Prediction of the Fermi surface as a test of density-functional approximations to the self - energy

Abstract

Prediction of alkali-like Fermi surfaces is used as a test of the local and nonlocal density-functional approximations to the electron self-energy proposed by Sham and Kohn. This test is carried out in a Hartree-Fock (HF) model system where a Yukawa interaction between the electrons is used in order to simulate screening. The Fermi surfaces resulting from the density-functional approximations to the exchange term are compared to the exact HF Fermi surface. It is found that the local and nonlocal approximations produce Fermi surfaces which are too distorted and too spherical, respectively. This reconciles previous local and nonlocal Fermi-surface calculations in the alkali metals with known experimental results. It is shown that the Fermi surface is much more sensitive to the approximations made to the self-energy than other properties such as the density and chemical potential, which we find are treated with sufficient accuracy by the local approximation.