Inhomogeneous Electron Gas

P.Hohenberg

W.Kohn

P. Hohenberg and W. Kohn

Phys. Rev. 136, B864 – Published 9 November 1964

ABSTRACT

This paper deals with the ground state of an interacting electron gas in an external potential $v\left(r\right)$. It is proved that there exists a universal functional of the density, $F\left[n\right(r\left)\right]$, independent of $v\left(r\right)$, such that the expression $E\equiv \int v\left(r\right)n\left(r\right)dr+F\left[n\right(r\left)\right]$ has as its minimum value the correct ground-state energy associated with $v\left(r\right)$. The functional $F\left[n\right(r\left)\right]$ is then discussed for two situations: (1) $n\left(r\right)=n_0+\tilde{n}\left(r\right)$, $\frac{\tilde{n}}{n_0}\ll 1$, and (2) $n\left(r\right)=\varphi \left(\frac{r}{r_0}\right)$ with $\varphi$ arbitrary and $r_0\to \infty$. 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.

• Received 18 June 1964

DOI:https://doi.org/10.1103/PhysRev.136.B864

©1964 American Physical Society

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