Density-functional formulation of the generalized pseudopotential theory

Abstract

The generalized pseudopotential theory of $d$-band metals is rederived using the self-consistent-field equations of Kohn and Sham as the starting point. The basic features of the original theory are recovered, but a number of important and unifying refinements are achieved. Central to the development is the careful approximation of the total exchange and correlation potential in the form of a constant plus a sum of overlapping, but structure-independent, intra-atomic potentials. This result, combined with our previously introduced zero-order-pseudoatom technique of defining core and $d$ states, permits and accurate first-principles evaluation of all matrix elements entering the theory, including direct $d$ state overlap integrals. In addition, the structure dependence of the hybridization potential, which has been previously ignored or only spherically averaged, is now treated explicitly. As a result, new second-order terms in the total energy are uncovered, leading to a modified energy-wave-number characteristic and $d$-state overlap potential. Also derived is a moderately simple, but very accurate (to within 3%), formula for the binding energy of the metal. Partial application to copper and full application to nineteen other simple and d-band metals are discussed.