Local Exchange Potentials for Electronic Structure Calculations
MathematicS In Action, Volume 2 (2009) no. 1, pp. 1-42.

The Hartree-Fock exchange operator is an integral operator arising in the Hartree-Fock model as well as in some instances of the density functional theory. In a number of applications, it is convenient to approximate this integral operator by a multiplication operator, i.e. by a local potential. This article presents a detailed analysis of the mathematical properties of various local approximations to the nonlocal Hartree-Fock exchange operator including the Slater potential, the optimized effective potential (OEP), the Krieger-Li-Iafrate (KLI) approximation and the common-energy denominator approximation (CEDA) to the OEP, and the effective local potential (ELP). In particular, we show that the Slater, KLI, CEDA and ELP potentials all can be defined as solutions of certain variational problems, and we provide a rigorous derivation of the OEP integral equation. We also establish an existence result for a coupled system of nonlinear partial differential equations introduced by Slater to approximate the Hartree-Fock equations.

Published online:
DOI: 10.5802/msia.2
Classification: 35P30, 81Q05, 35J60
Keywords: Hartree-Fock model, Density Functional theory, nonlinear eigenvalue problem
Eric Cancès 1; Gabriel Stoltz 1; Gustavo E. Scuseria 2; Viktor N. Staroverov 3; Ernest R. Davidson 4

1 Université Paris Est, CERMICS, Project-team Micmac, INRIA-Ecole des Ponts, 6 & 8 Av. Pascal, 77455 Marne-la-Vallée Cedex 2, France
2 Department of Chemistry, Rice University, Houston, Texas 77005, United States of America
3 Department of Chemistry, University of Western Ontario, London, Ontario N6A 5B7, Canada
4 Department of Chemistry, University of Washington, Seattle, Washington 98195, United States of America
     author = {Eric Canc\`es and Gabriel Stoltz and Gustavo E. Scuseria and Viktor N. Staroverov and Ernest R. Davidson},
     title = {Local {Exchange} {Potentials} for {Electronic} {Structure} {Calculations}},
     journal = {MathematicS In Action},
     pages = {1--42},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
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     year = {2009},
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Eric Cancès; Gabriel Stoltz; Gustavo E. Scuseria; Viktor N. Staroverov; Ernest R. Davidson. Local Exchange Potentials for Electronic Structure Calculations. MathematicS In Action, Volume 2 (2009) no. 1, pp. 1-42. doi : 10.5802/msia.2. https://msia.centre-mersenne.org/articles/10.5802/msia.2/

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