Computing the kekule structure count for alternant hydrocarbons

摘要

A fast computer algorithm brings computation of the permanents of sparse matrices, specifically, molecular adjacency matrices. Examples and results are presented, along with a discussion of the relationship of the permanent to the Kekule structure count. A simple method is presented for determining the Kekule structure count of alternant hydrocarbons. For these hydrocarbons, the square of the Kekule structure count is equal to the permanent of the adjacency matrix. In addition, for alternant structures the adjacency matrix for N atoms can be written in such a way that only an N/2 X N/2 matrix need be evaluated. The Kekule structure count correlates with topological indices. The inclusin of the number of cycles improves the fit. When comparing with previous results, the variance decreases 74%. The calculated standard heat of formation correlates with the logarithm of the Kekule structure count. This heat increments 349 kJ/mol each time the Kekule structure count increases by one order of magnitude.