Electronic Structure of MgF2:Co++

The ${\mathrm{F}}^{19}$ superhyperfine structure of the EPR spectra of ${\mathrm{Co}}^{++}$ in Mg${\mathrm{F}}_2$ is interpreted with simple molecular-orbital theory. A necessary preliminary analysis is made of the $g$ tensor and of the spacing of the six Kramers doublets derived from the ${}_{}{}^4{}_{}{}^{}T_1^{}{}_{}{}^{}$ ground manifold. The ligand-field parameters of the rhombic field, $\Delta \cong 510$ ${\mathrm{cm}}^{-1\mathrm{}}$ and $\Gamma \cong -390\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, and the spin-orbit coupling, $\lambda \cong -157\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, are significantly different from values derived from less complete data. The reported superhyperfine interactions provide sufficient data to determine, without recourse to much less certain orbital-reduction factors, the $s$-, sigma-, and pi-bonding fractions: $f_s=(0.61\mathrm{}\pm 0.02)\%$, $f_{\sigma }=(3.9\mathrm{}\pm 0.3)\%$, and $f_{\pi }=(0.9\mathrm{}\pm 0.3)\%$ for the two equivalent fluorine ions along [110]. For the other four fluorine ions similar estimates are obtained. These results are at variance with the suggestion, made for octahedral ${\mathrm{Co}}^{++}$, that sigma and pi bonding are of comparable magnitude.