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 mu xc for ground state problems and Vxc for excitation spectra. The potential mu xc(r) is written as a factor beta ( rho (r)), which depends on the local density rho (r), times the Kohn-Sham-Gaspar potential mu x=-e2kF/ pi . The factor beta , which is represented by a simple analytical formula, varies between 1 for very high densities and about 1.5 for very low densities, where mu xc 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.