On the use of the $V^{N-M}$ approximation in atomic calculations
  We demonstrate that $V^{N-M}$ approximation is a good starting point for the configuration interaction calculations for many-electron atoms and ions. $N$ is the total number of electrons in the neutral atom, $M$ is the number of valence electrons. $V^{N-M}$ is the self-consistent Hartree Fock potential for a closed-shell ion with all valence electrons removed. Using of the $V^{N-M}$ approximation considerably simplifies the many-body perturbation theory for the core-valence correlations. It makes it easier to include higher-order correlations which often significantly improves the accuracy of the calculations. Calculations for krypton and barium and their positive ions are presented for illustration. 
V. A. Dzuba