Orthogonalized linear combinations of atomic orbitals: Application to the calculation of energy bands of Si III

Abstract

The method of linear combinations of atomic orbitals has been modified by orthogonalizing Bloch sums of the valence states to those of the core states so that the latter can be deleted from the basis-function set in order to reduce the size of the secular equations. In case the overlap of the core wave functions between different atoms is small, the expansion coefficients in the orthogonalization process are simply related to the overlap matrix elements. This methods of orthogonalized linear combinations of atomic orbitals (OLCAO) is applied to Si III which has eight atoms in a primitive cell, and its accuracy is verified by comparing the OLCAO results with those obtained by directly including the core wave functions in the basis set. Our calculations give a band gap of 0.029 eV for Si III and the density of states for Si III is found to be substantially different from that of the ordinary silicon crystals. The small band gap provides an explanation for the drastic decrease of electric resistivity at high pressure and the metallic behavior of highly compressed silicon.