Theoretical investigation of the polarization and band intensities of the optical transitions of theVKcenter using a valence-bond wave function for the halogen-molecule anion

The transition probabilities and relative band intensities for the ultraviolet (${}_{}{}^2{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}\to {}_{}{}^2{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$) and infrared (${}_{}{}^2{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}\to {}_{}{}^2{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$) absorption bands of the $V_K$ center have been calculated using an approximate valence-bond wave function for the halogen-molecule anion. The most significant feature of this wave function is that it permits an approximate treatment of correlation between electrons of opposite spin. Intra-atomic electron correlation is included by using ionic orbitals for $A$ and neutral-atom orbitals for $B$ in valence-bond structures of the form $X_A^{-}\cdots X_B$ and vice versa in structures of the form $X_A\cdots X_B^{-}$. Interatomic electron correlation is treated by a perturbation-theory calculation of the polarization of $X_A$ by the negative charge on $X_B^{-}$ in the $X_A\cdots X_B^{-}$ structures and vice versa in the $X_A^{-}\cdots X_B$ structures. It is found that the correction for intra-atomic electron correlation yields considerably improved agreement between the calculated and observed intensities of the $\pi$-polarized part of the infrared transition. Calculations of the other transition intensities, such as the uv transition, and the $\sigma$-polarized part of the infrared transition which is "stolen" from the uv transition by spin-orbit mixing of $\sigma$ and $\pi$ states, are unaffected by the correction for electron correlation. It is also found, however, that interatomic electron correlation makes a major contribution to the isotropic hyperfine interaction in these molecules.