1964/11/09 by P. C. Hohenberg, W. Kohn · 3 citations
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paper · pdf · doi:10.1103/physrev.136.b864
openalex publication_date 1964/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02
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[n(r)], independent of v(r), such that the expression E\ensuremath≡\ensuremath∫v(r)n(r)dr+F[n(r)] has as its minimum value the correct ground-state energy associated with v(r). The functional F[n(r)] is then discussed for two situations: (1) n(r)=n0+\stackrel\ifmmode \else \~\fin(r), \frac\stackrel\ifmmode \else \~\finn0\ensuremath≪1, and (2) n(r)=\ensuremathφ(\fracrr0) with \ensuremathφ arbitrary and r0\ensuremath→\ensuremath∞. 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.