Remarks on Brillouin's theorem in the atomic variational approach

An analysis is made of the validity of Brillouin's theorem for atomic Hartree-Fock (HF) results. Consequences are derived for the use of the multiconfigurational HF method. Brillouin's theorems adapted to the unrestricted HF methods are recalled. As an application, the quality of HF results in hyperfine structure and isotope-shift problems is discussed. The computation of screening factors for field isotope shift is shown to be the most favourable case.