Iteration-Perturbation Theory of Covalent Bonding in Crystals

Abstract

An iteration-perturbation approach is suggested which enables the calculation of the binding energy and equilibrium lattice parameters of non-metallic crystals. Making use of the single­band-gap model, the selfconsistent Schrödinger equation can be solved in terms of the effective matrix elements, W(g)′s, which, in general, satisfy the set of nonlinear equations. The latter are solved for those reciprocal lattice vectors g for which the perturbation theory requirements are violated. Since the matrix elements of ion-electron interaction are not small for some g’s the screening of all the interactions in the crystal is not linear. The exchange-correlation contributions both in the screening and in the total energy are accounted for by means of the Kohn-Sham density-functional-formalism. A charge transfer is shown to result in excluding part of the electrons from the screening processes. The theory allows also for the possibility of a strongly non-homogeneous electron density distribution in the crystal. The results of the calculation for magnesium hydride MgH2 are presented in paper II.