A Watson sphere removed to infinity is used to calculate, doubly charged negative ions of the atoms B, C, N, O, Al, Si, P, and S by the electron-correlation and self-interaction corrected generalized exchange local-spin-density functional theory. These second electron affinities are compared to other theoretical calculations and show the doubly charged negative ions of these atoms to be unstable even when the Watson sphere radius is made infinite by an algebraic equation, but less unstable than in ionic crystals.