Density-dependent potentials for simple metals

The authors have calculated the total energy for a simple metal within pseudopotential theory to second order in the pseudopotential. Their work is based on a first-principles nonlocal pseudopotential. The results presented here contain an extra term accounting for the density dependence of the higher-order terms in the total energy. This term is required to equilibrate the system at the observed density and should be included in any low-order expansion of the total energy. A closed-form expression for the energy-wavenumber characteristic is given, from which the pair potential can readily be obtained by a Fourier transform. Also included is a simple and accurate expression for the local field, which gives the electron gas screening.