Spin-Optimized Self-Consistent-Field Function. II. Hyperfine Structure of Atomic Nitrogen

The spin-optimized self-consistent-field (SOSCF) method, based on optimizing the spin function in the whole ($S, M_s$) space simultaneously with spatial orbital optimization, is applied to the ${}_{}{}^4{}_{}{}^{}S$ ground state of the nitrogen atom. The maximally paired Hartree-Fock (MPHF) function, where both $1s$ and $2s$ electron pairs are associated with the singlet factor $\alpha \beta -\beta \alpha$, is also calculated, as are functions in which either the $1s$ or the $2s$ electrons are thus paired. The SOSCF energy is -54.421 67 Hartree, compared with -54. 400 93 by the restricted Hartree-Fock (RHF) and -54. 417 22 by the MPHF methods. The net spin density at the nucleus, responsible for the hfs of nitrogen, is 0. 1200 a.u., compared with 0. 1853 a.u. by the spin-extended Hartree-Fock method and the experimental value of 0.0972 a.u. (the RHF and MPHF methods give 0). The contributions of the $1s$ and $2s$ pairs, obtained from two separate calculations employing two-dimensional subspaces of the six-dimensional spin-function space, add very nearly to the full SOSCF results for the energy and spin density. The SOSCF orbitals are also described. Their most interesting feature is the nonexistence of radial nodes in any of them.