Theoretical investigation of the hyperfine-structure constants of theVKand(XY)−centers using a valence-bond wave function for the halogen-molecule anions

An approximate valence-bond wave function which includes correlation between electrons of opposite spin is used to calculate hyperfine-structure constants (hfc) for the halogen molecule ions ${\left(XY\right)}^{-}$ as functions of the internuclear distance and charge distribution of the molecules. The principal contributions to the isotropic hfc in these molecules are: (a) orthogonality requirements which transfer part of the unpaired electron density in the $p$ orbital of one atom into the $s$ orbitals of the other atom; (b) the electrostatic polarization of one atom by the negative charge on the other; (c) a cross term involving the previous two effects; and (d) a purely atomic term reflecting the partial halogen-atom character of each component of the molecular anion. The anisotropic hfc are due primarily to the unpaired electron densities in the valence $p$ orbitals. Comparison of calculated hfc with experimental values for the ${\left(XY\right)}^{-}$ centers in various alkali-halide crystals yields estimates of the internuclear distance and charge distribution of these molecules. These estimates are consistent with consideration of ion sizes and electronegativities.