Electron correlations in the ground state of covalent semiconductors

Abstract

We describe a simple and transparent method for studying electronic correlations in the ground state of covalent semiconductors. The starting point is a single-determinantal ground-state wave function in the bond-orbital approximation. Electronic correlations are taken into account by applying a variational ansatz. Analytical expressions are obtained for the interatomic or bond correlation energy as well as for the pair-correlation function. Both are discussed in detail. The intra-atomic correlation energy is estimated in two different ways which give identical results. One is based on an ‘‘atoms in solids’’ method which requires a population analysis of the ground-state wave function, while the other is based on an analysis of the correlation energies of hydrocarbon molecules. The theory is applied to diamond, Si, Ge, and α-Sn. The correlation-energy contributions to the cohesive energy and the radial force constant are discussed and compared with experimental data. By using a diagrammatic representation, a comparison is made with ground-state correlation-energy calculations which use the ‘‘GW approximation’’ of Hedin [Phys. Rev. 139, A796 (1965)].