion of configuration, while those that need to coordinate to the metal to experience some Lewis acid catalysis, are apt to react with retention of configuration, because the electrophile is necessarily being held on the same side as the metal. One of the complicating factors in trying to explain the stereochemistry is that organolithium reagents are not monomeric in solution, or usually at the time of reaction. 5.1.2 Elimination Reactions 5.1.2.1 The E2 Reaction. -Elimination, which is usually but not always stereospecifically anti,466 is the frequent accompaniment to substitution, as we saw in Section 4.5.2.6. We have also already seen in Section 2.2.3.4 some discussion about why anti arrangements are preferred in the anomeric effect, where we saw that it is not solely because it allows all the groups to be staggered and not eclipsed. The same is true for elimination reactions. While both conformations for -elimination, 5.24 and 5.25 in Fig. 5.4, obey the primary rule of having the orbitals developing into a p bond coplanar, the syn elimination 5.24 has all the substituents eclipsed, while the anti elimination in 5.25 has them staggered. The energy DE associated with the eclipsing in 5.24 is still substantially present in the transition structure, whereas it has not developed to the same extent in the transition structure corresponding to 5.25. Since both reactions are giving the same product, the difference in energy DE between the starting conformations is still present to some extent DE‡ in the transition structures, and the anti elimination is therefore faster. As with the anomeric effect, this is not the whole story, because there are systems where this factor is not present, and yet there is still a preference for anti elimination. Thus the anti elimination of the vinyl chloride 5.26 giving the acetylene 5.27 is over 200 times faster at 97 C than the syn elimination of the vinyl chloride

5 IONIC REACTIONS—STEREOCHEMISTRY B

H

211

X E‡

syn E2 elimination 5.24

5.24

E B

5.25

H

alkene product

X anti E2 elimination 5.25

Fig. 5.4

The difference in energy of two starting materials affecting the energy of the transition structures

5.28,467 and this in spite of the almost certainly higher energy of the latter, which has the two large substituents, the phenyl groups, cis. H

NaOH

Ph

Ph

Ph

k rel 208

Cl

H

NaOH

Ph

Cl

Ph k rel 1

Ph

5.27 5.26

5.28

In one sense, the stereochemistry at the carbon carrying the nucleofugal group X in the anti-periplanar process 5.29 can be seen as an inversion of configuration, since the electrons supplied by the C—M bond flow into the p bond of the product 5.30 from the side opposite to the C—X bond, just as they do in an SN2 reaction. This is the simplest perception available to the organic chemist to account for why E2 reactions take place with an anti-periplanar geometry.468 This crude idea can be reformulated somewhat more explicitly using the tau bond model (see p. 61). The pair of electrons originally in the C—M bond in the starting material 5.29 moves into the upper tau bond, marked in bold in the product 5.31, effectively creating the new bond from behind the C—X bond with inversion of configuration. Since the electrons coming from the C—M bond move into the tau bond on the top side of the molecule, this corresponds to retention of configuration at the carbon atom carrying the electrofugal group M. In a syn elimination, the events would have to be seen as either retention at both sites or inversion at both sites—retention in an SN2 reaction is essentially unknown, and inversion in an SE2 reaction is less common than retention.469 Thus the stereochemistry for the anti-periplanar process bears some resemblance to the only acceptable event for the SN2 reaction and to the more common event in an SE2 reaction, but this is hardly a satisfying account for why E2 reactions are so often faster if the stereochemistry can be anti-periplanar rather than syn-coplanar.

M

H H

H H

M+ H H

H H

X 5.29

retention

M+ H H

X–

X– 5.30

inversion

H H 5.31

212

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS 1.111Å HH

H F

F

1.405Å

+ HH

HF H

F

2.234Å H H 2.268Å

F H 1.394Å

H H H H

F

F

F H

HH

HH

H H

H H

F

H H

1.503Å

Fig. 5.5

F

Energetics of the gas-phase anti E2 reaction

As with substitution reactions, calculations have been performed, and the anti stereochemistry is the pathway found to be lower in energy.424 In the gas phase, the energy profile is not like that shown in Fig. 5.4—there is again a well with a reactant complex before the transition structure for elimination (Fig. 5.5). In the reactant complex for ethyl fluoride, the base, modelled by a fluoride ion, is bonded to the hydrogen atom that is about to leave, stretching that H—C bond, and allowing the C—F bond to stretch too. From here it is easy to see how the molecular orbitals flow into those of the product, an exercise we saw earlier (see p. 144) without the benefit of a good nucleofugal group. The transition structure, in the absence of solvation, has the hydrogen atom coordinated to both carbons, but both bonds are long and the C—F bond even longer. The corresponding transition structure for syn elimination is higher in energy, it has an even longer H—C bond but a shorter C—F bond, and the transition structure resembles that for carbanion formation ahead of elimination, in other words an E1cb mechanism. 5.1.2.2 The E20 Reaction. The stereochemistry of the E20 process is even less well understood. It is exemplified by some decarboxylative eliminations 5.32 ! 5.33 and 5.34 ! 5.35 set off by treatment with dimethylformamide dineopentylacetal. They are stereospecific and largely, although not exclusively, syn. The same reaction with -hydroxy acids is highly anti selective, in the usual way for  eliminations. There are a number of other examples of largely syn elimination mostly in cyclic systems.470 CO2H

HO H

H

(ButCH2O)2CHNMe2 syn 5.33 (syn:anti 90:10)

5.32 HO

H H 5.34

CO2H

(ButCH2O)2CHNMe2 syn

5.35 (syn:anti 83:17)

5 IONIC REACTIONS—STEREOCHEMISTRY

213

The tau bond model appears to provide a quick and easy explanation. An anti interaction between each of the breaking bonds and the lower tau bond leads to a syn selective reaction for each diastereoisomer. HO H

CO2H H

HO

H

H

5.33

CO2H HH

H

5.35

H 5.32

5.34

The change from anti for an E2 reaction to syn for an E20 is a satisfying pattern, for it matches the change from retention for SE2 to inversion for SN2—in both cases adding two electrons to the transition structure changes the stereochemistry. The same pattern is found for aromaticity, where each added pair of electrons changes the system from aromatic to antiaromatic, and back again. There is a natural supposition that each added pair of electrons ought to cause stereochemistry to alternate. We shall see that alternation of stereochemistry as the number of electrons changes works well for pericyclic reactions (Chapter 6), but it is not reliable here. In the first place, we already know that the SE2 reaction does not always take place with retention of configuration, and in the second place, adding one more double bond for the E200 reaction does not cause it to change back to being selectively anti. The tau bond model would support this expectation—successive anti overlap through the tau bonds down the chain 5.36 and 5.39 suggests that decarboxylative elimination should be anti. In practice, the base-induced elimination of the ethers 5.37 and 5.40 is largely syn, with the major products in each case being the dienes 5.38 and 5.41, respectively. (The decarboxylative elimination of the corresponding hydroxyacids, similar to the reactions of the acids 5.32 and 5.34, was without significant stereoselection from either isomer.) Pr edicted: MOMO H

Obser ved: H

HH

H

CO2H MOMO H

H

CO2H

6MeLi syn

5.37

5.36

5.38 (syn:anti 86:14)

overall anti MOMO H

H

MOMO HH

HH CO2H

5.39 overall anti

H

CO2H

6MeLi syn

5.40

5.41 (syn:anti 90:10)

Furthermore, several constrained systems, designed to make anti-periplanar overlap with the tau bonds impossible, do not show the pattern of stereoselectivity implied by the tau bond model. The nucleofugal group in both hydroxyacids 5.43 and 5.46 is held rigidly so that the overlap with the tau bond must be syn 5.42 and 5.45, and this ought to force anti eliminations. In practice, the hydroxy acids 5.43 and 5.46 undergo elimination with syn selectivity, just like their less constrained counterparts 5.32 and 5.34, giving largely the dienes 5.44 and 5.47, respectively. The predicted anti elimination in the latter would have led to the lower-energy diene 5.44, and yet this is the minor product.

214

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

Pr edicted:

Obser ved: CO2H

OH

H

H

OH

H

H

H (ButCH2O)2CHNMe2

H

H

CO2H

H

syn

5.42

5.44 (syn:anti 99:1)

5.43 CO2H

OH H

H

OH H

HH

H syn

CO2H

H

H

(ButCH2O)2CHNMe2

5.45

5.47 (syn:anti 60:40)

5.46

Clearly some other electronic factors are at work. One possibility is that the electrofugal group (derived from the carboxylic acid) has substantially broken off, making the stability of the intermediate allyl anion a factor in determining the stereochemistry, and weakening or removing the element of concertedness. That sickleshaped anions are favoured over the W-shaped and U-shaped (see p. 108) has been invoked to explain the stereochemistry of some desilylative E20 reactions, where there was a notable selectivity for the formation of a Z double bond at the carbon atom losing the silyl group, but no stereospecificity of the kind seen in the decarboxylative eliminations above.471 The tau bond model is an intriguing, but evidently defective approach to understanding the stereochemistry of elimination reactions. The problem therefore remains—there is no simple and satisfying way to explain the stereochemistry beyond the simple -elimination. We shall return to the problem later, when we come to discuss how  bonds adjacent to a p bond influence the stereochemistry of attack on the p bond, but first we must discuss the angle of attack on a p bond, and the stereochemistry of their addition and substitution reactions.

5.1.3 Nucleophilic and Electrophilic Attack on a p Bond 5.1.3.1 Nucleophilic Attack on a p Bond—The Bu¨rgi-Dunitz Angle.472 Nucleophilic attack on the p bond of a carbonyl group is widely recognised to take place from above (or below) the plane of the double bond, but not directly down the axis of the pz orbital 5.48. Bu¨rgi and Dunitz deduced, from an examination of a large number of X-ray crystal structures, that the angle  in the transition structure 5.49 was obtuse, typically close to 107 and not 90. The angle  is called the Bu¨rgi-Dunitz angle. It is a common misunderstanding to think that the Bu¨rgi-Dunitz angle implies that the two angles f are acute. They can be sometimes, but they are not usually—the angles f are also obtuse in the transition structure, but to a somewhat smaller extent. Nu–

Nu(–) O

5.48

O(–) 5.49

That both  and f will be obtuse is hardly surprising—as the reaction proceeds, the carbon atom of the carbonyl group is changing from trigonal to tetrahedral, and the transition structure is almost certain to have a geometry at this atom somewhere in between. Only at long distances, with little bonding developed, is there any chance that f will be acute. This is borne out by the X-ray structures, which show that f is less than 90

5 IONIC REACTIONS—STEREOCHEMISTRY

215

1st t er m:

2nd term:

3r d t er m:

HOMO

HOMO –

Nu–

Nu

antibonding

repulsion

repulsion

HOMO

Nu–

O

5.50

Fig. 5.6

(+) (–) O

LUMO O

5.51

5.52

The Salem-Klopman equation applied to the Bu¨rgi-Dunitz angle

˚ from the carbon atom. The essence of Bu¨rgi and Dunitz’s only when the nucleophile is more than 2.5 A perception is that  is a slightly larger angle than f. There are several reasons why  should be larger than f. On the product side of the reaction coordinate, the tetrahedral intermediate will have a large repulsion between the charge developing on the oxygen atom and any charge on the nucleophile, especially when it is based on an electronegative atom. On the starting material side (Fig. 5.6), the repulsive interaction of the filled orbitals with the filled orbitals 5.50, the first term of the Salem-Klopman equation 3.13, will push the nucleophile away from the oxygen atom, because the HOMO of the carbonyl group has the larger coefficient there. The Coulombic forces alone, the second term of the equation, will lead the nucleophile to approach along the line of the C—O bond 5.51. For the third term, the attraction is between the HOMO of the nucleophile and the LUMO of the carbonyl group, which has the large coefficient on the carbon atom, but there will also be a repulsion from the oxygen atom, because of the orbital of opposite sign on it 5.52. All three factors make  an obtuse angle, but only the first, with repulsions from the filled orbitals of the substituents, makes f an obtuse angle. Calculations suggest that the repulsion between the filled orbitals 5.50 is quantitatively the most important of the three factors.473 Superimposed on the Bu¨rgi-Dunitz angle is an angle defined by in the view of an unsymmetrical carbonyl group seen from above 5.53. This angle is called the Flippin-Lodge angle, and it is expected to be positive when the group R1 is larger than the group R2. A calculation, for example, makes it 7 for hydride attack on pivalaldehyde (R1 ¼ But, R2 ¼ H).474 It becomes more significant when one of the substituents R is an electronegative group. At the extreme of a carboxylate ion, when one of the R groups is an oxyanion, the angle would be 60 5.54, with full eclipsing with the remaining R group. Carboxylate ions are not susceptible to nucleophilic attack, but esters and amides are. We can predict, from considerations like those embedded in the drawings 5.50–5.52 in Fig. 5.6, that the angle will be positive for esters and amides 5.55 if the steric repulsion from the R group is not too forbidding. Calculations suggest that the angles are close to 40 for an ester and 50 for an amide.473 Considerations about the angles of approach, sometimes called ‘trajectory analysis’,475 become important in the discussion of how stereogenic centres adjacent to the carbonyl group affect the stereoselectivity. O R1

Nu–

O R2

O

(–) O (–)O

R

R

O R2N or RO

R

60° 5.53

5.54

5.55

The same angles, the Bu¨rgi-Dunitz and the Flippin-Lodge, will have their counterparts for nucleophilic attack on a C¼C bond, but the former at least ought to be muted, because all three factors 5.50–5.52 will be reduced when the oxygen atom of the carbonyl group is replaced by a carbon atom.

216

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

5.1.3.2 Electrophilic Attack on a C=C Double Bond by Nonbridging Electrophiles—Nonstereospecific Addition Reactions.476 Electrophilic attack by a proton or a cationic carbon on a C¼C double bond is not quite so straightforward, because it may give an open cation 5.57 or a bridged cation 5.59. We have met the problem of hyperconjugating and bridged cations before (see p. 90), and the same problem arises here, for we cannot be sure that protons and carbon electrophiles will always create open cations. E

E

E

5.56

E

5.57

5.58

5.59

If we assume that the cations are not usually bridged, then we can expect protons and carbon electrophiles to attack from outside the double bond 5.56. As with nucleophilic attack, the carbon atom is moving from trigonal to tetrahedral, and the angle analogous to the Bu¨rgi-Dunitz angle will be obtuse in the transition structure. On the starting material side of the reaction coordinate (Fig. 5.7), the first term of the SalemKlopman equation would push the electrophile away from the centre of the double bond 5.60 and discourage attack there, or anywhere else, but the other two terms would encourage attack from inside 5.58, 5.61 (where the concentration of charge in the p cloud is represented as a minus sign) and 5.62.477 It seems likely that, while the early approach may be from inside 5.58, the electrophile may have moved outside to give an obtuse angle by the time the transition structure has been reached. Thus the angle of approach in an electrophilic attack, acute or obtuse, will depend upon how early the transition structure is.

HOMO

E

repulsion

E

E repulsion

bonding

LUMO bonding

HOMO

HOMO 5.60

5.61

5.62

Fig. 5.7 The Salem-Klopman equation applied to electrophilic attack on a C¼C bond

The stereochemistry of the second step of an addition initiated by a nonbridging electrophile like a proton will be controlled by which surface of the intermediate cation 5.57 is more easily attacked by the nucleophile. The addition of hydrogen chloride to an alkene is not stereospecifically anti, because the chloride does not necessarily attack the cation either specifically anti or syn to the proton,478 in contrast to addition initiated by bridging electrophiles like bromine, or metallic electrophiles like the mercuric ion, described below. The stereochemistry will depend instead on ion pairing or on the substituents in the cation 5.57, and how they influence the conformation at the time the nucleophile attacks. 5.1.3.3 Nucleophilic and Electrophilic Attack by One p Bond on Another. A combination of nucleophilic and electrophilic attack on double bonds is the core of the aldol reaction, where both the nucleophile and the electrophile are p bonds.479 The ideas we have seen in the previous two sections can be combined to understand the transition structure 5.63 calculated for this reaction in the gas phase.480 This transition

5 IONIC REACTIONS—STEREOCHEMISTRY

217

structure has obtuse approach angles both for the electrophilic and for the nucleophilic double bonds, the two reagents have all their substituents staggered, when viewed down the developing bond 5.63b, and the two oxygen atoms are as far apart as possible, presumably repelling each other because of the partial negative charges they both carry. However, there are alternative conformations such as 5.64, which maintain the obtuse angles and the staggered groups 5.64b, and are not much higher in energy. The transition structure 5.63 is described as anti-periplanar and the transition structure 5.64 is described as synclinal.

(–)

H H

O

H ≡ H O (–)

H H 5.63a

H

O (–)

H (–) O

H

H

H H (–) O

H H

5.63b

≡ H O (–)

5.64a

(–)

H

O

H

O (–)

H

H H 5.64b

Those aldol reactions in which a lithium or boron atom is coordinated to both oxygens are certainly synclinal, since the metal coordinates to both oxygens and the transition structure is cyclic,480 and usually chairshaped—as first proposed by Zimmerman and Traxler. There are, however, many related reactions, when a C¼C and C¼O group or two C¼C groups combine, in which this problem is less settled, either by theory or experiment. Examples are the reactions between enamines and Michael acceptors, and the Lewis acidcatalysed reactions between allylsilanes or allylstannanes and aldehydes 5.65, and between the same reagents and Michael acceptors 5.66, in none of which is there a cyclic component holding the reagents in a synclinal geometry. There is experimental evidence for synclinal481,482 and anti-periplanar483 preferences for various examples of these reactions, and we must conclude that there is only a small energy difference between them. In most of the open-chain reactions thought to be synclinal, one or other of the oxygen atoms in the aldol reaction (or both of them) is replaced by a carbon atom, reducing both the Coulombic repulsion and the repulsion between the filled orbitals that favour the anti-periplanar transition structure. There will also be a frontier orbital attraction,484,485 favouring the synclinal transition structure, which can be modelled by the interaction 5.67 between an allyl anion and an alkene, but it hardly seems likely that this can be of overriding importance.

O MXn

O MXn

LUMO

HOMO MR3 5.65

MR3 M = Si or Sn

5.66

5.67

5.1.3.4 Electrophilic Attack on a C=C Double Bond by Bridging Electrophiles—Stereospecific Addition Reactions. Heteroatom electrophiles, like peracids, sulfenyl halides and the halogens, all of which are based on electronegative heteroatoms, nearly always give bridged products in the first step. The difference between these electrophiles and the proton or carbon electrophiles discussed above is that the electrophilic atoms carry a lone pair, so that the bridging bonds 5.69 have a total of four electrons. (The bridging in the structure 5.59 only had two electrons to share between the two bonds.) The factors from the SalemKlopman equation illustrated as Fig. 5.7 now lead the electrophile straight onto the p bond 5.68, since they match the product-like character, instead of opposing it. In detail, the two bonds may be unequal, if the double bond is unsymmetrical, with the electrophile tilted to the side carrying the higher electron

218

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

population or charge. Depending upon what E is, the intermediate 5.69 may be stable, or it may open to give the product of anti addition 5.70, as a consequence of the preference for inversion of configuration in the SN2-like ring-opening step. E E

inv.

E Nu

5.68

Nu

5.69

5.70

The more available the lone pair, the more firmly is bridging followed. Epoxidation gives directly a bridged product, with no intermediate, and often stops there; the addition of sulfenyl halides is well established as the electrophilic addition most strictly following the anti rule;486 and halogenation, with relatively tightly bound lone pairs, shows significant loss of stereospecificity, corresponding to some degree of attack avoiding the bridged intermediate, especially when the alkene has a good cation-stabilising substituent like a phenyl group and the solvent is polar.487 Hydroboration, oxymercuration, oxypalladation and other additions to alkenes in which the electrophilic heteroatom is electropositive, are less straightforward. They probably involve coordination by the metal to the alkene as a first step, but whether that coordination is best represented as a bridged structure 5.58 or 5.59 is not so clear, since these metals do not necessarily have accessible lone pairs to create two full bonds 5.69. Whether it is represented as bridged or involved in hyperconjugation 5.57, the transition structure for the next step has the nucleophile attacking with high levels of stereocontrol—syn in hydrometallation, carbometallation and metallo-metallation reactions, but anti in oxymetallation reactions. The hydro-, carbo- and metallo-metallations are stereospecifically syn because the nucleophile is delivered from the metal 5.71.488 (These reactions look superficially like pericyclic cycloadditions, and we shall return to them in Chapter 6.) The oxymetallations are stereospecifically anti, either because the nucleophile attacks a bridged intermediate, or because it attacks anti-periplanar to the donor substituent in the lowest-energy conformation 5.72, in which the empty p orbital is stabilised by hyperconjugation with the M—C bond (see p. 92). This kind of addition is the reverse of a -elimination, and responds to the same stereochemical constraints in favour of the anti-periplanar pathway. Just because a reaction is stereospecifically anti does not prove that it takes place by way of a bridged intermediate.

M

H

sy n

M

M H

ant i –

5.71

Nu

M Nu

5.72

5.1.3.5 Baldwin’s Rules. The direction of attack on  and p bonds affects the ease with which rings can form. Baldwin pointed out that when a nucleophile is tethered to an electrophile, it matters whether the bond being attacked, whether single, double or triple, is part of the ring or outside it.489 He noted that essentially all the reactions in which the bond was outside the ring were straightforward, and usually favourable processes. In contrast, when the bond was within the ring, there were some cases where ring formation appeared to be difficult, even when the ring being formed was not strained. Thus conjugate additions of the type 5.73 are easy and high yielding, but the superficially similar conjugate addition 5.74 does not take place; instead, the oxyanion attacks directly at the carbonyl group 5.75.490

5 IONIC REACTIONS—STEREOCHEMISTRY

219

O O O

OEt O EtO

O

OMe 5.73

5.74

O

5.75

Baldwin identified the problem as occurring most dramatically when a five-membered (or smaller) ring was being formed by attack on a double bond within the ring being formed, as in 5.74. He labelled this reaction a 5-endo-trig process, with the 5 referring to the size of the ring being formed, the endo referring to the double bond being within the ring, and the trig referring to the trigonal carbon under attack. Thus the easy reactions, 5.73 and 5.75, are both 5-exo-trig, with which there is evidently no difficulty. The explanation for this difference comes when we look at the ease with which the nucleophilic atom in each case can reach the appropriate position in space for attack on the double bond. In both cases, the nucleophile must approach from above and behind the p bond with approach angles resembling those in the transition structure 5.49. We can flesh this out for the 5-exo-trig reactions 5.73 and 5.75 in the drawing 5.76. The carbon under attack, C-1, will be on its way to becoming tetrahedral, and the chain of atoms attached to it, culminating in the oxyanion, can easily fold to put the oxyanion in a nearly ideal position 5.76. For the corresponding 5-endo-trig process 5.77, the chain of atoms C-1, C-2 and C-3 must all be in the same plane. The oxyanion is then only two atoms away from C-3 and it cannot reach to the position it needs to in order to attack at C-1. The chain is simply too short when it is trying to form a five-membered ring. Baldwin suggested that the problem is much less serious with a chain of six atoms, which is evidently just long enough to reach, but a chain of four atoms is even more problematic. O

O 1

1

X

2

3

O

EtO 5.76

5.77

Similar arguments apply to reactions in which the double bond is the nucleophile. Thus 5-exo-trig enolate reactions of the type 5.78 are easy and high yielding, but the superficially similar 5-endo-trig enolate alkylation 5.79 does not take place, and O-alkylation 5.80 takes place instead.491 5-exo-tr ig O

Br

Br

O

5-endo-trig

O 5.78

O

Br 5.79

5.80

With electrophilic attack on a C¼C double bond, the angle of approach depends upon the type of electrophile—bridging or nonbridging. In ring-forming reactions it is not often going to be a bridging electrophile, and an obtuse approach angle leading to a tetrahedral intermediate 5.56 is likely. The geometric constraints for electrophilic attack will make the 5-exo-trig process 5.81 easy and the 5-endotrig process 5.82 difficult, just as they did for nucleophilic attack. The O-alkylation 5.80 does not meet the

220

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

problem because there are lone pairs on the oxygen atom which can easily line themselves up with the back side of the C—Br bond. X

X

1

2

1

O

3

O

5.81

5.82

Baldwin considered all the possibilities, of ring size and of tetrahedral, trigonal or digonal atoms under attack, and produced a set of rules for which reactions are favoured and which disfavoured. Briefly, and augmented by later work, the disfavoured reactions are the n-endo-tet processes with n<9, the n-endo-trig processes with n<6 discussed above, and the n-exo-dig processes with n<5. Exceptions to some of the rules are known, but many of these are only apparent exceptions, because the compounds involved find different mechanisms, avoiding the disadvantageous features of a more obvious mechanism.492 Others simply have no alternative paths, and the constraints are not so forbidding as to make the disfavoured path absolutely impossible. Pericyclic reactions (Chapter 6) abound with exceptions—Baldwin’s rules appear to have little validity there, where there are many electrocyclic reactions that are 5-endo-trig, 4-endo-trig and even 3-endo-trig at both ends. Nevertheless the rules are a most helpful guide in planning a synthesis—if you choose one of the disfavoured reactions for a key step, it is just as well to have a good reason for expecting it to work in your case before you embark on the earlier steps. That the 6-endo-tet process is disfavoured had been established by Eschenmoser, who showed that the alkylation 5.83 only took place in an intermolecular sense.493 This is understandable from our knowledge that the SN2 process takes place with inversion of configuration (see p. 207). There is evidently, a strong preference, not only for inversion, but also for a nearly linear transition structure, which becomes reasonable only with a ring size of 9 in the reaction 5.84.494,495 There must be a considerable energetic penalty for bending, as Ingold observed when drawing attention to why even primary neopentyl substrates are so extraordinarily resistant to SN2 displacements496—the transition structure 5.85 would have to be bent. O

O S

O

O

O S

O

O S

CH3

CH3

SO2Tol

SO2Tol

H H

H N

5.83

5.84

X

O

O

H H Nu

5.85

The epoxide opening 5.86, giving a product with a four-membered ring, is unusual because five-membered rings are usually formed more rapidly than four-membered rings, and there appears at first sight to be a perfectly reasonable pathway 5.87 giving a five-membered ring. The explanation lies with Baldwin’s rules. The opening 5.86 is uncomplicatedly 4-exo-trig at the nucleophilic carbon, which is an anion derived from a nitrile. At the electrophilic end, the observed reaction 5.86 is 4-exo-tet, whereas the alternative reaction 5.87 is 6-endo-tet, which is not favoured by Baldwin’s rules.497 Note that there is a source of confusion in the naming of this process for Baldwin’s rules—the reaction 5.87 is simultaneously 5-exo-tet and 6-endo-tet. This reaction, if it were to occur, would set up a five-membered ring, and the opening of the 5-6 bond is exocyclic to that ring—hence the designation 5-exo-tet. Alternatively, and more pertinently in this case, following the chain of

5 IONIC REACTIONS—STEREOCHEMISTRY

221

atoms sequentially from 1 to 6 shows that breaking the 5—6 bond is endo to that chain, and it is this 6-endo-tet aspect that makes the reaction giving a five-membered ring less favourable than that giving the four-membered ring. As with the earlier endo-tet reaction 5.84, the problem lies in aligning the nucleophile more or less directly behind the C—O bond being broken, namely the 5—6 bond in the epoxide 5.87. N 3

4-exo-trig NC

4

1

and not

O

4-exo-tet

2

5

O

6

OH

N 5-exo-tet and 6-endo-tet

5.86

5.87 4

5-exo-tet

5

3

O

OH

and not

7

O

6

2 1

5-exo-trig

CN 6-exo-tet and 7-endo-tet N

N

5.88

5.89

The similar reaction 5.88 of another epoxide is unexceptionally 5-exo-trig at the nucleophilic carbon and 5exo-tet at the epoxide carbon. The alternative reaction 5.89 would be simultaneously 6-exo-tet and 7-endotet, the latter because the 6—7 bond is endo within a seven-membered ring. In this case, the normal kinetic preference for the formation of a five-membered ring is amplified by the difficulty in a 7-endo-tet reaction. Although these reactions show Baldwin’s rule being obeyed, other intramolecular openings of epoxides and related species provide special cases of endo-tet reactions that appear to break the rule. Changing the level of substitution so that the terminus is less substituted than the other carbon, or is made allylic, allows the 7-endo-tet processes 5.90 and 5.91 to take place even in competition with the 5-exo-tet. 497,498 The structural changes encourage the SN2-like reaction at the less-substituted or allylic carbons, overcoming their endo-tet nature. Evidently it is not difficult to overcome the barrier to six-membered ring formation. The most probable explanation for these reactions with endotet character taking place at all is that the strain inherent in epoxides changes the angles of productive attack, so that the rule of strict linearity in the SN2 reaction is lifted. This idea can be seen more precisely in the orbitals of cyclopropane (1.38 or Fig. 1.53), which are not on the direct line between the atoms in the ring. Attack by a nucleophile on orbitals like these will similarly not be diametrically opposite the line of the bonds that we draw on paper. Calculations also support the delicate balance between the five- and six-membered ring-forming reaction, and the acceptability of a less than perfectly colinear transition structure when epoxides are involved.499 OH

OH O

O H

N

7-endo-tet and 6-exo-tet 5.90

O

CN

O 7-endo-tet and 6-exo-tet

5.91

222

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

Surprisingly 5-endo-dig cyclisations appear to be favoured. One example of many is the formation of the carbocyclic ring 5.93.500 The nucleophilic carbon and the electrophilic carbon in the starting material 5.92 appear to be nowhere near within reach of each other, yet somehow they have become bonded. At first it was suspected that the approach angle for nucleophilic attack on alkynes might be acute, but this seems to be neither reasonable nor supported by good evidence—an obtuse angle of approach is surely preferred.501 The best suggestion for why the far end of the triple bond can be reached is that C—C bending in alkynes, as measured by the bending frequencies in IR spectra, is much easier than in alkenes, allowing the carbon under attack to bend reasonably often towards the nucleophilic centre, and thus allow an approach angle 5.94 closer to the optimal.411 Ph

Ph Li

Ph

Li

Li

5.92

5.93

5.94

5.1.4 The Stereochemistry of Substitution at Trigonal Carbon Both nucleophilic and electrophilic attack on trigonal carbon can take place by two pathways (Fig. 5.8)— direct attack on one of the  bonds attached to the double bond (path a), or by attack on the p bond (path b), with the formation of an ionic intermediate, followed by the loss, respectively, of a nucleofugal group X or an electrofugal group M. There are also formally unimolecular pathways, SN1 and SE1, with ionisation followed by capture by the nucleophile or electrophile, but the former is neither favourable nor common,502 and the latter unknown. The stereochemistry of the direct attack can be expected to resemble the corresponding reactions at a saturated carbon (Sections 5.1.1.1 and 5.1.1.2)—inversion for nucleophilic substitution, and retention, or perhaps occasionally inversion, for electrophilic substitution. In practice, SN2 reactions at trigonal carbon are rare,503 and their stereochemistry, where inversion is known,504 barely established. Electrophilic attack, like the reactions of vinyllithium reagents with protons, aldehydes and carbon dioxide, takes place invariably

a

Nu

X

a

Nu

M

E

M

E

a

a

b

b

Nu

X

E

M

b

b

Nucleophilic substitution

Fig. 5.8

X

Electrophilic substitution

Direct and stepwise substitution reactions at a double bond

with retention of configuration. This pattern ties in with the greater difficulty of configurational inversion at trigonal atoms than at tetrahedral atoms that we saw in Section 2.4.1. The necessity for inversion in SN2 reactions makes them very difficult at trigonal carbon, and the delicate balance between retention and inversion in SE2 reactions at tetrahedral carbons becomes overwhelmingly in favour of retention at trigonal

5 IONIC REACTIONS—STEREOCHEMISTRY

223

carbon. The more remarkable stereochemical features are found in those reactions that take the indirect path (path b), with addition followed by elimination. 5.1.4.1 Nucleophilic Substitution by Addition-Elimination.505 Nucleophilic attack takes place on the p bond in the activated alkene 5.95, creating an intermediate, typically an enolate 5.96. Rotation about the  bond can take place either clockwise by 60 to give the intermediate 5.97, or anticlockwise by 120 to give the intermediate 5.99. Since the C—X bond is lined up with the p system of the enolate in each of these intermediates, the loss of the nucleofuge can take place to give, respectively, the products 5.98 of retention of configuration, or 5.100 of inversion of configuration. There is a similar sequence of events for attack from below the p bond, which would give the enantiomers of all the intermediates, and is therefore equally probable, and there is a similar sequence for the reaction taking place on the s-trans conformation of the starting material 5.95. 60°

H

Nu Z

O clockwise O H

Z

X

O

5.95

H

O H

X

Z X

Z Nu X 5.98

5.97

Nu Nu

fast

slow

5.96 O anticlockwise

X

X

120° Nu

O Nu

Z H

H

Z

5.100

5.99

In practice, retention of configuration is commonly observed, as in the stereospecific reactions of the geometric isomers 5.101 ! 5.102,506 showing that the 60 rotation, to give the intermediate 5.97, is understandably more frequent than the 120 rotation. Cl Cl

CN E-5.101

EtS EtS E-5.102

CN

SEt CN

Z-5.101

EtS

CN Z-5.102

Furthermore, the loss of the nucleofugal group is evidently faster than rotation about the single bond 5.97 !5.99. The 60 clockwise rotation causes the stabilising negative hyperconjugation (Section 2.2.3.2) between the X—C  bond and the p system of the enolate steadily to increase as the dihedral angle between the two systems drops from 60 to 0. This rotation probably occurs in concert with the formation of the X—C bond and the intermediate 5.96 may never be formed as such. Only when the intermediate 5.97 has a long lifetime, either because X is a poor nucleofugal group like alkoxide or fluoride, or because the anionstabilising substituents Z are especially good like nitro, is the stereospecificity lost. However, the possibility of a very short lifetime for the intermediate, like less than one bond vibration, is equivalent to a mechanism that merges with the SN2 mechanism, and a continuum of mechanistic possibilities has been proposed. 5.1.4.2 Electrophilic Substitution by Addition-Elimination. Electrophilic attack has an exactly parallel series of events, which is best known from the electrophilic substitution of vinylsilanes. The electrophile attacks from above (or below) the p bond in the vinylsilane 5.103, moving towards the creation of an intermediate carbocation 5.104. Rotation about the  bond can take place either clockwise by 60 to give the

224

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

intermediate 5.105, or anticlockwise by 120 to give the intermediate 5.107. Since the C—Si bond is lined up with the empty p orbital in each of these intermediates, it is thermodynamically stabilising, but it is simultaneously kinetically unstable because it is aligned for removal by a silicophilic nucleophile X to give, respectively, the products of retention of configuration 5.106, or inversion of configuration 5.108. 60°

H A

clockwise E H

B SiMe3

A H

5.103

H

SiMe3

E

A

fast

E B

X

5.105 B SiMe3

A E XSiMe3

B

5.106

slow X

5.104

XSiMe3 A B E H

SiMe3

120°

B H

A E

anticlockwise

5.107

5.108

In practice507 retention of configuration is the normal pattern in protodesilylation, aliphatic Friedel-Crafts reactions, and similar reactions with other cationic carbon electrophiles. Examples are the ring closures 5.109 ! 5.110 and 5.111 ! 5.112, stereospecifically setting up the exocyclic double bond geometry with retention of configuration by the intramolecular attack of an oxocarbenium ion on the vinylsilane.508 The intermediate 5.105 is stabilised by hyperconjugation (Section 2.2.2) to such an extent that rotation 5.105 ! 5.107 is slow relative to the ease with which the silyl group is removed. Again, the 60 rotation is easier than the 120 rotation, and the attack and the 60 rotation are probably concerted without formation of the intermediate 5.104 as such. Bu

Bu SnCl4

O

SiMe3

Bu O

O

SnCl4

SiMe3

Bu O

MEMO

MEMO 5.109

5.110

5.111

5.112

The exception to this pattern is bromodesilylation, and a few similar reactions, in which the electrophilic attack 5.113 is followed by nucleophilic opening of the bridged intermediate 5.114.507 Rotation 5.115, followed by anti elimination of the silyl group and bromide ion 5.116, give the product of inversion of configuration 5.117. Br Br

H

A

X

inv. Br B SiMe3

H Me3Si

Br A B Br

5.113

5.114

AB

H Me3Si

Br 5.115

Me3Si

AB

XSiMe3 Br

Br H

A H

Br 5.116

B Br

5.117

Except for this type of reaction, retention of configuration is observed in electrophilic substitution, whether it is direct with a vinyllithium (path a in Fig. 5.8) or indirect with a vinylsilane (path b in Fig. 5.8). It is conceivable that even reactions with vinyllithium reagents take the indirect path, for a concerted attack on

5 IONIC REACTIONS—STEREOCHEMISTRY

225

the p system and a 60 rotation would lead to an even better stabilised cation with an Li—C bond than with an Si—C bond, and the stabilisation would lead to faster reaction.

5.2

Diastereoselectivity509

We have been concerned so far only with double bonds in which the top and bottom surfaces are either the same or enantiotopic and it has made no difference to the argument which we chose to use to illustrate the principle. We must now turn to those cases where the attack on one surface gives one diastereoisomer, and attack on the other surface gives a different diastereoisomer, when the surfaces are said to be diastereotopic. Early success in controlling stereochemistry came by tying a molecule into a tight ring system, so that only one stereochemistry was possible, or only one surface of a double bond was exposed. This approach, breathtaking in its day and still much used, achieves a high level of stereocontrol, sometimes complete, at the expense of having to build in to the synthetic scheme many extra steps to set up the ring systems, and yet more to unravel them. Control in open-chain reactions has, more often than not, been achieved by arranging for the reactions to have cyclic transition structures for which one conformation was much preferred over another—a chair-like six-membered ring, for example, with the larger substituents in equatorial positions. Some high levels of stereocontrol have been achieved in this way, but rarely complete, since inherently the energy differences between conformations is not all that great. Understanding how to control genuinely open-chain reactions, those without even a cyclic transition structure, has become possible from a combination of empirical observation and an appreciation of the electronic forces at work. This approach rarely achieves the high levels of selectivity that the constraints in a ring system can impart, whether from the starting material, the product, or the transition structure. The differences between one stereochemistry and another are rarely more than a few kJ mol1, often less than 20. Fortunately for synthetic chemistry, even differences as small as 10–20 kJ mol1 are enough to get very workable levels of selectivity. Understanding in terms of the charge and molecular orbital interactions is hampered by having only a crude and approximate tool with which to explain small differences in energy. Nevertheless, whenever a measurable, and especially a useful level of control is achieved, it is beholden upon the discoverer to make some attempt to explain it. Some explanations are inevitably feeble, because there is nothing obviously better, but it is always worth trying. Steric effects,510 in which a large substituent hinders the approach of a reagent from one direction, is nearly always a component of such explanations. This is, in one sense, an orbital interaction, since steric effects are the results of the interaction of filled orbitals with filled orbitals, for which there is nearly always an energetic penalty. There have been several attempts to explain, with more or less rigour, the transmission of electronic effects into a double bond and along a conjugated chain, but none has yet settled in as the accepted way to picture what is happening in orbital terms. In the most colourful approach, the electrostatic attraction of a point positive charge to the surface of each of the conformations of a starting material is calculated, and then mapped onto the surface with a colour code—red for maximum attraction and blue for minimum attraction.181,511 The results are beautiful pictures showing red hot spots on the molecular surface, and they give an immediate and vivid sense of where electrophilic reagents are likely to attack. There are methods based on the molecular orbitals, critically compared by Dannenberg,512 introduced by Klein513 (and modified by Ashby514), by Fukui,515 by Burgess and Liotta (called the Principle of Orbital Distortion),516 by Gleiter and Paquette,517 by Morokuma,518 by Dannenberg (given the abbreviation PPFMO),519 by Tomoda (given the abbreviation EFOE),520 and by Ohwada,521 as well as electrostatic models presented by Chandrasekhar and Mehta,522 and by Wipf.523 The problem is that a p orbital on its own must be symmetrical on the top and bottom surfaces. For the top and bottom surfaces to have differently sized lobes, whether it leads simply to pyramidalisation (if the p orbital is filled), or to differential electrophilicity (if it is empty), some fraction of an s orbital must be mixed in to create a hybrid (Fig. 5.9). An s orbital of one phase will push the lobe up, and an s orbital of the opposite phase will push it down. The problem comes in finding out what sign the s orbital will have in the frontier

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MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

+

+

Fig. 5.9

Mixing in s orbital character to desymmetrise a p orbital

orbital, or any other orbital for that matter, in any given situation. The sign can be extracted from calculations,181 but the sense is far from intuitive when it is induced by a neighbouring stereogenic centre. None of the methods listed above is simple enough to work at the level aimed at in this book. They cannot easily be taken and used with confidence in everyday situations, and the best that can be said is that this problem is still a challenge to theoreticians and physical organic chemists alike. The following sections attempt to indicate what factors might be involved, especially those associated with the molecular orbitals. They should be viewed with some suspicion, for comprehension in this area of chemistry is neither complete nor agreed. Steric effects and other electronic effects are difficult to disentangle, and the discussion here might be accused of exposing the wound more than healing it. 5.2.1 Nucleophilic Attack on a Double Bond with Diastereotopic Faces The earliest reaction to be studied showing open-chain diastereoselectivity was nucleophilic attack on a carbonyl group, either a carbonyl group with a stereogenic centre adjacent to it, first systematised by Cram in the formulation of his rule, or a carbonyl group like that in 4-tert-butylcyclohexanone, where the diastereotopic surfaces are distinguished by being axial or equatorial. We must now try to explain the stereoselectivity found in reactions like these. We shall find that this is still a hotly debated area. 5.2.1.1 The Felkin-Anh Rule.524 The attack of a nucleophile on a carbonyl group adjacent to a stereogenic centre is covered by Cram’s rule. When the three substituents differ only in size, and not in electronic nature, there is little difficulty. The explanation suggested by Felkin and Anh is now so widely accepted that it is often referred to as the Felkin-Anh rule. The code used has the groups ranked simply as large L, medium-sized M, and small S. Felkin suggested that the incoming nucleophile would attack the p bond anti to the large substituent,525 and Anh added that we must take the Bu¨rgi-Dunitz angle into account too.526 There are therefore two possibilities 5.118, with the medium-sized group ‘inside’ (i.e. eclipsing or partly eclipsing the C¼O double bond) and 5.119 with the small group ‘inside’. The latter is higher in energy, because the incoming nucleophile is pushed back, close to the medium-sized group, by the forces controlling the Bu¨rgiDunitz angle, whereas in the former it is close to the small group. They also reasoned that the steric repulsion from any eclipsing between the medium-sized group and the carbonyl group would be small, since there are no substituents on the oxygen atom. As it happens there is no need for special pleading to account for why the medium-sized group sits ‘inside’, since propanal adopts the conformation 2.187a (see p. 123) with the methyl group inside, with the two hydrogen atoms on C-2, one above and one below the plane of the p bond. The sense of attack is therefore firmly covered by 5.118. Ketones (R ¼ alkyl or aryl) and aldehydes (R ¼ H) reliably react predominantly in this sense, with aldehydes a little less selective than ketones, perhaps because they react some of the time in the sense 5.119 with the medium-sized group avoiding the inside position.

S

Nu

L

Nu– M R

O L

lower in energy than

S

M R –

Nu 5.118

5.119

M O

S O

R L 5.120

5 IONIC REACTIONS—STEREOCHEMISTRY

227

Just as the attack angle is not exactly 90, so none of the angles in the transition structure has to correspond to those drawn schematically in 5.118, and in particular the large group does not have to be exactly at right angles to the p bond. Angles close to those shown in 5.120 would seem to be near the minimum, although obviously affected in detail by the relative steric requirements of the R, Nu, S, M and L groups.476,527 We need to graft onto this picture consideration of the Flippin-Lodge angle (see p. 215). In aldehydes, with only a hydrogen atom on one side of the carbonyl group, the nucleophile will be tilted away from the stereogenic centre, and hence away from its influence, offering a second and perhaps better explanation for why aldehydes show lower selectivity than ketones. In those reactions in which a Lewis acid is coordinated to the oxygen atom, it will be cis to the hydrogen atom, increasing the steric bulk on that side, and making the Flippin-Lodge angle smaller. In agreement, the degree of stereoselectivity increases for these reactions, and for Lewis acid catalysed attack on acetals.528 The Felkin-Anh rule is reasonably, but not invariably,529 followed when the argument is based only on steric effects, but the picture becomes more complicated when one of the groups on the stereogenic centre is either more electropositive than carbon or more electronegative, when we need to take into account the electronic effect of having polarised bonds next to the reaction site. The lowest-energy conformations of the starting materials are fairly understandable for both cases. A bond to an electropositive element like a silicon atom will be conjugated to the carbonyl p bond 5.121, because hyperconjugation with an electron deficient group like a carbonyl is stabilising (see p. 94). However, Cornforth argued that a bond to an electronegative element, like a halogen, oxygen or nitrogen, will avoid the conjugation with the carbonyl group, since it is energy raising, and an -haloketone will have the lowest energy when the dipoles are opposed 5.122.530 A σ-donor (electropositive) substituent

A σ-withdrawing (electronegative) substituent H

H R

X

O

H Me3Si

H

O R 5.122

5.121

In both cases, calculations support the idea that conformations close to these are the lowest in energy, although the dihedral angles vary slightly from calculation to calculation, and they are, of course, affected by whatever groups R and X are present on the stereogenic centre.531,532 In both cases, the stereochemistry of attack corresponds to attack from the less hindered side of these conformations, as in the examples 5.123 ! 5.124533 and 5.125 ! 5.126.534,535 Li H

Me C5H11 O

Prn SiMe3 5.123

ClMg

HO C5H11

Prn SiMe3

5.124

91:9

Me

Cl H

HO

H O

H

Me

Cl

5.125

5.126

88:12

The problem with these explanations is that the lowest energy conformations are in neither case necessarily the most reactive. We have to take the Curtin-Hammett principle into account. The conjugation of the Si—C bond with the carbonyl group in the -silyl aldehyde 5.121 should raise the energy of the LUMO. Both the overall stabilisation and the higher-energy LUMO ought to make this a less reactive conformation than one in which the silyl group is orthogonal to the p bond. Nevertheless, the silyl group is the large group, and a transition structure 5.127 with the silyl group anti to the incoming nucleophile might be expected to be preferred, simply using the Felkin-Anh arguments based on steric effects. Furthermore, Cieplak has argued that the incompletely formed bond to an incoming nucleophile is inherently electron deficient in the

228

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

transition structure.536,537 This orientation also matches the preferred anti-periplanar arrangement for  elimination, which is essentially the reverse of nucleophilic attack. It follows that the transition structure will be lowered in energy if a donor substituent is placed anti-periplanar to the incoming nucleophile, and this picture, in which we ignore the thermodynamic stabilisation and LUMO-lowering, is more or less accepted. However, there is some evidence that the argument needs to be a little more subtle. Calculations on the transition structure for lithium hydride attack on an -silyl aldehyde, with an SiH3 group in place of the SiMe3 group, show that the hydride approaches the carbonyl group syn to the silyl group 5.128, presumably because there is an electrostatic attraction between the negatively charged hydride and the positively charged silicon.538 This is the opposite to the experimental observations, but a similar calculation, using an SiMe3 group, confirms that attack anti to the silyl group 5.127 is lower in energy.539 Evidently the steric effect is the dominant reason for the attack in the usual Felkin-Anh sense, with the three methyl groups shielding the positively charged silicon nucleus. Nu– H

R

H O

R

SiMe3 5.127

Me O R H Li SiH3 5.128

When one of the three groups on the stereogenic centre is an electronegative element like chlorine, the problem is more vexing. This time, the substituent could be activating—in the higher-energy conformation 5.129 the overlap of the C—Cl bond with the p bond lowers the energy of the LUMO, and therefore activates the carbonyl group for nucleophilic attack. The sense of the attack in this transition structure is the same as in the transition structure 5.125. The outcome, whatever the explanation, corresponds to the Felkin-Anh rule if the electronegative element is treated as the large substituent, whatever its actual size relative to the other substituents, and this is how the rule is usually presented. If this is the correct picture, rather than 5.125, then the effect of the chlorine atom can most easily be understood as two-fold—in the first place it activates the carbonyl group to attack, and in the second the fraction of negative charge it carries will repel the incoming nucleophile. However, if Cieplak is right, an electron-withdrawing group like this ought to raise the energy of the transition structure, since it is anti-periplanar to the electron-deficient bond that is forming to the nucleophile. This uncomfortable perception is often disguised when the incoming nucleophile is seen as providing electrons, and that therefore the electron-withdrawing group stabilises the transition structure. At the present time, it is not clear what the right answer is. Calculations for transition structures for nucleophilic attack by hydride and cyanide on aldehydes and ketones with electronegative substituents like fluorine, chlorine, methoxy, and dimethylamino give a transition structure similar to 5.129,526,540 –542 but a good case has been made for reviving the Cornforth explanation.543 Nu– H R

R O

Cl 5.129

Thus, for both electropositive and electronegative substituents, the stabilisation or destabilisation of the transition structure and the activation or deactivation of the starting material are in opposition, yet experimentally they appear to react in the same sense. What makes the present situation so uncomfortable is that we are accepting the steric effect as paramount for electropositive substituents like the trimethylsilyl group, but accepting the activating effect on the starting material as paramount for electronegative substituents like

5 IONIC REACTIONS—STEREOCHEMISTRY

229

chlorine. It is worth remembering that the differences in electronegativity between Si and C is actually greater (0.62) than the difference between Cl and C (0.33), but this is misleading as a guide to the relative degree of polarisation in the Si—C and Cl—C bonds. The polarisation of an Si—C bond caused by the difference in electronegativity between the two elements is shared among four bonds, whereas the whole of the difference in the Cl—C bond is located there. Nevertheless, true consistency to the Anh formulation that the most electronegative substituent be treated as the large group, would require that we placed the carbon group R in the -silyl ketone 5.121 anti to the incoming nucleophile, since it is the most electronegative substituent, but this would give the wrong diastereoisomer. Alternatively, consistency to the Felkin model 5.127 would require that we placed the halogen in the -halo ketone 5.122 ‘inside’ and the R group anti to the incoming nucleophile, which also gives the wrong diastereoisomer. Organic chemists are notorious for accepting explanations that work, without being too concerned about consistency; this is one of those cases. There is one further complication, but this time easily resolved, well understood, and supported by high level calculations.541 When the electronegative element coordinates to a metal that can simultaneously coordinate to, and activate, the carbonyl group, the conformation will be that of a ring. The electronegative element and the carbonyl oxygen are held synclinal, or at most gauche, to each other, both in the lowest energy conformation and in the transition structure. The attack from the less hindered side, opposite to the group R, is then relatively easily predicted 5.130, and is the opposite of that predicted from the Felkin-Anh rule. It has long been known as Cram-chelation control. R

Me

R

O

M O

H Nu– 5.130

5.2.1.2 Nucleophilic Attack on Cyclohexanones. At first sight, attack on a cyclohexanone with a locked conformation 5.131 would appear to resemble the problem covered by the Felkin-Anh arguments. The equatorial hydrogen atoms on C-2 and C-6 are forced to be the inside groups, more or less eclipsing the carbonyl group. The top surface of the carbonyl group, as drawn, is conjugated to the bonds between C-2 and C-3 and between C-5 and C-6, and the bottom surface is conjugated to the axial hydrogen atoms on C-2 and C-6. The steric difference between the two surfaces is therefore clear—the lower surface is less hindered, and we predict that equatorial attack should be favoured, giving more of the axial alcohol 5.132 than of the equatorial alcohol 5.133. This is what happens with large nucleophiles, and with hydride delivered from hindered reagents like selectride.544 The problem comes with small nucleophiles like hydride delivered from lithium aluminium hydride or sodium borohydride, or with cyanide or acetylide ion, when axial attack is favoured, giving more of the equatorial alcohol 5.133.514 There is evidently some electronic effect making axial attack inherently favourable. H

5

O

6 3

OH Nu–

Nu

H H

H 5.131

2

Nu +

OH

+

(+ H ) LiBH(Bus)3 LiAlH4

5.132

5.133 93:7 10:90

All sorts of explanation have been invoked for this curious result, which is not a consequence of differential solvation, since it is observed in the gas phase too.545 The most simple is Cieplak’s.472,546 He argues that

230

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

C—H bonds are better donors by hyperconjugation than C—C bonds (H is more electropositive than C, see pp. 50 and 89), and that the better donors should stabilise the transition structure for nucleophilic attack when they are anti-periplanar to the incoming nucleophile. This idea does not command universal agreement, the more obvious problem, already alluded to above, is that it is not universally accepted that the better donor should be anti to the incoming nucleophile, and the less obvious problem is that it is not possible to be dogmatic about which group actually is the better at hyperconjugation. The subject of C—H versus C—C hyperconjugation has a long and not particularly dignified history,547 but there is structural and spectroscopic evidence in favour of the relatively heterodox idea that C—H bonds are intrinsically better donors, of which the following are representative: (a) propionaldehyde in its lowest-energy conformation in the gas phase has both C—H bonds conjugated to the p bond 5.134 (¼ 2.185a), and the methyl group is in the sterically most crowded position;216,548 (b) triethylborane 5.135, with the empty p orbital on boron making it isoelectronic with a tertiary carbocation, has the C—H bonds conjugated to the empty orbital;549 (c) enolate formation from the ,-unsaturated ester 5.136 favours the formation of the cis double bond 5.137, indicating that the starting material has the C—H bonds conjugated through the double bond to the carbonyl group;550 (d) UV spectra in the gas phase show longer wavelength 0-0 maxima for toluene than for tertbutylbenzene, and for trans-2-butene than for trans-1,2-di-tert-butylethylene; (e) the chemical shifts in the NMR spectra of alkenes551 and p-alkylbenzyl cations552 indicate greater electron release successively from methyl groups than from ethyl, i-propyl and tert-butyl groups, which is known as the Baker-Nathan order; and (f) the Perlin effect (see pp. 64 and 85) indicates the a C—H bond is more effective in hyperconjugation than a C—C bond.

H

H Me

H

O

Me

H

H

H

H

H

5.134

B Me

Me H

5.135

H

H

MeO Me

LiNPri2

O

H

H

H

MeO Me

OLi H

H 5.136

5.137

There are other explanations for each of these pieces of evidence, and there is also plenty of contrary evidence suggesting that the larger alkyl groups are better donors,553 especially when the electron demand is high. Presumably the larger number of electrons available in the larger alkyl groups can be drawn upon, inverting the Baker-Nathan order. Since the attack of a nucleophile on a carbonyl group is not making a large demand, the idea that it is controlled by superior C—H hyperconjugation cannot easily be dismissed. Because of the unsettled reception for Cieplak’s idea, other theories are still current. The most thoroughly accepted draws attention to the fact that the C¼O bond is not perfectly eclipsing the equatorial C—H bonds on C-2 and C-6—it is pointing 4–5 lower, as can be seen in the Newman projection 5.138 along the C-1 to C-6 bond of 5.131. Equatorial attack, therefore, would have to squeeze in closer to the axial C—H bonds on C-2 and C-6, and push the oxygen past the two equatorial hydrogen atoms. Axial attack, however, creates an approach to the transition structure 5.138, in which the oxygen can move down into an equatorial position without developing any eclipsing. H

5 3

Nu

O

6

5

H O

H 2

H H

5.131

4-5°

2

H 5.138

The energetic cost of the eclipsing which has to occur when the attack is equatorial is described as torsional strain. It is evidently greater than the energetic cost suffered by small nucleophiles from the

5 IONIC REACTIONS—STEREOCHEMISTRY

231

1,3-diaxial interactions with the hydrogen atoms on C-3 and C-5 during axial attack.527,540,554 Somewhat similar considerations apply to tertiary methylcyclohexyl cations, which are slightly pyramidalised, like the carbonyl carbon, with the methyl group moved towards an equatorial orientation, exposing the axial direction to attack.555 Further complications arise when there is a substituent  to the carbonyl group.556 An  chlorine with an axial configuration encourages axial nucleophilic attack, and hence anti to the halogen, in conformity with a picture combining 5.129 and 5.138. However if the axial halogen is fluorine, or the  halogen is in an equatorial configuration, nucleophilic attack is predominantly equatorial. In contrast to cyclohexanones, the dioxan-5-one 5.139 (R¼tBu) is attacked by nucleophiles in the gas phase from the equatorial direction,557 because of electrostatic repulsion from the fraction of negative charge carried by the two oxygen atoms in the ring, as Houk had predicted.558 The selectivity is not particularly high (67:33), because the usual torsional strain is still present, enhanced in this case by the shorter C—O bond lengths making the ring less puckered, and increasing the dihedral angle by which the carbonyl oxygen atom is pushed below the neighbouring C—H bonds. In solution, however, the ketone 5.139 (R¼Ph) is attacked from the axial direction,559 just like cyclohexanones. Evidently the solvent insulates the charge on the OH

O

n-BuSiH4– t Bu gas phase

O

H

O

67:33 S

O R

O 5.139

OH

O R

H LiAlH4 Et2O

O Ph

O

OH

S S

R

S

H

R = tBu, n-BuSiH4–, gas phase: 84:16 5.140 R = Ph, LiAlH4, Et 2O: 85:15

97:3

incoming nucleophile from the electrostatic repulsion, the torsional strain remains high and there are no axial substituents hindering axial attack. The sulfur atoms in the dithia analogues 5.140 are less electronegative than the oxygen atoms in the acetals 5.139, but the axial lone pairs bulge further up, and are not heavily solvated. However, the carbonyl group is displaced even further down by the changes in bond length and bond angles from having two C—S bonds in the ring. The one effect makes axial attack less favourable, and the other makes equatorial attack less favourable. In the event both solution and gas phase reactions take place with a strong preference for equatorial attack. 5.2.1.3 Nucleophilic Attack on Cyclic Oxonium and Iminium Ions. Whatever the final reception for Cieplak’s idea, there is little doubt that nucleophiles attack cyclic oxonium ions and iminium ions from the direction that builds an anti-periplanar lone pair. This is another version of the anomeric effect (Section 2.2.3.3), but applied now to reactivity instead of simply to structure. We have already seen that axial anomeric bonds are longer than their equatorial counterparts, that they are weaker, and that they ionise more easily. The corollary, because the transition structure is low in energy for both the forward and back reactions, is that nucleophiles attack more rapidly from the anomeric direction. There is an abundance of evidence that the more lone pairs that can be anti to the leaving group or incoming nucleophile, the easier the reaction is in either direction.560 Thus the orthoester 5.141 reacts with Grignard reagents to give the product 5.142 of axial attack, whereas the equatorial isomer is unreactive.561 Both the departure of the methoxy group and the attack by the nucleophile are axial, which can be explained by the contribution of the anti-periplanar lone pairs to weakening the axial bond, and yet stabilising the forming bond in the second step.

232

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

MeBrMg

BrMg Me

OMe MeMgBr O

O

O O

O

O

5.141

5.142

The same pattern is seen, with only one lone pair, in tetrahydropyrans, when nucleophiles like allylsilanes and allylstannanes attack axially in Lewis acid catalysed reactions in pyranyl sugars.562 The same pattern is also found in imminium ions563 as Stevens demonstrated in several syntheses. He showed that nucleophiles attack from the direction that most easily sets up an anti and axial lone pair, especially if it can create a chair conformation, as in the reduction of the imminium ion 5.143 to give monomorine-I 5.144.564

Nu

H

NaCNBH3 N

N Bu

Bu 5.144

5.143

5.2.1.4 Vinylogous Felkin-Anh Rules. There are two reactions that can be called vinylogous versions of attack on a carbonyl group adjacent to a stereogenic centre, in the first of which an intervening double bond makes the attack vinylogous with respect to the carbonyl group 5.145.565 The most common reactions of this type are organocuprate conjugate additions,566 although others with heteroatom nucleophiles are known. Bu Ph Nu–

Bu2CuLi, BF3

CO2Et

Ph

CO2Et

O Me

L

Me

S

M

Bu2CuLi, BF3

Ph 5.145

Me

70:30 Bu

E-5.146

CO2Et

Ph

CO2Et Me

70:30

Z-5.146

The factors affecting which side of the double bond is attacked ought to be the same as in the Felkin-Anh rule, but with the conformation of the starting material affected by the fact that it is a C¼C double bond and not a C¼O.567 The presence of a substituent on the double bond cis to the stereogenic centre, even when it is only a hydrogen atom, increases the A1,3 allylic interaction with the medium-sized group 5.147. H

Ph

Nu– Me H CO2Et

H

Felkin product

Me

H H

CO2Et H

anti-Felkin product

Ph 5.147

Nu– 5.148

When the medium-sized group is a methyl group, and when the substituent cis to it is a hydrogen atom, as in the trans alkene E-5.146, it appears that the Felkin-Anh conformation for the transition structure 5.147, with the medium-sized group inside, is still the lowest in energy in spite of the A1,3 allylic interaction, and attack

5 IONIC REACTIONS—STEREOCHEMISTRY

233

on the double bond takes place in the Felkin-Anh sense from above, as drawn. The conformation with the methyl group inside is almost certainly higher in energy, but in the transition structure 5.147 it allows the nucleophile to approach close to the hydrogen atom, lowering the energy of this transition structure. This is called the ‘inside-methyl’ effect. However, when the substituent cis to the stereogenic centre is larger, as in the corresponding cis alkene Z-5.146 (or the alkene with two ester groups), this conformation gives way to the alternative 5.148 in which the small group is rotated into the inside position, and the nucleophile is therefore directed to the bottom surface, in order for it to be anti to the large group. This picture works reasonably well, provided that the group cis to the stereogenic centre is a hydrogen atom and the mediumsized group is relatively small like a methyl group, accounting for the major products in the examples above. The rule is sometimes referred to as a modified Felkin-Anh rule—as well as being modified, it is more complicated, because of the ‘inside-methyl’ effect. It is also more sensitive to variation in the nucleophile, possibly because the nucleophile changes the mechanism.568 When one of the substituents is an electronegative element, the story becomes even more complicated.569 The conjugate additions to the silyl ethers E-5.149 and Z-5.149570 have the opposite stereochemistry to that which might have been expected from the reactions of the esters E-5.146 and Z-5.146. They follow the modified Felkin-Anh rules only if the silyloxy group is treated as the medium-sized substituent, or if it is delivering the reagent after coordination in conformations like 5.147 and 5.148 with the silyloxy group occupying the same position as the phenyl group. A silyloxy group is not thought to be a strong Lewis base, and coordination is not usually a problem with it; no other coherent picture emerges. Me t

Bu Me2SiO

CO2Et

Me2CuLi, BF3

t

Bu Me2SiO

Me E-5.149

Me

73:27 Me

Me2CuLi, BF3

ButMe2SiO

ButMe2SiO

CO2Et

Me

CO2Et

CO2Et Me

87:13

Z-5.149

These explanations applied to cuprate reactions assume that the stereochemistry-determining step is the initial coordination of the copper to the C¼C double bond, with the subsequent -bonding of the copper to the  carbon and the reductive elimination step which establishes the C—C bond taking place from this intermediate. This may not always be the case, and it is possible that the relative ease with which either the -bonding or the reductive elimination takes place determines the stereochemistry. Thus lithium dimethylcuprate and the cyclic enone 5.150 give mainly the conjugate addition product 5.153 with the incoming nucleophile syn to the oxygen atom. In the presence of trimethylsilyl chloride, however, the major product is 5.151 with the methyl group anti to the oxygen atom.571 Corey’s explanation is that the intermediate 5.152, although the minor isomer formed in the coordination step, is the more rapidly broken down in the absence of the silyl chloride. CuMe2 major

O

O slow

O

O

O O

O 5.150 minor

O

CuMe2 5.152

5.151 O

fast O

5.153

234

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

Changing the nucleophile from a cuprate to an amide anion causes the conjugate addition 5.154 ! 5.155 to change sense—it straightforwardly obeys the modified Felkin-Anh rule with the silyloxy group taken as the large substituent and the methyl inside with the trans alkene. The degree of selectivity is low, but becomes quite high when the silyloxy group is made even larger.572 Many other examples of stereoselective conjugate addition with an electronegative substituent on the stereogenic centre exist, but with no comprehensively satisfying explanation, and sometimes with no explanation at all. Ph ButMe2SiO

CO2But

LiNBnSiMe3

SiMe3

N

ButMe2SiO

Me

CO2But Me

5.154

5.155

54:46

The other kind of vinylogous reaction related to the Felkin-Anh rule is direct attack on the carbonyl group 5.156 instead of the conjugate attack 5.145. The stereochemical information must now be transmitted either through the double bond or through space. Except when coordination delivers the reagent from one of the three substituents,573 or when the double bond is cis and the stereogenic centre is close enough to exert its effect predominantly through space as a steric effect,471,574 these reactions usually,575 but not always, show little diastereoselection. One remarkable exception is the open chain ketone 5.157, which is reduced to give largely the alcohol 5.158.576 Another exception is in the relatively rigid cyclohexadienone system 5.159, which is more or less free from ambiguity about the conformation at the time of reaction. The ring is flat, and the two surfaces of the p system are different by virtue of one being cis to the C—O bond and the other cis to a C—C bond. Grignard reagents add selectively to the surface syn to the alkyl group and anti to the oxygen to give the alcohol 5.160.523 SPh

SPh

LiEt3BH

O O

L

OH

5.157 S

5.158

97:3

M Nu– 5.156

O

O

MeMgBr

O

OH

O

O 5.159

5.160

97:3

To try to explain these results, we need a theory that allows us to identify the differential effect of the two  bonds, C—C and C—S or C—O, on the upper and lower surfaces of the p system. To some extent we did this in considering how electropositive and electronegative groups influenced the attack on a carbonyl group, but the way the argument was developed there only applies to attack at the neighbouring carbon—it cannot be extended along a conjugated system. 5.2.1.5 Pyramidalisation. The simplest possibility is to extend the idea used to explain axial attack on cyclohexanones by unhindered nucleophiles (see p. 230). The carbon atom and the oxygen atom of the carbonyl group and the two substituents C-2 and C-6 do not lie perfectly in the same plane—C-1 is a little above the plane defined by C-2, C-6 and the oxygen atom in the drawing 5.138. The carbon is said to be pyramidalised.577 Attack from the axial direction merely increases the degree of pyramidalisation, avoiding

5 IONIC REACTIONS—STEREOCHEMISTRY

235

the torsional strain induced by equatorial attack, which would have forced the equatorial hydrogens to pass through a conformation in which they eclipse the C—O bond. There is therefore the possibility that all we need to know is the sense of pyramidalisation to predict the stereochemistry of attack on a trigonal carbon,578 and to a large extent the stereochemistry of many reactions is well correlated to the sense of quite small degrees of pyramidalisation as measured by X-ray crystal structure determinations.579 The direction of pyramidalisation in open-chain systems is also fairly easy to predict from first principles—it takes place away from the substituent held most nearly at right angles to the plane of the carbonyl group, because it leads to a greater degree of staggering 5.161 in that direction. It is independent of whether the substituent is an electron donor or an acceptor, as calculations for 2-silylacetaldehyde 5.162 and 2-fluoroacetaldehyde 5.163 show.580 The former, with an Si—C—C—O dihedral angle of 92.4 is the global minimum (compare 5.121), but the latter has to be constrained to the same angle before optimisation of bond and dihedral angles, otherwise a structure with the fluorine in the plane of the carbonyl group is obtained (compare 5.122). The fluorine atom leads to a slightly greater degree of pyramidalisation, perhaps because it has some of the character of an anomeric effect. The sense of pyramidalisation in these two cases matches the sense of nucleophilic attack discussed in Section 5.2.1.1. H3Si

R R R

O R

1.6° H

O H

H

5.161

92.4°

5.162

F frozen O H H

3.2° H

5.163

Another suggestion, based on high level calculations on cyclohexanone,581 is that p*CO is unsymmetrically disposed, bulging axially, above the plane of the p bond when the ring is drawn as in 5.131 and 5.138. Since this is the LUMO, overlap with the HOMO of the nucleophile is better from the axial direction. If pyramidalisation is induced by increasing the degree of staggering, the trigonal carbon atoms in a conjugated chain ought to be pyramidalised along the chain in alternating directions. Thus a C¼C double bond 5.164 pyramidalised downwards at C-2 by the anti-periplanar R group on C-1 ought, other factors being equal, to be pyramidalised upwards at C-3, and so on, alternating down a longer chain. Thus we can try to predict what the pyramidalisation will be in the ketones 5.157 and 5.159. If we assume that they react with nucleophiles when the electronegative substituent is conjugated to the carbonyl group, lowering the energy of the LUMO, as in the usual Felkin-Anh picture 5.129, then the reactive conformations will be pyramidalised as shown exaggerated in 5.165 and 5.166, both of which imply preferred attack from below, which is O

SPh

R 2 3

1

5.164

O

H

O O

5.165

5.166

what is observed. A simple application of predictions like these, however, is not reliable, because the benzyl ether, corresponding to the phenythioether 5.157, gives largely the opposite diastereoisomer on reduction. The difficulty of using pyramidalisation is further compounded by some known cases where the X-ray structure shows pyramidalisation in one direction, when reactions are known to take place from the opposite, but these are from electrophilic attack on a C¼C double bond, which we shall deal with later in Section 5.2.2. 5.2.1.6 The SN20 Reaction. The SN20 reaction, in which an allyl system equipped with a nucleofugal group undergoes attack at C-3, is the vinylogous version of the SN2 reaction. As discussed earlier (see p. 181), an

236

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

allyl halide usually undergoes a straightforward SN2 reaction, with direct attack at C-1 and inversion of configuration at that centre. On the special occasions when the SN20 reaction does take place, it can, in principle, do so with syn 5.167 ! 5.168 or anti stereochemistry 5.167 ! 5.169, and the story is complicated further by there being two syn reactions and two anti reactions. The characteristic feature of a stereospecific SN20 reaction would be that it gave a mixture of only two of the four possible products, say both of the syn products 5.168a and 5.168b, not necessarily in equal amounts since that only depends upon which conformation 5.167a or 5.167b is the more reactive, but neither of the anti products 5.169a and 5.169b. The two syn products 5.168 differ from each other in two respects—double bond geometry and configuration at the stereogenic centre, whereas they each differ from one of the anti products in only one stereochemical feature. Equally a stereospecific reaction might give both of the anti products but neither of the syn. BA Nu

syn C

D

Nu

Nu

syn

X

Nu H

A B Nu

anti

5.167a

anti B

H CD

A B

Nu

A

syn

anti

5.168a

A

Nu

syn

B

X

C

C 5.168b

D

5.167b

BA

anti

C

D

D

Nu

5.169a

C

D

5.169b

Both syn and anti reactions have been observed, and it is not yet clear what all the factors are that favour the one over the other. The heart of the problem is to know how the stereogenic centre carrying the nucleofugal group X differentially affects the charge and the orbitals on the top and bottom surfaces of the double bond. We can begin again by treating this as a problem of predicting the direction of pyramidalisation, with the advantage that this time we can be confident that the nucleofugal group in a concerted reaction will be conjugated to the double bond at the time of reaction as it is in each of the conformations 5.167, and will therefore be the prime influence inducing the pyramidalisation. The picture we obtain, using the 5.167b conformation is 5.170, implying that the preferred reaction ought to be on the upper surface of C-3 in this case, syn to the leaving group X. We come to the same conclusion with tau bonds—the attack on the upper surface of C-3 is anti to the lower tau bond 5.171, showing inversion of configuration at that atom, and that in turn is anti to the leaving group X, which is also effectively displaced with inversion. A similar sequence using either pyramidalisation or the tau bonds can be drawn for the 5.167a conformation which would suggest that the preferred side of attack was from below. The expectation is for the SN20 reaction to be stereospecifically syn. X 2

A B

3

H

syn

Nu

syn

1

C D

A

B

C

D

Nu H

A B

inv. inv.

5.170

5.168b

X

C

D

5.171

However primitive these treatments are,582 the conclusion has a certain appeal for it implies that having two more electrons in the transition structure changes the stereochemistry, from inversion in the SN2 reaction to syn in the SN20 reaction. We saw the same change in substitution reactions, retention for SE2 to inversion for SN2, and for elimination reactions, anti for E2 to syn for E20 (Section 5.1.2.2), but in both those cases, and in the SN20 reaction, it is not reliable.

5 IONIC REACTIONS—STEREOCHEMISTRY

237

Experimentally, the first problem to overcome is that allylic electrophiles nearly always react by the SN2 pathway, rather than by the SN20 pathway (Section 4.5.2.2). This can be overcome by building up steric hindrance near the nucleofugal group, and there is then a trend in favour of the syn reaction. In the first examples to which stereochemistry was assigned, Stork found that the trans allylic mesitoate trans-5.172 gave largely the trans amine trans-5.173, and the cis mesitoate cis-5.172 gave largely the cis amine cis-5.173, showing that these reactions were stereospecifically syn.583 However, Stork found that changing to a sulfur nucleophile reduced the degree of stereospecificity from almost completely syn to variably syn or anti, depending upon the solvent, showing that the syn stereospecificity is not fixed immutably.584 O2CAr

O2CAr sy n

sy n N

HN

N

HN

trans-5.172

cis-5.172 tr ans-5.173

cis-5.173

In this pair of stereoisomeric starting materials, the problem had been simplified by using a cyclic alkene so that there are no longer two conformations a and b to complicate the analysis, but this device brings with it its own complication. Studying stereochemistry using compounds with rings and resident stereochemical labels like the isopropyl group in these compounds means that the ring system and the resident centres create a conformation in the starting materials that can override whatever inherent stereochemistry the reaction itself might have. In an open-chain system 5.174, designed to minimise this problem by having only the one stereocentre, only the difference between hydrogen and deuterium at C-3 and relying on the preference for forming a trans double bond, the reaction 5.174 ! 5.175 was highly syn stereospecific (>96:4),585 but a closely similar reaction with a carboxylate leaving group was syn to a much less marked degree (<64:36).586 Other examples of SN20 reactions showing syn stereochemistry, without having any obvious bias in the system, are some cyclobutenyl halides with oxygen nucleophiles,587 and an intramolecular cyclopropaneforming reaction in which the nucleophile was an enolate carbon atom.588 Et2NH H

H D

Cl

H

syn

Et2N H

Me

D

5.174

H

Me

5.175

There are also a few reactions showing more or less preference for an anti SN20 reaction, including a cyclopentane-forming reaction with an enolate nucleophile,589 and a sulfur nucleophile.590 In addition, the reactions of alkyl cuprates with allylic acetates are always stereospecifically anti 5.176 ! 5.177, although the formation of racemic product shows that regiocontrol has been lost.

Me2CuLi

+

OAc 5.176

anti SN2'

5.177

inversion SN2

238

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

The cuprate reactions are not mechanistically SN20 reactions, since they involve in the first step coordination of the copper on the lower surface of a p-allyl system, followed by the delivery of the methyl to the same surface, and equally to both ends of the allylic system, in a reductive elimination step.591 It seems likely that the decisive step determining the stereoselectivity is the coordination of the copper. It might well coordinate reversibly and equally easily to both surfaces, in an alkene like 5.176, but the chloride will only depart when the copper is anti to it. The same explanation might be offered for a similar result in the reduction of propargyl derivatives with lithium aluminium hydride, in which coordination by the aluminium is probable.592 If we move on to the SN200 reaction, with one more double bond, there are reactions in which nucleophilic attack has changed sides again, and is anti 5.178 ! 5.179.593 In this example, the ring system has a bias that is likely to lead nucleophiles to attack from the side opposite the oxygen atom, whether this reaction takes place in one step or two, whatever inherent preference there might be for the SN200 reaction. OMe

OMe

t

Bu O2C

t

NaOMe

OH

Bu O2C

O anti 5.178

5.179

5.2.2 Nucleophilic and Electrophilic Attack on Cycloalkenes We have seen cycloalkenes in the previous section, but in those cases it was the fundamental stereochemistry of the reaction that was under consideration. We now turn to the stereochemistry governed by the ring system itself, and we shall look at both nucleophilic and electrophilic attack, since they usually have similar stereochemical preferences rather than contrasting preferences. There is a problem with electrophilic attack that we do not meet with nucleophilic attack—the attacking reagent does not always reveal the stereochemistry. If the electrophile is a proton, for example, it usually attaches itself to the less-substituted carbon, where there may already be a hydrogen atom, and the stereochemistry observed is that of the subsequent nucleophilic attack. Similarly, the initial electrophilic attack may take place rapidly and reversibly on either surface, but it is the ease with which the second step, a loss of a proton, for example, or the gain of a nucleophile, which may determine which of the intermediates leads on to the major product.594 We shall not be concerned with reactions like these here. However, in addition to several reactions that are straightforwardly electrophilic attack, we shall be concerned with several which can be described as electrophilic in nature, like the reactions of alkenes with osmium tetroxide, with peracids, with some 1,3-dipoles, and with boranes, and of dienes with dienophiles in Diels-Alder reactions. Some of these reactions are pericyclic, the pericyclic nature of which we shall meet in Chapter 6. For now, it is only their diastereoselectivity that will concern us. 5.2.2.1 Monocyclic alkenes. Cycloalkenes have a preferred conformation, which may or may not influence the stereochemistry of attack upon the double bond. The attack is always more or less along the line of the p orbitals, as discussed in Section 5.1.3, but there may be steric or electronic effects operating to affect which of the two surfaces of the double bond is best presented to an incoming reagent. At its most simple, a single substituent on a four- or five-membered ring usually causes electrophiles (and nucleophiles) to attack anti to it as in the allylation of the enolate 5.180.595 The uncomplicated explanation is that the large group hinders approach from the side it occupies, and supporting this argument the enolate 5.180 is highly selective only when the side chain carries a noticeably large protecting group.

5 IONIC REACTIONS—STEREOCHEMISTRY

239

H O Ph3CO

H

Br O

O Ph3CO

5.180 MCPBA

But

But

+ O

O H

O

But

60:40

5.181

The relatively small degree of kinking away from a flat conformation in these small rings can usually be ignored, but it cannot be ignored with six-membered and larger rings. In a six-membered ring a large group will be equatorial in the most abundant conformation, but the two surfaces of a cyclohexene like 5.181 are sterically not very different. This alkene is attacked by peracid with little selectivity, and what little there is happens to be in favour of attack syn to the resident group.596 In the epoxidation reaction, electrophilic attack is taking place concertedly at both carbons of the double bond. If pyramidalisation is important, it gives us no help, because one of the carbon atoms of the double bond can be expected to be pyramidalised upwards and one down. In contrast, when the attack is only at one of the two carbons, the degree of stereocontrol in a six-membered ring becomes high. One simple way to appreciate this is to see the pyramidalisation as taking place to move the cyclohexene conformation from a half chair closer to a full chair. The enolate methylations 5.182 and 5.184 are selective for axial attack, leading to chair conformations 5.183 and 5.185 in the product.597 In the former, the attack is anti to the tert-butyl group and in the latter it is syn, in contrast to what happens in five-membered rings. The reason can be seen on both sides of the reaction coordinate—in the presumed pyramidalisation of the starting material, and in the greater ease of forming a chair conformation rather than a boat in the product. There are similar explanations for the stereochemistry of nucleophilic attack in six-membered rings such as 5-substituted cyclohexenones,598 which again allow stereochemistry to be transmitted effectively from one stereogenic centre to another three atoms away. CD3I

But

But

CD3

O

O

5.182

CD3I

But

But O

O

5.183 70:30

5.184

CD3

5.185 83:17

Medium-sized rings have a different feature allowing high levels of diastereoselectivity.599 In these rings, a double bond does not lie flat in the average plane of the ring. Instead it presents one face towards reagents, while the other is obscured by the ring wrapped around behind it. If the conformation can be controlled, high levels of stereocontrol can be achieved, whether attack is by an electrophile 5.186 or a nucleophile 5.187. The problem with medium-sized rings is to predict their conformation. Only with simple cases is it easy to see why conformations like 5.186 and 5.187 are the most populated, with the rings kinked in the direction that makes the methyl group equatorial, and why attack from the front surface as drawn is most favourable.

O

O

MeI O

O

Me I

5.186

O

O

BF3:OEt2

O 86:14

Me2CuLi

O

CuMe2 5.187

99:1

240

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

5.2.2.2 Bicyclic alkenes. Bicyclic systems like the alkenes 5.188 and 5.189 are well known to be attacked from the exo direction,600,601 on the less hindered convex face of the bicyclic system. Similarly high levels of stereocontrol are found for nucleophilic attack on bicyclic systems, as in the reduction of the ketone 5.190, in which the preference for exo attack overwhelms the steric hindrance offered by the adjacent methyl group.602 Bicyclic systems, especially like these with a zero bridge, are often used in synthesis to give reliably high levels of stereocontrol, with the penalty that there may be many steps needed to open them up to reveal a target structure. N

CH2N2

H

1. B2H6

OH

N 2. NaOH, H2O2 5.188

5.189 OMe

OMe

O

O

NaBH4

H MeO2C

MeO2C

O 5.190

OH

However, there are anomalies, where a steric effect is clearly not enough to explain the observed stereoselectivity. The steric argument, although commonly invoked, is weak for norbornene 5.191 and for the bicycloocta[2.2.2]diene 5.192, but the selectivity for exo attack in the former and endo in the latter is strong.603,604 exo

O

OsO4

OH OH

O

O O

O endo O 5.192

5.191

More convincingly, the steric argument is nearly nonexistent for the diene 5.193, but it shows high levels of diastereoselectivity in Diels-Alder reactions, with attack in the endo direction, which is, if anything, the more hindered.605

CO2Me CO2Me endo 5.193

One possible explanation for these results is based on the sense of pyramidalisation at the reacting trigonal carbons. In norbornene they are measurably pyramidalised with the p orbitals bulging in the exo direction 5.194, anti to the two-carbon bridge, since the  bonds leading to them, marked in bold, are better aligned for overlap with the orbitals of the p bond 5.195 than the  bonds of the one-carbon bridge.606 Even though the degree of pyramidalisation is small, electrophilic attack from the exo direction will induce less torsional strain,607 just as axial attack by nucleophiles does on cyclohexanones. The double bond undergoing attack in

5 IONIC REACTIONS—STEREOCHEMISTRY

241

the bicyclooctadiene 5.192 pyramidalises with the p orbitals bulging downwards 5.196, because the  bonds from the tetrahedral carbons, marked in bold, are more effective donor substituents than the  bonds from the trigonal carbons. The latter have more  bonding involving the 2s orbitals than the former, making the tetrahedral carbons effectively more electropositive than the trigonal carbons (Fig. 1.57). This can be justified most succinctly using hybridisation—they are sp3 and sp2, respectively—but, even without using hybrid orbitals, it can be seen that using one p orbital exclusively in the p bond, inherently means that more of the 2s orbital contributes to bonding in the  bonds to the trigonal carbons. In the diene 5.193, the alternation of pyramidalisation along a chain of double bonds (see p. 235) implies that the termini of the double bonds would be pyramidalised downwards, exaggerated and shown for the HOMO in 5.197, and that is the direction from which the electrophilic dienophile attacks.

