MOMENTS AND CHARACTERISTIC POLYNOMIALS OF BIPARTITE HUCKEL GRAPHS

Moments (u(k)) and coefficients of characteristic polynomials (a(k)) have been evaluated in terms of molecular fragments up to k = 12 for bipartite Huckel graphs. Based on combinatorial analysis, each coefficient can be derived as a combination of binomial factors mapping to the corresponding multi-component graphs. The general formula becomes lengthy as k increases, but can be considerably simplified for a homologous series. This has been illustrated by dealing with the cata-condensed benzenoid hydrocarbons as a corollary where a rather compact set of ak has been deduced. On combining the present result with Coulson's formula, one gains insight into the relative stability of isomers in relationship to the energy contribution of fragments classified as stabilized and destabilized species.