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Muller's exchange-correlation energy in density-matrix-functional theory
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2007 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 76, no 5, 052517- p.Article in journal (Refereed) Published
Abstract [en]

The increasing interest in the Muller 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 gamma(x,x(')) is replaced by the square of gamma(1/2)(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 gamma's have unique densities rho(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 gamma, which is more complex than for HF theory. We state some open mathematical questions about the theory together with conjectured solutions.

Place, publisher, year, edition, pages
2007. Vol. 76, no 5, 052517- p.
National Category
Mathematics Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-37012DOI: 10.1103/PhysRevA.76.052517ISI: 000251326400076Scopus ID: 2-s2.0-36649024812OAI: oai:DiVA.org:kth-37012DiVA: diva2:431825
Available from: 2011-07-26 Created: 2011-07-26 Last updated: 2017-12-08Bibliographically approved

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