Spin-Optimized Self-Consistent Field Wave Functions

A method is given for determining a spin-optimized self-consistent-field (SO-SCF) function based on optimized spatial orbitals and a spin function which is optimum in the $S$, $M_S$ spin space. Results are presented for $\mathrm{Li}\left({}_{}{}^2{}_{}{}^{}S\right)$, $\mathrm{Li}\left({}_{}{}^2{}_{}{}^{}P\right)$, ${\mathrm{Be}}^{+}\left({}_{}{}^2{}_{}{}^{}S\right)$, ${\mathrm{B}}^{++}\left({}_{}{}^2{}_{}{}^{}S\right)$, and $\mathrm{Be}\left({}_{}{}^1{}_{}{}^{}S\right)$. SO-SCF wave functions and energies are very similar to those obtained with restriction to the normally paired spin function, but the use of the entire spin space greatly improves the description of spin-dependent properties. Whereas single-spin-function calculations of the spin density at the nucleus are for $\mathrm{Li}\left({}_{}{}^2{}_{}{}^{}S\right)$ and $\mathrm{Li}\left({}_{}{}^2{}_{}{}^{}P\right)$, respectively, 9% and 100% in error, the corresponding SO-SCF errors are only 2% and 7%.