Exact Thomas—Fermi method in perturbation theory

A variational principle is constructed which leads directly to the March-Murray perturbation series relating the particle density ρ(r) with the one-body potential V(r) in an electron gas. An explicit, though perturbative, form for the Hohenberg-Kohn universal functional, which is essentially the kinetic energy density, is thereby obtained. When the spatial variations of density and potential are slow, the usual Thomas-Fermi ρ5/3 relation between kinetic energy density and particle density is regained. The present approach also leads to a systematic formulation of the gradient expansion of the kinetic energy density.