The nonrelativistic limit of Dirac-Fock codes: the role of Brillouin   configurations
  We solve a long standing problem with relativistic calculations done with the widely used Multi-Configuration Dirac-Fock Method (MCDF). We show, using Relativistic Many-Body Perturbation Theory (RMBPT), how even for relatively high-$Z$, relaxation or correlation causes the non-relativistic limit of states of different total angular momentum but identical orbital angular momentum to have different energies. We show that only large scale calculations that include all single excitations, even those obeying the Brillouin's theorem have the correct limit. We reproduce very accurately recent high-precision measurements in F-like Ar, and turn then into precise test of QED. We obtain the correct non-relativistic limit not only for fine structure but also for level energies and show that RMBPT calculations are not immune to this problem. 
Paul Indelicato (LKB - Jussieu), Eva Lindroth (APSU), Jean-Paul   Desclaux