Charge densities and interionic potentials in simple metals: Nonlinear effects. I

Abstract

Starting from the Hohenberg-Kohn-Sham equations, expressions are derived for the linear-response charge density induced by a nonlocal pseudopotential embedded in an electron gas and for the corresponding interionic pair potential. It is emphasized that an accurate calculation of the charge density is an essential prerequisite for the generation of a reliable potential. This point is illustrated by making a comparison with Dagens's self-consistent calculations of the charge density induced by an isolated ${\mathrm{Na}}^{+}$ ion. It is shown that nonlinear effects in both the density and the potential cannot be ignored. However by adjusting the pseudopotential parameters to fit the self-consistent charge density and thus simulate the nonlinear terms, a reliable and useful interionic potential is generated. Thus the essential simplicity of the pseudopotential perturbation approach to the theory of metals can be retained and nonlinear effects can be incorporated into it in a straightforward manner.