# Müller's exchange-correlation energy in density-matrix-functional theory

Frank R, Lieb É, Seiringer R, Siedentop H. 2007. Müller’s exchange-correlation energy in density-matrix-functional theory. Physical Review A - Atomic, Molecular, and Optical Physics. 76(5).

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Frank, Rupert L;
Lieb, Élliott H;
Seiringer, Robert

^{IST Austria}^{}; Siedentop, Heinz KAbstract

The increasing interest in the Müller density-matrix-functional theory has led us to a systematic mathematical investigation of its properties. This functional is similar to the Hartree-Fock (HF) functional, but with a modified exchange term in which the square of the density matrix γ(x, x′) is replaced by the square of γ1 2 (x, x′). After an extensive introductory discussion of density-matrix-functional theory we show, among other things, that this functional is convex (unlike the HF functional) and that energy minimizing γ 's have unique densities ρ(r), which is a physically desirable property often absent in HF theory. We show that minimizers exist if N≤Z, and derive various properties of the minimal energy and the corresponding minimizers. We also give a precise statement about the equation for the orbitals of γ, which is more complex than for HF theory. We state some open mathematical questions about the theory together with conjectured solutions.

Publishing Year

Date Published

2007-11-30

Journal Title

Physical Review A - Atomic, Molecular, and Optical Physics

Volume

76

Issue

5

IST-REx-ID

### Cite this

Frank R, Lieb É, Seiringer R, Siedentop H. Müller’s exchange-correlation energy in density-matrix-functional theory.

*Physical Review A - Atomic, Molecular, and Optical Physics*. 2007;76(5). doi:10.1103/PhysRevA.76.052517Frank, R., Lieb, É., Seiringer, R., & Siedentop, H. (2007). Müller’s exchange-correlation energy in density-matrix-functional theory.

*Physical Review A - Atomic, Molecular, and Optical Physics*. American Physical Society. https://doi.org/10.1103/PhysRevA.76.052517Frank, Rupert, Élliott Lieb, Robert Seiringer, and Heinz Siedentop. “Müller’s Exchange-Correlation Energy in Density-Matrix-Functional Theory.”

*Physical Review A - Atomic, Molecular, and Optical Physics*. American Physical Society, 2007. https://doi.org/10.1103/PhysRevA.76.052517.R. Frank, É. Lieb, R. Seiringer, and H. Siedentop, “Müller’s exchange-correlation energy in density-matrix-functional theory,”

*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 76, no. 5. American Physical Society, 2007.Frank, Rupert, et al. “Müller’s Exchange-Correlation Energy in Density-Matrix-Functional Theory.”

*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 76, no. 5, American Physical Society, 2007, doi:10.1103/PhysRevA.76.052517.**All files available under the following license(s):**

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