Self-consistent total-energy approximation for electron gas systems

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.