≡ H

H

H

H H

H 5.195

5.194

5.196

5.197

However, pyramidalisation is not the whole story, for there are alkenes known to be pyramidalised in one direction, which nevertheless react in another,608 and we shall come to further anomalies in using only pyramidalisation when we come to discuss SE20 reactions in Section 5.2.3.4. 5.2.3 Electrophilic Attack on Open-chain Double Bonds with Diastereotopic Faces 5.2.3.1 The Houk Rule for Steric Effects in Electrophilic Attack on Open-Chain Alkenes. As in nucleophilic attack on a C¼C double bond (Section 5.2.1.4), the conformation of an open-chain alkene with a neighbouring stereogenic centre is likely to have the small group inside 5.198, more or less eclipsing the double bond.609 Electrophilic attack on such a double bond, by a bridging or nonbridging electrophile, is then, in the absence of stereoelectronic effects, likely to be anti to the large group. This explanation for the stereochemistry of electrophilic attack on most alkenes has been advanced a number of times, first by Zimmerman,610,611 then by Barton,612 by Kishi,613 and most thoroughly, and with computational support by Houk.488 An exception to this pattern is when the medium-sized group M is small, as with a methyl group, and when, at the same time, the substituent A on the double bond, cis to the stereogenic centre, is a hydrogen atom. In this case, the conformation 5.199, with the medium-sized group inside, although not usually the lowest in energy, is populated, and attack from the less hindered side in this conformation becomes plausible, especially as it is now taking place syn to the small group instead of syn to a medium-sized group. This is the ‘inside-methyl’ effect, which we have already met on p. 233 in connection with nucleophilic attack on a double bond. Furthermore, the size of the group R will affect the outcome—if it is large, the conformation 5.199 can actually be lower in energy than conformation 5.198. As with nucleophilic attack on a carbonyl group, the dihedral angles will not have the large group precisely at right angles, and the transition structure may well be more like that shown in 5.200, which applies to a nonbridging electrophile attacking with an E+

L M

L S

R

M

S A B

R

A B

L

E+ 5.198

R M

S +

5.199

E 5.200

242

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

obtuse angle outside the double bond. Electrophilic attack is often exothermic, and the structure of the starting material is therefore likely to be a good guide to the transition structure. A straightforward example illustrating this sense of attack is the methylation of the lithium enolate 5.201. The substituent A (as in 5.198) is larger than a hydrogen atom, since it is either a methyl group or an oxyanion (the enolate is actually a mixture of stereoisomers), and the substituent R is a hydrogen atom. Thus the alternative conformation, corresponding to 5.199, is probably not significantly populated, and methylation takes place with a moderate degree of selectivity in the sense 5.201 to give mainly the ketone 5.203.614 When the group R is not too large, there is evidently no change to this pattern—when it is a methyl group and the electrophile is a proton, the reaction 5.202 still takes place in the sense 5.198, this time to give mainly the diastereoisomeric ketone 5.204. Other examples fitting this pattern are the epoxidation and hydroboration of alkenes having substituents A larger than a hydrogen atom.615 O H

+

H

or O

H

O

O

Me

Me

H

I

OH2

5.201

5.202

75:25 from 5.201 20:80 from 5.202

5.203

5.204

An example of a reaction in the alternative sense 5.199, with an inside methyl group, is the cycloaddition of a nitrile oxide to a terminal alkene, which gives mainly the diastereoisomer 5.207 by way of the transition structure 5.205.616 Nitrile oxide cycloadditions are among those dipolar cycloadditions (Chapter 6) which are electrophilic in nature. The substituent A (in 5.199) is a hydrogen atom, and the medium-sized group is only a methyl group, so it fits the criteria for an ‘inside-methyl’ effect. It is still a little surprising that reaction takes place in this sense, because a conformation like 5.199 in the starting material ought to be higher in energy than 5.198. Houk suggested that, with the electrophilic attack making obtuse angles at both carbon atoms, the transition structure 5.205 would leave room for the methyl group to sit inside with little energetic penalty. In the alternative conformation 5.206, the need for the methyl group to avoid eclipsing the incoming oxygen atom would force the isopropyl group closer towards eclipsing the double bond, raising the energy. Thus the relative energies of the transition structures are the other way round from the starting materials. N O

Ar H or

H

H

H

O

O N major 5.205

Ar +

H

minor 5.206

N

H O

Ar N

Ar 5.207

65:35

5.208

The ‘inside-methyl’ effect explains a puzzling result, in which the stereochemistry of the double bond of the enol ethers Z-5.209 and E-5.209 appears to control the diastereoselectivity of the protonation. The enol ether Z-5.209, with the alkoxy group cis to the stereogenic centre at C-17 is the normal one, reacting in the sense 5.198, with the hydrogen atom inside, and the proton attacking C-20 on the upper surface 5.211 anti to the tertiary alkyl centre at C-13 to give largely the aldehyde 20S-5.210. The enol ether E-5.209 has a hydrogen atom cis to the stereogenic centre and a relatively small group, the C-16 methylene group, which can sit comfortably inside, especially as it is effectively no larger than a methyl group with the rest of its bulk turned

5 IONIC REACTIONS—STEREOCHEMISTRY

243

away as part of the D-ring. Protonation now takes place anti to the tertiary centre but on the bottom surface 5.212 to give largely the diastereoisomeric aldehyde 20R-5.210.614,617 OR H 20 13

17

H

CHO

20

OR HF, MeCN

H

H

16

CHO

20

H

H

HF, MeCN

H

20S-5.210 80:20

Z-5.209

17 16

13

H

H

20

H 20R-5.210 80:20

E-5.209

H

13

OR

H

16

H

13

5.211

OR H

H 5.212

Bridging electrophiles, as in epoxidation, are fairly well behaved in the sense 5.198, possibly because the acute approach angle does not leave room for the medium-sized group to sit inside.614 Bromination, however, is reversible in the first step, and the stereochemistry actually observed, although often in the sense 5.198, is partly governed by the relative ease with which each of the diastereoisomeric epibromonium ions is opened. As a consequence, the ratio of diastereoisomers is not reliably a measure of the relative rates of attack on the diastereotopic faces of the alkene.618 5.2.3.2 The Influence of Electropositive Substituents. The story remains the same in the presence of the stereoelectronic effect of a donor substituent. A silyl group on the stereogenic centre is the best studied among these, where it is notable for imparting a strikingly high level of open-chain stereocontrol in the sense 5.198 in a wide variety of reactions: enolate alkylations 5.213,619 dihydroxylation, epoxidation620 and hydroboration 5.214621 of allylsilanes, and Diels-Alder reactions of pentadienylsilanes.622 In all of them, the silyl group is not only the donor substituent but also the large group, and it is not clear whether there is any electronic component to the diastereoselectivity.623 What is clear is that an electronic component will encourage attack anti to the silyl group, since it is generally agreed that the bond to an incoming electrophile is electron deficient, and that the transition structure will be especially well stabilised by an antiperiplanar donor substituent like silyl. Equally, a calculation580 of the pyramidalisation of the carbon atom adjacent to the stereogenic centre shows that it bulges 1.3 away from the donor substituent in the lowest energy structure 5.215, in which the Si—C bond is SiMe2Ph Ph

H H MeI

SiMe2Ph MeI OMe Li+ O

Ph

SiMe2Ph

CO2Me Ph dr 97:3

2. –OOH

H BR2 5.214

5.213 H3Si 1.3°

H Me

107.2°

H H H

H H 5.215

SiMe2Ph

1. 9-BBN Ph

OH dr >99:1

244

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

conjugated to the double bond, raising the energy of the HOMO. The problem which arose in attack on a carbonyl group, about whether a donor or an electron-withdrawing group ought to be anti-periplanar to an incoming nucleophile (see p. 228), does not arise here. The high level of diastereoselectivity in electrophilic reactions may be a consequence of the match between the steric and electronic effects, but there is no conclusive evidence on this point, since the silyl groups are unmistakably the large substituent. The only exceptions to attack taking place in the sense 5.198 are, as usual, when the medium-sized group is a methyl (or similarly small) group and the substituent A is a hydrogen atom, when reaction quite often, but not always, takes place in the conformation 5.199. Dihydroxylation by osmium tetroxide on a trans double bond 5.216 ! 5.217624 shows this pattern more strongly than the corresponding epoxidation, just as it did in the cases controlled only by steric effects, but when the group A is larger than a hydrogen atom, as with the corresponding cis double bonds, this reaction switches to the normal pattern 5.198. All these reactions, whether taking place from the conformation 5.198 or 5.199, still follow the pattern of attack anti-periplanar to the donor substituent, as also do the SE20 reactions discussed in the next section. OsO4 Me

H H

PhMe2Si

OH

H Me

PhMe2Si

OH

+

SiMe2Ph OH 5.216

OH

5.217

66:34

5.218

5.2.3.3 SE20 and SE200 Reactions. The SE20 reaction is a special case of electrophilic attack on a C¼C double bond with a donor substituent on the stereogenic centre—the difference from the reactions described in Section 5.2.3.2 is that the attack is at C-3, and it is followed by the loss of an electrofugal group from the stereogenic centre. The most studied of these are the electrophilic substitution reactions of stereodefined allylsilanes, which take place in the anti sense 5.219 ! 5.220 with a wide range of electrophiles, especially when the group R is large, as with R ¼ Ph.625,626

X–

E+

Me3Si R

1

3 2

5.219

E R

E = DO2CCF3 and t BuCl, RCHO and RCOCl + Lewis acid

5.220

In more detail, in the specific case of the enantiomerically pure allylsilane 5.219 (R ¼ Me) reacting with the adamantyl cation, the attack takes place in each of the conformations 5.221 and 5.226, since the mediumsized group is a methyl group and the substituent cis to the stereogenic centre is only a hydrogen atom. The intermediate cations 5.222 and 5.227 are stabilised by overlap of the empty p orbital with the Si—C bond (see p. 94), and are not substantially free to rotate to give their rotamers 5.224 and 5.229 before the silyl group is removed to give the major products 5.223 and 5.228. The attack appears to be very largely anti to the Si—C bond, as shown by the high level of enantiomeric enrichment in the Z-alkene products 5.228:5.225 (>99:1),627 but the E-alkene 5.223 was not enantiomerically pure, being contaminated with 10% of its enantiomer 5.230. This small loss of stereospecificity can be explained in two ways: either there was a small amount of leakage by rotation 5.227 ! 5.229, or there was a small amount of attack in the syn sense on the conformer 5.221. It seems likely that a small amount of rotation is the better explanation, and that the electrophilic attack is in fact very highly anti, because the same reaction in the corresponding allenylsilane

5 IONIC REACTIONS—STEREOCHEMISTRY

245

5.231 ! 5.233 is, within experimental error (–1%), completely stereospecific in the anti sense. In this case, there is no ambiguity about conformation and no opportunity for rotation in the intermediate cation 5.232.628 Ad+

+ 36%

Ad

H H

3

2

H Me3Si

H

Me3Si 5.221

Ad

36%

5.222

5.223

36%

<1% + Me3Si 3

Ad

Ad H

2

H

H 5.224

<1%

5.225

+ Me3Si

64%

Me3Si 3

H

H

2

H H

5.226

Ad

60%

Ad

Ad+

5.227

60%

5.228 4%

+ 3

+

H H

2

Ad =

Ad

H Ad

Me3Si

5.229

5.230

4%

Ad+ Ad

Ad

H Me3Si

Cl– 5.231 (er 99:1)

Me3Si

H 5.232

H 5.233 (er 99:1)

There are a number of syn SE20 reactions, which are significantly different in nature. The electrophile is typically an aldehyde, which is coordinated at the time of reaction to the electropositive group on the stereogenic centre, characteristically a metal like boron, tin, zinc or a silyl group carrying one or more electronegative elements. These reactions are cyclic in nature, usually use chair-like transition structures, are sometimes called metalla-ene reactions, and are inherently syn in their overall stereochemistry.629,630 In Section 5.2.3.2, we saw that attack on the atom adjacent to a stereogenic centre was regularly anti to an electropositive substituent. Now we find that the attack on the next atom, C-3, is also anti, whereas previously we have argued that there is some evidence for alternation in the side of attack as one moves atom by atom down a conjugated chain of double bonds. This is especially what we expect if we use only the argument based on pyramidalisation, where we saw on p. 235 that, if one end of a double bond is pyramidalised down, the next atom can be expected to be pyramidalised up. If we go back to the calculation on the allylsilane 5.215, but look at the other end of the double bond 5.234, we see that C-3 is indeed pyramidalised upwards, although only to a very small extent (0.2). Clearly this does not match the sense of electrophilic attack on this atom. There is another complication in using alternating pyramidalisation as a guide, in that a bridging electrophile would have to form

246

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

one of its two bonds to an atom pyramidalised the wrong way. The tau bond model 5.235, however, does not have problems with a bridging electrophile, and does correctly predict the sense of electrophilic attack, with the tau bond anti to the donor substituent M as the site of attack, whether the electrophile is attacking C-2 or C-3 or both together. M

H3Si 1.3°

3

H

H H

H

H

2

H

3

0.2°

ret.

ret. E

5.234

5.235

Predicting the stereochemistry of an SE200 reaction is even less convincing. Both alternating pyramidalisation, greatly exaggerated in 5.236, and the tau bond model 5.237 predict that electrophilic attack at C-5 should be from above, syn to the donor substituent. E M

4

2 3

5.236

5

M

2

3

4

5

5.237

In spite of this agreement, the small number of known examples of SE200 reactions prove to be anti, with a low degree of stereoselection, typically 60:40.627 Clearly the most simple theories do not explain the sense of selectivity, and there is nothing more convincing to fall back on than a general sense that a donor on the top surface of a conjugated system evidently encourages attack on the bottom surface. When the electrophile is large enough, and the silyl group is held close enough, by having the double bond between C-2 and C-3 cis, the level of stereoselection can rise to 90:10 in the anti sense but this is explained simply by steric repulsion between the silyl group and the incoming electrophile.631 Conceivably all these result with silyl substituents are essentially controlled by steric effects alone, with the silyl group able to hinder the surface it is on, even over quite large distances, and this is probably as good an explanation as we have at present. 5.2.3.4 The Influence of Electronegative Substituents. The real problem explaining the diastereoselectivity of electrophilic attack comes when one of the bonds on the stereogenic centre is to an electronegative atom, making it an electron-withdrawing group. We shall leave out of consideration those cases where an oxygen atom delivers the reagent by hydrogen bonding or Lewis acid-base coordination—reactions like epoxidation632 and the Simmons-Smith reaction on allylic alcohols.633 These reactions have cyclic transition structures, and the diastereoselectivity is determined by the conformation of the ring—any molecular orbital considerations are secondary. A C—X bond conjugated with a p bond will lower the energy of the HOMO, and make the alkene less reactive towards electrophiles. Consequently, when it is not delivering the reagent, an electronegative substituent often adopts a conformation in which the C—X bond is not in conjugation with the p bond. For example, in a cyclic alkene, dipolar cycloaddition takes place syn to the chlorine atoms in the dichlorocyclobutene 5.238,634 and the Diels-Alder reaction on acetoxycyclopentadiene 5.239635,636 takes place syn to the acetoxy substituent. These results are in striking contrast to the reactions on small rings, which usually take place anti to the resident substituents whatever they are. These compounds will be more reactive when the electron-withdrawing substituents are as little conjugated to the double bonds as possible. Relatively mild distortions of the conformation at the time of reaction can allow the C—H bonds to be lined up to overlap with the p bond, as drawn in 5.240 and 5.241, with the C—Cl and C—O bonds mostly lifted out of conjugation.

5 IONIC REACTIONS—STEREOCHEMISTRY

247

N CH2N2

Cl Cl 5.238

N

+

Cl Cl N

N

Cl Cl

96:4

AcO

AcO

OAc + "100:0" 5.239 H H OAc

Cl Cl

H

5.240

5.241

The incoming reagent will approach anti to the H, even though the approach is formally syn to the electronegative elements. In both cases pyramidalisation with the p orbital bulging away from the C—H bonds will be on the same side as the electronegative atoms. This simple explanation ties in with the theory advanced by Cieplak, mentioned earlier (see p. 230), in which he pointed out that the bond in the transition structure forming towards the incoming reagent was inherently electron-deficient, and so ought to line up anti to the better donor. This idea did not work to explain the Felkin-Anh rule when applied to nucleophilic attack on a carbonyl compound having an  electronegative substituent, but it does when applied to electrophilic attack instead of nucleophilic attack. We can feel comfortable with the idea that the electrons coming from the double bond towards the electrophile will leave antiperiplanar to a donor substituent, and will be helped if the electron-withdrawing groups are not in conjugation with the p bond. In open chain alkenes there is more flexibility for the bond to the electronegative substituent to avoid conjugation with the double bond. It can be in an outside position with respect to the C¼C double bond or inside.637 In either case, the preferred conformation at the time of reaction will have the bond to the substituent avoiding conjugation with the p bond, and hence avoiding being anti-periplanar in the transition structure. When the substituent A (in 5.198) is larger than a hydrogen atom, we might expect most reactions to take place with a transition structure like 5.198, with the electronegative atom as the medium-sized group oriented to be as little in conjugation with the double bond as possible. In practice this is rarely the case, and reaction in this sense appears to be most likely when the group A is significantly larger than a methylene group and the group R larger than a hydrogen atom. An example is the dihydroxylation of the Z-alkene Z-5.242 with osmium tetroxide, in which the A1,3 interaction between the inside hydroxyl group and the ethoxycarbonyl group is too severe for the conformation Z-5.242a to be significantly populated. The ethyl group counts as the large group, and the hydroxyl as the medium-sized group, and dihydroxylation takes place in the conformation Z-5.242b to give only the lactone 5.243.638 O H

OH

CO2Et H

Z-5.242a

OH HO

H

CO2Et H

OsO4 Z-5.242b

CO2Et

O 3

OH HO

HO 5.243

OH

248

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

When the substituent A is a hydrogen atom, it appears that the lowest energy conformation in the transition structure is often that with the electronegative substituent inside. Reactions therefore take place in the sense 5.199 with the electronegative element treated as the medium-sized group, which it often is, in contrast to its role in the Felkin-Anh rule, where it is treated as the large group whatever its actual size. An example is the dihydroxylation of the E-alkene E-5.242. Whereas the corresponding Z-alkene Z-5.242 reacts in a conformation avoiding an A1,3 interaction, the E-alkene can adopt a conformation E-5.242 with the hydroxyl group inside, and the product is the lactone 5.244 with the opposite stereochemistry at C-3 from that of the product 5.243 derived from the Z-isomer. 638640 This propensity for an electronegative substituent to be inside is known as the ‘inside oxygen’ or ‘inside alkoxy’ effect,641 when the electronegative atom is an oxygen substituent. Only when the substituent A is larger, as it is with the ethoxycarbonyl group in the alkene Z-5.242, is the hydroxy or alkoxy group pushed into an outside position. Other reactions cleanly showing this stereochemistry are nitrile oxide cycloadditions616,642 and Diels-Alder reactions with acetylenic dienophiles.643,644 OsO4 H

OH

OH

O

OH

H CO2Et

O CO2Et

OH

3

OH

OH 5.244

E-5.242

In contrast to the cases described in Sections 5.2.3.1 and 5.2.3.2 above, with purely steric effects and with donor substituents, reactions often take place with the oxygen substituent inside, even when the substituent A is larger than a hydrogen atom. Both the E- and the Z-alkenes 5.245 react in the sense 5.199 with oxygen inside, even though it has an A1,3 interaction with an alkyl group in the latter. The result is that the new stereogenic centre at C-3 in the major products syn-5.246 and anti-5.246 is created in the same sense from both alkenes, but the stereochemistries at C-4 are opposite to each other because of the stereospecificity of the syn addition.639 OsO4 Ph H

OBn

O H H

3

BnO

3

4

OH 4

OH

BnO E-5.245

OBn

OH

+ BnO 81:19

syn-5.246

OH syn-5.247

OsO4 Ph H

OBn

O H

3

4

H

BnO

3

OH 4

OH

BnO Z-5.245

anti-5.246

OBn

OH

+ BnO 90:10

OH anti-5.247

One puzzling feature in this pair of reactions is the higher degree of stereoselectivity in the Z-alkene Z-5.245 (90:10) relative to that in the E-alkene E-5.245 (81:19). This is the opposite of what might have been predicted by the theory advanced above, and it has led to the suggestion that electrophilic attack takes place

5 IONIC REACTIONS—STEREOCHEMISTRY

249

anti to the alkoxy group in a conformation 5.248 with the hydrogen atom inside. We dismissed this possibility earlier on the grounds that conjugation of the O—C bond with the double bond would reduce its nucleophilicity and destabilise the transition structure, but one suggestion is that in this conformation the oxygen lone pairs overlap through space with the p orbitals on the lower surface, and that this pushes the electron population out onto the upper surface 5.249.639 OsO4 OsO4 H

BnO Ph

BnO

H

H

H

H

O

Ph

O

5.248

5.249

Whatever the merits of this idea,645 it, like all the other approaches to explaining diastereoselectivity, cannot be applied to all the systems in which it might operate. For example, this idea applied to acetoxycyclopentadiene 5.239 suggests that it ought to react with dienophiles anti to the substituent, in contrast to the experimental result. In a related system to which it might also apply, the epoxide 5.250 does show complete attack anti to the oxygen atom,646 but it has been pointed out that the oxygen lone pairs, both in the cyclopentadiene 5.239 and in the epoxide 5.250, lie in a node of the HOMO of the diene, and cannot interact with what ought to be the most important orbital in a Diels-Alder reaction. Lifting this restriction with the diol diene 5.251 restores the syn selectivity (94:6),647 implying that the idea of through-space overlap is far from generally applicable. O O

O

N Ph

O

O PhN

5.250

OH

5.251

O OH

O

N Ph

O

O

OH OH

PhN O

In contrast to the dihydroxylations, the epoxidation of allylic halides648 is poorly selective in the sense 5.199, even when the substituent A is only a hydrogen atom, and there are several reactions which actually take place in the opposite sense 5.198. These include the hydroboration of both the E-allylic alcohol E-5.252 and, less surprisingly, the Z-allylic alcohol Z-5.252,649 and Diels-Alder reactions on the related dienes with dienophiles like maleimides.643 Evidently the ‘inside alkoxy’ effect, prominent in nitrile oxide cycloadditions and especially in osmium tetroxide dihydroxylations, does not apply to all reactions. The pattern that osmium tetroxide reactions are always the ones most showing attack in the sense 5.199, regardless of whether the medium-sized group is based on an oxygen atom or not, would again seem to argue against the explanation implied in 5.248. It is probably significant that the ‘inside alkoxy’ effect is most noticeable with reagents which are relatively electrophilic in nature, and much less so with boranes, which are only mildly electrophilic.

250

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

Bu OH

H

HO

H

H Bu

BBN

Bu

OH Bu

Bu

BBN

OH Bu

H

E-5.252

90:10

Bu OH

H

HO

H

Bu H

Bu

Bu

OH Bu

BBN

BBN

OH Bu

H

Z-5.252

>94:6

5.2.4 Diastereoselective Nucleophilic and Electrophilic Attack on Double Bonds Free of Steric Effects.521,650 On account of the delicate balance between steric and electronic effects, and the difficulty of teasing them apart, a number of reactions have been carried out on substrates designed as far as possible to remove the steric component, and to leave an electronic one. Substrates which have been used in this kind of experiment include the adamantanones 5.253 (Y ¼ O), the norbornanones 5.254 (Y ¼ O), and the cyclopentanone 5.255, for nucleophilic attack, and the corresponding alkenes 5.253 (Y ¼ CH2), 5.254 (Y ¼ CH2) and 5.256 for electrophilic attack by such electrophiles as peracid, dichlorocarbene and dichloroketene. These ketones and alkenes are designed to have the possibility of purely electronic effects transmitted rationally through the  framework, and they do all show diastereoselectivity, occasionally to a high degree. R Y

R

Y

O R R

R 5.253

5.254

5.255

5.256

As an example of the kind of experiment that is carried out in this area, borohydride attack on the ketone 5.257 (R ¼ F) gave the alcohol 5.258 (R ¼ F) as the major product, with attack syn to the electron-withdrawing substituent, whereas the ketone 5.257 (R ¼ SnMe3) gave the alcohol 5.259 (R ¼ SnMe3) as the major product, with attack anti to the electron-donating substituent. The degree of stereoselectivity is unimpressive, but the electronwithdrawing fluorine and the electron-donating trimethylstannyl group exert their effects in opposite senses. O

HO

H

H

OH 5.258:5.259

NaBH4

+

R 5.257

R=F R = SnMe3

R 5.258

R 5.259

62:38 48:52

5 IONIC REACTIONS—STEREOCHEMISTRY

251

In trying to explain these results, we no longer have to worry about which bond is conjugated to the carbonyl group at the time of reaction—the bonds are fixed in their orientation, and attack is always axial in one ring and equatorial in the other. Furthermore, the effect of the substituent on stereochemistry is no longer influenced by its effect on the overall rate, as it was with the ‘inside alkoxy’ effect. One explanation is that the C—F bond in the ketone 5.257 (R ¼ F) is conjugated to the C—C bonds, emphasised in 5.260. This conjugation makes these C—C bonds less electron-donating than the C—C bonds on the other side of the carbonyl group, emphasised in 5.261. Following the Cieplak argument, the nucleophile duly attacks the side opposite the better donor. With the electron-donating trimethylstannyl group, it is the bonds on the side of the stannyl group, emphasised in 5.262, that are made the better donors, and the nucleophile attacks anti to them. O

O

O

F

F

5.260

SnMe3

5.261

5.262

The azaadamantanone 5.263 is reduced selectively by sodium borohydride syn to the amine function. Here the argument is not so clear, because the lone pair on the nitrogen atom is conjugated to the  bonds in the sense of the bold lines in 5.264, making them better donors, and this ought to have encouraged anti attack. However, the nitrogen atom itself is an electronegative element, and one might argue that attack should take place syn to it just as it does for the fluoride 5.257 (R ¼ F). Support for the latter idea comes from the corresponding N-oxide 5.265, which is reduced with even greater selectivity in the syn sense now that the effect of the lone pairs has been removed.651 O

O

38

O

62

5

N

95

N

N O

5.263

5.264

5.265

Similarly, since Cieplak’s argument suggests that electrophiles will also attack anti to the better donor, the corresponding electrophilic attack on the alkenes 5.266 by borane is also syn selective for the fluoroadamantane system (R ¼ F), and anti selective for the trimethylsilyladamantane system (R ¼ SiMe3). Curiously, this selectivity is reversed in sense when the hydroboration is catalysed by rhodium complexes, and the explanation may be that coordination by the rhodium is best when it is anti to the electron-withdrawing group.652 OH

OH H

H 5.267:5.268

1. BH3.THF R 5.266

R=F R = SiMe3

+

2. NaOH, H2O2

R 5.267

R 5.268

63:37 47:53

252

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

Although these experiments, and several others similar to them, largely support Cieplak’s contention, there are enough exceptions and unexplained features to make this account of the selectivity neither complete nor accepted.653 For example, the substituents do affect the shape of the molecule,654 and hence the degree of pyramidalisation at the carbonyl carbon atom, and there are electrostatic effects operating through space, rather than being relayed through the bonds.655

6

Thermal Pericyclic Reactions

Pericyclic reactions656,657 are the second distinct class of the three, more or less exclusive categories of organic reactions—ionic (Chapters 4 and 5), pericyclic (this Chapter) and radical (Chapter 7). Their distinctive features are that they have cyclic transition structures with all the bond-making and bond-breaking taking place in concert, without the formation of an intermediate. The Diels-Alder reaction and the Alder ‘ene’ reaction are venerable examples. O

O

O

O O

O

O H

H O

O

O

A Diels-Alder reaction

O O

An Alder ene reaction

The curly arrows can be drawn in either direction. Here they are drawn so as to imply a clockwise movement of electrons, but the arrows could equally well have been drawn anti-clockwise. There is no absolute sense to the direction in which the electrons flow. Similarly, there is no absolute sense in which the hydrogen atom that moves from one carbon atom to the other in the ene reaction is a hydride shift, as seems to be implied by the curly arrows, or a proton shift, as it would seem to be if the arrows were to have been drawn in the opposite direction. In other words, neither component can easily be associated with the supply of electrons to any of the new bonds. The curly arrows therefore have a somewhat different meaning from those used in ionic reactions. In this they resemble somewhat the curly arrows used to show resonance in benzene, where the arrows show where to draw the new bonds and which ones not to draw in the canonical structure, but in the drawing of arrows interconnecting resonance structures there is neither a sense of direction nor even an actual movement. The analogy between the resonance of benzene and the electron shift in the Diels-Alder reaction is not farfetched, but it is as well to be clear that one, the Diels-Alder reaction, is a reaction, with starting materials and a product, and the other, resonance in benzene, is not. All pericyclic reactions share the feature of having a cyclic transition structure, with a concerted movement of electrons simultaneously breaking bonds and making bonds. Within that overall category, it is convenient to divide pericyclic reactions into four classes. These are cycloadditions, electrocyclic reactions, and sigmatropic rearrangements (Fig. 6.1), and the relatively less common group transfer reactions, each of which possesses features not shared by the others, and some of which employ a terminology that cannot be used without confusion if applied to a reaction belonging to one of the other classes. It is a good idea to be clear

Molecular Orbitals and Organic Chemical Reactions: Reference Edition Ó 2010 John Wiley & Sons, Ltd

Ian Fleming

254

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

(a) Cycloadditions

(b) Electrocyclic reactions

Fig. 6.1

(c) Sigmatropic rearrangements

The three major classes of pericyclic reactions

about which class of reactions you are dealing with, in order to avoid using inappropriate terminology. We shall begin by illustrating the identifying features of each of the classes, simply to establish what they are.

6.1

The Four Classes of Pericyclic Reactions

Cycloadditions are characterised by two components coming together to form two new  bonds, one at each end of both components, joining them together to form a ring, with a reduction in the length of the conjugated system of orbitals in each component (Fig. 6.1a). Cycloadditions like the Diels-Alder reaction are by far the most abundant, varied, featureful and useful of all pericyclic reactions. They are inherently reversible, and the reverse reaction is called a retro-cycloaddition or a cycloreversion. Cheletropic reactions are a special group of cycloadditions or cycloreversions in which the two  bonds are made or broken to the same atom. Thus sulfur dioxide adds to butadiene 6.1 to give an adduct 6.2, for which the sulfur has provided a lone pair to one of the  bonds and has received electrons in the formation of the other. As far as the sulfur dioxide is concerned, it is an oxidative addition, changing the sulfur from SIV to SVI. The reaction is readily reversible on heating, and so sulfur dioxide can be used to protect dienes, allowing the adduct 6.2 to be heated in the presence of dienophiles as a convenient (liquid) source of butadiene.

SO2

SO2

6.1

both bonds made to the same atom

6.2

Electrocyclic reactions are invariably unimolecular, in contrast to cycloadditions, which are characterised by having two components, usually two different molecules, coming together to form two new  bonds. They are characterised by the creation of a ring from an open-chain conjugated system, with a  bond forming across the ends of the conjugated system, and with the conjugated system becoming shorter by one p orbital at each end (Fig. 6.1b). The reactions are inherently reversible, with the direction they take being determined by thermodynamics. Most electrocyclic reactions are ring-closings, since a  bond is created at the expense of a p bond, but a few are ring-openings, because of ring strain. Representative electrocyclic reactions are the ring-opening of cyclobutene 6.3 on heating to give butadiene 6.1, and the ring-closing of hexatriene 6.4 to give cyclohexadiene 6.5. In the case illustrated, butadiene 6.1 is lower in energy than cyclobutene 6.9 by about 50 kJ mol1. 150°

6.3

132°

6.1

6.4

6.5

6 THERMAL PERICYCLIC REACTIONS

255

Sigmatropic rearrangements are often the most difficult to identify. They are unimolecular isomerisations, and formally involve overall the movement of a  bond from one position to another, with a concomitant movement of the conjugated systems in order to accommodate the new bond (Fig. 6.1c). The oldest known example is the first step in the Claisen rearrangement,658 when a phenyl allyl ether is heated. The first step is the sigmatropic rearrangement in which the single bond, drawn in bold, in the starting material 6.6 moves to its new position in the intermediate 6.7. It has effectively moved three atoms along the carbon chain (from C-1 to C-3), and three atoms along the chain of the oxygen atom and two carbon atoms (O-10 to C-30 ). This type of rearrangement is called a [3,3]-shift, with the numbers identifying the number of atoms along the chain that each end of the bond has moved. The second step forming the phenol 6.8 is an ordinary ionic reaction—the enolisation of a ketone. It is perhaps a timely reminder that ionic reactions often precede or follow a pericyclic reaction, sometimes disguising the pericyclic event. 1 1'

2

O

O

2'

OH

200°

3 3'

H 85%

6.6

6.7

6.8

A quite different looking sigmatropic rearrangement is the hydrogen atom shift 6.9 ! 6.10, also long known from the chemistry of vitamin D.659 In this case, the end of the H—C bond attached to the hydrogen atom (H-10 ) necessarily remains attached to the hydrogen, but the other end has moved seven atoms (C-1 to C-7) along the conjugated carbon chain. This reaction is therefore called a [1,7]-shift. 7

HO

1'

H

6

5

1

2 4

H

60°, 24 h HO

R

R

3

6.9

6.10

Another quite different looking sigmatropic reaction is the Mislow rearrangement 6.11 ! 6.12, which is invisible because it is thermodynamically unfavourable, but the ease with which it takes place explains why allyl sulfoxides, with a stereogenic centre at sulfur, racemise so much more easily than other sulfoxides.660 Here, one end of the C—S bond moves from the sulfur (S-10 ) to the oxygen atom (O-20 ) and the other end moves from C-1 to C-3. This is therefore called a [2,3]-shift, the bond marked in bold moving two atoms at one end and three at the other. Tol

1'

2'

S

O

1

51°

S 3

2

6.11

Tol O

t 1 2.5 h 2

6.12

Group transfer reactions make up the fourth category; they have few representatives, with ene reactions by far the most common. Stripped to their essence, ene reactions have the form 6.13 ! 6.14, but in practice the enophile usually needs to have electron-withdrawing groups attached to it. They usually take place

256

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

from left to right, since overall a p bond is replaced by a  bond, but they are, of course, reversible. They resemble [1,5]-sigmatropic rearrangements, since a  bond moves, and they also resemble cycloadditions like Diels-Alder reactions, since one of the p bonds of the diene has been replaced by a  bond in the ene. Nevertheless, since the reaction is bimolecular and no ring is formed, they are neither sigmatropic rearrangements nor cycloadditions. H

H

6.13

6.14

Ene reactions 6.13 have a hydrogen atom moving from the ene to the enophile, but other atoms can in principle move. In practice, the only elements other than hydrogen that are commonly found in this kind of reaction are metals like lithium, magnesium or palladium, when the reaction 6.15 is called a metalla-ene reaction.630 The carbon chain may also have one or more oxygen or nitrogen atoms in place of the carbons. Thus if the atom carrying the hydrogen is an oxygen atom and the atom to which it is moving is also an oxygen atom, it becomes an aldol reaction. Aldol reactions are usually carried out with acid or base catalysis, and most are not significantly pericyclic in nature. Other well known types of group transfer reaction are represented by the concerted syn delivery of two hydrogen atoms from the reactive intermediate diimide 6.16 to an alkene or alkyne,661 and the syn elimination of selenoxides 6.17, and related reactions. M

M

N N

6.15

6.2

H

H 6.16

N N

H +

Ph

Ph

O Se

H

O Se

H

H 6.17

Evidence for the Concertedness of Bond Making and Breaking

The characteristic feature of all pericyclic reactions is the concertedness of all the bond making and bond breaking, and hence the absence of any intermediates. Naturally, organic chemists have worked hard, and devised many ingenious experiments, to prove that this is true, concentrating especially on Diels-Alder reactions and Cope rearrangements. The following is an oversimplified description of some of the most telling experiments. The Arrhenius parameters for Diels-Alder reactions show that there is an exceptionally high negative entropy of activation, typically in the range 150 to 200 J K1 mol1, with a low enthalpy of activation reflecting the exothermic nature of the reaction.662 Bimolecular reactions inherently have high negative entropies of activation, but the extra organisation for the two components to approach favourably aligned, so that both bonds can form at the same time, accounts for the exceptionally high value in cycloadditions. The compact transition structure is also in agreement with the negative volumes of activation measured by carrying out the reaction under pressure.663 The rates of Diels-Alder reactions are little affected by the polarity of the solvent.664 If a zwitterionic intermediate were involved, the intermediate would be more polar than either of the starting materials, and polar solvents would solvate it more thoroughly. An example of a solvent effect on a stepwise reaction, and not on a Diels-Alder reaction, is illustrated on p. 280. Typically, a large change of dipole moment in the solvent, from 2.3 to 39, causes an increase in rate by a factor of only 10. In contrast, stepwise ionic cycloadditions take place with increases in rate of several orders of magnitude in polar solvents. This single piece of evidence rules out stepwise ionic pathways for most Diels-Alder reactions, and the only stepwise mechanism left is that involving a diradical.

6 THERMAL PERICYCLIC REACTIONS

257

Deuterium substitution on the four carbon atoms changing from trigonal to tetrahedral as the reaction proceeds, gives rise to inverse secondary kinetic isotope effects, small, but measurable both for the diene 6.18 and the dienophile 6.19.665,666 If both bonds are forming at the same time, the isotope effect when both ends are deuterated would be geometrically related to the isotope effects at each end. If the bonds are being formed one at a time, the isotope effects are arithmetically related.667 It is a close call, but the experimental results, both for cycloadditions and for cycloreversions, suggest that they are concerted. Similar isotope effects in Cope and Claisen rearrangements,668 and in the ‘ene’ reaction,669 come even more firmly to the conclusion that these are concerted reactions.670

H(D) H(D) (D)H + H(D) (D)H H(D) 6.18

6.19

(D)H H(D) H(D)

NC

CN NC

NC 6.20

R*O2C

vs.

+ H(D) (D)H H(D)

CN

6.21

CO2R*

CN 6.22

6.23

Another way of testing how one end of the dienophile affects the other end is to load up the dienophile with up to four electron-withdrawing groups, and see how each additional group affects the rate. A stepwise reaction between butadiene 6.20 and tetracyanoethylene 6.22 ought not to take place much more than statistically faster than a similar reaction with 1,1-dicyanoethylene 6.21, but a concerted reaction ought to, and does, take place much faster.671 Furthermore the relative rates can be compared with the rate of nucleophilic attack on the dienophile as a model for a stepwise reaction, and they prove to be very different. A somewhat similar device has been used with dienophiles like fumarate esters 6.23 having chiral auxiliaries R* on one or both ester groups. A stepwise reaction would be expected to show some chiral induction if the bond is formed next to the ester having the chiral auxiliary, but no extra chiral induction from having a chiral auxiliary at the other end at the same time. A concerted reaction, however, ought to have more than additive effects from having both chiral auxiliaries present. The results from both of these experiments support a concerted mechanism.672 High level molecular orbital calculations have been carried out, with ever increasing levels of sophistication, on the reaction between ethylene and butadiene. Most, but not quite all, agree that the concerted pericyclic pathway gives the lowest energy transition structure.673 Calculations even more strongly support the evidence for concertedness from the isotope effect studies.674 A diradical intermediate would have an allylic radical at one end of the diene and the configuration would not have changed from trigonal to tetrahedral. The two isotope effects in a stepwise diradical mechanism, that at the end undergoing bonding and that at the end carrying the odd electron, should therefore be very different. Since they are not, but more than arithmetically reinforce each other, the reaction is most probably concerted. There is one cycloadditionlike reaction, actually cycloreversion-like, that is unmistakably concerted. The gas phase pyrolysis of cyclohexa-1,4-diene 6.24 gives benzene and, syn stereospecifically, hydrogen.675 There is no sensible stepwise mechanism available, since free hydrogen atoms are much too high in energy to be plausible intermediates. In addition, the relationship between the primary isotope effect for replacing one hydrogen by deuterium kD/kH ¼ 0.5, and that for replacing them both kD2/kH ¼ 0.25 is geometric, i.e. related by the expression (kD/kH)2 ¼ (kD2/kH), and not arithmetic, i.e. related by the expression (kD2/kH) ¼ 2(kD/kH) – 1, providing compelling evidence for the only plausible mechanism, a concerted cycloreversion (6.24, arrows).676 The only complication here is that it is not strictly a cycloreversion since no ring is broken, but neither is it a member of any of the other classes. Its relationship to a cycloreversion and to a group transfer reaction is obvious, but this type of reaction is unique in pericyclic chemistry.

258

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

(D)H

H(D) 180°

+

H(D) H(D)

6.24

Finally, the single most impressive piece of evidence comes from the very fact that pericyclic reactions obey the rules that we are about to expand upon. These rules only apply if the reactions are concerted. To have a few reactions accidentally obeying the rules would be reasonable, but to have a very large number of reactions seemingly fall over themselves to obey strict stereochemical rules, sometimes in what look like the most improbable circumstances, is overwhelmingly strong evidence about the general picture. Of course, no single reaction can be proved to be pericyclic, just because it obeys the rules—obedience to the rules is merely a necessary condition for a reaction to be considered as pericyclic. In the case of cycloadditions, the suprafacial nature of the reaction on both components in a very high proportion of reactions at least says that the second bond, if it is not formed at the same time as the first, is formed very quickly after the first, before any rotations about single bonds can take place. It seems more than likely that most reactions thought to be pericyclic actually are.

6.3

Symmetry-allowed and Symmetry-forbidden Reactions

Between 1965 and 1969 Woodward and Hoffmann presented rules for each of the different classes of pericyclic reaction.677 They showed that the allowedness or otherwise of reactions depended critically upon the number of electrons involved and on the stereochemistry of the reaction. We shall go through the rules twice: first the rules class by class, and then again using the single generalised rule that they presented in 1969 that applies to all classes of pericyclic reactions. 6.3.1 The Woodward-Hoffmann Rules—Class by Class 6.3.1.1 Cycloadditions. A cyclic movement of electrons can be drawn for any number of cycloadditions, but not all of them take place. Thus butadiene undergoes a Diels-Alder reaction with maleic anhydride (see p. 253), but ethylene and maleic anhydride do not give the cyclobutane 6.25 when they are heated together. O

O heat

O O

O

6.25

O

It is not that this cycloaddition is energetically unprofitable—in spite of the ring strain, the cyclobutane is lower in energythanthetwoalkenes—sotheremustbeahighkineticbarriertothecycloadditionofonealkenetoanother.This is a deeply important point, and it is just as well that it is true—if alkenes and other double-bonded compounds could readily dimerise to form four-membered rings, there would be few stable alkenes, and life would be impossible. Diels-Alder reactions are classified as [4 þ 2] cycloadditions, and the reaction giving the cyclobutane would be a [2 þ 2] cycloaddition. This classification is based on the number of electrons involved. DielsAlder reactions are not the only [4 þ 2] cycloadditions, although they are by far the most numerous and the most important. Conjugated ions like allyl cations, allyl anions and pentadienyl cations are all capable of cycloadditions. Thus, an allyl cation can be a 2-electron component in a [4 þ 2] cycloaddition, as in the reaction of the methallyl cation 6.27, derived from its iodide 6.26, with cyclopentadiene giving a

6 THERMAL PERICYCLIC REACTIONS

259

seven-membered ring cation 6.28.678 The diene is the 4-electron component. The product eventually isolated is the alkene 6.29, as the result of the loss of the neighbouring proton, the usual fate of a tertiary cation. This cycloaddition is also called a [4 þ 3] cycloaddition if you were to count the atoms, but this is a structural feature not an electronic feature. In this chapter it is the number of electrons that counts.

I

AgO2CCF3

H

6.27

40%

SO2 6.26 6.28

6.29

An allyl anion such as the 2-phenylallyl anion 6.31, prepared in an unfavourable equilibrium by treating -methylstyrene with base, undergoes a cycloaddition to an alkene such as stilbene 6.30, present in situ, to give the cyclopentyl anion 6.32, and hence the cyclopentane 6.33 after protonation.679 The complication here is that anions are often ill-defined intermediates, usually being organometallic species with a carbon-metal bond with substantial covalent character, as we have seen before (see pp. 56, 78, 86, 96 and 117). It is not always legitimate to think of conjugated anions, let alone to draw them, simply as symmetrical conjugated systems of p orbitals. Nevertheless, the pericyclic pathway has the energetic benefit of forming both new  bonds in the same step, and so this type of reaction is quite plausibly pericyclic. The anionic product 6.32, having lost the allyl conjugated system, needs the anion-stabilising phenyl group to make the reaction favourable. Allyl anionþalkene cycloadditions are rare, and calculations suggest that the few that are known are actually stepwise.680 It is evidently a penalty of the fact that allyl anions are not usually simple conjugated systems of p orbitals, making it difficult for the overlap to develop at both ends simultaneously. Structurally this is a 3 þ 2 cycloaddition, but electronically it is a [4 þ 2] cycloaddition, just like the Diels-Alder and the allyl cationþdiene reactions. Ph

6.30 LiNPri2

Ph

Ph

Ph

Ph

+H+

Ph

41% Ph

THF 45°, 150 h

Ph

Ph

Ph

6.31

6.32

6.33

Yet another [4 þ 2] cycloaddition, rather rare, is that between a pentadienyl cation and an alkene. The best known example is the perezone-pipitzol transformation 6.34 ! 6.36, where it is heavily disguised, but all the more remarkable for that.681 It can be understood as beginning with an intramolecular proton transfer to give the intermediate 6.35, which can then undergo an intramolecular [4 þ 2] cycloaddition with the pentadienyl cation, emphasised in bold, acting as the 4-electron component and the pendant alkene, also bold, as the 2-electron component. H

O

O

H

HO O

O

O

O

O

6.34

6.35

O

6.36

260

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

1,3-Dipolar cycloadditions 6.37 þ 6.38 ! 6.39, however, are a large group of [4 þ 2] cycloadditions isoelectronic with the allyl anion þ alkene reaction. There is much evidence that these reactions are usually, although perhaps not always,682 concerted cycloadditions.683 They also have a conjugated system of three p orbitals with four electrons in the conjugated system, but the three atoms, X, Y, and Z in the dipole 6.37 and the two atoms A and B in the dipolarophile 6.38, are not restricted to carbon atoms. The range of possible structures is large, with X, Y, Z, A and B able to be almost any combination of C, N, O and S, and with a double 6.37 or, in those combinations that can support it, a triple bond 6.40 between two of them.684

6.37

Y

A

6.40 X

Y

Z

X

X A

B

6.38

Y

Z

Z

Y X

B

A

6.39

B

Z

A

6.38

B

6.41

All the reactions described so far have mobilised six electrons, but other numbers are possible, notably a few [8 þ 2] and [6 þ 4] cycloadditions involving 10 electrons in the cyclic transition structure. It is no accident, as we shall see in Section 6.4.1, that all these reactions have the same number of p electrons (4n þ 2) as those possessed by aromatic rings. A conjugated system of eight electrons would normally have the two ends of the conjugated system far apart, but there are several molecules in which the two ends are held more or less rigidly and close enough to participate in cycloadditions to a double or triple bond. Thus, the tetraene 6.42 has the two ends of the conjugated system pulled together by the methylene bridge, allowing it to react with dimethyl azodicarboxylate 6.43 to give the [8 þ 2] adduct 6.44.685 Tropone 6.45 adds as a 6-electron component to cyclopentadiene, which is a 4-electron component, giving the adduct 6.46.686

NCO2Me

20°

NCO2Me

40%

6.43

NCO2Me NCO2Me 6.44

6.42 O r.t, 3 d O

6.45

6.46

Very crudely, but adequately for most purposes, we may state a rule for which cycloadditions can take place and which not.

A thermal pericyclic cycloaddition is allowed if the total number of electrons involved can be expressed in the form (4nþ2), where n is an integer. If the total number of electrons can be expressed in the form 4n it is forbidden.

6 THERMAL PERICYCLIC REACTIONS

261

This rule needs to be qualified, because it applies to those reactions taking place in the sense shown in Fig 6.2a, in which the orbital overlap that is developing to form the new  bonds takes place on the same surface of each of the conjugated systems, represented here by a curved line, but implying a continuous set of overlapping p orbitals from one end to the other. The dashed lines represent the two developing  bonds. Most cycloadditions have this stereochemistry, but an alternative possibility is that one of the two components might develop overlap with one bond forming on the top surface and the other on the bottom surface in the sense shown in the component on the left in Fig. 6.2b. Obviously considerable twisting in the conjugated systems has to take place before this kind of overlap can develop, and reactions showing this feature are exceedingly rare. Yet another possibility, even more farfetched, is that both components have this feature in the sense shown in Fig. 6.2c.

suprafacial component

antarafacial component

antarafacial component suprafacial component

antarafacial component

suprafacial component

(a) Supraf acial overlap developing in both components

Fig. 6.2

(b) Supraf acial overlap developing in one component and antaraf acial overlap developing in the other

(c) Antaraf acial overlap developing in both components

Suprafacial and antarafacial defined for cycloaddition reactions

When both new bonds are formed on the same surface of the conjugated system, that component is described as undergoing suprafacial attack. When one bond forms to one surface and the other bond forms to the other surface, that component is described as undergoing antarafacial attack. The rule above applies to the common, indeed almost invariable, case where both components are attacking suprafacially on each other. In principle it also applies to the case where both components are antarafacial, but reactions with this awkward geometry are essentially unknown. The generalisation does not apply to the case where one component is suprafacial and the other antarafacial—these are allowed when the total number of electrons is a (4n) number. One example of this type of reaction may be the [14 þ 2] cycloaddition 6.47 of heptafulvalene to tetracyanoethylene, where the heptafulvalene is attacked in an antarafacial manner 6.48, one of the dashed lines, on the left, showing overlap developing to the bottom surface of the conjugated system, and the other to the top surface, presumably helped by some twisting in the conjugated system. This reaction may not be pericyclic, and the suprafacial attack on the tetracyanoethylene is not proved, but it is striking that the two hydrogens at the point of attachment in the product 6.49 are trans to each other, revealing that the heptafulvalene behaved as an antarafacial component, whatever the detailed mechanism.687

NC

CN

NC

CN 6.47

H NC NC 6.48

6.49

H CN CN

262

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

A more complete set of rules for cycloadditions can now be expressed, but we should remember that the all-suprafacial rule in the box above covers a very high proportion of the known cycloadditions.

If the total number of electrons involved can be expressed in the form (4nþ2), where n is an integer, a thermal pericyclic cycloaddition is symmetry allowed when both components react in a suprafacial manner (or both components react in an antarafacial manner). If the total number of electrons can be expressed in the form (4n), it is allowed if one of the components reacts in a suprafacial manner and the other antarafacial.

6.3.1.2 Electrocyclic Reactions. The parent members of the most simple electrocyclic reactions, both those of neutral polyenes and of conjugated ions are shown below. They are the equilibria between butadiene 6.50 and cyclobutene 6.51, between hexatriene 6.52 and cyclohexadiene 6.53, between octatetraene 6.54 and cyclooctatriene 6.55, between the allyl cation 6.56 and the cyclopropyl cation 6.57, between the pentadienyl cation 6.58 and the cyclopentenyl cation 6.59, between the heptatrienyl cation 6.60 and the cycloheptadienyl cation 6.61, and between the corresponding anionic systems 6.62–6.67. There are of course heteroatomcontaining analogues, with nitrogen or oxygen in the chain of atoms, and the systems can be decked out with substituents and other rings. The strained ring of the cyclobutene 6.51 makes this reaction take place in the ring-opening sense, while the hexatriene 6.52 and octatetraene 6.54 reactions are ring closures. There are heteroatom-containing analogues of the anionic systems, with nitrogen and oxygen lone pairs rather than a carbanion centre. These reactions are rarely seen in their unadorned state, and the direction in which they go is determined by such factors as ring strain, the gain or loss of aromaticity, and the substituents or heteroatoms stabilising the ionic charge on one side of the equilibrium or the other.

6.50

6.51

6.56

6.57

6.62

6.63

6.52

6.53

6.58

6.59

6.64

6.65

6.54

6.55

6.60

6.61

6.66

6.67

In contrast to cycloadditions, which almost invariably take place with a total of (4nþ2) electrons, there are many examples of electrocyclic reactions taking place when the total number of electrons is a (4n) number. However, those electrocyclic reactions with (4n) electrons, like the butadiene-cyclobutene equilibrium, 6.50 6.51, differ strikingly in their stereochemistry from those reactions mobilising (4nþ2) electrons, like the hexatriene-cyclohexadiene equilibrium, 6.52 ! 6.53. This is only revealed when the parent systems are

6 THERMAL PERICYCLIC REACTIONS

263

decked out with substituents. The stereochemistry is not dependent upon the direction in which the reaction takes place, but it does depend upon whether there are (4n) or (4nþ2) electrons. There are two possible stereochemistries for the ring-closing and ring-opening reactions. They are called disrotatory and conrotatory, and are illustrated for the general cases in Fig. 6.3. Looking at the ring-closing disrotatory reaction 6.68 ! 6.69, the two outer substituents R move upwards, so that the top lobes of the p orbitals turn towards each other to form the new  bond. The word disrotatory reflects the fact that the rotation about the terminal double bonds is taking place clockwise at one end but anticlockwise at the other. In the corresponding ring-opening, 6.69 ! 6.68, there is similarly a clockwise and anticlockwise rotation as the  bond breaks, and the two upper substituents R that start off cis to each other move apart to become the outer substituents in the open-chain conjugated system. There is an equally probable disrotatory ring closure, not illustrated, in which both R groups fall, with the lower lobes of the p orbitals forming the new  bond, and there is a possible alternative disrotatory ring opening, in which both R groups move towards each other, although whether this happens depends, among other things, upon the size of the R groups, and the extent to which they meet steric hindrance by moving inwards. developing overlap

R

the movement of the cis substituents away from each other disrotatory ring closing

R clockwise rotation anticlockwise rotation

R R

disrotatory ring opening 6.68

6.69

R

R

conrotatory ring closing R

R conrotatory ring opening 6.70

clockwise rotation clockwise rotation

6.71

Fig. 6.3

Disrotatory and conrotatory defined

In contrast, in conrotatory ring-closing, 6.70 ! 6.71, one of the outer substituents and one of the inner substituents, both labelled R, rise to become cis, so that the bottom lobe of the p orbital at one end forms a  bond by overlap with the top lobe of the p orbital at the other end. The rotations are now in the same sense, either both clockwise or both anticlockwise. It follows that the two R groups become cis to each other on cyclisation but the two outer substituents, in contrast to the disrotatory path, become trans to each other on cyclisation. In the ring-opening, 6.71 ! 6.70, the two substituents that are cis to each other move in the same direction, one to an outer position and the other to an inner position by clockwise rotations, as drawn here, or, of course, they could both move by anticlockwise rotations. The rules for which stereochemistry is followed by which system are summarised in Table 6.1. These were the first of the rules, introduced by Woodward and Hoffmann in 1965. They look difficult to absorb all at once, but a simplification makes them easy to learn.

Thermal electrocyclic reactions involving a total number of electrons that can be expressed in the form (4nþ2) are disrotatory, and thermal electrocyclic reactions in which the total number of electrons can be expressed in the form (4n) are conrotatory.

264

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS Table 6.1 The Woodward-Hoffmann rules for electrocyclic reactions

Parent equilibrium Butadiene ¼ cyclobutene Hexatriene ¼ cyclohexadiene Octatetraene ¼ cyclooctatriene Decapentaene ¼ cyclodecatetraene Cyclopropyl cation ¼ allyl cation Cyclopropyl anion ¼ allyl anion Pentadienyl cation ¼ cyclopentenyl cation Pentadienyl anion ¼ cyclopentenyl anion Heptatrienyl cation ¼ cycloheptadienyl cation Heptatrienyl anion ¼ cycloheptadienyl anion Nonatetraenyl cation ¼ cyclononatrienyl cation Nonatetraenyl anion ¼ cyclononatrienyl anion

Electrons

Stereochemistry

4 6 8 10 2 4 4 6 6 8

conrotatory disrotatory conrotatory disrotatory disrotatory conrotatory conrotatory disrotatory disrotatory conrotatory

8 10

conrotatory disrotatory

Examples showing stereochemistry in agreement with these rules are the cyclobutene openings 6.72 ! 6.73 and 6.74 ! 6.75,688 and the hexatriene closings 6.76 ! 6.77 and 6.78 ! 6.79.689 The conrotatory opening 6.72 ! 6.73 and the disrotatory closing 6.76 ! 6.77 are stereochemically contrathermodynamic, with the products in both cases the less stable stereoisomer. It was this striking feature that led Woodward to an appreciation of the special nature of pericyclic reactions, because it was clear that some powerful factor was overriding the normal thermodynamic preferences.

CO2Me

CO2Me 130°, 20 min con

CO2Me

130°, 20 min con

CO2Me

CO2Me

CO2Me

CO2Me

6.72

CO2Me

6.73 6.74

6.76

6.75

140°, 5.5 h

140°, 5.5 h

dis

dis 6.77

6.78

6.79

Among ions, the cyclisation of an allyl cation to a cyclopropyl cation is exemplified by the fate of the intermediate 6.82 when the diazoalkane 6.81 reacts with the ketene 6.80. The intermediate enolate ion will have the E-configuration, because the attack on the ketene will take place anti to the tert-butyl group. The diazonium ion then loses nitrogen to give the W-cation 6.83, which undergoes a disrotatory electrocyclisation to give the cyclopropanone 6.84. The cyclopropyl cation product in this case is a ketone—it is not uncommon to think of a carbonyl group as a highly stabilised carbocation, and in this case it drives the reaction in the direction of ring closure. The tert-butyl groups are forced by the rules to be cis, in spite of the steric forces against such an arrangement. In detail, it is likely that the cation itself is not an intermediate, but that the cyclisation takes place concertedly with the departure of the nitrogen molecule. Nevertheless the rules still apply in the transition structure, in which electron deficiency has started to develop at the carbon to which the nitrogen is attached.690

6 THERMAL PERICYCLIC REACTIONS

265

N O

+

O

N

O

O dis

6.80

6.81

H

H

N2 6.82

6.83

6.84

The same power of the rules to override a powerful steric effect is seen in the ring closure of an allyl anion created by the loss of a nitrogen molecule from the dihydrothiadiazole 6.85. The loss of the nitrogen is a 6-electron all-suprafacial 1,3-dipolar cycloreversion, and will have taken place, with the nitrogen molecule leaving from the lower surface as drawn, to create the sickle-shaped zwitterion 6.86. The p system in this intermediate is isoelectronic with an allyl anion, and its ring closure is therefore conrotatory, forcing the two tert-butyl groups into the hindered cis arrangement in the episulfide 6.87.691 But N

S N

N

But S

–N2

But

con

S

S

6.85

H

H

But

N 6.86

6.87

This reaction does not prove the stereospecificity, because it has only the one stereoisomer, although that is a telling one since it leads to the more hindered product. The full stereospecificity of the cyclopropyl anion to allyl anion interconversion is exemplified by the conrotatory opening of the trans and cis aziridines 6.88, which are isoelectronic with the cyclopropyl anion. They open to give the W and sickle-shaped ylids 6.89, respectively, which are isoelectronic with the corresponding allyl anions. This step is an unfavourable equilibrium, which can be detected by the 1,3-dipolar cycloaddition of the ylids to dimethyl acetylenedicarboxylate, which takes place suprafacially on both components to give the cis and trans dihydropyrroles 6.90, respectively.692 Ar

MeO2C

N MeO2C

CO2Me

N

CO2Me

N

MeO2C

CO2Me

W-6.89 MeO2C

tr ans-6.88

Ar

Ar

con

CO2Me

MeO2C

CO2Me

cis-6.90 Ar

MeO2C

N MeO2C

CO2Me cis-6.88

Ar

Ar

con

N

N

MeO2C

CO2Me

sickle-6.89 MeO2C

CO2Me CO2Me

MeO2C

CO2Me

trans-6.90

The conrotatory closing of a pentadienyl cation can be followed in the NMR spectra of the ions 6.91,693 and the disrotatory closing of a pentadienyl anion can be seen in what is probably the oldest known pericyclic reaction, the formation of amarine 6.93 from the anion 6.92.694

266

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

–83°

–83°

con

con

E,E-6.91

Z,E-6.91

Ph N Ph

Ph

Ph

H PhLi

N Ph

–130°

N

dis

N

Ph

N

NH

+H+

Ph

Ph

Ph

6.92

6.93

6.3.1.3 Sigmatropic Rearrangements. Sigmatropic rearrangements in which a hydrogen atom moves are all [1,n] sigmatropic rearrangements. Those involving a total of (4nþ2) electrons take place with the hydrogen atom moving from one surface of the conjugated system to the same surface at the other end in the general sense of Fig. 6.4a. This is called a suprafacial shift. Those involving a total of (4n) electrons show the alternative stereochemistry in which the hydrogen atom leaves one surface of the conjugated system and arrives at the other end on the opposite surface in the general sense of Fig. 6.4b, which shows the hydrogen atom leaving the upper surface, above C-1, but arriving on the lower surface, below C-n. This is called an antarafacial shift. Note that, although there is an obvious relationship between the words suprafacial and antarafacial used here and the same words used in the section above on cycloadditions, they refer to somewhat different features. In the section on cycloadditions, they refer to the stereochemical sense of the developing overlap, whilst here they refer to the structural change.

1

H 1

[1,n]

H

n 1

[1,n]

H

H

n 1

(a) Supraf acial shif t of H

Fig. 6.4

(b) Antaraf acial shif t of H

Suprafacial and antarafacial defined for a [1, n] migration of hydrogen

Sigmatropic rearrangements of hydrogen are suprafacial if the total number of electrons is a (4nþ2) number and antarafacial if the total number of electrons is a (4n) number.

The [1,5]-suprafacial shift is found in open-chain systems695 and in rings, where it is striking that the shift in the cyclopentadiene 6.94 equilibrates the three isomers 6.94–6.96 at room temperature,696 whereas the cycloheptatriene 6.97 does not undergo the analogous but forbidden suprafacial [1,7]-shift. Instead it undergoes the geometrically more contorted, but allowed, suprafacial [1,5]-shift, 6.97 (arrows) at a much higher temperature.697 Both reactions 6.94 and 6.97 are described as [1,5]-shifts, because they are made possible by the overlap along the set of atoms from C-1 to C-5. The former is structurally a [1,2]-shift, since the hydrogen atom moves to the adjacent carbon, but it is not mechanistically a [1,2]-shift. The bond between C-1 and C-5 plays no electronic part in the mechanism—it merely serves to hold the two atoms close to each other, speeding up the reaction. The same reaction can take place when that bond is not present, but is

6 THERMAL PERICYCLIC REACTIONS

267

then much slower. Similarly the reaction 6.97 ! 6.98 might have been called a [1,4]-shift, but again that would only refer to one way of looking at the structural change, whereas electronically it is a [1,5]-shift. H1

5

4

H

H

H

H

r.t.

3 1

2

6.94

6.95 H

6.96

1 1

5

>146°

H etc.

4 3

H

2

6.98

6.97

[1,7]-Antarafacial shifts in heptatrienes can only occur in open-chain systems, as in the reaction 6.9 ! 6.10, because it is sterically impossible in a ring like that in a cycloheptatriene 6.97 for a hydrogen atom leaving one surface of the ring to develop overlap onto the other side of the ring. The antarafacial stereochemistry of the reaction 6.9 ! 6.10 was deduced from its appearance only in open-chain systems, but it has been supported by the proof of antarafacial shifts in the model system 6.99, which gives only the 10S-6.100 by antarafacial deuterium shift from C-15 (arrows), and only 10R-6.100 by antarafacial hydrogen shift from C-15 on the top surface of the triene 6.99 to the bottom surface at C-10 (using steroid numbering).698 C8H17

C8H17 H

C8H17

15

100° D

D OH 6.99

10

10S-6.100

H OH

+

D 10

H OH

10R-6.100

When the migrating group in a [1,n]-shift is a carbon atom, two more possibilities arise, not available to hydrogen atoms. In addition to moving either suprafacially or antarafacially, the migrating group can migrate with retention of configuration or with inversion of configuration.

When the total number of electrons is a (4nþ2) number, [1, n] sigmatropic rearrangements of elements other than hydrogen are either suprafacial with retention of configuration in the migrating group or are antarafacial with inversion of configuration in the migrating group. When the total number of electrons is a (4n) number, [1, n] sigmatropic rearrangements of elements other than hydrogen are either antarafacial with retention of configuration in the migrating group or are suprafacial with inversion of configuration in the migrating group.

Thus the [1,2]-shift of an alkyl group towards an electron deficient atom always takes place with retention of configuration, whether it be towards carbon in a Wagner-Meerwein rearrangement 6.101, towards nitrogen in a Beckmann or Curtius rearrangement, or towards oxygen in a Baeyer-Villiger rearrangement.

268

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

These reactions use two electrons, and the allowed suprafacial migration is geometrically reasonable. In the corresponding anion, there would be four electrons, and neither of the allowed pathways 6.102 and 6.103 is reasonable. Accordingly anions do not normally rearrange, and when they do they use a stepwise pathway (see p. 281).699 retention

inversion

suprafacial

suprafacial

retention

antarafacial 6.102

6.101

6.103

Examples for which inversion of configuration in the migrating group has been proved are the suprafacial [1,3]-shift of the bridge in the bicyclo[3.2.1]heptene 6.104700 and the [1,4]-shift in the bicyclo[3.1.0]hexenyl cation 6.105.701 The stereochemistry in the latter case is overwhelmingly proved simply by the NMR spectrum: as the rearrangement takes place all the methyl groups attached to the five-membered ring become equivalent on the NMR timescale, but the signals of the two methyl groups labelled i (for inside) and o (for outside) remain distinct. It is sometimes a source of confusion that the inside methyl group remaining inside corresponds to an inversion of configuration, but the bond between C-1 and C-10 is on the front face of C-10 in 6.105, and the bond that is forming from C-4 to C-10 is on the back side, which marks the event as an inversion of configuration at C-10 , which is the migrating group. 1'

i

i

o

o

inversion AcO

D 6.104

AcO D inversion

4 3

2

1

6.105

The rules for [m,n]-sigmatropic rearrangements, where m 6¼ 1 and n 6¼ 1, are more complex still. The bond can migrate suprafacially or antarafacially on either component, with the great majority of known reactions being suprafacial on both components, as in Fig. 6.5a, where the heavy bond labelled 1,1 is migrating to the dashed bond labelled m,n. The carbon atoms labelled 1 and 1 are tetrahedral in the starting material, and the atoms labelled m and n are trigonal. In the product, the atoms that were labelled 1 and 1 have become trigonal and the atoms that were labelled m and n have become tetrahedral. This is the most common event, simply because it is relatively easy for molecules to adopt this arrangement. In principle, however, both migrations could be antarafacial, as in Fig. 6.5b. Alternatively, one could be antarafacial and the other suprafacial as in Fig. 6.5c. In almost all cases, if the rules demand an antarafacial component, it is difficult to maintain continuous overlap in such systems—they have to be long and flexible—and [m,n]-sigmatropic rearrangements with antarafacial components are correspondingly rare. The rules for [m,n]-sigmatropic rearrangement are:

When the total number of electrons is a (4nþ2) number, [m,n]-sigmatropic rearrangements are allowed if both migrations are suprafacial or both antarafacial. When the total number of electrons is a (4n) number, [m,n]-sigmatropic rearrangements are allowed if one migration is suprafacial and the other antarafacial.

6 THERMAL PERICYCLIC REACTIONS

269 m

1

m

1

n

[m,n]

[m,n]

n 1 1

(a) Supraf acial shif t in both components

(b) Antaraf acial shif t in both components

m

1

n

[m,n]

1

(c) Supraf acial shif t in one component (n), antaraf acial shif t in the other (m)

Fig. 6.5

Suprafacial and antarafacial defined for [m(n]-shifts in general

The great majority of [m,n]-sigmatropic rearrangements involve the all-suprafacial participation of (4nþ2) electrons. Much the most common are the various [3,3]-sigmatropic rearrangements, such as the Claisen rearrangement 6.6 ! 6.7, the Ireland-Claisen rearrangement 6.106 ! 6.107, which is demonstrably stereospecific, with a chair-like transition structure,702 and the all-carbon version, which is called a Cope rearrangement, as in the reaction of cis-1,2-divinylcyclobutane giving cis,cis-1,4-cyclooctadiene 6.109, which must have a boat-like transition structure 6.108.703 Whether a boat or a chair is intrinsically favoured is discussed in Section 6.5.5.1.

O

OSiMe3 LDA, –78°

O

25°, 1 h O

Me3SiCl

anti:syn O

87:13

Me3SiO E-6.106

anti-6.107

O

OSiMe3 LDA, –78°

O

HMPA Me3SiCl

25°, 1 h O

O

Me3SiO Z-6.106

syn-6.107

H 120°, 10 min

H 6.108

6.109

19:81

270

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

Other common all-suprafacial [2,3]-sigmatropic rearrangements are the Mislow reaction 6.11 ! 6.12, and the anionic 2,3-Wittig rearrangement 6.110 ! 6.111 of the anions made from diallyl ethers by treatment with strong base.704

BuLi

Pri Pri

Pri 6.110

Pri

[2,3]

O

O

O

OH 6.111

There are a few sigmatropic rearrangements with more than six electrons, such as the 10-electron doubly vinylogous Stevens rearrangement 6.112 ! 6.113,705 and the 10-electron benzidine rearrangement 6.114 ! 6.115.706

Ph

NMe2 NaOMe

Ph

NMe2

Ph

NMe2

[4,5]

r.t., 12 h

6.112 H2N

NH2

NH2

6.113

NH2

[5,5] H2N

H 6.114

H

NH2 benzidine

6.115

6.3.1.4 Group Transfer Reactions. There are so few of these reactions that a fully general rule for them can wait until the next section, where we see the final form of the Woodward-Hoffmann rules. For now, we can content ourselves with a simplified rule which covers almost all known group transfer reactions.

When the total number of electrons is a (4nþ2) number, group transfer reactions are allowed with all-suprafacial stereochemistry.

The stereochemistry of the ene reaction 6.116 þ 6.117 ! 6.119 is such that the hydrogen atom delivered to the enophile 6.117 leaves from the same surface of the ene 6.116 as the surface to which the C—C bond is forming, and the hydrogen atom is delivered to the same surface of the enophile as the forming C—C bond 6.118, so that both components are reacting suprafacially.707 The full stereochemistry is not proved in this example, because neither the methyl group, C-1, nor the  carbon has any stereochemical label, but the all-suprafacial pathway provides a plausible explanation for the relative stereochemistry set up between the  carbon and C-3.

6 THERMAL PERICYCLIC REACTIONS

1

MeO2C

H

Cl

271

EtAlCl2

AlEtCl2

MeO

+ R

O

Cl

MeO2C *

H

3

R

6.117

R 6.118

6.116

H Cl

* 3

6.119

In a double hydrogen atom transfer between cis-9,10-dihydronaphthalene 6.120 and 1,2-dimethylcyclohexene 6.121, analogous to the diimide reduction 6.16, the two hydrogens leave from the same surface of the dihydronaphthalene, and arrive on the same surface of the cyclohexene to give the cis-dimethylcyclohexane 6.122 in another all-suprafacial reaction.708 However, the 10-electron reaction in which 1,4-cyclohexadiene 6.123 reduces anthracene 6.124, is also allowed in the all-suprafacial mode, but deuterium labels on the cyclohexadiene show that it is not stereospecifically a syn delivery of hydrogen; it is almost certainly stepwise, with two successive hydrogen atom transfers, and neither pericyclic nor governed by the rules of pericyclic chemistry.709 This is a timely reminder that not all reactions that appear to obey the rules can be assumed to be pericyclic. However, reactions that do not obey the rules are almost certainly not pericyclic. H

150°, 48 h

+

H

H 6.120

H

6.121

6.122 200°

+

6.123

+

6.124

6.3.2 The Generalised Woodward-Hoffmann Rule We have now seen a large number of rules, presented in the boxes above, expressed differently for each kind of pericyclic reaction. Learning them would seem to impose a considerable burden, but Woodward and Hoffmann saved us from this effort by rewriting them in 1969656 in one all-encompassing rule that applies to all thermal pericyclic reactions:

A ground-state pericyclic change is symmetry allowed when the total number of (4qþ2)s and (4r)a components is odd.

This admirably concise statement is compelling, but we must now see what it means, and learn how to apply it to each of the classes of pericyclic reaction. 6.3.2.1 Cycloadditions. Let us begin with the bare bones of the Diels-Alder reaction in Fig. 6.6. The components of a cycloaddition are obvious enough—we have been using the word already to refer to the core electronic systems undergoing change. For a Diels-Alder reaction the components are the p orbitals of the

272

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS 4s (4q+2)s: 1 (4r)a: 0 Total: 1 √ 2s

Fig. 6.6

The Diels-Alder reaction as a [p4sþp2s] reaction

diene, containing four electrons, and the p bond of the dienophile, containing two electrons. We ignore all substituents not directly involved, treating them only, for the purposes of following the rule, as stereochemical labels. What we have to do is to ask ourselves two questions: (1) which of these components is acting in a suprafacial manner and which in an antarafacial manner; and (2) in which of these components can the number of electrons be expressed in the form (4qþ2) and in which in the form (4r), where q and r are integers? For the Diels-Alder reaction both components are undergoing bond formation in a suprafacial sense, as shown by the dashed lines in Fig.6.6, and so the answer to the first question is: both components. The diene has four electrons, a number that can be expressed in the form (4r), with r ¼ 1. Since the new bonds are forming on the diene in a suprafacial manner, both lines coming to the lower surface, the diene is a (4r)s component, where the subscript s denotes a suprafacial pathway. The dienophile has two electrons, a number that can be expressed in the form (4qþ2), with q ¼ 0. Since the new bonds are forming on the dienophile in a suprafacial manner, both lines coming to the upper surface, the dienophile is a (4qþ2)s component. Thus, the Diels-Alder reaction has one (4qþ2)s component and no (4r)a components. We ignore (4qþ2)a and (4r)s components, when there are any. The total number of (4qþ2)s and (4r)a components is therefore 1, and, since this is an odd number, the reaction is identifiably symmetry-allowed by the rule. The Diels-Alder reaction is, as we have been calling it all along, a [4 þ 2] cycloaddition. Since it takes place suprafacially on both components, it is more informatively described as a [4sþ2s] cycloaddition, and finally, because both components are p systems, it is fully described as a [p4sþp2s] cycloaddition. The description [p4sþp2s] for a Diels-Alder reaction does not supplant the older name—it is not the only reaction that is [p4sþp2s]. 1,3-Dipolar cycloadditions 6.37 þ 6.38 are equally easily drawn as [p4sþp2s], and so are the combinations: allyl cation 6.27 and diene, allyl anion 6.31 and alkene, and pentadienyl cation 6.35 and alkene. Furthermore, [p4sþp2s] is not the only way of describing a Diels-Alder reaction. It would be easy to overlook the fact that the diene can be treated as one component, and to see it instead as two independent p bonds. Although it makes extra work to see it this way, it does not cause the rule to break down. For example, the drawing on the left of Fig. 6.7 might have been used instead of the one in Fig. 6.6. The dashed line representing the developing overlap for the formation of the p bond is from the lower lobe on C-2 to the lower lobe on C-3. This makes all three components suprafacial—the p bond between C-1 and C-2 has both dashed lines to the lower lobes, and the p bond between C-3 and C-4 also has both dashed lines to the lower lobes. In other words both are suffering suprafacial development of overlap. The same is true for the p bond of the

2s

2a

2 3

1 4

2s 2s

Fig. 6.7

2

(4q+2)s: 3 (4r)a: 0 Total: 3 √

1

3

2a

4

(4q+2)s: 1 (4r)a: 0 Total: 1 √

2s

The Diels-Alder reaction as a [p2sþp2sþp2s] and as a [p2sþp2aþp2a] reaction

6 THERMAL PERICYCLIC REACTIONS

273

dienophile. Overall the sum is changed to having three (4qþ2)s components, which is still an odd number, and so the reaction remains allowed. It is now described as a [p2sþp2sþp2s] cycloaddition, but it is of course, no matter which of these descriptions we use, the same reaction. Another drawing, on the right of Fig. 6.7, still representing the same reaction, places the dashed line between the upper lobes on C-2 and C-3. This changes each of the p bonds of the diene to suffering notional antarafacial development of overlap. It is just as valid a representation as either of the earlier versions, and the sum still comes out with an odd number of (4qþ2)s components and no (4r)a components. The two p2a components do not have to be counted, because they are (4qþ2)a and not (4r)a. The reaction is now a [p2sþp2aþp2a] cycloaddition. Clearly, the three designations [p4sþp2s], [p2sþp2sþp2s] and [p2sþp2aþp2a] are all the same reaction, and none of them defines a Diels-Alder reaction. The three designations, in fact, define where the dashed lines have been drawn in the three drawings in Figs. 6.6 and 6.7, and no reaction should be described in this way in the absence of a drawing like these. It is easy enough to see how to extend the labelling of cycloaddition reactions to those involving larger conjugated systems. As just one example, the cycloaddition of heptafulvalene to tetracyanoethylene is shown in Fig. 6.8. The developing overlap is taking place on opposite sides of the 14-electron component, which is therefore a (4qþ2)a component, and does not count towards the sum. The overlap on the 2-electron component, although not proved, is probably suprafacial, and the (4qþ2)s component does count.

14a

(4q+2)s: 1 (4r)a: 0 Total: 1 √ 2s

Fig. 6.8

The cycloaddition of heptafulvalene to tetracyanoethylene as a [p14aþp2s] reaction

6.3.2.2 Electrocyclic Reactions. In order to move on to electrocyclic reactions, we need to see how the words suprafacial and antarafacial are defined for  bonds. In order to have a single orbital associated with the bond, it is a great convenience to use orbitals made from overlapping spn hybrids. Just as a suprafacial event on a p bond has overlap developing to the two overlapping lobes that contribute to bonding, so with  bonds (Fig. 6.9a), overlap that develops to the two large lobes of the spn hybrids is suprafacial. Less obviously, overlap that develops to the two small lobes is also suprafacial, because it is the counterpart to overlap developing to the other two lobes in a p bond. Antarafacial overlap is when one bond is forming to an inside lobe and one to an outside lobe, either way round (Fig. 6.9b). The electrocyclic interconversion of the cyclobutene 6.72 and the cis,trans-butadiene dicarboxylic ester 6.73 is shown in Fig. 6.10a. The components for the ring opening are the  bond made from two sp3 hybrids drawn in front and the p bond drawn at the back, and the conrotatory ring opening is shown as a [2aþp2s] process. In the ring-closing direction there is only one component, the p system of the diene, and the conrotatory ring closing is shown as a [p4a] process. The small sums show that they are allowed by the

(a) Supraf acial bond f ormation

Fig. 6.9

(b) Antaraf acial bond f ormation

Suprafacial and antarafacial defined for  bonds

274

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS 4a

2s (4q+2)s: 1 (4r)a: 0 MeO2C Total: 1

CO2Me

√

CO2Me

CO2Me

(4q+2)s: 0 (4r)a: 1 Total: 1

√

2a

(a) The allowed conrotatory interconversion of a cyclobutene and a butadiene

6s

4s

(4q+2)s: 1 (4r)a: 0 Total: 1

√

Me Me

Me

(4q+2)s: 1 (4r)a: 0 Total: 1

√

Me 2s

(b) The allowed disrotatory interconversion of a hexatriene and a cyclohexadiene

Fig. 6.10

The allowed electrocyclic reactions

Woodward-Hoffmann rule. Notice how the dashed lines and the curved arrows correspond to the clockwise direction in which the substituents move in the ring opening and anticlockwise in the ring closing, and that the geometry shown in the products matches these movements in both directions. We could have drawn the equally probable reaction with anticlockwise conrotatory movements, but we would have had to change both dashed lines so that the ends coming into the p bond came into the lower lobes of the p orbitals instead of the upper. A drawing of the ring opening could also have been made by replacing the left hand dashed line with a dashed line coming out of the inside lobe of the  bond and dropping to overlap with the lower lobe of the left-hand p orbital. The ring opening would have been the same as that shown in Fig. 6.10a, clockwise conrotatory, but the description would then have been [2sþp2a]. The symmetry-allowed disrotatory ring closing of the trans,cis,trans-dimethylhexatriene 6.76 and the disrotatory ring opening of the cis-dimethylcyclohexadiene 6.77 are shown in Fig. 6.10b as [p6s] and [2sþp4s] processes. Again there are other dashed lines that could be drawn to describe these movements, and there is a similar reaction in both directions interconverting the cis,cis,cis-triene and the cis-dimethylcyclohexadiene, in which the methyl substituents move inwards in the ring opening, instead of outwards, following an energetically less favourable pathway, but one that is equally allowed by symmetry. In order to describe the ring opening of the aziridine 6.80, we need to define what suprafacial and antarafacial mean when applied to a p orbital. This is shown in Fig. 6.11, and applied there to the conrotatory aziridine opening. When both lines are drawn into the same lobe it is suprafacial, and when there is one line dawn into the top lobe and one into the bottom, it is antarafacial. Since this is neither a p nor a  orbital, it is given the Greek letter o. The same designations apply whether the orbital is filled (on the left) or unfilled (on the right), and whether it is a p orbital or any of the spn hybrids. In the aziridine opening shown in Fig. 6.11, the aryl group behind the nitrogen atom is left out. The dashed lines are drawn from the large lobes of the  bond, making this a [2s] component. Both substituents move anticlockwise in the conrotatory mode, so the dashed line on the left of the  bond goes up to overlap with the upper lobe of the p orbital on the nitrogen atom, and the dashed line on the right goes down to overlap with the lower lobe. With one overlap drawn as developing to the top and one to the bottom, the p orbital is an [o2a] component, making the overall reaction drawn in this way a [2sþo2a] process. In the opposite direction, the clockwise conrotatory ring closing of the azomethine ylid 6.81 is simply a [p4a] process. The conrotatory process taking place in the clockwise direction would place both methoxycarbonyl groups inside in a U-shaped ylid; this would be thermodynamically less favourable but just as allowed by

6 THERMAL PERICYCLIC REACTIONS

275

2s

0s

2a

2a (4q+2)s: 1 (4r)a: 0

4a con

MeO2C

N

Total: 1

2s

N

MeO2C

√

Fig. 6.11

0a

CO2Me

(4q+2)s: 0 (4r)a: 1 Total: 1

√

CO2Me

Suprafacial and antarafacial defined for a p orbital, and the allowed conrotatory interconversion of an aziridine with an azomethine ylid

symmetry. In the corresponding cis-disubstituted aziridine, the stereochemistry is still conrotatory, but now the geometry of the ylid is sickle-shaped, with one of the methoxycarbonyl groups outside and the other inside. 6.3.2.3 Sigmatropic Rearrangements. The overlap developing in a suprafacial [1,5]-hydrogen shift in a diene is drawn at the top in Fig. 6.12 both as a [2sþp4s] process and as a [2aþp4a] process. In both cases, the [1,5]-shift is suprafacial in the structural sense, but the overlap developing is selected in different ways in the two drawings—all-suprafacial on the left and all-antarafacial on the right. Thus the word suprafacial does not have the same meaning in the two contexts in which it is used here, although there is an obvious relationship. Both drawings, of course, are equally valid, and both would show that the reaction is symmetry-allowed if we were to complete the little sum that has accompanied all the drawings up to this point, but which we shall leave out from now on. The antarafacial [1,7]-hydrogen shift is similarly drawn in two ways at the bottom of Fig. 6.12. One component is suprafacial and one antarafacial in each, but in both the hydrogen atom shifts in a structurally antarafacial sense, and the reaction is the same.

4a

4s H

H A suprafacial [1,5]-shift in a diene:

2a

2s

6a

6s

An antarafacial [1,7]-shift in a triene: H

H 2s

2a

Fig. 6.12 The [1,5]-suprafacial shift of an H atom drawn as [2sþp4s] and [2aþp4a] processes and the [1,7]-antarafacial shift of an H atom drawn as [2sþp6a] and [2aþp6s] processes

276

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

The [1,2]-shift of an alkyl group with retention of configuration in the migrating group, shown for the carbocation 6.101 on p. 268 has a dashed line identifying it as a suprafacial migration. A second dashed line connecting the lower end of the  bond to the same lobe of the empty p orbital would make it [2sþo0s], but the same reaction could equally be described with a different line coming from the lower lobe of the empty p orbital to the lower side of the carbon atom of the  bond, making it [2aþo0a]. Similarly, the [1,3]-shift of an alkyl group with inversion of configuration in the migrating group, shown for the bicyclo[3.2.0]heptene 6.104, already has the dashed lines identifying it as a [2aþp2s] process, and the [1,4]-shift of an alkyl group with inversion of configuration, shown for the bicyclo[3.1.0]hexyl cation 6.105, has the dashed lines for a [2aþp2s] process, both of which are allowed by the unified rule. The [3,3]-sigmatropic rearrangement, found in the Claisen and Cope rearrangements, is drawn for the chair and boat transition structures 6.125, each of which is known and each of which is allowed. In both cases they are drawn as all-suprafacial processes in the middle of Fig. 6.13, and as one suprafacial and two antarafacial processes on the right. In both cases, the bold bond marked 1,10 is leaving the lower surface of the conjugated system from C-1 and arriving on the lower surface at C-3; the same bond is leaving the upper surface at C-10 and arriving on the upper surface at C-30 . Thus the reaction, whether chair-like or boat-like and however it is described for the purposes of the Woodward-Hoffmann rule, involves a structurally suprafacial migration of the  bond across each of the surfaces as defined for the general case in Fig. 6.5a. [2,3]-Sigmatropic rearrangements, like the 2,3-Wittig rearrangement 6.110, which has sulfur and aza analogues, are drawn for the general case in Fig. 6.14, where X¼O, S, SRþ, or NR2þ. An envelope-shaped transition structure is almost always involved, because this allows the smooth development of head-on overlap in the formation of the  bond between C-20 and C-3 at the same time that the  bond between C-10

2 3

1'

2a

2s 2'

3'

2s

chair-6.125 1

2a

2s

1'

3'

2a 2s

2 3

2s

2s

1

2s 2a

2s

2'

boat-6.125

Fig. 6.13

A [3,3]-sigmatropic rearrangement drawn as [2sþp2sþp2s] and [2sþp2aþp2a] processes

2s 2'

X

1'

X

X 3

1

Fig. 6.14

2s

2s

2

A [2,3]-sigmatropic rearrangement drawn as a [2sþo2sþp2s] process

6 THERMAL PERICYCLIC REACTIONS

277

and C-1 is conjugated with the p bond. These reactions all have an o component in the form of a lone pair or the p or hybrid orbital of a carbanion, and can be described in the all-suprafacial mode drawn in Fig. 6.14 as [2sþo2sþp2s]. 6.3.2.4 Group Transfer Reactions. The ene reaction 6.118 is drawn again on the left of Fig. 6.15, showing that it can be described as a [2sþp2sþp2s] process, and a dihydrogen transfer similar to that in diimide reduction or the reaction of 9,10-dihydronaphthalene 6.120 is redrawn on the right of Fig. 6.15, showing that it can be described as a [2sþ2sþp2s] process.

