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

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 ${\overrightarrow{\mathrm{l}}}^2$ 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 ${\overrightarrow{\mathrm{L}}}^2$ and ${\overrightarrow{\mathrm{S}}}^2$. 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.