Calculations on the hyperfine-splitting constants for the atoms B, C, N, O, and F have been carried out by both the unrestricted Hartree-Fock (UHF) method and a method corresponding to optimizing the orbitals of a Slater determinant after spin projection (the GF method). This is equivalent to one form of Löwdin's extended Hartree-Fock method. These calculations account for core-polarization contributions to the spin density but not for any significant part of the electron correlation. It is found that the core-polarization term is significantly larger (for N about 65% larger) than the experimental value, indicating that the remaining correlation effects significantly decrease the magnitude of the spin density at the nucleus.

Since these calculations used analytic expansions, an extensive set of basis sets was examined in order to determine what type of basis set is required in order to obtain accurate values for various properties.

On the basis of these calculations and the observed hyperfine structure, we obtain a magnetic moment (in nuclear magnetons) of ${\mu }_{\mathrm{N}}=\pm 0.97$ for ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ and electric quadrupole moments (in barns) of $Q=0.037\mathrm{}$ for ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$, $Q=0.031\mathrm{}$ for ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ (assuming ${\mu }_{\mathrm{N}}$ for ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ to be negative), and $Q=-0.025\mathrm{}$ for ${}_{}{}^{17}{}_{}{}^{}\mathrm{O}$.

• Received 9 September 1968

DOI:https://doi.org/10.1103/PhysRev.182.48