TY - JOUR

T1 - Müller's exchange-correlation energy in density-matrix-functional theory

AU - Frank, Rupert L.

AU - Lieb, Elliott H.

AU - Seiringer, Robert

AU - Siedentop, Heinz

N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2007/11/30

Y1 - 2007/11/30

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevA.76.052517

DO - 10.1103/PhysRevA.76.052517

M3 - Article

AN - SCOPUS:36649024812

SN - 1050-2947

VL - 76

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

IS - 5

M1 - 052517

ER -