Self-Consistent-Field Wave Functions for Hole States of Some Ne-Like and Ar-Like Ions

Abstract

Analytic self-consistent-field (SCF) wave functions were computed for the ground states of the closed-shell atomic systems ${\mathrm{F}}^{-}$, Ne, and ${\mathrm{Na}}^{+}$, and ${\mathrm{Cl}}^{-}$, Ar, and ${\mathrm{K}}^{+}$; and for those ground and excited states of the open-shell systems which are obtained by removing a single electron from any one of the occupied shells of these closed-shell systems. Details of the calculation of the functions are presented, with emphasis on a justification of the procedures used for the calculations for excited states. A high accuracy is obtained; the calculations for the closed-shell systems give the most accurate analytic SCF wave functions which have yet been reported. Ionization potentials are calculated and compared with experimental values. Computed ionization potentials for the removal of a $2s$ electron from ${\mathrm{Cl}}^{-}$, Ar, and ${\mathrm{K}}^{+}$, for which no direct experimental data are available, are estimated to be accurate to 1%. It is found that the removal of an electron from the outermost $s$ shell increases the correlation energy, in contradiction to the predictions of a recently proposed semiempirical scheme for estimating the correlation energy. For example, the magnitude of the correlation energy of the lowest ${}_{}{}^2{}_{}{}^{}S$ state of ${\mathrm{Ar}}^{+}$ is ∼4 eV greater than the magnitude of the correlation energy of neutral Ar. The effect of the nonzero off-diagonal Lagrangian multipliers is considered and found to be important for the inner shell hole states.