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Müeller's Exchange-Correlation Energy in Density-Matrix-Functional Theory

Frank, Rupert L. and Lieb, Elliott H. and Seiringer, Robert and Siedentop, Heinz (2009) Müeller's Exchange-Correlation Energy in Density-Matrix-Functional Theory. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170510-091442211

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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 functional, but with a modified exchange term in which the square of the density matrix (x, x′) is replaced by the square of y^(1/2)(x,x′). After an extensive introductory discussion of densitymatrix-functional theory we show, among other things, that this functional is convex (unlike the HF functional) and that energy minimizing y’s have unique densities p(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 y, which is more complex than for HF theory. We state some open mathematical questions about the theory together with conjectured solutions.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/0705.1587arXivDiscussion Paper
Additional Information:Dated: September 28, 2009. (Submitted on 11 May 2007 (v1), last revised 29 Sep 2009 (this version, v3)). Rupert Frank and Heinz Siedentop thank the Departments of Mathematics and Physics at Princeton University for hospitality while this work was done. The following partial support is gratefully acknowledged: The Swedish Foundation for International Cooperation in Research and Higher Education (STINT) (R.F.); U.S. National Science Foundation, grants PHY 01 39984 (E.H.L and H.S.) and PHY 03 53181 (R.S.); an A.P. Sloan Fellowship (R.S.); Deutsche Forschungsgemeinschaft, grant SI 348/13-1 (H.S.).
Funders:
Funding AgencyGrant Number
Swedish Foundation for International Cooperation in Research and Higher Education (STINT)UNSPECIFIED
NSFPHY-0139984
NSFPHY-0353181
Alfred P. Sloan FoundationUNSPECIFIED
Deutsche Forschungsgemeinschaft (DFG)SI 348/13-1
Classification Code:PACS numbers: 31.15.-p, 71.10.-w
Record Number:CaltechAUTHORS:20170510-091442211
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170510-091442211
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77333
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:16 May 2017 20:41
Last Modified:16 May 2017 20:41

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