A linear relationship between the total π-electron energy and the characteristic polynomial

Abstract

A linear relationship between the total π-electron energy ( E π) and the coefficients of the characteristic polynomial of the molecular graph is analysed. It is deduced that (a) the main part of E π depends on the number of bonds, (b) the Hückel 4 m+2 rule holds generally, but corrections regarding the role of the size of the rings are to be added, (c) the perimeter rule can be justified, and (d) E π is increased proportionally to the number of Kekulé and Dewar resonance forms. A quantitative measure of all these topological factors is estimated.