Symmetry Breaking of Relativistic Multiconfiguration Methods in the Nonrelativistic Limit

Maria J. Esteban (1) , Mathieu Lewin (2) , Andreas Savin (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 AGM - UMR 8088 - Analyse, Géométrie et Modélisation
3 LCT - Laboratoire de chimie théorique

The multiconfiguration Dirac-Fock method allows to calculate the state of relativistic electrons in atoms or molecules. This method has been known for a long time to provide certain wrong predictions in the nonrelativistic limit. We study in full mathematical details the nonlinear model obtained in the nonrelativistic limit for Be-like atoms. We show that the method with sp+pd configurations in the $J=1$ sector leads to a symmetry breaking phenomenon in the sense that the ground state is never an eigenvector of L² or S². We thereby complement and clarify some previous studies.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Chimie théorique et/ou physique; Equations aux dérivées partielles [math.AP]

Maria J. Esteban, Mathieu Lewin, Andreas Savin. Symmetry Breaking of Relativistic Multiconfiguration Methods in the Nonrelativistic Limit. Nonlinearity, 2010, 23, pp.767-791. ⟨hal-00425326v2⟩