Symmetry-Adapted Pair Correlations for Open-Shell Systems: Correlation Energy and Hyperfine Structure of the Nitrogen Atom

Using two different extended basis sets of Slater-type orbitals, we have carried out a study of the correlation energy and hyperfine structure of the ${}_{}{}^4{}_{}{}^{}S$ ground state of the nitrogen atom. Symmetry-adapted pair correlations were evaluated with respect to a multiconfiguration reference state, the first-order wave function. It was found that each symmetry-adapted pair correlation energy could be rather accurately (to about 3%) approximated as a sum of effects due to symmetry-determined classes of configurations. Using the larger of the two basis sets, the effects of 1633 configurations, constructed from 19 530 distinct Slater determinants, were considered. With this basis set the correlation energy obtained was 0.181 75 hartree, compared to the estimated correlation energy 0.186 hartree. It was found that pair correlations had large canceling effects on the hyperfine structure, the net result of which was a spin density 77% of experiment, and only slightly larger than the first-order spin density, which includes core polarization effects. Several points in common are found in a comparison with the many-body perturbation theory results of Dutta, Matsubara, Pu, and Das. The most useful and interesting result of the present work is a clear picture of the different effects which contribute to the correlation energy and hyperfine structure of ${}_{}{}^4{}_{}{}^{}S$ N.