MeO2C

Cl 2s

2s

2s H R

Fig. 6.15

H 2s

2s

H 2s

An ene reaction drawn as a [2sþp2sþp2s] process and a dihydrogen transfer drawn as a [2sþ2sþp2s] process

6.3.2.5 Some Hints about Drawing Diagrams for the Woodward-Hoffmann Rule. The first requisite for a good understanding of a pericyclic reaction is to have a good drawing of the transition structure. Begin with the flat, curly arrow-based representation, because this helps to identify the components—they are the lone pairs and the bonds that the curly arrows apply to—the bonds that are broken and the bonds that are made, and the lone pairs that are mobilised or localised. Then try to draw a three-dimensional view, in order to assess how reasonable the reaction is. Boat-like, chair-like and envelope transition structures are common, easily drawn, and are likely to be a good starting point. A good drawing will show the component orbitals lined up to develop overlap with the right geometry—head-on if it is creating a  bond or sideways-on if it is creating a p bond—as drawn for the ene reaction in Fig. 6.15. Sometimes this is not possible, especially with electrocyclic ring-closing reactions. Any attempt to bring the orbitals at the ends of the diene in Fig. 6.10a and the triene in Fig. 6.10b into a position to show the developing  overlap will so distort the conjugated systems that the drawing will be hard to read. The reactions take this path, but it is probably wise to avoid drawings close to the transition structures in cases like these. Then there is the problem of assessing whether the reaction is symmetry-allowed or not using the Woodward-Hoffmann rule. If there is an odd number of curly arrows, then the overall reaction uses (4nþ2) electrons. All such reactions are allowed in the all-suprafacial mode, and so it is helpful to draw the dashed or solid lines (or better still use a line with a distinctive colour) to show the developing overlap with only suprafacial components, as in Fig. 6.6, for example. The (4qþ2)s components will then add up to an odd number, and the task is done. If the dashed, bold or coloured lines are not those for an all-suprafacial reaction, as in the right-hand side of Fig. 6.7, for example, all is not lost—simply do the sum to find out whether the drawing corresponds to an allowed reaction or not. The all-suprafacial drawing is no better than the other representations, but it is a quick way to arrive at a drawing showing that a (4nþ2) reaction is reasonable and allowed. This simplification works for a very high proportion of pericyclic reactions. Reactions involving a total of (4n) electrons, in which the number of curly arrows is even, are relatively rare. They will be allowed if there is one antarafacial component and all the others are suprafacial. In this case, if the dashed, bold or coloured lines include only one antarafacial component, the number of (4qþ2)s and (4r)a components will add up to an odd number, and the drawing will show the geometry of a symmetry-allowed reaction.

278

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

When working out whether or not a reaction is obeying the rule, it is inappropriate to shade the orbitals— what we have been doing in the whole of Section 6.3 is not a frontier orbital treatment, which we shall come to later. No particular orbital is being considered when analyses like those in Figs. 6.6–6.15 are carried out. There is no real need to draw the lobes at all, as long as the perspective used to make the drawings and the placing of the dashed, bold or coloured lines clearly identify the surfaces of the conjugated systems onto which the new bonds are developing and from which the old bonds are breaking. The dashed lines on the drawings 6.104 and 6.105 on p. 268 clearly illustrate [p2sþ2a] processes without drawing the lobes. 6.3.2.6 Some Symmetry-Allowed but Geometrically Unreasonable Reactions. Some reactions are symmetry-allowed, but they do not take place because they cannot attain a geometry that allows the continuous development of overlap. The [2 þ 2] reaction shown in Fig. 6.16a is a [p2sþp2a] reaction, fully allowed by the Woodward-Hoffmann rule, but it does not take place because the molecule is not flexible enough for the overlap developing on the left-hand side to take place at the same time as the overlap developing on the right-hand side. A longer conjugated system might have the necessary flexibility, and this could be the case in the reaction between heptafulvalene and tetracyanoethylene in Fig. 6.8. As we shall see in the next section, the development of the overlap on the left-hand side alone is not forbidden, but the reaction is not then pericyclic. 2a 2a

2s 2a

1

2s

2

1

2 3

3

2s (a) A symmetry-allowed but unreasonable [ 2s+ 2a] cycloaddition

Fig. 6.16

(b) A symmetry-allowed but unreasonable [ 2a+ 2s] [1,3]sigmatropic rearrangement

(c) A symmetry-allowed but unreasonable [ 2s+ 2a] [1,3]sigmatropic rearrangement

Symmetry-allowed but geometrically inaccessible reactions

Another examples of an allowed but essentially impossible pathway is the [1,2]-shift in an anion, whether it is suprafacial with inversion of configuration in the migrating group 6.102 or antarafacial with retention of configuration in the migrating group 6.103. Slightly less unlikely are [1,3]-sigmatropic shifts, which are also allowed to be either suprafacial with inversion ([2aþp2s] in Fig. 6.16b) or antarafacial with retention ([2sþp2a] in Fig. 6.16c). Neither looks geometrically reasonable, but the former may just possibly explain the stereochemistry of the reaction of the bicyclo[3.2.0]heptene 6.104,710 and it appears to make a contribution, if not an overriding one, to the stereochemistry of the [1,3]-shift seen in vinylcyclopropanes giving cyclopentenes.711 Perhaps most convincingly it is seen in the [1,3]-shift of a silyl group, which takes place with inversion of configuration at the silicon atom.712 This reaction is made easier than it is in the carbon series by the bonds to the migrating silicon atom being longer than those to a migrating carbon atom, giving greater flexibility, and to the possbility that the bond making to the silicon atom and breaking from it need not be so precisely oriented as they would be in the corresponding carbon shift. There is no good example of an antarafacial [1,3]-shift with retention of configuration, a symmetry-allowed but geometrically even less probable reaction. 6.3.2.7 Some Geometrically Reasonable but Symmetry-Forbidden Reactions. Equally, there are symmetry-forbidden reactions, for which the small sum adds up to an even number. As a result, most of them do not take place, and none of them takes place in a concerted manner. Let us take [2 þ 2] and [4 þ 4]

6 THERMAL PERICYCLIC REACTIONS

279

cycloadditions, for which the only reasonable transition structures are for suprafacial attack on both components. The dashed lines are shown in Fig. 6.17, where we see in both cases that, however geometrically reasonable the reactions may look, there are either two p2s components or two p4s components, and the sums add up to even numbers.

2s

4s

(4q+2)s: 2 (4r)a: 0 Total: 2 x

2s

Fig. 6.17

(4q+2)s: 0 (4r)a: 0 Total: 0 x

4s

Symmetry-forbidden [2 þ 2] and [4 þ 4] cycloadditions

[2 þ 2] Cycloadditions and [4 þ 4] cycloadditions are only forbidden if they are concerted—there is nothing forbidden about the formation of one bond, provided that the other is not forming at the same time. The dashed line on the left in Fig. 6.17 can lead to a bond, as long as overlap is not developing at the same time in the sense of the dashed line on the right. If only one bond forms, it will create either a zwitterionic or a diradical intermediate. The ionic pathway becomes reasonable if either or both of the ionic centres in the zwitterionic intermediate is equipped with stabilising groups: C or Z for anions and C or X for cations. Thus the enamine 6.126 reacts with the ,-unsaturated ester 6.127 to give the cyclobutane 6.129.713 This reaction is stepwise with the intermediate zwitterion 6.128 having a cationic centre stabilised as an iminium ion by the lone pair of the amino group, and an anionic centre stabilised as an enolate ion by the adjacent carbonyl group. The reaction is still a cycloaddition, but it is not pericyclic. O Me2N

6.126

O OMe

Me2N

85°, 2 h Me2N

6.128

6.127

CO2Me

OMe

6.129

Equally, not all [4 þ 2] cycloadditions are concerted.714 If a zwitterionic or diradical intermediate is well enough stabilised, one bond can form ahead of the other, as in the reaction between the same enamine 6.126 and the ,-unsaturated ketone 6.130 giving the dihydropyran 6.132.715 This is formally a hetero DielsAlder reaction, but it is almost certainly stepwise, taking place by way of the zwitterion 6.131. The advantage for a stepwise reaction is that forming only one bond does not suffer from the same high negative entropy of activation that forming both together does. The advantage for a concerted Diels-Alder reaction, although it suffers from a high negative entropy of activation, is that it does not demand the high degree of stabilisation found in intermediates like 6.128 and 6.131. Me2N

6.126

O

6.130

r.t., 20 min

Me2N

O

6.131

Me2N

O

6.132

280

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

A beautiful illustration of a delicate balance between a stepwise and a concerted reaction has been found in the reactions of 1,1-dimethylbutadiene 6.133.716 This diene rarely adopts the s-cis conformation necessary for the Diels-Alder reaction with tetracyanoethylene giving the cyclohexene 6.136. However, it can react in the more abundant s-trans conformation in a stepwise manner, leading to a moderately well stabilised zwitterion 6.134. The intermediate allyl cation is configurationally stable, and a ring cannot form to C-1, because that would give a trans double bond between C-2 and C-3 in the cyclohexene 6.137. Instead a cyclobutane 6.135 is formed. All this is revealed by the solvent effect. In the polar solvent acetonitrile the stepwise ionic pathway is favoured, and the major product (9:1) is the cyclobutane 6.135. In the nonpolar solvent hexane, the major product (4:1) is the cyclohexene 6.136 with the Diels-Alder reaction favoured. NC NC

NC NC

CN CN

NC NC

CN CN

CN CN

H

H

3

2

1

6.134

s-trans-6.133

6.135

s-cis-6.133 NC NC NC

CN CN

CN H

CN CN

NC

CN CN

H

CN

6.136

6.137

Stepwise reactions by way of diradical intermediates are also possible; such reactions often require rather high temperatures, but radicals are probably involved in the formation of cyclobutanes like that from the halogenated alkene 6.138 and butadiene giving the cyclobutane 6.140.717 As we saw in Chapter 2 (Section 2.1.5), any group, C, Z or X, can stabilise a radical. Both radical centres in the intermediate 6.139 are stabilised, the one on the left by the -chlorines and the -fluorines, and the one on the right because it is allylic. There are a number of reactions like this—all that is required is enough radical-stabilising substituents. F

Cl

F

Cl 6.138

F

82° 13 h

F

F F

Cl Cl 6.139

Cl Cl 6.140

Again, the diene does not need to be in the s-cis conformation—as long as the substituents stabilise the radicals well enough, as they do here, the first bond can form while the diene is still in its more abundant strans conformation. The allyl radical 6.139 produced from the s-trans diene is configurationally stable, just as the allyl cation 6.134 was, and it will not be able to cyclise to give a trans-cyclohexene. Rotation about the bond between C-2 and C-3 is evidently too slow to compete with the radical combination giving the cyclobutane 6.140. Some other stepwise reactions, puzzling at one time, because they seemed to disobey the rules, are the [1,2]-shifts of ylids, like the Stevens rearrangement 6.141 ! 6.143.718 The symmetry-allowed geometry, like that in the [1,3]-shifts in Fig. 6.16b and 6.16c, is either suprafacial-with-inversion or

6 THERMAL PERICYCLIC REACTIONS

281

antarafacial-with-retention. These pathways are unreasonable—there is no flexibility for migration across only two atoms, and yet reactions like this take place easily. It is now clear that most such reactions take place stepwise by homolytic cleavage 6.141 ! 6.142, followed by a rapid recombination of the radicals 6.142 ! 6.143.719 It is probably significant that the radical 6.142 is captodative. No matter how reliable that idea is (see p. 82), the radical is highly stabilised, making the reaction even easier than it might at first seem. Ph Ph

Ph

53°, 4 h N

Me2N

Me2N

Ph

Ph

O 6.141

Ph

O

O

6.142

6.143

6.3.2.8 Reactions of Ketenes, Allenes and Carbenes which Appear to be Forbidden. Some [2 þ 2] cycloadditions only appear to be forbidden. One of these is the cycloaddition of ketenes to alkenes. These reactions have some of the characteristics of pericyclic cycloadditions, such as being stereospecifically syn with respect to the double bond geometry, and hence suprafacial at least on the one component, as in the reactions of the stereoisomeric cyclooctenes 6.144 giving the diastereoisomeric cyclobutanones 6.145.720 However, stereospecificity is not always complete, and many ketene cycloadditions take place only when there is a strong donor substituent on the alkene. An ionic stepwise pathway by way of an intermediate zwitterion is therefore entirely reasonable in accounting for many ketene cycloadditions.

O

r.t.

H

O

H

Cl Cl

+ Cl

Cl

cis-6.144

cis-6.145 O

r.t.

H

O

H

Cl Cl

+ Cl trans-6.144

Cl

trans-6.145

Somewhat similarly, dimethylallene 6.146 undergoes a cycloaddition to dimethyl fumarate and dimethyl maleate giving mainly the cyclobutanes trans- and cis-6.147, respectively, together with a little of the regioisomers trans- and cis-6.148, but with a high level of stereospecificity, implying either that the reaction is concerted and suprafacial on the unsaturated ester, or, less probably, that any intermediate diradical or zwitterion has not had time to lose configurational information.721 Allenes also undergo cyclodimerisation, with enantiomerically enriched allenes leading to enantiomerically enriched products, with the details in agreement with the possibility that the reactions are concerted cycloadditions.722

282

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

CO2Me MeO2C

+ MeO2C

CO2Me

trans-6.147

MeO2C

92:8

CO2Me

tr ans-6.148

6.146 + CO2Me

MeO2C

MeO2C

CO2Me

cis-6.147

MeO2C

~85:15

CO2Me

cis-6.148

It seems likely that some of these ketene and allene cycloadditions are pericyclic and some not, with the possibility of there being a rather blurred borderline between the two mechanisms, with one bond forming so far ahead of the other that any symmetry control from the orbitals is essentially lost.723 However, if it is pericyclic, how does it overcome the symmetry-imposed barrier? One suggestion is that the two molecules approach each other at right angles, with overlap developing in an antarafacial sense on the ketene or allene like that in Fig. 6.16a, making the reaction the allowed [p2sþp2a] cycloaddition that we have dismissed as being unreasonable. This is the simplest explanation, but it is unsatisfactory. Calculations uniformly fail to support it; alkynes, which can easily achieve a transition structure with the same or less steric hindrance in the approach of the two p bonds as this, do not undergo cycloadditions to alkenes at all easily. The probability of some [2 þ 2] cycloadditions of ketenes and allenes being concerted is more likely to be a consequence of the fact that ketenes and allenes have two sets of p orbitals at right angles to each other.724 Overlap can develop to orthogonal orbitals 6.149 (solid lines), and in addition there might be some transmission of information from one orbital to its orthogonal neighbour (dashed line). In the case of the allene 6.150 there is an implied direction of rotation of the terminal groups on the double bond not involved in forming the cyclobutane ring, a detail which becomes important later when we consider regio- and stereochemistry.725 2s

2a 2a

O

2s 6.149

(4q+2)s: 1 (4r)a: 0 Total: 1 √

2s

2s

(4q+2)s: 3 (4r)a: 0 Total: 3 √

6.150

This is a legitimate but somewhat contrived way of making the electronic connection cyclic and hence pericyclic. This version identifies the reactions as allowed [p2sþ(p2aþp2a)] or [p2sþ(p2sþp2s)] cycloadditions. The [p2sþ(p2aþp2a)] version is shown for the ketene and the [p2sþ(p2sþp2s)] for the allene, but the dashed lines and these descriptions could have been interchanged. In essence the ketene or allene is able to take up the role of antarafacial component by using an orbital that has turned through 90° towards the alkene component. Several calculations support this picture, giving a transition structure with substantial C—C ˚ ) and much less (2.43–2.47 A ˚ ) at the other C—C bond, and with bonding to the carbonyl carbon (1.71–1.78 A 726,727 There is also experimental evidence, from the microwave a severely twisted four-membered ring.

6 THERMAL PERICYCLIC REACTIONS

283

spectrum of a ketene-ethylene van der Waals complex, that the two molecules stick together in an orientation similar to that calculated for the transition structure, but with much longer C—C bond distances.728 A variant of the approach, perhaps the simplest way of thinking about these reactions, is to omit the overlap drawn with dashed lines in 6.149 and 6.150, and to concentrate on the key, -bond-forming events. This removes the symmetry-imposed barrier, because the reaction is no longer being thought of as strictly pericyclic. The two bonds are still being formed more or less in concert, but independently, without having to worry about symmetry information being transmitted from one orbital to the other. Related to ketene cycloadditions are the group of cycloadditions with vinyl cation intermediates. The reaction between 2-butyne 6.151 and chlorine giving the dichlorocyclobutene 6.153 is the Smirnov– Zamkow reaction,729 and there is a similar reaction between allene 6.154 and hydrogen chloride giving the dichlorocyclobutane 6.156.730 The Smirnov-Zamkow reaction takes place by cycloaddition of the vinyl cation 6.152 to another molecule of the acetylene, and the allene reaction takes place by attack of the vinyl cation 6.155 on another molecule of allene. Vinyl cations, like ketenes, have two p orbitals at right angles to each other, and overlap can develop to each simultaneously, just as it did with ketenes. In a sense, a ketene is merely a special case of a vinyl cation, with the carbonyl group a highly stabilised carbocation. Cl

Cl

Cl2, BF3 –20° 6.151

Cl

Cl

Cl

6.152 6.151

6.153

H+

Cl

+ H+

Cl

HCl + Cl– 6.154

6.155 6.154

Cl 6.156

There are several reactions in organometallic chemistry which also, at first sight, appear to contravene the rule, but which can be explained in a somewhat similar way. Hydrometallation 5.71 on p. 218, carbometallation, metallo-metallation, and olefin metathesis reactions all have the feature of being stereospecifically suprafacial additions to an alkene or alkyne. Hydroboration, for example, might be classed as a [2 þ 2] addition of a  bond to a p bond, for which the all-suprafacial pathway is forbidden. Although hydroboration begins with electrophilic attack by the boron atom, it is known not to be fully stepwise, because electron-donating substituents on the alkene do not speed up the reaction anything like as much as they do when alkenes are attacked by electrophiles. Nevertheless, the reaction is stereospecifically syn— there must be some component of hydride addition more or less concerted with the electrophilic attack.731 The empty p orbital on the boron is the electrophilic site and the s orbital of the hydrogen atom in the B—H bond is the nucleophilic site. These orbitals are orthogonal, and so the addition 6.157 is not properly pericyclic.732

B

H

6.157

284

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

Another anomalous cycloaddition is the cheletropic insertion of a carbene into an alkene. Six-electron cheletropic reactions are straightforwardly allowed pericyclic reactions, which we can now classify with the drawing 6.158 for the suprafacial addition of sulfur dioxide to a diene.733 Similarly, we can draw 6.159 for the 8-electron antarafacial addition of sulfur dioxide to a triene.734 The problem comes with the insertion of a carbene into a double bond, which is well known to be stereospecifically suprafacial on the alkene with singlet electrophilic carbenes (see p. 201) like dichlorocarbene.735 This is clearly a forbidden pericyclic reaction if it takes place in the sense 6.160. O 2s

S

Cl 6a

O (4q+2)s: 1 (4r)a: 0 Total: 1 √

4s

Cl

2s 2s (4q+2)s: 1 (4r)a: 0 S O Total: 1 O √

6.158

2s

(4q+2)s: 2 (4r)a: 0 Total: 2 x

6.160

6.159

This is known as the linear approach, in which the carbene, with its two substituents already lined up where they will be in the product, comes straight down into the middle of the double bond. The two sulfur dioxide reactions above, 6.158 and 6.159, are also linear approaches, but these are both allowed, the former because the total number of electrons (6) is a (4nþ2) number, and the latter because the triene is flexible enough to take up the role of antarafacial component. The alternative for a carbene is a nonlinear approach 6.161,736 in which the carbene approaches the double bond on its side, and then has the two substituents tilt upwards as the reaction proceeds, in order to arrive in their proper orientation in the product 6.162. 2s

0a Cl Cl

Cl Cl

Cl

Cl 2s

6.161

6.162

(4q+2)s: 2 (4r)a: 1 Total: 3 √

6.163

There is experimental evidence for the nonlinear approach based on isotope effects,737 and calculations also support it, although they suggest that the reaction takes place in two steps by way of a short-lived diradical.738 Whatever the detailed mechanism, the carbene is effectively able to take up the role of the antarafacial component; as with ketenes, it is possible to connect up the orthogonal orbitals, as in 6.163 (dashed line), to make the nonlinear approach classifiably pericyclic and allowed. This avoids any problem there might be with reactions like 6.158 and 6.159 being pericyclic and the clearly related reaction 6.161 ! 6.162 seeming not to be. Somewhat similar considerations apply to the insertion of carbenes into  bonds, except that in this case the reaction can only involve four electrons, and there is no 6-electron alternative.739 We shall return to the carbene insertion reactions later when we discuss periselectivity: why carbenes choose to react with a double bond by the nonlinear approach even with dienes, which would make a 6-electron linear approach analogous to the sulfur dioxide reaction 6.158 allowed. 6.3.2.9

Reactions of Singlet Oxygen, Nitroso Compounds and Triazolinediones which are Symmetry-Allowed but may be Stepwise.740 The three reactive compounds, singlet oxygen 6.164, nitroso compounds 6.166 and triazolinediones 6.168 are anomalous in treading a delicate balance between a pericyclic pathway in some of their reactions, and taking a stepwise pathway, even when an allowed pericyclic pathway is available. All three show a capacity to undergo Diels-Alder reactions with

6 THERMAL PERICYCLIC REACTIONS

285

dienes but all three show a propensity to form one strong bond in the transition structure to one of the two electronegative heteroatoms, and a relatively weak or essentially nonexistent bond to the other. When the second bond is relatively weak the pathway is that of an asynchronous pericyclic reaction, but when it is nearly nonexistent, the pathway is diradical in nature. 1

+

O

O 1.886Å

O

O

O

O 2.962Å

6.164

+

6.165

O

O 2.049Å

O

N

N

N

R

R 6.166

N N

R

6.167

O +

2.690Å

O

2.000Å N

NR

NR

O N N

N

NR

2.668Å O

O 6.168

O

6.169

These three reagents share the singular feature of having a high-energy HOMO in the form of the p* combination of two adjacent lone pairs, like that in the -effect (see pp. 155–156), and a low-energy LUMO, which is a p* orbital low in energy, low because it is made up from the p orbitals of two electronegative elements. In the case of singlet oxygen, the unperturbed HOMO and the LUMO are identical except for the one being occupied and the other empty. The presence of a high-energy HOMO and a low-energy LUMO leads to exceptional reactivity, and accounts for why these reagents can take a stepwise pathway and dispense with the high level of organisation needed for a pericyclic reaction. The LUMO of the dienophile can interact with the HOMO of the diene at the same time as the HOMO of the dienophile can interact with the LUMO of the diene. The combined energy-lowering effect of these interactions is strong enough to allow a bond to develop at one atom on each component. In detail, calculations for the Diels-Alder reactions suggest that nitroso compounds and triazoline diones adopt a highly asynchronous but concerted pathway with transition structures 6.167 and 6.169, respectively (bond lengths calculated for R ¼ H).741,742 Singlet oxygen, the most reactive of the three, however, adopts a stepwise pathway by way of a diradical intermediate 6.165.743 Aromatic compounds behaving as dienes, being inevitably less reactive, induce singlet oxygen to revert to an asynchronous concerted pathway. The same three reagent types also undergo ene reactions with alkenes having an allylic hydrogen atom. Calculations744 suggest that all three reagents take a highly asynchronous course, probably best described as being by way of a diradical 6.170, with a substantial bonding interaction marked with a dashed curve, together with a weak hydrogen bond from the Y atom to the hydrogen on C-3, restricting the rotation about the C1—C2 bond. This explains why these reactions are stereospecific, as they are known to be, without necessarily following a pericyclic pathway. The zwitterionic structures 6.171 have been suggested as intermediates—they may even be formed, but they are not on the direct pathway, because they open back to the same diradical structure before giving the ene product by way of the hydrogen abstraction step. The three reagents have subtly different features, but all three appear more or less to follow this type of pathway.

286

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

X

Y

R

H

X

Y

R

1

Y

R

H

H

2

X

3

6.170 R X

Y H

6.171

With these three reagents, and their singular properties, we are straying into an unusual borderline region between pericyclic and stepwise reactions. Elsewhere, this is less of a problem, and the existence of a large class of reactions safely called pericyclic is well established. We must now turn to the ideas, based on molecular orbital theory, which have been advanced to explain why the Woodward-Hoffmann rules work so well.

6.4

Explanations for the Woodward-Hoffmann Rules

Broadly speaking three levels of explanation have been advanced to account for the patterns of reactivity encompassed by the Woodward-Hoffmann rules. The first draws attention to the relationship between aromaticity, with its (4nþ2) electrons in a cyclic conjugated system, and the (4nþ2) electrons found in most cycloadditions, which could be seen as having an aromatic transition structure.745 The second makes the point that the interaction of the appropriate frontier orbitals in the bimolecular reactions matches the observed stereochemistry, and that even unimolecular reactions could be covered if, rather artificially, the molecule is separated into two fragments, with one assigned the role of the HOMO and the other the role of the LUMO.4 The third is to use orbital and state correlation diagrams in a compellingly satisfying treatment for those cases with identifiable elements of symmetry.746 Molecular orbital theory is the basis for all these related747 explanations, and all organic chemists must now have some familiarity with molecular orbital theory in order to understand pericyclic reactions. 6.4.1 The Aromatic Transition Structure We saw earlier that the all-suprafacial [4 þ 2], [8 þ 2], and [6 þ 4] thermal cycloadditions are common, and that [2 þ 2], [4 þ 4], and [6 þ 6] cycloadditions are rare, mostly stepwise or, as we shall see in Chapter 8, photochemically induced. The total of electrons in the former are (4nþ2) numbers, analogous to the number of electrons in aromatic rings. This wonderfully simple idea was the first explanation for the patterns of allowed and forbidden pericyclic reactions. At first sight, it is a bit more difficult to explain those pericyclic reactions that take place smoothly in spite of their having a total of 4n electrons. They all show stereochemistry involving an antarafacial component, but it is possible to include this very feature in the aromatic transition structure model. If the p orbitals that make up a cyclic conjugated system have a single twist, like a Mo¨bius strip, then the appropriate number of electrons for an aromatic system becomes 4n rather than (4nþ2).748 The antarafacial component in a conrotatory electrocyclic closure, for example, with overlap developing from the top lobe at one end to the bottom lobe at the other (6.70 in Fig. 6.3), is equivalent to the twist in a Mo¨bius conjugated system. The concept of Mo¨bius aromaticity can be applied to many topologically complex reactions.749

6 THERMAL PERICYCLIC REACTIONS

287

6.4.2 Frontier Orbitals The second explanation is based on the frontier orbitals—the highest occupied molecular orbital (HOMO) of one component and the lowest unoccupied orbital (LUMO) of the other. Thus if we compare a [2 þ 2] cycloaddition 6.172 with a [4 þ 2] cycloaddition 6.173 and 6.174, we see that the former has frontier orbitals that do not match in sign at both ends, whereas the latter do, whichever way round, 6.173 or 6.174, we take the frontier orbitals. LUMO

2

HOMO repulsion

1

1

4 1

2'

2' 1'

LUMO

4

1'

HOMO

2' 1'

LUMO

6.173

6.172

HOMO

6.174

In the [2 þ 2] reaction 6.172, the lobes on C-2 and C-20 are opposite in sign and represent a repulsion—an antibonding interaction. There is no barrier to formation of the bond between C-1 and C-10 , making stepwise reactions possible; the barrier is only there if both bonds are trying to form at the same time. The [4 þ 4] and [6 þ 6] cycloadditions have the same problem, but the [4 þ 2], [8 þ 2] and [6 þ 4] do not. Frontier orbitals also explain why the rules change so completely for photochemical reactions, as we shall see in Chapter 8. Applying frontier orbital theory to unimolecular reactions like electrocyclic reactions and sigmatropic rearrangements is inherently contrived,750 since we are looking at only one orbital. To set up an interaction between frontier orbitals, we have artificially to treat a single molecule as having separate components. To take one of the less dubious examples, since the component orbitals are at least orthogonal, the electrocyclic conrotatory opening of a cyclobutene can be treated as the cycloaddition of the HOMO of the single bond  with the LUMO of the double bond p* 6.175, where the dashed lines connect the lobes of the atomic orbitals of the same sign. For the ring-closing direction, which is more dubious, since the component orbitals are conjugated, we can treat the double bonds as separate components 6.176, one bond providing the HOMO, p on the left, and the other the LUMO, p* on the right. Alternatively, we can look only at the HOMO of the diene, 2 in 6.177, where the development of bonding from C-1 to C-4 corresponding to conrotatory ring-closing does not have a sign change. It is hardly compelling to take just one orbital out of the set, even if it does work. LUMO LUMO

HOMO

HOMO or

HOMO 6.175

6.176

6.177

The frontier orbital treatment for vinyl cation cycloadditions, such as those of ketenes, has some merits. It satisfyingly shows that the bond forming between C-1 and C-10 develops mainly from the interaction of the LUMO of the ketene (p* of the C¼O group) and the HOMO of the alkene 6.178, and that the bond between C-2 and C-20 develops mainly from the interaction of the HOMO of the ketene ( 2 of the 3-atom linear set of orbitals analogous to the allyl anion) and the LUMO of the alkene 6.179. LUMO

1

2

O

HOMO

1

O

2

2' 1'

2' 1'

HOMO 6.178

LUMO 6.179

288

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

Hydroboration is another case where the frontier orbital pictures 6.180 and 6.181 reinforce the perception that the two bonds are formed independently. The former illustrates the electrophilic attack by the borane, and the latter the nucleophilic attack by the borane, simultaneously explaining the regioselectivity for an X-substituted alkene. LUMO

HOMO

LUMO

B

H

HOMO

6.180

B

6.181

Carbene cycloadditions following the nonlinear pathway 6.163 are also illuminated by the frontier orbitals 6.182 and 6.183, where the HOMO of the carbene is the lone pair and the LUMO is the empty p orbital. Each of these orbitals, when presented to the double bond with the carbene on its side, matches the signs of the appropriate atomic orbitals on the double bond (dashed lines). Once again, by separating the formation of the two  bonds into overlap developing independently to orthogonal orbitals on the carbene, we no longer need to see the reaction as strictly pericyclic. Carbenoids, in which a C—M bond and a C—halogen bond are typically present in place of the filled and empty orbitals of a genuine carbene, give rise to equivalent pictures, and equally favour the nonlinear pathway.751 LUMO

HOMO Cl

Cl

LUMO 6.182

Cl

Cl

HOMO 6.183

Nevertheless, frontier orbital theory, for all that it works, does not explain why the barrier to forbidden reactions is so high. Perturbation theory uses the sum of all filled-with-filled and filled-with-unfilled interactions (Chapter 3), with the frontier orbitals making only one contribution to this sum. Frontier orbital interactions cannot explain why, whenever it has been measured, the transition structure for the forbidden pathway is as much as 40 kJ mol1 or more above that for the allowed pathway. Frontier orbital theory is much better at dealing with small differences in reactivity. We shall return later in this chapter to frontier orbital theory to explain the much weaker elements of selectivity, like the effect of substituents on the rates and regioselectivity, and the endo rule, but we must look for something better to explain why pericyclic reactions conform to the Woodward-Hoffmann rules with such dedication. 6.4.3 Correlation Diagrams Correlation diagrams provide a compelling explanation, at least for those reactions that have well defined elements of symmetry preserved throughout the reaction. The idea is to identify the symmetry elements maintained throughout the reaction, classify the orbitals undergoing change with respect to those symmetry elements, and then see how the orbitals of the starting materials connect with those of the product. The assumption is that an orbital in the starting material must feed into an orbital of the same symmetry in the product, preserving the symmetry throughout the reaction. Substituents, whether they technically break the symmetry or not, are treated as insignificant perturbations on the orbitals actually undergoing change.

6 THERMAL PERICYCLIC REACTIONS

6.4.3.1 Orbital Correlation Diagrams.

289

We shall begin with an allowed reaction, the ubiquitous Diels-Alder.

Step 1. Draw the bare bones of the reaction 6.184, and draw the curly arrows for the forward and backward reactions. Ignore any substituents that may be present, in order to focus on the key bonds being made and broken.

6.184

Step 2. Identify the molecular orbitals undergoing change. The curly arrows help you to focus on the components of the reaction—what we want now is the molecular orbitals of those components. For the starting materials, they are the p orbitals ( 1- 4*) of the diene unit and the p orbitals (p and p*) of the C¼C double bond of the dienophile. For the product, they are the p bond (p and p*) and the two newly formed  bonds ( and * for each). Step 3. Identify any symmetry elements maintained throughout the course of the reaction. There may be more than one. For a Diels-Alder reaction, which we know to be suprafacial on both components, there is only the one, a plane of symmetry bisecting the bond between C-2 and C-3 of the diene and the p bond of the dienophile 6.185. Any substituents, even if they make the diene or dienophile unsymmetrical, do not fundamentally disturb the symmetry of the orbitals directly involved.

3 2

a plane of symmetry intersects the page here

3 2

6.185

Step 4. Rank the orbitals by their energy, and draw them as energy levels, one above the other, with the starting material on the left and the product on the right (Fig. 6.18). Step 5. Beside each energy level, draw the orbitals, showing the signs of the coefficients of the atomic orbitals. All the p bonds are straightforward, but we meet a problem with the two  bonds in the product, which appear at first sight to be independent entities. In the next step we have to identify the symmetry these orbitals have with respect to the plane of symmetry maintained through the reaction, and it is not obvious how to do this for a pair of independent-seeming orbitals. The answer is to combine them; they are, after all, held one bond apart, and they must interact in a p sense. The interaction of the two bonding  orbitals (Fig. 6.19a) and the two antibonding * orbitals (Fig. 6.19b) leads to a new set of four molecular orbitals 1, 2, 3* and 4*, one pair (1 and 3*) lowered in energy because of the extra p-bonding, and the other pair (2 and 4*) raised in energy because of the extra p-antibonding. Step 6. Classify each of the orbitals with respect to the symmetry element. Starting at the bottom left of Fig. 6.18, the lowest energy orbital is 1 of the diene, with all-positive coefficients in the atomic orbitals, in other words with unshaded orbitals across the top surface of the conjugated system. The atomic orbitals on C-1 and C-2 are reflected in the mirror plane, intersecting the page at the dashed line, by the atomic orbitals on C-3 and C-4, and 1 is therefore classified as symmetric (S). Moving up the left-hand column, the next orbital is the p bond of the dienophile, which is also symmetric with respect to reflection in the plane. The next orbital is 2 of the diene, in which the atomic orbitals on C-1 and C-2 have positive coefficients, and those on C-3 and C-4 have negative coefficients, because of the node half way between C-2 and C-3. The atomic orbitals on C-1 and C-2 are not reflected in the mirror plane by the orbitals on C-3 and C-4, and this orbital is antisymmetric (A). It is unnecessary to be any more sophisticated in the

290

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

4*

A A

* 3*

A

4*

S

3*

A

*

S

A 2

S

S

S

1

a plane of symmetry intersects the page here

Fig. 6.18

A

2

S

1

Orbital correlation diagram for the Diels-Alder reaction

description of symmetry than this. The remaining orbitals can all be classified similarly as symmetric or antisymmetric. Likewise with the orbitals of the product on the right, 1 is symmetric, 2 antisymmetric, and so on. Step 7. Fill in the orbital correlation (Fig. 6.18). Following the assumption that an orbital in the starting material must feed into an orbital of the same symmetry in the product, draw lines connecting the orbitals of the starting materials to those of the products nearest in energy and of the same symmetry. Thus, 1 (S) connects to 1 (S), p (S) connects to p (S), and 2 (A) connects to 2 (A), and similarly, with the unoccupied orbitals, 3* (S) connects to 3* (S), p* (A) connects to p* (A), and 4* (A) connects to 4* (A). Let us go through the same steps for a symmetry-forbidden reaction, the [p2sþp2s] cycloaddition 6.186. We first draw the reaction and put in the curly arrows—the orbitals are evidently the p and p* of each of the p bonds. There are two symmetry elements maintained this time—a plane like that in the Diels-Alder reaction, bisecting the p bonds, but also another between the two reagents, which reflect each other through that plane. a plane of symmetry intersects the page here a plane of symmetry intersects the page here 6.186

6.187

6.188

6 THERMAL PERICYCLIC REACTIONS

291

4*

2

*

* 3*

1

(a) The combination of the

Fig. 6.19

orbitals

(b) The combination of the * orbitals

Molecular orbitals from a pair of interacting  orbitals

In order to classify the symmetry of the orbitals with respect to that plane, we have to take the approaching p bonds and pair them up in a lower energy symmetric 6.187 and a higher energy antisymmetric combination 6.188. These are the molecular orbitals developing as the two molecules approach each other. Pairing the orbitals like this is essentially the same device as pairing the  bonds in setting up 1-4* in Fig. 6.19. We shall also have to repeat that exercise in this case, to deal with the two  bonds in the cyclobutane product. We are ready to construct the orbital correlation diagram Fig. 6.20, but we must classify the symmetry of the orbitals twice over, once for the plane bisecting the p bonds, represented by the vertical dashed line in Fig. 6.20, and then for the plane between the two reagents, the horizontal dashed lines. Thus the lowest energy orbital in the starting materials is the bonding combination p1 of the two bonding p orbitals. This orbital is reflected through both planes and is classified as symmetric with respect to both (SS). The next

AA 4*

AA 4*

SA 3*

AS

2

SA

1

SS AS

SS

Fig. 6.20

3*

2

1

Orbital correlation diagram for a [p2sþp2s] cycloaddition

292

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

orbital up is the antibonding combination p2 of the two bonding p orbitals. This orbital is reflected through the first plane, but not in the second, so it is classified as symmetric with respect to one and antisymmetric with respect to the other (SA). Working up through the two antibonding p orbitals reveals that p3* and p4* are AS and AA, respectively. The product side is similar—except for the addition of the second symmetry classification, it reproduces the pattern for the  bonds that we saw in Fig. 6.18. We can now complete Fig. 6.20 by correlating the energy levels, feeding the orbitals in the starting materials into orbitals of the same symmetry in the product, SS to SS, SA to SA, AS to AS, and AA to AA. This time, the filled, bonding orbitals of the starting materials, p1 and p2, do not lead to the ground-state orbitals of the product—one of them, p1, leads to the lower bonding orbital 1, but the other, p2, leads to one of the antibonding orbitals 3*. It is normal to stop at the orbital correlation diagrams, because we can already see in Fig. 6.18 for the allowed reaction that the electrons in the bonding orbitals of the starting materials move smoothly into the bonding orbitals of the product, whereas, in Fig. 6.20 for the forbidden reaction, the electrons in the bonding orbitals in the starting materials move into both bonding and antibonding orbitals in the product. However, an important feature is revealed if we construct state correlation diagrams. 6.4.3.2 State Correlation Diagrams. Going back to the Diels-Alder reaction in Fig. 6.18, the ground state of the starting materials is designated ( 12p 2 22). Because all the terms are squared (each of the orbitals is doubly occupied), it is also described as overall symmetric (S). Similarly the ground state of the product is (1222p2), and it too, with all its terms squared, is symmetric. The lines connect the orbitals of the ground state on the left with the orbitals of product on the right, and the state correlation diagram is correspondingly easy, at least as far as we need to take it. Because the individual orbitals of the ground state in the starting material correlate with the individual orbitals of the ground state of the product, the important part of the state correlation diagram (Fig. 6.21) consists simply of a line joining the ground state with the ground state, and for present purposes we do not need to know what any of the other states correlates with. 2 2 2 1 2

GS

S S GS

2 2 2 1 2

Fig. 6.21 State correlation diagram for the Diels-Alder reaction

In contrast, the state correlation diagram for the forbidden cycloaddition (Fig. 6.22) is not so simple. The ground state of the starting materials on the left, p12p22, is overall symmetric, because both terms are squared. Following the lines across Fig. 6.20, we see that this state feeds into a doubly excited state, 123*2, in the product, which is also symmetric because both terms are squared. If we now start at the ground state of the product, 1222, and follow the lines (SS and AS) in Fig. 6.20 back to the orbitals of the starting material from which they are derived, we find another doubly excited state p12p3*2. Both of these states, with both terms squared, are again symmetric. Any hypothetical attempt by the molecules to follow these paths in either direction, supposing they had the very large amounts of energy necessary to do so, would be thwarted because states of the same symmetry cannot cross. The hypothetical reaction would in fact lead from ground state to ground state, but it would have to traverse a very substantial barrier, represented in Fig. 6.22 by the line E, which leads up to the avoided crossing. This barrier provides, at last, a convincing explanation of why the forbidden [2 þ 2] cycloaddition is so difficult—the energy needed to surmount it is far above that available in most thermal reactions.

6 THERMAL PERICYCLIC REACTIONS

293 2 2 1 3*

S 2 2 1 3*

S

A 2 1 2 3*

1st ES

A

1st ES

2 1 2 3*

E 2 2 1 2

GS

S S

Fig. 6.22

GS

2 2 1 2

State correlation diagram for a [p2sþp2s] cycloaddition

We should look now at the first excited state in the starting materials, p12p2p3*, which is produced by promoting one electron from p2 to p3*. Following the lines in Fig. 6.20 from the occupied and the two halfoccupied orbitals on the left (SS, SA and AS), we are led to the orbitals of the first excited state of the product on the right, 1223*. In the state correlation diagram, Fig. 6.22, both of these states are antisymmetric, and there is a line joining them, passing close to the avoided crossing in the ground-state correlation. The value of E is approaching the energy of electronic excitation. It also explains why the photochemical [2 þ 2] reaction is allowed—the electrons in the orbitals of the first excited state move smoothly over into the orbitals of the first excited state of the product. This does not mean that the reaction ends there, for the electron in 3* must somehow drop into 2 to give the ground state, disposing of a large amount of energy—by no means a simple event. All we need to understand in the present context is that the photochemical reaction does not meet a symmetry-imposed barrier like that for the ground-state reaction. Correlation diagrams have given us a convincing sense of where the barriers come from for those reactions that we have been calling forbidden. In principle, of course, no reaction is forbidden—what these reactions have is a formidable symmetry-imposed barrier, and something very unusual is needed if barriers of this magnitude are to be crossed. Correlation diagrams take quite a bit of thought, and there are some pitfalls in their construction— however satisfying they may be, they are not for everyday use, and it was for this reason that Woodward introduced the simple rule that we covered in Section 6.3.2. 6.4.3.3 Following Orbitals along the Reaction Coordinate. It is possible by calculation to follow the substantial electronic reorganisation taking place in a Diels-Alder reaction, and to estimate the degree of - and p-bonding that has developed, and the degree of p-bonding lost, as the reaction proceeds.752,753 In the orbital correlation diagram in Fig. 6.18 the electrons from 1 of the diene move into the 1 orbital of the product, those in 2 move into 2, and the electrons in the p orbital of the dienophile move into the p orbital of the product. In that diagram the connections were straight lines, because we were concerned only with matching symmetry. Now we can look at them again, and reconsider what happens to the energy of these orbitals and the electron distribution as the reaction proceeds from left to right in the diagram. Greatly simplified it looks like Fig. 6.23, with the abscissa showing the distance apart of the two carbon atoms becoming bonded, C-1 and C-10 (and C-4 and C-20 ), and the ordinate showing the orbital energy. Fig. 6.23 allows us to see a connection between the correlation diagrams and the explanations based on frontier orbital interactions. The two solid curves follow the interaction of the symmetric orbitals, 1 and

294

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

2

1

2

E TS 3.5

3.0

2.5 d(C1—C1')

Fig. 6.23

1

2.0

1.5

Å

Orbital following along the reaction coordinate of a Diels-Alder reaction

˚ apart. As they are both filled, have the same p, which begin to interact when C-1 and C-10 are about 3.5 A symmetry, and are not far apart in energy, they repel each other strongly.754 The lower curve, in which they interact in phase, drops steadily in energy as -bonding develops, and the upper, in which they interact out of phase, rises. To begin with, the rise in p is steeper than the drop in 1, making the overall effect ˚ the drop in repulsive, as usual when two filled orbitals interact. At the transition structure at about 2.2 A energy is estimated to be about 95 kJ mol1 and the rise about 206 kJ mol1. Shortly after passing the transition structure, as the energy of p rises to become closer to that of 3*, a HOMO(dienophile)/ LUMO(diene) interaction takes over, lowering the energy, and moving the electrons into the p orbital of the product. The dashed curve follows this other frontier orbital interaction, and is notably different. The energy begins to rise a little at first, as the p system distorts, reaching 55 kJ mol1 at the transition structure. Only at about ˚ , do these frontier orbitals, 1 and p*, start to interact to lower the energy, turning the curve over just 2.4 A before the transition structure is reached. After this point the curve falls rapidly as -bonding develops in the orbital 2. It thus appears that both pairs of frontier orbitals have significant but different parts to play, with the HOMO(diene)/LUMO(dienophile) countering the mildly repulsive interaction in the dashed curve, and the HOMO(dienophile)/LUMO(diene) countering the strongly repulsive interaction in the upper full curve. Thus we have a better, but less immediately applicable version resembling frontier orbital theory. The bond-order changes indicate that the p bond between C-2 and C-3 is well advanced (66%) in the transition structure 6.189, whereas the p bonds in the dienophile and the diene are not much weakened (32% and 22%, respectively). Likewise, the  bonds are little formed (22%). The larger changes in the p-bonding in the diene suggest a late transition structure, and the small changes in the -bonding and in the p-bonding of the dienophile suggest an early transition structure. This asynchronicity reflects the sum of the HOMO(diene)/HOMO(dienophile) interactions and substantial contributions from both frontier orbital interactions when the effect of the change in their energies as the reaction proceeds is taken into account.

6 THERMAL PERICYCLIC REACTIONS

1.33Å

295

1.37Å

2.20Å

1.51Å

1

1.47Å

1.34Å

2

1'

3

2'

1.39Å

1.40Å

1.35Å

1.53Å

4

6.189

6.5

Secondary Effects

The Woodward-Hoffmann rules arise fundamentally from the conservation of orbital symmetry seen in the correlation diagrams. These powerful constraints govern which pericyclic reactions can take place and with what stereochemistry. As we have seen, frontier orbital interactions are consistent with these features, but they are not the best way of explaining them. In contrast, there are many secondary effects for which the frontier orbitals do provide the most immediately telling explanation. These are the substituent effects on rates and regioselectivity; secondary stereochemical effects like the endo rule for Diels-Alder reactions; periselectivity; and torquoselectivity. We are still on weak ground, for all the usual reasons undermining frontier orbital theory when it is applied too ruthlessly (see p. 143), but for the organic chemist seeking some kind of explanation for all these phenomena, it is nearly indispensable. 6.5.1 The Energies and Coefficients of the Frontier Orbitals of Alkenes and Dienes In order to apply frontier orbital arguments to these phenomena, we need to know the effect of C-, Z- and X-substituents on the frontier orbitals of alkenes. In Section 2.1.2 we deduced, without carrying out any calculations, that all three kinds of substituents, C, Z and X, lowered the overall energy. Using the same arguments, we also deduced the relative energies of the frontier orbitals of C-, Z- and X-substituted alkenes. The effect of a C-substituent (vinyl and phenyl) poses no problem, because it is seen in the orbitals of a simple alkene and a diene—the HOMO is raised in energy in going from ethylene to butadiene (or to styrene), and the LUMO is lowered in energy (Figs. 1.39 and 2.2). For a Z-substituted alkene like acrolein, we saw in Fig. 2.4 that the HOMO energy is close to that of a simple alkene at 1 below the  level. It lies somewhere between the HOMO of an allyl cation ( 1), lower in energy, and the HOMO of a diene ( 2), higher in energy, having the character of both. However, the LUMO energy of a Z-substituted alkene is well below that of a simple alkene, because it lies somewhere between the LUMO of an allyl cation ( 2 at 0) and the LUMO of butadiene ( 3* at 0.62), both of which are lower in energy than p* of a simple alkene at 1 above the  level. The argument for an X-substituted alkene was even easier: we saw in Fig. 2.6 that it simply mixes in a bit of allyl anion-like character to the unsubstituted alkene, raising the energy of the HOMO relative to the energy of the HOMO of the simple alkene on the left, and, to a smaller extent, raising the energy of the LUMO relative to the energy of the LUMO of the simple alkene. The same arguments can be used for dienes with a substituent on C-1. A C-substituent raises the energy of the HOMO and lowers the energy of the LUMO, in going from butadiene to hexatriene (Fig. 1.42). For a Z-substituent, the comparison would be between a pentadienyl cation on the one hand and hexatriene on the other, and for an X-substituent, the comparison would be between a pentadienyl anion and the unsubstituted diene. The orbitals for these systems can be found in Fig. 1.42, and estimating an average between the extremes will show that the HOMO of a Z-substituted diene is either unaffected or lowered slightly in energy relative to the HOMO of butadiene, and that the LUMO is distinctly lowered in energy relative to the LUMO of butadiene. Similarly, the HOMO of a 1-X-substituted diene is distinctly raised in energy relative to the HOMO of butadiene, and the LUMO is slightly raised in energy.

296

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

For dienes with substituents at C-2, similar arguments are used and similar results obtained, as seen in Fig. 6.24. For the Z-substituent, some allyl cation character is mixed into the orbitals of 2-vinylbutadiene, and, for an X-substituent, some allyl anion character is mixed into the orbitals of butadiene.

0.44 –0.23

0.518

–0.33

LUMO

–0.23

0

Z

0.63 0.44

0.44 0.23

0.518

–0.71

0.71

–0.33

HOMO

0.23

1.414

–0.63

0.44

Z –0.50–0.71–0.50

(a) 2-Z-Substituted diene –0.71 0.50

–0.37

0.50

1.414

0.60

0.618

C-

LUMO 0.71

–0.37

–0.71

X

0

0.60 0.60 0.37

HOMO 0.618

X

–0.37 –0.60

Fig. 6.24

(b) 2-X-Substituted diene

Estimating the frontier orbitals of a 2-substituted diene

In summary, the conclusions with respect to the energies of the frontier orbitals, are:

C- (extra conjugation) raises the energy of the HOMO and lowers the energy of the LUMO Z- (an electron-withdrawing group) slightly lowers the energy of the HOMO and substantially lowers the energy of the LUMO X- (an electron-donating group) substantially raises the energy of the HOMO and slightly raises the energy of the LUMO

6 THERMAL PERICYCLIC REACTIONS

297 X

3.0 3 2

1.5

C

1.0

1

Z

0

0 –1

C

–8

–9.1

X

–9.0

–9 –10

–10.5

Z

–10.9

–11

(a) Dienophiles X 3 2

1.0

1

Z 0.5 –0.5

0 –1

–8

2.5

C

C

X Z

–8.2 –9.1

–8.5 –9.5

–9 –10 –11

(b) 1-Substituted dienes

2.3

3 2

1.0

1

0.7

X –0.3

0

C

–1

–8 –9

Z

–9.1

–8.5 –9.3 C

–10

–8.7 X

Z

–11

(c) 2-Substituted dienes Fig. 6.25 Frontier orbital energies (in eV) and coefficients of alkenes and dienes. The energies are representative values for each class of alkene and diene (1 eV ¼ 23 kcal ¼ 96.5 kJ)

298

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

Another way of looking at the effect of a 2-substituent is to say that the C-, Z- and X-substituents are attached to the carbon atom of butadiene which has the smaller coefficient in the HOMO and the LUMO, the effect of a substituent being roughly proportional to the square of the coefficient at the point of attachment. The result is that the energies are shifted in the same direction, but to a lesser extent than they are when the substituent is attached to C-1. The HOMO and LUMO are brought closer in energy by extra conjugation, the HOMO and LUMO are lowered by a Z-substituent, and the HOMO and LUMO are raised by an Xsubstituent; but none of these effects is quite as large as it is in a 1-substituted diene. The rates of cycloadditions are principally accounted for by looking at the energies of the frontier orbitals. They must also be affected by the size of the coefficients in the frontier orbitals, but this factor is rarely needed.755 The relative sizes of the coefficients are principally used to account for regioselectivity. We now need to return to the similar arguments that were used in Section 2.1.2 to estimate the relative magnitude of the coefficients of the atomic orbitals in the frontier orbitals. We saw in Figs. 1.37 and 2.2 that a C-substituted alkene has higher coefficients at the unsubstituted terminus than at the atom carrying the substituent, both in the HOMO and the LUMO. We saw in Fig. 2.5 that a Z-substituent has only a small effect on the HOMO, with the coefficient at the unsubstituted terminus probably the larger. We also saw that the LUMO was strongly polarised, with the coefficient at the terminal carbon substantially the larger. Finally, we saw in Fig. 2.7 that an X-substituent increases the coefficient in the HOMO at the terminal carbon and reduces it in the LUMO. Similar arguments can be carried over to 1- and 2-substituted dienes. Putting all these arguments onto a firmer base, Houk estimated energies for the HOMOs and LUMOs of alkenes and 1- and 2-substituted dienes with representative C-, Z- and X-substituents, using experimental measurements of photoelectron spectra for the occupied orbitals, and a combination of electron affinity measurements, charge transfer spectra and polarographic reduction potentials for the unoccupied orbitals.63 They are summarised in Fig. 6.25, to which we shall constantly refer in discussing the rates and regioselectivity of Diels-Alder reactions and 1,3-dipolar cycloadditions. The circles represent a cross-section of the lobes of the p orbitals looked at from above the plane of the paper, and the shaded and unshaded circles are of opposite sign in the usual way. They are not s orbitals.

6.5.2 Diels-Alder Reactions662 In discussing the frontier orbtial explanation for the Woodward-Hoffmann rules, we were indifferent as to which of the two components of a cycloaddition would provide the HOMO and which the LUMO. The two pairs of frontier orbitals bear a complementary relationship to each other, and they invariably give the same answer with respect to the rules, as in the drawings 6.173 and 6.174 for the Diels-Alder reaction. To explain the effects of substituents on rates, we need to know the effect they have on frontier orbital energies,756,757 6.5.2.1 The Rates of Diels-Alder Reactions. Most Diels-Alder reactions require that the dienophile carries a Z-substituent before they take place at a reasonable rate. Butadiene will react with ethylene, but it needs a temperature of 165 °C, high pressure and gives a low yield.758 It reacts with itself a little easier, at 150 °C, but the reaction with acrolein 6.190 is easier taking less time at the same temperature.759 A second Z-substituent increases the rate even more, with methylenemalonate 6.191760 and maleic anhydride761 reacting at room temperature. An X-substituent on the diene, on C-1 or C-2, increases the rate further, with trans-piperylene 6.192 and isoprene 6.193 reacting with acrolein at 130 °C,762 and 1-methoxybutadiene 6.194763 and 2-methoxybutadiene 6.195764 at slightly lower temperatures. Times and temperatures are not a reliable way of measuring relative rates, but all these reactions were taken to the point where the yields of isolated product are close to 80%.

6 THERMAL PERICYCLIC REACTIONS

299

165°, 17 h

+

150°, 10 d

+

900 atmospheres

CHO +

MeO2C +

CHO

150°, 0.5 h

6.190 1

CHO 130°, 6 h

CHO

CHO +

2

6.193

6.190

OMe 1

CHO

130°, 6 h

6.190

OMe CHO

+

100°, 2 h

CHO 120°, 6 h

CHO +

2

6.195

6.190

CHO

MeO

MeO 6.194

CO2Me CO2Me

25°, 24 h

6.191

+ 6.192

CO2Me

6.190

Since the substituents are not stabilising charge in a zwitterionic intermediate, it is not at first obvious how they can affect the rates so dramatically. The simplest explanation comes from the frontier orbitals. In the reaction of butadiene with acrolein, the Z-substituent lowers the energy of the LUMO. Fig. 6.26a shows the energy separations between the frontier orbitals of butadiene and an unsubstituted dienophile, and Fig. 6.26b shows that the energy separation between the HOMO of butadiene and the LUMO of a Z-substituted dienophile is less than that between the HOMO of butadiene and the LUMO of ethylene. The smaller the energy gap in any particular case, the faster the reaction ought to be because a strong and a weak interaction

LUMO LUMO

LUMO

LUMO

LUMO

LUMO HOMO HOMO

HOMO

HOMO

HOMO

HOMO

X Z

(a) Frontier orbital interactions for butadiene with an unactivated dienophile

Fig. 6.26

(b) Frontier orbital interactions for butadiene with a Z-substituted dienophile

Z

(c) Frontier orbital interactions for an X-substituted butadiene with a Z-substituted dienophile

Frontier orbital interactions for Diels-Alder reactions

300

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

(as in Fig. 6.26b) is more effective at lowering the energy of the transition structure than two medium-sized interactions (as in Fig. 6.26a). (This may not be immediately obvious, but it follows from the fact that the energy separation, ErEs, is in the denominator of the Salem-Klopman equation, Equation 3.13.) Taking numbers from Fig. 6.25, a normal Diels-Alder reaction is dominated by the interaction of the HOMO of the diene (at 9.1 eV) and the LUMO of the dienophile (at 0 eV). The difference in energy is 9.1 eV, emphasised with a bold, double-headed arrow in Fig. 6.26b, whereas the difference in energy of the LUMO of the diene (at 1.0 eV) and the HOMO of the dienophile (at 10.9 eV) is 11.9 eV. To be a good dienophile in a normal Diels-Alder reaction, the most important factor is a low-lying LUMO. Thus, the more electron-withdrawing groups we have on the double bond, the lower the energy of the LUMO, the smaller the separation of the HOMO(diene) and the LUMO(dienophile), and the faster the reaction. Tetracyanoethylene is a very good dienophile. Similarly, with an X-substituent on the diene raising the energy of the HOMO, the energy separation between the HOMO of the diene and the LUMO of the Z-substituted dienophile, 8.5 eV in Fig. 6.25, is even smaller (Fig. 6.26c). The interaction is correspondingly stronger, and the reaction faster still. Another way of producing a low-lying LUMO is to have an oxygen or nitrogen atom in the p bond. Because p orbitals on these atoms lie so much lower in energy than those on carbon, the p molecular orbitals that they make will inevitably have a lower-energy HOMO and LUMO. This is what happens with O¼O and —N¼N— double bonds, which is one reason why singlet oxygen, and azadienophiles like dimethyl azodicarboxylate, are such good dienophiles.765 In principle, it ought to be possible to increase the rate of a Diels-Alder reaction by adding electrondonating (X-) groups to the dienophile; these raise the energy of the HOMO, and we might expect to approach the situation in Fig. 6.27b, which has one pair of frontier orbitals LUMO(diene)/HOMO(dienophile) separated in energy to a similar extent to the HOMO(diene)/LUMO(dienophile) in Fig. 6.26b. In practice, dienes with electron-donating substituents do not react with simple dienes. However, by attaching a Z-substituent to the diene as well, the energy separation between the HOMO of an X-substituted dienophile and the LUMO of the diene (9 eV from Fig. 6.25) becomes small enough for reaction to occur (Fig. 6.27c). Dienes with

LUMO

LUMO

LUMO

LUMO LUMO

LUMO

HOMO

HOMO

HOMO

HOMO HOMO

HOMO

Z X

(a) Frontier orbital interactions for butadiene with an unactivated dienophile

Fig. 6.27

(b) Frontier orbital interactions for butadiene with an X-substituted dienophile

X

(c) Frontier orbital interactions for a Z-substituted butadiene with an X-substituted dienophile

Frontier orbitals for Diels-Alder reactions with inverse electron demand

6 THERMAL PERICYCLIC REACTIONS

301

electron-withdrawing substituents reacting with dienophiles with electron-donating substituents are described as Diels-Alder reactions with inverse electron demand.766 For example, the ‘diene’ 6.196, which must have a low-energy LUMO, since it is an iminium ion, reacts faster with the enol ether 6.197a, a dienophile with electron-donating substituents, than with acrylonitrile 6.197c, a dienophile with an electron-withdrawing substituent.767 Allyl alcohol 6.197b, which probably has HOMO and LUMO energies very close to those of ethylene itself, reacts at an intermediate rate. R1 R1

R2

R2

+ N

N

*

* 6.196

6.197 a R1=R2=OEt b R1=CH2OH, R2=H c R1=CN, R2=H

75% reaction in 4 min at 25 °C 75% reaction in 275 min at 100 °C 75% reaction in 1080 min at 100 °C

It has long been known that it is much more effective to carry out Diels-Alder reactions with X-substituted dienes and/or Z-substituted dienophiles, than to use inverse electron demand. Diels-Alder reactions with inverse electron demand are much less common and require more powerful donor and acceptor groups before they work. A striking example is seen when a diene with a donor substituent 6.198 and a diene with an electron-withdrawing substituent 6.199 are allowed to react with each other—the diene with the electron-withdrawing substituent always takes up the role of dienophile, and the diene with the electron-donating substituent is the diene.768 Since the separation in energy of the frontier orbitals is identical, whichever diene takes up the role of dienophile, it is not obvious why it should always be the one with the Z-substituent. Even more general, the two HOMO/LUMO separations for butadiene and ethylene are the same but it is much better to raise the energy of the HOMO on the diene and lower the energy of the LUMO on the ethylene than to try to influence the orbital energies the other way round. Me3SiO

MeO2C

Me3SiO

+

OMe

6.199

CO2Me OMe

6.198

The different ways in which the two frontier orbitals influence the orbital changes, and the asynchronicity in their operation, discussed on p. 294 using Fig. 6.23, may explain this long-standing puzzle. Other suggestions have been made,769 but a particularly simple way of appreciating the same set of interactions has been suggested by Fukui.770 He points out that as the reaction proceeds electrons are moving from the p bonds into the space between the reacting components to make the  bonds. If the major supply of electrons is from the diene, the node in the HOMO 2 ensures that the electrons flowing from the diene are not concentrated in the centre of the reacting system, but are concentrated at the sides where the  bonds are forming (Fig. 6.28a). In Fig. 6.23 this was seen in the way the electrons in 2 move into 2. In contrast, if the major supply of electrons is from the dienophile, the HOMO of this component has no node and the electrons are moving into the space in the middle (Fig. 6.28b), interacting strongly with the filled orbitals of the diene, and repelling it. In Fig. 6.23 this was seen both in the way the electrons in p in the dienophile move into p in the product, and in the repulsion between p and 1. There is a useful contrast here with the reaction of a bridging electrophile like bromine with an alkene, where the same movement of electrons into the middle is exactly what is required to produce the two  bonds of the bridged epibromonium ion intermediate.

302

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

HOMO

HOMO

(a) Normal Diels-Alder reaction HOMO(diene)/LUMO(dienophile)

Fig. 6.28

(b) Inverse electron demand LUMO(diene)/HOMO(dienophile)

Differences in the dominant electron shift in normal Diels-Alder reactions and Diels-Alder reactions with inverse electron demand

In addition to normal and inverse electron demand, we can set up other situations by adjusting the energies of the HOMO and LUMO of both the diene and the dienophile. For example, Konovalov771 found that tetracyclone 6.200 reacts with the unsubstituted styrene 6.201 (R ¼ H) slower than with the substituted styrenes, whether the substituent is electron-donating or electronwithdrawing. The energies of the HOMO and LUMO of this diene are evidently so placed, with respect to those of the styrenes, that when R is H neither HOMO/LUMO interaction is much stronger than the other. When R is an electron-withdrawing substituent, the LUMO of the dienophile is lowered, bringing it closer in energy to the HOMO of the diene, and when R is an electron-donating substituent, the HOMO of the dienophile is raised, bringing it closer in energy to the LUMO of the diene.

O

Ph Ph

Ph O

Ph

+

Ph

R

Ph

Ph Ph R

6.200

6.201 R: k 2 ( 106 mol–1s–1):

p-NMe2 338

p-OMe H p-Cl m-NO2 102 73 78 79

p-NO2 88

Sustmann collected data for a wide range of Diels-Alder reactions of normal electron demand.772 Using the electron affinities of the dienophiles and the ionisation potential of the dienes, he estimated the separations in energy between the LUMOs of the dienophiles and the HOMOs of the dienes, and showed that they correlated quite well with the log of the rate constant—with the higher rates for the reactions having the smaller energy gap. The points fitting least well on the graph were for cyclopentadiene, which was too fast, and cycloheptatriene, which was too slow. In cyclopentadiene, the termini of the diene unit are held closer together than in open-chain dienes, and in cycloheptatriene they are held further apart. It seems likely that this explains why cyclopentadiene is regularly a good dienophile and cycloheptatriene a poor one, and there are now several other dienes showing reactivity dependent upon the distance apart of the ends of the diene.773 There have been many other studies since Sustmann’s pioneering work establishing correlations between Diels-Alder rates and frontier orbital properties as measured by ionisation potentials and electron affinities, and as calculated from molecular orbital theory.774

6 THERMAL PERICYCLIC REACTIONS

303

6.5.2.2 The Regioselectivity of Diels-Alder Reactions. Regioselectivity refers to the orientation of a cycloaddition: for example, methoxybutadiene 6.194 reacts with acrolein 6.190 to give more of the ‘ortho’ adduct 6.202 than of the ‘meta’ adduct 6.203.775 To explain regioselectivity we look at the coefficients of the atomic orbitals in the more important pair of frontier orbitals. We should perhaps remind ourselves that the sign of the lobe that is overlapping with another lobe is a much more important factor in determining the energy change than is the second-order effect of its size, but from now on we shall ignore the sign because we shall only be looking at allowed (and hence observed) reactions. OMe

OMe CHO

OMe CHO

+

and not CHO

6.194

6.190

6.202

6.203

We already know from the data in Fig. 6.25, and from the arguments used to create Fig. 6.26, that the important interaction in a case like this with normal electron demand will be between the HOMO of the diene and the LUMO of the dienophile, shown on the left in Fig. 6.29 (Er – Es ¼ 8.5 eV), not the other way round shown on the right (Er – Es ¼ 13.4 eV). We see that the two larger atomic orbitals overlap (dashed line) in forming the observed product 6.202. It is not self evident that the choice of the large-large interaction in Fig. 6.29 is better than two largesmall interactions. Here is a simple theorem which proves that it is right. Consider two interacting molecules X and Y in Fig. 6.30: let the square of the terminal coefficients on X be x and xþn, and let the square of the coefficients on Y be y and yþm. For the large-large/small-small interaction (Fig. 6.30a), the contribution to the numerator of the third term of the Salem-Klopman equation, Equation 3.13, will be: xyþ(xþn)(yþm). For the large-small/small-large case (Fig. 6.30b), the contribution will be: x(yþm)þ(xþn)y. Subtracting the latter from the former gives nm. In other words, the former interaction is greater so long as n and m are of the same sign; that is, xþn and yþm are either the two large (as shown)

OMe

OMe CHO

CHO

LUMO

HOMO

ELUMO – EHOMO = 8.5 eV

LUMO

HOMO

ELUMO – EHOMO = 13.4 eV

Coefficients of the frontier orbitals of methoxybutadiene and acrolein

Fig. 6.29

x

x

y+m

y

y

y +m x+n

x+n

(a) Large-large small-small

(b) Large-small large-small

Fig. 6.30

(c) Large-large small-small

(d) Large-small large-small

Large-large/small-small pairing of frontier orbitals compared with large-small/large-small

304

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

or the two small lobes. Pictorially, this conclusion can be even less rigorously demonstrated by Fig. 6.30c and 6.30d, which shows that overlap develops earlier with the large-large/small-small combination. The implication of a large-large interaction leading over the small-small interaction, as in Fig. 6.30c, is that the transition structure of an unsymmetrical Diels-Alder reaction is itself unsymmetrical, having the two  bonds being formed to different extents. The reaction is still concerted, with both bonds forming at the same time, but it is not synchronous, with them both formed to an equal extent in the transition structure. Secondary deuterium isotope effects, which are so successful in confirming that Diels-Alder reactions are concerted cycloadditions, have also been applied to asynchronous reactions, where they match the calculated values allowing for the asynchronicity.776 You may feel that we have laboured hard to justify an example of regioselectivity which experienced organic chemists would have predicted would go this way round. They would have drawn curly arrows 6.204 (or 6.205 creating the canonical structures 6.206) to express the feeling that C-4 of the diene is a nucleophilic carbon and C-30 of the acrolein an electrophilic carbon. This reasoning is fine, but it cannot be applied to all cases. OMe 1

O 2'

OMe

O

H

OMe

O

H

H

3'

3'

4

4

6.204

6.205

6.206

For example, it would not work in the case of the reaction between butadiene carboxylic acid 6.208 and acrylic acid 6.209. The curly arrows 6.207 establish that C-4 of the diene carboxylic acid can be expected to be electrophilic, just like C-30 of the acrylic acid. The partial positive charges ought to repel each other and the adduct expected would be the ‘meta’ adduct 6.211. In contrast, the reaction gives mainly the ‘ortho’ adduct 6.210.777 O

OH

O

OH

O

OH

O OH

+

CO2H CO2H

150°

+

3'

4

6.207

CO2H

6.208

CO2H

6.209

6.210

90:10

6.211

Clearly this valence bond argument is not good enough, whereas the frontier orbital argument does work. Taking the orbitals and the energies from Fig. 6.25, we get Fig. 6.31, in which the usual HOMO(diene)/ LUMO(dienophile) combination has the smaller energy gap. These orbitals are polarised with the marginally

Z

Z Z HOMO

Z LUMO

ELUMO – EHOMO = 9.5 eV

Fig. 6.31

LUMO

HOMO

E LUMO – E HOMO = 10.4 eV

Frontier orbitals for a Z-substituted diene and a Z-substituted dienophile

6 THERMAL PERICYCLIC REACTIONS

305

higher coefficient in the HOMO of the diene on C-4, which stems from the hexatriene-like character of the conjugated system (see p. 313). As a result, the counter-intuitive combination with bonding between C-4 and C-30 wins. The somewhat less favourable LUMO(diene)/HOMO(dienophile) combination has little effect on regiochemistry, because the HOMO of the dienophile is barely if at all polarised. The anions of these acids also undergo a Diels-Alder reaction. The contribution of a carboxylate ion group (CO2) to the frontier orbitals will be even more like that of a simple C-substituent and less like that of a Z-substituent. The prediction from the frontier orbitals is therefore the same—an ‘ortho’ adduct—but this time the negative charges will strongly repel each other, favouring the ‘meta’ adduct. The observation778 of a 50:50 mixture of ‘ortho’ and ‘meta’ adducts shows how powerful a directing effect the orbital contribution must be. Another example, in which the simple curly arrow argument would not have predicted the right answer, is the reaction between the azoniaanthracene cation 6.196 and acrylonitrile 6.197c. The electrophilic carbon atoms (*) have become bonded to each other in both adducts, which differ in stereochemistry but not in regiochemistry. There are 18 possible combinations of C-, Z- and X-substituted dienes and C-, Z- and X-substituted dienophiles. The ‘ortho’ adduct is predicted (and found) to be the major product for eight of the nine possible combinations with 1-substituted dienes, and the ‘para’ adduct predicted (and found) for eight of the nine possible combinations of 2-substituted dienes. The reactions of Z-substituted dienophiles with the 1-X-substituted diene 6.194 (see p. 303) and with the 1-Z-substituted diene 6.208 (see p. 304) illustrate two of these combinations, and here are examples of most of the rest which obey the ‘ortho-para’ rule. Z-substituted dienophiles:779,780 1-C-Substitued diene Ph

2-C-Substitued diene Ph CHO

CHO

Ph

+

Ph

Ph

+

CN

CN

80:20

only adduct 2-X-Substituted diene MeO

CN

+

2-Z-Substituted diene MeO

(RO)2B

(RO)2B +

+ CHO

CHO

CHO

X-substituted dienophiles:781 1-Z-Substituted diene CO2Me

MeO2C N

CHO only adduct

only adduct

N

+ only adduct

306

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

C-substituted dienophiles:782 1-Z-Substituted diene CO2H

2-Z-Substituted diene CO2H

CO2H Ph

Ph +

NC

NC +

+

NC

Ph

CN

86:14

only adduct

1-C-Substituted diene Ph

2-C-Substituted diene

Ph

Ph Ph

Ph +

Ph

Ph

Ph

+

+

Ph

Ph

Ph

+ Ph 95:15

89:11

The two exceptions to the ‘ortho-para’ rule are the reactions between an X-substituted diene, with the X-substituent at C-1 or C-2, and an X-substituted dienophile. The frontier orbitals in Fig. 6.32, taken from Fig. 6.25, indicate that the preferred combination, whichever pair of frontier orbitals and whichever diene, 1-substituted or 2-substituted, is taken, will lead to the ‘meta’ adduct.

X

X

X

X

X

X

X HOMO LUMO

LUMO

ELUMO – EHOMO = 11.5 eV

ELUMO – EHOMO = 11.5 eV

HOMO

(a) A 1-X-Substituted diene with an Xsubstituted dienophile

Fig. 6.32

X

HOMO

LUMO

ELUMO – EHOMO = 11.7 eV

LUMO

HOMO

ELUMO – EHOMO = 11.3 eV

(b) A 2-X-Substituted diene with an Xsubstituted dienophile

FOs for the combination of X-substituted dienes with an X-substituted dienophile

Neither frontier orbital interaction is between orbitals close in energy (>11 eV in all combinations), with the result that these reactions can be expected to be very slow, and they are in practice exceedingly rare. The most revealing are two reactions which take advantage of aromatisation of the diene to make them feasible: the combination of the (vinylogous) 2-X-substituted diene 6.212 and ethyl vinyl ether 6.213 gives more of the ‘meta’ adduct, and so does the combination of the 1-X-substituted diene 6.214 and propyne 6.215.783 Neither reaction is usefully regioselective, partly because they take place at quite high temperatures, necessary to open the benzocyclobutene precursors of the dienes, but the direction of the effect is clear.

6 THERMAL PERICYCLIC REACTIONS

307

MeO

180°

MeO

OEt MeO

+

+ OEt

6.212

2d

OEt

6.213

61:39

190° +

+ 7d

6.214

6.215

65:35

In summary, we predict the regioselectivity of a Diels-Alder cycloaddition by the following sequence:

1. Estimate the energies of the HOMO and the LUMO of both components. 2. Identify which HOMO/LUMO pair is closer in energy. 3. Using this HOMO/LUMO pair, estimate the relative sizes of the coefficients of the atomic orbitals on the atoms at which bonding is to take place. 4. Match the larger coefficient on one component with the larger on the other.

An alternative explanation for regioselectivity to that based on the molecular orbitals has been the diradical theory, in which the major adducts correspond to those which would be obtained if a diradical intermediate were to be involved.784,785 Thus, taking a 2-substituted diene, the intermediate diradical 6.216 leading to the ‘para’ adduct 6.217 can be expected to be better stabilised than either of the diradicals 6.218 or 6.219 leading to the ‘meta’ adduct 6.220, given that any substituent, C, Z or X, stabilises a radical (Section 2.1.5). This explanation works for the majority of cases but not for the combination of X-substituted diene and X-substituted dienophile, which is therefore telling support for an orbital-based explanation.

X,Z,C

X,Z,C

X,Z,C

C,Z,X

C,Z,X

C,Z,X

6.216

6.217 C,Z,X

X,Z,C a

C,Z,X

X,Z,C a b

X,Z,C

6.218

C,Z,X

b a

X,Z,C

C,Z,X

b

6.220 6.219

308

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

A special case is the effect of a sulfur lone pair. On its own, this is clearly an X-substituent but a curious feature of its influence on regioselectivity in Diels-Alder reactions is that it appears to be a more powerful X-substituent than an alkoxy group. A sulfur lone pair is higher in energy than an oxygen lone pair, and any inductive effect towards sulfur will be less than towards oxygen. Both factors should make sulfur a better p donor, but a sulfur atom is too large to allow good overlap between its lone pair and a p orbital on carbon. On balance, the latter appears to be usually more important, and an alkyl- or arylthio substituent is less effective at stabilising a cation than the corresponding oxygen substituent. In contrast, Trost found that the 2,3-disubstituted diene 6.221 reacted with methyl acrylate to give the two adducts 6.222 and 6.223 in a ratio of 4:1. His calculation for the HOMO coefficients, shown on 6.221, nicely agreed with this result, but in more detail frontier orbital explanations were not effective on their own in accounting for all his observations.786 –0.292

MeO

CO2Me

MeO

CO2Me MeO

+

+

PhS

PhS

CO2Me

PhS

0.512

6.221

6.222

6.223

80:20

Another special case is the effect of a boron substituent. Since it is electropositive and has an empty p orbital, it will be a  donor and a p acceptor. If the effect in the p system overrides that in the  system, it should be like a Z-substituent activating a dienophile by lowering the LUMO energy. It almost certainly does, as shown by the easy reaction of vinyl-9-BBN 6.224 with butadiene, which takes place at room temperature, 200 times faster than the corresponding reaction with methyl acrylate.787 The energy calculated for the LUMO is –0.08 eV, close to that of acrylic acid (0.07 eV at the same level of calculation). Vinyl boronic acids and esters, in which the empty p orbital is conjugated to oxygen lone pairs, have a higher energy LUMO (0.82 eV at the same level of calculation), and they are in practice much less reactive.788,789 Vinylboranes also show unexpected regioselectivity, giving mainly (>98:2) the ‘meta’ adduct 6.225 with trans-piperylene, in spite of the large difference in the coefficients of the LUMO suggesting that the ‘ortho’ adduct should, as usual, be the major product. This appears to be a steric effect, since the reaction with the piperylene is significantly slower than the reaction with butadiene, which is not the normal pattern, and the less sterically hindered vinyldimethylborane is no longer selective for the ‘meta’ isomer. Furthermore, if the vinyl group has a trimethylsilyl group at the other end, that provides the major steric interaction, and the regioselectivity changes to be ‘ortho’ (88:12) with respect to the boron substituent. All the reactions of vinylboranes are remarkably endo selective (92:8), which we shall discuss in Section 6.5.2.4.

B

25 °C

0.64

0.37

+ B

B

–0.62

LUMO –0.08 eV 6.224

6.225

A number of other examples of regioselectivity in Diels-Alder reactions are less straightforwardly categorised. Thus, citraconic anhydride 6.226 and l-phenylbutadiene react to give the ‘ortho’ adduct 6.227.790 This might be described as the combination of a 1-C-substituted diene with an X-substituted dienophile, since the two carbonyl groups make the dienophile symmetrical with respect to the Z-substituents. If we ignore the carbonyl groups for the moment and treat the dienophile simply as an X-substituted alkene, the LUMO of the diene and the HOMO of the dienophile would be the closer pair of frontier orbitals in energy, from which we would

6 THERMAL PERICYCLIC REACTIONS

309

predict the ‘ortho’ adduct, as observed. However, appearances are misleading. With two carbonyl groups on the dienophile, the correct HOMO and LUMO to take in this case is HOMO(diene) and LUMO(dienophile), from which the prediction would be the ‘meta’ adduct. It is obviously unreasonable to ignore the carbonyl groups. One simple-minded way of looking at it, similar to the discussion on p. 191, is to say that the hyperconjugation 6.228 of the methyl group, through the double bond, with the carbonyl group attached to C-3 will reduce the electron-withdrawing effect of that carbonyl group. The result is that the carbonyl group attached to C-2 is more important in guiding the reaction: the C¼C orbital is more polarised by the C-2 carbonyl than by the C-3 carbonyl, and this reaction thus becomes another example of a Z-substituted dienophile.791 Ph

Ph

O

H

O H

+

O

O H

O 6.226

H

O O H

2

O

O

3

2

H

O

O 3

H

O 6.228

6.227

An unfortunate consequence of this regiochemistry was a set-back to a steroid synthesis. 2,6-Xyloquinone 6.230 reacted with the diene 6.229 to give the adduct 6.231, and not the adduct which would have been useful for a steroid synthesis. The polarisation of the LUMO of citraconic anhydride deduced using the same arguments as for citraconic anhydride, and the HOMO of a 1-substituted diene, explain the observed regioselectivity. Evidently the 2-aryl substituent has not changed the relative sizes of the coefficients, although it might have been expected to boost the coefficient at C-2. Substituents at C-2 are usually less effective in polarising a frontier orbital than those at C-1. For a sequel to this set-back, see p. 319. O

O H

HOMO +

2

H

1

LUMO O

MeO

O

MeO 6.229

6.230

6.231

Another special case, in which the unsymmetrical diene is part of a conjugated system which cannot easily be placed in any of the categories, C-, Z- or X-substituted, is tropone 6.232 when it reacts as a diene. On account of its symmetry, we have to work out the coefficients of the atomic orbitals by some other means than by the simple arguments used above and in Chapter 2 (see pp. 70–76). The coefficients of the HOMO and LUMO are shown in Fig. 6.33.241 The numbers for the HOMO are not easily guessed at, and we must be content, in this more complicated situation, to accept the calculation which led to them.

0.653

HOMO

–0.187 –0.393 –0.093 0.326

0O

O

0 –0.521

LUMO

0.232 0.418

Fig. 6.33 The frontier orbital coefficients of tropone

310

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

With this pattern in mind, we can see that the regioselectivity shown when tropone reacts as a diene to give the adduct 6.233 with styrene792 and the major adduct 6.234 with acrylonitrile793 is readily explained, whichever pair of frontier orbitals we take in the second case. LUMO

O

O

HOMO 6.232 O

Ph

Ph

6.233 O

O

LUMO

O

HOMO

HOMO CN

6.232

LUMO

CN 6.234

CN

6.232

6.234

CN

6.5.2.3 The Regioselectivity of Hetero Diels-Alder Reactions. In a few cases, carbonyl, nitrosyl, cyano, and a few other double bonds with one or more electronegative heteroatoms have acted as dienophiles in Diels-Alder reactions.794 The carbonyl group has the HOMO and LUMO shown in Fig. 1.66 (see p. 58). The energies of both orbitals are relatively low, and most of their Diels-Alder reactions will therefore be guided by the interaction between the HOMO of the diene and the LUMO of the carbonyl or similar compound. The examples with formaldehyde 6.235, the dithienium ion 6.236 and p-chloronitrosobenzene 6.237 illustrate that this works.795

O

+ H

O

S

+

H

S S

6.235

S

6.236

R +

R = Ph, CO2Me or OAc

O

O

N

N

Cl

+ H Cl

O 6.190

CHO 6.190

O

CHO

6.238

6.237

There are also Diels-Alder reactions in which the heteroatom is part of the diene system.796 The most notable of these is the dimerisation of acrolein 6.190 giving the adduct 6.238.797 This reaction had been a longstanding puzzle. As in the reaction of butadienecarboxylic acid 6.208 with acrylic acid 6.209 (see p. 304), the ‘electrophilic’ carbon atoms, labelled , are the ones which have become bonded. The first calculations of the frontier orbitals for acrolein gave the larger HOMO coefficient to the  carbon of the C¼C double bond of acrolein. This failed to explain the regiochemistry, but only because the simple Hu¨ckel theory that was used is notoriously weak in dealing with electron distribution in heteroatom-containing systems. Later calculations798,799 gave a better set of coefficients, one of which375 is shown in Fig. 6.34.

