Kekulé Index for Valence Bond Structures of Conjugated Polycyclic Systems

Abstract

Individual formal valence structures of conjugated hydrocarbon systems have been characterized by an index K, called the Kekulé index, which relates a given set of molecular orbitals to orbitals localized on pairs of adjacent carbons. The localized orbitals can be associated with valence bond structures in a simple and unique way. It is then shown that for systems built from condensed benzene rings the valence structure with the largest values of the Kedulé index corresponds to Kekulé-type valence structures with the largest number of formal benzene Kekulé-type formulas, i.e., to structures for which the empirical Fries rule predicts the greatest stability. The Kekulé index orders different valence structures in a series which should qualitatively indicate relative importance of the individual structures. The approach can be extended also to excited formal structures as discussed for naphthalene. Application of such analyses to a number of alternate polycyclic conjugated systems confirms an intuitive extension of the Fries rule to systems constructed from rings of various sizes. © 1973, American Chemical Society. All rights reserved.