Two-Determinant Spin-Polarized Calculation of the Hyperfine Structure ofB11

A two-determinant spin-polarized function derivable from the spin configurations ${\Pi }_i{\left(\alpha \beta \right)}_i{\Pi }_j{\alpha }_j$ and ${\Pi }_i{\left(\beta \alpha \right)}_i{\Pi }_j{\alpha }_j$ is presented and applied to the boron atom using modified Slater orbitals which are solved non-self-consistently. For purposes of comparison, single-determinant polarized and nonpolarized functions with the same orbital base are also determined. For all three functions the hyperfine constant is calculated, and it is found that the constant $a_s$ [equal to 0.11 atomic units (a.u.) experimentally] changes from -49.96 to -40.33 a.u. from the one- to the two-determinant spin-polarized functions with the corresponding energy improvement from -24.503 to -24.527 a.u. (as compared to the experimental energy of -24.66 a.u. and the best spin-polarized Hartree-Fock value of -24.529 a.u.). In addition it is pointed out that cancellation difficulties in determining charge density at the nucleus from $\mathrm{ns}$ pairs is greatly alleviated, and that in order to use a proper eigenfunction of ${\mathrm{S}}^2$ we are required to include many more determinants than we are presently prepared to deal with.