Explanations for the Woodward-Hoffmann Rules

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 frequency with which pericyclic reactions have a transition structure with (An + 2) electrons in a cyclic conjugated system, which can be seen as being aromatic. The second makes the point that the interaction of the appropriate frontier orbitals matches the observed stereochemistry. The third is to use orbital and state correlation diagrams in a compellingly satisfying treatment for those cases with identifiable elements of symmetry. Molecular orbital theory is the basis for all these related explanations. 

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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... 

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