On Enumeration of Kekule Structures for Benzenoid Tori

概要

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Hypothetical benzenoid tori serve as models for estimating the properties of graphite because their electronic states are found rapidly to converge to that of graphite. We present an algorithm for enumeration of Kekule structures of these benzenoid tori. The basis for our algorithm is consideration of those CC connecting lines which convert a 2-dimensional benzenoid into a torus. By successive selection of such "connecting" lines as CC single and CC double bonds we effectively transform a benzenoid torus into a collection of planar benzenoids, the Kekule structures of which are thus enumerated. The number of benzenoids and rump benzenoids derived by excision of "connecting" bonds and adjacent bonds is governed by the binomial distribution. The approach is illustrated on benzene and coronene tori. The results for a few other simple benzenoid torus networks are presented including also the result for a torus based on circamcoronene with over 15,000 Kekule valence structures.
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