Self‐consistent total‐energy approximation for electron gas systems

Abstract

Employing a local formula of Parr [J. Chem. Phys. 93, 3060 (1988)] for the electron–electron interaction energy, we derive a self‐consistent approximation for the total energy of a general N‐electron system. Our scheme works as a local variant of the Thomas–Fermi approximation and yields the total energy and density as a function of the external potential, the number of electrons, and the chemical potential determined upon normalization. Our tests for Hooke's atoms, jellium, and model atoms up to 1500 electrons show that reasonable total energies can be obtained with almost negligible computational cost. Our approximation may serve as a useful tool to provide initial results for more advanced approaches that also include binding.