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R. B. lPoodward and R. Hoffmann The Conservation of Orbital Symmetry R. B. Woodward and R. IloJJmann The Conserv~l'iior1 or Orbi'ial Syrr1nc-1e·iry 1971 Vcrlgg C:i1cmlc Grnt.~: .1\.caucmlc Press Inc. With 45 Figures Prof. Robert Bums Woodward Department of Chemistry, Harvard University 12 Oxford Street Cambridge, Mass. 02138 (USA) Prof. Roald Hoffmann Department of Chemistry, Cornell University Ithaca, N.Y. 14850 (USA) First Edition 1970 First Printing January 1970 Second Printing May 1970 Third Printing January 1971 LIBRARY OP CoNGRESS CATALOG CARD NUMBER 79-103636 Printed in Germany C 1971 Verlag Chemic, GmbH, Weinheim{Bergstr. All rights reserved (including those of translation into foreign languages). No part of this book may be reproduced in any form · by pbotoprint, microfilm, or any other means · nor transmitted, nor translated into a machine language without the permission in writing of the publishers. Printed by Main-Echo, Aschaffenburg - Verlagsnummer: 7044 Contents 1. Introduction 1 2. Orbitals and Bonding 2 3. Correlation Diagrams 10 3.1. General Comments on the Construction of Correlation Diagrams 27 3.2. Precautions in the Construction of Correlation Diagrams 31 4. The Conservation of Orbital Symmetry 37 5. 'fheory of Electrocyclic Reactions 38 5.1. Electrocyclic Reactions Exemplified 48 6. Theory of Cycloadditions and Cycloreversions 65 6.1. Cycloadditions and Cycloreversions Exemplified 73 6.2. l2+2] Cycloadditions in the Photochemistry of the Cyclohexa- dicnones and Cyclohexenones 89 6.3. The (2-1 2-f-2] Cycloaddition Reaction 101 6.4. Prismane 107 6.5. [2-1 2-i-2·1 2] Cycloadditions 112 7. 'l'heory of Sigmatropic Reactions 114 7.1. Sigmatropic Reactions Exemplified 120 7 .2. Sequential Sigmatropic Shifts 132 8. Group 'l'ransfers and Eliminations 142 9. Secondary Effects 145 10. Divertissements I 152 10.1. Cheletropic Reactions 152 10.2. Cycloaddition Reactions of Ketenes 163 11. Generalized Selection Rules for Pericyclic Reactions 170 12. Violations 173 13. Other Theoretical Work 176 14. Conclusion 178 1. Introduction Of the various ways in which the phenomena of chemical bonding have been treat- ed from the theoretical point of view, the molecular orbital method may fairly be deemed to have been the most fruitful in the hands of the organic chemist, and most adaptable to his needs. None the less, the method, with a few conspicuous ex- ceptions, has been used mainly in the study of the static properties of molecules- in ground and excited states-and only rarely have its potentialities been explored in relation to reacting systems. In 1965, in a series of preliminary communications[l·3 1, we laid down some fun- damental bases for the theoretical treatment of all concerted reactions. The history of the genesis of these ideas has been described elsewhere[4J. The basic principle enunciated was that reactions occur readily when there is congruence between orbital symmetry characteristics of reactants and products, and only with difficulty when that congruence does not obtain-or to put it more succinctly, orbitai!JtnnJe- try i1 con1erved in concerted reaction!. This principle has met with widespread interest; the applications made of it, the tests which it has survived, and the corollary pre- ructions which have been verifed are already impressive. In this paper we develop our views at some length, survey some of the developments - in our hands and those of others-of the three years just past, and make some new projections. [1) R.B. Woodw.1rdand Roald Hoffmann, J. Amer. chem. Soc. 87,395 (1965). [2] Roald Hoffm4nn and R. B. Woodward,]. Amer. chem. Soc. 87,2046 (1965). [3] R. B. Woodward and Roald Hoffmann, J. Amer. chem. Soc. 87,2511 (1965). [4) R. B. Woodward: Aromaticity. Special Publication No. 21. The Chemical Society, London 1967, p. 217. 2. Orbitals and Bonding It is worth while to review the elementary aspects of the molecular orbital theory of bond.ing£51. Molecular orbitals are constructed as combinations of atomic orbitals, and are then populated by electron pairs. When two equivalent atomic orbitals, x1 and x2, combine, they always yield a bonding combination and a corre- sponding antibonding orbital (1 ) . ..: ,...---.,.··\ X1- : .