ThePMO if Theory Organic Chemistry ThePMO Theoryof Organic Chemistry J Michael S. Dewar Department of Chemistry University of Texas Austin, Texas and Ralph C Dougherty Department of Chemistry Florida State University Tallahassee, Florida SPRINGER SCIENCE+BUSINESS MEDIA, LLC Library of Congress Cataloging in Publication Data Dewar, Michael J ames Steuart. The PMO theory of organic chemistry. HA Plenum/Rosetta edition." Includes bibliographical references. 1. Molecular orbitals. 2. Perturbation (Mathematics) 3. Chemistry, Organic. I. Dougherty, Ralph C., 1940- joint author. 11. Title. [QD461.D49 1974b] 547 74-26609 ISBN 978-1-4613-5705-6 ISBN 978-1-4615-1751-1 (eBook) DOI 10.1007/978-1-4615-1751-1 First paperback printing 1975 © 1975 Springer Science+Business Media New York Originally published by Plenum Press,New York in 1975 Softcover reprint of the hardcover 1st edition 1975 United Kingdom edition published by Plenum Press, London A Division of Plenum Publishing Company, Ud. Davis House (4th Floor), 8 Scrubs Lane, Harlesden, London, NW10 6SE, England All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher Preface This textbook introduces the perturbation molecular orbital (PMO) th,eory of organic chemistry. Organic chemistry encompasses the largest body offactual information of any of the major divisions of science. The sheer bulk of the subject matter makes many demands on any theory that attempts to systematize it. Time has shown that the PMO method meets these demands admirably. The PMO method can provide practicing chemists with both a pictorial description of bonding and qualitative theoretical results that are well founded in more sophisticated treatments. The only requirements for use of the theory are high school algebra and a pencil and paper. The treatment described in this book is by no means new. Indeed, it was developed as a complete theory of organic chemistry more than twenty years ago. Although it was demonstrably superior to resonance theory and no more complicated to use, it escaped notice for two very simple reasons. First, the original papers describing it were very condensed, perhaps even obscure, and contained few if any examples. Second, for various reasons, no general account appeared in book form until 1969,* and this was still relatively inaccessible, being in the form of a monograph where molecular orbital (MO) theory was treated mainly at a much more sophisticated level. The generality of the PMO method is illustrated by the fact that all the new developments over the last two decades can be accommodated in it. Indeed, many of these would have been facilitated had this approach been more generally known. One might add that while the value of perturbation theory has been increasingly realized in recent years, many of its exponents are still unaware of the real potential of the PMO approach. * M. 1. S. DEWAR, The Molecular Orbital Theory of Organic Chemistry, McGraw-Hili, New York, 1969. v vi Preface The lack of publicity concerning the PMO method has of course been reflected in current textbooks of organic chemistry, where it is barely men tioned. An obvious way for us to have remedied this deficiency would have been to write a new textbook based on the PMO theory. However, there are many different views concerning the manner in which the factual background of organic chemistry should be taught; we did not want to commit those who might wish to use the PMO approach to our particular choice. We therefore decided instead to write a general account of the PMO method that could be used in conjunction with any existing textbook of organic chemistry. We see no reason why this should not be done at the undergraduate level and we have therefore included an introduction to quantum mechanics and molecular orbital theory that is based on physical principles and which illustrates the foundations and power of the PMO method (Chapters 1 and 2). Those who wish to delve deeper into the mathematical details of MO theory will find suggestions for further reading at the ends of the chapters. Chapter 1 also discusses bonding in diatomics, the basis for the localized bond ap proximation, the assumptions involved in the concept of hybridization, and the places where these assumptions break down. Chapter 3 deals with the electronic structure and relative stabilities of n-electron systems. Chapters 4 and 5, respectively, illustrate the application of the PMO method to the breadth of problems in chemical equilibrium and ground-state reactions in condensed phases. The last two chapters are at a different level, discussing topics (organic photochemistry, reactions of ions in the gas phase, etc.) that are not adequately treated in current texts. This omission is due partly to the fact that these areas have only recently been explored; however, it is also largely because the lack of a satisfactory theoretical background has made them difficult to teach. As we show, the PMO method can provide such a basis and we hope that this may encourage the inclusion of these topics in organic courses. Since the current textbooks are deficient, we have also included the necessary background information together with numerous examples and references to the literature. Throughout this text we have attempted to show how the "starring" of alternant hydrocarbon systems (see p. 74), e.g., the benzyl radical, provides a graphic model for discussions of bonding and also emphasizes the wave mechanical nature of chemical bonds. In the example above the starred atoms are the ones that will carry the bulk of the spin density in the radical. In Preface vii this case, one drawing takes the place of the five lowest energy resonance struc tures for the benzyl radical. The combination of valence bond-like structures with easily accessible qualitative wave mechanics seems to us to be the major power of the PMO method. Austin, Texas Michael J. S. Dewar Tallahassee, Florida Ralph C. Dougherty Contents CHAPTER 1. Introduction to MO Theory 1.1. The Hydrogen Atom; Orbits and Orbitals ................ 