6 THERMAL PERICYCLIC REACTIONS

311

0.59

0.58 0.58

0.38

2.5

–0.48

0.48

O

0.51

LUMO

–14.5

–14.5

–0.30

CHO

0.59

0.48

O

2.5

–0.38

CHO

–0.58

HOMO

HOMO

LUMO

Frontier orbital energies and coefficients for acrolein

Fig. 6.34

Both LUMO(diene)/HOMO(dienophile) and HOMO(diene)/LUMO(dienophile) interactions have to be considered, because both energy separations are the same for dimerisations. The former interaction is directly appropriate for the formation of the observed product, as shown on the left of Fig. 6.34, but the latter interaction, as shown on the right, has no obvious polarisation in the diene—the C and O atoms have accidentally identical coefficients. However, the resonance integral, , for the formation of a C—O bond is smaller than the resonance integral for the formation of a C—C bond. (This is ˚ apart, but no one has suggested that the transition only true when the atoms are more than 1.75 A structure is likely to have a shorter distance than this, though several people have used longer distances.) Thus the (c)2 term of Equation 3.13 is smaller at oxygen than at carbon in this orbital, and consequently this interaction also explains the regioselectivity. The regioselectivity in this reaction is delicately balanced,800 but it also matches several cycloadditions between ,-unsaturated aldehydes, ketones and imines with C-, Z- and X-substituents on the dienophile, although some of the reactions may be stepwise, and not pericyclic.801 6.5.2.4 The Stereoselectivity of Diels-Alder Reactions. One of the most challenging stereochemical findings is Alder’s endo rule for Diels-Alder reactions. The favoured transition structure 6.239 has the electron-withdrawing substituents in the more hindered environment, under the diene unit, giving the kinetically more favourable but thermodynamically less favourable adduct 6.240. Long heating eventually equilibrates this isomer with the thermodynamically favoured exo adduct 6.241, by a retro-cycloaddition re-addition pathway. The endo rule is also obeyed by open-chain dienes like diphenylbutadiene 6.242, which gives the adduct 6.243 with all the substituents cis on the cyclohexene ring as the major adduct (90:10).802 This too equilibrates on heating with the minor isomer 6.244 with the carboxylic acid substituent trans to the two phenyl substituents. Any reaction in which a kinetic effect overrides the usual thermodynamic effect on reaction rates is immediately interesting, and demands an explanation.

H

r.t.

O

H O H

O 6.239

6.240

6.241 Ph

Ph r.t. Ph HO2C

O

O

H

O

Ph HO2C

Ph H H

Ph CO2H

CO2H

100°

H Ph

6.242

190°

H

H

O

O O

6.243

Ph 6.244

312

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

4

70°

O

S Ph MeN

24 h O 6.245

S

N Me Ph

6.246

The usual explanation is based on the signs of the coefficients in the frontier orbitals—the HOMO of the diene and the LUMO of the dienophile. As a model, we use 2 of butadiene for the former, and 3* of acrolein as the latter. If we place these orbitals in the appropriate places for the endo reaction (Fig. 6.35a), we see that there is the usual primary interaction (solid bold lines), with overlap of orbitals with matching signs, consistent with the rules, but there is an additional bonding interaction (dashed line) between the lower lobe of the p orbital on C-2 of the diene and the upper lobe on the carbonyl carbon of the dienophile, since they have the same sign. This interaction, known as a secondary orbital interaction,803 does not lead to a bond, but it might make a contribution to lowering the energy of this transition structure relative to that for the exo reaction, where it must be absent. It is equally effective in explaining the endo selectivity of a reaction showing inverse electron demand 6.245 ! 6.246,804 although there is some doubt whether this example is actually pericyclic—it could so easily be stepwise. The frontier orbitals are now the LUMO of the diene and the HOMO of the dienophile, for which the secondary interaction shown in Fig. 6.35b is again attractive, because the lobes have the same sign.

HOMO

2

LUMO

1 4

O

O

S Ph

H LUMO (a) HOMO(diene)/LUMO(dienophile)

Fig. 6.35

R2N

HOMO

(b) LUMO(diene)/HOMO(dienophile)

Secondary interactions and the endo rule for the Diels-Alder reaction

Secondary orbital interactions have also been invoked to explain regiochemistry as well as stereochemistry. Whereas 1-substituted dienes sometimes have only a small difference between the coefficients on C-1 and C-4 in the HOMO, they can have a relatively large difference between the coefficients on C-2 and C-3. Noticing this pattern, Alston suggested that the regioselectivity in Diels-Alder reactions may be better attributed, not to the primary interactions of the frontier orbitals on C-1 and C-4 that we have been using so far, but to a secondary interaction with the orbital on C-2 (Fig. 6.36a) being stronger than the secondary interaction with the smaller lobe on C-3 (Fig. 6.36b), even though it is not forming a bond.331,799 We can easily enough estimate the relative sizes of the coefficients on C-2 and C-3, using the same analogies that we used to estimate the coefficients on C-1 and C-4. The presence of a larger (in absolute magnitude) coefficient in the HOMO on C-2 than on C-3 for 1-C-substituted dienes is unambiguous: hexatriene has coefficients of 0.418 and 0.232 on these atoms (Fig. 1.42). 1-X-Substituted dienes are also unambiguous: the pentadienyl anion has coefficients in the HOMO of 0.576 and 0 on these atoms.

6 THERMAL PERICYCLIC REACTIONS HOMO

313 C,X,Z

2

HOMO

3

C,X,Z

2

3

O R

R

LUMO

LUMO

O (a) Transition structure f or f ormation of an 'ortho' adduct

Fig. 6.36

(b) Transition structure f or f ormation of a 'meta' adduct

Secondary interactions as an influence on the regioselectivity of a Diels-Alder reaction

However, the crude way we have handled the problem does not immediately demonstrate this for 1-Zsubstituted dienes, which we need to explain the reaction of butadiene carboxylic acid 6.208 and acrylic acid 6.209: thus we can see in Fig. 6.37 that the contribution of the triene-like character and the pentadienyl cation-like character have opposite effects on the coefficients on C-2 and C-3. However, the differences in the coefficients on each component are noticeably large, and it is therefore easy to accept that C-2 and C-3 could have quite different coefficients if either contribution should dominate. Alston’s calculation gives the values 0.384 and 0.314; it seems that, the triene-like character is more important than the pentadienyl cation-like character, and the arrangement giving the ‘ortho’ adduct (Fig. 6.36a) has a larger secondary interaction than that leading to the ‘meta’ adduct (Fig. 6.36b). As it happens, Alston’s calculation gives the opposite polarisation to C-1 and C-4 (0.483 and 0.460) to the generic picture for a Z-substituent in Fig. 6.25 from Houk. Experimental support for this theory is the formation of the adducts 6.247 and 6.248 from piperylene with fumaric acid, with the former the major,805 perhaps because it can benefit from secondary overlap with the larger coefficient in the HOMO of the X-substituted diene on C-2. Similar results have been reported for 1-acetoxybutadiene with dimethyl fumarate806 but see the diene 6.251 for a contrasting observation.

CO2H 0.418

HOMO

–0.418

+

0.232

0

–0.384

=

HOMO

0.314

0.500

0.521

Fig. 6.37

–0.483

–0.500

0.500

0.460

Crude estimate of the coefficients on C-2 and C-3 of a l-Z-substituted diene

HO2C

CO2H

+

CO2H +

CO2H

CO2H 6.247

75:25

CO2H 6.248

314

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

O O

H

O H

H

Me

H O 6.249

Me

H

H

6.250

OMe OMe

ClOC +

OMe COCl

+ COCl COCl

COCl

COCl 6.251

6.252

28:72

6.253

Explanations for stereochemistry and regiochemistry based on secondary orbital interactions, like frontier orbital theory itself, have not stood the test of higher levels of theoretical investigation.807 Calculations, low level808 and high level,809,810 produce transition structures which have an endo preference, and a substantial ˚ shorter degree of asynchronicity, with the bond from C-4 of the diene to the  carbon of the acrolein 0.3 A than the bond from C-1 to the  carbon. One consequence of this is that the atoms which would be involved in ˚ , for their orbitals to have any significant overlap.811 A any secondary overlap are too far apart, at about 2.8 A few experimental observations also call secondary orbital interactions into question. Whereas acrolein unexceptionally gives mainly (74:26) the adduct 6.249 with the formyl group endo, methacrolein gives mainly (83:17) the adduct 6.250, in which the methyl group is endo rather than the formyl group.812 Furthermore, in contrast to the reaction of piperylene giving the adduct 6.247, 1-methoxycyclohexadiene 6.251 and fumaroyl chloride give more of the adduct 6.253 which, if secondary overlap were important, would benefit from secondary overlap with the orbital with the smaller coefficient on C-3 than of the adduct 6.252 which would benefit from secondary overlap with the p orbital on C-2.813 1-Phenylbutadiene and 2methoxycyclohexadiene give 50:50 mixtures of adducts with fumarates, even though the frontier orbitals have significantly different coefficients on C-2 and C-3, implying insignificant secondary orbital effects.814,815 Also, there is a substantial solvent effect on endo:exo ratios, with the preference for the endo adduct significantly increased in polar solvents,816 implying that electrostatic interactions are playing some part. H HH (+) repulsion O

H (+) repulsion O

(+) H 6.254

O (–) attraction O

(+) H 6.255

(+) 6.256

One possibility for an electrostatic effect is a repulsion in the exo transition structure.807 Since H—C bonds are polarised towards the carbon, hydrogen atoms carry a partial positive charge, and therefore the inhydrogens and the carbonyl carbon, which also carries a partial positive charge, will repel each other 6.254. There will be even greater repulsion from the methylene group of cyclopentadiene 6.255 than from the inhydrogens of butadienes, which agrees with the greater propensity for forming the endo isomer with this diene. There will be a similar Coulombic repulsion in the methacrolein reaction between the methyl group and the methylene group of cyclopentadiene, and an attraction, a weak hydrogen bond, between the methyl group and C-2. Working in the opposite direction—a Coulombic attraction favouring exo attack—the oxygen atom of a furan, carrying a partial negative charge, will be attracted to the carbonyl group of

6 THERMAL PERICYCLIC REACTIONS

315

cyclopropenone 6.256, and an exo adduct is, unusually, kinetically as well as thermodynamically favoured.817 The unusually high endo selectivity shown by vinylboranes has led to an alternative explanation. The boron substituent with its empty p orbital is not part of a double bond, and so its effect on the frontier orbitals will not be the same as that of a Z-substituent like a carbonyl group—a vinylborane is even more like an allyl cation, with a more highly polarised LUMO than a Z-substituted alkene. This explains the high reactivity of vinylboranes, but the highly polarised LUMO does not account for the low levels of regioselectivity. An explanation for the endo selectivity is based on the calculated transition structure 6.257 for the endo reaction of vinylborane with butadiene.818 It has C-1 of the diene closer to the boron atom than to C-10 of the vinylborane, and with negligible overlap between the boron atom and C-2 of the diene, the normal atom invoked for secondary interactions. This matches the LUMO coefficients (see p. 308): the coefficient on the boron is larger than that on C-10 , and they have the same sign. The exo transition structure 6.258 still has some bonding to the boron atom, but C-1 is now closer to C-10 than to the boron atom, and the energy is not as low. In both cases, the reaction is concerted and asynchronous, with the leading bond from C-4 to C-20 , which are the atoms in the starting materials with the larger coefficients in the HOMO and LUMO, respectively. The transition structure is somewhere in between the usual transition structure for a [4 þ 2] Diels-Alder reaction and the transition structure for a diene reacting with an allyl cation to give a cyclohept-4-enyl cation. 2.27Å 1 2.53Å 2.05Å

H

4

H

B 2'

6.257

2.45Å 1

2.06Å

2.67Å

4

H

1'

1' 2'

B H

6.258

This explanation also accounts for the low electronic component to the regioselectivity. The LUMO coefficients that are important are not just those at C-10 and C-20 , they must also include the coefficient at the boron atom, since it is close to C-1 of the diene. Since the coefficients at the boron and at C-20 are comparable, the regioselectivity is low. In detail, the calculations suggest that the transition structure for the ‘ortho’ adduct from piperylene and the unsubstituted vinylborane should be slightly lower in energy than that for the ‘meta’ adduct, which would be in line with the frontier orbital predictions. They also suggest that the two methyl groups in dimethylvinylborane introduce enough of a steric effect to reduce the regioselectivity to zero, and, as we saw earlier, makes vinyl-9-BBN selective for the formation of the ‘meta’ adduct. The frontier orbitals of a normal dienophile like acrolein, especially when it is coordinated to a Lewis acid, are similar in magnitude and sign to those for a vinylborane. There ought therefore to be a strong attraction between C-1 of the diene and the carbonyl carbon of a dienophile in the endo transition structure, just as there is for the vinylborane, and maybe this is the explanation for the endo rule. Yet another approach to explaining the endo rule draws attention to some of the details in a transition structure calculated for the dimerisation of cyclopentadiene (Fig. 6.38).819 As usual this reaction is kinetically in favour of the formation of the endo adduct 6.260, and thermodynamically in favour of the exo adduct. Old bottles of the dimer usually contain more of the exo adduct, and so, if you want to use the endo adduct for a synthesis, it is necessary first to crack the dimer, and then allow the monomer to dimerise. The transition structure 6.259 calculated for the dimerisation shows a high degree of asymmetry in the ˚ long, whereas the C—C bond formation of the two  bonds. The leading bond between C-1 and C-10 is 1.96 A 0 ˚ that is still to form between C-4 and C-2 is 2.90 A. The interesting feature of the transition structure is that ˚ , and the reaction can continue in two equally probable the C—C distance between C-2 and C-40 is also 2.90 A 0 directions, one closing the bond from C-4 to C-2 and the other closing the bond from C-2 to C-40 . The products 6.260 and 6.261, whichever of the two bonds develops, have the same structure. These products are

316

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

C-4—C-2' 2 3 4' 2.90Å

1

6.260

1.96Å

4

1.64Å

1' 2' 2.90Å

3'

6.259

6.262 C-2—C-4' 6.261

The transition structure for the dimerisation of cyclopentadiene

Fig. 6.38

also connected by a Cope rearrangement, but the transition structure for that reaction 6.262 is different, having a full bond between C-1 and C-10 , and is slightly lower in energy than the transition structure 6.259 for the Diels-Alder reaction. In another calculation, the bonding from C-1 to C-10 in the transition structure is estimated to be half the strength of a full  bond, and the bonds between C-2 and C-40 and between C-4 to C-20 are one-quarter as strong as the bond between C-1 and C-10 .820 That the two bonds in a cycloaddition may not form to the same extent is what we have been assuming in matching the large coefficients with the large coefficients in unsymmetrical Diel-Alder reactions, and we have called such reactions asynchronous. The idea was first suggested by Woodward and Katz821 when they examined the rearrangement of the tricyclic diene 6.263 to its isomer the tricyclic diene 6.265, in both of which the hydroxy substituents are stereochemical labels. This rearrangement might reasonably take place by either of two pathways: retro-cycloaddition and readdition, or a single Cope rearrangement. They observed that the diastereoisomeric alcohol 6.266 gave the diastereoisomeric product 6.268, which showed that the retro-Diels-Alder pathway was not being followed, and that it must be a Cope rearrangment. This is easier to see from the bold lines, which identify the 1,5-diene system undergoing the Cope rearrangement, redrawn without moving the atoms in 6.264 and 6.267. At the time, the Cope rearrangement was barely known, and they identified the transition structure for the rearrangement as that of an asynchronous DielsAlder reaction. We can now see that the transition structures for the asynchronous Diels-Alder reaction 6.259 and the Cope rearrangement 6.262 are subtly different, but this work was significant historically, because it established the idea of concerted but asynchronous reactions. HO heat OH

OH 6.264

6.263

6.265 OH

heat

HO 6.266

HO 6.267

6.268

6 THERMAL PERICYCLIC REACTIONS

317

Another way of looking at the bonds in the transition structure for the dimerisation of cyclopentadiene is to see that they develop from the best frontier orbital overlap: the leading bond comes from overlap between the large lobes on C-1 and C-10 in both the HOMO/LUMO interaction marked in bold in the drawing 6.269 and the equally effective LUMO/HOMO interaction marked in bold in the drawing 6.270. The two partly formed bonds, marked with dashed lines, come from overlap between a large lobe on C-4 and a small lobe on C-20 and between a large lobe on C-40 and a small lobe on C-2,822 either of which can develop into the full bond of the product.

2

HOMO

1

LUMO

4

LUMO

4'

1'

HOMO

2'

6.269

6.270

The traditional secondary orbital interaction drawn in Fig. 6.35, first suggested by Woodward and Hoffmann, and redrawn with the orientation and numbering we are using here as 6.271, is effectively between C-3 and C-30 . Both of these atoms have small lobes in the frontier orbitals, whereas now, at least in this case with two identical partners, the secondary orbital interaction between C-2 and C-40 , as in the drawing 6.272, uses one large and one small lobe. This whole picture is dependent upon the dienophile being s-cis, which it must be in a cyclic diene. It may not apply to open-chain dienophiles, where the energetic penalty of having an s-cis conformation in the component acting as a dienophile may not lead it to be in the transition structure with the lowest energy. 2 3

secondary overlap

primary overlap

secondary overlap

primary overlap

4' 3'

6.271

6.272

With butadiene itself, the two lowest-energy transition structures are one similar to that in 6.259, and the other leading to an exo adduct.823 The difference in energy is small and this is in agreement with experimental results showing that the endo selectivity with butadiene itself, only measurable when there are deuterium substituents, is small.824 The reason for the lower degree of stabilisation for the endo transition structure is probably that the ends of the diene are further apart in butadiene than in cyclopentadiene, and the two diene fragments in the transition structure are both twisted a great deal more than in the drawing 6.259 to try to overcome this problem. One exceptional endo rule is found in the triazoline dione reaction on p. 285, which shows a strong preference for the endo transition structure. This can be ascribed to the presence of the lone pairs on the dienophile—it is known as the exo lone pair effect. A lone pair, if it were in the endo orientation, meets an antibonding interaction with the diene orbitals, and is strongly repelled. Sadly, this has no synthetic usefulness, since the two nitrogen atoms are not stereogenic centres, and the endo and exo transition structures, although very different in energy, give the same product. In conclusion, the standard textbook secondary orbital interaction depicted in Fig. 6.35 is not fully accepted, yet it remains a simple and much cited explanation for many observations.825 It would be wise to be cautious in using it, for there are several other possibilities.

318

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

6.5.2.5 The Effect of Lewis Acids on Diels-Alder Reactions. Diels-Alder reactions are, as we know, little influenced by polar factors, such as changing the solvent from a nonpolar to a polar one, yet Lewis acids exert a strong catalysing effect. Furthermore, Lewis-acid-catalysed Diels-Alder reactions are not only faster but also more stereoselective and more regioselective than the uncatalysed reactions. For this reason, catalysed reactions are of great synthetic importance. An early example was the use of cupric ion to catalyse the DielsAlder reaction of the 5-substituted cyclopentadiene 6.275 to make the 7-substituted intermediate 6.276 in Corey’s prostaglandin synthesis. The rate constants k1 for the 1,5-hydrogen transfers, which interconvert the cyclopentadienes 6.273–6.275, is unaffected by the Lewis acid, but the rate constant k2 for the Diels-Alder reaction is increased considerably. In the absence of the Lewis acid, the other dienes, which have an extra Xsubstituent on the diene, are more reactive than the isomer 6.275.826 MeO OMe

OMe

OMe +

5

k1 6.273

6.274

7

k2 Cl 2+ CN Cu

Cl 6.275

CN 6.276

The effects of Lewis acids on regioselectivity is illustrated by the reaction of piperylene and methyl acrylate giving mainly the ‘ortho’ adducts 6.277, as usual, but this preference was increased with Lewis acid catalysis.827 Similarly, isoprene and 3-methylbut-3-ene-2-one gave the ‘para’ isomer 6.279 as the major product in the synthesis of a natural product, but it could only with great difficulty be separated from the unwanted ‘meta’ isomer. The synthesis of the ‘para’ isomer alone was achieved by adding stannic chloride to the reaction mixture.828 Similarly, the effects of Lewis acids on stereoselectivity are illustrated by the reaction of cyclopentadiene with methyl acrylate giving endo-6.280 as the major product, with the proportion of this isomer higher when aluminium chloride was present.829 A similar increase in endo selectivity was seen in the reaction of piperylene giving the ‘ortho’ products 6.277. The unsymmetrical fumarate 6.281, with a soft and hard site for coordination by the Lewis acid, has the hard site endo with the hard Lewis acid boron trichloride, and the soft thiocarbonyl endo with the soft Lewis acid copper(II) triflate.830 CO2Me

CO2Me

+

+

SnCl4

+ CO2Me

6.277 without AlCl3 with AlCl3

O

6.278

O

90 : 10 98 : 2

MeO2C +

CO2Me

+ CO2Me endo-6.280

MeO2C +

without AlCl3 at 0 °C with AlCl3 at 0 °C with AlCl3 at –80 °C

CSOMe + CO2Me

CSOMe 6.283

6.282:6.283

with BCl3 with Cu(OTf)2

CSOMe 6.282

endo:exo 88 : 12 96 : 4 99 : 1

exo-6.280

CO2Me

6.281

6.279

4 : 96 89:11

6 THERMAL PERICYCLIC REACTIONS

319

All the features of Lewis acid catalysis can be explained by the effect of the Lewis acid on the LUMO of the dienophile.375,331,831 The Lewis acid forms a salt, which is the more active and selective dienophile. For simplicity, protonated acrolein is used as a model dienophile for calculations instead of the Lewis salt. When we were trying to estimate the energies and polarities of the frontier orbitals of acrolein itself (see p. 72), we added to the orbitals of a simple diene a contribution from the allyl cation-like character of acrolein. The effect of adding a proton to acrolein is to enhance its allyl cation-like character (see p. 187). For the frontier orbitals of acrolein, we add a larger contribution from the allyl cation. The results are: (i) both HOMO and LUMO are even lower in energy; (ii) the HOMO will have the opposite polarity at the C¼C double bond, the contribution from the allyl cation now outweighing the contribution from butadiene-like character; and (iii) the LUMO will have even greater polarisation, the -carbon carrying an orbital with an even larger coefficient, and the -carbon carrying an orbital with an even smaller coefficient. The calculation we used earlier in Section 4.5.2375 sets values on these energies and coefficients, repeated in Fig. 6.39. The lowering in energy of the LUMO makes the ELUMO(dienophile)–EHOMO(diene) a smaller number and therefore increases the rate. The increased polarisation of the LUMO of the C¼C double bond increases the regioselectivity. Finally, the increased LUMO coefficient on the carbonyl carbon makes the secondary orbital interaction (Fig. 6.35a) and the electrostatic repulsion 6.254 greater, accounting for the greater endo selectivity whichever of those explanations we adopt for endo selectivity.

0.51

O

X

X

O

H

–0.48

HOMO

–0.70

–0.39

–0.09

0.59

0.60

LUMO 2.5 eV

Without acid catalysis

Fig. 6.39

0.37

HOMO

LUMO –7 eV

With acid catalysis

Frontier orbitals showing increased regioselectivity for acid-catalysed Diels-Alder reactions

We can conclude this section on Lewis acid catalysis with a striking example of its use in solving a problem in steroid synthesis. We saw, on p. 309, how 2,6-xyloquinone 6.230 added to the diene 6.229 with inappropriate regioselectivity for steroid synthesis. When boron trifluoride was added to the reaction mixture, it formed a salt 6.284 at the more basic carbonyl group, the one conjugated to the two methyl groups, which is also the less hindered. The result was that the polarisation of the LUMO of the C¼C double bond was reversed, the major adduct was the isomer 6.285, appropriate for a steroid synthesis.832,833 O

O

+

H H O

MeO 6.229

6.284

BF3

O

MeO 6.285

6.5.2.6 The Site Selectivity of Diels-Alder Reactions. Site selectivity is another kind of regioselectivity, in which a reagent reacts at one site (or more) of a polyfunctional molecule when several sites are,

320

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

in principle, available. In cycloadditions, site selectivity usually involves a pair of sites; thus, butadiene reacts faster with the quinone 6.286 at C-2 and C-3 than at C-5 and C-6,834 and Diels-Alder reactions of anthracene 6.287 generally take place across the 9,10-positions rather than across the 1,4 or 3,9a.835 The familiar explanation for this example of site selectivity is that reaction at the 9,10-position creates two isolated benzene rings, whereas reaction at the 1,4-position would create a naphthalene nucleus, which is a less stable arrangement of two benzene rings. This explanation relies on the influence of product-like character in the transition structure, but we may also note that the same product is accounted for by looking at the frontier orbital coefficients of the starting materials: the largest coefficients in the HOMO of 6.287 are at the 9,10-positions (see p. 174). O

O

6

2

CN

5

3

CN

O

CN

CN

+

+

O 6.286

O 9

CN

CN O

O

1 9a

O +

O

O

3 10

O

80:20

4

O

6.287

In cycloadditions, the frontier orbital interactions are almost always between orbitals well separated in energy, and consequently they are second order and follow the form of the third term of Equation 3.13. As long as only the frontier orbitals are being considered, we can ignore the Er–Es term when assessing site selectivity, because, for any particular pair of reagents, it is always the same, whichever way they combine. Furthermore, as long as the atoms at the reaction sites in each component are the same (for instance, if they are both carbon atoms in one reagent, and both carbon atoms or both oxygen atoms in the other) then we can, as a first approximation, also ignore the  2 term. Thus all we have left is the Sc2 term. The dimerisation of hexatriene, in which the dimer formed is 6.288 and not 6.289, will serve as an example.836

–0.418

–0.418

–0.232

+ 0.521

HOMO

+ 0.521

–0.418 0.418

0.521

LUMO

6.288

HOMO

LUMO

6.289

The former, which retains a conjugated diene system, is likely to be lower in energy than the latter, which has lost all conjugation; the product 6.288 is therefore thermodynamically favoured. In this example, the frontier orbitals also suggest that this will be the major product. Thus we have the coefficients for the HOMO and LUMO from Fig. 1.42. The Sc2 term for the observed reaction is given by: Sc2 ¼ (0.418  0.232)2 þ (0.521  0.521)2 ¼ 0.083 and for the reaction which is not observed by: Sc2 ¼ (0.418  0.418)2 þ (0.521  0.418)2 ¼ 0.078

6 THERMAL PERICYCLIC REACTIONS

321

The former reaction is unsymmetrical, like many Diels-Alder reactions, and the transition structure will also be unsymmetrical. This will make , which is distance-dependent, different for each of the C—C bonds being formed, and will effectively increase the difference between the Sc2-values calculated above. Asynchronicity involving initial overlap of the two largest lobes will also be enhanced by the stabilisation of whatever radical character the transition structure has, and hence will augment the frontier-orbital explanation for the site selectivity in several other conjugated systems. For example, heptatriene 6.290 and 1-cyanobutadiene 6.294 react with maleic anhydride and isoprene 6.293 to give mainly the lower-energy adducts 6.291 and 6.295, respectively, rather than the alternatives 6.292 and 6.296.837 These reactions are similarly governed both by the formation of the thermodynamically favoured products and by the initial overlap with the larger frontier orbital coefficient in each component leading to the unsymmetrical transition structure.

O O

O O

+

O

+

O

O O

O

6.290

6.291 CN

6.292

75:25 CN

CN and not

+

6.293

6.295

6.294

6.296

Frontier orbital theory, however, comes into its own when we consider the dimerisation of 2-phenylbutadiene. In this case, the less stable dimer 6.297 is obtained.838 Furthermore, its formation involves attack at the more crowded double bond, so that neither a product-stability, which would favour the conjugated product 6.298, nor a steric argument works. The frontier orbitals have the coefficients shown, and the major pathway has the leading bond formed between the two larger coefficients (0.625) and a much higher Sc2-value (0.178) than the minor pathway (0.103). Another example of the same kind of site selectivity can be found in the dimerisation of 2-cyanobutadiene on p. 306, indicating that orbital control does have some importance in site selectivity.

Ph + Ph

0.625

HOMO

–0.475

–0.337 0.625

LUMO

+ Ph

Ph 6.297

Ph

Ph

Ph

–0.475

–0.256 0.475

0.625

HOMO

LUMO

Ph 6.298

The formation of Thiele’s ester 6.302839 is a remarkable example of several of the kinds of selectivity that we have been seeing in the last few sections, all of which can be explained by frontier orbital theory. The particular pair of cyclopentadienes which do actually react together 6.301 and 6.300 are not the only ones present. As a result of the rapid 1,5-sigmatropic hydrogen shifts (see p. 267), all three isomeric cyclopentadiene carboxylic

322

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

esters are present, and any combination of these is in principle possible. As each pair can combine in several different ways there are, in fact, 72 possible Diels-Alder adducts. The regioselectivity is a vinylogous version of the combination of a 2-Z-substituted diene with a Zsubstituted dienophile, for which the ‘para’ isomer is expected, and for which we had the earlier example of 2-cyanobutadiene on p. 306 without discussion. The HOMO and LUMO energies of the three isomeric dienes will be close to the representative values used in Fig. 6.25, and these are repeated under the structures. The isomer 6.299 ought to be the most reactive diene, because it has the highest-energy HOMO, but it is known to be present only to a very small extent—evidently too low a concentration to be a noticeable source of products. Leaving this isomer out of the account, the smallest energy separation is between the HOMO of 6.301 and the LUMO of 6.300. These isomers, therefore, will be the ones to combine, and they can react in either of two main ways: 6.301 as the diene and 6.300 as the dienophile or 6.301 as the dienophile and 6.300 as the diene. The second of these suffers from steric hindrance, because two fully bonded carbon atoms would have to be joined, always a difficult feat. This leaves the combination of 6.301 as the diene and 6.300 as the dienophile, the reaction actually observed. The endo selectivity is normal. Now, knowing about the site selectivity of the reaction with 1-cyanobutadiene 6.294, we finally see that the terminal double bond of 6.300 will be the double bond to react.

CO2Me MeO2C

MeO2C 6.299 1.0

LUMO

MeO2C 6.300

–0.5

MeO2C 6.301

–0.3 9.2

–9.1 HOMO

–9.5

–9.3

6.300

6.302

CO2Me

–0.5 8.8 –9.5

There is a further addition to this argument, because 2-Z-substituted dienes in general are unusually reactive as dienes, in spite of their having low-energy HOMOs.840 It may be that the isomer 6.301 is actually a more reactive diene than the isomer 6.299. One explanation is that the asymmetry in the transition structure, especially pronounced in cyclopentadiene dimerisations (Fig. 6.38), puts a premium on the initial bonding between the two large coefficients, marked with a heavier dashed line between 6.301 and 6.300. As a result, the transition structure like that in Fig. 6.38 has radical character in the incompletely bonded fragments, which a Z-substituent can stabilise, an explanation moving towards the position adopted by those in favour of an explanation based on diradical intermediates without actually losing concertedness in the bond forming processes. Another way of looking at this phenomenon is based on the perception in Fig. 6.23: the importance of the HOMO(dienophile)/LUMO(diene) interaction in advancing the bonding between C-2 and C3 in the diene component of the transition structure may make a Z-substituent on C-2 of the diene as good as having a 2-X-substituent.753 Further evidence that a Z-substituent at C-2 is rate-accelerating is found in the reactions of dienes with a boron substituent in this position. They are unusually reactive in Diels-Alder reactions in spite of boron, with its empty orbital, being a powerful Z-substituent.780

6.5.3 1,3-Dipolar Cycloadditions684 The range of possible 1,3-dipolar cycloadditions is large, as we saw with the generic dipole 6.37 and the generic dipolarophile 6.38. We are not restricted to carbon atoms in the five atoms that form the ring; we can

6 THERMAL PERICYCLIC REACTIONS

323

have an allyl-like or allenyl-like conjugated system in the dipole, and a double or triple bond in the dipolarophile. Fig. 6.40 shows the parent members of the most important 1,3-dipoles, and gives their names.

CH N CH2 nitr ile ylids

CH N NH nitrile imines

CH N O nitr ile oxides

CH2 N N diazoalkanes

NH N N azides

N N O nitr ous oxide

H

H

H

N CH2 CH2 azomethine ylids

N

N CH2 O nitrones

H

H

H

N NH NH azimines

N NH O azoxy compounds

N O O nitr o compounds

O CH2 CH2 carbonyl ylids

O NH CH2 carbonyl imines

O O CH2 car bonyl oxides

O NH NH nitr osimines

O O NH nitr osoxides

O O O ozone

Fig. 6.40

CH2 NH azomethine imines

The parent members of the most important 1,3-dipoles

6.5.3.1 The Rates of 1,3-Dipolar Cycloadditions. Some 1,3-dipoles, like diazomethane, have high-energy HOMOs, and react faster with alkenes carrying electron-withdrawing substituents. In this context these alkenes are called dipolarophiles, and they have low-energy LUMOs, just as they had when we called them dienophiles. 1,3-Dipoles like diazomethane can be described as nucleophilic in character, and the frontier orbital interactions resemble those of a normal Diels-Alder reaction. In support of this picture, the rates of the cycloadditions of diazomethane with alkenes correlate well with estimates of the difference in energy of the HOMO of diazomethane and the LUMOs of the dipolarophiles.841 Other 1,3-dipoles, like azomethine imines, have low-energy LUMOs, and react faster with dipolarophiles carrying electron-donating substituents, which have high-energy HOMOs. They can be described as electrophilic in character, and their frontier orbital interactions resemble those of a Diels-Alder reaction with inverse electron demand. Attaching electron-donating or electron-withdrawing substituents to a dipole can change this pattern. For example, a diazoketone is an electrophilic dipole, reacting faster with X-substituted alkenes instead of with Z-substituted alkenes. Putting an acyl group, a Z-substituent, onto the diazoalkane lowers the energy of the LUMO in the usual way, changing the balance of frontier orbital interactions.842 A few dipoles, like phenyl azide 6.303, are neither particularly nucleophilic nor particularly electrophilic. Like tetracyclone 6.200 in its Diels-Alder reactions with styrenes, phenyl azide reacts more slowly with simple alkenes than with alkenes having either an electron-withdrawing group or an electron-donating group. Sustmann843 has plotted the rate constants for this reaction against the energy of the HOMO of a wide variety of alkenes, and obtained a U-shaped curve (Fig. 6.41), showing that orbital energies are key factors in determining rates. An upwardly curved plot like this is characteristic of a change of mechanism (as distinct from a change of rate-determining step). The change of mechanism in this case is the change from a dominant HOMO(dipole)-LUMO(dipolarophile) interaction on the left, where we assume, reasonably enough,

324

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS N N Ph CO2Me

N

N +

N N Ph N

6.303

log k CO2Me

E HOMO of the dipolarophile

Fig. 6.41 Correlation between the energy of the HOMO of a range of dipolarophiles and the rates of their reaction with phenyl azide

that a low-energy HOMO implies a low-energy LUMO, to a dominant LUMO(dipole)-HOMO(dipolarophile) interaction on the right. C-, Z- and X-Substituents will affect the energies of the molecular orbitals of both dipoles and dipolarophiles in the same way that they affect the orbitals of dienes and dienophiles, but it is not possible to estimate the energies of the frontier orbitals of the parent dipoles in the crude but easy way that it was possible for dienes. To begin with, there are so many kinds of dipole. Even if we restrict ourselves to the elements carbon, nitrogen and oxygen, we still have many possible types of unsymmetrical dipole (Fig. 6.40), and with very few of them can we find simple arguments from which to deduce the relative energies of the frontier orbitals. Fortunately, Houk has calculated representative energies for the HOMOs and LUMOs of a wide range of dipoles, with and without C-, Z- and X-substituents. They are presented in Table. 6.2, together with Houk’s calculations of ‘coefficients’ needed for the discussion of regioselectivity in the next section.844,845 We can see that diazoalkanes have a high-energy HOMO, and that azomethine imines have a low-energy LUMO, matching the assertions above. Also, phenyl azide has neither a particularly high-energy HOMO nor a particularly low-energy LUMO, explaining the pattern of its reactivity with alkenes seen in Fig. 6.41. The data in the two columns labelled HOMO refer to the 4-electron p orbital taking part in the reaction, and not to any nonbonding lone pairs that might in some cases be higher in energy. Likewise the important unoccupied orbital for cycloadditions is not, in a number of cases, strictly the lowest in energy of the unoccupied orbitals, which in several cases is an orbital at right angles to the reaction plane. The data in the two columns labelled LUMO therefore refer to the lowest of the unoccupied orbitals which is in the reaction plane, and therefore capable of participating in a 1,3-dipolar cycloaddition. 6.5.3.2 The Regioselectivity of 1,3-Dipolar Cycloadditions. Regiochemistry in a 1,3-dipolar cycloaddition can be illustrated by the reaction of diazomethane 6.304 with methyl acrylate, in which the first-formed intermediate 6.305 undergoes tautomerism to give the better conjugated product 6.306.846 There is no guessing the regiochemistry by just looking at the reagents. If we draw the resonance structures 6.304a and 6.304b, they show that both the C and the N termini are simultaneously nucleophilic and electrophilic, as the

6 THERMAL PERICYCLIC REACTIONS Table 6.2 Dipole

325 Energies and ‘coefficients’ of 1,3-dipoles HOMO (c )2/15 Energy (eV)

Nitrile ylids

–7.7

CH

N

1.07

PhC

N

CH2

Nitrile imines

–6.4 –9.2

N

NH

Nitrile oxides

CH

N

N

O

Diazoalkanes

CH

N

N

N

Nitrous oxide

CH2

N

–6.9

Ar RO2CCH

N

HN

N

Azomethine imines

PhCH CH2

N N

NPh NCOR

Nitrones

–5.6

–9.7

PhCH

H N

O O

Carbonyl ylids O Ar(NC)C O (NC)2C

N

N

CH2

H N

0.1

O

–1.1

CH2

1.4

N

N 0.56

HN

N

N 0.76

N

N

CH2

O 0.19

H N

CH2

0.73

–0.6

CH2

H N

1.15

NH 1.24

–0.3 –1.4

CH2

H N

0.87

NH 0.49

–0.4

CH2

H N

O

–0.5

1.06

O CH2

CH2

0.4

1.29

–0.6

C(CN)2

–9.0

–1.1 O

0.82

–0.2

1.34

O CH2

NH

O

O CH2

O CH2

1.25

1.30

–2.2

NH 0.49

O CH2

CH2 0.82

1.06

–0.9

O 0.32

0.82

–6.5

CH2

CH2

H N

0.98

–0.4

–13.5

CH2

0.73

–8.0

–10.3

O 0.17

0.96

C(CN)Ar

Carbonyl oxides

N

0.37

0.3

–8.6

CH

0.66

1.28

1.04

Ozone

1.8

1.33

1.29

Carbonyl imines

NH 0.36

1.18

–8.7

–7.1

N

–0.2

1.11

N

N

–9.0

R CH2

N

–7.7 –8.6

–0.5

0.72

1.28

CHCO2R

CH 0.92

0.85

0.67

Azomethine ylids

O

–9.5 –12.9

CH2 0.64

–1.0

1.55

PhN

0.1

1.24

1.57

–11.5

N

–0.5

–10.0 –9.0

Azides

NH 1.45

0.81

PhC

CH 0.69

0.6

–7.5 –11.0

0.9

1.50

0.90

PhC

CH2

LUMO (c )2/15 Energy (eV)

O 0.24

326

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

arrows show. It is an ambident reagent. If we were to think only of the total charge distribution, we might guess that the electronegative end of the dipole, the nitrogen, will have more negative charge than the carbon atom. However, as an ambident nucleophile, diazoalkanes are known to react with electrophiles like carbonyl groups at the carbon end. Neither of these considerations offers a safe way of predicting the regioselectivity of a cycloaddition. Until Houk introduced frontier orbital theory to explain the regioselectivity of 1,3-dipolar cycloadditions, they remained an outstanding mystery.847 Both sets of arrows 6.304a and 6.304b are reasonable, both describe what happens, but they do not reveal which atom, C or N, will bond to the electrophilic  carbon of the dipolarophile. N 6.304a

CO2Me

N CO2Me

N N N 6.304b

–H+ +H+

N

CO2Me

HN

CO2Me 6.305

N

6.306

Turning to the frontier orbitals, we already have a picture of the polarisation of the dipolarophile: it is the same as a dienophile with a Z-substituent, as shown in Fig. 6.25. What we need is a corresponding picture for the dipole, and this is not easy to estimate, any more than it was easy to estimate the energies of the parent dipoles. Furthermore, in most cases, the bonds being made are no longer always C—C bonds, as they are in the common Diels-Alder reactions. Just as with heterodienes and heterodienophiles, we must include an estimate of the appropriate resonance integral, , as well as the coefficients of the atomic orbitals, c. Fortunately, all this work has been done for us by Houk, and we shall take his figures in Table 6.2 on trust.844 Instead of straightforward coefficients for the atomic orbitals, as we had for dienes and dienophiles, he has calculated (c)2 values in their place, and divided them by 15 to bring the numbers close to 1. They are calculated assuming that the new bonds are being made to carbon atoms in the dipolarophile from the carbon, nitrogen or oxygen atoms of the dipole. They would need to be changed if the bond forming is between two heteroatoms. Because  contains S, the overlap integral, it is a distance-dependent function, which is also dependent upon whether the element is C, N or O, as we saw in Section 1.7.2 (see p. 54). The values chosen by Houk involve a guess about the distance apart of the atoms in the transition structure. Table 6.3 gives some values for  for the different combinations of C, N and O, where we can see that the choice of distance is ˚ on the basis that cycloaddition reactions show large critical: Houk used a representative distance of 1.75 A negative activation volumes and sizeable steric effects. If more detail were needed, the (c)2 values would

˚ ) calculated for  overlap between all combinations of 2p Table 6.3 -Values (in eV) as a function of distance (in A orbitals of C, N and O ˚ A

 CC

CN

 CO

NN

NO

OO

1.50 1.75 2.00 2.50 3.00

6.97 6.22 5.00 2.63 1.20

7.20 5.83 4.35 2.14 0.78

7.05 5.38 3.77 1.53 0.55

7.18 5.35 3.65 1.40 0.45

6.92 4.81 3.02 1.04 0.28

6.63 4.19 2.45 0.68 0.17

6 THERMAL PERICYCLIC REACTIONS

327

have to be adjusted to take account of unsymmetrical transition structures, but such detail is inappropriate for the general discussion we need here. To account for the regioselectivity of 1,3-dipolar cycloadditions, we must first assess whether the reaction that we are looking at has a smaller separation between the HOMO of the dipole and the LUMO of the dipolarophile or between the LUMO of the dipole and the HOMO of the dipolarophile. The former is called dipole-HO controlled and the latter dipole-LU controlled. We can do this simply by taking the energies of the dipoles in Table 6.2, and the energies of the representative dipolarophiles in Fig. 6.25, and transferring them to a diagram like that in Fig. 6.42. Here we see that diazomethane has frontier orbital energies with the smallest separation in energy of all of the possible frontier orbital interactions (the double-headed arrows) for the reaction between diazomethane and a Z-substituted alkene, for which ELUMO(dipolarophile)–EHOMO(dipole) is 9 eV. Reactions of diazomethane with electron-deficient alkenes are the fastest and most often encountered of the cycloaddition reactions of diazoalkanes, and we can now see that the strong frontier orbital term for this particular combination accounts for the chemoselectivity. This reaction is therefore dipole-HO-controlled, and we can now look at the ‘coefficients’.

X

3 0.56

LUMO

N

1.8

N

1

C

LUMO

0.66

0 10.8

10

Z

12

12.7 9

9.8

X

–8 0.85

HOMO

N

–9

–9

C HOMO

N

1.57

–10.9

Fig. 6.42

Z

Frontier orbitals for diazomethane and representative dipolarophiles

In this case they will be the (c)2 values for the HOMO of the dipole from Table 6.2 and the coefficients of the LUMO of the dipolarophile from Fig. 6.25. Regioselectivity should follow in the usual way from the large-large/small-small interaction 6.307, which we can see has the carbon end of the dipole bonding to the  carbon of the Z-substituted alkene, as observed, and used as an example at the beginning of this book in posing the problem of how we should explain such selectivity. 0.85

CO2Me

N N

HOMO

LUMO

N

CO2Me

N

N

CO2Me

HN

1.57

6.307

6.305

6.306

328

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

The reactions of diazomethane with C- and X-substituted alkenes are much slower, and consequently there are fewer known examples. The slower rate of reaction is explained easily by the larger energy separation in the frontier orbitals (10 and 9.8 eV, respectively, in Fig. 6.42). The regioselectivity, however, is the same: Dl-pyrazolines like 6.309 and 6.311 with the substituent at C-3 are obtained with both C- and X-substituted dipolarophiles.848 This at first sight surprising observation can be explained by the change from dipole-HO control in the cases of the Z- and C-substituted alkenes 6.307 and 6.308 (supported, incidentally, by the positive Hammett -value for the latter) to dipole-LU control 6.310 in the case of the X-substituted alkene ethyl vinyl ether.849 R 0.85

R

N

N

0.56

3

N

N

OEt

N

N

1.57

3

OEt

N

N 0.66

LUMO

HOMO

HOMO

6.309

6.311

LUMO

6.308

6.310

In general, substituents present on a dipole will modify the energies and coefficients shown for the unsubstituted cases in Table 6.2, but it should be an easy matter, at least qualitatively, to predict how these substituents will affect the energies and (c)2/15 values, which we shall call ‘coefficients’, by taking advantage of our qualitative understanding of the effects of C-, Z- and X-substituents on alkenes. Table 6.2 shows the effect of a few of the commonly found substituents on the energy of the frontier orbitals—phenyl groups do indeed raise the HOMO and lower the LUMO energy, and ester and cyano groups lower both the HOMO and the LUMO energy. The effect of substituents on the diazoalkane can be accounted for using such reasoning. X-Substituents raise both the HOMO and the LUMO energies, and will speed up reactions with Z-substituted alkenes. In agreement, alkyl diazomethanes are more reactive than diazomethane in cycloadditions.850 Z-Substituents, which lower both the HOMO and the LUMO energies of the dipole, speed up the normally slow reactions with X-substituted alkenes like enamines. Furthermore, with a Z-substituent on the carbon atom of the diazomethane, the coefficient on the carbon atom will be reduced in the LUMO, just as it is in the LUMO of an alkene with a Z-substituent. Since the (c)2/15 terms for the LUMO of diazomethane are rather similar 6.312, the Z-substituent is enough to polarise them decisively in the opposite sense 6.313. This reaction is now dipole-LU-controlled, and the regioselectivity changes to that shown in the pyrazole 6.314, where the methyl substituent has served as a marker to show that the nitrogen end of the dipole has bonded to C-2 of the enamine.851 0.56

N

N

N

N

N

N

0.66

LUMO 6.312

Z LUMO

X HOMO

6.313

H N

2

+

N N

EtO2C

EtO2C 6.314

The following discussion is limited to a few other dipoles, in order to illustrate some of the less straightforward cases. The balance of factors leading to a particular chemo- and regioselectivity is often close—the choice of which pair of frontier orbitals to take is sometimes difficult, the fact that some frontier orbitals are not strongly polarised forces us to judge each case carefully on its merits, and the outcome is not quite always in agreement with the experimental results. There is more discussion of these and all the other cases in Houk’s papers.843

6 THERMAL PERICYCLIC REACTIONS

329 X

3

0.76

1

N

0.1

N

N 0.37

Z

0

–0.2

12.5

N

N

H

C

Ph

LUMO

N

8.8

10.5

10.7 9.5 7.8 X

–8 N

N

C HOMO

N

N

0.72

–9 –9.5

–11.5 Ph

Z

–10.9

N

1.55

N

H

Fig. 6.43

Frontier orbitals for phenyl azide and representative dipolarophiles

Let us look at azides so popular in ‘click’ chemistry,852,853 although that chemistry largely uses a coppercatalysed version of azide cycloadditions,854 and not the simple thermal 1,3-dipolar cycloadditions discussed here. The parent hydrazoic acid is not the usual dipole of this class; a frequently used one is phenyl azide. The phenyl group is a C-substituent, which will raise the energy of the HOMO and lower that of the LUMO. We can see from Table 6.2 that in the HOMO of hydrazoic acid the nitrogen carrying the substituent (H in hydrazoic acid, Ph in phenyl azide) has the larger coefficient, and that in the LUMO of hydrazoic acid it has a smaller value. The consequence of this is that the phenyl group is more effective in raising the energy of the HOMO than in lowering the energy of the LUMO. The result, taking the values from Table 6.2, is shown in Fig. 6.43. The smallest energy separation (7.8 eV) is with X-substituted dipolarophiles, which implies that they will be dipole-LU-controlled reactions. The orientation should therefore be that shown as 6.315. The reactions with C- and X-substituted alkenes 6.316 and 6.318 should be, and are, fast. Orientation like this has often been observed, as in the formation of the triazolines 6.317 and 6.319 with the C- and X-substituent at the 5-position.855,856 N N C,X N Ph HOMO LUMO 6.315 N

N N Ar

N

N

+ Ph

N

N Ph Ph

Ph 6.316

N

N 5

6.317

N

N

+ O

5

N Ar

6.318

6.319

O

330

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

However, when the dipolarophile is phenylacetylene 6.320 instead of styrene 6.316, the regioselectivity is sharply reduced, and nearly equal amounts of the 1,5-diphenyltriazole 6.321 and the 1,4-diphenyltriazole 6.322 are obtained.857 This puzzling observation can be explained, by the frontier orbitals. The second p bond of an acetylene is stronger than the first, because it is made between two atoms held close together by the first p bond. The overlap of the p orbitals on carbon is therefore stronger, and an acetylene has a lowerenergy HOMO than ethylene.

N Ph

N

+

5

N

N

Ph

+ Ph

Ph

6.320

Ph

N

N

N

6.321

55:45

4

N N

Ph 6.322

This argument is supported by photoelectron spectroscopy, where the HO level is generally found to be 0.4 to 0.9 eV lower than that of the corresponding alkene. We can also relate this observation to the familiar notion that alkynes are less reactive towards electrophiles like bromine than are the corresponding alkenes. Curiously, the LUMO is not raised for alkynes relative to alkenes. This is shown by UV spectroscopy, where phenylacetylene (lmax 245 nm) and styrene (lmax 248 nm) would appear to have rather similar separations of their HOMOs and LUMOs. Thus, with a LUMO also lowered in energy, it is not unexpected to find that acetylenes with Z-substituents are more reactive towards nucleophiles than are the corresponding alkenes. The effect of going from styrene to phenylacetylene is therefore to lower both the HOMO and the LUMO by about, say, 0.5 eV. This makes what was clearly a dipole-LU-controlled reaction into one which is affected by both interactions (Fig. 6.44). Since dipole-HO control leads to the opposite regioselectivity, it is not so surprising that both orientations are now observed. The poor regioselectivity in the reaction of azides with terminal acetylenes is overcome in the copper-catalysed version, which gives cycloaddition exclusively in the sense 6.322.

1 N

C

C 0.5

–0.2

N Ph

N

N

8.8

10.5

–9 –9.5

9.3

10.0

C

C (–9.5)

N Ph

Fig. 6.44

N

Frontier orbitals for phenyl azide, styrene and phenylacetylene

With Z-substituted dipolarophiles and phenyl azide, the situation is again delicately balanced and only just dipole-HO-controlled (9.5 eV against 10.7 eV from Fig. 6.43). For the dipole-HO-controlled reaction, we should expect to get adducts oriented as in Fig. 6.45a. However, a phenyl group reduces the coefficient at the neighbouring atom both for the HOMO and for the LUMO, and this will reduce the polarisation of the

6 THERMAL PERICYCLIC REACTIONS

331 Z

N

Ph

N

N

N

N

N

Ph

HOMO

LUMO

LUMO

Z HOMO

E LUMO – E HOMO = 9.5 eV

E LUMO – E HOMO = 10.7 eV

(a) Dipole-HO-controlled regiochemistry

(b) Dipole-LU-controlled regiochemistry

Fig. 6.45 Regioselectivity for phenyl azide reacting with a Z-substituted alkene

HOMO. Conversely, it will increase the polarisation for the LUMO and hence increase the effectiveness of the interaction of the LUMO of the dipole with the HOMO of the dipolarophile, as in Fig. 6.45b. The difference in energy for the two cases is small enough that firm prediction is not possible. In practice, dipoleHO control appears to be dominant, as shown by the formation of the adduct 6.323 from methyl acrylate, but it only needs the addition of an -methyl group, for some dipole-LU control to become evident in the formation of some of the adduct 6.324 from methyl methacrylate, in addition to the aziridine 6.326 derived from the normal regioisomer 6.325.858 Perhaps the methyl group has raised the energy of both the HOMO and the LUMO of the dipolarophile, making the HOMO/LUMO separations still more nearly equal. CO2Me

N +

N Ph

CO2Me

N N N

N

Ph 6.323

N N Ph

N

N

CO2Me +

N N

N CO2Me

+

Ph

N

CO2Me

CO2Me Ph

N

N Ph

6.324

25:75

6.325

6.326

Turning now to azomethine imines, the commonly used reagents have at each end aryl groups, which raise the energies of the HOMOs and lower the energies of the LUMOs relative to the unsubstituted system. Because the ‘coefficients’ at the terminal atoms of the dipole are smaller in the LUMO than they are in the HOMO, the phenyl groups do not lower the energy of the LUMO as much as they raise the energy of the HOMO. These effects on the energy are included in Table 6.2, and are reproduced in Fig. 6.46. With simple conjugated dipolarophiles like styrene, the reaction is only just dipole-HO-controlled (6.6 and 7.6 eV), and mixtures can be expected. Styrene does, in fact, give both regioisomers 6.328 and 6.329 in not very different amounts, but with the major product that corresponding to dipole-HO control.684 With an acetylenic dipolarophile, phenylacetylene, the lowering of the energy of the HOMO of an acetylene relative to that of the corresponding alkene should make the reaction more predominantly dipole-HO-controlled. The experimental observation is, in fact, the opposite of what we would expect: phenylacetylene with the same azomethine imine 6.327 gives only the adduct

332

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS X

3 H 0.49

N

N

–0.3

N

C Z

0 –1.4

LUMO

N

H

0.87

1

Ph

H

H Ph

6.6

Ph N

H 1.24

N

5.6

9.5

8.6

–5.6

–8.6

H

X

–9

HOMO

C

Ph

H

6.6 –8

N

N 1.15

7.6

Z

–10.9

H

Frontier orbitals for azomethine imines and representative dipolarophiles

Fig. 6.46

6.330.684 The dipole-HO has very similar ‘coefficients’ on nitrogen and carbon, and other factors, such as steric and dipole repulsions, are more likely to make themselves felt.

Ph

+ N

N

N

N Ph

Ph N

dipole-LU-control 6.328

6.327

Ph

N

6.330

N

36:62

dipole-HO-control 6.329

N Ph

However, with Z-substituted dipolarophiles, the reaction ought to be even more decisively dipoleHO-controlled, and the regioselectivity observed is easily and correctly accounted for: the reaction with acrylonitrile gives only the adduct 6.331.684 Placing an acyl group on the nitrogen end of the dipole 6.332 lowers the energy of both the HOMO and the LUMO relative to the unsubstituted azomethine imine (to 9 and 0.4 eV). Reaction with conjugated alkenes like styrene will now change to dipole-LU control (8.6 eV as against 10 eV). The LUMO has a large difference between the (c)2 terms, which will be enhanced by the acyl substituent, explaining the regioselectivity in the formation of the adduct 6.333 actually observed.859

6 THERMAL PERICYCLIC REACTIONS

N

HOMO

333

N

N

LUMO

N

NC 6.331

NC

O

O N

N

LUMO

N

Ph

HOMO

Ph

N Ph

Ph 6.332

6.333

Placing an acyl group on the carbon atom end of the dipole also lowers the energy of the LUMO and leads to dipole-LU control 6.334, but this time the acyl group will reduce the difference between the coefficients. An overwhelming preference for one orientation is not to be expected, but all three kinds of dipolarophile should give adducts of the type 6.335. O LUMO

O

N

N

N N

HOMO X,Z,C

X,Z,C 6.334

6.335

This is exactly what has been observed for the cycloaddition reactions of sydnones 6.336 with all three kinds of dipolarophile. An intermediate is produced in the first instance with the general structure 6.337; this loses carbon dioxide in a retro 1,3-dipolar cycloaddition, followed by tautomerism giving the 3-substituted pyrazolines 6.338 as the major products.860 Ph R Ph

Ph

N –CO2

O

R = Me, CN or Ph

N N

O N

N

6.338

O 6.336

Ph MeO2C

N N R

6.337 O

–H

+H+ R

R

N

Ph +

Ph

N N

N +

N

–CO2 MeO2C

CO2Me 6.339

76:24

6.340

334

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS X

3 0.17

O

1

C Z

0

–0.5

N 1.18

LUMO

C 8.5

H

12

10.4

11 7.5 14

–9 1.24

0.81

C

O N

X

–8

Z

–10.9

–11

HOMO

C H

Fig. 6.47

Frontier orbitals for a nitrile oxide and representative dipolarophiles

In the reaction of the same sydnone with an acetylenic dipolarophile, slightly more dipole-HO control can be expected, and this has been observed. Propiolic ester still gives mainly the 3-substituted pyrazole 6.339, but also a substantial amount of the 4-substituted pyrazole 6.340.861 Two dipoles especially important in organic synthesis are nitrile oxides and nitrones. In both cases cycloaddition to an alkene makes a C—C bond, and the N—O bond in the product can be easily cleaved by reduction to establish heteroatom functionality with a 1,3-relationship. The frontier orbital picture for a simple nitrile oxide is shown in Fig. 6.47, where we can see that the easy reactions ought to be decisively dipole-LUcontrolled, and fast with C- and X-substituted alkenes. This matches well with the reactions of benzonitrile oxide with styrene, terminal alkenes, enol ethers and enamines which all give only the 5-substituted isoxazolines 6.341. In the reactions with Z-substituted alkenes, however, the frontier orbitals are not strongly in favour of either of the pairings, and the polarisation gives opposite predictions, with dipole-LU control marginally in favour of the isoxazoline 6.342 and dipole-HO control strongly in favour of the isoxazoline 6.343. In practice, the regiochemistry with Z-substituted alkenes is delicately balanced, and it may be that the decisive factor is simply steric, since the two ends of the nitrile oxide are very different in their steric demands.862 Methyl acrylate gives largely the isoxazoline 6.342 (R ¼ H), but when the -position has two methyl groups, the regiochemistry is completely inverted in favour of the isoxazoline 6.343 (R ¼ Me).863 O N

R +

N

HOMO

Ph LUMO

R R HOMO

R = Ph, alkyl, OEt

Ph 6.341

CO2Me +

R

N

Ph LUMO O

5

O

CO2Me

O N

O N

R +

R Ph

R 6.342

Ph HOMO

6.342:6.343

R

R

O

R

N

CO2Me LUMO Ph 6.343

CO2Me

R = H 96:4 R = Me 0:100

6 THERMAL PERICYCLIC REACTIONS

335 X

3 C

1 0.32

R

O

0.3

0.58

C

Z

0

N

LUMO

H 9.3

H

9.7

8.7

11.2

13.9

8.3 X

–8 1.15

R

O

–8.7

C

–9

HOMO

N C

1.11

Z

–10.9

H

H

Fig. 6.48

Frontier orbitals for a nitrone and representative dipolarophiles

The frontier orbital picture for a simple nitrone is shown in Fig. 6.48, where we can see that the easy reactions will be dipole-LU-controlled with X-substituted alkenes and dipole-HO-controlled with Z-substituted alkenes. In practice, phenyl, alkoxy and methoxycarbonyl substituents speed up the cycloadditions. Any substituent on the carbon atom of the dipole introduces a steric element in favour of the formation of the 5substituted isoxazolidines 6.344. The usual selectivity with monosubstituted alkenes is in favour of this regioisomer, decisively so with C- and X-substituents, but more delicately balanced with Z-substituents, since the HOMO of the dipole is not strongly polarised.864 With methyl crotonate, having one X- and one Zsubstituent, the adducts are stereoisomers with the same regiochemistry 6.346, having the methyl group on the 5-position and the ester group on the 4-position.865

R

O Ph

+

N C H LUMO

R

O Ph

5

N

+

O Ph

N

4

Ph

R Ph

Ph

HOMO

6.344

6.345

O N Ph

O +

N CO2Me

6.344:6.345 R = Me 98:2 R = Ph 100:0 R = CO2Et 70:30

Ph

5 4

CO2Me 6.346

Dipolarophiles with electronegative heteroatoms such as carbonyl groups, imines and cyano groups also show an orientation in agreement with frontier orbital theory. Because these heterodienophiles all have lowenergy LUMOs, they will more often than not be involved in dipole-HO-controlled reactions. The orientation observed will therefore depend upon the LUMO of the dipolarophile, which will have the large coefficient on the carbon atom. The reaction of diazomethane 6.304 with benzylidine aniline 6.347 giving one regioisomer 6.348 fits this pattern.

336

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

N HOMO

N

Ph

6.304

N

N

N Ph

Ph

N

Ph

LUMO

6.347

6.348

Another example is the third stage of the ozonolysis sequence; the first step 6.349 has no regiochemistry, the second step 6.350 is a cycloreversion, but the third stage 6.351, the cycloaddition of a ketone oxide to a carbonyl group, is highly regioselective and just one representative of many others that might have been chosen.856,866

HOMO

O

O

O O

O

+

O

O

O H

O

O 6.349

6.350

O

O

LUMO H

6.351

We are far from exhausting the subject of regioselectivity in dipolar cycloadditions with these few examples. Frontier orbital theory, for all its success in accounting for most of the otherwise bewildering trends in regioselectivity, is still fundamentally defective. We must keep in mind that the frontier orbitals used here must reflect some deeper forces than those that we are taking into account in this essentially superficial approach. Nevertheless, no other easily assimilated theory, whether based on polar or steric factors, or on the possibility of diradical intermediates,683 has had anything like such success. It is plain that, as so often happens in science, a large body of data has been reduced to an amenable set of principles. 6.5.3.3 The Stereoselectivity of 1,3-Dipolar Cycloadditions. The exo or endo stereochemistry of 1,3dipolar cycloadditions is not as straightforward as it is for Diels-Alder reactions. Stereoselectivity, more often than not, is low, as shown by the nitrone reactions that we saw on p. 335 when we were looking only at regiochemistry. We now see that the major regioisomer 6.344 from the reaction of C,N-diphenylnitrone with methyl acrylate is a mixture of exo and endo isomers, exo- and endo-6.344. Similarly, the only regioisomer 6.346 from the reaction of N-benzyl-C-ethylnitrone with methyl crotonate is a mixture of exo-6.346 and endo-6.346. In both cases, the reaction is a little in favour of the exo product.867 Ph N

O Ph CO2Me

exo

Ph N

Ph N

O Ph CO2Me

exo-6.344 Bn N

O

exo

Bn N

Ph

57:43

CO2Me

CO2Me exo-6.346

O Ph

MeO2C

O Et

MeO2C 77:23

Ph N

endo-6.344 Bn N

Et

endo

MeO2C

O Et

O

endo

Bn N

O Et

MeO2C

endo-6.346

However, 1,3-dipolar cycloadditions are sometimes highly stereocontrolled in the exo sense, as in the cycloaddition 6.352 of a cyclic nitrone to a vinyl ether giving largely (97:3) the exo adduct exo-6.353.868

6 THERMAL PERICYCLIC REACTIONS

337

In contrast, other reactions are endo selective, as in the cycloaddition 6.354 of an azomethine ylid to dimethyl maleate giving largely (80:20) the endo adduct endo-6.355.869,870 Thus the stereoselectivity depends in a not always predictable way upon the dipole, the dipolarophile and their substituents, in contrast to Diels-Alder reactions, which more often than not obey the endo rule. It is advisable, when planning a synthesis, to look up close analogies before relying upon the exo or endo stereoselectivity of a 1,3-dipolar cycloaddition. O

N

N exo

N

O

O

+

O

O

O

major 6.352 H

97:3

exo-6.353

Ph N

endo

MeO2C MeO2C MeO2C

major

6.354

H

Ph N

MeO2C MeO2C MeO2C endo-6.355

endo-6.353 Ph N

H

H +

H

MeO2C

CO2Me CO2Me

80:20

exo-6.355

In trying to explain these results, we can look at the generic secondary orbital interactions in Fig. 6.49. The HOMO of the dipole will be similar to the HOMO of an allyl anion (see p. 27), which has a zero coefficient on the central atom. In unsymmetrical dipoles it will still only have a small coefficient, which could be either way up, depending upon the relative electronegativity of X and Z. We would therefore predict that dipoleHO-controlled reactions can only have small secondary orbital interactions, and low endo-exo selectivity. However, we can predict that the endo mode might be favoured for dipole-LU-controlled reactions, since there is potentially a favourable secondary orbital interaction. This does not match the observations. Nitrone reactions are likely to be dipole-LU-controlled, especially the reaction 6.352 with the X-substituted alkene, yet this is one of the most exo selective. The reaction 6.354 of the azomethine ylid with dimethyl maleate is likely to be dipole-HO-controlled (7.7 eV as against 10.3 eV), and yet this is the one that is endo selective. In reactions like these, the nature of the substituents changes the orbital energies, making the assignment of HO or LU control less certain than the numbers used above imply. It is not even clear in every case what the geometry of the dipole is (Z or E), or whether the results are kinetically or thermodynamically controlled. Nevertheless, we may conclude that the theory of secondary orbital interactions is not well supported by the evidence from 1,3-dipolar cycloadditions, although it is still invoked, for want of a better, in trying to explain their stereochemistry.

LUMO

HOMO Y weak interaction, could be bonding or antibonding

X

X,Z,C LUMO (a) Dipole-HO control

X

Y

Z

Z stronger bonding interaction

X,Z,C HOMO (b) Dipole-LU control

Fig. 6.49 Possible secondary orbital interaction in 1,3-dipolar cycloadditions

338

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

6.5.3.4 The Site Selectivity of 1,3-Dipolar Cycloadditions. The site selectivity of 1,3-dipolar cycloadditions is the same as for the Diels-Alder reactions in Section 6.5.2.6. To give just two examples, the unsaturated ester 6.356 reacts with diazomethane at the 4,5-double bond, to give the adduct 6.357,871 and diazoacetic ester adds to the terminal double bond of l-phenylbutadiene 6.358, giving the pyrazoline 6.359, with the product actually isolated after the loss of nitrogen being the corresponding cyclopropane.872 CO2Me

CO2Me N N

N

N +

N

N 6.356

Ph

Ph

6.357

N +

EtO2C

N 6.358

EtO2C 6.359

6.5.4 Other Cycloadditions 6.5.4.1 [4 þ 6] Cycloadditions. Secondary orbital interactions have been cited as an explanation for the stereochemistry of [4 þ 6] cycloadditions such as that between cyclopentadiene and tropone 6.45 ! 6.46, which favours the exo transition structure 6.360. The frontier orbitals have a repulsive interaction (wavy lines) between C-3, C-4 on the tropone and C-2 on the diene (and between C-5 and C-6 on the tropone and C3 on the diene) in the endo transition structure 6.361. However, in this reaction the exo adduct is thermodynamically favoured, the normal repulsion between filled orbitals in the endo transition structure is an adequate explanation, and the electrostatic explanation given in Section 6.5.2.4 works just as well. There is no real need to invoke secondary orbital interactions. LUMO 3

O

O

4

2 3

6.360

HOMO 6.361

6.5.4.2 Diyl Cycloadditions. Trimethylenemethane is a reactive intermediate, usually drawn as a diradical 6.362, which can exist in singlet and triplet states. The triplet shows the properties of a radical, but the singlet is better thought of as a cross-conjugated system of four p orbitals which can participate in pericyclic reactions. The p molecular orbitals of trimethylenemethane in Fig. 6.50 are 1, bonding across the whole system, then higher in energy a formally degenerate, nonbonding pair 2 and 3, and finally a fully antibonding combination 4*. If the degeneracy can be lifted, one of the middle pair will be the HOMO and the other the LUMO. For example, the singlet trimethylenemethane 6.365 can be produced by heating the strained bicyclic hydrocarbon 6.363 or the diazene 6.364, or by photolysis of the latter. It dimerises to give a mixture of at least three hydrocarbons out of the eight possible, of which one stereoisomer of the fused-bridged product 6.366 is the major. The exocyclic methylene carbon is the unique carbon, and can be assigned to be the one with the large coefficient in 2 and a zero coefficient in 3. The experimental result can then be explained if the former is the HOMO and the latter the LUMO.873

6 THERMAL PERICYCLIC REACTIONS

339

4*

2

3

6.362 1

Fig. 6.50

The p molecular orbitals of trimethylenemethane

heat

LUMO

6.363 h or heat

6.365

H

HOMO

N

6.366

N 6.364

When the same intermediate is generated in methyl acrylate, only the four possible fused products 6.367 are formed, and no bridged products. This regioselectivity corresponds to that expected if 2 is the HOMO.

CO2Me

6.365

LUMO

CO2Me

HOMO

CO2Me

6.367

The same reaction in cyclopentadiene gives a mixture of two of the fused products 6.368 and a single bridged product 6.369. The fused products are similar to those from the reaction with acrylate, and the bridged product is allowed, whether one takes the frontier orbitals as HOMO(trimethylenemethane)/ LUMO(cyclopentadiene) or the other way round as illustrated. One hint that the other way round is important is the endo-like selectivity, which might follow from the secondary interaction shown as dashed lines.873,874

340

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

HOMO

LUMO

+

and 6.365 6.368

6.369

LUMO

HOMO

The oxyallyl system, another reactive intermediate usually written with two charges 6.370 instead of as a diradical, has a similar conjugated system, except that the coefficients will be different, and the central carbon atom, although close to a node in 2 and 3, will not have a node exactly through it. When generated on its own, it dimerises with different regioselectivity from trimethylenemethane, giving the 1,4-dioxan 6.371.875 LUMO

HOMO

O O

Cr(II) R=Me

O O

O

O

O

6.370 O Br R

6.371

LUMO

HOMO

Br R O

HOMO

LUMO O

O O

Cr(II) and R=H 6.372 6.373 HOMO

LUMO

This looks as though each of the C—C bonds is independently the result of both HOMO/LUMO interactions, with an endo selectivity as well. In the presence of dienes, these species behave as allyl cations (see p. 259) and undergo clean [4 þ 2] cycloadditions, as in the reaction of the oxyallyl 6.372 giving the tricyclic ketone 6.373, which is similar to the diene 6.369. Normally, oxyallyls are in equilibrium by disrotatory electrocyclic ring closures with cyclopropanones and with allene oxides, but the presence of the five-membered ring in these particular examples makes these pathways counter-thermodynamic. 6.5.4.3 Ketene Cycloadditions As we saw in Section 6.3.2.7, ketenes undergo cycloadditions to double bonds 6.149 (repeated below) to give cyclobutanones. In practice, the reaction is faster and cleaner when the ketene has electron-withdrawing groups on it, as in dichloroketene, and when the alkene is relatively electron-rich, as in cyclopentadiene. The product from this pair of reagents is the cyclobutanone 6.374.876

6 THERMAL PERICYCLIC REACTIONS

341

2a 2a

O

O

O + Cl

Cl Cl

2s

Cl

6.374

6.149

Already we can see that the effects of substituents on rate follow the same pattern as in the Diels-Alder reaction, and we can explain them in the same way, using the interaction between the LUMO of the ketene and the HOMO of the ketenophile. The conjugation of the C—Cl bonds with the carbonyl group of the ketene will lower, by negative hyperconjugation, the energy of the LUMO, which is more or less p*CO. A C- or Xsubstituent on the alkene will raise the energy of its HOMO, and the energy separation between the frontier orbitals is reduced. This interaction contributes to the bonding represented by the left-hand bold line in the transition structure 6.149. The other pair of frontier orbitals may also be important. The HOMO of the ketene is more or less the p-bonding orbital of the C¼C double bond conjugated to the lone pair on the oxygen atom, which is an X-substituent raising its energy. The LUMO of the ketenophile will be lowered by the Csubstituent, and this frontier orbital interaction may also contribute to the bonding represented by the righthand bold line in the transition structure 6.149. The orbital contribution from a lone pair is not present in keteniminium ions, which are highly reactive in cycloadditions to alkenes and show similar regioselectivity.877 The energies and coefficients of the frontier orbitals of ketene are shown in Fig. 6.51.878 The regioselectivity in the reaction between cyclopentadiene and dichloroketene giving the cyclobutanone 6.374 is explained by the overlap from the large LUMO coefficient on the central atom of the ketene and the larger coefficient in the HOMO of the diene at C-1. Evidently this pair of frontier orbitals is the more important. The same regiochemistry is seen with a Z-substituted ketenophile 6.375 (actually a doubly vinylogous Z-substituted ketenophile),879 and with the X-substituted ketenophiles 6.376 and 6.377.880

3.8 O

LUMO

–12.4 HOMO

Fig. 6.51

O

Energies and coefficients of the frontier orbitals of ketene

A rather special case is presented by the reaction of ketenes with enamines, such as that between the enamine 6.378 and dimethylketene. This reaction between a strongly nucleophilic alkene and the inherently electrophilic ketene seems more likely to be stepwise than the other reactions of ketenes, with the regioselectivity largely determined by the formation of the well stabilised zwitterionic intermediate 6.379. The formation of this intermediate is also consistent with frontier orbital control, in that the atoms with the large coefficients in the HOMO of the enamine and the LUMO of the ketene are the first to become bonded. However, the interesting aspect of this reaction is that the ring closure to give the cyclobutanone 6.380 ought not to be easy because it would be 4-endo-trig at the enolate end (6.379 arrows) (see pp. 218–222). It may well be that this pathway, even though the

342

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

O

O Ph

Ph

6.375 O

+

Ph

O Ph

Ph O

O

O

+ O

Ph

Ph O

+ O

Ph

Ph Ph

OEt

6.376

Ph

Ph

EtO

Ph Ph

6.377

zwitterion 6.379 is formed, is sterile. There is in fact evidence that this reaction at least in part takes a concerted pathway directly to the cyclobutanone 6.380, in which case it is another obedient case of the regioselectivity shown by an X-substituted alkene with a ketene.881 O

O

O

? +

N

N

N 6.379

6.378

6.380

When the two substituents on the ketene are different, as in methylketene 6.381, the stereoselectivity is usually in favour of the product 6.382 with the larger substituent in the more hindered endo position.882 This follows from the approach 6.383, in which the ketene is tilted so that both bonds can develop simultaneously (dashed lines), and tilted in the direction with the larger substituent, the methyl group, up and away from the C¼C bond, and the smaller substituent, the hydrogen atom, tilted down towards the C¼C bond. As the bonds develop further, the methyl group moves down into the more hindered environment, but this must only become perceptible after the transition structure has been passed.726,883 O O

Me

H

O H

+

Me Me

H 6.381

6.382

98:2 6.383

The cycloaddition of ketenes to carbonyl compounds also shows the expected regioselectivity. In this case, both HOMO(ketone)/LUMO(ketene) and LUMO(ketone)/HOMO(ketene) interactions may be important, but they lead to the same conclusions about regioselectivity, with the carbonyl oxygen atom bonding to the carbonyl carbon atom of the ketene as in the reactions of the quinone 6.384 and formaldehyde

6 THERMAL PERICYCLIC REACTIONS

343

6.385.884 Lewis acid catalysis is commonly employed in this reaction; presumably the Lewis acid lowers the energy of the LUMO of the ketene (or that of the ketone) in the same way that it does with dienophiles (see pp. 318–319).885 O

O O

Ph

O

Ph Ph

O

+

O O

Ph H

O

O

ZnCl2

+ H

H

O

H

6.385

6.384

Ketenes also dimerise with ease, since they are carbonyl compounds, and the regiochemistry, whether it is forming a -lactone 6.386 or a 1,3-cyclobutanedione 6.387, is that expected from the frontier orbitals of Fig. 6.51.886 O

O

O O +

+

H H

O

O H

O

H

O

6.386

6.387

The reaction of the imine 6.388 with the ketene 6.389,887 one of many Staudinger reactions, is more plausibly stepwise. The imine is nucleophilic enough to attack a ketene carbonyl group directly from the lone pair on the nitrogen atom,888 just as the enamine 6.378 was probably nucleophilic enough to attack from the  carbon. In the case of the imine, however, the ring closure of the intermediate 6.390 to give the -lactam 6.391, even though it is 4-endo-trig at both ends, will not be difficult, because it is an electrocyclic reaction. Electrocyclic reactions do not seem to suffer unduly from the strictures of Baldwin’s rules (see p. 220). O

Ph

Ph N

Ph 6.388

Ph

O N

Ph

Ph 6.389

O N

Ph Ph Ph 6.390

Ph

Ph Ph 6.391

When the imine is ,-unsaturated, a [4 þ 2] cycloaddition is in competition with the -lactamforming reaction, but the latter usually wins.889 The imine 6.392 and methoxyketene give the intermediate 6.393 from attack anti to the methoxy group, and the conrotatory electrocyclic step then places the methoxy and the vinyl groups cis in the product 6.394. In this case the s-cis conformation 6.395 is easily accessible, making the disrotatory electrocyclic closure to a six-membered ring 6.396 a plausible alternative. That only the four-membered ring is formed is in fact because of the nature of the substituents at the termini, a methoxy group and a substituted vinyl group in this case. The methoxy group on the outside and the vinyl group on the inside in 6.393 leads to a

344

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

low energy transition structure, because the torquoselectivity (Section 6.5.7) is favourable for this arrangement. When the substituents are changed to those found in 2-chloro-2-methylketene, the two intermediates, also in rapid equilibrium, have more evenly balanced torquoselectivity forces at work in the two conformations of the intermediate, and both the four- and six-membered rings are formed.

O

Me

Me

N

Me

O N

H

O N

OMe

OMe

Ph

H OMe Ph

Ph 6.393

6.392

6.394

fast Me

O

O

N

N

OMe

OMe Ph

Ph 6.396

6.395

Site selectivity in ketene cycloadditions is also explained by the frontier orbitals. Diphenylketene reacts with isoprene 6.397 mostly at the more substituted double bond to give the cyclobutanone 6.398 as the major product.890 In contrast, it reacts with cis-piperylene 6.399891 and with cis-butadiene-l-nitrile 6.400890 at the less substituted double bond. In all three cases the site of attack is the double bond having the largest coefficient in the HOMO. O

O

O

–0.614

+ Ph

+

–0.420

Ph

0.506

Ph Ph

0.348

6.397 HOMO O

Ph Ph 70:30

6.398 O

O

O

–0.534

+ Ph

Ph

+

–0.350

CN

CN

0.531 0.456

6.399 HOMO

Ph Ph

Ph

Ph Ph

Ph 6.400

In the [p8þp2] cycloaddition of the bromoketene 6.402 to the pyridinium betaine 6.401 giving the lactone 6.403, the oxygen atom has the highest coefficient in the HOMO, and the next highest is the pyridinium 2position, which is the other site of attack when the group R is not large.892

6 THERMAL PERICYCLIC REACTIONS

0.32

O

345

–0.67

HOMO

O

O

O

–HBr

O

+

O

0.55

N

N

Br Ar

R 6.401

HBr

R

6.402

N

Ar

R

Ar

6.403

6.5.4.4 Allene Cycloadditions. As we saw in Section 6.3.2.7, allenes undergo cycloadditions similar to those of ketenes, except that allenes react faster if they have X-substituents and the alkene has Z-substituents. The HOMO and LUMO of allenes are higher in energy than those of ketene, and they are polarised with larger coefficients on the terminal atoms in the degenerate HOMOs (Fig. 6.52).893 The degenerate LUMOs are essentially unpolarised.

0.77 –0.78

–0.78

0.77

8.7 LUMO

–8.8 HOMO 0.66

Fig. 6.52

0.56

0.56 0.66

Energies and coefficients of the frontier orbitals of allene

The regiochemistry of the cycloadditions of allenes is not easily explained by these frontier orbitals. Penta2,3-diene and acrylonitrile give the adducts Z- and E-6.404 in which the central carbon of the allene, with the smaller HOMO coefficient, has bonded to the  carbon of the Z-substituted alkene.894 Equally unexplained is the regiochemistry of the reaction between allene itself and diazomethane, which gives more of the adduct 6.405 than of its regioisomer 6.406.893 2

H

4

+

+

H NC Z-6.404

NC

+

N

NC E-6.404

+

N

N

N N

N 6.405

97:3

6.406

Energetically this reaction can be expected to be dipole-HO-controlled (ELUMO – EHOMO ¼ 15.5 eV), but this should have little regiocontrol since the LUMO of the allene is so little polarised. The LUMO(dipole)/ HOMO(allene) interaction (ELUMO – EHOMO ¼ 16.75 eV) might come into play, since the allene HOMO is polarised, but the orbitals do not match up to explain the high level of regioselectivity, since the larger ‘coefficient’ in the LUMO of diazomethane is on carbon. Finally, the hydroboration of allenes gives mainly the product with the boron on the central carbon 6.407.895 With boron as the electrophilic atom, frontier

346

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

orbitals ought to have directed it to the terminal carbon. It is possible that steric effects play a major part. Steric effects are manifestly important when enantiomerically enriched penta-2,3-diene is used in the reaction with acrylonitrile—both adducts 6.404 have the absolute configuration corresponding to attack on the allene from the lower surface, as drawn, approaching C-2 from the opposite side from the methyl group on C-4.

H + H

BH2

H

BH2 6.407

Similarly, in the Diels-Alder reaction between 1,1-dimethylallene and tetracyclone 6.200 giving the product 6.408 which loses carbon monoxide to give the triene 6.409, attack has taken place on the double bond carrying the methyl groups, but orthogonal to them 6.410, avoiding the steric clash which would have taken place had it attacked the less substituted double bond 6.411.896 However, this result may be an anomaly, perhaps because phencyclone is so large, because maleic and fumaric esters predominantly attack the lesssubstituted double bond in [2 þ 2] reactions (see p. 282).

Ph

O Ph

O Ph

Ph

Ph

Ph

Ph

Ph Ph Ph

Ph 6.200

Ph 6.408

phencyclone

6.409 phencyclone

H

Me

Me Me

H H H 6.410

Me 6.411

This raises the question of the direction of twist in the methylene group not undergoing attack, and for that we need to return to the picture 6.150 on p. 282. A revealing reaction is the dimerisation of buta-1,2-diene 6.412.897 The stereochemistry in the major product 6.414 is comfortably accounted for using the [p2sþp2sþp2s] picture, with the [p2s] component at the bottom in 6.413 approaching the upper allene from the side opposite to the methyl group on C-3 (bold lines), but with its own methyl group orthogonal, just as the two methyl groups were in the Diels-Alder reaction 6.410. The direction of rotation at C-3, determined by the dashed curve, brings the methyl group towards the viewer, and into the inside position of the diene in the product making it a Z-alkene.725 The corresponding product with the E-double bond will be lower in energy, yet it is a relatively minor product (18%). The direction of rotation at C-1 in the lower component will be conrotatory, but that is not detectable in this isomer. The next most abundant product is that from the reaction 6.415 ! 6.416 in which both methyl groups are orthogonal to the bonds forming at C-3. The C-3 atoms will approach each other to minimise steric interactions by having the methyl groups mutually in the sectors between the hydrogen and methyl groups, which leads to the trans arrangement of the methyl groups in the product 6.417.

6 THERMAL PERICYCLIC REACTIONS

Me

1

347

Me 3

H H

3

H

H H

Me

H

Me

Me Me

H

1

H

6.412 H

Me

3

H H

Me

6.414 37%

6.413

H

3

Me H

Me

Me Me

H

6.415

6.417 25% 6.416

The picture of allene cycloadditions as [p2sþp2sþp2s] reactions is by no means proved but it does provide an explanation for most of the puzzles in these remarkable reactions. 6.5.4.5 Carbene Cycloadditions. Carbene and carbenoid cycloadditions show substantial and orderly regioselectivity. The carbenoid Simmons-Smith reaction with isoprene (6.418 þ 6.397) takes place on the double bond with the highest coefficient in the HOMO.898 Dichlorocarbene, an electrophilic carbene, reacts at the terminal double bond of cycloheptatriene 6.419,899 and at the central double bond of heptafulvalene 6.420.900 In both cases the site of attack is the double bond having the largest coefficient in the HOMO. In the former, the Sc2-values would lead one to predict attack at the central double bond [(0.4182 þ 0.4182) is a little larger than (0.5212 þ 0.2322)], but it is likely that the asymmetry of carbene cycloadditions (see pp. 284 and 288) makes the single largest coefficient disproportionately important.

