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Inhomogeneous Electron Gas

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


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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