Electron Transfer Properties of Alternant Hydrocarbons in Terms of Inverse Adjacency Matrices of Molecular Graphs

Abstract

Abstract. The study addresses electron transfer (ET) properties of systems of the type D-AH-A, where D and A are external electron-donating and accepting subsystems, respectively, and AH is an alternant hydrocarbon playing the role of the bridge. The main attention is paid to the dependence of the ET properties upon the sites of the AH, the external subsystems are attached to. As is usual in one-electron models of ET properties, the latter are considered to be proportional to off-diagonal Hamiltonian matrix elements (resonance parameters) representing effective interactions of orbitals of external groups D and A via the bridge. The block-diagonalization procedure for the common Hückel type Hamiltonian matrix of AHs is applied to derive explicit algebraic expressions for the above-specified decisive parameters. As a result, a relation is established between these parameters and elements of the inverse adjacency matrix (IAM) of the graph of the given AH referring to sites (vertices) under consideration. The common constitution of IAMs of all AHs then yields a simple and general selection rule for the effective parameters concerned. Moreover, the unified IAM of AHs is shown to be expressible in terms of entire submatrices (blocks) of the initial AM. This allows the ET properties of composite AHs to be analyzed in terms of increments of separate fragments (subgraphs) and of their interaction. The results of the study are illustrated by consideration of specific examples including the simplest benzenoids.