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Phys Rev Lett. 2017 Dec 15;119(24):243001. doi: 10.1103/PhysRevLett.119.243001. Epub 2017 Dec 13.

Hartree and Exchange in Ensemble Density Functional Theory: Avoiding the Nonuniqueness Disaster.

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Qld Micro- and Nanotechnology Centre, Griffith University, Nathan, QLD 4111, Australia.
CNR-Istituto di Nanoscienze, Via Campi 213A, I-41125 Modena, Italy.


Ensemble density functional theory is a promising method for the efficient and accurate calculation of excitations of quantum systems, at least if useful functionals can be developed to broaden its domain of practical applicability. Here, we introduce a guaranteed single-valued "Hartree-exchange" ensemble density functional, E_{Hx}[n], in terms of the right derivative of the universal ensemble density functional with respect to the coupling constant at vanishing interaction. We show that E_{Hx}[n] is straightforwardly expressible using block eigenvalues of a simple matrix [Eq. (14)]. Specialized expressions for E_{Hx}[n] from the literature, including those involving superpositions of Slater determinants, can now be regarded as originating from the unifying picture presented here. We thus establish a clear and practical description for Hartree and exchange in ensemble systems.

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