–0.614

IZn

I

+

+

+

–0.420

0.506 0.348

6.418 6.397

0.521

0.521

Cl2C: +

Cl

0.232Cl

0.232

–0.418 –0.418

6.419

64:32:4

HOMO

0.253

Cl2C: +

–0.300 –0.199 –0.199–0.300 0.253 0.336

0.253 –0.300

Cl

Cl

0.336

0.253 –0.199 –0.199 –0.300

6.420

Nucleophilic carbenes, which might show a different site selectivity, rarely undergo cycloadditions (see p. 199), but methoxychlorocarbene adds to the exocyclic double bond of 6,6-dimethylfulvene 6.422, to give the cyclopropane 6.421, whereas dichlorocarbene adds to one of the ring double bonds to give the cyclopropane 6.423. These match the sites with the largest coefficients in the LUMO and HOMO, respectively.901

348

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

OMe Cl

MeOClC:

0.72

0

–0.27

0

–0.42

–0.42

0.35

6.421

LUMO

–0.56

0.56

–0.38

0.35

Cl2C:

6.422

Cl

0.38

6.423

HOMO

Cl

6.5.4.6 Epoxidations and Related Cycloadditions. The so-called K-region of polycyclic hydrocarbons is implicated in the carcinogenicity of these compounds. It is believed that these hydrocarbons are epoxidised at a site called the K-region; for example the benzanthracene 6.424 gives the epoxide 6.425, which is then an electrophilic species capable of alkylating the pyrimidines and purines of nucleic acids. On the whole, but only very approximately, the more nucleophilic the K-region (i.e. the larger the coefficients and the higher the energy of the HOMO), the more carcinogenic the hydrocarbons prove to be, presumably at least partly because they are epoxidised more readily. Epoxidation is like a cycloaddition, in that the new bonds to the oxygen atom are formed simultaneously from each of the carbon atoms. In cycloaddition reactions in general, in which both bonds are being made to more or less the same extent in the transition structure, the highest single coefficient is not the most important, as it was in the less symmetrical reactions of carbenes. Instead, it is the highest adjacent pair of coefficients, which is often found in the K-region. Thus if benzanthracene 6.424 is to take part in a cycloaddition in which it provides the 2-electron component, a high value of Sc2 is found in the K-region. (0.2982 þ 0.2882 is larger than 0.1942 þ 0.3242 or any other sum of adjacent coefficients not involving the angular carbons; reaction at the angular carbon atoms presumably involves the loss of too much conjugation.) This is also the site of attack by osmium tetroxide,902 which probably reacts in a cyclic process to give the ester 6.426 as an intermediate, and it is also the site of attack by ethoxycarbonylcarbene, derived from diazoacetic ester, giving the cyclopropane 6.427.903

biological oxidation O HOMO coefficients

0.203

–0.003 –0.301

0.393

0.095 –0.204

–0.236

–0.100

0.078

0.194

–0.047

–0.154

0.324

–0.445

6.425

–0.160 –0.167

OsO4

0.288

0.298

K-region 6.424

O O OsO2 6.426

:CHCO2Et

6.427

CO2Et

6 THERMAL PERICYCLIC REACTIONS

349

The same idea accounts for the site selectivity in the reactions of the carcinogenic hydrocarbons 6.428 and 6.429, both of which react with osmium tetroxide in the K-region. The contrast is with the behaviour of these hydrocarbons with other oxidising agents, like lead tetraacetate, chromic acid and sulfuryl chloride, which react only at one site at a time: none of the hydrocarbons 6.424, 6.428 or 6.429 reacts in the K-region with these reagents.904 Instead, reaction takes place at the site with the highest single coefficient in the HOMO, just as we would expect for an electrophilic substitution (see p. 174).

0

–0.054

–0.368

0.368

–0.164

0.164

0.296

–0.340

–0.296

K-region 0.296

–0.296

–0.164

0.164

–0.368

OsO4 :CHCO2Et O3

0.320

0.294

–0.275

0.180

–0.275

K-region

0.368 0

OsO4

0.434

CrO3 SO2Cl2

0.175 0.235

–0.268 –0.088

6.428

6.429

CrO3 SO2Cl2 Pb(OAc)4

6.5.5 Other Pericyclic Reactions It is more difficult to explain the effect of substituents on the rates, and on the regio- and stereoselectivities of the unimolecular pericyclic reactions. We cannot strictly look at the HOMO and LUMO of each component, as we could with bimolecular reactions, and therefore cannot properly use frontier orbitals to explain the effects of electron-donating and electron-withdrawing substituents on the rates.905 The effects are profound, sometimes even strong enough to override the WoodwardHoffmann rules.906 6.5.5.1 [3,3]-Sigmatropic Rearrangements. Cope and Claisen rearrangements may take place with a chair-like transition structure, chair-6.125 (see p. 276), or with a boat-like transition structure, boat6.125, both of which are allowed. The stereoselectivities like those seen in the Ireland-Claisen rearrangements 6.106 ! 6.107 (see p. 269) show that, other things being equal, the chair-like transition structure is favoured. Doering had elegantly proved a few years earlier that the Cope rearrangement showed the same preference.907 However, when other things are not equal, a boat-like transition structure 6.108 is easily adopted. We cannot strictly define the secondary orbital interactions that might explain the preference for the chair-like transition structure, which may simply be a steric effect. Nevertheless, we can pretend to, and it works. The orbitals can be divided artificially into two groups: one is an isolated p bond (between C-20 and C-30 ) and the other a p bond conjugated to a  bond (C-10 , C-1, C-2 and C-3). If we ignore the fact that they are connected, we can assign to the former the role of LUMO and to the latter the role of the HOMO (with a node between the p and the  bond, just as there is between the two p bonds in the HOMO of butadiene). While the primary interaction between the lobes on C-3 and C-30 is bonding in both conformations 6.430 and 6.431, the secondary interaction between the atoms on C2 and C-20 in the boatlike conformation 6.431 is out of phase, and the repulsion should make the chair even more favourable than it already was from the normal steric repulsion between the filled orbitals. This is not convincing, but it illustrates how far we can extend, some would say distort, frontier orbital theory if we have a mind to.

350

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

2

1

1

2

3

3 1'

3'

antibonding

1' 3'

2'

2'

6.431

6.430

There are however, important substituent effects that do need explaining. The most striking example of a rate acceleration in an allowed reaction is that of an anionic substituent on the periphery of a [3,3]-sigmatropic rearrangement. The bold lines in the drawings of the dienes 6.432 and 6.435 identify the 1,5-hexadiene systems undergoing Cope rearrangements, and the bold lines in the drawings of the first-formed products 6.433 and 6.436 identify the same six carbon atoms. The extraordinary feature of the first reaction is that the oxyanion substituent in 6.432 increases the rate enormously relative to the corresponding reactions without the oxyanion substituent.908 The rate is increased even further when the potassium counterion is completely removed from the oxygen atom by 18-crown-6, and yet more again in the gas phase.909,910 Similarly, in the second reaction, although the tosylate 6.434 is a stable compound, with the Cope rearrangement taking place only at 140 °C, the cation 6.435 derived from it by solvolysis rearranges rapidly at 95 °C to give the cation 6.436.37,911 The effect is even more dramatic when a related iodide is treated with silver ion, when the cation rearranges at –15 °C. In each case, a charged substituent attached to the periphery of the rearranging system dramatically increases the rate. H OM MeO

OM

≡ MeO

MeO

6.432

OM

H

M

k rel

H K K + 18-C-6

1 1012 1017

6.433

TsO ≡

6.434

6.435

6.436

The oxyanion —OM in 6.432 is an X-substituent, and the carbocation in 6.435 is a Z-substituent (but without having any double bond character in the way that a carbonyl group does). Any explanation of the substituent effect must be able to encompass this change from a strong electron donor to a strong electron withdrawer. One approach to explaining the substituent effect has been suggested by Carpenter.912 It uses simple Hu¨ckel molecular orbitals, and avoids the need to rely on frontier orbitals. The basis of the idea is to return to the picture of a pericyclic transition structure as having aromatic character (see p. 286). Let us use the Cope rearrangements as an example, for which the starting material has two independent p bonds, and the transition structure, with six electrons in motion, has some of the character of a benzene ring. To provide a baseline from which to compare the substituted system, we first compute the p energy of the unsubstituted starting material on the left in Fig. 6.53a and the fully aromatic version of the corresponding transition structure on the right. The starting material will have the p energy of two independent p bonds,

6 THERMAL PERICYCLIC REACTIONS

351 2 3

1

–4.00

(a) Unsubstituted 4

8

–4.72

(b) Substituted by X- or 'Z'-substituent 4

8.72

–4.43

(c) Substituted by C-substituent 6

Fig. 6.53

10.43

p-Energy changes for a Cope rearrangement with a substituent on C-3

each doubly occupied, 4 below the  level (Figs. 1.31 and 1.33), and the transition structure will have the p energy of benzene, 8 below the  level (Fig. 1.44). If there is an anionic substituent on C-3, the starting material in Fig. 6.53b, will still have the p energy of two independent p bonds, 4 below the  level, but the aromatic version of the transition structure will have the p energy of a benzyl anion, 8.72 below the  level (Fig. 4.9). The presence of the substituent lowers the energy barrier between the starting material and the transition structure by 0.72 relative to the unsubstituted case. As it happens, the p energy of a benzyl cation is the same as the benzyl anion, because the highest of the orbitals in the anion is on the  level, and makes no contribution to the p energy. The calculation for having a cationic substituent is therefore the same as for the anionic substituent. An empty orbital is a crude model for the usual Z-substituents, although it was appropriate for the cation 6.435, so we ought to do the comparison again with a vinyl group as a model for a C-substituent, and we can then guess that the usual Z-substituents will have an effect somewhere in between the two. The starting material in Fig. 6.53c has three independent p bonds, 6 below the  level, and the transition structure is modelled by styrene, 10.43 below the  level. The difference therefore is 0.43 relative to the unsubstituted case, not quite as effective as an isolated p orbital, whether filled or empty. A substituent on C-2 will have a different effect. The unsubstituted system is the same as in Fig. 6.53a, and the empty or filled p orbital will again be equally effective, as shown in Fig. 6.54a. The starting material will have p energy of one isolated p bond, 2 below the  level and one allyl system, 2.83 below the  level, making a total of 4.83. The transition structure will be modelled by a benzyl system, 8.72 below the  level, and the overall stabilisation is 3.89, which is less than the change of 4 seen in the unsubstituted case. A donor or withdrawing substituent on C-2 might therefore be expected to slow the rearrangement down. The corresponding calculation for a C-substituent in Fig. 6.54b makes it 0.06 less than the unsubstituted case, and so it ought to be rather less rate-retarding. In practice a phenyl substituent on this position is mildly rate accelerating,913 but this has been explained as a substituent stabilising a transition structure with radical character on C-2. The main point to be seen here is the dramatically greater effectiveness of a substituent on C-3 than on C-2. Claisen rearrangements are in general faster than the corresponding Cope rearrangements, and this has been explained using frontier orbitals, by counting the oxygen atom as a substituent on the sigmatropic rearrangement divided into two arbitrary parts in the same way as we saw on pp. 349 and 350 in explaining the preference for a chair transition structure in the Cope rearrangement.914 The experimentally observed effect of donor and withdrawing substituents on Claisen rearrangements are summarised in 6.437 and 6.438.

352

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

(a) Substituted by X- or 'Z'-substituent

–3.89 4.83

8.72

(b) Substituted by C-substituent

–3.96 6.47

Fig. 6.54

10.43

p-Energy changes for a Cope rearrangement with a substituent on C-2

Claisen rearrangements introduce the complication of oxygen lone pairs within the rearranging system, rather than as substituents on the perimeter. They may be ignored and the transition structure treated as benzene-like, or they may interrupt the conjugation, and the transition structure is then like a heptatrienyl anion.915 Predictions based on the simple theory above, whichever of these models is taken, match most of the substituent effects, and more elaborate treatments with calculations account for the anomalous accelerating effect of a donor substituent at C-6.916 faster

X

O

2

4 5

faster faster

1 6

faster

Z faster

slower 6.437

O

slower

2

4 5

1 6

faster

slower faster 6.438

This simple way of explaining substituent effects is effective, and even gives quite good quantitative correlations for electrocyclic reactions and sigmatropic rearrangements.917 It can also be applied to cycloadditions, although the latter are usually explained by the frontier orbitals discussed in Section 6.5.3. The same is true for Cope rearrangements in general, which can be accounted for by accepting the chameleon-like918 nature of substituents.919 Most substituents at C-1 and C-3 accelerate the reaction, and with more than one of them, their effects are cooperative. Substituents at C-2, however, shift the balance of the transition structure towards a biradical-like intermediate in which the new  bond is formed ahead of the old one breaking. Substituent effects at this site are not cooperative with substituent effects at C-1 and C-3, because they change the nature of the transition structure rather than contribute to it in the same way. Some substituents, like an amide ion at C-3920 and a thio group at C-6,921 can tip the reaction close to or actually into being stepwise ionic or stepwise radical. 6.5.5.2 [1, n]-Sigmatropic Rearrangements. [1,5]-Sigmatropic shifts have another kind of selectivity— the migratory aptitude of the groups that are migrating. It is clear that hydrogen migrates exceptionally easily, as we have seen in cyclopentadienes; carbon groups are more reluctant. The ease with which hydrogen atoms migrate is easily understandable—it is related to the ease with which their bonds to electronegative heteroatoms are made and broken in acid-base chemistry. At the extreme, a proton in between two fluoride ions is in the transition structure for the transfer from one to the other. Thus hydrogen

6 THERMAL PERICYCLIC REACTIONS

353

bonding (see pp. 118–121) is a paradigm for the exceptional properties of hydrogen, and, although much stronger when the hydrogen atom sits between electronegative atoms, it is not restricted to them. Another factor is the relative ease with which bonding can develop in any direction towards an s orbital. Carbon atoms, with bonding made from s and p orbitals has much stricter limits on the direction from which a bond can be made. In [1,5]-sigmatropic rearrangements, hydrogen does not have to obey the constraints of retention or inversion, but can lean over towards the carbon atom it is bonding to, and start to form a bond (Fig. 6.12, top). Likewise with antarafacial [1,7]-sigmatropic rearrangements, their is no difficulty for the hydrogen atom moving from the top surface at one end to the bottom surface at the other (Fig. 6.12, bottom), to develop overlap so that it sits half way between, making a nearly linear connection between the two ends. When a migrating group R is based on carbon they vary in their willingness to migrate, and there appears to be some correlation to the LUMO energy of the migrating group, with vinyl migrating faster than alkyl, and acyl faster than vinyl.922 Clearly a double bond allows overlap to develop to the p orbitals, before the  bond breaks, in a way that an alkyl group cannot. Similarly, a boryl group, with an empty p orbital orthogonal to the migrating  bond, can undergo suprafacial [1,7]shifts, formally forbidden, but made possible by the new  bond forming before the old one has broken. 923 In the most simple of sigmatropic carbon shifts, the [1,2]-shift in a carbocation, or the related Beckmann, Curtius and Baeyer-Villiger reactions, major factors are the capacity of the migrating carbon to carry partial positive charge, together with the capacity of the carbon atom from which it is migrating to take up the developing positive charge—the [1,2]-shift is accelerated when either or both are capable of supporting an electron deficiency, because both are electron deficient in the transition structure 6.439 with two half-formed bonds. However, other things being equal, phenyl and vinyl groups migrate more easily than alkyl, even though phenyl and vinyl are less stabilised cations than alkyl. They do so by participation in a stepwise event—the new bond forms from the empty p orbital to the p bond to give a cyclopropylmethyl cation 6.440 with two full bonds, which then breaks the old bond to give the product. When the overlap creating the  bond in the intermediate 6.440 is geometrically impossible, phenyl and vinyl groups are much slower to migrate than alkyl, because they do not easily support positive charge. R

R

R

6.439

6.440

For example, the oxime tosylate 6.441, in which an alkyl group, the bridgehead, migrates, undergoes Beckmann rearrangement rapidly when warmed above room temperature in ethanol; in contrast, the isomer 6.442 can be distilled at 200°C largely unchanged.924 In this case, the rigidity of the bicyclic system prevents the vinyl group from bonding in the sense 6.440—the p orbitals are orthogonal to the  bond between the nitrogen atom and the tosylate group, directly behind which the new bond must start to form.

354

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

200 °C

r.t. EtOH

HN

N 6.441

N

O

OTs

N H

O

TsO 6.442

6.5.5.3 Electrocyclic Reactions. The benzocyclobutyl oxide 6.443 is a reactive intermediate obtained by trapping benzyne with the lithium enolate of acetaldehyde. It opens rapidly, even at 0 °C, to give the diene 6.444, which is trapped in situ by another molecule of benzyne to give the anthracene hydrate 6.445, and hence anthracene itself.925 In contrast, a benzcyclobutene 6.446 without the benefit of the oxyanion substituent has to be heated in refluxing decane (bp 174 °C) for 30 h before it gives the aromatic product 6.448 by an intramolecular Diels-Alder reaction,926 and there is evidence that it is the ring opening 6.446 ! 6.447 that is rate-determining, not the intramolecular Diels-Alder reaction 6.447 ! 6.448.927 O O

O

0 °C

6.443

6.444

O

6.445 O

O

174 °C

6.446

6.447

6.448

To explain the increase in the rate of an electrocyclic ring opening like 6.443 ! 6.444, we need to remember that the conrotatory pathway will have a Mo¨bius-like aromatic transition structure, not the antiaromatic Hu¨ckel cyclobutadiene that we saw in Fig. 1.46. We have not seen the energies for this system expressed in  terms, nor can we do it easily here, but the numbers are in Fig. 6.55, where we can see that a donor, a withdrawing group, and a C-substituent on C-3 can each accelerate the reaction—the numbers on the right, 4.29 and 4.06, are more negative than for the unsubstituted system, 3.66. 2

3

–3.66

(a) Unsubstituted 1

2

5.66

(b) Substituted by X- or 'Z'-substituent

–4.29 2

6.29

(c) Substituted by C-substituent

–4.06 4

Fig. 6.55

8.06

p-Energy changes for a conrotatory cyclobutene opening with a substituent on C-3

6 THERMAL PERICYCLIC REACTIONS

355

6.5.5.4 Alder ‘Ene’ Reactions. Like the Diels-Alder reaction, Alder ‘ene’ reactions usually take place only when the enophile has a Z-substituent, the regiochemistry is that expected from the interaction of the HOMO of the ‘ene’ and the LUMO of the enophile, and Lewis acids increase the rate. All these points can be seen in the reaction of -pinene 6.449 with the moderately activated enophile methyl acrylate, which takes place at room temperature in the presence of aluminium chloride,928 but which would not have taken place easily without the Lewis acid. The lowering of the LUMO energy of the methyl acrylate accounts for the increase in the rate of reaction. Similarly, the rates of diimide reductions of alkenes show some correlation with ionisation potential and hence orbital properties.929 LUMO CO2Me HOMO

CO2Me

AlCl3

H

6.449

6.5.6 Periselectivity Periselectivity is a special kind of site-selectivity. When a conjugated system enters into a pericyclic reaction, a cycloaddition for example, the whole of the conjugated array of electrons may be mobilised, or a large part of it, or only a small part of it. The Woodward-Hoffmann rules limit the total number of electrons (to 6, 10, 14, etc., in all-suprafacial reactions, for example), but they do not tell us which of 6, 10 or 14 electrons would be preferred if they were all geometrically feasible. Thus in the [4 þ 6] reaction of cyclopentadiene with tropone 6.45 ! 6.46,686,930 there is a possibility of a Diels-Alder reaction, leading to the [2 þ 4] adduct 6.450 (Fig. 6.56). The products 6.46 and 6.450 are probably not thermodynamically much different in energy, so that will not be a compelling argument to account for this example of periselectivity, although it may be a factor.

HOMO

HOMO –0.371

0.371

–0.600

O

0.600

–0.371

0.371

–0.600

0.600

O

O –0.232 –0.521 0.232

O –0.521

0.418

–0.232

6.46

–0.418

0.418

0.521

–0.418

0.521

0.232

6.450

LUMO

LUMO (a) [4+6] Favoured path

Fig. 6.56

(b) [2+4] Less-f avoured path

Frontier orbitals of cyclopentadiene and tropone

The frontier orbitals, however, are clearly set up to make the longer conjugated system of the tropone more reactive than the shorter. The coefficients of the frontier orbitals of tropone were given in Fig. 6.33. The largest coefficients of the LUMO of tropone are at C-2 and C-7 (Fig. 6.56a), with the result that bonding to these sites lowers the energy more than bonding to C-2 and C-3 (Fig. 6.56b), when this frontier orbital is the

356

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

more important, as it usually is. In general, the ends of conjugated systems carry the largest coefficients in both frontier orbitals, and we can therefore expect pericyclic reactions to use the longest part of a conjugated system compatible with the Woodward-Hoffmann rules, regardless of which frontier orbital is the more important. This proves to be true up to a point, with the important qualification that the reactions have also to be geometrically reasonable. Some examples of this pattern come from the cycloadditions of heptafulvene 6.451 and hexatriene 6.452,931 from electrocyclic reactions of an octatetraene 6.453 and a heptatrienyl anion 6.454,932 and from a sigmatropic rearrangement of a pentadienyl phenyl ether 6.455,933 to which we can add several reactions illustrated earlier: 6.42 þ 6.43 ! 6.44 to the cycloadditions, and 6.9 ! 6.10, 6.112 ! 6.113 and 6.114 ! 6.115 to the sigmatropic rearrangements. All these cases show the largest possible number of electrons being mobilised, when smaller, but equally allowed numbers might have been used instead.

CO2Me CO2Me

+

CO2Me

CO2Me 6.451

SO2

+ SO2

SO2 6.452

6.453

6.454 OH

O

OH

OH

[5,5] +

+

major 6.455 50%

7%

27%

However, carbenes react with dienes 6.457 to give vinylcyclopropanes 6.458, avoiding the symmetryallowed [2 þ 4] cycloaddition with a linear approach giving cyclopentenes 6.456. Almost the only exceptions to this pattern are the reaction of difluorocarbene with norbornadiene, where a [2 þ 2 þ 2] reaction is in competition with the [2 þ 2],934 and the [2 þ 4] pathway taking place in the opposite direction in the easy loss of carbon monoxide from strained cyclopentenones as in the decarbonylation 6.408 ! 6.409.

6 THERMAL PERICYCLIC REACTIONS

357

Cl Cl :CCl2

:CCl2

Cl Cl 6.456

s-cis-6.457

6.458

s-tr ans-6.457

We have seen that the cyclopropane-forming reaction is allowed when it uses a nonlinear approach 6.161, but we need to consider why the nonlinear approach is preferred when the linear approach giving a cyclopentene could profit from overlap to the atomic orbitals with the two large coefficients at the ends of the diene. One factor which must be quite important is the low probability that the diene is in the s-cis conformation s-cis-6.457 necessary for overlap to develop simultaneously at both ends. Since the cyclopropane-forming reaction can take place in any conformation, it goes ahead without waiting for the diene to change from the s-trans-6.457 to the s-cis conformation. Cyclic dienes like cyclopentadiene, fixed in an s-cis conformation, also react to give cyclopropanes, probably because the alternative would create a strained bicyclo[2.1.1]hexene ring system. Cyclic dienes in larger rings also form the cyclopropanes, but they have the two ends of the diene held so far apart that they cannot easily be reached from the one carbon atom of the carbene. All these factors may be enough to account for the periselectivity leading to cyclopropanes, but it has been found from a calculation that even when the 1,4-addition is forced on the s-cis diene, there is an unexpected repulsion embedded in the transition structure, whereas the nonlinear approach of a carbene to an alkene meets virtually no barrier. The barrier in the linear approach can be ascribed to repulsion between the subjacent orbital NHOMO with the filled orbital of the carbene (Fig. 6.57a) counteracting the attractions from the frontier orbitals themselves (Fig. 6.57b and c).935

HOMO

LUMO

NHOMO

1

Fig. 6.57

*

HOMO

2

(a) Repulsion

HOMO

(b) Attraction

LUMO (c) Attraction

Frontier orbital interactions in the 1,4-addition of a carbene to an s-cis diene

Ketenes also seem to be avoiding the higher coefficients in their reactions with dienes. We have already seen on pp. 281 and 341 that they can undergo [2 þ 2] cycloadditions in an allowed manner giving adducts like 6.374, but we also have to account for why they do so, even when [2 þ 4] reactions are available. The [2 þ 4] reactions giving the adduct 6.459 or 6.460 would involve the higher coefficients in the HOMO of the diene, which seemingly ought to make these reactions faster. The reason why the C¼C double bond of a ketene does not react as the p2s component of a [p2sþp4s] reaction, giving the adduct 6.460, is that the orbital localised on the C¼C double bond is at right angles to the O O

O or Cl

Cl 6.459

Cl Cl 6.460

[2+4]

O

[2+2] + Cl

Cl

Cl 6.374

Cl

358

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

p orbitals of the C¼O double bond. Consequently, the C¼C p bond does not have a low-lying LUMO. Its LUMO is raised in energy by the conjugation with the lone pair on the oxygen atom, and it is not, therefore, a good dienophile. In the [2 þ 2] reaction, however, it is the LUMO of the C¼O p bond that is involved in forming the leading C—C bond, and this is low-lying in energy, especially as it is in this case conjugated to two C—Cl  bonds.936 The [4 þ 2] isomer in which the carbonyl group is the dienophile, giving the ether 6.459, is presumably unfavourable just as any other Diels-Alder with a carbonyl group is unfavourable (Section 6.5.2.3), but a [4 þ 2] cycloaddition of this type is known for diphenylketene, which gives the adduct 6.461 at low temperature. On warming, this adduct undergoes a [3,3] Claisen rearrangement to give what looks like a [2 þ 2] adduct 6.462. 1-Methoxybutadiene works the other way round, giving initially the [2 þ 2] adduct 6.463, which undergoes a [3,3] Claisen rearrangement to give what looks like a [4 þ 2] adduct 6.464.937 Periselectivity is evidently delicately balanced, and the direct [4 þ 2] pathway is probably seen only because cyclopentadiene is inherently in the s-cis conformation. The fact that the Claisen rearrangement interconverts the two isomers makes it possible that other apparent [4 þ 2] and [2 þ 2] reactions may actually be a consequence of rearrangements. O +

[4+2]

O

[3,3]

O

–20 °C

0 °C

Ph

Ph Ph

Ph Ph

Ph

6.461

MeO

6.462 OMe

MeO O

Ph [2+2]

Ph

+ Ph

O

[3,3]

Ph

Ph

0 °C

25 °C O

Ph 6.464

6.463

Another example where the longest possible conjugated system is not used is the dimerisation (see p. 320) of hexatriene 6.465, and of many similar compounds. This takes place in a Diels-Alder manner to give the cyclohexene 6.288, not only for the trans isomer but also for the cis, which might, in principle, have undergone a [4 þ 6] dimerisation to give the cyclodecatriene 6.466. Presumably the hexatriene is rarely in the right planar conformation to be a p6 component, even though this would be preferred on frontier orbital grounds. In open-chain and in some cyclic systems, therefore, reactions often take the path which uses the longest part of the conjugated system consistent with a symmetry-allowed reaction, but several other factors, spatial, entropic, steric, and so on, have obviously to be taken into account. Thus various sesquifulvalenes, with HOMO coefficients in the parent system 6.467, react in a variety of ways. The reaction giving the [8 þ 2] adduct 6.468 finds the sites with the highest Sc2 value, but the three reactions with tetracyanoethylene giving the adducts 6.469–6.471 show different selectivities, for no obvious reason. These examples serve to emphasise the pitfalls of a too easy application of frontier orbital theory.

–0.418

–0.418

–0.232

+ 0.521

HOMO

–0.521

+ 0.521

6.465

0.521

LUMO

6.288

0.521

HOMO 6.465

LUMO

6.466

6 THERMAL PERICYCLIC REACTIONS

359

–0.426 0.183

HOMO

0.531

NC

CN [8+2]

NC

CN

+

–0.064

CN CN

–0.284 –0.098

CN CN

0.228

6.467

6.468 Ph

Ph

Ph

Ph

Ph NC +

CN

NC

CN

[4+2]

Ph

Ph

Ph

CN CN CN CN 6.469

But H But

NC

CN

NC

CN But

But

CO2Me

But

CO2Me CO2Me

CN CN CN CN

[12+2]

CO2Me

But

[4+2]

H

6.470

6.471

More readily identifiable geometrical factors probably outweigh the contribution of the frontier orbitals in the remarkable reaction 6.47 between tetracyanoethylene and heptafulvalene giving the adduct 6.49 (see p. 261). The HOMO coefficients for heptafulvalene 6.420 (see p. 347) are highest at the central double bond, but a Diels-Alder reaction, with one bond forming at this site is impossible. The best reasonable possibility for a pericyclic cycloaddition, from the frontier orbital point of view, would be a Diels-Alder reaction across the 1,4-positions (HOMO coefficients of –0.199 and 0.253), but this evidently does not occur, probably because the carbon atoms are held too far apart. This is well-known to influence the rates of Diels-Alder reactions: cyclopentadiene reacts much faster than cyclohexadiene, which reacts much faster than cycloheptatriene (see p. 302). The only remaining reaction is at the site which actually has the lowest frontier-orbital electron population, the antarafacial reaction across the 1,10 -positions, which have HOMO coefficients of 0.199. Dimethylfulvene 6.422, which we have already seen on p. 348 showing different site selectivity in its reactions with electrophilic and nucleophilic carbenes, also shows a variety of different periselectivities in which the longest conjugated system available is not always the one involved in cycloadditions, but this time frontier orbital theory is rather successful in accounting for the experimental observations. The frontier orbital energies and coefficients are illustrated again in Fig. 6.58.938,939 The result of there being a node through C-l and C-6 in the HOMO is that when a relatively unsubstituted fulvene might react either as a p6 or as a p2 component with an electron-deficient (low-energy LUMO) diene or dipole, it should react as a p2 component because of the zero coefficient on C-6 in the HOMO. This is the usual reaction observed with electrophilic dienes like the nitrile 6.473, derived from the benzcyclobutene, and

360

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS 0

+2

0.72

–1 6

–0.42

1

–0.49

–0.42

0.35

5

NLUMO

–0.27

LUMO

0 0.49

0.74

–0.74

0.35

2 4

3

0

–8.6 6.422

HOMO

–0.56 –0.38

Fig. 6.58

–0.44

0 0.56

–9.5 NHMO

–0.54 –0.03

–0.03

0.38

0.40

0.40

Energies and coefficients of the frontier orbitals of 6,6-dimethylfulvene

dimethyldiphenylcyclopentadienone 6.474, and with dichloroketene 6.477 and electrophilic dipoles like benzonitrile oxide 6.478 giving adducts 6.472, 6.475, 6.476 and 6.479, respectively. 940–942 Ph O H

Ph

CN 6.473

Ph

6.474 CO

Ph

H CN 6.472

O

6.476

Cl Cl

6.475

O

Cl

Cl

6.422

O

N

Ph

Ph

O

6.478

NH +

6.477 39%

Ph

N 31%

O

6.479

Equally, when it reacts with tropone 6.480 as a p4 component, it does so at C-2 and C-5 to give the tricyclic ketone 6.481, because the coefficients in the HOMO are large at these two positions.943 O HOMO

LUMO + O

6.422

6.480 6.481

In contrast, if the important frontier orbital in the cycloaddition is the LUMO of the fulvene, and if the fulvene is to react as p2 or p6 component, it will now react as a p6 component, because the largest coefficients are on C-2 and C-6. For this to be feasible, its partner must have a high-energy HOMO, since it does not itself have a particularly low-energy LUMO. This pattern of periselectivity is found with the electron-rich diene

6 THERMAL PERICYCLIC REACTIONS

361

1.8 1

LUMO

LUMO

–1 LUMO

10.4

9.6

8.0

8.1 –8.6

–9

HOMO

HOMO

–9.1 HOMO

N N

Fig. 6.59

Frontier orbital interactions for dimethylfulvene, diazomethane and butadiene

6.483 and with diazomethane.944,945 The LU(fulvene)/HO(diazomethane) interaction is probably closer in energy than the HO(fulvene)/LU(diazomethane) (Fig. 6.59), and this explains the formation of the adduct 6.484. The regiochemistry is also appropriate for this pair of frontier orbitals. HOMO O N 6.483 O

N

N

N

[4+6]

[4+6]

H

NH

–H+

N

+H+

LUMO 6.482

6.422

6.484

Similarly, although reaction with a simple diene ought also to be dominated by the LU(fulvene)/HO(diene) interaction (Fig. 6.59), the observed product 6.485 from the reaction of dimethylfulvene with cyclopentadiene has the fulvene acting as a p2 component rather than as a p6 component.941 This anomaly has been explained by invoking the next-lowest unoccupied orbital (NLUMO) of fulvene (Fig. 6.58).938 This orbital has zero coefficients on C-l and C-6, and hence relatively large coefficients on C-2 and C-3. The interaction of this orbital with the HOMO of cyclopentadiene is apparently large enough to tip the balance in favour of the [2 þ 4] adduct 6.485. This result is in contrast to the result with the diene 6.483 having the higher energy HOMO, for which the interaction with the LUMO of the fulvene is proportionately greater than that with the NLUMO. The same change to a [4 þ 6] reaction is also seen with 1aminobutadienes, which also have higher level HOMOs.946 These examples come as another useful reminder that the frontier orbitals are not the only ones to be interacting as the reaction proceeds. They usually appear to be the most important orbitals but they can never be assumed to be decisive. 6 1 5

2 4

3

6.422

[2+4] 6.485

6-Dimethylaminofulvene 6.486 has a powerful X-substituent on C-6, raising the energy of the HOMO and losing the symmetry, so that the coefficient on C-6 is no longer zero and the coefficient on C-2 is raised. The

362

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

reaction with a Z-substituted diene 6.487 now leads to a mixture of regioisomers of the hydroazulenes 6.488, in both of which the new bonds are to C-2 and C-6 on the fulvene from C-1 and C-4 on the diene. The result was an expeditious synthesis of the azulenes 6.489.947 Me Me(Et) Me2N

Me(Et)

Me2N

O2S 6.487 Et

O2S

[4+6]

H

Et(Me) 6.488

6.486

Et(Me) 6.489

This section on periselectivity has been disproportionately long. It is one of those subjects which frontier orbital theory has rationalised reasonably well, for all its inherent limitations. It is a fitting close to this section to reflect upon the bewildering variety of cycloadditions shown by dimethylfulvene, and to reflect upon how difficult it would be to explain the pattern of their reactions without frontier orbital theory. 6.5.7 Torquoselectivity Torquoselectivity applies only to electrocyclic ring openings and closings, and refers to which of the two possible senses in which an electrocyclic ring opening can take place is the faster. In a conrotatory ring opening with a total of (4n) electrons, the two outer substituents R in the drawing 6.71 can follow each other to the right in a clockwise rotation, as illustrated in Fig 6.3, or they can follow each other to the left in an anticlockwise rotation. If the two groups R are the same, there is no difference in the energies, since the transition structures are enantiomeric. If they are different, there is a remarkable level of torquoselectivity determining which substituent shall turn up on the cis double bond and which on the trans. The observation is that X-substituents selectively move outwards to be on the trans double bond. The benzcyclobutene opening 6.443 ! 6.444 on p. 354 might have been put down to a purely steric effect, but torquoselectivity is not driven only by steric effects, for the more powerfully electron-donating the X-substituent is in the cyclobutenes 6.490, the stronger is the preference for the formation of trans-6.491.948 The activation energy for ring opening is lower when electron-donating substituents are rotating outwards than it is for the ring opening of cyclobutene itself, with a methyl group and an ethoxy group lowering the energy by 3.8 kJ mol1 (0.9 kcal mol1) and 38 kJ mol1 (9.0 kcal mol1), respectively. The activation energy for ring closing is similarly lower when there is a methoxy group in the outside position of a diene as we saw earlier when it determined the ease of the cyclisation of the intermediate 6.393 on p. 344. Furthermore, the activation energy for ring opening is raised if an electron-donating substituent is forced to rotate inwards. Dramatically, the better X-substituent moves outwards in the ring opening of the cyclobutene 6.492, even though this places the tert-butyl group in the more hindered position in the diene 6.493.949 R R heat

+

6.490

tr ans-6.491

R

cis-6.491 MeO

MeO heat

6.492

tr ans:cis R = EtO > AcO > Cl > Me

6.493

6 THERMAL PERICYCLIC REACTIONS

363

Even more remarkable, Z-substituents move inwards to be on a cis double bond. Examples are the formation of the cis,cis-diene 6.495, in which the trifluoromethyl groups have moved inwards from the trans-3,4-disubstituted cyclobutene 6.494,950 and the formation of the cis-butadienal 6.497 from the cyclobutene 6.496, in which the aldehyde group has moved inwards.951 Steric effects are not absent, since the corresponding methyl ketone 6.498, with a larger Z-substituent, gives the trans-butadienyl ketone trans6.499, but in the presence of Lewis acids, when coordination to the carbonyl group makes it into a more powerfully electron-withdrawing substituent, the ring opening gives the cis-butadienyl ketone cis-6.499 in spite of the fact that the substituent is larger when coordinated to the Lewis acid.952 F F

CF3 F

heat

F CF3

F

COMe

F

CF3

heat

CF3

F

COMe

F 6.495

6.494

trans-6.499

CHO heat

heat

CHO

COMe

6.498 Lewis acid 6.496

cis-6.497

cis-6.499

Houk has explained this pattern in two ways.953 The most simple is to note that the transition structure for conrotatory opening with a filled p orbital inside 6.500 has a three-atom, four-electron conjugated system (ignoring the electrons of the p bond for the moment), which will be antiaromatic, whereas an empty orbital inside 6.501 has a three-atom, two-electron conjugated system, which will be aromatic. His calculations indicate that there is very little involvement of the p orbitals of the p bond in the transition structure, but even if they are included, the conjugated system is then of the Mo¨bius kind and the systems are still antiaromatic and aromatic, respectively. Furthermore, an orbital outside, whether filled or unfilled, is becoming part of a longer conjugated system as the reaction proceeds, and this will lower the p energy. The net result is that there is a preference for X-substituents to rotate outwards, and a weaker preference for Z-substituents to rotate inwards, as observed. The formation of cis,cis stereochemistry in the perfluorohexa-2,4-diene 6.495 is driven more by the fluoro substituents on C-2 and C-5, which are p donors, moving outwards, than by the trifluoromethyl groups, which are p acceptors, moving inwards.

6.500

6.501

The second explanation is a more thorough dissection, which will only be summarised here, of what amounts to the same perception. The frontier orbitals of the transition structure for an unsubstituted cyclobutene undergoing conrotatory opening are approximately  and * in the centre of Fig. 6.60, related to the original  and * orbitals of the  bond, and having so little interaction with the p bond at the back that we can neglect that complication. The effect of the substituent can be estimated by looking at how a filled p orbital on oxygen will interact with these orbitals when it is held one bond away from the left-hand atom, either on the inside, on the left, or on the outside, on the right. In both cases, the interaction of the p orbital with  and * will have a bonding combination, largely resembling the original p orbital, but lowered in energy.

364

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS O

O

* O

O

O

Fig. 6.60

Orbital interactions in conrotatory opening of a 3-substituted cyclobutene

The interactions in an antibonding combination will create orbitals raised in energy. The difference between inside and outside is that, on the inside, on the left, there is an extra antibonding interaction, marked with a wavy line, with the atomic orbital of the more distant atom, raising the energy of  more than when the p orbital is on the outside, where that interaction is missing. In addition, the interaction with * is less antibonding on the left, because there is a small attraction, marked with a dashed line, which is absent on the right. These orbitals are empty, and have no direct effect on the energy of the transition structure, but these same interactions have consequences on the p orbital energy, which is pushed lower on the right just as * is pushed higher. The net result is that the overall energy of the filled orbitals is lower in the arrangement on the right than on the left. A trimethylsilyl group is a weak Z-substituent, because the Si—Me bonds are polarised away from silicon towards the carbon. Weak though its p electron-withdrawing properties are, the silyl group in the cyclobutene 6.502 moves predominantly inwards in spite of the steric crowding in the product cis-6.503. Furthermore, the presence of the silyl group accelerates the electrocyclic opening relative to the rate for the corresponding cyclobutene lacking the silyl group, just as a methoxy group accelerates the opening when it is moving outwards.954 An Si—C bond is polarised towards the carbon atom of the cyclobutene ring, making the silyl group like an anion; this perception is matched by the torquoselectivity for the electrocyclic opening of a 3-azacyclobutene, in which the lone pair has been predicted to move inwards, just as the silyl group does, and the substituent on the nitrogen to move outwards.955 n-C8H17

140 °C

n-C8H17

n-C8H17 + SiMe3

SiMe3 SiMe3 6.502

cis-6.503

83:17

tr ans-6.503

The Nazarov reaction, in which the key electrocyclic step is the conrotatory process 6.505, has one more atom in the ring but the same number of electrons. The question with respect to torquoselectivity now, since this reaction is taking place in the opposite direction, namely ring-closing, is which reacts faster, a dienone

6 THERMAL PERICYCLIC REACTIONS

365

with an X- or a Z-substituent inside, or with an X- or a Z-substituent outside? In the absence of chirality, there is no torquoselectivity as such in a cyclisation, but there is by implication, in that the reverse reaction, were it to take place, would have torquoselectivity. Nothing much is known about substituent effects, but calculations have predicted that the same pattern as that found in cyclobutene openings obtains—a silyl group should accelerate the ring closure if it is inside 6.504, but a methyl group, a weak X-substituent, should slow it down if it is inside 6.506.956 OH

OH

OH

predicted to be faster than: SiH3 6.504

predicted to be faster than: H

Me

6.505

6.506

Another silicon-assisted kind of torquoselectivity is in the allylsilane-type of Nazarov cyclisation. Now there is chirality, and there is a high level of torquoselectivity in the sense shown by the allylsilane 6.507, determined by the chirality.957

Me3Si

Me3Si

O

O

FeCl3

O H

FeCl3 H 6.507

H

6.509

6.508

It is perhaps more simple to note that both the vinylsilane reaction 6.504 and the allylsilane reaction 6.507 are showing the normal pattern of stereochemistry for their reactions with electrophiles: a preference for retention of configuration in the double bond geometry for a vinylsilane, and anti for an allylsilane, where anti refers to the side of the double bond to which the new bond is formed relative to the side on which the silyl group resides. In the product 6.509, the new C—C bond has formed to the lower surface of the left-hand double bond, while the silyl group was conjugated to the top surface in the allylsilane 6.508. With two more electrons, the disrotatory ring opening of a hexatriene, with a total of (4nþ2) electrons, has the two upper substituents R in 6.69 able to move outwards, as illustrated for the reaction going from right to left in Fig. 6.3, or able to move inwards. In general, steric effects seem to dominate, and the larger substituents move outwards. More usually, the reaction seen is in the other direction, and the question is then: which reacts faster, a hexatriene with one substituent on a cis double bond and the other on a trans, or to have them both on a trans double bond. The former leads to a cyclohexadiene with the two substituents trans to each other, which is usually the lower in energy. Nevertheless the ring closure cis-6.510 ! anti-6.511 is slower than the ring closure trans-6.510 ! syn-6.511 by a factor of about 20.958 Ph

Ph Ph

Ph cis-6.510

anti-6.511

20 slower than tr ans-6.510

Ph

Ph

Ph

Ph syn-6.511

366

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

Houk has explained this by pointing out that the same considerations apply as in cyclobutene openings, but, with two more electrons, an X-substituent on the inside will contribute to an antiaromatic transition structure, and a Z-substituent on the inside will contribute to an aromatic transition structure.959 In both cases the effect will be less than it was for the conrotatory opening and closing in cyclobutenes, electronically because the orbitals in a disrotatory process 6.512 and 6.513 will be less well aligned for overlap, whether energy-raising as in 6.512 or energy-lowering as in 6.513. Furthermore, a transition structure looking like 6.514 must have a substantial steric clash between two of the substituents, which makes the steric component deterring any substituent from occupying the inside position more severe than it was for a conrotatory process. The prediction is that the electronic nature of the substituents will have only a small contribution, and that steric effects are likely to be more important than they were in cyclobutene openings.

6.512

6.513

6.514

Torquoselectivity of a different but more powerful kind is found in the ring opening of cyclopropyl halides. These reactions are formally related to the disrotatory opening of a cyclopropyl cation to give an allyl cation, but the opening is concerted with the loss of the leaving group. Cyclopropyl cations themselves are high energy species, and are not intermediates, as can be seen in the reactions of the stereoisomeric halides 6.515– 6.517, which give the stereoisomeric cations 6.518–6.520, respectively.141 These cations are configurationally stable at the low temperatures used. If the free cyclopropyl cation had been involved the cyclopropyl halides 6.515 and 6.516 would have given the same allyl cations instead of one giving the W-shaped cation 6.518 and the other giving the U-shaped cation 6.519. In all three cases, although only the first and second prove it, the torquoselectivity is such that the chloride ion leaves from the same side as that in which the substituents move towards each other.

H H

Cl H 6.515

H

Cl H

6.516

6.517 –100 °C

SbF5SO2ClF

6.518

H

Cl

6.519

6.520

The most simple explanation is that if the substituents on the same side as the leaving group, the methyl groups in the cyclopropyl chloride 6.516, are moving towards each other, and the substituents on the opposite side are moving apart, as they do in forming the allyl cation 6.519, then the bulk of the electron population from the breaking  bond is moving downwards 6.521 (arrow) through a transition structure 6.522 to the allyl cation 6.523, effectively providing a push from the backside of the C—Cl bond.

6 THERMAL PERICYCLIC REACTIONS

367

Torquoselectivity in this series is a powerful force, overriding any steric clash of the two methyl groups moving towards each other. Cl

Cl (–)

Cl Me

Me

Me

Me

(+) Me

H

H H

H

Me

H

H 6.521

6.522

6.523

It is powerful enough to lead the cyclopropyl bromide 6.524 to give the trans-cyclooctenol 6.526, in spite of the strain from having a trans double bond in a ring of this size.960 The arrow on the drawing 6.524 is like that in 6.522 showing the electrons moving in behind the C-halogen bond, and creating in the disrotatory opening a W-shaped cation 6.525. No matter which end of the cation is attacked by the nucleophile, a trans double bond must be formed.

H

H2O

Br H H

H2O, dioxan

H H

reflux, 28 h

6.524

t HO 6.526

6.525

The isomeric cyclopropanes 6.527 and 6.529 lose fluoride and chloride, respectively, in spite of the much better nucleofugal properties of the latter. The sense of torquoselectivity is determined because only a Ushaped cation can be formed in the six-membered ring leading to the products 6.528 and 6.530, and this in turn determines which of the halide ions leaves.961

F

Cl

F

150 °C

Cl

150 °C

Cl

F Cl

6.527

6.528

F 6.529

6.530

The reverse reaction of this general class—an allyl cation giving a cyclopropyl cation—is found in Favorskii rearrangements. The diastereoisomeric cis and trans -chloro enolates 6.531 give the cis and trans cyclopropanones 6.532, respectively, with the cis and trans designation referring to the relationship between the nucleophilic enolate carbon C-20 and the resident methyl group on C-2 that is acting as a stereochemical label. Thus the reaction is stereospecific with inversion of configuration at C-1, at least in a nonpolar solvent. Evidently the allyl cation is not formed, otherwise the two chlorides would give the same product or mixture of products. The cyclisation step is presumably disrotatory with the torquoselectivity determined by which side of the allyl system the chloride leaves from. The cyclopropanone is not isolated, because the alkoxide attacks the carbonyl group with subsequent cleavage of the bond towards the methyl group giving the esters cis and trans 6.533.962

368

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

O

2'

2'

2' –

Et2O

1

Cl

O

cis-6.531

OBn

cis-6.532

CO2Bn cis-6.533

O CO2Bn

Cl 1

O

Et2O

–

2'

OBn

2'

2'

tr ans-6.531

trans-6.532

tr ans-6.533

In a more polar solvent, Favorskii reactions cease to be stereospecific,963 and presumably take place by ionisation of the chloride to give the same cation from each diastereoisomer. Whether the reaction takes place by way of the cation, when it is 3-endo-trig at both ends, or with concerted loss of the chloride ion, when it is 3-endo-trig at the enolate carbon, this reaction presented a serious puzzle before its pericyclic nature was recognised. The  overlap of the p orbital on C-20 of the enolate with the p orbital at the other end of the allyl cation 6.534 (or with the orbital of the C—Cl bond 6.535) looked forbiddingly unlikely. We can now see that it is made possible by its pericyclic nature, where the tilt of the orbitals can begin to sense the development of overlap, even though it is not at first  in character, and is a further illustration of the extent to which Baldwin’s rules do not apply in pericyclic reactions. The torquoselectivity in the development of overlap 6.535, however improbable it looks, corresponds to the usual inversion of configuration at the carbon atom from which the chloride departs. Cl O

O 2'

2'

6.534

6.535

With two more electrons, and rather more complicated structures, the Nazarov-like reactions of the carbamates 6.536 and 6.538 are conrotatory, with the torquoselectivity determined, as in the Favorskii reactions, by which side of the conjugated system the nucleofugal group departs from, clockwise as drawn for the carbamate 6.536 and anticlockwise for its diastereoisomer 6.538.964 The topological sense of the event in the left-hand allylic system corresponds to an anti SN20 reaction in both cases. OCONPri2 Br

OLi

Ph

Pri2NCOO Br

O

6.536

But

OLi

Ph

Ph H

Br

6.537

O

But

Ph

t

Bu

Br

H 6.538

But 6.539

Notice how the two starting materials 6.536 and 6.538 differ from each other stereochemically in two respects: the configuration at the carbon atom carrying the carbamate group and the configuration of the allenolate system. Likewise, the products 6.537 and 6.539 differ in two respects: the configuration of the carbon atom carrying the phenyl group and the geometry of the exocyclic double bond. The stereospecificity is shown by the absence of the other pair of diastereoisomers in the product mixtures.

7

Radical Reactions

Much of the selectivity seen in radical reactions may be explained by frontier orbital theory, in contrast to ionic reactions, where it makes a relatively small contribution. Frontier orbital theory may not be well founded as a fundamental treatment, but it is appropriate that it might come to the fore with radicals, where Coulombic forces are usually small, orbital interactions likely to be strong, and the key steps usually exothermic. Most of the discussion in this chapter will use frontier orbital theory, and will seem to do so uncritically.965 It is important to remember that it is not as sound as its success in this area will make it seem.

7.1

Nucleophilic and Electrophilic Radicals

We saw in Chapter 2 that all substituents, C-, Z- or X-, stabilise radicals, that carbon-based radicals are usually pyramidal, with a low barrier to inversion of configuration, and that the energy of the singly occupied molecular orbital (SOMO) was inherently close to the nonbonding  level, unchanged by C-substitution, lowered by Z-substitution and raised by X-substitution. In contrast to the frontier orbitals in ionic and pericyclic reactions, the SOMO can interact with both the HOMO and the LUMO of the reaction partner to lower the energy of the transition structure (Fig. 7.1).966,967 Plainly the interaction with the LUMO will lead to a drop in energy (E3 in Fig. 7.1b) but so does the interaction with the HOMO, and, for that matter, with each of the filled orbitals. Because there are two electrons in the lower orbital and only one in the upper, there will be overall a drop in energy (2E1 – E2) from this interaction. We can combine these effects in the frontier

LUMO E2

SOMO

SOMO E1

(a) SOMO-HOMO

Fig. 7.1

E3

HOMO

LUMO

SOMO HOMO

(b) SOMO-LUMO

(c) SOMO-HOMO/LUMO

The interaction of the SOMO with the HOMO and the LUMO of a molecule

Molecular Orbitals and Organic Chemical Reactions: Reference Edition Ó 2010 John Wiley & Sons, Ltd

Ian Fleming

370

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

orbital picture in Fig. 7.1c. Radical reactions are consequently fast, and, in favourable cases, are even diffusion controlled, having little or no activation enthalpy. Radicals are soft: most of them do not have a charge, and in most chemical reactions they react with uncharged molecules. Thus the Coulombic forces are usually small while the orbital interactions remain large. This is borne out by such well-known reactions as the attack of radicals at the conjugate position of ,-unsaturated carbonyl compounds like methyl methacrylate 7.1, rather than at the carbonyl group, and the attack by the ambident -carbonylmethyl radical 7.2 from the carbon atom, not from the oxygen atom. The clean and industrially important polymerisation giving poly(methyl methacrylate) (PMMA) demonstrates both of these typically soft patterns of behaviour.

R

OMe

R

OMe

O 7.1

OMe

O 7.2

O

OMe etc.

R CO2Me

O

7.1

Highly reactive species like radicals are not usually expected to show high levels of selectivity (the reactivityselectivity principle), and so it had always been something of a puzzle why they did, nevertheless, have nucleophilic and electrophilic character—some radicals showing higher reactivity with reagents normally thought of as electrophilic, and others higher reactivity with reagents normally thought of as nucleophilic. These observations are easily explained by frontier orbital theory. Radicals with a high-energy SOMO (Fig. 7.2a) will react fast with molecules having a low-energy LUMO, characteristic of electrophiles, and radicals with a low-energy SOMO (Fig. 7.2b) will react fast with molecules having a high-energy HOMO, characteristic of nucleophiles. The former are therefore the nucleophilic radicals and the latter are the electrophilic radicals.

LUMO

LUMO

SOMO

SOMO HOMO

HOMO

(a) High-energy SOMO—a nucleophilic radical (b) Low-energy SOMO—an electrophilic radical

Fig. 7.2

Frontier orbital interactions for a nucleophilic and an electrophilic radical

This insight is strikingly illustrated by the observation of alternating copolymerisation from a 1:1 mixture of dimethyl fumarate 7.3 and vinyl acetate 7.5.968,969 The radical-initiated polymerisation takes place largely970 to give a polymer in which the fragments derived from the two monomers alternate along the chain. In this case it is evident that a growing radical such as 7.4 attacks vinyl acetate rather than fumarate; but the new radical 7.6, so produced, attacks fumarate rather than vinyl acetate. The radical 7.4, because it is flanked by a carbonyl group, in other words by a Z-substituent, will have a low-energy SOMO (see p. 81), and will be an electrophilic radical. It therefore reacts faster with the molecule having the higher energy HOMO, namely the X-substituted alkene 7.5. Furthermore, the coefficient in the HOMO of the X-substituted alkene 7.5 will be particularly large (see p. 76) at the terminal carbon atom where bonding takes place The new radical 7.6 is

7 RADICAL REACTIONS

371

next to an oxygen atom, in other words an X-substituent, and will have a high-energy SOMO (see p. 81). It will be a nucleophilic radical, closer in energy to a low-lying LUMO. Of the two alkenes 7.3 and 7.5, the fumarate, because it is a Z-substituted alkene, has the lower energy LUMO (see p. 73), and it is therefore this molecule which reacts with the radical 7.6—and so on, as the polymerisation proceeds. This explanation for alternating polymerisation satisfyingly avoids the vague terms, such as ‘polar factors’, which had been used in the past. CO2Me

CO2Me

OAc

R

R

CO2Me

CO2Me 7.3

CO2Me MeO2C

OAc

MeO2C R

7.4

OAc

CO2Me etc.

R CO2Me

7.5

CO2Me

7.6

CO2Me

CO2Me

7.3

In general: radicals with a high-energy SOMO show nucleophilic properties and radicals with a low-energy SOMO show electrophilic properties.

Radicals show three types of reaction: substitution 7.7, addition to double bonds 7.8, and radical-with-radical combination 7.9, and the reverse of each of these reactions. We shall now look at these in turn to see how the various kinds of selectivity in each of them can be explained. R

X

R

R

RX + 7.7

7.2

R

R

7.8

R

R

7.9

The Abstraction of Hydrogen and Halogen Atoms

7.2.1 The Effect of the Structure of the Radical Substitution 7.7 most commonly takes place by the radical abstracting a hydrogen atom (X ¼ H), a chalcogen substituent (X ¼ SR or SeR), or a halogen (X ¼ Br or I). Most work on the effect of the structure of the radical has been carried out for hydrogen atom abstraction. At first glance the story is simple: the less-stabilised the radical the faster it abstracts a hydrogen from such reagents as tributyltin hydride. Thus methyl, ethyl, isopropyl and tert-butyl radicals have relative rates of 5.6, 1.2, 0.8 and 1, respectively, more or less reflecting the exothermicity of the reaction.971 The story is actually more complicated because different radicals abstract different hydrogen atoms from butyrolactone 7.11: alkoxy radicals selectively abstract the hydrogens from the methylene group adjacent to the oxygen atom, whereas a boryl radical abstracts the hydrogens from the position  to the carbonyl group.972 The bond dissociation energies of the two kinds of C—H bond are about the same, and both product radicals, 7.10 and 7.12, are stabilised. There must be some extra kinetic factors not included in the simple thermodynamics of the overall event. t

O

BuO

H

H O

O 7.10

H2B-NEt3 O

O 7.11

O 7.12

372

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

The frontier orbitals are the SOMO of the radical and the local  or * orbitals of the C—H bonds (Fig. 7.3). The tert-butoxy radical, based on an electronegative element, will have a low-energy SOMO, and will have a stronger interaction D with the  orbital which is high in energy for having an adjacent X-substituent. In contrast, the boryl radical, based on an electropositive element, will have a high-energy SOMO, and it will have a stronger interaction A with the lower-energy * orbital of the C—H bond adjacent to the Z-substituent. The interaction A is more effective than C for the boryl radical, and D more effective than B for a butoxy radical. If A and D are the dominant interactions, then the observed pattern of reactivity is explained. H LUMO

O O H

LUMO

A

O

Et3N-BH2 SOMO

O

B C t

BuO

SOMO

H

D

HOMO O O H HOMO O O

Fig. 7.3 Interactions for the attack of tert-butoxy and boryl radicals on butyrolactone

Another example of this type of selectivity, more muted but still easily measurable, is the different selectivities shown by methyl radicals and chlorine atoms for the methylene and methyl groups of propionic acid 7.14. Methyl radicals abstract the hydrogen atoms on C-2 5.2 times faster than the hydrogen atoms on the methyl group C-3. However, chlorine atoms abstract the hydrogen atoms on the methyl group 50 times faster than the hydrogen atoms on C-2.973 Me

H

Me H

k rel 1

2 3

CO2H

k rel 5.2

7.14 CO2H

CO2H

7.13

Cl k rel 50

k rel 1

H

Cl H

2 3

7.16

CO2H

7.14

From the picture of C—H bonding in Chapter 1, we can deduce that the SOMO of a methyl radical is close to half way between the local  and * orbitals of a C—H bond, or, to put it another way, at the  level of Hu¨ckel theory. The interactions should be more or less equally the SOMO of the methyl radical with the HOMO and with the LUMO of a simple C—H bond.974 In this case, the lowering of the LUMO for the C—H

7 RADICAL REACTIONS

373

bond adjacent to the carbonyl group makes it closer in energy to the SOMO of the methyl radical, and there must be a small contribution from the greater stability of the radical produced 7.16 than of the primary alkyl radical 7.13. The chlorine atoms, however, will have a much lower energy SOMO, and will be relatively electrophilic in character, selecting the C—H bonds that are not conjugated to the carbonyl group. A number of radicals abstracting the hydrogen atom from p-substituted toluenes have been studied, and Hammett -values from the relative rates of these reactions plotted against the SOMO energy, as measured by the ionisation potential (Fig. 7.4). The -value for a methyl radical in this reaction is only –0.2, confirming that it is if anything slightly electrophilic. Other radicals give larger values, but they are all fairly small compared with the -values found for many ionic reactions. Some radicals give larger negative -values, indicating that the attack is by a more electrophilic species, and others give positive values indicating attack by a nucleophilic species. Although agreement among the numbers is not perfect, the trend seems to suggest that those radicals with high-energy SOMOs, like the triethylsilyl and substituted alkyl radicals, show nucleophilicity (with positive -values), whereas the oxy and halogen radicals, with low-energy SOMOs, are distinctly electrophilic. The alkyl series shows a reasonably good correlation between SOMO energies and -values.975

1.0

H

0.8 0.6 0.4

H

H

R

But

C5H11

C9H21

0.2

SiEt3

X

0 Me

–0.2

Ph

ButO

–0.4

OOBut

–0.6 Cl

–0.8

CH2CO2H

–1.0 –1.2 –1.4

Br

–1.6 –13

–12

CCl3 –11

–10

–9

–8

–7

–6

Ionisation potential (eV) (SOMO energy)

Fig. 7.4

-Values for hydrogen abstraction from p-substituted toluenes

When the SOMO/HOMO interaction is the more important, and assuming, as is usually true for hydrogenabstraction reactions, that the SOMO energy lies between that of the HOMO and the LUMO, the radical with the higher-energy SOMO will be less reactive than the one with the lower-energy SOMO (because 2E1 – E2 in Fig. 7.1 will be smaller). This explains why the ButOO • radical is 10 000 times less reactive in hydrogen abstraction than the ButO • radical.976 Here we see the -effect making an electrophilic radical less reactive, whereas it made a nucleophile more reactive (see p. 155); the cause is the same, namely the raising of the energy of the HOMO. It may be that the lower reactivity of the ButOO • radical makes it more selective than the ButO • radical, and similar factors may explain the other anomalous entries in Fig. 7.4. 7.2.2 The Effect of the Structure of the Hydrogen or Halogen Source 7.2.2.1 Selectivity Affected by the Nature of the Radical. Selectivity is also seen in which atom is abstracted when there is more than one to choose from, as we have seen already in the reactions of the lactone 7.11 and propionic acid 7.14. When the tributyltin radical has a choice of a C—S, a C—Se, or a C—halogen bond,

374

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

they are selected, other things being equal, in the order I > Br > SeAr > Cl > SAr > SMe. This is roughly in the order of the strengths of the Sn—X bond being made, and is again explained simply as a consequence of the most exothermic reaction being the most rapid (see p. 135). Furthermore, these reactions are faster than attack on a C—H bond, since the halogens and Se and S are soft sites, and can accept bonding to a radical ahead of the bond breaking—the interaction of the SOMO with the nonbonding, lone-pair orbitals is likely to be stronger than with  or * of a C—H bond, as well as forming a stronger bond. The relatively less nucleophilic methyl radical, however, abstracts a hydrogen atom from benzyl chloride rather than the chlorine atom. Even more subtle examples of selectivity come when it is a question of which kind of C—H bond is attacked. Most radicals attack hydrogen atoms in the order: allylic > tertiary > secondary > primary. The most important factor here is again that the faster reactions are producing the product with the lower energy. In addition, the more neighbouring groups a C—H bond has, the more overlap (hyperconjugation) can be present. Since such overlap is between filled orbitals and filled orbitals, the effect is to raise the energy of the HOMO. This effect therefore puts the energy of the HOMOs of the C—H bonds in the same order as their ease of abstraction.977 More quantitatively, Fukui showed that it is possible to calculate a parameter, called the delocalisability D(R), for different kinds of hydrogen atom attached to carbon, from the coefficient on the hydrogen atom cri of the atomic orbital on atom r in each molecular orbital i, having energy Ei, when the SOMO of the attacking radical has energy  (Equation 7.1).978 occ

DðRÞ r ¼ S i

unocc c2ri c2ri ðÞ ðÞ þ S i   Ei Ei  

7:1

This parameter correlates well with the rate constant for abstraction of the different kinds of hydrogen atoms, primary, secondary and tertiary in hydrocarbons and in alkyl fluorides. It works, both for a relatively neutral radical like methyl, and for electrophilic radicals like trifluoromethyl, because it takes into consideration both SOMO/OMO and SOMO/UMO interactions.979 Selectivity between hydrogen atom abstraction and addition to an alkene (Section 7.3) is very dependent upon the structures of the radical and of the substrate. Tin radicals abstract halogen atoms even when there is a double bond to add to, but that is probably because of the strong bond being formed. Simple alkyl radicals attack H—Sn bonds competitively with their conjugate addition to Z-substituted alkenes, showing that there is a fairly delicate balance, even though the H—Sn bond is notably weak. tert-Butoxy radicals remove allylic hydrogens faster than they add to the terminus of simple alkenes, but quite small changes, to perfluoroalkoxy radicals for example, reverse this selectivity.980 One of the complications in assessing the selectivity between atom abstraction and addition to an alkene is that one or the other might be reversible. The best known case where this appears is in two well-known reactions of bromine atoms. One of these is the allylic bromination of alkenes 7.16 ! 7.18 using N-bromosuccinimide (NBS). Radical brominations using NBS are known to take place by the NBS slowly releasing bromine, since the same results can be obtained using bromine in low concentration. This detail is irrelevant here, but it is well known. In the key step of the allylic bromination using NBS, a bromine atom derived from the bromine molecule abstracts an allylic hydrogen atom 7.16, and the allylic radical produced 7.17 then abstracts a bromine atom from another molecule of bromine to give the allylic bromide 7.18, together with a bromine atom which can continue the chain reaction. Unsymmetrical allyl systems give mixtures of products, because the allyl radical is ambident. Br Br

Br

Br

H 7.16

7.17

+ HBr

7.18

7 RADICAL REACTIONS

375

The other reaction is the peroxide-catalysed addition of HBr to alkenes 7.19 giving the anti-Markovnikov product 7.21. The peroxide generates a bromine radical by abstracting the hydrogen atom from the HBr. The key step is the addition of the bromine atom to the double bond 7.19, which takes place to give the moresubstituted radical 7.20, and this in turn abstracts a hydrogen atom from another molecule of HBr to give the primary alkyl bromide 7.21. Br

Br

Br

H

Br

7.20

7.19

7.21

It seems that the bromine atom can show different selectivity, allylic abstraction 7.17 or addition 7.19, depending upon its source, but this is an illusion. One of these reactions, 7.16 or 7.19, must be reversible, and the second step must be proceeding slowly enough to allow the alternative pathway to dominate. The better candidate for the slow second step is the bromination 7.17 ! 7.18, since the concentration of bromine is so low. 7.2.2.2 Selectivity Affected by Stereoelectronic Effects. Molecules with a more or less rigid relationship between a lone pair and a C—H bond can be used to probe the effect of conjugation between the two. Ethers, acetals and orthoesters show a range of reactivity towards hydrogen atom abstraction by tert-butoxy radicals, with some telling stereochemical features. The acetal 7.22 shows a selectivity between the three different kinds of hydrogen atom that matches the energy of the radicals produced. The most stable is the tertiary radical 7.23 flanked by two oxygen atoms, which is produced nearly seven times faster than the secondary 7.24, which is flanked by only one. It is normal to correct for the statistical factor that there are four times as many hydrogens that can produce the secondary radical as the tertiary, and so the selectivity for tertiary is actually 27 times the secondary. The third possibility would be the primary radical, with no lone pair stabilisation, produced by abstraction from the methyl group, which is not observed at all. However, the rigid acetal 7.25 loses a hydrogen atom only from the secondary position to give the radical 7.26, which is stabilised by syn overlap with one of the lone pairs, whereas the tertiary radical that would be created at the bridgehead 7.27 would not be stabilised, because the singly occupied orbital would be gauche to all the lone pair orbitals.981 OBut

O O

H

O

O +

H

O

7.22

7.23

H

O 87:13

7.24

H O

OBut

O

O +

O

O

O

H 7.25

7.26

100:0

7.27

Orientation affects not only the stability of the radicals being produced, but also the energies of the orbitals of the C—H bond. If the angles are right, a lone pair will raise the energy of the local HOMO and LUMO of a C—H bond. Thus the axial hydrogen atom in the acetal 7.28 is selectively removed by tert-butoxy radicals, partly because it gives a well stabilised tertiary radical 7.29, similar to 7.23. More significantly, the axial hydrogen atom in the acetal 7.28 is removed more than 10 times faster than the equatorial hydrogen atom in

376

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

its diastereoisomer 7.30.982 Since they give the same radical 7.29, and the same final products, this is an effect from the nature of the C—H bonds, and not just an effect from the stability of the radical. The SOMO/ HOMO interaction will be the most important, since the butoxy radical, based on an electronegative atom, will have a low-energy SOMO, which will select the higher energy HOMO of the C—H bond conjugated to the X-substituent. Similar effects have been seen with nitrogen lone pairs.983 H k rel 11

O O

H

O

O

7.28

7.3

krel 1

O

O

7.29

7.30

The Addition of Radicals to p Bonds

7.3.1 Attack on Substituted Alkenes There is a great deal of information available about the addition of radicals to p bonds, since it is such an important step in radical polymerisation, as we have already seen.969 The regioselectivity in a lot of these reactions is easily explained: the more stable ‘products’ 7.2, 7.6, 7.20, 7.31984 and 7.32,985 with the radical centre adjacent to the substituent are almost always obtained, and the site of attack usually has the higher coefficient in the appropriate frontier orbital. With C- and Z-substituted alkenes, the site of attack will be the same regardless of which frontier orbital is the more important—both have the higher coefficient on the carbon atom remote from the substituent (Figs. 2.2 and 2.5). 25

Br 75

CCl3

Br

Cl3C

Cl3C

Br + Cl3C

Cl3C 7.31

25:75 Et B

O

Et

Et

O Et

Et

H

OBEt2

Et

+

Et

H 7.32

With X-substituted alkenes, however, the HOMO and the LUMO are polarised in opposite directions (Fig. 2.7). For most X-substituted alkenes, the HOMO will be closer in energy to the SOMO of the radical, because X-substituted alkenes generally have high-energy HOMOs and high-energy LUMOs (see p. 75). Together with the usual pattern for forming the more stabilised radical, this explains the direction of addition, as we saw when the electrophilic radical 7.4 adds to the unsubstituted terminus of vinyl acetate 7.5. Similarly, oxygen atoms, which will also be electrophilic, attack but-l-ene to give more butanal 7.33 than 2-butanone 7.34.986 O O

+

O H

7.33

92:8

7.34

7 RADICAL REACTIONS

377 But

1.1 0.8 0.8

R

0.6

X C4H9

0.4 0.2 0 –0.2

OBut

–0.4 –0.6

CCl3 –12

–11

–10

–9

–8

–7

–6

Ionisation potential (eV) (SOMO energy)

Fig. 7.5

-Values for the addition of radicals to p-substituted styrenes

Although the regioselectivity is usually high in all these reactions, the relative rates reveal that orbital interactions are important, in addition to the thermodynamic factors favouring the formation of the more stable radical. Thus, a plot of the Hammett -values for addition to substituted styrenes (Fig. 7.5)987,988 is similar to that for the abstraction of hydrogen atoms in Fig. 7.4. The methyl radical, with a SOMO close to half way between the HOMO and the LUMO of a simple alkene, reacts 1.4 times faster with ethylene than with propene. Presumably the lower energy of the HOMO and LUMO of ethylene relative to propene allows the SOMO-LUMO interaction to be slightly greater than the SOMOHOMO, whereas with propene the SOMO is more nearly placed equally between the frontier orbitals. The methyl radical gives the more substituted radical when it reacts with propene with a regioselectivity of 5:1, with the product character overriding any frontier orbital effect with respect to regiochemistry. However, the more electrophilic trifluoromethyl radical adds to propene 2.3 times faster than it attacks ethylene, and with a higher regioselectivity of 10:1, evidently responding to the closer energy of the HOMO, and it gives the more substituted radical, with both frontier orbital effects and product character working in the same direction.989 The radical 7.36 produced by addition of an alkyl radical to diethyl vinylphosphonate 7.35 will be very similarly stabilised no matter what the alkyl group R is, yet the relative rates for the different radicals are in the order: tBu > i Pr > Et > Me.990 This is opposite to the usual expectation that the more stable the radical the less reactive it is. The simplest explanation is that the more substituted radical has the higher-energy SOMO, closer in energy to the LUMO of the vinylphosphonate 7.35, which, because it is a Z-substituted alkene, will be low in energy. R

R

PO(OEt)2 7.35

Me

PO(OEt)2

k rel 1

7.36

Et

Pri

But

1.04

4.8

23.6

In contrast, for electrophilic radicals attacking an X-substituted alkene, adding an X-substituent like methyl to the Z-substituted radicals 7.37 lowers the rate of attack on 1-decene 7.38.991 Thus the radical 7.37 with R1 ¼ R2 ¼ H reacts 4 times faster than with R1 ¼ Me, R2 ¼ H, and the radical 7.37 with R1 ¼ R2 ¼ Cl reacts 2.5 times faster than with R1 ¼ Me, R2 ¼ Cl. The other numbers here are not so easy to interpret, since the chlorine atoms, although p-donating, are also -withdrawing, and it is more than likely that steric effects are also contributing to these results. CO2Me

CO2Me 1

R

R2

7.37

C8H17 7.38

1

R

C8H17

R2 7.39

R1,R2

H,H

k rel

45

H,Me H,Cl 11.2

4.5

Cl,Cl Cl,Me 2.5

1

378

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

With an alkene having an X-substituent at one end and a Z-substituent at the other, radicals can show different regioselectivity depending upon their SOMO energy, since both possible products are stabilised. Thus nucleophilic radicals like the cyclohexyl radical react with methyl crotonate 7.40 selectively (92:8) at C-3, responding to the large coefficient at that site in the LUMO. The electrophilic benzoyloxy radical, however, is less selective and actually attacks a little more rapidly (55:45) at C-2, which has the larger coefficient in the HOMO.992

CO2Me

PhCO2

3

CO2Me

CO2Me

2

OCOPh 55:45

7.40

92:8

Varying the alkene instead of the radical leads to the same pattern. The lower the energy of the LUMO of the alkene 7.41, the faster a nucleophilic radical like the cyclohexyl radical will add to it, but an electrophilic radical like the malonate radical adds more rapidly the higher the energy of the HOMO. 993 Ph

R

7.41

Ph

Me

3.6

1

R

k rel

440

42

R

CO2Et

Ph

Me

R

k rel

1

3.5

3.7

Ph R

CN CO2Et

EtO2C EtO2C

EtO2C

Ph

EtO2C

MeO Me2N 2.7

23

The general rule, therefore, is that radicals add to the less substituted end of C-, Z- or X-substituted alkenes to give the more stable radical, this usually matches the coefficients in the appropriate frontier orbitals, and the relative rates are usually, but not always, in line with the appropriate frontier orbital separations.994 This is true of fluoroethylene 7.42, which unexceptionably adds methyl and trifluoromethyl radicals predominantly at the less-substituted carbon. Me Me

F 7.42

Me

F

+

83:17

CF3 F

CF3

F 7.42

CF3

F

+

F

91:9

However, in one of the most striking reversals of the usual regioselectivity, methyl radicals add to trifluoroethylene 7.43 with what looks like the ‘wrong’ regioselectivity. It is tempting to suggest that this is an example in which the SOMO of the radical interacts with the LUMO of an X-substituted alkene, where the higher coefficient is on the carbon atom carrying the substituent. It is appropriate that it should be seen with a relatively nucleophilic radical like methyl, rather than with the electrophilic trifluoromethyl radical, but the complexity of the factors at work here,995,996 together with the ambiguity that a fluorine substituent, like chlorine, is p-donating but -withdrawing, should make us pause.

7 RADICAL REACTIONS

379

F

F Me

Me

Me

F

F

+

7.43

CF3

F F

F

F

32:68

F

F

F

CF3

F

7.44

F F

F

CF3 F +

F F

7.43

95:5

Even less obvious in this particular case is evidence that the less-substituted radical is actually more stabilised, presumably by negative hyperconjugation with the  C—F bonds, than the more-substituted radical is by the attached F atoms.997 Furthermore, in the other striking reversal of expectations, the tertbutoxy radical, which is certainly more electrophilic than methyl, adds to 1,1-difluoroethylene 7.45 at the substituted carbon with a selectivity of 80:20,998 whereas the methyl radical is ‘normal’ in this case. Thus the coefficients in the LUMO are hardly likely to be the explanation, and one suggestion in this particular case is that there is a growing anomeric effect between the oxygen atom and the two fluorine substituents in the transition structure for the formation of the major intermediate 7.46.988 F

t

BuO

t

BuO

+

7.45

7.47

tBuO

F

F

R1 R2

F

F

7.46

(R1 = CN, R2 = CO2Et)

80:20

R1 R2

fast

7.48

F

CN CO2Et

slow

7.49

Whatever the complexities of the fluorine-containing alkenes, and their ‘right’ and ‘wrong’ regioselectivity, the regioselectivity in which the more-substituted carbon is attacked is much more common in the cyclisation of hex-5-enyl radicals 7.48 (R1 ¼ R2 ¼ H). These cyclise to give the less stable, primary radical 7.47 (R1 ¼ R2 ¼ H) with a selectivity of 98:2. Radicals attack alkenes with an obtuse Bu¨rgi-Dunitz-like angle,999 for the same reasons that anions and cations do (see pp. 214–217), and for this reason Baldwin’s rules can be expected to apply. They are called the Baldwin-Beckwith rules when applied to radicals. Although the 6-endo-trig pathway giving the radical 7.49 is not explicitly disfavoured, it is more strained than the observed 5-exo-trig pathway giving the radical 7.47, inhibiting the electronic control of regioselectivity seen in open chain systems. The pattern of exo closure is also seen with electronegative heteroatom-centred radicals,1000 with addition to triple bonds, and for ring sizes ranging from threemembered to eight-membered.1001 A suggestion has also been made that the preference for five-membered ring formation may be connected to the symmetry of the orbital relationships in the intervening chain when it has an odd number of bonds.1002 Three situations where the 6-endo-trig pathway1003 is observed are understandable. Cyclisation to give the secondary radical 7.49 does take place when the groups R1 and R2 are electron withdrawing, as a result of thermodynamic control.1004 The well-stabilised radical 7.48 (R1 = CN, R2 = CO2Et) forms the five-membered ring 7.47 more rapidly, but the latter is able to open again under the reaction conditions to give the thermodynamically preferred product 7.49 with a secondary radical and a six-membered ring. The selectivity is 84:16, but dependent, of course, on how rapidly the two radicals are being quenched in competition with the ring opening

380

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

and closing. It may also be that the ring closure in the 6-endo-trig sense (7.48 ! 7.49) is assisted when the substituents are electron withdrawing: the electrophilic radical 7.48 (R1 ¼ CN, R2 ¼ CO2Et) will have a relatively low-energy SOMO, and it will therefore be more sensitive to the polarisation of the HOMO of the alkene group. In the radical without electron-withdrawing groups 7.48 (R1 ¼ R2 ¼ H), the interaction with the p bond will be more affected by the LUMO of the alkene, and this might be part of the reason for contrathermodynamic cyclisation. When R1 is a hydrogen atom and R2 an aryl ring, the substituents on the aromatic ring affect the ratio, with Z-substituents increasing the proportion of endo closure and X-substituents decreasing it, showing that there is an electronic component to the selectivity, and not just the extent of reversibility.1005 The second category where the 6-endo-trig pathway is observed is when there is a second substituent on the inside carbon. The radical 7.51 adds at the terminus faster than at the inside carbon by a factor of 1.6,1006 because the steric effect slows down attack at the more substituted carbon, and the tertiary radical produced 7.52 will be more stabilised than it was without the substituent, whereas the primary radical 7.50 is of comparable stability. When the substituent is at the terminus, it naturally speeds up exo attack, especially when the substituent is electron withdrawing.1007

fast

slow krel 38

krel 62

7.50

7.51

7.52

The third category where the 6-endo-trig pathway is observed is exemplified by the silicon-containing radicals 7.53,1008 7.54 and 7.55.1009 None of these reactions is thermodynamically controlled—the radical addition step is not reversible in these reactions, so they must all be under kinetic control. The probable explanation is that the long Si—C bonds ease the strain in the 6-endo-trig transition structures, especially for the second pair 7.54 and 7.55, since they have two such bonds in the chain connecting the radical centre to the double bond. It is also true in the second case 7.54 that the silyl group is effectively a Z-substituent, which will further encourage attack by the radical on the terminus which has the higher coefficient in the HOMO. The silyl radical itself 7.53 has a high-energy SOMO, and can be expected to be nucleophilic, but the regioselectivity is not controlled by the LUMO coefficients of the alkene, it is simply that producing the more stable radical. When the silyl group is attached to the double bond in the vinylsilane 7.56 it should stabilise the radical produced by endo closure, but that is not what is seen. In this case the length of the Si—C bond is not helpful to endo closure, since the vinyl-to-Si bond actually takes the silicon atom, still held in the plane of the p bond, further away from the double bond terminus, and the second Si—C bond can only partly compensate. Thus the transition structure for endo closure in this case has approximately the same level of strain as in the all-carbon system 7.48, and like it gives exo closure.

SiMe2

6-endo

6-endo

SiMe2 SiMe2

endo:exo 98:2 7.53

7.54

6-endo Si Me2 7.55

endo:exo 70:30

endo:exo 100:0

5-exo Si Me2

Me2Si 7.56

Me2Si endo:exo 9:91

SiMe2

7 RADICAL REACTIONS

381

Orbital interactions have also been used to explain the counterthermodynamic regiochemistry in a ringopening reaction. Ringopening is the reverse, in principle, of what we have been seeing in the ring-closing reactions. The unusual feature is that cyclopropylmethyl radicals with the substitution pattern 7.57 open to give selectively the primary radical 7.58 rather than the more stabilised secondary radical 7.59.1010 The explanation offered is that the methyl substituent, conjugated to the bond that would have to break to give the secondary radical 7.59, raises the energy of the local LUMO. The radical centre in 7.57, with a highenergy SOMO, is nucleophilic, and it will interact more favourably with the lower-energy LUMO, which is that of the other bond, and the primary radical is therefore produced.

+ OSiMe3

7.57

OSiMe3 7.58

OSiMe3

85:15 at –90 °C 7.59

In support of this explanation, having a trifluoromethyl group in place of the methyl on the cyclopropane ring, or having a Z-substituent on the radical centre, changes this pattern to the more obvious one of opening to give the secondary radical.1011 The trifluoromethyl substituent lowers the energy of the local LUMO of the cyclopropane bond, and the Z-substituent makes the radical electrophilic, for which the interaction with the LUMO will be less important. 7.3.2 Attack on Substituted Aromatic Rings The rates of attack of radicals on aromatic rings correlate with ionisation potential,1012 with localisation energy1013 and with superdelocalisability (see p. 174),1014 a picture reminiscent of the situation in aromatic electrophilic substitution. As in that field, there are evidently a number of related factors affecting reactivity. Frontier orbitals provide useful explanations for a number of observations in the field, as the following examples show. The partial rate factors of Table 7.1 show that a phenyl radical reacts with nitrobenzene and anisole faster than it does with benzene. This can readily be explained if the energy levels come out, as they plausibly might, in the order shown, somewhat exaggerated, in Fig. 7.6. With anisole the SOMO/HOMO interaction (B) is strong, and with nitrobenzene the SOMO/LUMO interaction (A) is strong, but with benzene neither is significantly stronger than the other. Product development control can also explain this, since the radicals produced by attack on nitrobenzene and anisole will be more stabilised than those produced by attack on benzene. However, this cannot be the explanation for another trend which can be seen in Table 7.1, namely that a p-nitrophenyl radical reacts faster with anisole and benzene than it does with nitrobenzene. This is readily explained if the SOMO of the p-nitrophenyl radical is lower in energy than that of the phenyl radical, making the SOMO/HOMO interactions (C and D) strong with the former pair.

Table 7.1 Partial rate factors for radical attack on benzene rings;1015 f is the rate of attack at the site designated relative to the rate of attack at one of the carbon atoms of benzene itself Attacking radical

Ring attacked

p-O2NC6H4• Ph• p-O2NC6H4• Ph•

PhNO2 PhNO2 PhOMe PhOMe

fo

fm

fp

0.93 9.38 5.17 3.56

0.35 1.16 0.84 0.93

1.53 9.05 2.30 1.29

382

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS LUMO LUMO LUMO

A

SOMO B

HOMO

C

SOMO

O2N

D

HOMO HOMO NO2

OMe

Fig. 7.6 Interactions for the attack of an aryl radical on substituted benzene rings

In hydrogen abstraction reactions (see pp. 371–376), alkyl radicals change, as the degree of substitution increases, from being mildly electrophilic (the methyl radical) to being mildly nucleophilic (the tert-butyl radical). In addition radicals attacking pyridinium cations, the Minisci reaction, are all relatively nucleophilic, as shown by their adding exclusively to the 2-position 7.60. This change is reasonable, because the LUMO of an aromatic ring like this will be substantially lower in energy than that of a C—H bond and the SOMO of the radical can interact more favourably with it. The addition is the rate-determining, as well as the site-determining, step. The second step, the removal of the hydrogen atom 7.61!7.62, is usually easy, and resembles the loss of the proton in aromatic electrophilic substitution. The loss of a proton requires a base, but the solvent will often be adequate; the loss of the hydrogen atom requires the presence of another radical or a molecule like oxygen. In neither case is there the loss of a free proton or a free hydrogen atom. Y

R

N

Y

R H

N

Y

R

N

H

H

H

7.60

7.61

7.62

The more substituted radicals continue to be measurably the more nucleophilic. The relative rates with which the various alkyl radicals react with the 4-cyanopyridinium cation (7.60, Y ¼ CN) and the 4-methoxypyridinium cation (7.60, Y ¼ OMe) are given in Table 7.2.1016 The LUMO of the former will obviously be lower than that of the latter. The most selective radical is the tert-butyl, which reacts 350 000 times more rapidly with the cyano compound than with the methoxy. This is because the tert-butyl radical has the highestenergy SOMO, which interacts (B in Fig. 7.7) very well with the LUMO of the 4-cyanopyridinium ion, and not nearly so well (A) with the LUMO of the 4-methoxypyridinium ion. At the other end of the scale, the methyl radical has the lowest-energy SOMO, and hence the difference between the interactions C and D in Fig. 7.7 is not so great as for the corresponding interactions (A and B) of the tert-butyl radical. Therefore, it is the least selective radical, reacting only 50 times more rapidly with the cyano compound than with the methoxy. The other alkyl radicals in the table show a regular pattern, consistent with this analysis.

