Comptes Rendus
no. 4
The multiconfiguration methods in quantum chemistry: Palais–Smale condition and existence of minimizers
[Les méthodes de multiconfiguration en chimie quantique : condition de Palais–Smale et existence de minima]
Mathieu Lewin1
1 CEREMADE, Université Paris IX Dauphine, place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France
Comptes Rendus. Mathématique, Volume 334 (2002) no. 4, pp. 299-304.

Dans cette Note, nous proposons une nouvelle preuve de l'existence d'un minimum pour les méthodes de multiconfiguration en Chimie Quantique. Nous utilisons une propriété de Palais–Smale (avec information de type Morse), dont la démonstration repose sur les équations d'Euler–Lagrange écrites sous une forme compacte aisément utilisable.

In this Note, we propose a new proof for the existence of a minimum in the multiconfiguration methods in Quantum Chemistry. We use a Palais–Smale condition with Morse-type information, whose proof is based on the Euler–Lagrange equations, written in a simple and useful way.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02252-5
Mathieu Lewin 1

1 CEREMADE, Université Paris IX Dauphine, place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France 
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Mathieu Lewin. The multiconfiguration methods in quantum chemistry: Palais–Smale condition and existence of minimizers. Comptes Rendus. Mathématique, Volume 334 (2002) no. 4, pp. 299-304. doi : 10.1016/S1631-073X(02)02252-5. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02252-5/

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[2] G. Friesecke, The multiconfiguration equations for atoms and molecules: charge quantization and existence of solutions, Preprint, Mathematical Institute, University of Oxford, UK, 1999 (to appear in Arch. Rat. Mech. Anal.)

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[4] N. Ghoussoub Duality and Perturbation Methods in Critical Point Theory, Cambridge University Press, 1993

[5] C. Le Bris A general approach for multiconfiguration methods in quantum molecular chemistry, Ann. Inst. H. Poincare Anal. Non Linéaire, Volume 11 (1994) no. 6, pp. 441-484

[6] M. Lewin, The multiconfiguration methods in quantum chemistry (in preparation)

[7] E.H. Lieb; B. Simon The Hartree–Fock theory for Coulomb systems, Comm. Math. Phys., Volume 53 (1977), pp. 185-194

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