Multiple-scattering approach to band theory

Abstract

Some new developments in multiple-scattering theory are described in connection with the problem of band theory. Functions that are the logical extension of incoming and outgoing waves are defined for points within the sphere that bounds the range of an atomic scattering potential. Taking these functions into account, a multiple-scattering equation for band theory with general non-muffin-tin potentials is derived. This equation contains terms that were not included in earlier formulations of this problem. A new set of formulas for calculating the scattering from an atomic potential is introduced. It is shown that, among other things, these formulas can be used to derive simplified and linearized band-theory equations entirely within the multiple-scattering framework. Both algebraically and numerically, it is shown that these linearized equations work well. In particular, for the special case of a muffin-tin potential, they will give exactly the same results as a fully converged Korringa-Kohn-Rostoker calculation at any chosen energy. Linearized band-theory equations derived earlier by combining the variational and multiple-scattering approaches are obtained by manipulating the equations from this study.