--- res: bibo_abstract: - 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.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Rupert foaf_name: Frank, Rupert L foaf_surname: Frank - foaf_Person: foaf_givenName: Élliott foaf_name: Lieb, Élliott H foaf_surname: Lieb - foaf_Person: foaf_givenName: Robert foaf_name: Robert Seiringer foaf_surname: Seiringer foaf_workInfoHomepage: http://www.librecat.org/personId=4AFD0470-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-6781-0521 - foaf_Person: foaf_givenName: Heinz foaf_name: Siedentop, Heinz K foaf_surname: Siedentop bibo_doi: 10.1103/PhysRevA.76.052517 bibo_issue: '5' bibo_volume: 76 dct_date: 2007^xs_gYear dct_publisher: American Physical Society@ dct_title: Müller's exchange-correlation energy in density-matrix-functional theory@ ...