7 RADICAL REACTIONS

383

Table 7.2 Relative rates of reaction of alkyl radicals with the pyridinium cations 7.60 Attacking radical Me• n-Bu• sec-Bu• tert-Bu•

kY ¼ CN/kY ¼ OMe

SOMO energy (–IP in eV)

46 203 1300 350,000

–9.8 –8.0 –7.4 –6.9

LUMO A

LUMO B

C tBu

Me

Fig. 7.7

SOMO

D OMe

CN

N

N

H

H

SOMO

Interactions of frontier orbitals for the reaction of alkyl radicals with pyridinium cations

The most vexed subject in this field is the site of radical attack on substituted aromatic rings. Some react cleanly where we should expect them to. Phenyl radicals add to naphthalene 7.63, to anthracene 7.641017 and to thiophene 7.65,1018 with the regioselectivity shown in the diagrams. In all three cases, the frontier orbitals are clearly in favour of this order of reactivity; we should note that, because of the symmetry in these systems, both HOMO and LUMO have the same absolute values for the coefficients, so there is no ambiguity here as to which to take. Ph

87%

Ph

84% 14%

13%

0.425 0

0.440

0.263

0.311 0.091

7% 2% 0.371

Ph 93%

0.220 0.600

S 7.63

7.64

7.65

However, there is a lot of evidence that radicals are much less selective than cations and anions. Thus, dimethylamino radicals attack toluene1019 to give 10% ortho-, 47% meta- and 43% para-dimethylaminotoluenes; phenyl radicals attack pyridine with little selectivity,1020 and chlorine atoms attack naphthalene unselectively.1021 Since all substituents stabilise radicals, substituted benzenes usually (but not invariably, see Table 7.1) react faster than benzene itself, and most of them, whether C-, Z- or X-substituted, show some preference for ortho/para attack, no doubt because attack at these sites gives the more stable intermediate radicals. In assessing the contribution of the frontier orbitals, we are back with the problem (see pp. 170–173) of how to describe the orbitals of substituted benzene rings—in other words, how to estimate the relative importance of the two high-lying occupied orbitals ( 2 and 3) and the two low-lying unoccupied orbitals

384

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

( 4* and 5*). Thus the HOMO and the LUMO shown in Fig. 7.6, for example, are best thought of, not as single orbitals, but as composites of the kind discussed in Chapter 4. One trend seems clear, and it is a trend readily explained by the frontier orbitals. In an X-substituted benzene, like toluene or anisole, the proportion of meta attack falls as the energy of the SOMO of the attacking radical rises (Table 7.3). This trend is usually put down to the increasing ‘electrophilicity’ of the radicals. Because the HOMO and LUMO energies of X-substituted benzenes will be raised, we can expect that the HOMO of the aromatic ring is the more important frontier orbital. We have already seen (see p. 171) how the frontier electron population is effectively higher in the ortho and para positions for an X-substituted benzene. Thus, the lower the energy of the SOMO of the radical, the better the interaction with this weighted combination of orbitals, as we have already seen in Fig. 7.6, and hence the more ortho and para attack there is.

Table 7.3

Regioselectivity in the attack of a range of radicals on anisole1022

Attacking radical

%o

%m

%p

(%oþ2%p)/%m

SOMO energy (–IP in eV)

Me3Si• cyc-C6H11• Ph• Me• HO2CCH2•

62 67 69 74 78

31 28 18 15 5

7 5 13 11 17

2.5 2.8 5.3 6.4 22.4

–7 –7.8 –9.2 –9.8 –10.9

7.4

Synthetic Applications of the Chemoselectivity of Radicals

The perception of four or five decades ago that radical reactions were too unselective and uncontrollable to be of much use in organic synthesis has been replaced by an active sense that, with careful thought beforehand, they can be used effectively. Reactions can be designed to take advantage of what is known about radical reactivity and selectivity—combining nucleophilic radicals with electrophilic partners, electrophilic radicals with nucleophilic partners, using ring-forming steps that are inherently faster than intermolecular reactions, and using high dilution for one of the components when the relative rate constants are less favourable. Here we shall merely look at some short synthetic sequences showing how selectivity at each step allows a chain of events to take place, to give largely one product, with a number of different radical intermediates, each of which does what is wanted in competition with other pathways. One commonly used sequence is the conjugate addition of a radical derived from an alkyl halide to an electrophilic alkene. The first step is the thermal cleavage of 2,20 -azobisisobutyronitrile (AIBN) to give the initiator radical 7.66. This radical is formed easily simply by heating the AIBN, because it is highly stabilised (see pp. 81–83), because there is a favourable entropy term for the formation of three molecules from one, and because its formation releases molecular nitrogen, which keeps the two isobutyronitrile radicals far enough apart to minimise their coupling. Coupling would otherwise be a fast step (Section 7.7), removing them from the scene. The isobutyronitrile radical 7.66 faces three possible reaction partners: the tin hydride 7.67, the alkyl halide 7.68 and methacrylonitrile 7.70. It is neither particularly nucleophilic nor electrophilic, having two weak X-substituents and one Z-substituent, which roughly cancel each other out.1023 The highest rate constant for reaction with any of the substrates present is for attack on the tin hydride, because it has a weak H—Sn bond (bond dissociation energy 308 kJ mol–1, compared with a range from 385 to 435 kJ mol–1 for the H—C bonds in alkanes) with a high-energy HOMO. The tin radical, with a high-energy SOMO, is powerfully nucleophilic, and tin forms a strong bond to halogens. Accordingly it selectively attacks the alkyl halide 7.68 to displace the alkyl radical 7.69. This mildly nucleophilic radical selects the electrophilic alkene 7.70 with its low-energy LUMO, and gives the new radical 7.71, with the usual regioselectivity. This radical

7 RADICAL REACTIONS

385

is constitutionally similar to the initiator radical 7.66, and so it continues the chain by abstracting a hydrogen atom from the tin hydride to give the product 7.72 together with the tin radical, which can recirculate by attacking another molecule of alkyl halide. AIBN is only needed in catalytic amounts to initiate this chain of reactions. It is a key feature that the radical 7.71 is not nucleophilic enough to add rapidly to another molecule of the electrophilic alkene 7.70, propagating its polymerisation. The rate constant for the hydrogen atom abstraction is approximately 300 times larger than that for the attack on the alkene.1024 Thus each of the three key steps has well matched components with high selectivity, and the overall yield is correspondingly high. CN N

cleavage

H

N

CN

CN 7.66

AIBN

SnBu3 7.67 hydrogen abstraction

CN

I SnBu3 halogen abstraction

7.68

7.69

7.70

addition to an alkene

CN

CN

hydrogen abstraction

H +

7.72

SnBu3

7.71

SnBu3

A complementary sequence uses an alkyl halide 7.73 with a Z-substituent to create an electrophilic radical 7.74 in the presence of a nucleophilic alkene 7.75. In this case, the radical 7.76 expels the low-energy tributyltin radical to regenerate the tin radical, achieving overall the allylation of the ester, catalytic in both the AIBN and the tin hydride, to give the ester 7.77.1025 MeO2C

Br

7.73

SnBu3

HSnBu3, AIBN catalysts

MeO2C

MeO2C

SnBu3 7.75

7.74

MeO2C

7.77

+

SnBu3

SnBu3 7.76

The components used in these two sequences cannot be interchanged without some adjustment. Thus the Z-substituent in the radical 7.74 is necessary for an efficient reaction—in its absence the allylstannane has to be used in large excess. Similarly, a vinylogously X-substituted radical 7.79, derived from cyclohexenone 7.78, will have a high-energy SOMO; it does not add at all to allyltributyltin 7.75, but it does add to the allylstannane 7.80 equipped with a Z-substituent to give the radical 7.81 and hence the ester 7.82.1026

386

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

O

OSnBu3

SnBu3

CO2Et

HSnBu3, AIBN catalysts

SnBu3 7.78

7.79

OSnBu3

7.80

OSnBu3 CO2Et

CO2Et SnBu3

7.82

+

7.81

SnBu3

Similarly, the cyclohexyl radical 7.69 only adds to the vinylstannane 7.83 to give the radical 7.84 and hence the ester 7.85 provided that it is equipped with a C- or Z-substituent.1027 HSnBu3, AIBN catalysts

Bu3Sn

CO2Et

Br SnBu3

7.69

7.83

CO2Et 7.85

+

SnBu3

CO2Et 7.84

SnBu3

Similar sequences can add yet another step without loss of control, by having either a cyclisation or an atom transfer, which, because of their intramolecular nature, can be faster than the alternative steps. Thus, the tributyltin radical selectively removes the halogen from the starting material 7.86 to produce the primary alkyl radical 7.87 but this undergoes the cyclisation to give the secondary radical 7.88, not because the reaction of a simple alkyl radical with an unconjugated double bond is inherently fast, but because it is intramolecular and forming a five-membered ring. Only then does the radical 7.88 continue on its normal course of reacting with the electrophilic alkene 7.89, to give the radical 7.90. Since this has been equipped with a stannyl leaving group it gives the prostaglandin precursor 7.91, and regenerates a tributyltin radical, completing the catalytic cycle.1028

7.5

Stereochemistry in some Radical Reactions1029

Unlike alkyl halides in SN2 reactions or alkyllithiums in SE2 reactions, radicals have no intrinsic stereochemical preference at the reactive centre, except that trigonal radicals, and even cyclopropyl radicals, provided that there is an  electronegative substituent, can retain the configuration of their halide precursors.1030 Otherwise, radicals, being somewhere in between cations and anions, show some of the same stereochemical preferences discussed in Chapter 5, such as attack on the exo face of bicyclic systems, and on the less hindered face of open-chain double bonds, which is useful when the less hindered face can be

7 RADICAL REACTIONS

387

identified with confidence. Radical additions to alkenes have transition structures early on the reaction coordinate, with the bond being formed still quite long, making steric effects relatively weak. This has the advantage that bonds between heavily substituted centres can often be made more easily by radical reactions than by ionic reactions, but it also means that diastereocontrol in radical reactions is sometimes rather worse. For example, in additions to alkenes attached to chiral auxiliaries like Oppolzer’s sultam, radicals are much less selective than the additions of organometallic nucleophiles. OEt

OEt

OEt SnBu3

I

O

O

O

H

Bu3SnH

H Bu3Sn

C5H11

AIBN catalysts TBDMSO 7.86

O

TBDMSO

TBDMSO 7.87

7.88

OEt

7.89

OEt

O

O

H

H H

H

TBDMSO

TBDMSO

O 7.91

+

Bu3Sn

Bu3Sn

O 7.90

The stereochemistry of exo closure in a case like the radical 7.92, giving the cis product 7.94 (cis:trans 72:28), is controlled by the usual preference for the resident substituent to adopt an equatorial orientation 7.93 and for the chain of atoms to adopt a chair-like conformation.1031 In the case of a radical like 7.95, however, there is a clearly contrathermodynamic preference for the formation of the cis product 7.97.1032 It has been suggested that the endo-like transition structure 7.96 might have an attractive secondary orbital interaction from the filled hyperconjugative orbitals with the p* orbital, rather like that used to explain the endo rule for Diels-Alder reactions. The preference for cis products like 7.97 does not extend to all substituents on the radical centre, and Z-substituents often lead to trans products, possibly because they lack the same set of orbitals, but probably also because they are larger than a methyl group.

7.93

7.92

7.94

LUMO 1ry

H H

7.95

2ry

7.96

H H H

SOMO

7.97

388

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

Radical reactions have some stereochemical features that can be compared directly with their ionic counterparts, especially when the radical centre is adjacent to an existing stereogenic centre. The oxophilic tris(trimethylsilyl)silyl radical adds to chiral ketones like 3-phenyl-2-butanone to give a radical 7.98 flanked by a stereogenic centre. The next step, the hydrogen atom abstraction from a thiol, determines the relative stereochemistry. The products 7.99 and 7.100 are analogous to those from the hydride reduction of the ketone, and are formed in the same sense, and to closely the same degree, as those governed by Cram’s rule for the corresponding lithium aluminium hydride reductions. It seems likely that the explanation 7.101 is similar to that for nucleophilic attack given by Felkin and Anh 7.102 (see p. 226). The SOMO of the radical is similar to the LUMO of the ketone, since it is similar to the radical produced from a ketone by putting an electron into p*. The pyramidalisation will be in the same sense, the equivalent of the Bu¨rgi-Dunitz angle is likely to be obtuse, and the transition structure is likely to be early for this strongly exothermic reaction. The same stereochemical outcome is seen in C—C bondforming reactions when similar radicals attack allyltributylsilane.1033 If there is an electronegative substituent like a methoxy group on the stereogenic centre, it appears to adopt the role of the large substituent, just as it does in hydride reductions (see p. 228), and this sense of attack can similarly be inverted by chelation control.1034 OSi(SiMe3)3 Ph

H

HSC12H25

Me Me

OSi(SiMe3)3

Ph

(Me3Si)3SiO

Me

Me

7.99 SR

AlH3 H Me

Me

7.100

74:26

H H

Me

+

Me

7.98

H

Ph

H

OSi(SiMe3)3 Ph 7.101

Me

Me O Ph 7.102

However, there are many cases where an open-chain radical gives stereoselectivity that is less obvious. The radical 7.103 can be expected to attack anti to the donor substituent, but the major product 7.104 in the capture of a bromine atom implies a conformation which is no longer obviously the preferred one, since the two alkyl substituents are gauche rather than anti.1035 This is another ‘inside methyl’ effect (see pp. 233 and 242) allowing the bromide to attack close to the small substituent, the hydrogen atom. R Br H

O

Me

SiMe2Ph

O

O

O

–78 °C H

SiMe2Ph

N

N

O Br

7.103

O

7.104 91:9

In a cyclic system with nucleophilic radicals, the cyclohexyl radical 7.105 attacks tin deuteride, and other reagents with a small steric demand, to give the cyclohexanes 7.106 with the incoming group axial. When the

7 RADICAL REACTIONS

389

reagent is more sterically demanding, as with acrylonitrile, the preference changes to equatorial attack, in line with the reactions of cyclohexanones with sterically demanding nucleophiles (see pp. 229–231).1036

H H

X

7.105

7.106

X

axial:equatorial

D OH Cl CH2CH2CN

70:30 80:20 77:23 45:55

Similarly, the cyclohexene 7.107 selectively loses the axial hydrogen from the allylic position with the C—H bond best aligned with the p bond, and the intermediate radical 7.108 selectively picks up the chlorine atom from the axial direction to give the less stable of the two possible diastereoisomers 7.109.1037 The cyclohexyl radical 7.111 derived from pyrolysis of the oxalate 7.110 again loses the axial hydrogen selectively to give the alkene 7.112, although the alternative 7.113 is the more stable isomer.1038 OBut

H

OBut

Cl

t

Cl

t

Bu

t

Bu

7.107

Bu

7.108

7.109

H t

100 °C Bu

t

t

Bu

OCOCO2But

t + Bu

Bu

H 7.110

7.111

7.112

88:12

7.113

With better electronic support than that in the simple cyclohexyl radical 7.105, the anomeric radical 7.114, attacks tin deuteride and, more significantly, even acrylonitrile axially with high selectivity, anti to the lone pair, to give with the latter the -C-glycoside 7.115.1039 In the abstraction of a hydrogen atom from an anomeric carbon, which is the reverse of this type of reaction, we have already seen the highly selective removal of a hydrogen atom anti-periplanar to two lone pairs in the acetal 7.28. This stereoelectronic effect in radical reactions, called the ‘-oxygen effect,’ may be the basis for the selective activation of this type of hydrogen in the ozonolysis of acetals.560 The same activation is seen in the higher rate of radical formation from anomeric xanthates than from those without the anomeric orientation, but this explanation has been questioned.1040

AcO AcO AcO

CN

O H AcO 7.114

–20 °C

AcO AcO AcO

O H AcO

7.115

CN

98:2

In open-chain systems with electrophilic radicals, the conformation for attack on the enol radicals 7.116 and 7.117 is similar to that for enolate alkylation 5.201 and protonation 5.202, respectively (see p. 242), but in contrast to the selectivity shown by the nucleophilic radical 7.98.1041,1042 As usual, the radical centre is attacked anti to the large substituent, but the small substituent is ‘inside’.

390

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

O H H

OEt O

O OEt

7.116

+

OEt

62:38 SnBu3 O H

Me

OMe O

O OMe

OMe

96:4

H 7.117

+

SnBu3

One final stereochemical point is that the abstraction of a hydrogen atom has a high preference for a linear transition structure. This can be explained using the orbitals for hydrogen bonding (see p. 118); the system with two electrons is the transition structure for hydride transfer between carbocations, and with four electrons it is the conventional hydrogen bond, both of which have linear arrangements. The transition structure for hydrogen atom transfer is the same system, but with three electrons, which will also be linear. This accounts for the high selectivity for g-hydrogen transfer 7.118 in intramolecular reactions.1043 Smaller rings cannot attain even approximately the linear arrangement, and larger rings are less probable; since C—H bonds are shorter than C—C bonds, the transition structure with the six-membered ring is close to ideal, and could perhaps be better described as a five-and-a-half-membered ring.1044

O

H

O OAc

O

7.6

7.118

Ambident Radicals

7.6.1 Neutral Ambident Radicals The regioselectivity argument for an ambident radical is a simple one—the site of attack should be determined on the product side of the reaction coordinate by the relative stability of the regioisomeric products, and on the starting material side by the coefficients of the SOMO. This is commonly what is observed. Thus, a monosubstituted allyl radical, generated by adding a radical to a diene, usually reacts at the unsubstituted end of the allyl radical, as in the bromination of the radical 7.31 on p. 376. This gives the more substituted alkene, and the radical also has the larger coefficient at the terminus, since it is an allyl system with an X-substituent (see p. 162), for which the SOMO will be similar to the LUMO of an ,-unsaturated carbonyl compound. The same factors are even more powerfully present in the radical 7.79, which is completely selective for attack at the site remote from the X-substituent. We have already seen with the radicals 7.2, 7.74 and 7.116, that -carbonylmethyl (enol) radicals react more readily at the carbon atom than at the oxygen atom, and we know that the coefficient on carbon is higher than at oxygen in the SOMO, just as it was for the HOMO of the enolate ion. With radicals, however, we do not have the complicating factor that differential solvation may be the whole explanation.

7 RADICAL REACTIONS

391

If orbital and product development arguments are in conflict, we might expect orbital effects to be more important, since the key steps of radical reactions are so often strongly exothermic. The cyclohexadienyl radical 7.119 should have a higher coefficient at C-3 (see p. 164) than at C-l, and indeed it seems that this site most readily extracts a hydrogen atom from another molecule.1045 The unconjugated product 7.120 is clearly not thermodynamically the more stable of the two possibilities, and so this result is more likely to be orbital control and not product-development control. Cyclohexadienyl radicals usually combine with other radicals predominantly in this sense,1046 but open-chain pentadienyl radicals are not so completely regioselective.1047 Cathodic electrolysis of pyridinium ions 7.121 causes an electron to be added to the ring. This electron is in an orbital resembling the LUMO of pyridine (see pp. 60 and 184), which has the largest coefficient at the 4-position. This is the site of dimerisation giving largely the 4,4-dimer 7.122.1048 Ph Ph

Ph

H 1

3

H

Ph

H

H

H

7.119

+e

N

+ Ph

Ph

7.120

N

N

4

H 4 4

H 7.121

N

7.122

The best-known neutral ambident radicals are phenoxy radicals. Many substituted phenoxy radicals couple to give the polymers in wood, and dimerise or couple intramolecularly in the biosynthesis of a number of alkaloids,1049 It is believed that many phenoxy radical couplings are actually the coupling of radical with radical and not of radical with neutral molecule, although the attack of a radical on a phenate ion may occasionally be an important pathway. A radical coupling with a radical is inherently a very fast process, since it is so exothermic, but only relatively stable radicals live long enough to encounter another radical; phenoxy radicals may well belong in this class. In any event, we can expect a large number of possible products. As it happens, all these possibilities have been observed with one compound or another. In general, o-p, p-p, and o-o are rather more common than O-p and O-o, and these are much more common than O- O. This is in line with the aptitude for enol radicals to react at carbon rather than oxygen. We can obtain a measure of the electron distribution in the SOMO of a phenoxy radical from ESR, which shows high coupling constants to the hydrogen atoms at the ortho and para positions (1.65 ¼ 7.123, Fig. 7.8).1050 In addition, we know that there must be some odd-electron population on the oxygen atom (a coupling of 10–23 G has been observed to 17O in the radical 7.124).1051 We can use the McConnell equation (see p. 66) to O

O t 6.7

10.23

O

0.25

But

Bu

0.27

–1.9

–0.07

10.2

0.40 t

7.123

Bu

7.124

7.125

Fig. 7.8 Hyperfine coupling constants measured for phenoxy radicals 7.123 and 7.124 and estimated spin populations 7.125

392

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

estimate this. The value of Q for a C—H coupling is generally about –24, and the value of Q for the coupling of an electron in a p orbital on oxygen to the oxygen nucleus when all the electron population is in that orbital has been estimated to be about –40 (measured on p-semiquinone).1052 Using these numbers we get spin populations as shown in 7.125, but these numbers must be regarded as orders of magnitude only—the hyperfine splittings and the Q-values were obtained from different compounds, and the McConnell equation is far from fool proof. This electron distribution tells us that all three positions—oxygen, ortho, and para— have high coefficients. We should remember that the -value for C—O bond formation is less than for C—C bond formation, further enhancing the tendency for bonding to carbon. It is not clear from the experimental evidence whether p-p coupling really is preferred, as these numbers would suggest. The problem is that products are often obtained in low yield, and the mass balance is usually poor. In addition there is the statistical effect of there being two ortho positions to one para. We can guess that there will not be much in it, and that does seem to be the case, judging by the natural products that can be found with all these patterns. One simple example of much-preferred para attack is in the Elbs persulfate oxidation of phenol. The reaction is usually written as the combination of a phenoxy radical 7.123 with the persulfate radical anion 7.126, but it could be phenoxide ion undergoing electrophilic substitution: in any event, para attack is substantially favoured over ortho attack.1053 O

OH

OH OH

OSO3

+

7.126 OH

7.123

91:9

A phenoxy radical conjugated into a side chain 7.127 is derived from coniferyl alcohol. Here we would expect the -carbon of the styrene unit to be the site of highest odd-electron population. The three major products, 7.128, 7.129 and 7.130, shown with the critical bonds in bold, are formed by reaction at this site in steps that are important because they model the reactions involved in lignification.1054 HO

MeO

O

MeO

o

OH

OH

HO

HO

O

OMe

O OMe 7.128

-o

~40%

7.129 ~15%

-

MeO

OH

O HO

o-o

o

-O 7.127

OMe HO

o o

OH OH

small amount

OH MeO

OH

MeO

OMe

O HO 7.130

~9%

7 RADICAL REACTIONS

393

7.6.2 Charged Ambident Radicals 7.6.2.1 Radical Cations.1055 Radical cations are usually prepared using an oxidising agent to remove one electron from substrates with a high ionisation potential, in other words a high-energy HOMO. The result, if the starting material is uncharged, is a radical cation with a SOMO having a similar energy to the original HOMO. Thus the SOMO can interact strongly with the HOMO of the same or another molecule, and in both the large coefficients of the atomic orbitals are the nucleophilic sites. The result is that bonds are often formed between two nucleophilic sites, achieving an umpolung of reactivity.

AcO

OAc

H

1

OAc Mn3+ 7.132

7.131

For example the radical cation 7.131 is generated by oxidation of 2-methylnaphthalene. The odd electron is in the HOMO of naphthalene, the highest coefficient of which is at C-1. The methyl group, as an X-substituent, will further enhance the coefficient at this site relative to the other -positions; thus, the total electron population at this site will be higher than at the other -positions, and yet the nucleophile, an acetate ion, attacks at this site. That an anion should attack a site of relatively high electron population is easily accounted for by the SOMO/HOMO interaction. The intermediate radical 7.132 eventually gives l-acetoxy-2-methylnaphthalene when a radical abstracts the hydrogen atom. More surprising looking, but essentially the same story, is the anti-Markovnikov addition of water or methanol to some alkenes under photo-oxidation conditions. 1-Phenylcyclopentene, for example, on irradiation in the presence of a single-electron acceptor like 1-cyanonaphthalene loses an electron to give the radical cation 7.133. The single electron is in the HOMO of a C-substituted alkene, which has the larger coefficient at C-2, and this is where the nucleophile attacks. The product radical 7.134 subsequently picks up a hydrogen atom from the solvent to give the anti-Markovnikov product 7.135.1056

Ph

Ph h , MeOH 2-cyanonaphthalene

1

Ph MeOH

H

O

2

7.133

Ph

H

OMe Me

7.134

7.135

Anodic electrolysis of aniline and dimethylaniline give radical cations 7.136 and 7.138, which are stable enough to dimerise, giving predominantly N-p and p-p coupling 7.137 and 7.139, respectively.1057 This is just like the phenoxy radical coupling except that, with nitrogen being less electronegative than oxygen, there will be a larger coefficient on nitrogen than there was on oxygen, and there will also be a higher -value for N—C bond formation than there was for O —C bond formation. No doubt the methyl groups in the dimethylaniline 7.138 exert a mild electronic and more severe steric effect to tip the balance in favour of C—C coupling. As with phenolic coupling, N-N bonding remains relatively unfavourable.

394

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

NH2

–e

H N

NH2

p

p

H 7.136

–e

N

several products

NH2

7.137

N

p

N

H p

N

p

H 7.138

7.139

The oxidation of enol ethers can be carried out using such reagents as ceric ammonium nitrate (CAN). The SOMO of the radical cation is essentially the same as the HOMO of the starting material, which is an Xsubstituted alkene. The interaction of this orbital, with its large coefficient on carbon, with the HOMO of the same or another enol ether, leads to C—C bonding and the formation of 1,4-dicarbonyl systems.1058 The silyl dienol ether 7.140 has a higher energy HOMO than the silyl enol ether 7.142, and is therefore the more easily oxidised. The radical cation 7.141 then couples with the silyl enol ether 7.142 with regioselectivity that gives, after further oxidation and hydrolysis, the most stable possible product 7.143, having joined the carbon atoms which have the highest coefficients in the SOMO and HOMO, respectively.1059 CAN –e

Me3SiO

OSiMe3

O

Me3SiO OHC

MeCN 7.140

7.141 7.142

7.143

Similarly, oxidation of the silyl enol ether 7.144 using photoinduced electron transfer (PET) in an aprotic solvent gives the radical cation 7.145. This cyclises onto the double bond by the unusual 6-endo path, in contrast to the usual 5-exo preference of the neutral -keto radical 7.146, which is generated from the same source in a hydroxylic solvent.1060 The radical centre in the radical cation 7.145 is conjugated to a more powerful Z-substituent, the coordinated and charged carbonyl group, than the radical centre in the radical 7.146, and it may be that this lowers the energy of the SOMO, increasing the SOMO/HOMO interaction that should favour bond formation to the terminus of the double bond, as discussed on p. 379. OSiMe3

O H

–e OSiMe3

PET MeCN

H 7.145 O

O H

7.144

–e PET MeOH

H 7.146

The radical cations of conjugated systems can also take part in pericyclic reactions. Examples are known of cycloadditions, electrocyclic reactions and sigmatropic rearrangements. One noticeable feature of some of

7 RADICAL REACTIONS

395

these reactions is that formally forbidden reactions like [2 þ2] cycloadditions and 1,3-sigmatropic rearrangements, seem to take place relatively easily. One reason might be that the radical cations simply act as radicals, and the reactions are stepwise. It is also possible, with only one electron, that the barrier to the forbidden reaction is significantly less. Another feature of these reactions that might be significant in their photochemical reactions is that it is formally possible for a radical cation in an excited state to correlate in a state correlation diagram with the radical cation product in its ground state. This is not possible in singly excited neutral molecules, which correlate only with the excited state of the product.1061 7.6.2.2 Radical Anions. Radical anions are complementary to radical cations: they are usually prepared using a reducing agent to add one electron to substrates with a high electron affinity, in other words a lowenergy LUMO. If the starting material is uncharged, the result, is a radical anion with a SOMO having a similar energy to the original LUMO. The radical anion can either couple or its SOMO can interact strongly with the LUMO of the same or another molecule, and in both pathways the large coefficients of the atomic orbitals are the sites that were originally or are still electrophilic. The net result is that bonds are often formed between two electrophilic sites, achieving again an umpolung of reactivity, as shown by the pinacol coupling of acetone 7.147,1062 the ,-coupling of methyl vinyl ketone 7.148,1063 the cross-coupling of the ,-unsaturated ester 7.149 with diethyl ketone in the presence of a Lewis acid,1064 and the 4,4-coupling of pyridine 7.150.1065 In each case, the odd electron has been fed into the orbital which was the LUMO of the starting material; the site of coupling therefore should, and does, correlate with the site at which nucleophiles attack the neutral compounds. O

O

Mg

O

HO

O

OH

7.147 O

O

O

O

cathode 7.148

O

O

O

O

O

O

cathode OMe

OMe

OMe

7.149 Me3Si Me3Si

N 7.150

O

OSiMe3

O

Mg N

OMe

N

4

4

N

+

2,4

+

2,2

95:4:1

In protic solvents, radical anions derived from ketones can pick up a proton instead of coupling, and the resultant radicals pick up a second electron, in competition with the pinacolisation. When this pathway is observed, the stereochemistry of the alcohol product appears to be determined at the radical anion or anion stage, and not in the final protonation step, which is probably faster than the pyramidal inversion of the anion.1066 The pyramidalisation of the radical anion in a conformation 7.151, like that of Felkin and Anh 5.120, has a steric clash that is greater than it was in the ketone itself. The alternative conformation 7.152, with the R group sitting between the small and medium-sized groups, is lower in energy, and leads to the anti-Cram product.

396

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

R

M O

S R

M O

S L

L

7.151

7.152

The experimental observation is that hydride reduction (Felkin-Anh control) of the ketone 7.153 gives the anti-alcohol anti-7.154 as the major product, but electron-transfer reduction gives its syn diastereoisomer syn-7.154.1067 This is in contrast to the reduction on p. 423, which differs in having a silyl group on the oxygen atom in a neutral radical. O

OH

OH [H]

Ph

7.153

Ph

+

anti-7.154

[H]

anti :syn

LiAlH4 Li, NH3

74:26 24:76

Ph

syn-7.154

In cyclohexanones, the pyramidalisation is similarly greater in the radical anion 7.155 than it was in the ketone 5.138 (see p. 230), thus explaining the high degree of synthetically useful selectivity for the formation of the equatorial alcohol trans-7.157 from the ketone 7.156, as a result of axial protonation.1068 H O H 7.155 O

OH

H Li, NH3, tBuOH

7.156

OH + trans-7.157

H cis-7.157

98:2

This stereochemistry is similar to that of a synthetically useful reduction of ,-unsaturated ketones. Stork found that octalones like 7.158 and sodium in liquid ammonia in the presence of an alcohol gave exclusively the trans-decalone 7.160, even when that was less stable than the corresponding cis-decalin.1069 In this reaction, an electron is fed into the LUMO of the unsaturated ketone 7.158, and hence the radical anion 7.159 will have a higher total electron population on C-5 (steroid numbering) than in the starting material, and C-5 can be expected to be more nearly pyramidal than planar trigonal. In other words, it will bend towards a tetrahedral geometry and, in so doing, relieve some of the steric strain in the rest of the molecule. This will be more efficient if the larger lobe of the atomic orbital on C-5 is on the lower surface, because the AB ring system will then be more like that of a trans decalin. Accordingly protonation takes place on the lower surface, and the product is the trans-decalone.

t

BuOH

Na, NH3 O

5

7.158

O

3*

7.159

O

H 7.160

7 RADICAL REACTIONS

397

Another radical anion is the intermediate in Birch reduction,1070,1071 where aromatic rings are reduced with sodium in liquid ammonia in the presence of an alcohol. The solvated electron adds to the benzene ring of anisole 7.161, for example, to give the radical anion 7.162. This is protonated by the alcohol present at the ortho position.1072 The cyclohexadienyl radical 7.163 from ortho protonation is the lowest-energy radical possible, and the ortho position has the highest total electron population. The SOMO will mostly be like the orbital 5* (see p. 35), with large coefficients on both ortho and meta positions. A computation shows that it has marginally the largest coefficient at one of the meta positions, indicating that frontier orbital control is not at work here, and that ortho-protonation simply takes place at the site of highest charge, which also leads to the most stable possible intermediate. The radical 7.163 is reduced to the corresponding anion 7.164 by the addition of another electron, and the new anion is protonated at the central carbon atom of the conjugated system, for reasons discussed on pp. 164–165, and also studied explicitly in connection with the regiochemistry of Birch reduction.1073 Thus, we can see how it is that X-substituted benzenes in general are reduced to 1-substituted cyclohexa-1,4dienes 7.165. OMe

OMe

OMe

OMe H

+e

ROH

OMe H

+e

H

H H ROH

H H H

7.161

7.162

7.163 O 1.300

7.164

Me

O

0.955 1.302

–0.554

1.259

+0.528

1.219

7.165 Me

+0.019 +0.503 –0.568

1.008

+0.047

-electron populations

5*

coefficients

In contrast, C-substituted benzenes like biphenyl 7.166 are reduced to 3-substituted cyclohexa-1,4-dienes 7.169,1071 and this too fits the analysis. The Hu¨ckel coefficients for the SOMO of the radical anion 7.167 also reflect the total p-electron distribution, since the other three filled orbitals lead to a more or less even distribution of p-electron population. So, regardless of whether it is the Coulombic or the frontier orbital term that is more important, both contributions lead to protonation at C-4 to give the radical 7.168. Reduction and protonation of this intermediate (or possibly a mixture with the 1-protonated isomer) leads to the observed product 7.169.1074 It is amusing that further reduction of this molecule also takes place, but now the benzene ring is an X-substituted one. The major final product, accordingly, is the hydrocarbon 7.170, which has been reduced 1,4 in one ring and 2,5 in the other. Ph

Ph

Ph

Ph

0.351

+e

0.299

+e

ROH

–0.140

ROH

–0.398

7.166

7.167 SOMO coefficients

H

H

7.168

7.169 7.170

398

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

The Birch reduction of benzoic acid is the same type as that of biphenyl, and the product, with protonation successively at C-4 and C-1 is the acid 7.172.1075 In the reaction medium, it will be benzoate ion 7.171 that is being reduced. As a result of the delocalisation of the negative charge in the benzoate ion, we should probably regard the carboxylate ion more as a C- than as a Z-substituent. O

O

CO2H +e ROH

1

+e ROH

4

7.171

7.172

Several other compounds which are easily reduced in a comparably explicable manner are exemplified by butadiene 7.173,159 already discussed on p. 108, diphenylethene 7.174,1076 naphthalene 7.175,1077 anthracene 7.1761078 and phenanthrene 7.177.1079 In reductions in liquid ammonia without alcohol present, two electrons must be added to the LUMO of the starting material before it is basic enough to abstract a proton from ammonia. The addition of the second electron to the radical anion is sometimes so slow that dimerisation occurs to some extent, as we can see in the case of diphenylethene and have already seen in earlier reactions. Na, NH3 +

+

7.173 Ph 1. Na, NH3

Ph Ph

2. NH4Cl

Ph

+ Ph

Ph

Ph Ph

7.174 Na, NH3, EtOH

Na, NH3, EtOH

7.175 1. Na, NH3 2. NH4Cl 7.176 1. Na, NH3 2. NH4Cl

7.177

7.7

Radical Coupling

Nevertheless, radical coupling is uncommon in organic synthesis. Most radicals are highly reactive, and it is rare for a high enough concentration of radicals to build up for it to be probable that a radical will collide with another radical before it has collided productively with something else. The coupling of radicals, of course,

7 RADICAL REACTIONS

399

brings radical chains of the kind used in alkene polymerisation (Section 7.1) and in organic synthesis (Section 7.4) to a halt. In polymerisation it brings chain elongation to an end, and leads the polymers to have a wide spread of chain lengths. In organic synthesis it creates by-products and requires more initiator to be present. We have seen several cases of radical coupling when the radicals or radical ions were relatively well stabilised, and therefore long-lived. Benzyl radicals are moderately well stabilised, and their coupling therefore is not uncommon. In contrast to phenoxy radicals, they have the highest oddelectron population on the exocyclic atom, and in one reaction in which coupling may be the pathway, benzyl radicals 7.178, derived by halogen abstraction from benzyl chloride, do give largely dibenzyl 7.179.1080

Cl

7.178

7.179

Radical coupling is more frequently seen when the two radicals are created together, typically within a solvent cage or within the same molecule, so that they are more likely to meet each other before something else can happen to them. If a single electron transfer (SET) takes place from one molecule to another, the result is a pair of radicals which can combine. We saw (see pp. 145–149) that there is one school of thought that this is the mechanism of a high proportion of organic reactions, where the argument is that the radical coupling is so fast that the individual radicals cannot easily be detected. However, when the radicals are relatively well stabilised, their coupling is slow enough for them to be detected. In Kornblum’s reaction 1081 7.180 þ 7.181, which looks superficially like an SN2 reaction, radicals are well established intermediates. The nitronate 7.180 transfers an electron to the nitrobenzene 7.181 to give the 2-nitropropyl radical 7.182 and the radical anion 7.183. The loss of chloride ion from the radical anion gives the benzyl radical 7.184, which couples regioselectively at the exocyclic carbon with the radical 7.182, regioselectively on carbon just as we should expect from the coefficients in the SOMOs. Cl

O N

O

+

N

transfer NO2

7.180

Cl

O electron

O

+ NO2

7.182

7.181

7.183 –Cl– radical

O2N

coupling NO2

NO2 7.185

7.184

Another reaction that cannot be an SN2, because of the impossibility of carrying it out on an aryl halide, is the displacement from the aryl bromide 7.187. The mechanism is an SRN1 reaction (see p. 147), involving an electron transfer from the enolate 7.186 to the halide 7.187. The radical anion 7.189 loses the bromide ion to give the aryl radical 7.190, and this couples with the radical 7.188 derived from the nucleophile to give the ketone 7.191.252 The m-methyl group shows that the reaction did not take place by way of a benzyne.

400

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

O

electron

+

+

transfer

Br 7.186

O Br 7.188

7.187

7.189 –Br–

radical

O

coupling 7.191

7.190

The discussion on pp. 140–141 established the many reasons why an allyl anion and an allyl cation react with electrophiles and nucleophiles, respectively, at C-l (and C-3) of the allyl system. The force of these arguments is less when they are applied to the reaction of an allyl radical with a radical. Although the frontier orbital interaction will still favour attack at C-l in the usual way, the interaction of the SOMO of a radical, especially a low-energy SOMO, with 1 of an allyl radical will not be negligible. Since 1 has the larger coefficient on C-2, reaction at this site is made less unfavourable than it might at first appear, and, with radicals, there is little contribution from Coulombic forces. All this, in addition to the usual preference for forming a six-membered ring over a seven-membered ring, may explain why the reaction of the diradical 1,8-dehydronaphthalene 7.192 and butadiene takes place predominantly at C-2 of the allyl system 7.193 (arrows) to give the diradical 7.194.1082 Alternatively, if the diradical 7.193 is a triplet, then radical coupling will be slowed down, giving it time to undergo an electrocyclic change to the cyclopropyl radical 7.195 before coupling to give the cyclopropane 7.196. We shall see some more examples of radical coupling in the next chapter, where the radicals are created by irradiation with light.

N

N

N

NH2 Pb(OAc)4

7.192

7.193

7.194

7.195

7.196

8

Photochemical Reactions

Radicals, as we have just seen in Chapter 7, are highly reactive. Thermodynamically, they are high in energy, since one electron is in a nonbonding orbital instead of being low in energy in a bonding orbital. Furthermore, the single electron is able to interact with both frontier orbitals of the other component, making radicals kinetically unstable too. The same pattern is seen in photochemical reactions, but to a greater degree. The promotion of one electron from a bonding to an antibonding orbital raises the energy even more, making excited states thermodynamically highly unstable. The presence of two singly occupied orbitals in the excited state doubles the number of energetically profitable frontier orbital interactions, and the frontier orbitals are likely to be even closer in energy to the orbitals with which they interact than they were for radical reactions. The interactions are now first-order, and Equation 3.13 is no longer appropriate. Photochemistry therefore is replete with remarkable reactions—with the large amount of energy trapped in the excited state, it is hardly surprising that many of the familiar patterns of reactivity in ground-state chemistry are turned on their heads. Nevertheless, we shall see that there is some order in this subject when we take account of the orbitals that are involved.

8.1

Photochemical Reactions in General

In most bimolecular photochemical reactions, the first step is the photoexcitation of one component, usually the one with the chromophore which most efficiently absorbs the light. This molecule is usually the one with the smallest separation in energy between the HOMO and the LUMO. Typically, if a conjugated system of carbon atoms is present in one component, it can absorb a photon of relatively long wavelength, and in doing so an electron leaves the HOMO and arrives in the LUMO. Alternatively, an electron in a nonbonding orbital, like that of the lone pair on the oxygen atom of a ketone, which usually is the HOMO, is promoted from this orbital to the LUMO of the carbonyl group. The excited states produced are called p-p* and n-p*, respectively. They may react directly in their singlet state, or later, after intersystem crossing, in their triplet state. The second step of the reaction, if it is bimolecular, is between the photochemically excited molecule and a second molecule, which may or may not be the same compound, in its ground state. For this kind of reaction, there will generally be two energetically profitable orbital interactions (Fig. 8.1): (1) the interaction between the singly occupied p* orbital of the excited molecule, labelled ‘LUMO’ and the LUMO of the molecule which is in its ground state; and (2) the interaction of the singly occupied n or p orbital of the excited molecule, labelled ‘HOMO’ and the HOMO of the molecule which is in its ground state.756,1083 Both interactions will usually be strong because the interacting orbitals are likely to be close in energy. Partly for this reason, this step of a photochemical reaction is often very fast. As they are so strong,

Molecular Orbitals and Organic Chemical Reactions: Reference Edition  2010 John Wiley & Sons, Ltd

Ian Fleming

402

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

'LUMO'

'HOMO'

Excited molecule

Fig. 8.1

LUMO

HOMO

Ground-state molecule

Frontier orbital interactions between a photochemically excited molecule and a ground-state molecule

the perturbations are first order, and the mathematical treatment of them would not take the form of the third term of Equation 3.13. Fig. 8.1 is shown for the singlet excited state, with the electrons having opposite spins in the singly occupied orbitals, but the interaction is not significantly different for the triplet state, when they have the same spin—it creates a similar set of four new orbitals. The triplet state cannot give the ground-state product until another intersystem crossing has taken place, and this delays the final bond-forming steps. Singlet photochemistry and triplet photochemistry are often different in their final outcome, and it is important to find out which pathway is being followed. However, it does not affect many of the arguments in this chapter, which are about the first step. What it does significantly affect is the lifetime and pathways available for the intermediate created by the orbital interactions. In ground-state reactions, the first-order interactions of occupied orbitals with occupied orbitals are antibonding in their overall effect, and there is therefore a large repulsion between the two components of a bimolecular reaction. The bonding interactions of occupied orbitals with unoccupied orbitals are merely second-order effects lowering the energy of the transition structure. In photochemical reactions, however, the strong interactions shown in Fig. 8.1 can create an intermediate in which the total energy is lower than when the two components of the reaction were not interacting. This lower-energy intermediate can be identified as the excimer or exciplex, now well established in some photochemical reactions.1084 The two molecules have become stuck together. They are still in an excited state, many steps may have to be taken before they can settle down into the ground state of the product or products, but we shall not always be able to deal with these later steps in any simple way. Usually, in a bimolecular photochemical reaction following p-p* excitation:

The HOMO and the LUMO of one component in its ground state interact with what were the HOMO and LUMO, respectively, of the other component when it was in its ground state.

8 PHOTOCHEMICAL REACTIONS

403

A useful convention:

The orbitals which were the HOMO and LUMO when the excited molecule was in its ground state can be labelled the ‘HOMO’ and the ‘LUMO’, respectively. (The single quotation marks remind us that these orbitals are no longer the actual HOMO and LUMO at the time of the reaction, but were the HOMO and LUMO in the ground state, before the excitation took place.)

The generalisation for p-p* excitation does not necessarily apply to reactions set off by n-p* transitions, where only the LUMO/‘LUMO’ interaction is certain to be important. The interaction of the HOMO of the molecule in its ground state with the half-empty lone-pair orbital may or may not play a part, but the interaction of the HOMO of the molecule in its ground state with a lower lying but still fully occupied orbital of the molecule in its excited state will be repulsive as usual. Even with p-p* reactions, the acronym ‘HOMO’ used in this generalisation needs some qualification, since the important high-lying p orbital from which the electron was promoted may not precisely be the occupied orbital with the highest energy. Any lone pairs that may be present, but playing no direct part, are often the occupied orbitals with the highest energy, and when they are, it is not uncommon to see the p orbital that is involved referred to as the HOMO-1 or HOMO-2, or whatever it happens to be. Bearing these qualifications in mind, the important frontier orbitals in a photochemical reaction are HOMO/‘HOMO’ and LUMO/‘LUMO’. The HOMO/‘LUMO’ and LUMO/‘HOMO’ interactions are still bonding in character, as usual, but the energy separations are so much greater than for the HOMO/ ‘HOMO’ and LUMO/‘LUMO’ interactions that they are much less effective: their interactions involve only second-order perturbations. We now see why so many photochemical reactions are complementary to the corresponding thermal reactions. Photochemical reactions often seem to do the opposite of what you would expect of the equivalent thermal reaction, when there is one. In the latter it is the HOMO/ LUMO interactions which predominate in bond-making processes, and in the former it is HOMO/ ‘HOMO’ and LUMO/‘LUMO’. We shall now examine some ionic, pericyclic and radical reactions in which a molecule while still in its excited state reacts with another molecule, and how this greatly simplified but powerful perception explains some of the otherwise more puzzling features of these reactions.

8.2

Photochemical Ionic Reactions335

8.2.1 Aromatic Nucleophilic Substitution In certain cases, light promotes substitution reactions in aromatic compounds. One of the fascinating features of these reactions is an almost complete change in regioselectivity from that observed in the ground-state reactions.1085,1086 When the nitrocatechol ether 8.1 is irradiated in alkali1085 or in methylamine,1087 the nucleophilic substitution takes place meta to the nitro group. The nucleophilic substitution of p-nitroanisole 8.2, however, takes place para to the X-substituent.1085 Furthermore, with the meta isomer 8.3, it takes place meta to the Z-substituent.1088 3-Bromopyridine 8.4 readily gives 3-hydroxypyridine 8.5 on irradiation in aqueous alkali.1089

404

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

NO2

NO2

NO2

h NHMe

h

MeNH2

NaOH

OMe

OMe

OH

OMe

OMe

8.1 NO2

NH2

OMe

NH2

h

h

NH3 OMe 8.2

NO2

NH3

NO2

OMe 8.3 Br

NaOH

N 8.4

OH

h N 8.5

All these examples have a nucleophile attacking a photoexcited aromatic ring at a site where nucleophiles do not attack the aromatic ring in the ground state. We can now easily see why this should happen. In the ground-state reaction, the HOMO of a nucleophile interacts productively only with the LUMOs of the aromatic ring, which we defined as a weighted average of the orbitals 4* and 5* (see pp. 170–173). However, in the excited-state reaction, the HOMO of the nucleophile can interact productively with what were, before excitation, the HOMOs of the benzene ring (ignoring any unconjugated lone-pair orbitals), and these are a weighted average of 2 and 3. These orbitals, as we saw in Chapter 4, are those which, in aromatic electrophilic substitution, lead to meta attack on Z-substituted benzenes, and to ortho and para attack on X-substituted benzenes. It is the same here. The oxygen and nitrogen nucleophiles will have lowlying HOMOs, because they are electronegative. Thus we can expect that it will be these orbitals (essentially lone pairs) which provide the important frontier orbital for the right-hand side of Fig. 8.1. The LUMOs in the nucleophiles will be high in energy and out of range. Benzene 8.6 without activating substituents can also be attacked by nucleophiles, provided that it is in an excited state; this time the result is an addition reaction, since there is no nucleofugal group.1090 This is clearly another consequence of the ability of the HOMO of the nucleophile to interact productively with a singly occupied bonding orbital of the benzene ring when the latter is in an excited state. hν

N

hν

8.6 N H

N H

HN

Equally, with a single leaving group, and that not a good one, fluorobenzene 8.7 gives some substitution from the intermediate in which it is attacked at the ipso position, but the major products are the result of addition ortho and para.1091 Fluorine is an X-substituent by virtue of its lone pair, but not a powerful one, and the attack ortho and para by a nucleophile is therefore indicative of an interaction with the ‘HOMO’.

8 PHOTOCHEMICAL REACTIONS

405

NHBut

F

F

F NHBu

h + t

F

t

+

+

BuNH2

NHBu

8.7

t

NHBut

24:24:4:48

8.2.2 Aromatic Electrophilic Substitution A nearly complementary pattern of reactivity has been found for photochemical electrophilic substitution.1085,1086 Proton exchange in the photolysis of toluene 8.8 takes place most rapidly at the meta position.1085 In anisole 8.9, the corresponding reaction is predominantly ortho and meta. Nitrobenzene 8.10, however, exchanges protons most rapidly at the para position.1092 OMe

OMe

h

OMe D

h

+ CF3CO2D

CF3CO2D 2h

D

8.8

8.9 NO2

NO2

D 11%

NO2

NO2

D

h

+

+

CF3CO2D 4h 8.10

12%

D <1%

5%

8.6%

D

Again, because of photoexcitation, the important frontier orbital of the electrophile (the LUMO) is able to interact productively with an orbital (a p* orbital) of the benzene ring which was not productive in the ground state of any drop in energy (because there were then no electrons in it). Certainly 5* (see p. 35) has an electron distribution ideal for explaining ortho/meta attack in anisole, and, as we saw in Chapter 4, the LUMOs of nitrobenzene do lead to reactivity at the para position. Now that photoexcitation has placed an electron in these orbitals, an electrophile can take advantage of this electron distribution, whereas, in the ground state, only a nucleophile could. Of course, with charged electrophiles, the Coulombic term of Equation 3.13 will probably be more important than the frontier orbital term. However,the changes in electron distribution which are occasioned by photoexcitation all take place in frontier orbitals. So an argument based on changes in the total electron distribution is very similar to the one just given. Table 8.1 summarises the effect of frontier orbitals on aromatic nucleophilic and electrophilic substitution, both in the ground state and in the excited state. As we saw in Chapter 4 (see pp. 170–173), the orbitals of the benzyl system can be used as models for the orbitals of Z- and X-substituted benzenes. (The more important frontier orbital for attack by a nucleophile is shown in Table 8.1 in bold, and the more important frontier orbital for attack by an electrophile is shown in italics.) It is then clear how the favoured sites of attack listed at the bottom follow from the orbital picture. In those cases where meta attack is observed, this simple picture predicts both ortho and meta attack. We must not forget that 2 is very little lower in energy than 3, and 6* is very little higher in energy than 5*. When the contribution of these orbitals is taken into account, the reactivity at the meta position is enhanced. A particularly striking example of the change from ground-state chemistry is provided by the electrophilic substitution in tryptamine 8.12, where the 4-position of the indole ring has overtaken both the 3- and the 2-position (see p. 174) as the most nucleophilic site, in line with the large ‘LUMO’ coefficient at that site 8.11.1093

406

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS Rationalisation of photochemical aromatic substitution

Table 8.1

Model for Z-substituted benzene Ground state

Excited state

LUMO

‘LUMO’

LUMO

‘LUMO’

HOMO

‘HOMO’

o/p (o)/m

(o)/m o/p

Model for X-substituted benzene Ground state

Excited state

HOMO

‘HOMO’

(o/m) o/p

o/p (o)/m

ψ5*

ψ4

ψ3 energy

Attack by nucleophilea Attack by electrophile a a

The parentheses identify the less common or unobserved reactions.

ND3

ND3 D

–0.502 4

0.310

3

0.251

0.131 0.392

N H

–0.458

8.11

h 2

–0.414

N D

0.251

LUMO

D2O

N D

8.12

8.13

8.2.3 Aromatic Side-chain Reactivity A parallel series of changes in reactivity is found in the side-chains of aromatic compounds. Whereas in thermal reactions, the hydrolysis of phenolic esters and ethers is faster if there is a para Z-substituent, the corresponding photochemical reactions are faster with a meta Z-substituent,1094,1095 as in the m-nitrophenyl phosphate meta-8.14. O

O O

P

O OH

O

O

P

meta-8.14

O

h , H2O

h , H2O NO2

O OH

slow

fast

NO2 meta-8.15

NO2 para-8.14

NO2 para-8.15

The breaking of the P—O bond in the first excited singlet state is the rate-determining step. It is evidently faster for the phosphate meta-8.14 giving the phenate ion meta-8.15 than it is for the phosphate para-8.14 giving the phenate

8 PHOTOCHEMICAL REACTIONS

407

ion para-8.15. In thermal reactions, the p-nitro group is conjugated to the oxyanion, and so stabilises the phenate ion para-8.15, making it into a better nucleofugal group. In the photochemically excited state, either the m-nitrophenate anion meta-8.15 must have become better stabilised, or the p-nitrophenate anion para-8.15 must have become worse. To try to explain this change, we can use, as a crude model, the orbital of a carbanion in place of the oxyanion and of a carbocation in place of the nitro group. When these p orbitals are attached to a benzene ring in the p-positions 8.18, they are equivalent to p-xylylene 8.19. In the meta arrangement 8.16, which can equally sensibly be drawn as a diradical 8.17, the m-xylylene does not have a structure with all the electrons paired in bonds, illustrating thereby the lack of ground-state conjugation between the two substituents. The p molecular orbitals for these two systems are shown in Fig. 8.2, where we can see that the orbitals, 1-4 in the p-xylylene case on the right are all bonding, below the  level, but that the highest orbitals in the m-xylylene on the left are the degenerate pair 4 and 5, which are nonbonding, at the  level. In the ground state, with 1-4 filled in both cases, the overall p energy is 0.5 lower for p-xylylene than for m-xylylene. In the excited state illustrated in Fig. 8.2, however, m-xylylene is at least 0.1 lower in p energy than p-xylylene, even with this crude model. Effectively, the nitro group and the oxyanion are better conjugated in the first excited state when they are meta to each other than when they are para. 0.576 –0.179 –0.260 5* 0.576

–0.577 4

5

0.179 –0.260 4

–0.500

0.500

0.577

–0.500 –0.408 3

0.358

3

0.530

–0.230

0.214

2

0.628

0.500

0.354 –0.204 0.354

2 0.199

0.354

0.432 0.370

0.408 1

1

0.444 0.325 0.354

8.16

Fig. 8.2

0.204

8.17

8.18

8.19

p Orbitals of the first excited state of m- and p-xylylene—models for m- and p-nitrophenate ions and for m- and p-methoxybenzyl cations

There is a complementary pattern for the photochemical ionisation of benzyl acetates 8.20 and 8.22 giving benzyl cations 8.21 and 8.23, in which a meta-methoxy group is effective in promoting the reaction, but a paramethoxy group is not (in fact, the para isomer 8.22 cleaves homolytically rather than heterolytically).65,1096 The explanation is the same, except that the roles of the cationic and anionic sites in the xylylene models 8.16 and 8.18 have been exchanged.

408

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

OAc

OAc

h , H2O

h , H2O OMe 8.20

8.3

slow

fast

OMe

OMe

8.21

OMe

8.22

8.23

Photochemical Pericyclic Reactions and Related Stepwise Reactions

8.3.1 The Photochemical Woodward-Hoffmann Rule The most striking consequence of the change from thermal to photochemical reactions is the complete reversal of the Woodward-Hoffmann rule quoted on p. 271. Thus, for a photochemical reaction, [p2sþp2s] cycloadditions are allowed and [p4sþp2s] cycloadditions forbidden, as we saw in Fig 6.22. The photochemical [p2sþp2s] reaction does not meet a symmetry-imposed barrier like that for the ground-state reaction. More simply, but less rigorously, the frontier orbitals in Fig. 8.3a show that the HOMO/‘HOMO’ and the LUMO/‘LUMO’ interactions for a photochemical [2 þ2] cycloaddition are bonding, and in Fig. 8.3b the same orbitals for a Diels-Alder reaction are antibonding at one end. This is borne out in practice: there are very few photochemical Diels-Alder reactions (and none that is known to be concerted), and a great many [2 þ2] cycloadditions, some of which have been proved to be stereospecifically suprafacial on both components.1097 'HOMO'

'LUMO'

HOMO

LUMO

'HOMO'

HOMO

'LUMO'

LUMO

(a) Photochemically allowed [π2s+π2s] cycloaddition (b) Photochemically f orbidden [π2s+π4s] cycloaddition

Fig. 8.3

Frontier orbitals for photocycloadditions

We saw on p. 402 that orbital interactions like those in Fig. 8.3a are strong enough for the energy to fall as the two components of a photochemically initiated reaction approach one another. In contrast, we saw on p. 293, in the context of a thermal pericyclic [2 þ2] cycloaddition, that the energy rises dramatically as two alkenes approach each other, leading to the symmetry-imposed barrier for the concerted cycloaddition. The similarity between the attractive ‘HOMO’/HOMO interactions in photochemical reactions and the repulsive HOMO/HOMO interactions in thermal reactions, means that the bottom of the one curve and the top of the other will have similar geometries and energies, and so we can follow the overall change in energy in the photochemical [2 þ2] reaction as one in which the two curves meet, allowing the exciplex or photoexcited molecule to cross over to the ground-state curve, following the dashed line in Fig. 8.4. The downward-sloping curve in photochemical reactions in general, not just pericyclic reactions, has been pictured as a funnel reaching down to the energy surfaces of the ground state, providing the electronic pathway that eventually allows an excited-state molecule or pair of molecules to give a ground-state product.1098

8 PHOTOCHEMICAL REACTIONS

409

h

Energy change in a photochemical reaction giving a ground-state product

Fig. 8.4

Here are several examples of photochemical reactions, for which the thermal equivalents were forbidden. In most cases the corresponding thermal reactions simply did not occur, like the [2 þ2] suprafacial cycloadditions 8.24 ! 8.25,1097 the [4 þ4] suprafacial cycloadditions 8.26 ! 8.271099 and 8.28 ! 8.29,1100 and the 1,3-suprafacial sigmatropic rearrangement 8.32 ! 8.33.1101 In others, the thermal reactions have a different stereochemistry, as in the antarafacial cheletropic extrusions of sulfur dioxide 8.30 ! 8.31,1102 or a different regiochemistry, as in the 1,7-suprafacial sigmatropic rearrangement 8.34 ! 8.35.1103,1104 Cycloadditions: h

h +

+

+

+

[2+2] cis-8.24

[2+2] syn,anti-8.25 syn,syn-8.25

tr ans-8.24

syn,anti-8.25 anti,anti-8.25 O

h

h O [4+4] 8.26

[6+6] 8.27

8.28

8.29

Cheletropic reactions:

h

h

SO2

syn-8.30

SO2

E,Z-8.31

anti-8.30

E,E-8.31

O

410

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

Sigmatropic rearrangements: H O

h

[1,3] suprafacial

H

h

H

[1,7] suprafacial O

8.32

8.33

8.34

8.35

Electrocyclic reactions:

h

h OH

4e disrotatory E,E-8.31

OH 4e disrotatory

8.37

cis-8.36 Ar N

8.38

h MeO2C

MeO2C

CO2Me

CO2Me

4e disrotatory

cis-8.39

W-8.40

Ar N

h MeO2C

MeO2C

Ar N

CO2Me

Ar N

4e disrotatory CO2Me sickle-8.40

trans-8.39 h 6e conrotatory 8.41

8.42

Likewise, in the electrocyclic reactions, 692,1105–1107 the 4-electron processes E,E-8.31 ! cis-8.36, 8.37 ! 8.38, cis-8.39 ! W-8.40 and trans-8.39 ! sickle-8.40 are now disrotatory, and the 6-electron processes 8.41 ! 8.42 conrotatory. In all of these examples, the observed reaction fits the opposite of the WoodwardHoffmann rule for thermal reactions. The rule for photochemical reactions is therefore:

A pericyclic change in the first excited state is symmetry allowed when the total number of (4qþ2)s and (4r)a components is even.

In photochemical reactions, it is even harder to prove the pericyclic nature of a process than it was in thermal reactions. Thus we should remember that some of the reactions in the examples above may not actually be pericyclic, and many of the reactions discussed below are certainly not straightforwardly pericyclic, since they take place from the excited triplet state. The large amount of energy imparted to a molecule when it

8 PHOTOCHEMICAL REACTIONS

411

absorbs a quantum of light might be enough to set off a large number of reactions that would not be feasible when a molecule is merely heated in the normal temperature range used in organic synthesis. Nevertheless, the contrast in the patterns of reactivity above with the corresponding thermal reactions in Chapter 6 is striking, and lends some support to the idea that some of these reactions are controlled by the orbital symmetry constraints expressed in the photochemical Woodward-Hoffmann rule. However uncertain their pericyclic status may be, at least they do not meet a symmetry-imposed barrier. 8.3.2 Regioselectivity of Photocycloadditions We have just seen that many photochemical reactions are complementary to the corresponding ground-state reactions. As with thermal pericyclic reactions, the frontier orbitals can explain some of the finer points of these reactions, most notably the regioselectivity of photocycloadditions.64 It is not important when predicting regiochemistry whether the cycloadditions are pericyclic or stepwise—regardless of whether both bonds are formed at once, or whether they are formed one at a time, the orientation should be determined by the large-large interaction in the appropriate frontier orbitals, and it is largely immaterial whether the second bond is forming at the same time or later. 8.3.2.1 The Paterno-Bu¨chi Reaction. One well-known class of photocycloadditions is the Paterno-Bu¨chi reaction in which aldehydes or ketones combine with alkenes to give oxetanes.1108,1109 The excited state of the ketone is n-p*, and it is the orbitals of this state which interact with the ground-state orbitals of the alkene. Often it is the triplet state which is involved,1110 but occasionally the singlet state is important. The orientation usually observed for C- and X-substituted alkenes is usually counter-thermodynamic, with the more-substituted atoms bonded to each other.1111,1112

O Ph

O

+

8.44

8.45

h

+ Ph

O

O Ph Ph 8.47

8.46

O

O +

Ph Ph

Ph Ph

Ph 8.43

Ph

O

h

+

Ph Ph 90:10 8.48 H

h

+ O Ph

Ph Ph

H Ph

8.43

8.49

8.50

8.51

We can explain the orientation if we assume that the major interaction is from the singly occupied n orbital of the benzophenone 8.43 with the HOMO of the alkene 8.44. X-substituted alkenes have high-energy HOMOs, which makes it reasonable that there should be a strong interaction with a nonbonding orbital. The carbon atom with the larger coefficient in the HOMO of the alkene is the one to which the oxygen atom becomes bonded. We can also explain the orientation—and this is the more usual explanation—by looking at the energy of the intermediates produced 8.45 and 8.46. The lower energy diradical 8.45 usually gives the major product 8.47. This argument, of course, applies to the triplet-state reaction, where an intermediate is likely to be involved. Singlet-state reactions may be pericyclic and may or may not involve the diradical. The regioselectivity with a C-substituted alkene 8.49 is the same, except that in this case the oxetane 8.50 undergoes a cycloreversion. However, the photocycloaddition of ketones to Z-substituted alkenes does not fit the explanation based on the relative stability of the diradicals. Irradiation of a solution of acrylonitrile 8.53 in acetone 8.52 gives the

412

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

adduct 8.54, together with dimers of acrylonitrile.1113 This regioselectivity is consistent with a frontier orbital argument.

O

CN +

CN h

CN

O

O * 'LUMO'

8.52

8.53

LUMO

8.55

8.54

8.56

A Z-substituted alkene has a lower-energy HOMO than C- and X-substituted alkenes, and it has a correspondingly lower-energy LUMO. Thus the interaction of the p* orbital of the ketone 8.55 with the LUMO of the alkene 8.56 ought to be much more important for a Z-substituted alkene than it was for a C- or X-substituted alkene. In this interaction, the two larger lobes are on the carbonyl carbon and on the -carbon, and it is these two which become bonded. Furthermore, this reaction may be concerted. It is a singlet-state reaction, and, with -substituted acrylonitriles, the reaction is stereospecific, with retention of configuration on the alkene component. If both bonds are being formed at the same time, the other interaction, the interaction of the singly occupied n orbital with the HOMO of the acrylonitrile, should also be considered. The HOMO of a Z-substituted alkene is not strongly polarised, and in any case the energy separations probably make this a less important interaction. 8.3.2.2 Photodimerisation of Alkenes.1114 When alkenes are irradiated, they often dimerise to give cyclobutanes.1115 Sometimes a singlet-state reaction is involved, but more often it is a triplet-state reaction. Photochemistry is fraught with even more difficulties in proving or disproving concertedness than thermal reactions. Concerted stereospecific cycloadditions appear to be common with relatively unsubstituted alkenes in their singlet-state reactions. Fortunately, concertedness does not matter in explaining regiochemistry. As usual, there are the two potentially profitable interactions shown in Fig. 8.1. In a dimerisation reaction, however, the set of orbitals on the left of each pair and the set on the right will have identical energies. The bonding interactions should be very strong, and they should lead to the formation of what are known as head-to-head (HH) dimers. For example, if we take a Z-substituted alkene, the important interactions will be those shown on the right of Fig. 8.5. If the reaction takes place between the left-hand component in its excited triplet state and the right-hand component in its ground state, only the large-large bonding will actually take place, and, as it happens, the most stable of the possible diradicals will be produced. If we were to look only at the simplest examples of each kind of alkene C-,1116, X-1117 and Z-substituted,1118 in the form of butadiene 8.57, phenyl vinyl ether 8.58 and acrylonitrile 8.53, we would find that this analysis seemed to be supported.

C

C

'LUMO'

C

C

'HOMO'

Fig. 8.5

LUMO

HOMO

X

'LUMO' X

'HOMO'

X

LUMO X

HOMO

Z

'LUMO' Z

'HOMO'

Z

LUMO Z

HOMO

Frontier orbitals in the regioselectivity of photodimerisation of alkenes

8 PHOTOCHEMICAL REACTIONS

413

H h

H

H

H

PhO

h

+

sens.

PhO H

OPh H H PhO +

OPh H

sens.

8.57

8.58 NC

NC H

h

CN H

H NC

CN H

+

sens. 8.53

A ‘sensitised’ photolysis is one in which the light is absorbed by one compound, such as acetone or benzophenone, the excited state of which then interacts with the substrate in such a way that the latter is promoted to an excited state and the former reverts to the ground state. The sensitisers generally used fulfil this function from their triplet states, because they are molecules which rapidly undergo intersystem crossing from their excited singlet to excited triplet states. The triplet states then live long enough to collide with the substrate, which is similarly created in its triplet state, and so almost all sensitised photolyses are triplet-state reactions. For a singlet-state reaction, where both bonds might be being formed at the same time, we might make a further but tentative prediction. Since the orbitals which are interacting are identical on each component, the endo-HH adduct should be preferred over the exo-HH adduct, because the secondary interactions (Fig. 8.6, dashed lines) will always be bonding.

O 'HOMO'

O 'LUMO' O

O HOMO

Fig. 8.6

H H

CHO CHO

LUMO

Secondary orbital interactions (dashed lines) in photocycloadditions

In two cases, where the singlet- and triplet-state reactions have been carefully looked at and separated, this proves to be true. Thus coumarin 8.59, in the excited singlet state, dimerises to give only the HH dimer syn8.60, but in the triplet state it gives both HH isomers syn-8.60 and anti-8.60, with only a trace of head-to-tail (HT) products.1119 Acenaphthylene also gives the syn dimer from the singlet-state reaction and a mixture of the syn and anti dimers from the triplet-state reaction.1120 The whole truth about regio- and stereochemistry, however, is not nearly as simple as this. The experimental evidence has not been collected systematically, and it is not always known whether singlet or triplet states are involved. Scores of papers have been published in which reasonably reliable structures have been assigned to the cyclobutane dimers produced by irradiation of a great variety of unsymmetrical alkenes in solution. (The stereo- and regioselectivity in solid-state photodimerisation reactions have also received a lot of attention, but they are determined by the alignment of the monomers in the crystal lattice, not by orbital effects.) For irradiation in solution, head-to-head dimers are the major products in a majority of these papers, but head-to-tail dimers are the major products in a substantial minority.1121 [2 þ2] Cycloadditions are not the only ones for which the regiochemistry is difficult to predict—almost all [4 þ4] photodimerisations of 9-substituted anthracenes 8.61 give the head-to-head dimer 8.62,1122 whereas the photodimerisation of pyridones 8.63 gives the head-to-tail, centrosymmetric dimer 8.64.1123

414

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

O

O H

h

H

O

O

singlet state

H

O

H

syn-8.60

O O

O H

h 8.59

O

H

O

O

triplet state

H

O

H

H

R

H

anti-8.60 O

R h

H

O

+

syn-8.60 R

O H

h

NH

HN NH

O 8.61

8.62

8.63

O 8.64

The most obvious factors which might lead molecules to adopt the head-to-tail course are dipoledipole repulsions and steric effects.64 That both of these factors are often overridden is evidence for the importance of other effects, which may or may not be best accounted for by orbital interactions or by the formation of the most stable diradical. The single biggest complication is with those reactions which do pass through triplet diradical intermediates. With unpaired spins these have a long lifetime before intersystem crossing allows them to form the second bond to give the cyclobutane product. In this time, the diradical could break apart, and give back starting materials. The regiochemistry may therefore depend not only upon which bond is formed most rapidly, but also upon how efficiently each of the possible diradicals undergoes intersystem crossing in order to close to give a cyclobutane.1124 This complication has been revealed most strikingly in the photochemical cross-coupling of different alkenes described in the next section, but it may also be a factor in sensitised dimerisations. 8.3.2.3 The Photochemical Cross-Coupling of Alkenes.1125 When both alkenes have Z-substituents, the regiochemistry ought to resemble that shown by the dimerisation of alkenes with Z-substituents. However, irradiation of cyclopentenone 8.65 in the presence of methyl acrylate 8.66 gives four 1:1 cis-fused adducts, two stereoisomeric head-to-head products 8.71 and two stereoisomeric head-to-tail products 8.72. The regioisomers are formed in roughly equal amounts with the latter in slight excess. Similarly cyclopentenone alone dimerises to give both regioisomers with low selectivity in favour of the head-to-tail dimers.1126 These are examples of poor regioselectivity that turn up from time to time, even though the orbital predictions are in favour of head-to-head products (Fig 8.5). The reactions are known to take place with the cyclopentenone absorbing light in a p-p* transition, undergoing intersystem crossing to a triplet state, and then reacting with the methyl acrylate in its ground state. It must therefore involve one or more of the triplet diradicals 8.67–8.70.

8 PHOTOCHEMICAL REACTIONS

415

O

O

O

CO2Me

CO2Me

CO2Me

H

O CO2Me

8.67

h

+

O

toluene 8.65

H 8.71 46.5%

8.68 O

O H

8.66 CO2Me 8.69

CO2Me

CO2Me H 8.72 53.5%

8.70

Weedon showed that these diradicals can be efficiently intercepted by having hydrogen selenide present in the medium. Hydrogen selenide is a highly efficient radical trap, which reduces the radicals faster than ring closure and faster than fragmentation back to the starting materials. In the presence of hydrogen selenide, the products, ignoring stereochemistry, were the keto esters 8.73–8.75,1127 together with cyclopentanone, which is produced by reduction of the excited triplet state of cyclopentenone. O

O CO2Me

8.67

8.73 5% O

O

O CO2Me

h

H2Se

+ toluene 8.65

8.66

H2Se

CO2Me

H2Se

8.69

CO2Me

CO2Me

8.74 50% O

O H2Se

8.70

CO2Me

8.75 45%

CO2Me

Two striking contrasts with the earlier results stand out: the best stabilised of the four diradicals 8.68 is not formed to any significant extent (<1%), and the major products 8.74 and 8.75 (95%) are derived from diradicals that would lead to the head-to-tail product 8.72 if they were to close efficiently. The large amount of head-to-head product 8.71 in the cycloadditions appears to be the result of relatively efficient ring closure of the diradical 8.67. The bonds that are formed most easily are between the  position of one carbonyl compound and the  position of the other, the opposite of the frontier orbital prediction in Fig. 8.5 for the combination of two alkenes with a Z-substituent. When one of the alkenes undergoing a cross-coupling has an X-substituent and the other a Z-substituent, the frontier orbitals in Fig. 8.7 do not make unambiguous predictions. The energy separations for the HOMOs and LUMOs (Fig. 6.25) might suggest that the HOMO/‘HOMO’ interaction (DE 1.9 eV) is more effective than the LUMO/‘LUMO’ interaction (DE 3.0 eV). However, the HOMO of a Z-substituted alkene is not highly polarised, with some calculations, including some on cyclopentenone,1128 giving the  position the larger coefficient. Headto-head and head-to-tail regiochemistry are delicately balanced whatever the truth, and it may be that regiochemistry is determined more by the LUMO/‘LUMO’ interaction. In practice there is almost always a high level of selectivity in favour of the head-to-tail regioisomer. Clearly the frontier orbital analysis is insecure.

416

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS Z

Z

Z

X or

'HOMO'

'HOMO'

HOMO

X HOMO

X LUMO

'LUMO'

Fig. 8.7 Frontier orbitals for the photocycloaddition of an X-substituted alkene with a Z-substituted alkene

The best studied reaction in this class is that between cyclopentenone 8.65 and ethyl vinyl ether 8.76, which again gives four cis-fused 1:1 adducts, two stereoisomeric head-to-head products 8.81 and two stereoisomeric head-to-tail products 8.82.1127 The regioselectivity is slightly less than 3:1 in favour of the head-to-tail isomers, and there must have been intermediate diradicals, some or all of 8.77–8.80. O

O

O

OEt

OEt

H

OEt

O OEt

h

8.77

+ toluene 8.65

H 8.81 27.5%

8.78

O

O

O H

8.76 OEt

OEt

8.79

OEt H 8.82 72.5%

8.80

Weedon carried out the same reaction in the presence of hydrogen selenide, and obtained results in which only two diradicals 8.78 and 8.79 appeared to have been formed, and in equal amounts, as judged by the products 8.83–8.86 derived from them. It again seems that the regiochemistry of the cycloaddition is determined by the more efficient closure of the diradical 8.79, than by any selective interaction in the initial bond-making step. The efficiency in the ring closing may stem from faster intersystem crossing or from a less favourable fragmentation to the starting materials. O

O

O OEt

OEt

OEt

H2Se

O OEt

h

8.78

+ toluene 8.65

8.76

8.84 7%

8.83 43% O

O

H2Se

O

H2Se OEt 8.79

OEt 8.85 24%

OEt 8.86 26%

The cycloaddition of several cyclopentenones to 2-methylpropene show similar patterns,1129 and the corresponding cycloadditions of cyclohexenones also give largely head-to-tail products, except that the major product has a trans ring fusion.1130 One reason for this may be that the intermediate triplet derived from the cyclohexenone will twist,1131 because the two radicals will no longer be in overlapping orbitals. If the twist is maintained through the sequence it could lead to a trans ring junction. Alternatively, it is possible that a trans-cyclohexenone is an intermediate.1132

8 PHOTOCHEMICAL REACTIONS

417

It is not yet clear whether the regiochemistry of these photocycloadditions is substantially controlled by the relative rates of ring closure and fragmentation or by the site of initial coupling. One cause for concern is that some of the products 8.73-8.75 may have been formed by a different route from that shown (and similarly for 8.83-8.86). In both cases, cyclopentanone is a major byproduct, produced by reduction of the photoexcited triplet by the hydrogen selenide. Intermediates in this reduction will be radicals centred either at the -carbon or at the -carbon, depending upon which is the less readily reduced by the hydrogen selenide. These radicals might react with methyl acrylate (or with ethyl vinyl ether) to give new radicals, which on reduction would give the products 8.73-8.75 (or 8.83-8.86).1128As a consequence, an explanation based on the orbital interactions has continued to be popular, with several studies suggesting that it still has some merit.1128,1133 Houk has pointed out that in the twisted triplet from photoexcitation of an ,-unsaturated ketone, the  position will resemble a simple alkyl radical, with a high-energy SOMO, while the  position will be an alkyl radical conjugated to an acyl group, with a low-energy SOMO. These radicals should behave like ground-state radicals (Chapter 7), the  radical will be relatively nucleophilic and the  radical will be relatively electrophilic, and this difference may account for the regioselectivity if the cycloaddition is determined by the initial coupling.1134 The nucleophilic radical at the  position will interact most favourably with the  position of a Z-substituted alkene 8.87, leading to the head-to-head adduct found more often than not in that series. Similarly, the electrophilic radical at the  position will interact most favourably with the  position of an X-substituted alkene 8.88, leading to the head-to-tail adduct usually seen in that series. It remains to be seen whether this orbital control is actually a factor in the regioselectivity of photocycloadditions. The current position based on calculations for the simplest system, the gas-phase reaction of acrolein and ethylene, is that selectivity in both the initial attack and in the relative rates of ring closure are likely to be factors.1135 X

HOMO

Z O

LUMO high-energy SOMO

low-energy SOMO

O

8.87

8.88

One solution to the regiochemical problem is to tie the partners together, and make the reaction intramolecular. Thus both cyclohexenones cis- and trans-8.89 give a single regioisomer 8.91, but the reaction is still not stereospecific. The C—C coupling gives a triplet diradical 8.90 with a long enough lifetime to lose the configuration at the carbon atom carrying the methyl group. O

O

O H

h

O 8.89

O

O 8.90

8.91

The loss of stereospecificity was avoided by converting the ,-unsaturated ketones into the corresponding eniminium ions trans- and cis-8.92. These have no possibility of giving an n-p* transition, and will have a slow rate of intersystem crossing. The reaction can then be expected to stay in the singlet manifold and give rise to a concerted cycloaddition. It is indeed stereospecific, at least for the first-formed products trans- and cis-8.93, respectively, after short reaction times.1136

418

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

N

O

N

O

H

H

1. h

1. h

2. Na2CO3 O

O tr ans-8.92

2. Na2CO3

O

tr ans-8.93

O

cis-8.92

cis-8.93

In addition, there are some singlet-state cross-couplings that are straightforwardly explained as more or less concerted [2 þ2] cycloadditions. They are often but not always regioselective in the head-to-head sense, usually stereospecific, retaining the double bond geometry, and sometimes endo selective. Examples are the counter-thermodynamic formation of the more hindered cyclobutane 8.94 as the major adduct from transstilbene and methyl crotonate,1137 and the formation of the adduct 8.95 implying the maximum amount of p stacking, in the reaction of 9-cyanophenanthrene with trans-methylstyrene.1138 p Stacking between a benzene ring in an excited state and one in the ground state is bonding, whereas it was not, unless the stack was displaced (see p. 124), between two ground states. CN Ph

CO2Me

NC

CO2Me

Ph

h

h

+

+ Ph

Ph

8.94

8.95

Orbital energies play some part in intermolecular selectivities as shown by the competition between the crosscoupling of various alkenes with the dimerisation of methyl p-nitrocinnamate. Irradiation of a mixture of methyl cinnamate 8.96 andmethyl p-nitrocinnamate 8.97 gives mainlythecross-coupled product,thistime with more of the trans isomer 8.98 than the cis 8.99, showing that stacking is not always dominant. In contrast, a mixture of p-cyanocinnamate 8.100 and p-nitrocinnamate 8.97 gives more of the dimers of the latter than the cross-coupled cyclobutanes 8.101 and 8.102. The degree of cross-coupling correlates with the orbital energies, as measured by ionisation potentials.1139 CO2Me

CO2Me h

+

8.96 CO2Me

h

+ C6H4CN-p

C6H4NO2-p

8.100

8.97

CO2Me 8.98

CO2Me

+ dimers of 8.97 27% C6H4NO2-p

+

8.97

MeO2C

p-NCC6H4

Ph

8.99

31%

MeO2C

C6H4NO2-p + CO2Me

8.101 13%

CO2Me

MeO2C

C6H4NO2-p

Ph

C6H4NO2-p

Ph

MeO2C

p-NCC6H4

12% CO2Me

+ dimers of 8.97 32% C6H4NO2-p 8.102 5%

8 PHOTOCHEMICAL REACTIONS

419

Orbital energies and atomic orbital coefficients also appear to play a part in site selectivity. The photocycloaddition of cis-piperylene 8.103 to trans-stilbene 8.104 gives mostly the product of attack on the more substituted double bond, thereby giving the higher-energy pair of cyclobutanes 8.105 and 8.106,1140 in contrast to the regioselectivity piperylene shows in thermal [2 þ2] reactions with ketenes (see p. 344) and carbenes,1141 where the cycloadditions take place at the terminal double bond. Both the HOMO and the LUMO of piperylene will have the ‘highest adjacent pair’ at C-3 and C-4 (the coefficients should not be squared, since this is a first-order interaction); therefore, this observation is in agreement both with frontier orbital theory and with the reaction being a concerted one. HOMO –0.534 –0.350

Ph

0.456

Ph

h

+

0.531

Ph +

Ph 8.103

Ph

8.104

Ph

8.105

8.106

Acrylonitrile 8.53 adds to the benzene ring in the iminium salt 8.107, giving initially the cyclobutane 8.108, analogous to the dimer from acrylonitrile on p. 413. The regioselectivity changes to the C¼N double bond when the aryl group has a methoxy substituent 8.109 raising the energy of its orbitals. If the latter reaction is controlled more by the LUMO/‘LUMO’ interaction, it can be expected to take place at the site of the large coefficients, which are on the C¼N double bond and the regiochemistry 8.110 then resembles that of the Paterno-Bu¨chi reaction (see p. 412). Without the methoxy group, the orbital match might more likely be that of the HOMO/‘HOMO’ pair, and the orbitals will then have larger coefficients on the benzene ring. Calculations of the orbital energies and coefficients match these results.1142 'HOMO' 0.04 0.44

–0.51

h

N H

N H NC

0.58

–0.25

0.47

8.107

–0.65 0.44

–H+

NC 8.53 HOMO

N H NC

8.108

'LUMO' h

N H

–0.16 0.30

8.109

–0.65

OMe

OMe N

0.53

NC

CN 8.110

8.53 LUMO

It is perhaps worth concluding this section on photocycloadditions between two p bonds by noting how often the regioselectivity is the opposite of that which would be expected for a ground-state reaction. The corresponding ground-state reactions are not often observed, because of the symmetry-imposed barrier to the concerted reaction. However, one case in which a photochemical and a thermal cycloaddition with the same components have been observed is that of tropone 8.27 and the diethyl ketene acetal 8.111. They show the same periselectivity both in the ground and the excited state, but opposite regioselectivity. Neither reaction is necessarily concerted.1143

420

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

O

heat EtO

O

OEt

OEt

+

O

h

8.28

OEt

8.111

EtO OEt

8.3.2.4 Photocycloadditions with Cumulated Double Bonds The intramolecular photoreaction of the allene 8.112 tethered to the ,-unsaturated ketone shows the regioselectivity 8.113,1144 where it might be accounted for as the consequence of the easy formation of the relatively unstrained system. Wiesner discovered that this was also the regioselectivity in intermolecular reactions 8.114 ! 8.115,1145 which also showed high stereoselectivity for attack on the lower face of the double bond in 8.114. This was surprising, because the lower face is the more hindered, with the approach leading to the ketone 8.115 more crowded than the approach leading to the alternative 8.116. O

O 0.78

h

'LUMO' –0.77

LUMO 8.112

8.113

h O

5

N Ac 8.114

O

N Ac 8.115

and not

N Ac O

8.116

The regiochemistry is not easily explained using the frontier orbitals since the ,-unsaturated ketone is likely to be in the n-p* excited state. The ‘HOMO’ is then the singly-occupied orbital on the oxygen atom, which is not involved in the reaction. The ‘LUMO’ is 3*, with a large coefficient on the  carbon 8.112, but the LUMO of an allene (see p. 345) is not significantly polarised. Equally, but less likely, if it were a p-p* excited state, although the HOMO of the allene is polarised, the ‘HOMO’ of the enone, 2, is only a little polarised. With barely decisive frontier orbitals, it may be that the intermolecular reaction is a consequence only of steric effects. Somewhat unusually, the regiochemistry in these photochemical cycloadditions is the same as that of the thermal cycloaddition of an allene with a Z-substituted alkene (see p. 345). However, the stereochemistry in the reaction with the octalone 8.114 is explicable on the same basis as the stereochemistry of the dissolving metal reduction of similar ,-unsaturated ketones (see p. 396). The ‘LUMO’, 3*, will have a high electron population on C-5 (steroid numbering), which pyramidalises towards a tetrahedral geometry with the larger lobe in the atomic orbital on the lower surface, making the AB ring system more like that of a trans decalin. The allene bonds more strongly to the larger lobe on C-5, and the bond to C-4 follows because of the suprafacial nature of the cycloaddition. In this picture, the regioselectivity in the reaction of the ketone 8.112 follows from bonding to the  carbon developing first in a five-membered ring, and the second bond following on from that.

