Analysis of theS2Ground State of Lithium in Terms of Natural and Best Overlap (Brueckner) Spin Orbitals with Implications for the Fermi Contact Term

Some very accurate wave functions (containing explicitly $r_{\mathrm{ij}}$ terms) for the ${}_{}{}^2{}_{}{}^{}S$ ground state of Lithium have been analyzed in terms of natural spin orbitals (NSO) and best overlap orbitals (BO). Comparison of BO's determined from a wave function giving 99.9% of the correlation energy with the spin-polarized Hartree-Fock orbitals (HF), revealed very small differences at least for the core orbitals. The difference between BO's and NSO's was significant but negligible. The BO's can be transformed unitarily among themselves and such a transformation was made before the comparison to make the orbitals fit as much as possible. The calculation of the Fermi contact term in the hyperfine structure of the spectrum has been discussed and it was found that the small difference between the HF value and the exact value could be accounted for, to a large extent, by the difference between HF and BO (or NSO). The pure correlation effects were found to be only about 0.5%. The separated valence orbital model has been analyzed on the basis of the NSO results and it has been shown that the eigenvalues (except the largest one) are degenerate in pairs for this model and that the corresponding NSO's have the same spatial factor, if orthogonality is assumed between the valence orbital and the singlet core. It has been shown that this orthogonality constraint has serious consequences for the Fermi contact term.