Enumeration of the Kekulé structures in conjugated hydrocarbons

Abstract

A procedure is developed for evaluating the number of Kekulé structures in conjugated molecules employing the results on smaller systems which constitute fragments of the molecule. A particularly simple expression gives the number of Kekulé valence forms in cata-condensed benzenoid systems. It applies to branched cata-condensed structures as well as to closed cyclic structures built from cata-condensed benzenoid rings. Also, a general method which applies to any conjugated hydrocarbon, i.e., pery-condensed and even lattice-type structures, is outlined. It is based on a reduction of the molecular graph by excising all edges (bonds of the molecular skeleton) for which a unique assignment of the bond character is possible. By recognizing several regularities in the assignment procedure the subsequent elimination of bonds generally proceeds quickly. Both methods are illustrated on selected molecular structures.