Topological hamiltonian spectra of polycyclic benzenoid hydrocarbons

Abstract

A general theory which points out the relations between Huckelπ-electron energy, the number of Kekule structures and the HOMO-LUMO separation is presented. Some normalized topological invariants are derived from the concept of the spectral density function. A reasonably simple (three parameters) model spectral density function leads to universal relations between topological invariants that, although valid for any alternant molecule, were tested numerically for polycyclic benzenoid hydrocarbons. Some general conclusions concerning a distribution of the adjacency matrix eigenvalues are drawn.