Explicit local exchange-correlation potentials

The possibilities of the Hohenberg-Kohn-Sham local density theory are explored in view of recent advances in the theory of the interacting electron gas. The authors discuss and provide numerical data for the effective exchange-correlation potentials μxc for ground state problems and Vxc for excitation spectra. The potential μxc(r) is written as a factor β(ρ(r)), which depends on the local density ρ(r), times the Kohn-Sham-Gaspar potential μx=-e2kF/π. The factor β, which is represented by a simple analytical formula, varies between 1 for very high densities and about 1.5 for very low densities, where μxc thus approaches the Slater approximation. The potential Vxc is given in the form of a table. The explicit predictions of the approximate theories are mapped in their linearized versions. The theory is also developed for the case when the ion cores are treated separately, and the local density approximation is applied only to the valence electrons.