Recent Developments in Applying and Extending the Method of Tight Binding (LCAO) to Energy-Band Calculations

Abstract

The purpose of this paper is to investigate the computational aspects of the method of tight binding and is roughly divided into two parts. In the first part we present the formulation and application of the tight-binding problem in its most rigorous and straight-forward form without introducing any numerical approximations and then examine the effects of the “nearest-neighbor approximation” which was frequently employed within this scheme to reduce the computational complexity. The second part is devoted to investigating various methods for increasing the variational freedom over that of the traditional minimal basis set and to examining the versatility and applicability of this method to a broad spectrum of crystalline materials.