Existence of Minimizers for Kohn-Sham Models in Quantum Chemistry
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 6, pp. 2425-2455.
@article{AIHPC_2009__26_6_2425_0,
     author = {Anantharaman, Arnaud and Canc\`eS, Eric},
     title = {Existence of {Minimizers} for {Kohn-Sham} {Models} in {Quantum} {Chemistry}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {2425--2455},
     publisher = {Elsevier},
     volume = {26},
     number = {6},
     year = {2009},
     doi = {10.1016/j.anihpc.2009.06.003},
     mrnumber = {2569902},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2009.06.003/}
}
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Anantharaman, Arnaud; CancèS, Eric. Existence of Minimizers for Kohn-Sham Models in Quantum Chemistry. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 6, pp. 2425-2455. doi : 10.1016/j.anihpc.2009.06.003. http://www.numdam.org/articles/10.1016/j.anihpc.2009.06.003/

[1] A. Anantharaman, PhD thesis, Université Paris-Est, Ecole des Ponts, in preparation.

[2] Becke A. D., Density-Functional Exchange-Energy Approximation With Correct Asymptotic Behavior, Phys. Rev. A 38 (1988) 3098-3100.

[3] Blöchl P. E., Projector Augmented-Wave Method, Phys. Rev. B 50 (1994) 17953-17979.

[4] Catto I., Le Bris C., Lions P.-L., On the Thermodynamic Limit for Hartree-Fock Type Models, Ann. Inst. H. Poincaré Anal. Non Linéaire 18 (6) (2001) 687-760. | EuDML | Numdam | MR | Zbl

[5] Ceperley D. M., Alder B. J., Ground State of the Electron Gas by a Stochastic Method, Phys. Rev. Lett. 45 (1980) 566-569.

[6] Davidson E. R., Reduced Density Matrices in Quantum Chemistry, Academic Press, New York, 1976.

[7] Dreizler R. M., Gross E. K.U., Density Functional Theory, Springer, 1990. | Zbl

[8] Ekeland I., Nonconvex Minimization Problems, Bull. Amer. Math. Soc. 1 (1979) 443-474. | MR | Zbl

[9] Frank R. L., Lieb E. H., Seiringer R., Siedentop H., Müller's Exchange-Correlation Energy in Density-Matrix-Functional Theory, Phys. Rev. A 76 (2007) 052517.

[10] Giaquinta M., Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Princeton Univ. Press, Princeton, 1983. | MR | Zbl

[11] Gilbarg D., Trudinger N. S., Elliptic Partial Differential Equations of Second Order, third ed., Springer, 1998. | Zbl

[12] Hohenberg P., Kohn W., Inhomogeneous Electron Gas, Phys. Rev. B 136 (1964) 864-871. | MR

[13] Kohn W., Sham L. J., Self-Consistent Equations Including Exchange and Correlation Effects, Phys. Rev. A 140 (1965) 1133. | MR

[14] Langreth D. C., Perdew J. P., Theory of Nonuniform Electronic Systems. I. Analysis of the Gradient Approximation and a Generalization That Works, Phys. Rev. B 21 (1980) 5469-5493.

[15] C. Le Bris, Quelques problèmes mathématiques en chimie quantique moléculaire, Thèse de l'Ecole Polytechnique, 1993.

[16] Levy M., Universal Variational Functionals of Electron Densities, First Order Density Matrices, and Natural Spin-Orbitals and Solution of the V-Representability Problem, Proc. Natl. Acad. Sci. USA 76 (1979) 6062-6065. | MR

[17] Lieb E. H., Density Functional for Coulomb Systems, Int. J. Quantum Chem. 24 (1983) 243-277.

[18] Lieb E. H., Loss M., Analysis, Grad. Stud. Math., vol. 14, second ed., Amer. Math. Soc., Providence, RI, 2001. | MR | Zbl

[19] Lions P.-L., Solutions of Hartree-Fock Equations for Coulomb Systems, Comm. Math. Phys. 109 (1987) 33-97. | MR | Zbl

[20] Lions P.-L., The Concentration-Compactness Method in the Calculus of Variations. the Locally Compact Case. Part I, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984) 109-145, Part II, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984) 223-283. | Numdam | Zbl

[21] L. Tartar, Homogénéisation et compacité par compensation, Cours Peccot au College de France, 1977. | Zbl

[22] Perdew J. P., Burke K., Ernzerhof M., Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 77 (1996) 3865-3868.

[23] Perdew J. P., Wang Y., Accurate and Simple Density Functional for the Electronic Exchange Energy: Generalized Gradient Approximation, Phys. Rev. B 33 (1986) 8800-8802.

[24] Perdew J. P., Wang Y., Accurate and Simple Analytic Representation of the Electron-Gas Correlation Energy, Phys. Rev. B 45 (1992) 13244-13249.

[25] Perdew J. P., Zunger A., Self-Interaction Correction to Density-Functional Approximations for Many-Electron Systems, Phys. Rev. B 23 (1981) 5048-5079.

[26] Redner S., Citation Statistics From 110 Years of Physical Review, Phys. Today 49 (2005) 49-54.

[27] Reed M., Simon B., Methods of Modern Mathematical Physics, Vol. I, Functional Analysis, second ed., Academic Press, New York, 1980. | MR | Zbl

[28] Reed M., Simon B., Methods of Modern Mathematical Physics, Vol. IV, Analysis of Operators, Academic Press, New York, 1978. | MR | Zbl

[29] Simon B., Trace Ideals and Their Applications, London Math. Soc. Lecture Note Ser., vol. 35, Cambridge Univ. Press, 1979. | MR | Zbl

[30] Stampacchia G., Le Problème De Dirichlet Pour Les Équations Elliptiques Du Second Ordre À Coefficients Discontinus, Ann. Inst. Fourier 15 (1965) 189-257. | Numdam | MR | Zbl

[31] Troullier N., Martins J. L., Efficient Pseudopotentials for Plane Wave Calculations, Phys. Rev. B 43 (1991) 1993-2006.

[32] Vanderbilt D., Soft Self-Consistent Pseudopotentials in a Generalized Eigenvalue Formalism, Phys. Rev. B 41 (1990) 7892-7895.

[33] Vosko S. H., Wilk L., Nusair M., Accurate Spin-Dependent Electron Liquid Correlation Energy for Local Spin Density Calculations: a Critical Analysis, Can. J. Phys. 58 (1980) 1200-1211.

[34] Zhislin G. M., A Study of the Spectrum of the Schrödinger Operator for a System of Several Particles, Tr. Mosk. Mat. Obs. 9 (1960) 81-120. | MR | Zbl

[35] Zhislin G. M., Sigalov A. G., The Spectrum of the Energy Operator for Atoms With Fixed Nuclei on Subspaces Corresponding to Irreducible Representations of the Group of Permutations, Izv. Akad. Nauk SSSR Ser. Mat. 29 (1965) 835-860. | MR | Zbl

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