Analytic Hartree-Fock Wave Functions for the3p-Shell Atoms

Hartree-Fock wave functions have been obtained for the $3p$-row atoms, i.e., for neutral Al, Si, P, S, Cl, and Ar, and for ${\mathrm{Cl}}^{-}$. Solutions were determined in analytic form using a version of Nesbet's symmetry and equivalence restrictions to simplify the calculations for atoms with both closed and unclosed shells of the same $l$ value. These restrictions, the reason for their use, and their relation to other open-shell methods are discussed and the calculated one-electron wave functions and their eigenvalues are presented.