Müeller's Exchange-Correlation Energy in Density-Matrix-Functional Theory
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.
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.).Attached Files
Submitted - 0705.1587.pdf
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Additional details
- Eprint ID
- 77333
- Resolver ID
- CaltechAUTHORS:20170510-091442211
- Swedish Foundation for International Cooperation in Research and Higher Education (STINT)
- PHY-0139984
- NSF
- PHY-0353181
- NSF
- Alfred P. Sloan Foundation
- SI 348/13-1
- Deutsche Forschungsgemeinschaft (DFG)
- Created
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2017-05-16Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field