Cluster Expansion Method for the Density of Excited Electronic States of Substitutionally Disordered Crystals

Abstract

In this paper we introduce a cluster expansion method which is suitable for numerical calculations of the density of electronically excited states of substitutionally disordered molecular crystals. This method is based on an expansion of the density of states of the guest subband in terms of the localized densities corresponding to various clusters and is valid for a large scattering potential and for concentrations of guest molecules below the percolation concentration. The general features of the cluster expansion method are illustrated by calculations for a simple one-dimensional molecular crystal. These numerical calculations for the one-dimensional model are compared with the results obtained by the coherent potential approximation. The role of the localized states, which are not accounted for by the coherent potential method can be elucidated.