A tight-binding derivation of force constants : Application to covalent systems

Abstract

A method for calculating the total electronic energy as a function of the atomic displacements within the tight-binding approximation is presented. The sum of one electron energies is formally expanded to second order with the help of the perfect crystal Green's functions. The remaining contribution is expressed as a sum of repulsive pair potentials. A simple application to the molecular or bond orbital model of covalent semiconductors is described which already leads to fairly realistic phonon dispersion curves. The simplicity of the method thus makes it particularly suitable for the study of atomic rearrangements near defects or surfaces. It also allows its extension to much more complicated cases, such as amorphous systems, defect tetrahedral compounds and even transition metal oxides