The evaluation of moments for polycyclic hydrocarbons

Abstract

The evaluation of some moments of the energy in the Hückel theory of conjugated molecules is considered. It is shown that, for molecules consisting entirely of hexagons, the moments μ ₄ and μ ₆ can be expressed in terms of four graphical invariants. Partial results are given for other molecules. Since the total energy can be expressed as a series of moments the implications for the energy are discussed. In this discussion two other invariants play a major role. The conclusion is suggested that an analysis of moments in terms of graphical invariants should be of prime importance in understanding these molecules.