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Kohn-Sham theory for ground-state ensembles

Ullrich, C.A.; Kohn, W.

Physical Review Letters 87(9): 093001

2001

An electron density distribution n(r) which can be represented by that of a single-determinant ground state of noninteracting electrons in an external potential v(r) is called pure-state v-representable (P-VR). Most physical electronic systems are P-VR. Systems which require a weighted sum of several such determinants to represent their density are called ensemble v-representable (E-VR). This paper develops formal Kohn-Sham equations for E-VR physical systems, using the appropriate coupling constant integration. It also derives local density- and generalized gradient approximations, and conditions and corrections specific to ensembles.

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**Exchange methods in Kohn-Sham theory**. Physical Chemistry Chemical Physics 7(16): 2991-2998, 2005