Formal Theory of an Inhomogeneous Electron Gas

Abstract

Hohenberg and Kohn have dealt with the ground state of an interacting electron gas in an external potential and show that there exists a universal functional of the electron density n(r), G[n(r)], independent of an external potential. This functional plays a central role in a theory of inhomogeneous electron gas. In this paper, a formal theory for deriving the form of this functional is developed. The method of this derivation is based on the use of a nonlinear response theory. Our analysis shows that G[n] can be expressed entirely in terms of nonlinear response functions. We derive the full expression of G[n] which is written explicitly by the density n(r). Furthermore, we find the generalized form of “compressibility sum rule”.