Spin-Optimized Self-Consistent-Field Function. III. Ground States of Boron and Carbon Atoms

The spin-optimized self-consistent-field (SOSCF) function, a product of one-electron spatial orbitals multiplied by a spin function optimized in the relevant ($S,M_S$) space, is calculated for $\mathrm{B}\left({}_{}{}^2{}_{}{}^{}P\right)$ and $\mathrm{C}\left({}_{}{}^3{}_{}{}^{}P\right)$. The energy reduction relative to restricted Hartree-Fock values is considerable and includes most of the "radial correlation energy." The hfs constants are calculated and found to be in very good agreement with experiment, where experimental values are known. The use of partial spaces for the spin-function variation is considered. The spatial orbitals are described, and as observed previously for other atoms, they possess no radial nodes.