The recursion method and a first-principles tight-binding calculation of the band structures of diamond and silicon

A tight-binding first-principles calculation of the band structures of diamond and silicon is presented. The numerical crystal potential (including a local exchange-correlation term) is fitted to a superposition of simple analytic functions centred on each atom. A basis of localized s and p Orbitals is calculated from this potential and fitted to a combination of Gaussians. All Hamiltonian and overlap matrix elements are then evaluated analytically, and the local density of states can be calculated by a recursion method modified to deal with overlap. An extension of the method to the study of crystal defects is discussed.