Symmetry Breaking of Relativistic Multiconfiguration Methods in the Nonrelativistic Limit

TL;DR

This paper investigates the nonrelativistic limit of the multiconfiguration Dirac-Fock method, revealing a symmetry breaking phenomenon where the ground state fails to be an eigenvector of angular momentum operators.

Contribution

It provides a detailed mathematical analysis of symmetry breaking in multiconfiguration methods in the nonrelativistic limit, clarifying previous partial results.

Findings

Ground state not an eigenvector of L^2 or S^2 in certain configurations

Symmetry breaking occurs in the J=1 sector with sp+pd configurations

Clarifies previous studies on nonrelativistic limits of relativistic methods

Abstract

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 L^2 or S^2. We thereby complement and clarify some previous studies.