Archive for Rational Mechanics and Analysis

, Volume 171, Issue 1, pp 83–114 | Cite as

Solutions of the Multiconfiguration Equations in Quantum Chemistry

  • Mathieu LewinEmail author


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.


Excited State Saddle Point Simple Form Finite Number Quantum Chemistry 
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© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.CEREMADE, CNRS UMR 7534Université Paris IX DauphineParis Cedex 16France

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