Solutions of the multiconfiguration equations in quantum chemistry
Lewin, Mathieu (2004), Solutions of the multiconfiguration equations in quantum chemistry, Archive for Rational Mechanics and Analysis, 171, 1, p. 83-114. http://dx.doi.org/10.1007/s00205-003-0281-6
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00093510/en/
Journal nameArchive for Rational Mechanics and Analysis
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Abstract (EN)The multiconfiguration methods are the natural generalization of the well-known Hartree-Fock theory for atoms and molecules. By a variational method, we prove the existence of a minimum of the energy and of infinitely many solutions of the multiconfiguration equations, a finite number of them being interpreted as excited states of the molecule. Our results are valid when the total nuclear charge Z exceeds N–1 (N is the number of electrons) and cover most of the methods used by chemists. The saddle points are obtained with a min-max principle; we use a Palais-Smale condition with Morse-type information and a new and simple form of the Euler-Lagrange equations.
Subjects / KeywordsPhysique mathématique
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Global-in-time existence of solutions to the multiconfiguration time-dependent Hartree-Fock equations: A sufficient condition Trabelsi, Saber; Mauser, Norbert; Bardos, Claude; Catto, Isabelle (2009) Article accepté pour publication ou publié