Solutions of the Multiconfiguration Equations in Quantum Chemistry∗

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 PalaisSmale condition with Morse-type information and a new and simple form of the Euler-Lagrange equations.