8 PHOTOCHEMICAL REACTIONS

421

The regiochemistry of the reaction between an ,-unsaturated ketone and a ketene is the opposite, even in an intramolecular reaction which involves substantial twisting and ring strain 8.117 ! 8.118.1144 This time it is in the sense easily explicable by the frontier orbitals. The ‘LUMO’ of the unsaturated ketone and LUMO of the ketene show that the initial bonding will be between the  carbon of the enone and the carbonyl carbon of the ketene, and there is an orthogonal orbital on the other carbon atom of the ketene able to complete the cycloaddition, just as we saw on pp. 282 and 341 for thermal reactions. O

O

O

LUMO h

'LUMO'

O

8.117

8.118

8.3.2.5 Photocycloadditions to Aromatic Rings1146–1148 The benzene ring undergoes several remarkable photocycloadditions, sometimes behaving as a p2 component in a [2 þ2] cycloaddition, with bonds forming to the ortho carbons 8.119,1149 sometimes as a p4 component in a [4 þ4] cycloaddition, with bonds forming to the para carbons 8.121,1150 but more often than not in a more complicated cycloaddition involving a reorganisation of the molecule, but with bonds forming to the meta carbons 8.122.1151 At first sight, the formation of the [2 þ2] adducts 8.119, the intermediate in the formation of the compound actually isolated 8.120, looks like a photochemically allowed pericyclic reaction—it would be a [p2sþp2s] cycloaddition, which is common for one alkene with another. Surprisingly, a correlation diagram shows that this is not the case when one of the ‘alkenes’ is a benzene ring, and it is the meta adduct 8.122 that is the symmetry-allowed product.1152 Perhaps for this reason the great majority of cycloadditions between an alkene and a benzene ring give meta adducts. The diradical 8.122 is a possible intermediate in the formation of the product actually isolated 8.123, and invoking it is certainly a help in understanding the reorganisation of the bonds leading to the final product. O O

O

O h

+

O

O

O

O

O

O

O 8.6

8.119

8.120

h

8.121 h + 8.6

8.122

8.123

O

422

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

Let us look at the correlation diagrams for ortho and meta cycloadditions.1146 Neither the ground state nor the excited states of benzene can be described with the same simplicity as the ground state and excited states of alkenes and linear polyenes, because of the degeneracy of the HOMOs and the LUMOs in benzene. The lowest excited singlet state, 1B2u, is a combination of the configuration in which 2 has lost an electron and 5* has gained one, and the equally probable configuration in which 3 has lost an electron and 4* has gained one. The promotion of an electron from the ground state to the first excited state is actually forbidden by the symmetries of the four orbitals involved 2, 3 4* and 5*, and takes place only because of vibrational motions disturbing the strict symmetry. It is responsible for the low intensity absorption at 254 nm with its characteristic vibrational fine structure. We shall approximate the orbitals of a photoexcited benzene using only one of these configurations, namely 2 5*. Although it is only part of the full picture, it makes the point more clearly. The starting materials for a cycloaddition of photoexcited benzene to an alkene are shown on the left of Fig. 8.8, and the orbitals of the product of the [2 þ2] cycloaddition are shown on the right. The only element of symmetry which would be preserved in a [p2sþp2s] reaction is the plane perpendicular to the page bisecting both molecules. In contrast to the [p2sþp2s] cycloaddition of two alkenes (see p. 293), the first excited state on the left does not correlate with the first excited state on the right, but rather with a much higher-energy excited state corresponding to the promotion of an electron from the orbital labelled 2 to 2 of the diene unit and with 3* of the diene filled. Had we used the other configuration, with the electron promoted from 3 to 4*, we would have come to a similar conclusion, although a different set of orbitals in the product would have been occupied, reflecting the incompleteness of the picture we are using. In contrast to the correlation diagram for the ortho cycloaddition, the equivalent correlation diagram for the meta cycloaddition in Fig. 8.9 shows that the first excited state on the left correlates directly with the ground state for the diradical 8.122. The simplification using the one configuration 2 ! 5* for the excited state is to some extent further justified by a calculation treating the benzene and ethylene as a supermolecule, in which this configuration becomes dominant as the ethylene approaches the benzene.1153 It may be that the diradical 8.122 is not actually an intermediate, but the correlation diagram can only be constructed by using

A S

6*

A 5*

4*

A

S

*

3*

A

4*

S

3*

A

A

3 2

4*

S

2

S

A 1

S 1

S A S

Fig. 8.8

2

1

Correlation diagram for the [2 þ2] cycloaddition of ethylene to benzene

8 PHOTOCHEMICAL REACTIONS

423

A 4*

5*

4*

A S

6*

3*

3*

S A

S

A

* A

S

2

2

S S A

3

1

S S 1

2

A S

Fig. 8.9

1

Correlation diagram for the meta cycloaddition of ethylene to benzene

it. The final product may be formed directly in a fully concerted cycloaddition if the diradical in the transition structure is already starting to form the second bond. Photoreactions forming this type of product are common, and they show the necessary conditions for a concerted pericyclic reaction: they are singlet-state reactions, stereospecifically suprafacial on both components.1154 Correlation diagrams can be constructed for other cycloadditions to benzene,1152 in some of which, such as the known [2 þ2] and [4 þ4] cycloadditions of one benzene ring with another the benzene ring can be treated simplistically as though it were a conjugated system of three alkenes, just as it can for all thermal pericyclic reactions. In other photochemical reactions, the correlation diagrams reveal features at odds with that simplification. Thus the cycloaddition of a diene reacting as a p4s component across the meta position of benzene is allowed, even though there are two more electrons than in the p2s addition to an alkene, a change that normally reverses the rules. Similarly, a thermal [4 þ2] cycloaddition across the para positions of a benzene ring is allowed, but so is the corresponding photochemical reaction. Both of these seemingly anomalous photochemical reactions are known: furan 8.124 and benzene 8.6 give the adduct 8.126, perhaps by way of the diradical 8.125, and the intramolecular reaction in the alkene 8.127 gives the para adduct 8.128 as the major product.1155 O +

h

O

O

8.6

8.124

8.125

O

8.126

O O

h +

8.127

8.128

94:6

8.129

424

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

It appears to be a general feature of photocycloadditions that they are more likely to be rule-obeying if the interacting orbitals of the two components are close in energy.1156 In the particular case of cycloadditions to benzene, Bryce-Smith and Gilbert have pointed out that the formation of the meta adduct is favoured when the alkene is not strongly polarised, and they narrow this down, with some exceptions, to those alkenes having ionisation potentials between 9.6 eV and 8.65 eV.1154 This range, which straddles the HOMO energy of benzene at 9.24 eV, supports the idea that the concerted cycloaddition is best achieved when the HOMO/ ‘HOMO’ interaction is between orbitals close in energy, and it is normal, although not specifically covered by the Bryce-Smith generalisation, that the LUMO/‘LUMO’ interaction will also be between orbitals close in energy. More polar alkenes, like maleic anhydride, with high ionisation potentials, and correspondingly low-energy LUMOs, are more apt to react in the [2 þ2] mode, across ortho positions, as in the formation of the adduct 8.119, perhaps because the interacting orbitals do not match well for the concerted pericyclic process. Houk has suggested that the LUMO of a Z-substituted alkene is low enough in energy to encourage charge transfer from the ‘LUMO’ of the photoexcited benzene to the LUMO of the alkene (Fig. 8.10a),1157 and the subsequent reactions of the charge-transfer complex will have different selectivities from the direct concerted reaction. Alkenes with electron-donating substituents are also apt to give ortho adducts rather than meta, as in the reactions of tetramethylethylene, or para adducts, as in the reaction giving the adduct 8.128. In this case the charge transfer will be from the high-energy HOMO of the alkene with its X-substituent to the ‘HOMO’ of the photoexcited benzene (Fig. 8.10b), and again the subsequent reactions are those of the charge-transfer complex, with a kinetic preference for ortho bonding. It is possible to consider these same charge transfers as SET reactions, with the subsequent steps simply those of the derived diradicals.

CN 2.27 1.15

1.15 0.21 –8.34

–9.24

–9.24 –10.88

(a) Charge transf er f rom 'LUMO' to LUMO

Fig. 8.10

(b) Charge transf er f rom HOMO to 'HOMO'

Charge transfer between photoexcited benzene, and Z- and X-substituted alkenes

In the ortho adducts, which are the major products with Z- and X-substituted alkenes like acrylonitrile 8.53 and ethyl vinyl ether 8.76, the stereoselectivity is strongly in favour of the exo adducts 8.130 and 8.131.1158 The obvious explanation to try is to invoke secondary orbital interactions, when we take the most favourable frontier orbital interactions preceding the charge transfer. We can see from Fig. 8.10, that this will be the combination of the LUMO of the Z-substituted system with 5* of benzene, which has good primary overlap represented by the solid lines, and a secondary orbital repulsion 8.132 (wavy line) favouring the formation of the exo adduct. For the donor substituent, the most important combination of orbitals will be the HOMO of the X-substituted alkene, similar to 2 of the allyl system, with 3 of benzene, which introduces a secondary orbital attraction 8.133 (dashed curve) in the endo mode, and ought to favour the formation of the endo adduct. Secondary orbital interactions do not provide a reliable explanation.

8 PHOTOCHEMICAL REACTIONS

425

h

+

h

+

CN 8.6

OEt CN

8.53

8.6

OEt

8.76

8.130

8.131

O

X * 3 5*

8.132

8.133

However, they do provide an explanation for the preferred endo mode of cycloaddition for those alkenes giving meta adducts. Most cis-disubstituted alkenes like cyclopentene1159 give substantially more endo adduct 8.134 than exo 8.135. Because of the good HOMO/‘HOMO’ and LUMO/‘LUMO’ match with simple alkenes, there will be two sets of secondary orbital interactions to consider. One 8.136 will be between the HOMO of the doubly X-substituted alkene, crudely modelled by 3* of butadiene, and 2 of benzene, and the other 8.137 will be between the LUMO of the alkene, modelled by 4* of butadiene, and 5* of benzene. In both cases the secondary overlap is in favour of the endo mode of cycloaddition.1157

h

+

+ 8.134

88:12

3*

4*

5*

2

8.136

8.135

8.137

With unsymmetrical alkenes, there are two regioisomeric meta adducts,1154,1160,1161 which are easily understood as the consequences of bond formation from the diradical intermediates 8.138 and 8.141, with the isolated radical centre forming a bond to either end of the allyl radical with little selectivity stemming from the presence of the substituent on the alkene. The low degree of selectivity is equally accommodated by a concerted reaction in which there is no intermediate. The main effect of having an electron-donating group, as in the reaction with ethyl vinyl ether 8.76, is that the ortho adduct 8.131 is the major product. The meta adducts 8.142–8.145 (R ¼ OEt) are minor products (ortho:meta 65:35). With the rather less effective donor substituent, as in the reaction with vinyl acetate, the meta adducts 8.142–8.145 (R ¼ OAc) are the major products (meta:ortho 88:12). They show some selectivity in favour of the endo adducts (64:36 for R ¼ OEt), and the major product 8.142

426

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

(71% of the mixture of meta adducts for R ¼ OAc) has been used in a synthesis of isoiridomyrmecin.1162 The only adduct between benzene and the Z-substituted alkene acrylonitrile is the ortho isomer 8.130.

h

8.139:8.140 56:44

8.139

+ 8.138

8.140 OR OR h +

8.142 OR

OR

8.143

OR OR

8.141

8.144 8.145 R=OEt (8.142+8.143):(8.144+8.145) 51:49 R=OAc (8.142+8.143):(8.144+8.145) 75:25

The remaining regioselectivity we must try to explain is that shown by substituted benzenes. When the alkene is not polar, like cyclopentene 8.147, and therefore favours the meta cycloaddition pathway, a donor substituent on the benzene ring in anisole 8.146 encourages attack across the 2- and 6-positions 8.148, with a methoxy group significantly more effective than a methyl group.1163 The usual endo selectivity favours the formation of the adduct endo-8.149. Electron-withdrawing groups like cyano in benzonitrile 8.150, however, direct the cycloaddition across the 2- and 4-positions 8.151, and the endo selectivity is still apparent in the major regioisomer 8.152 but not in the minor 8.153. Addition across the 1,5-positions accounts for the remaining 3% of the 1:1 cycloadducts.1164

6

6

6

h OMe +

OMe

2

2

2

8.146

8.147

6

+

OMe OMe endo-8.149 87:13 exo-8.149

8.148

4

+ 2

8.150

2

2

CN

2

8.147

+

NC NC exo-8.152 16% endo-8.152 36%

h

NC

4

4

4

2

CN

+

NC 8.151 4

2

endo-8.153 22%

4

2

exo-8.153 23%

8 PHOTOCHEMICAL REACTIONS

427

The presence of polar substituents lifts the degeneracy of the HOMO pair and the LUMO pair of benzene orbitals, as summarised in Fig. 8.11, which repeats a perception first mentioned on pp. 171–172. The donor substituent raises the energies of 2 and 4*, and the electron-withdrawing substituent lowers their energy.1165 The energies of the orbitals 3 and 5* remain unchanged, because the substituents are at a node in both of these orbitals. Instead of having a mixture of configurations for the excited state, with no clear frontier orbitals, it is now somewhat more legitimate to identify the frontier orbitals of the excited state as possessing largely the configuration in which an electron has been promoted from 2 to 5* when a donor substituent is present, and from 3 to 4* when an electron-withdrawing substituent is present, because these have smaller energy separations.

X

Z

4* 5*

5*

4*

5*

X X

Z 4*

Z

2 2

3

X

3

3

X

Z

2

Z

Fig. 8.11

The effect of X- and Z-substituents on the frontier orbital energies of benzene

The major orbital interaction leading to meta bonding with an X-substituted benzene is therefore between the HOMO, p, of the alkene and the ‘HOMO’, the singly occupied orbital 2, of the aromatic ring. The effect of the X-substituent is not only to raise the energy of 2 but also to increase the atomic orbital coefficients at the ortho and para positions at the expense of the ipso and meta positions 8.154. The LUMO/‘LUMO’ interaction, p* with 5*, is neutral with respect to the two ortho positions 8.155, because the substituent will have no effect on the coefficients. In addition, any contribution from the interactions of 3 of the aromatic ring and p of the alkene, or of 5* and p*, have the wrong signs for productive bonding in a meta cycloaddition. *

* (+)

(–) X 5*

X 2

8.154

8.155

Z 4* 8.156

X Z 8.157

When the benzene ring has an electron-withdrawing substituent, the major frontier orbital interaction will be between p* and 4*. The large coefficients are at C-1 and C-4, and the effect of the Z-substituent will be to raise the coefficient at C-2. The regioselectivity for attack across C-2 and C-4 with the electron-withdrawing group is therefore equally easily explained in 8.156. The substituent will have no effect on the coefficients in the other frontier orbital 3, which has the wrong signs for any interaction with p to contribute towards meta cycloaddition.

428

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

A different explanation is based on a calculation,1153 which suggests that as the orbitals interact and the  bonds develop, some positive charge develops at the single-carbon bridge, and some negative charge develops in the allyl system. In this product-development argument, an intermediate and hence the transition structure will be favoured if the donor substituent is on the single carbon bridge and an electron-withdrawing group is conjugated to the allyl system 8.157. This explanation accounts equally well for the 2,6-selectivity seen with a donor substituent and the 2,4-selectivity with an electron-withdrawing substituent, and it ties in to a possibility that has been advanced on several occasions—that the intermediate (if there is an intermediate) may not be a diradical, as we have been drawing it up to now for clarity, but a zwitterion. Whether there is an intermediate or not, and whatever the explanation for the regioselectivity, it is reasonable that the formation of both pairs of regioisomers 8.152 and 8.153 is straightforward, with essentially no selectivity for which end of the allyl system forms the bond to the single-carbon bridge. Combinations of electron-donating and electron-withdrawing groups lead to ever more complicated pictures, but the outline is clear enough to use as a guide in synthesis. One example is the intramolecular photocycloaddition in Wender’s synthesis of (–)-rudmollin from the anisole 8.158, which gave largely the two adducts 8.159 and 8.160.1166 This single photochemical reaction achieves a dramatic increase in complexity (five new stereogenic centres) in one step, by taking advantage of the predictable regioselectivity for the 2,6-positions relative to the methoxy group, of the stereospecificity across the cis double bond, of regiochemistry determined by the presence of the tether, and of relative stereochemistry induced from the single stereogenic centre by avoided A1,3 interactions (see pp. 252 and 262). Even the formation of two adducts was inconsequential, because both were opened to give the alcohol 8.161 by selective cleavage of the allylic cyclopropane bonds.

OMe

OMe

H

H

h

OMe

H Hg(OAc)2

+

O OH

H2O, THF

TBSO TBSO 8.158

TBSO 8.159

TBSO 8.160

8.161

8.3.2.6 Photochemical Di-p-methane Rearrangements of Aromatic Systems The photochemical reaction of the aromatic alkene embedded in the bridged structure 8.162 does not result in cycloaddition of the double bond to the benzene ring, presumably because of the ring strain that would be created, if it was meta or ortho. Instead the excited state undergoes a rearrangement either before or after intersystem crossing. Best results are often obtained by triplet sensitisation, which excludes the singlet-state pathway. This type of rearrangement belongs to a class called di-p-methane rearrangements. The triplet-state reaction is likely to be stepwise, and to involve one or more of the diradical intermediates 8.163 and 8.164. The step from the intermediate 8.163 to 8.164 may be concerted with the formation of 8.163, but the last step giving the cyclopropane 8.165 is likely to be separate, since it must wait for or be concerted with the intersystem crossing during which the spins become paired.

h

8.162

8.163

8.164

8.165

8 PHOTOCHEMICAL REACTIONS

429

Overall the reaction 8.162 ! 8.165 corresponds to the cycloaddition of one of the p bonds to one of the allylic  bonds, and it is formally possible that this is a concerted process giving the cyclopropane 8.165 directly in a single symmetry-allowed [2aþp2a] step 8.166.656 The stereochemistry of most di-p-methane rearrangements, largely investigated by Zimmerman,1167 conforms to this pattern, and perhaps some of the singlet-state reactions are concerted. Nevertheless, they are more usually thought of as stepwise, and this certainly helps to explain the regiochemistry of the reactions observed when the aromatic ring has electrondonating and electron-withdrawing substituents. Zimmerman’s own approach,1168 which is different from the one we shall look at here, is more dependent upon calculation, and less transparent with respect to the influence of individual molecular orbitals. It is, however, based on the same principles, and is an equivalent, and in places more substantial treatment.

2a + 2a] 8.166

Paquette’s observations with respect to regioselectivity are that a donor substituent in the benzonorbornene 8.167,1169 when the substituents are meta related on the benzene ring, forms the first bond to the meta position, which is best pictured as giving the diradical 8.168, and hence the tricyclic product 8.169. However, an electron-withdrawing group in the benzonorbornene 8.170 forms the first bond to the para position, which is best pictured as giving the diradical 8.171, and hence the tricyclic product 8.172. Both of these reactions are highly regioselective. When the substituents are ortho related on the benzene ring, both donor and withdrawing substituents in the benzonorbornenes 8.173 form the first bond mainly to the ortho position, which is best pictured as giving the diradicals 8.174, and hence the tricyclic products 8.175.1170 These reactions are also highly, but detectably not quite completely, regioselective.

h sens. MeO

m

MeO 8.167

8.168 p

8.169

h sens. NC

NC

MeO

8.170

8.171

NC

8.172

h o

R

sens. R

8.173 R=OMe R=CN

R 8.174

8.175

The diradical 8.168 formed from the meta-methoxy derivative 8.167 is probably the less stable of the two possible radicals. We can however find an explanation for this striking regioselectivity by looking again at the orbitals in Fig. 8.11, which identifies the singly occupied orbitals in the major configuration of the

430

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

excited singlet state. The only difference in the triplet state is that the spins of two of the singly occupied orbitals are inverted, which does not affect the argument. With an X-substituent in the meta position 8.167, the frontier orbitals are the HOMO of the alkene and 2 of the aromatic ring, and the LUMO of the alkene and 5* of the aromatic ring. When we were looking at the meta cycloaddition in 8.154, only the former was relevant, but now the latter can play a part since we are only looking at the formation of one bond, and in this orbital the coefficient at the para position is zero 8.176. With a Z-substituent in the meta position 8.170, the frontier orbitals are the LUMO of the alkene and 4* of the aromatic ring, in which orbital the coefficient at the para position is large 8.177. With an X-substituent in the ortho position 8.173 (R ¼ OMe), 5* has equal coefficients ortho and meta, but 2 has the larger coefficient in the ortho position 8.178. Finally, with a Z-substituent in the ortho position 8.173 (R ¼ CN), 3 has equal coefficients ortho and meta, but 4* has the larger coefficient in the ortho position 8.179. 5*

4*

MeO

4*

2

NC OMe 8.176

8.177

CN

8.178

8.179

8.3.3 Other Kinds of Selectivity in Pericyclic and Related Photochemical Reactions 8.3.3.1 Electrocyclic Reactions Cycloheptatriene undergoes a photochemical, symmetry-allowed, disrotatory ring closure to give a bicyclo[3.2.0]heptadiene. A substituent placed at each of the three trigonal positions affects which pair of double bonds is involved, as summarised by the reactions of the three methoxycycloheptatrienes 8.180a–c and the three cyclohepatrienecarboxyl esters 8.181a–c. The regioselectivity in each case is different for the electron-donating and the electron-withdrawing substituent.1171 There are also similar but less complete data for the corresponding tropones.1172 1

OMe

OMe

1

CO2Et

h

h CO2Et 8.181a

8.180a h

CO2Et

h

2

2

OMe

CO2Et OMe

8.180b

8.181b

h

h

3

OMe 8.180c

3

MeO

CO2Et 8.181c

EtO2C

Clearly there is a strong electronic effect determining the regioselectivity, but accounting for it has not been straightforward. The frontier orbitals are 3 and 4* of hexadiene, modified by the presence of an X- or

8 PHOTOCHEMICAL REACTIONS

431

Z-substituent. Although there have been attempts to explain the regioselectivity using these frontier orbitals,1173 and using the changes in the overall charge distribution following excitation,1171 they are not as compelling as the kinds of arguments that work so well in the di-p-methane rearrangements. A different approach has been put forward by Houk, in which he concentrates on the change in conformation that must take place on excitation.1174 He argues that one of the two trigonal carbon atoms at the terminus of the triene unit must twist out of conjugation with the rest of the conjugated system to give an excited state with a different conformation from the more nearly planar ground state. This is a consequence of promoting an electron into the LUMO, which has a node between C-1 and C-2. With one electron in the HOMO, which has a bonding interaction between these two atoms, and one in the LUMO, the p-bonding between these atoms is removed. The question then is what the effect on the charge distribution is: is the isolated p orbital from C-1 more than half filled or less than half filled? As we saw in 8.157, calculations again support a preference for partial positive charge to reside at the isolated p orbital and for the partial negative charge to be in the conjugated system 8.182. The change in the charge distribution on photoexcitation has been called ‘sudden polarisation’.1175 The  bond of the cyclobutene ring then forms from the isolated p orbital, which is moving into the right position for bonding to C-4. H H

H

H

h (–)

4

1 2

H

4

2 (+)

1

H

1

8.182 (+)

X

1

(+)

(–)

6

1 (–)

4

3

8.183a

8.183b

(+)

(–)

X

(+)

Z

6

1

(–)

4

(–) 3

X 8.183c

4

8.184a

8.184b

(+)

(+)

Z

6

(–) 3

Z 8.184c

Positive charge at C-1 will be stabilised by a donor substituent at that site 8.183a. If the donor substituent is not at C-1 but at C-2 or C-3, it will be best accommodated if it is at the nodes in 3 of the pentadienyl anion 8.183b and 8.183c, where it will least destabilise that orbital. If an electron-withdrawing group is present it will best stabilise the negative charge if it is placed at the terminus or in the middle of the pentadienyl anion 8.184a–c. The pattern of charge distribution in the structures 8.183 and 8.184 matches the observed regioselectivity in all six cases. 8.3.3.2 Sigmatropic Rearrangements Cycloheptatriene also undergoes a photochemical, symmetryallowed, suprafacial [1,7]-shift of hydrogen 8.34 ! 8.35, and, less readily, of other groups. In an unsymmetrical cycloheptatriene, there are two directions in which it can shift, and a little is known about this preference.1176 A donor substituent at C-1 promotes the migration of the hydrogen atom towards C-1 8.185, whereas an electron-withdrawing group on C-1 promotes the migration in the opposite direction 8.186. H

H

H Me

H

Me

CN

h

8.185

CN h

8.186

432

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

The explanation for this electronically controlled selectivity is satisfyingly the same as that used in the previous section: in the excited state, either C-1 or C-6 experiences the sudden polarisation, and twists in whichever direction places either the positive charge on the carbon atom with the donor substituent 8.187 or the negative charge at the terminus of the pentadienyl anion system 8.188.1174 The shift of the hydrogen atom is then like the [1,2]-hydride shift in a cationic rearrangement, it takes place towards the carbon carrying the partial positive charge, C-1 in the former case and C-6 in the latter.

H

H

H X

(+) 1

Z (+)

(–)

8.187

H

6 (–)

8.188

The two pathways, electrocyclic closure to the bicyclo[3.2.0]heptadiene and the [1,7]-shift of hydrogen, are in competition. This makes the experimental work more difficult, because the four possible isomers of the cycloheptatriene interconvert during the photolysis. Nevertheless the pattern of reactivity is clear, and the observation is that the better the donor substituent, the more it favours the formation of the bicyclo[3.2.0]heptadiene at the expense of the [1,7]-shift. This too is reasonable, since the hydride migration towards the donor-substituted atom 8.187 leads to a less stable cation, and ought to be slowed down by that feature.

8.4

Photochemically Induced Radical Reactions

As so much energy can be introduced at once, one of the most common ways of setting up a pair of radicals is by photochemical excitation. The excited state has a chemistry of its own, as we have seen in the earlier part of this chapter, but one outcome for the excited state is for a bond to break homolytically, with the two radicals (or the diradical if it is a bond in a ring that breaks) either produced in, or able rapidly to revert to, their electronic ground states. When this happens, the radicals usually show the same patterns of reactivity and selectivity as the corresponding radicals generated by pyrolysis of a strained or weak single bond. An advantage of the photochemical method of generation is in sensitised photolysis, where the two radicals, or the diradical if they remain in the same molecule, are produced with unpaired spins, giving them a longer lifetime. An example is provided by the azo-compound 8.189, which gives octa-1,7-diene both on pyrolysis and on sensitised photolysis. The subtle difference is revealed by the deuterium labelling. In thermolysis, the diradical 8.190 is set up with the spins paired and with good overlap for easy cleavage of the  bond—the product is largely the E,E-diene E,E-8.191, in which the lifetime of the diradical 8.190 was too short to lose the conformation in which it was set up. In the sensitised photolysis, however, the triplet diradical 8.192 lived long enough for the molecule to change shape to some extent. The result is that the fragmentation of an intermediate, which might have a conformation something like 8.193, gives more of the diene E,Z-8.191 than of the diene E,E-8.191.1177 A molecular mechanics calculation showed that conformations like 8.193 are lower in energy by about 5.5 kJ mol–1 than conformations like 8.190. Although the precise shapes of the diradicals involved are not easily defined, the essential idea, that only the triplet lives long enough to find a lower energy conformation before the fragmentation, is secure.

8 PHOTOCHEMICAL REACTIONS

N N

433

H

H

H

heat

D

E

fast

D

D

D

D H

D

singlet

8.189

E E,E-8.191

8.190

h , sensitiser H

H

conformational change D

H

E

D

D

D

D

D triplet

Z

H 8.193

8.192

E,Z-8.191

In the axial -chloroketone 8.194, the conjugation of the C—Cl bond with the carbonyl group is destabilising, and since it is a Z-substituent on the carbonyl group, the energy of p* is lowered. Photolysis of this compound with an n-p* transition places an electron in the ‘LUMO’, weakening the C—Cl bond, and leading to its homolytic cleavage to give the radical 8.195.1178 The products are those expected from the radical, and include the coupling product with cyclopentyl radicals produced from the solvent. This cleavage is under stereoelectronic control—the isomer with the equatorial C—Cl bond is cleaved much less easily, since it is not activated by conjugation between the two functional groups. O O

O

h

But

O

O +

Cl 8.194

But

8.195

+

But

But

h Cl

* *

H

OSiMe3

NH2

8.196

OSiMe3

OSiMe3

8.197 Cl *

* *

OSiMe3 Cl 8.198

* OSiMe3 8.199

Similar orbital interactions help to explain how a p bond not directly conjugated to a C—Cl bond can assist its homolysis, as seen in the reactions of some silyl enol ethers.1179 The exo isomer 8.196 underwent photolysis with relatively easy homolysis of the C—Cl bond to give the radical 8.197, which picked up a hydrogen atom from the sec-butylamine included in the reaction mixture to make sure that any acid was scavenged. The

434

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

HOMO and LUMO of the alkyl halide will be low-lying, and the HOMO and LUMO of the alkene will be raised in energy by the X-substituent. As a result the * orbital is low in energy for a  bond and p* is high in energy for a p bond, and the major interaction lowering the energy of the transition structure is between these two orbitals (Fig. 8.12). *

*

* *

*

*

h

X C

Fig. 8.12

C

C

C

C

Cl

C

X

C

C

Cl

C

†

C

Frontier orbitals for the photochemical reaction of C—Cl with X—C¼C

The corresponding endo isomer 8.198 was relatively unreactive, because the C—Cl bond is badly aligned for overlap, one of the lobes within bonding distance having a bonding interaction but the other an antibonding. The 7-anti isomer 8.199 was also relatively unreactive because the two p orbitals of the ‘LUMO’ have different signs, and oppose each other in their interactions with the * orbital. This isomer would have been the most reactive in the ground state, because the more important interaction would then have been with the HOMO of the alkene system, where the p orbitals are in-phase. This type of alkene is well known635 to be unusually reactive with respect to ionisation of the halide for just this reason, and because the ion produced is bishomoaromatic (see p. 42). The photo-Fries rearrangement of phenyl esters 8.2001180 takes place by way of an acyl radical 8.201 created close to a phenoxy radical 8.202. The C—O bond is weakened in the starting material by the presence of an electron in the p* orbital of the ester conjugated system. The radical coupling then shows the usual selectivity for C—C bond formation, with the para selectivity in line with the coefficients of the SOMO of the phenoxy radical (see p. 391). O

O

OH Ph

Ph

O h

8.200

O

O

OH

8.201 Ph

8.202

+

42.:58

O

Ph

The photochemical reaction of the acridinium ion 8.203 in methanol is an example of a general reaction type in which radical ions and radicals are created by electron transfer to or from the excited state. As we saw earlier in the discussion about Fig. 8.10, the ‘HOMO’ of an excited state is a low-energy, half-filled orbital, into which another electron can be fed from a filled orbital of suitably close energy. In this case, the lone pair in methanol transfers an electron to the ‘HOMO’ of the excited state 8.204, giving the radical 8.205 and the radical cation 8.206. The latter easily loses a proton to give the radical 8.207, and the C—C coupling of this

8 PHOTOCHEMICAL REACTIONS

435

radical with the radical 8.205, and the self coupling of the well stabilised and hence long lived radical 8.205 are then normal radical reactions.1181 †

h N

N

CH3OH

8.203

8.204

–H+ CH2OH

CH3OH

8.207

8.206

N N

8.205 OH

H

H

N

N

The formation of benzpinacol 8.210 by the action of light on benzophenone 8.43 is one of the earliest organic photochemical reactions to have been discovered.1182 It is now known that the reaction takes place from the n-p* triplet state. Subsequently, and rapidly, the spin of one of the electrons inverts to give the triplet excited state 8.208 that is so often used to sensitise photochemical reactions. With two unpaired electrons, there is a question about which abstracts the hydrogen atom from the solvent. It is almost certainly the electron left behind in the p orbital on oxygen, which will be low in energy, and therefore close to the HOMO of the C—H bond of the solvent, B in Fig. 8.13. The other odd electron will be in the carbonyl p* orbital, which is

* LUMO

A

*

* h

n

n

ISC

B HOMO

O

O

† H

Fig. 8.13

Frontier orbitals for a ketone in the ground state, in the first excited triplet state and for a C—H bond

436

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS

comparatively low in energy for an antibonding orbital, and therefore well separated from the rather high energy of the * orbital of the C—H bond, A in Fig. 8.13. The interaction B is the same as that for most alkoxy radicals abstracting a hydrogen atom (see p. 372); the n-p* triplet state has long been recognised as an electrophilic radical. When the hydrogen abstraction has taken place, the radical produced 8.209 will be in its electronic ground state. It is well stabilised, and will survive long enough to dimerise to give benzpinacol 8.210 with the usual regioselectivity of a benzyl radical. OH H O Ph

ISC

Ph

†

O

h Ph

OH

OH Ph

Ph

Ph Ph

Ph Ph

Ph

OH 8.43

8.208

8.209

8.210

A slightly more complicated case is provided by the photoreaction of the ,-unsaturated ketone 8.211 in diethyl ether.1183 The excitation and hydrogen abstraction take place in the usual way, and the two radicals produced are represented by the localised structures 8.212 and 8.213. For the coupling of these radicals, the important frontier orbitals will be the SOMO in each case. The radical 8.212 has the odd electron in an orbital which is like that of the LUMO of protonated acrolein (Fig. 4.17), where the largest coefficient is on the carbonyl carbon atom, C-3. The other radical 8.213, derived from the ether, will have the odd electron in an orbital like the LUMO of a protonated carbonyl group, and the larger coefficient will therefore be on carbon. Thus the observed sites of coupling to give the product 8.214 are accounted for. The photolysis of ,-unsaturated carbonyl compounds in alcohol solvents requires the presence of titanium tetrachloride to achieve crosscoupling at the carbonyl carbon.1184 The Lewis acid or a proton, coordinated to the carbonyl oxygen, increases the coefficient in the LUMO at the carbonyl carbon.

h 3

O

HO

HO

8.211

8.212

+

+

O

O 8.214

O 8.213

Not all photochemical additions take place at the carbonyl carbon. Thus photolysis of the ketone 8.215 in isopropanol in the absence of any acid gives the product of attack in the conjugate position 8.218,1185 and this is quite a common and synthetically useful pattern of behaviour.1186 It is consistent with frontier orbital control only if the reaction is not a radical coupling 8.216 þ 8.217, but attack of the radical 8.217 on the ground-state ,-unsaturated ketone 8.215. This would be a photochemically initiated chain reaction, and should have a high quantum yield; the reaction is described as being ‘rapid’.

8 PHOTOCHEMICAL REACTIONS

437

O

OH

O OH

h OH

+ H H

OH

8.215

8.5

H

H

8.216

8.217

8.218

Chemiluminescence

One final reaction only marginally belongs in this chapter, but it is the opposite of a photochemical reaction—instead of an organic molecule absorbing light and then undergoing chemical reaction, some organic molecules undergo a chemical reaction in which light is emitted. This behaviour is called chemiluminescence, which is a general phenomenon when dioxetanes are heated, releasing the large amount of energy that must be available for a photon to be emitted. The dioxetane 8.219 is thermally unstable, and cleaves, in one or two steps, to give the radical cation 8.220 and the radical anion 8.221.1187 This step is helped by the presence of the nitrogen atom, which is an X-substituent stabilising the electron deficiency in the radical cation. The radical anion 8.221 transfers an electron to the radical cation 8.220 to give the acridone 8.222 and adamantanone 8.223. The remarkable feature of this reaction is that the former is produced in a photochemically excited state. (This feature has found a use in clinical diagnostics—a phosphatase enzyme can be tested for by its capacity to release an oxyanion X-substituent by hydrolysis of a phenol phosphate, triggering the fragmentation.)1188

O O

O

O warm

O

8.221 O

8.223 †

electron transfer

N

N

N

8.219

8.220

8.222

The electron in the high-energy SOMO of the radical anion 8.220 (effectively the p* orbital of the carbonyl group) is evidently transferred to the relatively low-energy LUMO of the acridone (Fig. 8.14), giving the product with the orbital occupancy of the n-p* excited state, which simply emits a photon when the excited state 8.222 decays to the ground state. Chemiluminescence can also occur with electron transfer in the opposite direction, as in the oxidation of sodium 9,10-diphenylanthracenide 8.224 by dibenzoyl peroxide.1189,1190 An electron is transferred from the anthracenide to the oxidising agent to give a benzoyloxy radical, a benzoate ion

438

MOLECULAR ORBITALS AND ORGANIC CHEMICAL REACTIONS *

*

*

* electron transfer

n

n

O

†

O O

O

N

N 8.221 8.220

Fig. 8.14

8.223 8.222

Orbitals for the electron transfer from the radical anion 8.221 to the radical cation 8.220

Ph

Ph

[O]

[O]

Fig. 8.15

†

Ph

Ph

8.224

8.225

Orbitals for the electron transfer from the anthracenide anion 8.224 to an oxidising agent

and the excited state of anthracene 8.225, which emits a photon. The  and * orbitals of an O—O bond are low in energy, a characteristic of an oxidising agent, and the electron transferred to it comes most easily from what was the HOMO of the anthracene rather than from the SOMO of the anthracenide, leading to the excited state of the anthracene (Fig. 8.15).1191 It is also likely that electron transfer takes place from the anthracenide to the benzoyl radical, the reaction being characteristic of an oxidising agent with a hydrocarbon anion.

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Index

(4q þ 2)s, defined 271 (4r)a, defined 271 [p4s þ p2s] describes a drawing 273 describes many cycloadditions

272

, energy level in Hu¨ckel theory defined as see also Coulomb integral

31

A1,3-allylic interaction 232, 247, 248 Absolute electronegativity, defined 130 Absolute hardness table of data for acids 132 table of data for bases 132 table of data for molecules 131 table of data for radicals 130 p-Acceptors, defined 70 -Acceptors, defined 70 Acetals anomeric effect in 96–99 hydrogen atom abstraction from 375, 376 radical attack on 375 Acetone electrophilicity 179 nucleophilic attack on 163 photochemistry of 412, 435 pinacol formation from 395 UV spectrum 94 Acetonitrile 197, 280 Acetophenone 179 1-Acetoxybutadiene from electrocyclic ring opening 362 in hetero-Diels-Alder reactions 310 5-Acetoxycyclopentadiene 246, 247 Acetyl, as a Z-substituent 70 Acetylenes benzyne compared to 194 by -elimination 206, 211

Molecular Orbitals and Organic Chemical Reactions: Reference Edition Ó 2010 John Wiley & Sons, Ltd

cycloaddition to vinyl cations 283 FOs of 330 IP of 66 less nucleophilic than alkenes 194 NMR coupling in 65 nucleophilic attack on 222 Smirnov–Zamkow reaction of 283 -Acyl anion, better represented as enolate ion 105 Acid chlorides, electrophilicity of 178, 179 Acids, tables of data for empirical hardness of 133 Acridinium ion 434, 435 Acridone, radical cation of 9-methyl 437, 438 Acrolein conformation of 108, 109 in Diels-Alder reactions 299, 303, 304, 305 dimerisation of 310, 311 FOs of 72, 74, 187, 303, 311, 319 IP of 66 -MOs of 72, 73, 187 photochemistry of 413, 417 protonated, as model for Lewis acid coordination 319 radical attack on 376 Acrylamide 188 Acrylic acid 304, 311 Acrylonitrile in cycloaddition to penta-2,3-diene 345 in Diels-Alder reactions 301, 310 in 1,3-dipolar cycloadditions 333 photochemistry of 412, 413, 419, 424, 425 radical attack on 389 Acryloyl chloride 188 Acyl cation destabilised 77 group, nucleophilic addition to 179 methyl anion, better represented as enolate ion 105 radical 434 silane, UV spectrum 94

Ian Fleming

476 Adamantanones 250 radical anion of 437 Adamantyl cation 245 Addition anti in oxymetallation 218 anti of bromine to alkenes 224 anti with bridging electrophiles 218 anti-Markovnikov 393 nucleophilic 179, 184 of radicals to alkenes 376–381 of radicals to arenes 381–384 radical to C¼C versus hydrogen atom abstraction 374 syn in hydrometallation 218 Addition-elimination reactions 223, 224 AIBN 384, 385 Aldehydes in aldol reaction 217 CH. . .O bonding in 119 conformation of 89, 227 electrophilicity of 178 nucleophilic addition to 179, 226–229 in Paterno-Bu¨chi reactions 411 Alder, K. 311 Alder ene reactions, see Ene reactions Aldol reactions 216, 217 as group transfer reaction 256 Mukaiyama 120 Alkaloids, radicals in biosynthesis of 391 Alkenes addition of hydrogen chloride to 216 anti-Markovnikov addition to 393 barriers to rotation in 110 bromination of 46 FOs of C-substituted, FOs of 72, 297 X-substituted, FOs of 75, 76, 297 Z-substituted, FOs of 73, 297 cycloaddition to [2 þ 2] forbidden 258 allyl anion 259 carbenes 284, 288 ketenes 281, 287 pentadienyl cations 259 stepwise radical 280 see also Diels-Alder reactions cyclooctatetraene like 39 diastereoselectivity electronegative substituent affecting 246–250 electropositive substituent affecting 243–246 geometry affecting 232, 233, 243, 248, 250 Houk rule for electrophilic attack 240–243, 244, 245

INDEX of nucleophilic attack on 232–234 pyramidalisation explaining 235, 236, 241, 243, 246 electrophilic attack on 146, 153–154, 216–218 ene reaction of 271 Hu¨ckel parameters for calculating MOs of 59 hydroboration of 283, 288 hyperconjugation stabilising 91, 92 IP correlation with with nucleophilicity 152 metathesis of 283 nucleophilic attack on 217 nucleophilicity of 142, 152, 154 photochemical reations cross-coupling 414 cycloaddition to benzenes 421 di--methane reactions of 428 dimerisation of 412 X-substituted in 412, 416, 433, 434 Z-substituted in 412, 416 product of elimination reaction 206 push-pull defined 101 radical attack on 370, 371, 375, 376–381, 386, 394 reduction of by dihydrogen transfer 277 substituent effects on 70–76, 295, 376–381 tau bonds of 61, 213, 246 see also Ethylene Alkoxide ion as hard nucleophile 188 Alkyl cations, hardness of 133 Alkyl groups destabilising anions 80 sigmatropic rearrangements of 267 as X-substituents 70, 87, 309 Alkyl halides electrophilicity of 179, 182 FOs of in SN2 reaction 208 in photochemistry 433, 434 rank order of LUMO energies 183 relative electrophilicity of 180 SN2 reactions of 151 softness of relative to carbonyl compounds 182 substitution versus elimination in 197 Alkyl radicals compared 383 Alkyl sulfonates 157, 160, 182, 220 Alkylamine as soft nucleophile 149 Alkylation, C- versus O- of enolate ions 160, 161, 239 Alkynes, see Acetylenes Allen electronegativities 50, 52 Allenes cycloadditions 281–283, 346 to alkenes 282 diazomethane 345 dimerisation 281, 347

INDEX photochemical 420 vinyl cations 283 FOs of 345 hydroboration of 345 rotation of C¼C in 101 two sets of  orbitals at right angles 282 Allenolate ion in electrocyclic ring closure 368 Allenylsilane 245 All-suprafacial mode allowed for reactions mobilising (4n þ 2) electrons 277 Allyl alcohol electrophilic attack on 247, 248, 250 Simmons-Smith reaction on 246 Allyl anions alkylation of 165 ambident nucleophilicity of 161–167 configuration of 108 C-substituted 163, 164–165 cycloaddition to alkenes 259 defined 23 electrocyclic ring closure of 262 FOs of 141, 162, 166 in reduction of butadiene 108  electron population 28 -MOs of 24–29, 105, 162 reaction of X-substituted with carbonyl electrophiles 162 reaction with allyl cation 140 sickle-shaped low in energy 265 with B, S or Si substituents 165 X-substituted 161–163 Z-substituted 165 Allyl cations configuration of 280, 366 in cycloaddition reactions 258, 259, 280 defined 23 electrocyclic ring closure of 262 FOs of 141 from electrocyclic ring-opening of cyclopropyl halides 366, 367 less stabilised than cyclopropylmethyl 88 not an intermediate in Favorskii reactions 367 oxyallyl systems behave as 340  electron population 28 reaction with allyl anion 140 regioselectivity of nucleophilic attack on 190, 191 Allyl esters in cuprate reactions 237 Allyl ether, conformation of 112 Allyl halides as ambident electrophiles 190 bromide 163 chloride 190 stereochemistry of nucleophilic substitution 236

477 SN2 reaction in 181, 190 Allyl phenyl ether 255 Allyl radicals configuration of 103, 108 defined 23 ESR of 67 in photochemical coupling 421, 423, 426 in reduction of butadiene 108 rotation in 83, 103 monosubstituted in reactions 390 Allyl sulfoxides 255 Allyl system canonical structures for 102 configurations of 102, 103 NMR coupling in 65  electron population of 28  MOs of 23–29, 33 reaction at C-2, 400 wave functions for 27 wire mesh representation 28 see also Allyl anion; Allyl cation; Allyl radical Allylborane anion, electrophilic attack on 165 Allylic epoxides 221 Allylic hydrogen, abstraction of by radicals 374 A1,3-Allylic interactions 232, 247, 248 Allyllithium reagents as allyl anions 161 Allyl-metal species, sickle configuration of 108 Allylsilanes attack on , -unsaturated ketones 217 conformation of 243 controlling torquoselectivity 365 electrophilic attack on anion of 165 hydroboration of 243 nucleophilicity of 154 pyramidalised 245 radical attack on 380 SE20 reaction of 244–246, 365 [1,3]-sigmatropic rearrangement in 278 stereochemistry of electrophilic attack on 243 Allylstannanes 154, 217, 385, 386, 390 Allylsulfoxide anion, electrophilic attack on 165 -diketones, see -Diketones -effect, see -Effect , energy level in Hu¨ckel theory defined as 31 see also Coulomb integral -fluorocarbonyl compound, see 2-Fluoroacetaldehyde -haloketones, see -Haloketones Alston, P. V. 312, 313 Alternating co-polymerisation 370, 371 Amarine 266 Ambident electrophiles 183–199 allyl halides 189–191 aromatic rings 183–186

478 Ambident electrophiles (continued) arynes 194–197 , -unsaturated carbonyl compounds 186–189 nitronium ion 159 substitution versus elimination 197–198 unsymmetrical anhydrides 191–192 unsymmetrical epoxides 192–194 Ambident nucleophiles 157–178 aromatic rings as 167 cyanide ion 158 cyclohexadienyl anion 164 dienolate ions 165 enolate ions 160 nitrite ion 158, 159 pentadienyl anion 163 pyridine-N-oxide 177 sulfenate ion 157 thiocyanate ion 158 Ambident radicals 370, 390–398 Ambident reactivity, HSAB in 159 Ambiphilic carbenes 203 Amide ion, as hard nucleophile 184 Amides conformation of 104, 106 electrophilicity of 178 Flippin-Lodge angle for 215 nucleophilic addition to 179 -overlap in 156 restricted rotation in 104 Z- and E-conformations of 105 Amines as soft nucleophiles 190, 237 configuration of 116 Hu¨ckel parameters for calculating MOs of 59 reaction with ester 157 Ammonia IP of 66 MOs of 117 in photochemical aromatic nucleophilic substitution 404 as soft nucleophile 186, 188 tert-Amyl cation 91 Anh, N. T. 226 Anhydrides as ambident electrophiles 191–192 regioselectivity of nucleophilic attack on cyclic 192 Anions, see Carbanions Anisole compared to benzyl anion 75 electrophilic substitution of 168 photochemistry of 405, 426 radical attack on 381, 382, 384

INDEX reduction of 397 restricted roatation about CO bond 111 Anisotropy, diamagnetic as measure of aromaticity 37 Annulenes [12] 39 [14] 35 [16] 39 [18] 35, 124, 125 diamagnetic ring current in 37 paramagnetic ring current in 42 Anomeric effects 96–100 affecting intermediate in nucleophilic attack on C¼O group 178 affecting regioselectivity of radical attack 379 anti versus syn 99, 100 in aromatic nucleophilic substitution 180 in conformation of esters 105 defined 96 effect on bond lengths 97, 98 effect on conformation 97 exo defined 97 explanation for 97 generalised 97 lop-sided 97 in nucleophilic attack on imines 231 in open-chain conformations 111 in radicals 375, 376, 389 Antarafacial defined for [1,2] sigmatropic rearrangements 268 defined for [1,n] shifts of H 266 defined for [m,n] sigmatropic rearrangements 269 defined for a p orbital 275 defined for a  bond 273 defined for cycloaddition reactions 261 Antarafacial component in cycloadditions to ketenes and allenes 282 odd number of in thermal pericyclic reactions mobilising (4n) electrons 277 Anthracene Diels-Alder reaction of 320 frontier electron populations of 174 LUMO of 184 photochemistry of 414, 421 product in photochemical reaction 438 radical anion of 67 radical anion of 9,10-diphenyl 438 radical attack on 383 radical cation of 67 reduction of 271, 398 site of electrophilic attack on 174 site of nucleophilic attack on 184 synthesis of 354

INDEX Anti versus syn stereochemistry in anomeric effect 99, 100 in elimination 205, 210–211 in decarboxylative elimination 212–214 in SN20 reactions 236 Antiaromaticity 37–42 Antibonding MOs, defined 3, 5, 6 Anti-Cram, see Anti-Felkin-Anh Anti-Felkin-Anh, product of dissolving metal reduction of ketones 395 Antiperiplanar arrangement in transition structures 217 attack relative to an MC bond 218 compared with synclinal 217 compared with syncoplanar 98 in hyperconjugation 85 see also Anomeric effect; Elimination reactions Apical positions electronegative substituents in 207 site of attacking and departing ligands 122 Aromatic carbenes 201 Aromatic electrophilic substitution 167–178 MOs of intermediates in 168 photochemical 405 pyridine N-oxide 177 site of in arenes 349 Aromatic nucleophilic substitution 179–180, 183–186, 404 Aromatic rings as ambident electrophiles 183–186 as ambident nucleophiles 167–178 di--methane rearrangements in 428 -stacking in 124 photochemical reactions of 421–430 radical attack on 381–384 reduction by sodium in liquid ammonia 397 UV spectra of 62 Aromatic transition structures as explanation for substituent effects 350–354 as explanation for torquoselectivity 363 as explanation for Woodward-Hoffmann rules 286 Aromaticity 34–37, 213 affecting direction of electrocyclic reactions 262 diminishes in long conjugated systems 37 Mo¨bius 354, 363 in transition structures 286, 351–354, 363 Arrhenius parameters 256 Arynes 194–197 Asynchronicity in Diels-Alder reactions 285, 301, 304, 316 Atomic orbitals 1s 1, 2 2p 10 2s 10 coefficients of, see Coefficients

479 d, unsuitable for conjugation 80, 121 energies of 51 linear combination of 2, 14, 24, 29 mixing of 15, 24, 26, 30 sign of s in computing steric effects 226 Aufbau method 8 Avoided crossing 293 Axial attack favoured stereoelectronically 229–232 in cyclohexanones 229, 234 in enolate methylations 239 Azaadamantanone 251 Azaadamantylidene 200 Azide ions defined 323 FOs of 325 as nucleophile in SN2 reaction 181 opening an epoxide 193 as soft nucleophile 190 Aziridines configuration of 116 electrocyclic opening of 265, 274 from decomposition of triazolines 331 photochemical opening of 410 Azobisisobutyronitrile, see AIBN Azomethine imines defined 323 1,3-dipolar cycloaddition to alkenes 333 FOs of 325 Azomethine ylids barrier to rotation in 103, 104 configuration of 274 defined 323 1,3-dipolar cycloadditions of 265, 336, 337 from electrocyclic opening of aziridines 265 FOs of 325 photochemical formation of 410 Azoniaanthracene cation 301, 305 Azulene from cycloaddition reactions 362 frontier electron populations of 174 LUMO of 184 site of nucleophilic attack on 184 site of electrophilic attack on 174 , see Resonance integral Baeyer-Villiger rearrangement 267, 353 Baker-Nathan order 230 Baldwin, J. E. 218, 219, 220, 343, 368, 379 Baldwin’s rules 218–222 Baldwin-Beckwith rules 379 Band gap 34 Barton, D. H. R. 241

480 Barton oxidation 390 Basal, site of less electronegative ligands 122 Bases, tables of data for empirical hardness of 134 -chloro anion 223 -elimination, see Elimination reactions Beckmann rearrangement 267, 353, 354 Benzanthracene 348 Benzcyclobutene, electrocyclic ring opening of 354 Benzenes Birch reduction of 397, 398 degeneracy of FOs lifted in mono-substituted 71, 170–172, 381, 427 edge-to-face coordination in crystal structure of 121 electrophilic substitution 168–173 exceptionally low  energy of 36 IP of 66 -MOs of 34–37, 71, 170–172, 422, 423, 427 photochemical reactions of 404, 405, 421–430 radical anion of 67 radical attack on 381, 382, 391 stacks with hexafluorobenzene 125 Benzidine rearrangement 270 Benznorbornadienes 428–430 Benzocyclobutyl oxide 354 Benzofuran 174 Benzoic acid, Birch reduction of 398 Benzonitrile 155, 172, 426 Benzonitrile oxide 360 Benzophenone 411, 435, 436 1,4-Benzoquinone 343 Benzoyl chloride 200 Benzoyl peroxide 118 Benzoyloxy radical 378 Benzpinacol 435, 436 Benzyl acetates, photochemical ionisation of 408 Benzyl anion as model for X-substituted benzene 168 compared to anisole 75 Benzyl cations 111 from photoionisation 407, 408 model for a Z-substituted benzene 169 Benzyl halide 155, 181, 374, 399 Benzyl radicals 399 coefficients of SOMO 171 ESR of 67, 171, 185 Benzyl system  MOs of 170, 171 -orbitals of as model for substituted aromatics 405 SN2 reaction in 181

INDEX Benzylidene aniline 1,3-dipolar cycloaddition to diazomethane 336 cycloaddition to diphenylketene 343 Benzynes chemoselectivity of 197 Diels-Alder reactions of 354 FOs of 194 nucleophilicity of reagents towards 196 regioselectivity in substituted 194, 195 see also Pyridynes Bicyclic alkenes bicyclo[2.2.1]hept-2-yl cation 89 bicyclo[2.2.1]heptane system 205 bicyclo[2.2.2]octadiene 241 bicyclo[3.1.0]hex-2-enyl cation 268 bicyclo[3.2.0]heptadiene 430, 431 bicyclo[3.2.0]heptene 268, 278 exo attack on 240–241, 386 pyramidalisation of 241 Bifluorenylidene, low barrier to rotation about the p bond 101 Biphenyl, reduction of 397 Biphenylene 174 Birch reduction 164, 397–398 Bishomocyclopentadienyl anion 42 Boat transition structure for Cope rearrangements 276 for Diels-Alder reactions 289, 294, 313 Bohlmann bands 86 Bohr radius 2 Bond angles 80 Bond lengths anomeric effect on 97, 98 in butadiene 295 in carbocations 89 of CH bonds 85, 88 in cyclohexene 295 in ethylene 295 in silyl ethers 80 Bond strength, defined 52, 54 Bonding MO, defined 3, 5, 6 p-Bonds attacking a  bond 216 defined 19 high barrier to rotation in 101–104, 108–110 in hydrogen bonding 120 LUMO of C¼C in ketenes 358 MOs of C¼C 20–34 MOs of C¼O 57–58 nucleophilic attack on, stereochemistry 214 radical attack on 376 weaker than , 19 see also Alkenes; Carbonyl groups

INDEX -Bonds bridging, with two-bonds with 2 electrons 90, 94, 119, 216 bridging, with two-bonds with 4 electrons 153, 217, 218 CC 18–20 CH 10–18, 123, 314 CLi 56 CM 56–58, 93 CSi 94, 380 CX 50–55 dissociation energy of, D0 133 HH 2–7 hydrogen, see Hydrogen bonds in hyperconjugation, see Hyperconjugation NH 115 OO 438 restricted rotation in 83, 93, 104–111, 223, 224, 245 in trigonal bipyramidal structures 122 cleavage in photochemistry 434 Boranes in radical chain reactions 376 Borneol 205 Boron empty orbital of 77 holding two molecules in cyclic transition structure 249 stabilising anions 78 substituent in Diels-Alder reactions 308, 322 trihalide 77, 319 Bridging 2-bond 2-electron 90, 94, 119, 216 2-bond 4-electron 153, 217, 218 in bromodesilylation of vinylsilanes 224 in electrophilic attack on alkenes 153 electrophiles 153, 216, 217, 218, 243, 245 versus hyperconjugation 94, 216 Bromination of alkenes, as soft-soft reaction 46, 143 of alkenes, stereochemistry of 243 Bromine atom as radical 374, 375 bridging electrophile in attack on an alkene 216, 218 in NBS reactions 374 as soft electrophile 142–143 Bromobenzene 147 Bromodesilylation, stereochemistry of 224 3-Bromopyridine 404 N-Bromosuccinimide, see NBS Brønsted plot 155 Bryce-Smith, D. 424 Bu¨rgi-Dunitz angle affecting stereoselectivity in nucleophilic attack on C¼O bond 226

481 defined 214 equivalent in electrophilic attack on C¼C 216 in explaining Baldwin’s rules 219 for radicals 388 in radical reactions 379 But-3-ene-2-one 109 Buta-1,2-diene, dimerisation of 347 Butadienes, see 1,3-Dienes Butadiene 1-carboxylic ester dipolar cycloaddition to diazomethane 338 in hetero-Diels-Alder reactions 310 Butadiene-1-carboxylic acid FOs of 313 in Diels-Alder reactions 304, 306 Butadiene-2-boronic acid in Diels-Alder reactions 305 Butadiene-2-carbonitrile in Diels-Alder reactions 306 Butadiene-2-carboxylic ester in Diels-Alder reactions 301 Butanal, synthesis from 1-butene 376 2-Butene carbene insertion into 200 cis and trans 101, 107, 108, 200 electrophilicity of 154 photodimerisation of 409 products from reducing butadiene 107 UV spectrum of 230 3-Butenyl cation 91 tert-Butoxy radicals 374, 379 tert-Butylamine 405 tert-Butyldiazomethane 265 tert-Butylketene 265 4-tert-Butylcyclohexanone 226, 396 2-Butyne 283

-Butyrolactone 371, 372 C,N-diphenylnitrone 336 C¼C double bond see Alkenes; Ketenes C¼O, see Carbonyl groups Calculations, see Hu¨ckel calculations, Transition structures C-Alkylation of enolate ions 160 CAN 394 Canonical structures 102, 105, 141, 253, 304 Captodative radicals 82–83 Carbamates 111 Carbanions allyl 102 CM bond as 56, 78, 79, 86, 96 rearrangements of not by [1,2]-sigmatropic 278 [2,3]-sigmatropic 270, 276 Stevens 270, 281

482 Carbanions (continued) stabilised ortho 195 by negative hyperconjugation 96 by neighbouring B 78 by neighbouring Si, P and S 79 by C- and Z-substituents 78–80 tetrahedral configuration of 116 see also Enolate ions Carbenes 199–203 ambiphilic 203 aromatic 202 cycloadditions of 200, 201, 281, 284, 347–348 electrophilic 201 FOs of 199, 201, 288, 357 insertion into CH 201, 284 methylene 13 MOs of 13, 199 non-linear approach 284, 288, 357 nucleophilic 199, 201 stabilised 199, 202 triplet 203 see also Dichlorocarbene Carbenoids 347 Carbocations -acyl 77 allyl 102 attacking allenes 245 bond lengths in 89 bridging in 90 carbonyl groups as 89, 113 conformation of 111 cyclobutenyl 42, 283 cyclobutyl 91 cyclodecyl 119 cycloheptatrienyl 34, 35 cyclohexadienyl 167 cyclopentadienyl 39 cyclopentenyl 266 cyclopropyl 366 cyclopropylmethyl 88, 89, 91, 353 destabilisation by negative hyperconjugation 95 Z-substituents 77 stabilisation of alkyl 87–89 of -metalloethyl 92–94 of -silyl-, 94, 112, 224, 244, 245 by substituents 76–78 by hyperconjugation 87–91 as electrophiles for alkenes 154, 245 pentadienyl 266 1,2-shift in 90, 91, 267, 353

INDEX tertiary not bridged 90 vinyl 283, 287 Carbometallation 218, 283 Carbon atomic orbitals of 10–12 hybridisation of orbitals of 15–18 Carbon dioxide as electrofugal group 212, 213, 214 Carbon disulfide 202 Carbon monoxide, cheletropic retrocycloaddition of 356 Carbon tetrachloride 118 Carbonium ions, see Carbocations Carbon-metal bonds, called anions 56, 78, 96 Carbonyl groups destabilising a cation 77 electrophilicity of 179 hardness of relative to alkyl halides 182 as heterodienophiles 310 as highly stabilised carbocation 89, 113 Hu¨ckel parameters for calculating MOs of 59 MOs of 57, 58 nucleophilic attack on, endothermic 182 nucleophilic attack on, stereochemistry 226–231, 214, 240 Carbonyl imines 323, 325 -Carbonylmethyl radical 390 Carbonyl oxides 323, 325, 336 Carbonyl ylids 323, 325 Carboxy group as a Z-substituent 70 Carboxylate ions Flippin-Lodge angle for 215 like a C-substituent 305 nucleophilic addition to 179 Carcinogenicity 348 Carotenoids 109 Carpenter, B. K. 350 Cathodic electrolysis 391 Cations, see Carbocations (c )2 values defined 326 (c )2 values listed for 1,3-dipoles 325 CC bond MOs of with hybridisation 20 MOs of without hybridisation 19 CCl bonds, see C-halogen bond; Alkyl halides; Methyl chloride Ceric ammonium nitrate, see CAN CF bond stabilising an anion 195 stabilising a radical 379 CH bonds hyperconjugation with 86, 90, 106, 192, 230 orbitals of using hybridisation 17 orbitals of without using hybridisation 10–15

INDEX polarised towards C 123, 314 radical attack on 371 Chair conformation control of diastereoselectivity by 217, 239, 269, 387 preferred for Cope rearrangements 269, 276, 350 Chalogen bond attack on back side of in electrocyclic ring-opening 368 conjugated to alkene lowers HOMO energy 246 destabilises neighbouring cation 95 orbital description of 93, 99, 100 radical attack on 373, 374 stabilises neighbouring anion 96 see also Alkyl halides; Methyl chloride Change of mechanism 324 identified by an upwardly curving plot 323 Charge distribution in conjugated systems 113–115 formal representation in resonance structures 113 transfer complex in SET reactions 147 transfer in photochemical cycloadditions 424 Chelation 163, 217, 229, 245 Cheletropic reactions carbene cycloadditions as 284 defined 254 diene-sulfur dioxide 254, 362, 409 hexatriene-sulfur dioxide 284 retrocycloaddition of carbon monoxide 356 Chemical potential, electronic 129 Chemical shifts affected by MOs 62 probe electron distribution 114 Chemiluminescence 437–438 Chemoselectivity of benzyne 197 of radicals used in synthesis 384 see also Electrophilicity; Nucleophilicity Chiral auxiliaries in Diels-Alder reactions 257 Chlorin rings, p-stacked 124 Chlorine atoms in radical reactions 372, 383 effect of as substituent 95, 96, 227, 246, 283 as an electrophile 175 Hu¨ckel parameters for calculating MOs of 59 as representative electronegative element 52 see also Halides; Halogen atoms Chloroacrylonitrile 223, 318 Chlorobenzene, site of electrophilic attack on 173 Chloroform 120 -Chloroketones nucleophilic attack on 227, 228 photochemistry of 433 Chloromethoxycarbene 203 Chloronitrobenzene, o- and p-, 185

483 Cholestenone 390, 396 Chromic acid oxidation of arenes 349 Cieplak, A. S. 227, 228, 229, 230, 231, 247, 251, 252 cis-trans isomerisation, see Rotation Citraconic anhydride Diels-Alder reaction of 308 reduction of 192 Claisen condensation 188 Claisen rearrangements chair transition structure 276 defined 255 effect of substituents on rates of 352 evidence for pericyclic nature of 257 following ketene cycloadditions 358 Ireland-Claisen, 269 CLi, MOs of 56 Click chemistry 329 Closed-shell repulsion in Salem-Klopman equation 139 CM bonds 49, 56–57, 92, 93 CO bonds, conformations around 97 Coalescence of NMR signals 110 Coefficients of atomic orbitals in MOs acrolein 72, 74, 187, 311, 319 allyl system 24 benzene 36 butadiene 29 butadiene-1-carboxylic acid 313 calculation of 7, 25, 30 Chalogen bonds 52–53, 93 CM bonds 56–57, 93 conjugated systems 33 C-, X- and Z-substituent effect on alkenes 70–76 defined 2 determining rates of Diels-Alder reactions 298–303 determining regioselectivity of Diels-Alder reactions 303–311 determining site of reaction 141 dienes and dienophiles 297 estimating 70–76, 313 importance of single highest 349 hexatriene 33 hydrogen molecule 7 measured by ESR 67 pentadienyl system 33 2-phenylbutadiene 321 in photochemical site-selectivity 419 in Salem-Klopman equation 138 styrene 71 see also (c )2 values; c2 values Components (4q þ 2)s defined 271 (4r)a defined 271

484 Components (continued) identifying for application in the Woodward-Hoffmann rule 277 identifying with curly arrows 289 Concertedness, characteristic of pericyclic reactions 256 Conduction band 34 Configuration defined 100 interaction 5, 124 inversion of in amines and phosphines 115 of radicals 369, 386 W-, sickle- and U-shaped allyl 103, 366 Conformation affecting negative hyperconjugation 95 defined 100 of 1,3-dienes 106, 107, 108, 280, 357 of 1,3-dioxans 123 of enol ethers 105 of esters 105 gauche in anomeric effects 111 of hydrogen peroxide 84 -bond rotamers 93, 94 staggered versus eclipsed 211 weak forces affecting 115 see also Chair conformation Coniferyl alcohol, oxidation of 392 Conjugate attack conjugate reduction 189 on , -unsaturated esters 188, 232, 233, 234, 239, 370 on , -unsaturated ketones 186–189, 217, 233 versus direct nucleophilic attack 186–188 vinylogous Felkin-Anh 232, 233 see also Michael reaction Conjugated systems 23–34 alternant, defined 30 charge distribution in 113 cross conjugated 177 linear 30, 177 Conjugation CH with CH 85 defined 23 energy-lowering 69, 145 energy-raising 78, 83, 85, 111 longer systems 32 of CCl with C¼O 433 present in glyoxal 84 p with , 110, 111  with , 79, 80, 85, 251 spiro 44 substituents in 69 see also Orbital interactions Conrotatory, defined 263

INDEX Conservation of orbital symmetry 288, 295 Contour plots formaldehyde 58 hydrogen atom 1 hydrogen molecule 6 ethylene 22 2p orbital on carbon 11 2s orbital on carbon 10 sp3 hybrid on carbon 16 Conventional representation 2s orbital on carbon 10 of bonds 17 2p orbital on carbon 11 sp3 hybrid on carbon 16 Convex face of bicyclic alkenes 240 Coordination stabilising organometallic compounds 80 Cope rearrangements 256, 257, 269, 276, 316, 349, 350–352, 358 Coplanarity necessary for p overlap 98 Corey, E. J. 233, 318 Cornforth, J. W. 227, 228 Correlation diagrams 288–293 as explanations of the Woodward-Hoffmann rules 288 orbital, for [2 þ 2]-cycloaddition 291 orbital, for [2 þ 4]-cycloaddition 290 photochemical meta cycloaddition 422–423 photochemical ortho cycloaddition 421–422 for radical cation reactions 395 state, for [2 þ 2]-cycloaddition 293 state, for [2 þ 4]-cycloaddition 292 Coulomb integral  corrections for heteronuclear bonds 59 defined 4 mathematical form of 5 Coulombic effects 80, 83, 122, 216 on Bu¨rgi-Dunitz angle 215 on allyl cation þ anion reaction 140 on aromatic nucleophilic substitution 185 attraction 124 on C- versus O- attack 160 destabilising Z-substituted cations 78 on Diels-Alder reactions 314 explaining stereochemistry of SN2 reactions 207 on ionic bonds 128 repulsion 5, 139, 124, 217, 314 weak in radical reactions 370, 400 Coumarin, photochemistry of 414 Coupling constants 1 H-13C 65, 85 1 H-1H 65 affected by orbital overlap 63

INDEX geminal 64, 65 long-range 65 one-bond 64, 65 sign of 64 vicinal 65 zero magnitude 63 Coupling, of radicals 384, 399, 400 Cram’s rule, see Felkin-Anh rule Cram-chelation control 229 Cross-coupling of alkenes, see Photochemical reactions Crotyl chloride 88 Cryptand, sequestering a lithium ion 187 CS bond, radical attack on 373, 374 CSe bond, radical attack on 373, 374 C-Substituents on allyl anions 163 defined 70 effect on FOs of alkenes 72, 154, 179, 295 effect on FOs of benzenes 172 stabilising carbanions 78 stabilising carbocations 76 stabilising radicals 81 Cumulated double bonds, see Allenes; Ketenes Cuprates conjugate addition by 232, 233, 239 reductive elimination step in reactions of 238 in SN20 reactions 237 Curly arrows different kinds of 253 even number identifies a reaction with (4n) electrons 277 identifying components 277, 289, 290 illustrate FOs 24, 168 illustrating overlap in the allyl system 23 illustrating -overlap 114 inadequate to explain regioselectivity in cycloadditions 304, 326 for intermediates in electrophilic aromatic substitution 168 odd number identifies a reaction with (4n þ 2) electrons 277 for pericyclic reactions 289 signifying reaction 110 Curtin-Hammett principle 227 Curtius rearrangement 267, 353 Curve crossing 135, 292, 293 Cyanide ion 157, 158, 184, 186, 190, 191 Cyano group as a heterodienophile 310 as a nucleophile 158 as a soft electrophile 155 as a Z-substituent 70 1-Cyanobutadiene 321, 344

485 Cyanohydrin formation 186 1-Cyanonaphthalene 393 Cyclisations by enolate alkylation 219 of radicals 379 see also Baldwin’s rule Cycloadditions defined 254 number of electrons, effect of in 258 periselectivity in 356–362 photochemical [2 þ 2] allowed 293, 408, 409, 421, 425, 429 cross-coupling 414–420 [2 þ 2] dimerisations 409, 412–414 [4 þ 4] dimerisations 409, 414 electron transfer in 424 m-to-benzene 421–428 o-to-benzene 421, 425 p-to-benzene 421, 423 rates of Diels-Alder affected by substituents 298–302 secondary orbital overlap in, see Secondary orbital overlap simple rule for pericyclic 260, 262 stepwise 280, 285, 287, 342 symmetry-imposed barrier in [2 þ 2] 292 thermal [2 þ 2] allenes þ alkenes 281–283, 345–347 carbene þ alkene 200, 284, 288, 347–348, 357 cyclopentadiene þ dichloroketene 357, 341 6,6-dimethylfulvene þ dichlorocarbene 348 6,6-dimethylfulvene þ dichloroketene 360 6,6-dimethylfulvene þ methoxychlorocarbene 348 FOs for 287 ketenes þ alkenes 281, 282, 340–345 kinetic barrier in pericyclic 258 linear approach forbidden for carbenes 284 1-methoxybutadiene þ diphenylketene 358 not forbidden if stepwise 279 orbital correlation diagram for 290, 291 state correlation diagram for 293 stepwise 280, 287, 342 of vinyl cations 283, 287 thermal [2 þ 4] allyl anion þ alkene 259 allyl cation þ diene 259, 340 cyclopentadiene þ diphenylketene 358 cyclopentadienylidenecycloheptatrienes þ dimethyl acetylenedicarboxylate 359 cyclopentadienylidenecycloheptatrienes þ tetracyanoethylene 359 6,6-dimethylfulvene þ a cyclopentadienone 360 6,6-dimethylfulvene þ cyclopentadiene 361 orbital correlation diagram for 290

486 Cycloadditions, thermal [2 þ 4] (continued) pentadienyl cation þ alkene 259 state correlation diagram for [2 þ 4] 292 see also Diels-Alder reactions thermal [2 þ 6] hexatriene þ sulfur dioxide 356 photochemical 425, 427 thermal [2 þ 8] avoided 358 bromoketene þ pyridinium betaine 344 heptafulvene þ dimethyl acetylenedicarboxylate 356 dimethyl azodicarboxylate þ tetraene 260 thermal [2 þ 14] 261, 273 thermal [4 þ 6] 6,6-dimethylfulvene þ tropone 360 6,6-dimethylfulvene þ isobenzofuran 361 6-dimethylaminofulvene þ a diene 362 tropone þ cyclopentadiene 260, 338, 355 trimethylenemethane þ cyclopentadiene 340 trimethylenemethane þ methyl acrylate 339 Woodward-Hoffmann rules for 258–262, 271–273 see also Cheletropic reactions; Diels-Alder reactions; 1,3-Dipolar cycloadditions; Retro-cycloadditions Cycloalkenes, stereochemistry of attack on 238–241 Cyclobutadiene 34, 37–41 1,3-Cyclobutanedione 343 Cyclobutanes from cycloadditions allenes þ alkenes 282, 345 vinyl cations þ alkenes 283 ketenes þ alkenes 281, 341, 342, 357, 358 dimerisation of allenes 347 [2 þ 2] photochemical 409, 412–419 stepwise 279, 280 from epoxide openings 221 lower in energy than two alkenes 258 not formed in [2 þ 2] thermal pericyclic cycloaddition 258 ring current in 48 Cyclobutenes 3,4-dichloro 247 electrocyclic ring opening of 254, 273, 287, 354 orbital interactions in electrocyclic opening 363, 364 stereochemistry of electrocyclic ring opening 263 torquoselectivity in electrocyclic ring opening 362 Cyclobutenyl cation 42, 283 Cyclobutyl cation 91 Cyclodecyl cation 119 Cycloheptatriene cycloaddition with dichlorocarbene 347 not homoaromatic 42–43

INDEX photochemical reactions of 410, 430 regioselectivity of 1,7-hydrogen shift in 431–432 1,5-shifts of H in 267 slow Diels-Alder reactions of 302 Cycloheptatrienyl anion 164 Cycloheptatrienyl cation 34, 35 Cycloheptatrienylidene 201, 202 Cyclohexa-1,3-diene from ring closing of hexatriene 254 Cyclohexa-1,4-diene concerted elimination of H2 from 257–258 NMR coupling in 65 transfer of hydrogen from 271 Cyclohexadienones 234, 235 Cyclohexadienyl anion 164, 165, 180 Cyclohexadienyl cation, see Wheland intermediate Cyclohexadienyl radical 164, 391, 397 1,2-Cyclohexanedione 84 Cyclohexanes axial Hs in 85 conformation of 112, 121 NMR coupling in 65 ring current in 48 Cyclohexanones conformation 230 nucleophilic attack on 229 reduction of 229 Cyclohexenes bond lengths in 295 electrophilic attack on 239 epoxidation of 239 trans 280 Cyclohexenones direct versus conjugate attack on 187 nucleophilic attack on 5-substituted 239 photochemistry of 416 trans 416 twisted excited state 416 Cyclohexyl radical 378, 384, 386, 388 Cyclonona-1,2-diene 346 Cyclooctadiene 269 Cyclooctatetraene 39, 101 Cyclooctene 281 Cyclopentadiene 5-acetoxy 247 cycloadditions of with acrolein 314 allyl cation 258–259 carbenes 357 dichloroketene 341, 357 6,6-dimethylfulvene 361 diphenylketene 358 maleic anhydrides 311, 240

INDEX

487

methyl acrylate 318 methylketene 342 oxyallyl cation 340 trimethylenemethane 340 tropone 260, 338 dimerisation of 316–317 exceptionlly reactive in Diels-Alder reactions 302 FOs of 317, 338, 340, 355 not homoantiaromatic 43 pyramidalisation of 241, 247 1,5-shifts of H in 267, 321, 322 see also Thiele’s ester Cyclopentadienone 360 Cyclopentadienyl anion 34, 35 Cyclopentadienyl cation 39 Cyclopentadienyl system 41 Cyclopentadienylidene 201, 202 Cyclopentanones 250 Cyclopentene 250, 425, 426 Cyclopentenone from electrocyclic ring closure 368 photochemistry of 414, 415, 416 Cyclopropane carboxaldehyde, conformation of 89 Cyclopropanes bromination of 46 formation from carbenes 200, 201, 203, 284, 347, 357 MOs of using Walsh orbitals 46 MOs of using hybridisation 46 ring current in 48 Cyclopropanones products of electrocyclic ring closure 265, 368 products of Favorskii reactions 367 Cyclopropenone 315 Cyclopropenyl cation 34–35, 201 Cyclopropenylidene 201–202 Cyclopropyl cations 366 Cyclopropyl halides 366–367 Cyclopropylmethyl cation 88, 89, 91, 353 Cyclopropylmethyl chloride 88 Cyclopropylmethyl radicals 381, 428, 429 Cycloreversion, see Retro-cycloadditions DABCO 186 Danishefsky’s diene, see 1-Methoxy-3trimethylsilyloxybutadiene Decalone, trans 396, 420 Decarboxylative elimination 212, 213, 214 Degeneracy of FOs lifted by substitution 60, 71, 170–172, 338, 427 Delocalisability parameter D(R) defined for radicals Delocalisation, defined 4 Density functional theory, used in HSAB 129

374

Desymmetrisation 226 Deuterium substituents test of concertedness 257 in photochemical reaction 432 Deuterodeprotonation 405, 406 Diaminosuccinate 83 Diarylmethyl cations as electrophiles for alkenes 153, 154 Diastereoselectivity 225–252 measure of as a ratio 205 weaker in radical reactions than ionic 387 Diastereotopic, defined 225 Diazaacetal 97 Diazoalkanes defined 323 1,3-dipolar cycloadditions of 240, 247, 324, 326–328, 336, 338, 345 FOs for 325, 327, 328 reaction with ketene 265 Diazomethane, see Diazoalkanes Diazonium ions in aromatic nucleophilic substitution 185 Dibenzoyl peroxide 437 Dibenzylidenecyclopentanone 119 Diborane 90, 119 -Dicarbonyl enolates, Michael reaction of 187, 188 Dichlorocarbene cycloaddition to alkenes 284, 288 cycloaddition to butadiene 357 cycloaddition to 6,6-dimethylfulvene 348 electrophilic nature of 201 1,2-Dichlorodioxan 98 Dichloroketene 281, 340, 341, 357, 360 Dicyanobenzoquinone 320 Dielectric constant in Salem-Klopman equation 138, 139 Diels-Alder reactions 298–322 anthracene þ maleic anhydride 320 butadiene þ acrolein 299, 314 þ 1,1-bismethoxycarbonylethylene 299 þ dicyanobenzoquinone 320 þ ethylene 290, 299 butadiene-2-boronic acid þ acrolein 305 butadiene-1-carboxylic acid þ acrylic acid 304 þ styrene 306 butadiene-1-carboxylic ester þ enamine 305 butadienylsulfone þ enamine 312 as [4 þ 2] cycloadditions 258 as [2s þ 2s þ 2s] cycloaddition 272 concerted but asynchronous 304, 316 curly arrows for 289 a cyclohexadiene þ maleic anhydride 421

488 Diels-Alder reactions (continued) cyclopentadiene þ acrolein 314 þ dimethyl fumarate 318 þ maleic anhydride 311 þ methacrolein 314 þ methyl acrylate 318 cyclopentadienylidinecycloheptatrienes þ dienophiles 359 defined 253 diastereoselectivity of 240, 246, 247, 248, 249 dimerisation of butadiene 299 of butadiene-2-carbonitrile 306 hexatriene 320, 358 of methyl cyclopentadienecarboxylates 322 of 2-phenylbutadiene 321 1,1-dimethylbutadiene þ tetracyanoethylene 280 6,6-dimethylfulvene þ cyclopentadiene 361 þ o-quinodimethane 360 effects of Lewis acid on 318 endo rule for 311–315 evidence for concertedness 256, 257 exceptions to ‘ortho-para’ rule 306 FOs for 287, 299 furan þ cyclopropenone 314 generalised Woodward-Hoffmann rule for 272 heptatriene þ maleic anhydride 321 intramolecular 354 inverse electron demand in 300, 301, 302, 305, 312, 323 inverse secondary deuterium isotope effects in 257 isoprene þ acrolein 299 þ 1-cyanobutadiene 321 þ methyl propenyl ketone 318 methoxybutadiene þ acrolein 299, 303, 304 þ propynal 305 methoxycyclohexadiene þ fumaroyl chloride 314 methoxymethylcyclopentadiene þ 2chloroacrylonitrile 318 2-methoxy-3-pheylthiobutadiene þ methyl acrylate 308 1-methoxy-3-trimethylsilyloxybutadiene þ butadiene-2-carboxylic ester 301 orbital correlation diagram for 289, 290 orbital following for 293, 294 orbital interactions for 272 ‘ortho-para’ rule for 306 orthoquinodimethane þ ethyl vinyl ether 307 þ propyne 307

INDEX penta-1,3-diene þ fumaric acid 313 of pentadienylsilanes 243 periselectivity of 355 phenylbutadiene þ 2-methylmaleic anhydride 309 þ acrolein 305 þ styrene 306 þ acrylonitrile 305 photochemically forbidden 408 piperylene þ acrolein 299 þ vinyl-9-BBN 308 pyrido[1,2-b]isoquinolin-5-ium ion þ alkenes 301 of 3,4-pyridyne,196 o-quinodimethane þ benzyne 354 rates of little affected by solvent 256 rates of 298–302 reaction coordinate of 294 regioselectivity of 303–310, 318, 319 secondary orbital overlap in 312, 313, 314, 315, 317 site selectivity 319–322 stereoselectivity of 311–317 symmetry elements for 289 tetracyclone þ styrenes 302 transition structures for 294, 295, 315–317, 322 tropone þ acrylonitrile 310 þ styrene 310 2,6-xyloquinone þ diene 309, 319 see also Hetero-Diels-Alder reactions 1,3-Dienes alternating pyramidalisation 246 barrier to rotation about the single bond 106 bond lengths in 295 conformation of 106, 107, 108, 280, 357 cycloadditions to allyl cation 259 C, X- and Z-substituted in 296, 297, 304, 309, 313, 319, 322 to dichlorocarbene 357 Diels-Alder 257, 258, 298, 299, 320 photodimerisation 413 to sulfur dioxide 254, 284 stepwise 280 diastereoselectivity of electrophilic attack on 249 electrocyclic formation of 254, 287 electrocyclic ring closure of 262, 410 endocyclic 107 FOs of 72, 167, 295–297, 361 IP of 66 MOs of 29–33 product of E20 reaction 212–214 radical anion of 108

