Solutions of the multiconfiguration Dirac-Fock equations

Antoine Levitt (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

The multiconfiguration Dirac-Fock (MCDF) model uses a linear combination of Slater determinants to approximate the electronic $N$-body wave function of a relativistic molecular system, resulting in a coupled system of nonlinear eigenvalue equations, the MCDF equations. In this paper, we prove the existence of solutions to these equations in the weakly relativistic regime. First, using results from Lewin on the multiconfiguration nonrelativistic model, and Esteban and Sere on the single-configuration relativistic model, we prove existence of critical points for the associated energy functional, under the constraint that the occupation numbers are not too small. Then, this constraint can be removed in the weakly relativistic regime, and we obtain non-constrained critical points, i.e. solutions of the multiconfiguration Dirac-Fock equations.

Mots clés: multiconfiguration methods; relativistic quantum mechanics; critical points

Domaines: Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Antoine Levitt. Solutions of the multiconfiguration Dirac-Fock equations. 2013. ⟨hal-00823185v1⟩