Enumeration of Kekule Structures of Polyhex Monoradical Having Only Linear Assemblies of Benzenoid Hydrocarbons

Abstract

A mathematical process of enumeration of Kekule structures of any polybenzenoid monoradical having only linear assemblies of benzenoid hydrocarbons is given by using a method which consisted of the excision of the radical center in order to obtain a conjugated hydrocarbon having a 12-annulene core ring appended to one or more polybenzenoid fragments, the partition of the resulting conjugated hydrocarbon into smaller independent resonant circuits. Polyhex monoradical skeletons are obtained from a building up procedure which consists to fuse in different ways the acenaphtyl moiety with one or more polybenzenoid fragments. Mathematical formulas are established for three cases of assemblies, one edge linear assemblies, two edges linear assemblies with two linear polybenzenoid fragments located at right angles θ = 60°, 120° or 180° and three edges linear assemblies with three linear polybenzenoid fragments located at right angles θ= 60°, 120° or 180°. Results show that the number of Kekule structures of any polybenzenoid monoradical having only linear assemblies of benzenoid hydrocarbons increases with the number of fused benzenoids according to results compiled in the table for h equal 1, 2, 3 and 4. Difficulty to represent graphs when the number of structures increases with the number of benzenoids cannot be neglected.