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Inhomogeneous Electron Gas

Phys. Rev. 136, B864 – Published 9 November 1964
P. Hohenberg and W. Kohn

Abstract

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 Ev(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+ñ(r), ñn01, and (2) n(r)=ϕ(rr0) with ϕ arbitrary and r0. 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.

DOI: http://dx.doi.org/10.1103/PhysRev.136.B864

  • Received 18 June 1964
  • Published in the issue dated November 1964

© 1964 The American Physical Society

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Published 21 October 1998

Authors & Affiliations

P. Hohenberg*

  • École Normale Superieure, Paris, France

W. Kohn

  • École Normale Superieure, Paris, France and Faculté des Sciences, Orsay, France and University of California at San Diego, La Jolla, California

  • *NATO Post Doctoral Fellow.
  • Guggenheim Fellow.

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