New theoretical method to study densities of states of tetrahedrally coordinated solids

A new simple method is proposed to calculate local densities of states of arbitrary tetrahedrally coordinated solids. It involves the selection of a finite cluster of atoms connected to an infinite Bethe lattice of coordination four. The method is accurate, is easily handled numerically, and converges fast. Low-order approximations yield sufficient information which is susceptible to consistent physical interpretation. This has been made for the diamond, BC-8 and ST-12 structures in terms of the ring topology around a given atom. Comparison with exact calculations is very good and the ring interpretation is physical and conceptually appealing.