Thermal properties of the inhomogeneous electron gas

Abstract

A variational property of the ground-state energy of an electron gas in an external potential v(r), derived by Hohenberg and Kohn, is extended to nonzero temperatures. It is first shown that in the grand canonical ensemble at a given temperature and chemical potential, no two v(r) lead to the same equilibrium density. This fact enables one to define a functional of the density F[n(r)] independent of v(r), such that the quantity Ω=v(r)n(r)dr+F[n(r)] is at a minimum and equal to the grand potential when n(r) is the equilibrium density in the grand ensemble in the presence of v(r). © 1965 The American Physical Society.