Pseudo Green's Functions and the Pseudopotential Theory ofd-Band Metals

Abstract

A general one-electron pseudo-Green's-function formalism is developed as an extension of the true-Green's-function techniques of Anderson. Pseudo-Green's-function equations are derived in an arbitrary, overcomplete basis representation for a general non-Hermitian pseudo-Hamiltonian. The flexibility in the choice of both the basis set and the pseudopotential makes the method useful for treating a variety of physical systems. Formal calculations of the pseudo Green's function and the density of states are considered for simple metals as well as $d$-band metals. The method is applied in detail to the case of a $d$-band metal. Using a basis set of plane waves and localized $d$ states, calculations of the electron screening field and the total energy are performed. These quantities are found as a function of both the pseudopotential and Harrison's hybridization parameter. Overlap between $d$ states enters in the total energy and is explicitly included. For the special case of a completely filled or empty $d$ band with no $d$-state overlap, the results obtained here reduce precisely to those found recently by Harrison via perturbation theory.