The Multiconnguration Methods in Quantum Chemistry

The multiconnguration methods are the natural generalization of the well-known Hartree-Fock theory for atoms and molecules. By a varia-tional method, we prove the existence of a minimum of the energy and of innnitely many solutions of the multiconnguration equations, a nite 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.