INDEX radical attack on 376, 390, 400 reduction of 107, 108, 398 tau bonds in 61, 246 UV absorption in 61 Dienol ethers, p-electron population of 166 Dienolates 165, 166, 230 Dienones, Nazarov reaction of 365 Dienophiles FOs of 297 substituent effects on rates 298–303, 322 on regioselectivity 303–311, 322 on stereoselectivity 311–315 Diethyl ether in photochemical reaction 436 Diethyl ketene acetal, cycloadditions of 420 Diffusion control 158, 203 1,2-Difluoroethane 111, 112 1,1-Difluoroethylene 379 1,2-Difluoroethylene 112 Difluoromethane 98 Dihydrofuran 329, 337 Dihydrogen transfer 271, 277 Dihydroxylation 240, 243, 244, 247, 248, 249 Diimide 256, 277 -Diketones electrophilicity of 179 high energy of 84 Dimerisations of acrolein 311 of anilines by electron transfer 393 of butadiene-2-carbonitrile 306 of buta-1,2-diene 347 of cyclobutadiene 39 of cyclopentadiene 315 of dimethylketene 343 of hexatriene 320, 358 of ketene 343 of oxyallyl cation 340 of 2-phenylbutadiene 321 [2 þ 2]-photochemical 414 [4 þ 4]-photochemical 414, 421 of a trimethylenemethane 339 Dimethoxycarbene 199, 200 Dimethoxycarbonylcarbene 201 Dimethoxymethane 98, 100 Dimethyl acetylenedicarboxylate 324, 359 Dimethyl azodicarboxylate 260, 300 Dimethyl fumarate 202, 282, 313, 370, 371 Dimethyl maleate 200, 282, 337 Dimethyl sulfide 202 1,1-Dimethylallene 282, 346 Dimethylallyl chloride 190

489 Dimethylamino radicals 383 6-Dimethylaminofulvene 362 Dimethylaniline, anodic electrolysis of 393 Dimethylbutadiene 1,1-, 280 1,3-, 310 1,4-, see Hexa-2, 4-diene 2,3-, 411 see also 1,3-Butadienes 2,3-Dimethyl-2-butene 424 6,6-Dimethylfulvene cycloaddition to cyclopentadiene 361 cycloaddition to dichlorocarbene 348 cycloaddition to methoxychlorocarbene 348 cycloaddition to o-quinodimethane 360 FOs of 184, 360 nucleophilic addition to 184 Dimethylketene 342, 343 Dimethylsuccinic anhydride 192 2,4-Dinitrohalobenzenes 180, 185, 186 Diosphenol 84 1,3-Dioxans 88, 123, 231, 232 Dioxetanes 437 1,4-Diphenylbutadiene 311 Diphenylketenes 342, 343, 344, 358 Di-p-methane rearrangements 428–430 1,3-Dipolar cycloadditions 322–338 azomethine imines þ alkenes 332, 333 þ alkynes 332 azomethine ylid þ dimethyl maleate 337 þ methyl acrylate 336 þ methyl crotonate 336 benzonitrile oxide þ 6,6-dimethylfulvene 360 defined 260 diastereoselectivity of 246 diazomethane þ benzylidene aniline 336 þ butadiene carboxylic ester 338 þ 6,6-dimethylfulvene 361 þ ethyl vinyl ether 328 þ methyl acrylate 326, 327 þ 1-phenylbutadiene 338 þ styrene 328 ethyl diazoacetate þ enamine 328 nitrile oxides þ alkenes 334 nitrones þ dihydrofuran 337 þ alkenes 335 as nucleophilic attack on alkenes 152 ozone þ isobutylene 336

490 1,3-Dipolar cycloadditions (continued) phenyl azide þ methyl acrylate 331 þ methyl methacrylate 331 as [4s þ 2s] reactions 272 rates of 323, 324 regioselectivity 324–336 relative rates of retro 265, 333, 336 site selectivity of 338 stereoselectivity of 336–337 sydnones þ alkenes 333 see also 1,3-Dipoles Dipolarophiles, defined 323 Dipole inducing a dipole 123 1,3-Dipoles FOs 325 azomethine imines 332 diazoalkanes 327 nitrile oxides 334 nitrones 335 phenyl azide 329, 330 HO and LU control, defined 327 parent members of illustrated and named 323 substituent effects on FOs of 324, 328 Diradicals 101 1,3 426, 428, 429 1,4 411, 415, 416, 417, 433 as alternative mechanism to concerted 256 in cycloadditions of singlet oxygen 285 1,8-dehydronaphthalene 400 in Diels-Alder reactions 322 in di--methane rearrangements 428, 429 as intermediates in cycloadditions 280, 286 in photochemistry 414 possibility in carbene cycloadditions 284 representation of trimethylenemethane 338 singlet and triplet compared 432 in square cyclobutadiene 40 in stepwise cycloadditions 279 theory to explain Diels-Alder regioselectivity 307 triplet 400 Disrotatory, defined 263 Dissociation energy, D0 133 Disulfides as  nucleophiles 156 Di-p-methane rearrangements 428–430 DNA, p-stack in 124 Doering, W. von E. 349 p-Donors, defined 70 -Donors, defined 70 d-orbitals, energy too high for conjugation 80, 121

INDEX Double bonds electrophilic attack on, SET in 146 nucleophilic attack on, SET in 146 photocycloaddition to cumulated 420–421 rotation about 101, 102, 109, 110 see also Alkenes; Carbonyl groups; Imines; Ketones Dougherty, R. C. 152 Dummy atoms 25, 36 Duroquinone 125 E2 reactions, see Elimination reactions Eclipsed versus staggered conformations 211 Eclipsing 99 Edge-to-face coordination 125 Edwards, J. O. 149, 151 -Effect, see Nucleophiles,  Elbs persulfate oxidation 392 Electrocyclic reactions allyl-cyclopropyl anion 262 allyl-cyclopropyl cation 262, 265, 366, 367 allyl radical-cyclopropyl radical 400 in [12]- and [16]-annulenes 39 2-azabutadiene- -lactam 343, 344 2-azahexatriene-dihydropyridone 344 azomethine ylid-aziridine 275, 410 butadiene-cyclobutene 254, 262, 264, 274, 287, 354, 362, 363, 364, 410 defined 254 4-electron processes disrotatory 410 6-electron processes conrotatory 410 heptatrienyl-cycloheptadienyl anion 262, 356 heptatrienyl-cycloheptadienyl cation 262 hexatrienes-cyclohexadienes 254, 262, 264, 274, 365, 366, 410 in homoaromaticity 43 in Nazarov reaction 365 octatetraene-cyclooctatriene 262, 356 oxyallyl-allene oxide 340 oxyallyl-cyclopropanone 340, 368 pentadienyl-cyclopentenyl anion 262 pentadienyl-cyclopentenyl cation 262, 266, 365, 368, 410 periselectivity in 356 photochemical 410 ring strain affecting direction of 254 ring-opening of cyclopropyl halides 367 substituent effects on 354, 430, 431 thermodynamic control of direction of 254 Woodward-Hoffmann rules for 262–266, 273–275 Electrofugal group carbon dioxide as 212, 213 defined 144 metals 211

INDEX proton as 206, 212 silyl as 244 Electron affinity affecting SET reactions 146 data 130 as measure of LUMO energies 61, 302 as measure of SOMO energy 395 in quantifying hardness 128 Electron cloud 1 Electron correlation 124, 145 Electron density, see Electron population Electron distribution 113–115 affecting aromatic stacking 125 in CH bonds 120, 123, 314 see also Electron population Electron in the box for allyl system 27 for benzene 36 for butadiene 29, 32 for cyclopentadienyl system 41 defined 21 dummy atoms in 21, 25, 36 wave functions derived from 22, 24 Electron population in acrolein 187 defined 1 in Salem-Klopman equation 138 site of influencing SE2 reactions 209 see also Electron distribution Electron transfer from CAN 394 to 1-cyanonaphthalene 393 in chemiluminescence 437, 438 from high-energy orbital to low 54 in photochemistry 434, 394 in redox reactions 85, 391, 395 between radicals 129 in SET reactions 146, 148 Electronegative elements affecting hardness 133 affecting Lewis acidity 130 apical preference of 122 bonding to 50, 93, 95 effect on diasteroselectivity of electrophilic attack 246–250 effect on diasteroselectivity of nucleophilic attack 233, 234 effect on inversion of configuration 117 in Felkin-Anh control 227–228 in hydrogen bonding 118 in hypervalency 121 preference for inside position in electrophilic attack 248

491 Electronegativity Allen’s 49, 50 basis for understanding electron movement 145 Mulliken’s 128 Pauling’s 49 Electronic chemical potential 129 Electronic effects separated from steric effects 250 Electronic energy 5 Electronic excitation close to energy needed for a forbidden reaction 293 Electrons, movement in pairs unlikely 145 Electron-transfer reduction, stereochemical contrast with hydride reduction 396 Electrophiles bridging 218 bridging versus non-bridging 216 hard and soft 141–143, 182–183 importance of LUMO in 142 Electrophilic addition by SET 146 Electrophilic attack on alkenes by bridging electrophiles 218 on cycloalkenes 238–241 on alkenes adjacent to a stereogenic centre 241–250 see also Electrophilic substitution Electrophilic character of some 1,3-dipoles 323 of radicals 369, 380, 417 Electrophilic substitution by addition-elimination 223 aromatic 168–178, 349 aromatic, photochemical 405–406 FOs for 209 of pyridine N-oxide 177 of pyrrole 176–177 SE20 reactions of allenylsilane 245 of allylsilane 244–245 with cyclic transition structures 245 in Nazarov cyclisation 365 SE200 reaction 246 SE2inv defined 209 SE2ret defined 209 stereochemistry of 209–210, 222, 365 of vinylsilanes 224 Electrophilicity 178–199 of acid chlorides 178 of aldehydes 178 of allyl halides 190–191 of ambident 183–199 of amides 178 of anhydrides 191–192 of aromatic electrophiles 183–186

492 Electrophilicity (continued) of arynes 194–197 of epoxides 193 of esters 178 FOs in 178 hard and soft 149, 182–183 of ketones 178 of tetrahedral electrophiles 180–182 of trigonal electrophiles 178–180 of , -unsaturated carbonyl compounds 186–189 Electropositive elements bonding to 56, 93 in Felkin-Anh control 227–228 influence of on stereochemistry of electrophilic attack 243–246 Electrostatic effects in aromatic stacking 125 attraction from 225 as basis of hard behaviour 128 Elimination reactions 210–212 anti versus syn 100, 210, 211 E20 reactions by decarboxylative elimination 212–214 forming acetylenes 211 gas phase reaction 212 MOs for 144, 198 nucleofugal group affecting 198 reverse of addition 218 syn, of selenoxides 256 tau bonds explaining stereochemistry 211 stereospecifically anti 205, 206, 224 transition structure for 212 versus substitution 197, 198 Empirical hardness table of data for acids 133 table of data for bases 134 Empty d orbitals, energy too high for effective conjugation 80, 121 Enamines barriers to rotation in 101–102, 104, 110–111 in cycloadditions 279 in Diels-Alder reactions 279, 305, 312 in 1,3-dipolar cycloadditions 324, 328 in Michael reactions 217 NMR of 114 -MOs of 105 in stepwise cycloadditions 279, 341, 342 Enantiotopic 225 Endo rule in Diels-Alder reactions 311, 319 in photocycloaddition m-to benzene 425 not applicable to 1,3-dipolar cycloadditions 337 Endothermic reaction 136

INDEX Endo-trig etc. reactions, see Baldwin’s rule; Baldwin-Beckwith rule Ene reactions defined 253, 256 Lewis acid effect on 355 metalla-, 245, 256 orbital interactions for 277 -pinene þ methyl acrylate 355 stepwise 286 stereochemistry of 270 transition structure for 271 Enediolate ion 84 Energies affecting strength of orbital interactions 30, 49, 52, 54, 137, 139 of atomic orbitals of elements 51 of barriers to rotation 83 electronic 131 of FOs of dienes and dienophiles 297 lowered by conjugation 31 of MOs in Salem-Klopman equation 138 formula for 3  of acrolein 72  of benzene 36  of butadiene 32  of conjugated systems 33  of cyclopentadienyl system 41  of styrene 71 of -bonds 93 raising and lowering, sign of 4 representation on diagrams 3 X-substituent effect on -MOs of alkenes 75 Z-substituent effect on -MOs of alkenes 73 Energy-raising conjugation 84, 101, 112 Enol ethers conformation of 104, 106 diastereoselectivity of protonation 242, 243 electron distribution in 114 oxidation of 394 Enol radical 389, 390 Enolate ions of acetaldehyde 354 alkylation of 160, 161, 219, 220 canonical structures for 105 -chloro in Favorskii reactions 367 electron distribution in 114 extended, see Dienolates geometry of 230 hard and soft character of 160 -MOs of 78, 105, 160 protonation of 160 regioselectivity of electrophilic attack on 160–161

INDEX soft nucleophile 184 stereochemistry of attack on 239, 242, 243 Entropy effect on reactivity 143 of activation, high and negative in Diels-Alder reactions 256 Epibromonium ion 216, 218, 224 Episulfide from electrocyclic closure 265 Episulfonium ions 158, 217 Epoxidation of alkenes 153, 218 of allylsilanes 243 of cyclohexenes 239 regioselectivity of 348 Epoxides allylic 221 as ambident electrophiles 192 Baldwin’s rules applied to opening of 220 nucleophilic opening of 218, 221, 238 protonated 193 regioselectivity of opening by nucleophiles 193, 194 Equatorial attack 229 Equilibration of Diels-Alder adducts 311 in attack on , -unsaturated ketones 187 Eschenmoser, A. 220 ESR 66–67 of benzyl radical 171, 185 of cyclohexadienyl radical 164 measures inversion of configuration in radicals 117 of nitrogen dioxide 159 of phenoxy radical 391 signal absent in cyclobutadiene 40 Esters conformation of 104, 106 cyclohexyl, conformation of 112 electrophilicity of 178 exchange of 188 Flippin-Lodge angle for 215 hydrolysis of 188 nucleophilic addition to 179 restricted rotation in 104 see also , -Unsaturated esters Ethane hyperconjugation in 85 model for -elimination 144 MOs of 18 NMR coupling in 65 Ethers conformation of 111 Hu¨ckel parameters for calculating MOs of 59 Ethoxide ion as hard nucleophile 188 Ethoxycarbonylcarbene 348, 349

493 Ethoxypropyne 342 Ethyl acetoacetate 161 Ethyl acrylate 188 in 1,3-dipolar cycloadditions 335 nucleophilic attack on see also Methyl acrylate Ethyl cation barrier to rotation in 87 may be only bridged cation 90 MOs of 88 Ethyl chloride, MOs of 197 Ethyl diazoacetate, FOs of 328 Ethyl fluoride, -elimination in 212 Ethyl vinyl ether in Diels-Alder reactions 307 in 1,3-dipolar cycloadditions 328, 334 nucleophilicity of 154 photochemistry of 416, 425, 426 Ethylene bond length in 295 energies of  MOs 25 FOs of substituted 70–78, 297 IP of 66 MOs of 20–22, 33 NMR coupling in 65 photochemistry of 417 -wave functions of 22 reaction with bromine 143 a soft nucleophile 143 tau bonds in 61 wire-mesh representation of MOs 22 Ethyne, see Acetylenes Excimer 402 Exciplex 402, 408 Exo, defining convex face of bicyclic alkenes 240 Exo-anomeric effect 97 Exo lone pair effect, defined 317 Exothermic reactions in allyl anion þ allyl cation 141 in attack on a benzyne 194 bromination of alkenes 127 in Diels Alder reactions 256 early transition structures on reaction coordinate 135, 136 in electrophilic attack on cyclohexadienyl anion 164 from matching hard-with-hard 129, 133 in radical reactions generally 146, 369, 371, 374, 388, 391 in reactions between enolates and electrophiles 242 in SN2 reactions 182, 209 Exo-trig etc. reactions, see Baldwin’s rule; Baldwin-Beckwith rule Extended enolates, see Dienolates

494 Face-to-face coordination 125 Favorskii reactions 368 Felkin, H. 226 Felkin-Anh rule 123 for cyclohexanones 230–231 modified 233 for open-chain aldehydes and ketones 226–229 for radical reactions 388, 395, 396 vinylogous 232–234 see also Anti-Felkin-Anh Filled orbitals interaction with filled orbitals 123 Flippin-Lodge angle 215, 227 Fluoride ion 128, 133, 149 Fluorine atom combining with methyl radical 129 as electronegative substituent 195, 251 Hu¨ckel parameters for calculating MOs of 59 substituent stabilising radicals 378, 379 2-Fluoroacetaldehyde 235 Fluorobenzene, photochemical addition to 405 Fluoromethanol 97 Formaldehyde cycloaddition to ketene 343 1,3-dipolar cycloaddition to acetone oxide 336 in hetero-Diels-Alder reactions 310 IP of 66  MOs of 58 wire-mesh plot of 58 Formamide, IP of 66 Formyl group, as a Z-substituent 70 Fragmentation, photochemical 433 -Framework allyl system 24 benzene 35 butadiene 29 ethylene 21 Frank-Condon principle 62 Friedel-Crafts reactions 176, 224 Frontier electron population 172, 173 Frontier orbitals for acrolein 72, 74, 187, 303, 311, 319 affecting Bu¨rgi-Dunitz angle 215 for alkenes C-substituted 71–72 reacting with electrophiles 216 reacting with radicals 387 X-substituted 75–76, 297, 306, 376 Z-substituted 72–74, 297, 377 for allene 345 for anthracene 383 for arenes 348, 349 for aromatic electrophilic substitution 170 for benzyl system 171

INDEX for butadiene 72, 167, 297, 361 for butadiene-1-carboxylic acid 313 for carbenes 199, 201, 288, 357 caution in application of 138, 139, 143, 144, 203, 336, 346 curly arrows representing 24, 168 for cyclobutene opening 287 for cyclohexadienyl anion 164 for cyclopentadiene 317, 338, 355 for cyclopentadienylidenecycloheptatriene 359 defined 28, 137 degeneracy lifted in monosubstituted benzenes 60, 71, 170, 427 for Diels-Alder reactions of C-, X- and Z-substituted dienes and dienophiles 297 explaining endo rule 313 with inverse electron demand 300 Lewis acid catalysis in 319 of 2-methoxy-3-pheylthiobutadiene in 308 rates 298–302 regioselectivity 303–311 secondary effects 295 stereoselectivity 311–317 Thiele’s ester 322 of tropone with cyclopentadiene 338, 355 of Z-substituted diene with Z-substituted dienophile 304 for 6,6-dimethylfulvene 348, 360, 361 for di--methane rearrangements 430 for 1,3-dipolar cycloadditions of 323–337 azides 325 azomethine imines 325, 332, 333 azomethine ylids 325 carbonyl imines 325 carbonyl oxides 325 carbonyl ylids 325 diazoalkanes 325, 327, 336, 361 hydrazoic acid 329 nitrile imines 325 nitrile oxides 325, 334 nitrile ylids 325 nitrones 325, 335 nitrous oxide 325 ozone 325 phenyl azide 329–331 for ene reactions 355 for enolate ions 160 explaining ortho/para ratios 175 explaining Woodward-Hoffmann rules 287 for hexatriene 320, 358 for hydroboration 288 for indoles 406

INDEX for interaction of allyl cation with allyl anion 140 for isoprene 344 for ketenes 287, 341 large-large versus large-small 303 for maleic anhydrides 192 for methyl chloride 53 for methyllithium 57 for naphthalene 383 for nitrite ion 159 for pericyclic reactions 287–288 for 2-phenylbutadiene 321 for photochemical reactions 402 allene cycloadditions 420 aromatic substitution 406 cross-coupling 412, 414–420 cycloadditions 411–421, 425–427 dimerisations 412–414 ionisations 402, 433, 434 of ketones 435 Paterno-Bu¨chi 411 Woodward-Hoffmann rule 408 for phthalic anhydrides 192 for piperylene 344, 419 for radical attack on arenes 381 for regioselectivity of enone reduction 189 relation to orbital following 293 for SE2 reactions 210 for SN2 reactions 209 for thiophen 383 for trimethylenemethane 339–340 for tropone 309, 310, 355, 360 for , -unsaturated ketones 396 Fukui, K. 171, 172, 174, 225, 301, 374 Fulvene, see 6,6-Dimethylfulvene Fumaric acid 313 Fumaroyl chloride 314 Furan dipole moment of 115 electrophilic substitution of 176 IP of 66 photochemistry of 421, 423 Furylmethyl chloride 191 Gas phase reactions E2 212 nucleophilic attack on a ketone 231  bond attacking a  bond 216 reduction of cyclohexanones 229 SN2 209 Geometrically unreasonable reactions 278 Gilbert, A. 424 Glucosides, configuration of 96 C-Glycoside by radical attack 389

495 Glyoxal, conformation of 84 Grignard reagents 86, 117, 187, 194, 231, 232, 234 Group transfer reactions defined 255 dihydrogen transfer 271 selenoxide eliminations 256 simple rule for 270 Woodward-Hoffmann rules for 270, 277 see also Ene reactions H2 molecule, see Hydrogen molecule H3 molecule 7–9 H4 ‘molecule’, 9–10, 12 Halides HOMOs of anions 151 nucleophilicity of anions 150 relative electrophilicity of alkyl and aryl 179 Halogens abstraction by radicals 371, 399, 400 as bridging electrophiles 217 as X-substituents 70, 173 stereochemistry of addition of to alkenes 218 Halogenobenzenes, electrophilic substitution in 173 Halogenonitrobenzenes, nucleophilic substitution of 185 -Haloketones conformation of 227 photochemical reaction of 433 SN2 reaction of 181 Hammett plots 81, 181, 328, 373, 377 Hammond postulate 136 Hantsch ester 184 Hard and soft acids and bases, see HSAB defined 128 hard and soft electrophiles 141–143, 182–183 hard and soft nucleophiles 141–143, 149–161 hard-hard interactions in Salem-Klopman equation 142 HC Bonds, see CH bonds He2 ‘molecule’, high energy of 5 Head-to-head, defined 412 Heat of combustion 69 Heat of hydrogenation 69, 91 Helium 5, 124 Hepta-1,3,5-triene 321 Heptafulvalene 359 cycloaddition to tetracyanoethylene 261, 273 cycloaddition to dichlorocarbene 347 Heptafulvene, dichlorocarbene reaction on 347 Heptatriene 321 Heptatrienyl anion 262 Heptatrienyl cation 262

496 Hetero Diels-Alder reactions 279, 310–311 acrolein dimerisation 310 1-acetoxybutadiene þ nitrosobenzene 310 defined 310 1,3-dimethylbutadiene þ formaldehyde 310 isoprene þ thienium ion 310 of ketenes þ dienes 358 1-methoxycarbonylbutadiene þ nitrosobenzene 310 of nitroso compounds 285 1-phenylbutadiene þ nitrosobenzene 310 stepwise 279 of triazoline diones 285 Heteroatom electrophiles, bridging in attack on alkenes 217 Heteroatoms, parameters for in Hu¨ckel calculations 59 Heterocyclic aromatic rings, see Furan; Pyrrole; Thiophen; Pyridine; Indole Heteronuclear bonds to carbon 49–60 Hex-5-enyl radicals 379 Hexa-2,4-diene 409 Hexafluorobenzene stacks with benzene 125 Hexaphenyldisiloxane 80 Hexatrienes conjugation compared with benzene 36 dimerisation of 320, 358 electrocyclic ring closure of 254, 262, 263, 274, 365, 410 FOs of 313, 358  MOs of 33 Highest adjacent pair, defined 348 Hoffmann, R. 258, 271, 317 HOMO cyclohexadienyl anion 164–165 defined 28 degeneracy lifted in monosubstituted benzenes 60, 71, 170, 427 electron leaves from in photoexcitation 401 energy as negative of IP energy correlates with rate of electrophilic attack on alkenes 154 energy lowered by conjugation with CX bond 246 energy raised by conjugation with SiC 244 ESR can measure coefficients of 67 estimation of for C-substituted allyl anion 164 estimation of for X-substituted allyl anion 162 estimation of for Z-substituted allyl anion 166 FO for nucleophiles 140, 142 high energy of in singlet oxygen 285 interaction with ‘HOMO’ important in photochemistry 403 interaction with LUMO as major effect 137 interaction with LUMO in Salem-Klopman equation 139

INDEX measured by IPs 66, 129 of pyrrole 176 repelled by LUMO in Jahn Teller distortion 41 see also Alkenes; Frontier orbitals ‘HOMO’ defined 401, 403 qualifications of true meaning 403 Homoantiaromaticity 43, 44 Homoaromaticity 42–44 Homocycloheptatrienyl cation 42 Homocyclopropenyl cation 42 Houk rule 241–250 see also Inside Houk, K. N. 70, 231, 241, 242, 298, 313, 324, 326, 328, 363, 366, 417, 424, 431 HSAB 128–134 absolute hardness 128, 129 applied to o/2p ratios 175 defined 127, 128 tables of data 131–134 HSn bonds BDE 384 radical attack on 374 Hu¨ckel calculations acrolein 72, 187 allyl system 105 cyclohexadienyl anion 164, 165 dimethylsuccinic anhydride 192 enamines 105 enolate ions 105 intermediates in aromatic electrophilic substitution 168 maleic anhydrides 192 of barriers to rotation 109 parameters for heteroatoms in 59 phthalic anhydrides 192 styrene 71 of transition structures for Diels-Alder reactions 257 for X-substituted alkene 76 Hu¨ckel theory 7, 21, 23–34, 61, 62, 173, 350, 372 Hudson, R. F. 155 Hybrid orbitals component for the Woodward-Hoffmann rule 273–278, 287 creation of hybrid orbitals 16, 225, 226 effect on electronegativity of C 49, 50 illustrated 16, 17 in methyl chloride 53 misleading in energy of LUMO 182 used in anomeric effect 97–100 used in correlation diagrams 290–291 used in hyperconjugation 86, 92, 93, 95, 241

INDEX Hybridisation 15–18, 92, 95, 100, 226 Hydrazine 84, 155 Hydrazones 117 1,2-Hydride shifts in a cation 90, 432 Hydroboration of allenes 345 of allyl alcohols 249, 250 of allylsilanes 243 of cyclonona-1,2-diene 346 as electrophilic probe 251 FOs for 288 orbital interactions for 283 stereospecificity of 218, 284, 288 Hydrocyanic acid 203 Hydrogen atom 1,2-shifts in a cation 90, 432 1,5-shifts in a diene 266, 267, 318, 321, 322, 352 1,5-shifts in a radical 390 1,7-shifts in photochemistry 431, 432 1,7-shifts thermally 255, 267 abstraction by radicals 371, 372, 373, 375, 376 abstraction from thiols 388 abstraction in photochemistry 433, 435, 436, 437 abstraction of versus addition to C¼C 374 orbitals of 1–2 sigmatropic migration exceptionally easy 352 Hydrogen bonding 118–121 CH . . . O 119 CH . . . , 120, 121 CH . . . X 119 in intramolecular delivery of electrophiles 246 like transition structure for H atom transfer 390 MOs of 118 NH . . . , 120 OH . . . , 120 XH. . .  120 XH . . . X 118 Hydrogen bromide, anti-Markovnikov addition to alkenes 375 Hydrogen chloride addition to an alkene 216 IP of 66 Hydrogen molecule 2–7 combining two to make H4 9 MOs and coefficients of 7 overlap integral for 4 Hydrogen peroxide conformation of 84 nucleophilic cleavage of 151 Hydrogen selenide as trap for radicals 416 1,5-Hydrogen shifts 266, 267, 318, 321, 322, 352 Hydrogen sulfide IP of 66

497 Hydrogen transfer from 1,4-cyclohexadiene 271 from 9,10-dihydronaphthalene 271 from diimide 256

, in radicals 390 Hydrometallation 218, 283 Hydroperoxide ion as  nucleophile 155 Hydroquinone anion of 85 by Elbs oxidation 392 Hydroxide ion as hard base 128 as hard nucleophile 142, 143, 184, 188 Hydroxylamine as  nucleophile 156 Hyperconjugation 85–95 affecting radical energy 374 with alkyl group 70, 76, 80, 90, 134 in alkyl halides 181 CH versus CC 86, 106, 192, 230 Cmetal 92, 93, 218, 224 Csilyl group 94 defined 85 effect of on bond angles 90 effect of on bond length in cations 89 effect of on cyclohexadienyl anion 164 negative 95–96 affecting regioselectivity of radical attack 379 anomeric effect as a special case of 96 anti versus syn 100 defined 96 lowering LUMO energy of dichloroketene 341 polarising 3,4-pyridiyne 196 stabilising intermediate of aromatic nucleophilic substitution 180 XC with anion 93, 223 no change in shape in 89 serious misnomer 85 stabilising alkenes 91 stabilising intermediate in electrophilic substitution 224 versus bridging 90–92, 216 Hypervalency 121–122 Imines configuration of 116, 117 cycloaddition to ketenes 343, 344 Hu¨ckel parameters for calculating MOs of MOs of 117 nucleophilic attack on 180, 189 Iminium ions charge distribution in 113 as highly stabilised carbocations 113

59

498 Iminium ions (continued) nucleophilic attack on 231, 232 photochemistry of , -unsaturated 418, 419 polarisation of 113 Indole FOs of 174 LUMO of 406 site of electrophilic attack 174 Initiation of radical chain reactions 384 Inside alkoxy effect 248, 249 defined 226 methyl effect 232, 233, 241, 242, 243, 244 oxygen effect 247, 248 Interactions, see Orbital interactions; Orbital overlap Intermediates absence of in pericyclic reactions 256 biradical-like in some Cope rearrangements 352 in hetero-Diels-Alder reactions 285 in photochemical side-chain ionisation 407 in stepwise cycloadditions 279, 280 tetrahedral in aromatic nucleophilic substitution 179 tetrahedral in nucleophilic susbtitution at C¼O 178 vinyl cations in cycloadditions 283 zwitterionic 342 Internuclear distance effect on overlap 4 Intersystem crossing 401, 402, 413, 414, 416, 417, 428 Inverse electron demand, see Diels-Alder reactions Inversion of configuration in bromodesilylation of vinylsilanes 224 in opening of epibromonium ion 224 in opening of episulfonium ion 158 in radicals 117 in SE2 reactions 209, 210 in sigmatropic rearrangements 268 in SN2 reactions 207, 209, 211, 236 Iodide ion 128, 133 Iodine atom 129 Ionic bonding 53 Ionic reactions photochemical 403–408 thermal 145–203 Ionisation potential (IP) affecting SET reactions 146 as measure of FO energies 61, 302, 373, 393 correlates with radical reactivity 381 data 66, 130 in quantifying hardness 128 IR spectroscopy bending in acetylenes 222 detecting hydrogen bonding 119 Ireland-Claisen rearrangements 269, 349 Isoborneol 205

INDEX Isobutylene 154, 336, 416, 411, 426 Isobutyronitrile radical 384 Isomerisation cis-trans, see Rotation Isonitriles 158 Isoprene cycloaddition to carbenoids 347 cycloaddition to diphenylketene 344 in Diels-Alder reactions 299, 318, 321 FOs of 344 in hetero Diels-Alder reactions 310 in Simmons-Smith reaction 347 Isopropanol in photochemical reaction 436, 437 Isoquinoline 174 Isothiocyanates 158 Jahn-Teller distortion

34, 41, 42, 116, 159

Katz, T. J. 316 Ketenes C¼C raised HOMO energy in 341 C¼C raised LUMO energy in 358 cycloadditions to alkenes 281–282, 340–342, 344 to dienes 358 to formaldehyde 343 to imines 343–344 to pyridinium-3-oxide 345 to diazoalkane 265 dimerisation of 343 FOs for 282, 287, 341, 358 photochemical 421 FOs for 287, 341, 358 two sets of  orbitals at right angles 282 Ketones as highly stabilised carbocations 89, 113 conformation of 226 electrophilicity of 178 hydride reduction of 388 in Paterno-Bu¨chi reactions 411 nucleophilic addition to 179 nucleophilic attack on 214, 215, 217, 226, 227, 228 polarisation of 113 pyramidalisation in 235 radical anion from 396, 438 reduction of 205, 229, 230, 231, 234, 235, 250, 251, 396 Ketyl radical 437 Kinetics stability defined 69 thermodynamics affecting 135 versus thermodynamics 127, 170, 186, 188, 190, 315 Kishi, Y. 241 Klopman, G. 128, 138, 144, 150, 152, 177

INDEX Konovalov, A. I. 302 Koopman’s theorem 129 Kornblum reaction 147, 399 K-region 348, 349 -Lactams from cycloaddition of imines to ketenes 343, 344 -Lactones 343 Lead tetraacetate 349, 400 Leaving group, see Nucleofugal group Lewis acids affecting Felkin-Anh transition structure 227 and bases 128 catalysis by for Diels-Alder reactions 318, 319 for ene reactions 355 for epoxide opening 193 for SE2 reactions 210, 217 chelating reagents 246 effect of ligands on acidity of 130 effect of substituents on 76 effect on FOs 319 effect on regioselectivity in unsaturated ketones 187 hard and soft in Diels-Alder reactions 318 Light, emission of 437 Lignification 392 Linear combination of atomic orbitals allyl system 24 butadiene 29 CH2 14 hydrogen 2 Lithium, as representative electropositive element 56 Lithium aluminium hydride reduction in pyridine 189 of camphor 205 of cyclohexanones 229 of 3,5-dioxanone 231 of an epoxide 193 of cyclic anhydrides 191, 192 of 2-phenylbutan-3-one 396 of unsaturated ketones 187 Lithium in liquid ammonia 396 Lithium reagents configurationally stable 117 not monomeric 210 often called anions. 56, 86 SE2 reactions of 210 Localisation energy 167, 381 Loganin, synthesis of 240 Lone pair of electrons anti to incoming nucleophile 232 contribution to bridging 217 as HOMO 60

499 involved in anomeric effect 96–100 isoelectronic with carbanion 80, 96, 262 in n!* transitions 94, 401, 403, 411, 420, 433, 435 as -donors 70, 75–76 Longer conjugated systems 32, 34 Long-range coupling 65 LUMO of acrolein 187, 310, 311, 319 of alkyl halides 183, 198 of aromatic electrophiles 184 of benzyne 194 coefficients correlate with electrophilicity 189 defined 28 degeneracy lifted in monosubstituted benzenes 60, 427 electron promoted to in photoexcitation 401 energy lowered by conjugation with CCl 341 energy of as negative of EA 129 ESR measures coefficients 67 high energy of C¼C in ketenes 358 important in electrophiles 140, 142 interaction with ‘LUMO’ important in photochemistry 403 interaction with HOMO as major effect 137 low energy of C¼O in ketenes 358 low energy of in Chalogen bond 182 low energy of in singlet oxygen 285 lowered energy by conjugation with CX 228, 235 of pyridinium cation 184 of pyridyne 195 of unsymmetrical allyl cations 191 ‘LUMO’ defined 401, 403 Maleic anhydride Diels-Alder reaction of 311, 320, 321 no [2 þ 2] with ethylene 258 photochemistry of 421 substituted 191, 192 Malonate ion 188 Manganese(III) 393 Mayr, H. 153 McConnell equation 66, 164, 391 Medium-sized rings, diastereoselectivity in 239 Meerwein-Ponndorf reduction 189 5-Membered rings, stereochemistry of attack on 239, 250 Mercuric ion 148, 178, 216 Merostabilised radicals, defined 82 Mesityl oxide, conformation of 109 Mesitylene 148 ‘Meta’ adduct from X-substituted diene with X-substituted dienophile 306 Metal-carbon bonds, see CM bonds

500 Metalla-ene reactions 245, 256 Metallo-metallation 283 Metals as electrofugal groups 211 Metathesis of alkenes 283 Methacrolein 314 Methacrylonitrile 384, 385 Methanal, see Formaldehyde Methane MOs of 12–13, 17 NMR coupling in 65 wire mesh drawings of MOs 13 Methanol in photochemical reaction 435 Methoxide ion as hard nucleophile 186 1-Methoxybutadiene FOs of 167, 303 in cycloaddition to diphenylketene 358 in Diels-Alder reactions 299, 303, 304  electron population of 167 2-Methoxybutadiene 299, 305 Methoxychlorocarbene cycloaddition to 6,6-dimethylfulvene 348 Methoxymethyl chloride 97 2-Methoxypropene 154 1-Methoxy-3-trimethylsilyloxybutadiene 301 Methyl acrylate 2-chloro 271, 277 conformation of 109 cycloaddition to chloromethoxcarbene 203 Diels-Alder dienes 308, 318 1,3-dipoles 324, 326, 327, 331, 334, 336 an enamine 279 a trimethylenemethane 339 in ene reaction 355 nucleophilic attack on 188 photochemistry of 414, 415 reduction of 395 see also Ethyl acrylate Methyl arenesulfonate, substrate for  nucleophile Methyl cation 133 Methyl chloride MOs of 52–53 wire-mesh diagram 54 Methyl cinnamate 418 Methyl crotonate in 1,3-dipolar cycloadditions 335, 336 photochemistry of 418 radical attack on 378 Methyl ethyl ketone 376 Methyl fluoride 98, 129 Methyl group hyperconjugation to 70, 134 inside 123, 226, 232, 233, 241, 242, 243, 244

INDEX

155

MOs of 88, 198 as X-substituent 70, 365 Methyl iodide 129, 149, 157, 163 Methyl methacrylate in 1,3-dipolar cycloadditions 331 polymerisation of 370 radical attack on 370 Methyl p-nitrobenzoate 155 Methyl propiolate 333 Methyl radicals 117, 129, 372, 377, 378, 379, 384 Methyl senecioate 334 Methyl triflate 157 Methyl vinyl ether 75 Methyl vinyl ketone conformation of 109 conjugate addition to 186 hetero-Diels-Alder reaction 279 reductive coupling of 395 Methylallene, see Buta-1,2-diene Methylamine 404 Methylation of enolate ions 239, 242 9-Methyl-9-BBN 78 2-Methyl-2-butene 91 2-Methylbutadiene, see Isoprene 1-Methylbutadiene, see Piperylene Methylene 13–15, 199 Methylketene, cycloaddition to cyclopentadiene 342 Methyllithium MOs of 56–57 wire-mesh diagram of 57 2-Methylmaleic anhydride in Diels-Alder reactions 309 reduction of 191 2-Methylnaphthalene 393 2-Methylpropene, see Isobutylene Metol anion 85 Michael reactions 186, 188, 189, 217, 239 Migratory aptitude of alkyl groups 353 of hydrogen high 352 of phenyl and vinyl groups 353 Minisci reaction 382 Mislow rearrangement 255, 270 Mixing of orbitals in hybridisation 15, 16, 52, 55, 85 Mo¨bius transition structures 354, 363 Molecular orbitals acrolein 72, 187, 303, 311, 319 allyl anion 105 allyl system 23–29 antibonding defined 3 benzene 35–37 bonding defined 3 butadiene 29–32

INDEX formaldehyde 58 by combining one  bond with another 291 cyclobutadiene 38 cyclopropane 47 enamines 105 energy of in Salem-Klopman equation 138 enol ethers 75 enolate ion 105 ethane 18–20 ethylene 20–22 explaining ortho/para ratios 174 explaining regioselectivity in aromatic electrophilic substitution 168 from a pair of interacting  orbitals 291 H3 8 H4 9 hydrogen 3 illustrations of 6, 13, 22, 28, 32, 54, 57, 58 in inversion of configuration 116 in substitution versus elimination 198 methane 13 methyl chloride 52–54 methylene 14, 199 methyllithium 56–57 nitrite ion 159 nitronium ion 159 spiroheptatriene 45  of Wheland intermediates 169 pyridine 60 pyridinium ion 60 pyrrole 60  and * 3 styrene 71 trimethylenemethane 338 see also Frontier orbitals Molecular recognition 115 Monomorine-I 232 Monosubstituted benzenes, FOs of 60, 71, 170, 172, 427 Monosubstituted butadiene, FOs of 167, 297 Morse plot 5 n!p* transitions 94, 401, 403, 411, 420, 433, 435 N,N,N0 ,N0 -tetramethyl-1,4-diaminobenzene 125 N¼N double bonds 300 Naphthalene electrophilic attack on 174 FOs of 174 LUMO of 184 nucleophilic addition to 184 -stacking 125 product of dihydrogen transfer 271 radical anion 67, 399 radical attack on 383

501 radical cation 67 reduction of 398 Nazarov reaction 364, 365, 368 N-bromosuccinimide, see NBS Negative hyperconjugation, see Hyperconjugation, negative Neopentyl system, SN2 reactions of 220 Newman, M. S. 97 Newman projection 97, 217, 223, 224, 226, 230, 235, 246 NH bond, dipole moment of 115 N-Hydroxyamide group, p-overlap in 156 Nitration, sites of in aromatic molecules 174 Nitrile imines 323, 325 Nitrile oxides defined 323 1,3-dipolar cycloadditions of 242, 248, 334 FOs for 325, 334 Nitrile ylids 323, 325 Nitriles 158 Nitrite ion 157, 159 Nitrites 158 Nitro group, as a Z-substituent 70 Nitroalkanes 158 Nitroalkenes 110 Nitrobenzene frontier electron population of 172 photochemistry of in TFAD 405 radical anion 67 radical attack on 381, 382 p-Nitrobenzyl chloride 147 Nitroenamine 110 Nitronate ions 147, 399 Nitrones defined 323 FOs of 325, 335 in 1,3-dipolar cycloadditions 335, 337 Nitronium cation as ambident electrophile 159 as hard electrophile 178 MOs of 159 Nitrophenate anion, m-, stabilised in excited state 407 Nitrophenyl phosphates, photochemical hydrolysis of 406 Nitroso compounds 285, 286, 310 Nitrous oxide 323, 325 NMR spectroscopy 62–65 of benzyl cations 230 13 C coupling constants 65 13 C-chemical shifts as probe of electron population 166 1 H chemical shift 114 1 H coupling constants 64, 65 1 H detecting hydrogen bonding 119, 120

502 NMR spectroscopy (continued) 1 H W-coupling 65 coalescence of signals 110 detecting rotamers 102, 110 stereochemistry of reaction followed by 265, 366 time scale of 110, 268 Non-bridging electrophiles 216 Non-classical ion 90 Non-covalent interactions 115–121 Non-linear approach for carbene cycloadditions 284, 288, 357 Norbornane system electrophilic attack on norbornenes 241 in steric versus electronic control 250 NMR coupling in 65 norbornanones 250 norbornyllithium 210 sigmatropic rearrangements in 268, 316 Normalisation in calculation of coefficients 7 of diastereoisomer ratios 205 Nuclear repulsion, effect on energy 5 Nucleofugal group affecting C- versus O-alkylation 160, 161 affecting substitution versus elimination 197, 198 anti to lone pairs 231 anti to silyl group 113 defined 144 Nucleophiles , 117, 155–157 carbenes as 199–200 1,3-dipoles as 323 hard and soft 141–143, 149–161 importance of HOMO in 142 nucleophilicity of 149–157 calculated for inorganic ions 151 hard and soft 149, 183 of anions towards benzyne 196 relative, of alkenes 154 two parameters in scale of 149 radicals as 369–371, 417 Nucleophilic attack on carbonyl groups 179, 214–215, 229–234 on cycloalkenes 238–239 conjugate versus direct 186, 188 on iminium ions 232 on open-chain alkenes 232–238 on pyridinium ions 184 SET in 146 see aslo Nucleophilic substitution Nucleophilic substitution on allyl halides 181, 190, 236 aromatic 185–186, 403–405

INDEX at silicon 207, 208 by addition-elimination 223 of halogenonitrobenzenes 185 SET in 146 SN1 191 at trigonal carbon rare 222 substituent effects on 181 SN10 190, 191 SN100 191 SN2 207–209 of allyl chlorides 181, 190 in aromatic side chain reactions 181, 406 donor substituents may accelerate 181 exothermic 182 FOs in 208 gas phase 152, 209 merging with addition elimination pathway 223 nucleofugal groups in 183 nucleophilicities in 151 rare at trigonal carbon 222 SET in 146 at silicon 207, 208 as soft-soft reaction 149 stereochemistry of 207–209 structure affecting electrophilicity in 180 transition structure 121, 209, 220 versus elimination 197, 198 SN20 reactions avoided 190, 236 defined 190 stereochemistry of 235–238 SN20 238 SRN1 147, 399, 400 at trigonal carbon 223 n-p* transitions 94, 401, 403, 411, 420, 433, 435 Octalones 396 Octatetraene 262 n-Octyl chloride 183 Offset in p-stacking 124 o, identifies p orbitals in Woodward-Hoffmann rules 274 O¼O, low energy of LUMO 300 Oppolzer, W. 387 O-Protonation of enolate ions 160 Orbital correlation diagrams for [2 þ 2]-cycloaddition 291 for [2 þ 4]-cycloaddition 290 for o-cycloaddition to benzene 422 for m-cycloaddition to benzene 423 Orbital following for Diels-Alder reactions 293, 294 in photochemical reactions 409

INDEX Orbital interactions affecting torquoselectivity in cyclobutene ring opening 363, 364 as basis for soft behaviour 128 for C with H2 14 for C with H4 12 for cheletropic reactions 284 for cycloadditions 261 [2 þ 2] 278, 279 [2 þ 4] 272 [2 þ 14] 273 [4 þ 4] 279 allenes þ alkenes 282 carbenes þ dienes 357 ketenes þ alkenes 282, 341 tropone þ cyclopentadiene 355 for dihydrogen transfer 277 for diimide reduction 277 for dimerisation of allenes 347 effect of energy separation on 30, 49, 52, 54, 137, 139, 419 for electrocyclic reactions 263 ring closure of azomethine ylids 275 ring closure of butadienes 274 ring closure of hexatrienes 274 ring opening of aziridines 275 ring opening of cyclobutenes 274 ring opening of cyclohexadienes 274 for ene reactions 277 filled with filled 137, 139, 225 filled with unfilled 139, 199 for hydroboration 283 for sigmatropic rearrangements 266, 268 [1,3] 278 [1,5] 275 [1,7] 275 [2,3] 276 [3,3] 276 for photochemical reactions 401, 402, 419 m-cycloaddition to benzene 425 o-cycloaddition to-benzene 425 hydrogen atom abstractions 435 large in radical reactions 370 large-large versus large-small 303 non-linear 45, 46 weak 115 see also Orbital overlap; Secondary orbital interactions Orbital overlap affecting coupling constants 63 antarafacial 273, 275 anti versus syn 98 CH with CC 86 CH with CH 86

503 CH with CO 88 CH with lone pair 86 CCl with C¼O 229, 341 CLi with S,P,SiC 79 C¼O with C¼O 84 CSi with C¼O 227 CSi with lone pair 95 curly arrows illustrating 113, 114 energy raising 84, 101 p with C¼O 77 p with CH bond 87 p with CLi 78 p with CS,P,Si 79 p with CX 95 p with d 80 p with  26, 27, 39, 40, 77, 81, 82, 84, 88, 89, 110, 111, 216 p with p 20, 21, 31, 37, 45, 52, 58, 93 p with p, long range 107 p with s 17, 56, 226 p with sp3 93, 95  with CX 181 - 124  with sp3 hybrid 92 s with s 3, 4, 8, 9 secondary in Diels-Alder reactions 312, 313 sideways on 45  with  251, 291 sp3 with sp3 84 suprafacial 273, 275 syncoplanar 98 transannular in homoaromaticity 42 see also Orbital interactions Orbitals, see Atomic orbitals; Frontier orbitals; Molecular orbitals Organic synthesis, radicals in 384–386 Organocuprates, see Cuprates Organolithium reagents, see Lithium reagents; Methyllithium Organometallic reagents often called anions 56, 78, 79, 86, 96 substrate for SE2 reaction 209 see also Carbanions; Grignard reagents; Lithium reagents; Methyllithium Ortho esters, ionisation of 232 Orthogonal orbitals in carbenes 199–202, 284, 288 in cycloadditions to ketenes and allenes 282, 421 in hydroboration 283 in nitrite ion 159 preventing NMR coupling 65 in pyramidal inversions 116 removing anomeric effect 99

504

INDEX

Orthogonal orbitals (continued) in selection rules 61 in sigmatropic boron shifts 353 in transition structure for rotation about  bond 101, 102 Ortho/para ratios 174 ‘Ortho-para’ rule in Diels-Alder reactions 306 Orthoquinodimethanes 307, 354 Osmium tetroxide 240, 244, 247, 248, 249, 348, 349 Overlap integral S angular dependence of 12 C with N, O and F 54, 159 for C¼C as function of distance 40 defined 3 of p with p 11, 19 of s with p 11 of s with s 4 in Salem-Klopman equation 138 of second-row elements 79 of 1sH with 2sC 10 Oxazaborolidine 120 Oxetanes 411 Oxidation, by electron transfer 437, 438 Oximes 117 Oxocarbenium ions 231, 232 Oxy radicals, hydrogen abstraction by 390 Oxyallyl cation cycloaddition to cyclopentadiene 340 dimerisation of 340 in electrocyclic ring closure 368 Oxyanion substituents accelerating Cope rearrangements 350 accelerating electrocyclic reactions 354 Oxy-Cope rearrangements 350 -Oxygen effects in radical reactions 389 Oxygen inside 247, 248 Oxymetallation 218 Ozone 1,3-dipolar cycloaddition to isobutylene 336 formation of ozonide as a 1,3-dipolar cycloaddition 336 FOs of 325 site of attack in arenes 349 P(V) compounds configuration 122 Paquette, L. A. 429 Paterno-Bu¨chi reaction 411, 412 Pearson, R. G. 127, 128, 133, 150 Peierls distortion 34 Pent-3-ene-2-one 94 1,3-Pentadiene, see Piperylene 2,3-Pentadiene, cycloaddition to acrylonitrile Pentadienal 363

345

Pentadienyl anions electrocyclic ring closure of 262, 266 HOMO of 164  MOs of 33 regioselectivity of electrophilic attack on 163, 164, 166 see also Cyclohexadienyl anions Pentadienyl cations cycloaddition to an alkene 259 electrocyclic ring closure of 262, 265, 266  MOs of 33, 313 in Nazarov reactions 364, 365, 368 Pentalene 39 Peracids, bridging electrophiles 217 Perchlorate as  nucleophile 156 Perezone-pipitzol transformation 259 Pericyclic reactions 253–368 classes of 254–256 defined 253 of radical cations 394 photochemical 408–414 Periodic table 50 Periselectivity 355–362 Perlin effect 85, 88 Peroxide effect 375 Perturbation theory 135, 136–138, 152, 288 PES 65, 330 PET 394 Phenalene 114 Phenanthrene 174, 398 Phenols, H-bonding in 120 Phenoxide ion 186 Phenoxy radicals coefficients 391 coupling 392 ESR measurements 67 in photo-Fries reaction 434 Phenyl anion 194 Phenyl azide 323, 324, 329, 330, 331 Phenyl benzoate, photochemistry of 434 Phenyl cation, high energy of 194 Phenyl as a C-substituent 70 radical 384, 391 1,2-shift of in cations 353 Phenyl vinyl ether 413 Phenylacetylene 1,3-dipolar cycloaddition to azomethine imines 332 1,3-dipolar cycloaddition to phenyl azide 330 UV spectrum of 330 1-Phenylbutadiene

INDEX Diels-Alder reactions 305, 306, 308, 309 dipolar cycloaddition to diazomethane 338 2-Phenylbutadiene in Diels-Alder reactions 305, 306 dimerisation of 321 1-Phenylcyclopentene 393 N-Phenylmaleimide 249 Phenylthioxide ion as soft nucleophile 186, 188, 190 opening an epoxide 193 N-Phenyltriazolinedione 286 Phosphines configuration 116 IP of 66 MOs of 117 Phosphorus anion stabilisation by 79, 96 Hu¨ckel parameters for calculating -MOs of 59 hypervalent bonding in 122 orbital interactions with 79 radical 118 Photochemical excitation creating radicals 432 effect on orbital occupancy 401 lowering energy of rotation about a double bond 102 Photochemical reactions 401–438 aromatic nucleophilic addition 404 aromatic nucleophilic substitution 404 cycloadditions [2 þ 2] 409, 411–421 [2 þ 8] 420 [4 þ 4] 409, 414, 421 [6 þ 6] 409 to aromatic rings 421–428 regioselectivity of 411–427 dimerisation in solid state 413 electrocyclic 410 energy change in 409 FOs in 415, 434 general pathways 401 hydrolysis of nitrophenyl phosphates 406 of alkyl halides 433 with n!* transitions 94, 401, 403, 411, 420, 433, 435 often complementary to thermal reactions 403, 420 side-chain ionisation 407, 408 sigmatropic rearrangements 410 see also Di--methane rearrangements; Paterno-Bu¨chi reaction; Photo-Fries rearrangement Photoelectron spectroscopy, see PES Photo-Fries rearrangement 434 Photoinduced electron transfer, see PET Physical methods supporting MO theory 61–67

505 p-acceptors defined 70 p-stacking 124 p-p* transition defined 401 Pinacol reaction 395, 435, 436 Pinacolone enolate ion 147 -Pinene 355 Piperidine, photochemical addition to benzene 404 Piperylene cycloaddition to diphenylketene 344 from electrocyclic ring opening 362 in Diels-Alder reactions 299, 313, 308, 318 FOs of 344, 419 Pivalaldehyde 163, 215 pKa as measure of hardness 151 Planes, xy, xz and yz, defined 8 Planes of symmetry in [2 þ 2]-cycloaddition 290 in [2 þ 4]-cycloaddition 289 in m-cycloaddition to benzene 423 in o-cycloaddition to benzene 422 of s and p orbitals in setting up CH2 14 of s and p orbitals in setting up CH4 12 of  orbitals in setting up H3 8 of  orbitals in setting up H4 9 Polarisability in HSAB 129 Polarisation in hydrogen bonding 119 of CCl 53 of CH 123, 314 of Chalogen 182 of CM 92 of C¼O 59 of CX 92 Polarity in conjugated systems 113 Polycyclic aromatic molecules electrophilic substitution in 173–174 nucleophilic attack on 184 Polyenes conjugation in 32, 34 UV spectra of 62 Polymerisation 370, 371 Porphyrins, p-stacking in 124 Potassium cyanide 158 Precalciferol 255 Prenyl Grignard reagent 163 Product influencing transition structure 136 Propanal 119, 123, 226, 230 Propanol 123 Propene in 1,3-dipolar cycloadditions 333, 335 nucleophilicity of 154 radical addition to 375, 377 radical attack on allylic hydrogen of 374

506 Propionaldehyde, see Propanal Propynal in Diels-Alder reactions 305 Propyne in Diels-Alder reactions 307 Prostaglandin synthesis 318, 386 Protein folding affected by weak forces 115 Protodesilylation 224 Proton as hard acid 128 as hard electrophile 142, 143, 155 hardness of 133 Protonated acrolein, p-MOs of 187 Protonation C- versus O- of enolate ions 160, 242 of alkenes 143 of anisole radical anion 397 relative rates of 151 Pseudorotation 208 Push-pull alkenes 101, 110 Pyramidalisation 234–238 in acetoxycyclopentadiene 247 in allylsilanes 243 alternating along chain 235, 241, 245, 246 in amines and phosphines 116–117 in bicyclic systems 241 in carbonyl compounds 235 in cyclohexanones 230 in cyclohexenes 239 in explaining diastereoselectivity 234 in ketones 235 from mixing s and p orbitals 225–226 in photoexcited state 420 in radical anion 388, 395, 396 in a silyl radical 118 in SN20 reactions 236 Pyridine electron distribution in 113 frontier electron populations of 174 IP of 66 lithium aluminium hydride in 189 LUMO of 184 nucleophilic addition to 184  MOs of 60 radical attack on 383 reduction of 395 site of electrophilic attack 174 soft nucleophile 186 Pyridine N-oxide 177 Pyridinium cations 382 as ambident electrophile 183 charge distribution in 184 electrolysis of 391 LUMO of 184 oxidation of 391

INDEX  MOs of 60 radical attack on 382, 383 Pyridinium-3-oxide 345 Pyrido[1,2-b]isoquinolin-5-ium ion 301 2-Pyridones 413, 414 Pyridynes 195–196 Pyrrocoline 174 Pyrrole dipole moment of 115 electrophilic substitution of 176, 177 frontier electron populations of 174 HOMO 176  MOs of 60 photochemical addition to benzene 404 site of electrophilic attack 174, 176 Quinhydrone 82, 85 o-Quinodimethane 354, 360 Quinoline 174 1,4-Quinone 85 Racemisation in radical reactions 118 Radial density 2 Radical anions 395–398 from anisole 397 from biphenyl 397 from butadiene 107, 398 in chemiluminescence 437 from 9,10-diphenylanthracenide 438 from ketones 396 from naphthalene 399 from 1,4-quinone 85 in SRN1 reactions 147, 400 from , -unsaturated ketone 396 Radical cations 393–395 from aniline 394 in chemiluminescence 437, 438 from 2-methylnaphthalene 393 from silyl enol ethers 394 Radical chain reaction 385 Radicals 369–400 abstracting H atom from tributyltin hydride 385 -acyl 370, 371, 372, 377, 378, 379, 384, 385, 390, 394, 400, 433 addition to alkenes 370, 371, 376–381 alkyl 373, 377 allyl 102, 103, 374, 376, 385, 386, 387, 400, 422, 426, 436, 437 ambident 390–398 anomeric effect in 375, 376, 389 attack on anisole 384 attack on anthracene 383 attack on naphthalene 383

INDEX attack on thiophen 383 axial attack by 376, 389 benzoyl 434 benzoyloxy 378 benzyl 399 boryl 371, 372 tert-butoxy 371, 372, 373, 374, 375, 377, 379 tert-butylperoxy 373 captodative 82, 83 chemoselectivity of used in synthesis 384 coupling of 398–400 in cathodic electrolysis of pyridinium ions 391 in di--methane rearrangements 428–430 in photochemical reaction of enones 437 in m-photocycloaddition to benzene 421, 423, 426 in photo-Fries rearrangement 434 in photoreduction of acridinium ions 435 in pinacol formation 395, 436 slow for 2-cyano-2-propyl 384 in SRN1 reactions 146–148 in stepwise cycloadditions 280, 411, 415–417 in Stevens rearrangements 281 coupling terminates radical chains 398 cyclohexadienyl 164, 391, 397 cyclohexyl 378, 384, 386, 388 cyclopropyl 386 cyclopropylmethyl 381, 428, 429 detected by ESR 66 dimethylamino 383 effect of structure on reactions 371–373 electrophilic 369, 370, 380, 384, 417 enol 389, 390 exothermicity of coupling 146 expulsion of -tributyltin radical 385, 386, 387 halogen abstraction by 374, 376 halogen atom as 372, 373 hydrogen atom abstraction by 371, 372, 373, 375 inversion of configuration of 117 isobutyronitrile 384 merostabilised 82 methyl 117, 372, 373, 378, 379, 384 2-nitropropyl 399 nucleophilic 369, 371, 384 -oxy 371, 372, 389, 411, 435, 436, 437 oxygen 376 phenoxy 391, 3992, 434 phenyl 373, 384 -phosphonyl 377 photochemically induced reactions 432–437 reaction types of 371 retention of configuration 432 ring formation by 379, 380, 387 silicon-containing 380, 388

507 silyl 118, 373, 380, 384, 388 -silyloxy 388 softness of 370 stability of governing regiochemistry 376 stereochemistry of reactions of 386–390 substituent effects on 81–83, 369, 378, 379 tributyltin 373, 374, 385, 386, 387 trichloromethyl 373, 376 trifluoromethyl 378, 379 trigonal 386 X-substituted, see Radicals, -oxy Z-substituted, see Radicals, -acyl Rate determining step in aromatic electrophilic substitution 167 in electrophilic attack on alkenes 153 Reaction coordinate for an ambident radical 390 for aromatic electrophilic substitution 170 defined 135, 136 for Diels-Alder reactions 294 for electrophilic attack on alkenes 216, 239 for -elimination 144 for endothermic reactions 135, 167 for exothermic reactions 135 for nucleophilic attack on carbonyl groups 178–179, 215 for nucleophilic attack on halogenonitrobenzenes 180 for nucleophilic attack on pyridynes 194 orbital following along for a Diels-Alder reaction 294 for radical attack on alkenes 387 Reactive intermediates, see Benzynes; Carbenes; Carbocations; Carbanions; Oxyallyl cation; Radicals; Trimethylenemethane Reactivity differential 139 perturbation theory of 136 -selectivity principle 370 Rearrangements Baeyer-Villiger 267, 353 Beckmann 267, 353, 354 Claisen 255, 349, 352, 358 Cope 316, 349, 350, 351, 352 Curtius 267, 353 di--methane 428, 429, 430 Mislow 255 photo-Fries 434 Wagner-Meerwein 90, 267, 353 see also Sigmatropic rearrangements Reduction cathodic 395 dissolving metal 395, 396, 397 by electron transfer 437, 438 of ketones 250

508 Reduction (continued) by lithium aluminium hydride 396 potentials 61 regioselectivity on , -unsaturated ketones 189 Regioselectivity in ambident electrophiles 183–199 in ambident nucleophiles 157–178 in ambident radicals 390 in carbene cycloadditions 347 in C- versus O- attack 160 in cycloadditions of allenes 345 defined 303 in Diels-Alder reactions 303–311 in electrophilic attack on X-substituted allyl anions 162 in intramolecular radical attack 379 photochemically in allene cycloadditions 420 in cross-coupling 415, 416 in cycloaddition to benzene 426 in dimerisations 413 in electrocyclic ring closure 430, 431 in ketene cycloaddition 421 in 1,7-sigmatropic hydrogen shift 431, 432 in substitution reactions 403 in radical addition to alkenes 377 in radical cyclisation 384 secondary orbital interactions explaining 312 SN1 versus SN10 190 SN2 versus SN20 190 Rehybridisation as a word to avoid 18 Relative rates of alkenes towards carbocations 154 of Diels-Alder cycloadditions 298–302 of 1,3-dipolar cycloadditions 324 of direct versus conjugate attack 186–189 of nucleophilic attack by different anionic nucleophiles on benzyne 197 on different carbonyl groups 179 on halogenonitrobenzenes 180, 185, 186 substitutions by different anionic nucleophiles 151, 155, 183 of ortho versus para atttack 174–176 Repulsion of filled orbitals with filled orbitals 10, 124 Resonance curly arrows illustrating 113, 114 illustrating orbital overlap 110 misleading about charge distribution 113 not an oscillation 4 unhelpful in predicting regiochemistry 324 Resonance integral affecting ambident reactivity 159 affecting hetero-Diels-Alder reactions 311

INDEX affecting regiochemistry of 1,3-dipolar cycloadditions 326 affecting regiochemistry of radical coupling 392 for C¼C as function of distance 40 corrections for heteronuclear bonds 59 defined 4 energy level in Hu¨ckel theory defined 31 mathematical form of 5 in Salem-Klopman equation 138 sign of 4 Restricted rotation about  bonds 101–104, 108, 110 about  bonds 104–111, 223, 224 Retention of configuration defined for [1,2] sigmatropic rearrangements 268 in electrophilic addition-elimination 365 in electrophilic substitution of vinylsilanes 224 in nucleophilic substitution at trigonal carbon 223 in radical substitution at Si 118 in SE2 reactions 209, 210, 211 in SN2 reaction at silicon 208 Retro-cycloadditions cheletropic 254, 356 Diels-Alder reactions 311, 316 1,3-dipolar 265, 333, 336 Ring closing, disrotatory or conrotatory 263 current affecting H-bonded atoms 120 in cyclobutane 48 in cyclohexane 48 in cyclopropane 47, 48 diamagnetic in aromatic systems 37 paramagnetic in antiaromatic systems 42 five-membered formed in radical cyclisations 379 formation, Baldwin’s rules affecting 218 medium sized 239 opening, disrotatory or conrotatory 263 strain affecting direction of electrocyclic reactions 262 Rotamers 83, 103, 104, 106, 109, 111, 112, 123, 244 Rotation about double bonds 101–104, 108–110 about single bonds 83, 93, 94–111, 223, 224 Rudmollin 428 S, see Overlap integral Salem-Klopman equation 138–141 affecting Bu¨rgi-Dunitz angle 215 both terms large 156 both terms small 156 in aromatic electrophilic substitution for Diels-Alder reaction 300, 303

174

INDEX for electrophilic attack on C¼C 216, 217 simplified 149 Schro¨dinger equation 5 SE2 reactions, see Electrophilic substitution Secondary effects in pericyclic reactions 295–368 Secondary orbital overlap in cycloadditions defined 312 of trimethylenemethane to cyclopentadiene 340 of tropone to cyclopentadiene 338 in Diels-Alder reactions 312, 313, 315 in dimerisation of cyclopentadiene 317 for 1,3-dipolar 337 for photochemical to benzene 425 for photochemical dimerisation 413 weakness of theory 314 Second-row elements stabilising anions 80 Selection rules for UV transitions 61, 422 Selectride 229 s-electrons in transmission of spin information 64 Selenoxide eliminations 256 Sensitisers defined 413 SET 145–149 -effect in 156 in aromatic electrophilic substitution 172 electron transfer in 146 involved or not involved? 148 radical coupling in 146 in SRN1 reactions 147, 399 1,2-Shift in cations 90, 91, 267, 268, 353, 419, 432 Sickle-shaped configuration 103, 214, 265 -acceptors, defined 70 -bonds, see Bonds c2 values in carbene cycloadditions 347–348 in Diels-Alder reactions 320–321 in other cycloadditions 358–359 in K-region 348–349 importance of in reactions with symmetrical transition structures 348 -framework allyl system 24 benzene 35 butadiene 29 ethylene 21 *-orbital, illegitimate representation of 99, 100 Sigmatropic rearrangements [1,2] in cations 90, 268, 353, 419, 432 [1,3] acyl shift photochemically 410 inversion in the migrating group 268 rare 278 stepwise homolytic 281

509 suprafacial allowed photochemically 409 [1,4] 268 [1,5] 266, 267, 275, 318, 322, 352, 353 [1,7] antarafacial 255, 267, 275, 353 of boron 353 suprafacial photochemically 409, 410, 431, 432 [2,3] 255, 270, 276 [3,3], see Claisen; Cope [4,5] 270 [5,5] 270, 356 [m,n] 269 Claisen 255, 269, 276, 349, 352, 358 Cope 256, 257, 269, 276, 316, 349, 350–352, 358 defined 254, 255 periselectivity in 356 photochemical 410 substituent effects on 349–353, 431–432 Woodward-Hoffmann rules for 266–270, 275–277 Silicon amines, low basicity of 80 holding two molecules in cyclic transition structure 245 Hu¨ckel parameters for calculating -MOs of 59 hydride as reducing agent 231 orbital interactions with 79 radical 118, 373, 380, 384, 388 SN2 reaction at 122 see also Silyl group Silver cation as a soft acid 128 cyanide as ambident nucleophile 158 Silyl dienol ethers oxidation of 394 regioselectivity of electrophilic attack on 166 Silyl enol ethers in Ireland-Claisen rearrangement 269 oxidation of 394 in photochemistry 433 radical attack on 394 Silyl ethers 80, 149 Silyl group affecting torquoselectivity 364, 365  to C¼O group 227, 228, 235 as electrofugal group in elimination 224 as electropositive substituent 227, 228, 243, 244, 245, 246 hyperconjugation with 94, 112 [1,3]-sigmatropic rearrangement of 278 stabilising  anion 79, 80, 96

510 Silyl group (continued) stabilising carbocations 94, 112, 224, 244, 245 trimethyl cyanide as ambident nucleophile 158 epoxide opening adjacent to 193 ethyl cation bridged 94 Simmons-Smith reaction 246, 347 Single bonds, see Bonds Single Electron Transfer, see SET Singlet oxygen 285–286 Singlet state 401, 402 Singly occupied molecular orbital, see SOMO Site selectivity defined for pericyclic reactions 319 of Diels-Alder reactions 319–322 of 1,3-dipolar cycloadditions 338 periselectivity a special kind of 355 Slater’s rules 10 Smirnov-Zamkow reaction 283 SN reactions, see Nucleophilic substitution Sodium borohydride 229, 240, 251 Sodium fluoride, bonding in 53 Sodium in liquid ammonia 107, 396, 398 Soft electrophiles 142, 143, 149–151, 182–183 Softness 129, 150 Solid-state photodimerisation 413 Solitons 34 Solvation 89, 102, 103, 115, 127, 134, 142, 147, 150, 152, 212, 229, 390 Solvent effects affecting C- versus O-alkylation 161 cage making radical coupling fast 146 on Diels-Alder stereochemistry 314 effect on reactivity 144 as explanation for ambident selectivity 159 in pericyclic reactions 256 as second-order perturbation 152 on stepwise cycloadditions 280 Solvolysis 88 Sommer, L. H. 207 SOMO coefficients of enol radical 390 of biphenyl radical anion 397 of phenoxy radical 391 defined 28, 369 energy of alkyl radicals 382, 383 correlates with selectivity of H atom abstraction 373 affecting rate of attack on styrenes 377 high energy for tin radical 384 low energy for electrophilic radicals 371

INDEX FO of a radical 81 of -methyl radical 387 of phenyl radical 382 in photochemical cross-coupling 417 of radical anion in chemiluminescence 437 Sparteine 210 Spiro conjugation 44–46 SRN1 reactions 146–148, 399, 400 p-Stacking 124 Staggered versus eclipsed conformations 211 Starting materials conformation of in explaining diastereocontrol 227 influencing transition structure 136 State correlation diagrams 292, 293 State crossing avoided in forbidden cycloadditions 293 Staudinger, H. 343 Stepwise reactions related to pericyclic ionic 279, 280, 342, 343, 344 radical 280, 285 Stevens rearrangement 281 Stereochemistry of electrophilic attack on C¼C adjacent to a stereogenic centre 241–250 of electrophilic substitution at trigonal carbon 222 of hydroboration 218, 284, 288 of ionic reactions 205–252 of nucleophilic attack on ketones 226–229, 214, 230–231, 240, 396 of nucleophilic attack on C¼C adjacent to a stereogenic centre 232–234 of nucleophilic substitution at trigonal carbon 222 of pericyclic reactions allene cycloadditions,347 cheletropic reactions 284, 288 Diels-Alder cycloadditions 261–262, 271–273, 311–318, 322 1,3-dipolar cycloadditions 336–337 electrocyclic reactions 263–266, 273–275 group transfer reactions 271, ketene cycloadditions 281–283, 342 sigmatropic rearrangements 266–269, 275–277, 350 torquoselectivity 362–368 of photochemical reactions 413 of radical reactions 386–390, 395, 396 in ring systems 225, 238–241 SE20 reactions 244 allenylsilanes 245 allylsilanes 244–245 with cyclic transition structures 245 in Nazarov cyclisation 365

INDEX SE200 reactions 246 SN2 reactions 207–209 SN20 reactions 236, 237 SN200 reactions 238 Stereoelectronic effects in radical reactions 375 of interaction of donor with acceptor 111 in SN2 reaction 181 see also Anomeric effect Stereoselectivity defined 205 Stereospecificity in cycloadditions to carbenes 200 in cycloadditions to ketenes 281 defined 205 degree of not necessarily 100%, 206 losses in 244 in photochemical cross-coupling 418 in photochemical fragmentation 433 Steric effects affecting substitution versus elimination 197 affecting vinylogous Felkin-Anh rule 234 avoided 250 in aromatic electrophilic substitution 176 in carbene reactions 203 in electrophilic attack on alkenes 152 encouraging SN20 237 explaining SE20 stereochemistry 246 fail to explain some diastereoselectivity 240 in Felkin-Anh control 227 from interaction of filled orbitals with filled orbitals 137 often explain diastereoselectivity 225, 238–241 overridden 190–192 in photochemistry 414 separated from electronic effects 250–252 in SN2 reactions 181 in unsymmetrical allyl cations 190, 191 weak in radical reactions 387 Steroid oxidation of 390 reduction of 396 synthesis of 309, 319 Stevens rearrangement 270, 281 Stevens, R. V. 232 Stilbene cis and trans 101 in cycloaddition to allyl anion 259 photochemistry of 418, 419 Stork, G. 237, 396 Strain A1,3-allylic 232, 247, 248 effect on reactivity 143 torsional 230

511 Styrenes Diels-Alder reaction of 302, 306, 310 1,3-dipolar cycloaddition to azomethine imines 332, 333 FOs of in 1,3-dipolar cycloadditions 328, 329, 330, 333, 334, 335 frontier electron population of 172 HOMO of 71 hetero-Diels-Alder reactions of 310 -MOs of 71 radical attack on 377 substituted in Hammett plot for radicals 377 UV spectrum of 330 Substituent effects on aromatic electrophilic substitution 168–173, 405 on carbenes 199 on -MO coefficients and energies of alkenes 70–76, 154, 179, 295, 297–298 of allyl anions 161–167 of benzenes 170–173 of carbanions 78–80 of carbocations 76–78, 87–90, 92–94, 112, 224, 244, 245 of dienes 295–297 of dienophiles 297–298 of 1,3-dipoles 324, 328 on nucleophilicity of alkenes 153 on pericyclic reactions on Claisen rearrangements 352 on Cope rearrangements 350, 351, 352 on Diels-Alder cycloadditions 298–302, 308 on electrocyclic reactions 354, 430, 431 on sigmatropic rearrangements 349–353, 431, 432 on photochemical reactions aromatic nucleophilic substitution 404 cross-coupling 418 cycloadditions to benzene 426, 427 di--methane rearrangements 429, 430 side-chain ionisation 407, 408 on radicals 81–83, 378, 379 on SN1 reactions 181 on SN2 reactions 180–182 Substitution, see Nucleophilic substitution; Electrophilic substitution Sudden polarisation 430, 431, 432 Sulfenyl halides 217, 218 Sulfonation 176 Sulfonium salts 101, 181 Sulfonyl group as a Z-substituent 70 Sulfoxides 121 Sulfur anion stabilisation by 79, 96 Hu¨ckel parameters for calculating MOs of 59

512

INDEX

Sulfur (continued) orbital interactions with 79 stabilising anion 162 substituent in Diels-Alder reactions 308 Sulfur dioxide photochemical cheletropic reaction with a diene 409 reaction with dienes 254, 284 reaction with trienes 284, 356 Sulfur trioxide as a hard electrophile 178 Sulfuryl chloride 349 Superdelocalisability 174, 381 Superoxide anions, -effect nucleophiles 156 Suprafacial overlap defined for a p orbital 275 defined for  bond 261 defined for a  bond 273 sigmatropic rearrangement defined for [1,2] 268 defined for [1,n] of H 266 defined for [m,n] 269 Sustmann, R. 302, 323 Sydnones 333 Symmetry axes, x, y and z, used in all drawings 8 elements for [2 þ 2]-cycloaddition 290 [2 þ 4]-cycloaddition 289 m-cycloaddition to benzene 423 o-cycloaddition to benzene 422 s and p orbitals in setting up CH2 14 s and p orbitals in setting up CH4 12  orbitals in setting up H3 8  orbitals in setting up H4 9 rules for interacting orbitals 7, 8 rules for UV transitions 61 Symmetry-imposed barrier absent in photo [2 þ 2] 293 in [2 þ 2] cycloadditions 292 Syn stereochemistry of SN20 reactions 236 Syn versus anti stereochemistry, see Anti versus syn Synclinal 217 Syncoplanar 85, 98 Tau bonds in dienes 246 defined 61 explain E20 stereochemistry 213 fail to explain E20 stereochemistry in SE20 reactions 246 in SN20 reactions 236 Tertiary cations, not bridged 90

214

1,2,4,5-Tetracyanobenzene 125 Tetracyanoethylene cycloadditions to cyclopentadienylidenecyclopheptatrienes 359 Diels-Alder 257, 300 to 1,1-dimethylbutadiene 280 to heptafulvalene 261, 273 in SET reaction 148 Tetracyclone 302, 323, 346 Tetrafluoromethane 98 Tetrahydropyranes, anomeric effect in 97 N,N,N0 ,N0 -tetramethyl-1,4-diaminobenzene 125 tetramethyltin 148 Thermodynamics affecting equilibrium 127 affecting kinetics 135, 371, 377 stability defined 69 versus kinetics 170, 186, 188, 190 Thiamine 200 Thiele’s ester 321, 322 Thiocyanate 157, 158 Thioketones Hu¨ckel parameters for calculating MOs of 59 methylation of 152 Thiolate anion 188 Thiophen electrophilic substitution of 176 radical attack on 383 Thiourea 186 Tight binding model 34 Tin holding two molecules in cyclic transition structure 245 radicals 118, 385–387, 390 Toluene photochemistry of in TFAD 405 radical abstraction of H atom from 373 radical anion 67 radical attack on 383 Torquoselectivity 344, 362–368 Torsional strain 230, 231, 235, 240 Trajectory analysis 215 Transition states, see Transition structures Transition structures adjust to match electron supply in SN2 181 anti preferred for E2 211 antiperiplanar versus synclinal in aldol 217 aromatic in [3,3]-sigmatropic rearrangements 351, 352 in electrocyclic ring opening 354 Mo¨bius 354, 363 in symmetry-allowed pericyclic reactions 286 boat-like 269, 276, 289, 294, 313

INDEX chair-like 163, 217, 269, 276, 350, 387 chelation control in 229 for Cope rearrangements 269, 276, 316, 350–352 cyclic 162, 163, 189, 217, 225, 245 cycloadditions alkenes þ ketenes 282 asynchronous 285, 301, 304, 316 cyclopentadiene dimerisation 316, 317 Diels-Alder 257, 294, 295, 313, 315, 316 1,3-dipolar 242 endo versus exo in 1,3-dipolar cycloadditions 336, 337 exo favoured in [4 þ 6]-cycloaddition 338 for 5-endo-trig reactions 220 envelope-shaped 276 for epoxide openings 193 for electrophilic attack on an alkene 243, 248 for ene reaction 271 gas phase E2 212 gas phase SN2 209 H atom transfer 390 hydrogen bonding in 120, 121 like starting material for exothermic 136, 242 like product for endothermic 136 medium-sized rings 239 for nucleophilic attack on C¼O 179, 214, 226, 228 number of electrons in 260  bond attacking  bond 216 for proton transfer 119 on reaction coordinate 135, 136 for radical attack 387, 390 for rotation 101, 102, 109, 110 for [1,2]-shift 90, 353 for SN2 reaction 122, 220 Zimmerman-Traxler 163, 217 Triazolinediones in cycloadditions 285 endo preference of 317 in ene reactions 286 Triazolines decomposition to aziridines 331 from 1,3-dipolar cycloadditions of azides 331 Tributyltin hydride 371, 390 Tributyltin radicals 118, 385–387 Trienes cycloaddition with sulfur dioxide 284, 356 dimerisation 320, 358 electrocyclic ring closure 254, 262, 264, 274, 365, 366, 410 -MOs of 33 Triethylamine 81, 149 Triethylborane 230, 376 Trifluoroethylene 378

513 Trifluoromethane 98 Trifluoromethyl anion stabilisation by 96 cation destabilised by 95 radical 377, 378, 379 Trifluoroperacetic acid 176 Trigonal bipyramid in hypervalent compounds 122 transition structure in SN2 reactions 207, 208 Trimethoxyborane 77 Trimethylenemethane cycloaddition to cyclopentadiene 340 cycloaddition to methyl acrylate 339 degeneracy lifted 338 dimerisation of 339 synthesis of 339 -MOs of 339 Trimethylsilyl, see Silyl group Trimethylstannyl group 251 Trinitrobenzene 119 Triple bonds, see Acetylenes; Cyanides; Cyano group; Nitriles Triplet states achieved using sensitisers 413 in di--methane rearrangements 428 intersystem crossing from 402 Triquinacene 42, 43 Tris(trimethylsilyl)silyl radical 388 Trishomocyclopropenyl cation 42 Trisilylamine 80 Tropone cycloaddition to cyclopentadiene 260, 338 cycloaddition to diethyl ketene acetal 420 Diels-Alder reactions 310 FOs of 184, 309, 310 nucleophilic addition to 184 photocycloaddition to 420 Tropylium cation 201 Trost, B. M. 308 Tryptamine 406 Ultraviolet spectroscopy, see UV spectroscopy Umpolung 393, 395 Unimolecular reactions difficulty in applying FO theory to 287 electrocyclic 254 sigmatropic rearrangements 255 , -Unsaturated esters conformation of 109, 230 conjugate addition to 188, 232, 233, 234, 239, 370 reductive coupling of 395 in stepwise cycloadditions 279

514 , -Unsaturated imines 189 , -Unsaturated ketones conformation of 109 direct versus conjugate attack 186–189, 217, 233 electron distribution in 113 FOs of 187 photochemistry of 415, 416, 417, 420, 421, 436, 437 reduction of 109, 234, 235, 395, 396 UV spectra of 62, 95 Unsymmetrical Diels-Alder transition structures 285, 301, 304, 315, 316 U-shaped configuration of allyl system 103, 366 curve for change of mechanism 324 UV spectroscopy 65 as measure of HOMO-LUMO gap 330 in comparison of alkene and alkyne FOs 330 , -insaturated ketones n!* transitions of ketones 94 dienes 107 polyenes 62 toluene versus tert-butylbenzene 230 Valence bond theory applied to aromatic electrophilic substitution 168 applied to Diels-Alder regioselectivity 304 applied to pyrroles 177 avoided 141 associated with resonance 4 curly arrows in 23 van der Waals attraction 123 radius 2 Vertical stabilisation, see Hyperconjugation Vibrational motions making photochemical transition allowed 422 Vinyl acetate radical attack on 371, 376 radical copolymerisation 370 boranes FOs of 308 in Diels-Alder reactions 308, 315 boronic acids 308 cations 283, 287 group as a C-substituent 70 1,2-shift in cations stepwise 353 lithium 224 phosphonic ester 377 photocycloaddition to benzene 426 silanes 223

INDEX bromodesilylation of 224 controlling torquoselectivity 365 electrophilic substitution of 224 radical attack on 380 stannane, radical attack on 386, 387 Vinylogous Felkin-Anh rule 232–234 Vinylogues 101, 111 Vitamin D, 1,7-sigmatropic rearrangement in 255 Volumes of activation, negative in cycloadditions 256 Wagner-Meerwein rearrangement 90, 267, 353 Walsh orbitals in cyclopropane 46, 47 in cyclopropylmethyl cations 89 Water, IP of 66 Wave functions for allyl system 24–27 contour plots ethylene 22 formaldehyde 58 hydrogen molecule 6 2p orbital on carbon 11 1s orbital on hydrogen 1 2s orbital on carbon 10 wire-mesh pictures allyl system 28 butadiene 32 ethylene 22 formaldehyde 58 methane 13 methyl chloride 54 methyllithium 57 W-configuration 265 W-coupling 65 Weedon, A. C. 415, 416 Wender, P. A. 428 Wheland intermediate 167–170 Wiesner, K. 420 Wire mesh drawings, see Wave functions 2,3-Wittig rearrangement 270, 276 Woodward, R. B. 107, 143, 145, 258, 263, 264, 270, 271, 278, 293, 316, 317 Woodward’s rules for UV spectroscopy 107 Woodward-Hoffmann rules 349, 355 affecting reactivity 143 chair and boat in Cope rearrangements allowed by 276 class by class 258–271 explanations for 286–295 generalised rule of 271 hints about drawing diagrams for 277 obedience to as evidence of concertedness 258 photochemical 408–411

INDEX simple rule for cycloadditions 260, 262 electrocyclic reactions 263–266 group transfer reactions 270 sigmatropic rearrangements 266, 268 substituent effects on may be ignored 289 may override 349 W-shaped configuration of allyl systems 103 X-ray crystal structures Bu¨rgi-Dunitz angle from 214 detecting hydrogen bonding 119 difficulty of detecting H-bonded hydrogen atoms in 118 -stacking 124 pyramidalisation detected in 235 used to measure van der Waals radius 2 X-Substituents alkyl groups classified as 70, 87, 239 defined 70 effect on coefficients of alkenes 76, 306 of allyl anions 162 of anions 80 of dienes 167, 295–297, 319, 303, 306 of radicals 81 effect on FO and  energy of alkenes 75, 154, 300 of anions 80 of carbonyl groups 179 of carbocations 76, 77 of dienes 295–297, 299

515 of radicals 81 of 1,3-dipoles 324, 328 stabilising organometallic compounds by coordination 80 Xylene radical anion 67 2,6-Xyloquinone 309, 319 Xylylenes, m- and p-, as models for MOs of a photo-excited state 407 Zimmerman, H. E. 429 Zimmerman-Traxler transition structure 163, 217 Zinc holding two molecule in cyclic transition structure 217, 245 Z-Substituents defined 70 effect on coefficients of alkenes 74, 303, 308 of allyl anions 166 of anions 80 of dienes 295–297,304, 313 of radicals 81 effect on FO and  energy of alkenes 73, 154, 299 of anions 78–80 of carbonyl groups 179 of carbocations 77 of dienes 295–297, 300, 319 of 1,3-dipoles 324, 328 of radicals 81 special kind without double bonds 165 Zwitterions as intermediates 101, 279, 280 representation of oxyallyl system 340