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Solutions of the Multiconfiguration Equations in Quantum Chemistry

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Abstract.

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.

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  1. CEREMADE, CNRS UMR 7534, Université Paris IX Dauphine, Place du Marchal de Lattre de Tassigny, 75775, Paris Cedex 16, France

    Mathieu Lewin

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  1. Mathieu Lewin
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Correspondence to Mathieu Lewin.

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Communicated by G. Friesecke

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Lewin, M. Solutions of the Multiconfiguration Equations in Quantum Chemistry. Arch. Rational Mech. Anal. 171, 83–114 (2004). https://doi.org/10.1007/s00205-003-0281-6

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