Hartree-Fock Wave Functions without Symmetry and Equivalence Restrictions and the Calculation of Hyperfine-Structure Expectation Values for the LowestP2States of Boron and Lithium

Abstract

The spin-polarized (SPHF) and unrestricted (UHF) Hartree-Fock equations are solved for the lowest $^{2}P$ states of Li and B. The orbitals are not symmetry adapted with respect to ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{l}}}^{2}$ in the UHF approximation for these states. The most important admixture, and the only one that has been taken into account here, is ${d}_{0}$ admixture into the $s$ orbitals. The UHF determinant is not an eigenfunction of ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{L}}}^{2}$ and ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}^{2}$. Various aspects of this fact are pointed out and discussed. The admixture of $d$ character into the orbitals will depend heavily on exchange. It will lead to substantial corrections to hyperfine-structure expectation values. The results agree well with Sternheimer's for the quadrupole terms for B and Li. For the spin dipolar term, the results agree with the first-order perturbation-theory results of Lyons et al. for Li and with the polarization function results of Schaefer et al. for B. Configuration interaction and second-order perturbation-theory results are also discussed in this connection.