This paper deals with the ground state of an interacting electron gas in an external potential v(r). It is proved that there exists a universal functional of the density, F t I(r) g, independent of v(r), such that the expression E-= fs(r)n (r)dr+Ft I(r) j has as its minimum value the correct ground-state energy associated with s(r). The functional FLn(r)j is then discussed for two situations: (1) n(r) @san(r), 8/ao((1, and (2) a(r) = q (r/ra) with p arbitrary and 1'p~~. In both cases F can be expressed entirely in terms of the correlation energy and linear and higher order electronic polarizabilities of a uniform electron gas. This approach also sheds some light on generalized Thomas-Fermi methods and their limitations. Some new extensions of these methods are presented.

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