~xz ··. ..._ _, .l· {1) The bonding combination is characterized by positive overlap, and by concentra- tion of electron density in the region between the nuclei. By contrast, the antibonding combination exhibits negative overlap, and a nodal surface in the region between the nuclei. When x and x~ are s orbitals, the bonding combination is 1 x1+ x2• and the antibondiag one x1-x2 • • • X1 + Xz When x1 and x2 are p orbitals interacting in a G manner, and oriented as shown in (2) the bonding combination is again x+x and the antibonding combination 1 2 7.t- X2· (2) Throughout this paper, the phases of wave-functions are color-coded: positive= blue, negative= green. When phase relationships are not relevant, the orbitals are presented in solid gray. [SJ In addition to the classical text by C. A. Couiion (Valence. 2nd ed., Oxford University Press, London 1961), we recommend: C. A. Coulson and E. T. Sltwarl inS. Palai: The Chemistry of Al- kenes. Wiley-lntersience, New York 1964, E. Htilbronntr and H. Bode: Das HMO-Modell und seine Anweodung. Verlag Chemic, Weinheim 1968, and R. S. Mulliktn, Science 157, 13 (1967): Aogew. Chern. 79, S41 (1967). 2. Orbilals and Bonding 3 It is important to realize, however, that were the basis orbitals initially arbitrarily oriented in some other fashion, such as ( 3), then, since x' 2 = - x2, the bonding (3) combination would be x1-x'2, and the antibonding one x1+X's· It should also be kept in mind that multiplying an entire wave function by -1 does not affect its energy. Thus, overlap of minus with minus lobes is precisely equivalent to plus with plus lobes, and-x1- x2 is the .rame bonding orbital as x1 + Xz· •• The description of u bonds in hydrocarbons is simple. Each formal chemical bond engenders au and au* orbital. The C-Hand C-C cases are: •••• a~H- • • • ac-e - • ••• The molecular orbitals a.re represented in our drawings as the overlap of two hy- brids of unspecified hybridization. It should be emphasized that this is only intend- ed as an artistic mnemonic device: the only essential features of au orbital are that it is approximately cylindricaJly symmetrical around the bond axis, that it concen- trates electron density in the region between the nuclei, and that there is no nodal plane between the atoms. Our simple picture of bonding in, say, cyclobutane, shows four C-C u levels, and eight C-H u levels, each with a matching u* level ( 4). The carbon l.r orbitals are 4 2. Orbitals and Bonding (~) not considered. Each of the a levels is occupied by two electrons. Spectroscop· ic studies indicate that the gap between occupied and unoccupied levels must be of the order of 10 electron volts. The orbitals we have constructed are semi-localized. They are delocalized over only two atoms. Such orbitals are satisfactory for an analysis of some properties of the molecules - those which depend on aU of the occupied molecular orbitals: bond lengths, energies, dipole moments. They are not the proper molecular orbitals of the molecule. The latter are completely delocalized, subject to the full symmetry of the molecule. For a discussion of physical properties depending on one or two specific molecular orbitals, such as spectra or ionization, it is absolutely necessary to construct these equivalent delocalized orbitals. The mechanics of delocalization will be described in Section 3. In addition to a bonds, the molecules of organic chemistry contain delocalized :n orbitals. Thus, the electronic structure of ethylene is described as follows: There are four a C-H bonds and a a C-C bond ( 5). Each generates a a and a u* level, and {5) (6) five pairs of electrons are placed in the a levels. There remain two electrons and two atomic p orbitals perpendicular to the plane of the molecule ( 6). These com- 2. Orbila/1 and Bonding 5 bine to give n and n* orbitals, differentiated by the absence or presence of a node between the atoms (Figure 1). There are two independent symmetry operations which may be used to classify these orbitals; the mirror plane m, perpendicular to the molecular plane and bisect- ing the molecule, and the two-fold rotation axis c2, passing through the center of the carbon-carbon bond. It should be noted carefully thatthesymmetryproper· ~· ....... c·~· u'' A s H s A 0 Figure 1. Molecular orbitals of ethylene and symmetry properties of the nand n* orbitals. A - antisymmetric, S - symmetric.. The horizont2l bars indicate the reL'ltive orbital energies.