Density functional approximation for the quasiparticle properties of simple metals. I. Theory and electron gas calculations

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Abstract
Calculations of the self-energy of the electron gas for energies near the Fermi energy are presented. The results of these calculations are required to quantify a previously suggested approximation for the self-energy of real metals. Two separate types of improvement on the random-phase approximation (RPA) for the self-energy are considered. The first type is similar to the Hubbard approximation while the second type explicitly evaluates terms of second and third order in the renormalised interaction expansion for the self-energy. Local exchange-correlation potentials from these and other recent calculations and parameterised in a form that will be useful in bandstructure calculations. Results for the correlation contribution to the ground-state energy are also obtained and inciate that RPA gives results that are about 25% too large at the lowest metallic densities.