1 1.2. The Orbital Approximation; Helium ..................... 7 1.3. Lithium; the Pauli Principle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.4. The Atoms Be-Ne; Hund's Rule. . . . . . . . . . . . . . . . . . . . . . . . . 12 1.5. The Hydrogen Molecule; Molecular Orbitals ..... . . . . . . . . . 13 1.6. The Born-Oppenheimer Approximation. . . . . . . . . . . . . . . . . . 16 1.7. HHe +, HHe, and HLi; Perturbation Theory. . . . . . . . . . . . . . . 17 1.8. Methane; Symmetry Orbitals ........................... 21 1.9. Photoelectron Spectroscopy and Ionization Potentials ...... 24 1.10. Methane, Continued; Hybridization and Localized Bonds '" 28 1.11. Diatomic Molecules. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 1.12. The Paraffins; Localized Bonds ......................... 38 1.13. Ethylene; n Bonds ..................................... 41 1.14. Acetylene ............................................ 45 1.15. Breakdown of the Localized Bond Model: Three-Center Bonds, Conjugated Molecules, and Reaction Intermediates. 47 1.16. Relationships between Different Types of Delocalized Systems. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . .. 50 1.17. Summary............................................. 52 Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Selected Reading ...................................... 55 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 ix x Contents CHAPTER 2. Perturbation Theory 2.1. The Usefulness of Perturbation Theory ................... 57 2.2. Types of Perturbations Involved in the Comparison of Conjugated Systems ..... ;........................... 59 2.3. Monocentric Perturbations ............................. 61 2.4. Intramolecular Union .............................. . . . . 64 2.5. Intermolecular Union .................................. 65 2.6. Multiple Union; Additivity of Perturbations. . . . . . . . . . . . . . . 69 Problems ............................................ 70 Selected Reading ...................................... 71 Reference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 CHAPTER 3. PMO Treatment of Conjugated Systems 3.1. Principles of the PMO Method; Alternant and Nonalternant Systems ............................ , . .. . . .. . . . . . . . . 73 3.2. The Pairing Theorem .................................. 75 3.3. Calculation of NBMO Coefficients ....................... 78 3.4. Distribution of Formal Charges in AHs . . . . . . . . . . . . . . . . . . . 81 3.5. Monocentric Perturbations; Correlation of Isoconjugate Systems.. . .. .. . .. . . .. . ... . . . .. .. ... .. .. ... .. .. . .. . . 83 3.6. Intermolecular Union of Even AHs . . . . . . . . . . . . . . . . . . . . . . . 83 3.7. Multiple Union of Even AHs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.8. Union of Odd AHs .................................... 86 3.9. Alternation of Bonds in Polyenes ........................ 88 3.10. Even Monocyclic Polyenes; Aromaticity and Antiaromaticity; Hiickel's Rule ........ . . . . . . . . . . . . . . . . 89 3.11. Bond Alternation in Annulenes .......................... 91 3.12. Polycyclic Polyenes .................. . . . . . . . . . . . . . . . . . . 93 3.13. Intramolecular Union; Monocyclic Nonalternant Hydrocarbons ...................................... 96 3.14. Essential Single and Double Bonds; General Rules for Aromaticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 3.15. Significance of Classical Valence Structures. . . . . . . . . . . . . . .. 101 3.16. Union of an Odd AH with an Even AH ................... 104 3.17. Huckel and Anti-HUcke! Systems ........................ 106 3.18. Effect of Heteroatoms .................................. 109 3.19. Polarization of 1t Electrons. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 115 3.20. Stereochemistry of Nitrogen. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 119 3.21. Resonance Theory in the Light of the PMO Method . . . . . . .. 121 Appendix. 1t Energy of Union of Even AHs . . . . . . . . . . . . . . .. 125 Problems ............ '. ........................ , , . . . . .. 127 Se!ected Reading ...................................... 130 Contents xi CHAPTER 4. Chemical Equilibrium 4.1. Basic Principles ....................................... 131 4.2. Factors Contributing to the Energy of Reaction ............ 135 4.3. Reaction of AHs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 138 4.4. Electron Transfer Processes; Redox Potentials ............. 152 4.5. Nonalternant Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 157 4.6. Effect of Heteroatoms .................................. 159 4.7. The n-Inductive Effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 164 4.8. Classification of Substituents ............................ 