Spin-Extended Wave Functions for First-Row Atoms

An extension of Brillouin's theorem, stating that matrix elements of $H-EI$ between the spin-extended Hartree-Fock (SEHF) function and the projected singly-excited functions derived from it vanish, is used to calculate the SEHF function itself. Functions are reported for C, N, O, and F, using two basis sets for each atom. Results are compared with earlier calculations for other first-row atoms. Appreciable energy reductions with respect to the restricted Hartree-Fock results were obtained only for the closed-shell atoms He and Be, and a spin density in good agreement with experiment was obtained only for Li. It is suggested that larger basis sets may be required to span the SEHF functions.