Non-Product Wave Function for a Negative Ion

A departure from the Hartree type wave function was attempted along lines found successful for ${\mathrm{H}}^{-}$. The basic $\psi$ taken was a product of the nine Hartree one-electron functions for ${\mathrm{O}}^{-}$ multiplied by a term including $r_{\mathrm{ij}}$ terms representing what were considered the most important electron interactions—those between four of the $2p$ electrons and a fifth, arbitrarily considered the added one. Since there are six possible configurations for five equivalent $2p$ electrons, the actual $\Psi$ was taken as a linear combination of the six possible $\psi \text{'}\mathrm{s}$ of the type described. Minimizing the energy with respect to the coefficients in this linear combination leads to the same type of secular equation as is obtained in perturbation theory. It is shown that only the diagonal elements of the determinant are non-vanishing, and one of these is chosen for the evaluation of the energy. The electron affinity to be obtained using this wave function is considerably greater than the value gotten by Hartree, Hartree, and Swirles, perhaps twice as much.