165 4.9. Inductive (I) Substituents ............................... 165 4.10. Electromeric Substituents; ±E Substituents ............... 167 4.11. + E Substituents ..... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 172 4.12. - E Substituents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 175 4.13. Summary of Substituent Effects ................... , . . . . .. 178 4.14. Cross-Conjugation..................................... 179 4.15. Mutual Conjugation ................................... 180 4.16. The Field Effect ....................................... 182 4.17. The Hammett Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 185 Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 191 Selected Reading ...................................... 194 References ........................................... 195 CHAPTER 5. Chemical Reactivity 5.1. Basic Principles ....................................... 197 5.2. The Transition State Theory ............................ 202 5.3. Transition States for Aliphatic Substitution . . . . . . . . . . . . . . .. 205 5.4. Reaction Paths and Reaction Coordinates. . . . . . . . . . . . . . . .. 210 5.5. The Bell-Evans-Polanyi (BEP) Principle; Relationships between Rates of Reactions and Corresponding Equilibrium Constants .......................................... 212 5.6. Reactions Where Intermediates Are Involved .............. 220 5.7. Solvent Effects; Electrostatic Interactions and the Hellman- Feynman Theorem. . .. . . . .. . .. . . . . . .. .. .. . . .. . .. . . . .. 222 5.8. Limitations of the BEP Principle. . . . . . . . . . . . . . . . . . . . . . . .. 230 5.9. Classification of Reactions .............................. 235 5.10. Prototropic Reactions of ISO + Type..................... 240 B 5.11. Prototropic Reactions of EO + Type ..................... 245 B 5.12. Nucleophilic Aliphatic Substitution. . . . . . . . . . . . . . . . . . . . . .. 253 A. SN1 Reactions .................................... 253 B. SN2 Reactions .................................... 256 5.13. Nucleophilicityand Basicity. . . . . . . . . . . . . . . . . . . . . . . . . . . .. 265 5.14. Electrophilic Aliphatic Substitution. . . . . . . . . . . . . . . . . . . . . .. 270 xii Contents 5.15. Radical Substitution Reactions (EOB~) . . . . . . . . . . . . . . . . . . .. 274 5.16. Elimination Reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 279 5.17. n-Complex Reactions (EnBt) ............................ 285 5.18. Electrophilic Addition (EnB t and EOB t) .................. 297 5.19. n Complexes vs. Three-Membered Rings. . . . . . . . . . . . . . . . .. 300 5.20. Nucleophilic Addition and Related Reactions (EO t) ....... 306 B 5.21. Radical Addition and Polymerization (EO t) .............. 310 B 5.22. Aromatic Substitution in Even Systems (EO t) . . . . . . . . . . . .. 316 B 5.23. Substitution vs. Addition ............................... 331 5.24. Neighboring Group Participation. . . . . . . . . . . . . . . . . . . . . . .. 333 5.25. Some OE t Reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 336 5.26. Thermal Pericyclic Reactions (EE At and 00 At) . . . . . . . . . . .. 338 5.27. Examples of Pericyclic Reactions. . . . . . . . . . . . . . . . . . . . . . . .. 347 A. Cycloaddition Reactions (EEAt and 00A t) ........... 347 B. Some Special Features of the Diels-Alder Reaction. . . .. 350 C. Sigmatropic Reactions (EEA t and 00A t) . . . . . . . . . . . .. 352 D. Electrocyclic Reactions ............................ 360 E. Chelotropic Reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 362 5.28. Alternative Derivations of the Woodward-Hoffman Rules. "Allowed" and "Forbidden" Pericyclic Reactions ..... . . .. 367 5.29. Catalysis of PericYclic Reactions by Transition Metals. . . . . .. 369 5.30. Reactions Involving Biradical Intermediates (ERA t). . . . . . . .. 373 5.31. The ±E Substituent Technique. . . . . . . . . . . . . . . . . . . . . . . . .. 378 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 383 Selected Reading ..................................... " 388 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 389 CHAPTER 6. Light Absorption and Photochemistry 6.1. Introduction.......................................... 391 6.2. The Nature of Electronically Excited States. . . . . . . . . . . . . . .. 393 6.3. The Franck-Condon Principle .......................... 395 6.4. Singlet and Triplet States ............................... 397 6.5. Extinction Coefficients and Transition Moments ........... 398 6.6. Excitation and Deexcitation; Lifetimes of States, Fluorescence, and Phosphorescence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 401 6.7. Excitation Energies of Even AHs . . . . . . . . . . . . . . . . . . . . . . . .. 403 6.8. Excitation Energies of Odd AHs ......................... 408 6.9. n --> n* and n --> n* in Even, Heteroconjugated Systems. . . . .. 409 6.10. n --> n* Transitions in Odd, Heteroconjugated Systems. . . . .. 410 6.11. Effect of Substituents on Light Absorption ................ 413 6.12. Basic Principles of Photochemistry; Types of Photochemical Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 419 6.13. The Role of the Born-Oppenheimer (BO) Approximation. . .. 422 6.14. The Role of Antibonding Electrons. . . . . . . . . . . . . . . . . . . . . .. 426