Model for O${\mathrm{H}}^{-}$, O${\mathrm{D}}^{-}$, and C${\mathrm{N}}^{-}$ Impurities in Alkali Halide Matrices

A model has been developed for calculating the potential barrier-hindering angular motion and possible off-center displacement of the polar impurities in the alkali halide matrices. The general method of the multipole expansion of the intermolecular interaction has been employed. The calculations have been done for the O${\mathrm{H}}^{-}$, O${\mathrm{D}}^{-}$, and C${\mathrm{N}}^{-}$ impurities in the KCl, KBr, NaCl, RbCl, and KI matrices. It has been found that the O${\mathrm{H}}^{-}$ and O${\mathrm{D}}^{-}$ impurities are displaced bv about 0.2-0.3 Å from the normal-lattice site in the different alkali halide lattices. For the C${\mathrm{N}}^{-}$ case, no appreciable displacement of the impurity c.m. is evidenced. In this case, the effect of the relaxation of the lattice near the impurity is also considered. This has been found to add a small tetragonal term of the type ${\left(4\mathrm{}\pi \right)}^{\frac{1}{2}}{K}^{\prime \prime }{Y}_0^2$ to the octahedral potential. The addition of such a small tetragonal term has recently been demonstrated by Pompi and Narayanamurti to explain successfully the rather unexpected infrared results and also the anomalous specific-heat results of Harrison et al. The calculated values of the barrier and the off-center displacement have been used successfully to explain the librational frequency and the tunneling splitting of these impurities in the matrices. The general validity of different approaches has been discussed in the light of the librational frequencies and their isotope effect.