Pericyclic reactions perturbation theory

We have discussed in Section 10.3 the application of perturbation theory to processes in which two molecules come together. We saw there that the most important interactions will be between the HOMO of one molecule and the LUMO of the other. This method can serve as a useful guide in deciding whether there will be a stabilization as a pericyclic reaction begins to occur. The HOMO-LUMO approach was the first one that Woodward and Hoffmann used for ana-... 

Professor Houk and I are coevals and we embarked on our research careers at about the same time. In the beginning of the 1970s, both he and I were independently working on mechanistic aspects of pericyclic reactions, using a combination of experiment, simple perturbational MO theory and semi-empirical MO calculations. My published work in this area was of variable quality whereas Ken s was uniformly... 

More recently, molecular orbital theory has provided a basis for explaining many other aspects of chemical reactivity besides the allowedness or otherwise of pericyclic reactions. The new work is based on the perturbation treatment of molecular orbital theory, introduced by Coulson and Longuet-Higgins,2 and is most familiar to organic chemists as the frontier orbital theory of Fukui.3 Earlier molecular orbital theories of reactivity concentrated on the product-like character of transition states the concept of localization energy in aromatic 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 state. Both influences on the transition state are obviously important, and it is therefore important to know about both of them, not just the one, if we want a better understanding of transition states, and hence of chemical reactivity. 

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 mol 1 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. 

The first insight on the mechanism of pericyclic reactions was provided by Woodward and Hoffmann in their famous monograph The Conservation of Orbital Symmetry. The basic idea is that reactions occur readily (are thermally allowed) when there is congruence between the orbital symmetry characteristics of the reactants and the products, while they occur with difficulty (are thermally forbidden) when that congruence does not pertain. In short, orbital symmetry is maintained in concerted reactions. This has been proved by Pearson by means of perturbation theory. While the Woodward and Hoffmann rules determine which reactions are allowed and which are forbidden, they do not establish what the real mechanism of the process is. Although this initial view of pericyclic reactions has been very much debated, it forms the basis of the important progress made in the understanding of these reactions. 

Configuration Interaction Coupled-cluster Theory Density Functional Applications Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field M0ller-Plesset Perturbation Theory Numerical Hartree-Fock Methods for Molecules Pericyclic Reactions The Diels-Alder Reaction Solvation Modeling Transition Structure Optimization Techniques. 

In a recent book Dewar (1969) has given a general account of the perturbation molecular orbital (PMO) approach and its relevance in discusrions on physical-organic chemistry. Of particular interest is one application which provides a general theory of pericyclic reactions (Dewar, 1969, 1971), The PMO treatment in this context has but one central concept, namely the potential aromaticity of pericyclic transition states (see p. 61), and may be generalized into a single definitive rule ... 

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