H-F−Potential Interaction and Local Mode Frequencies for an Interstitial Hydrogen Atom in Alkaline Earth Fluorides

The potential interaction between a hydrogen atom and a fluorine ion in an alkaline earth fluoride has been calculated and used to predict the local mode frequencies for A${\mathrm{F}}_2$: ${\mathrm{H}}^0$, where $A=\mathrm{Ca}$, Sr, or Ba. Born parameters for the repulsive H-${\mathrm{F}}^{-}$ interaction are obtained by a semiempirical method and also from self-consistent-field calculations using the Hartree-Fock-Roothaan method. The effect of the crystal field, which prevents electron detachment and leads to a repulsive interaction between the H and ${\mathrm{F}}^{-}$ ions in the crystal, is simulated by restricting the basis sets. The repulsive potential is used to calculate the local mode vibration frequency for an interstitial hydrogen atom in the alkaline earth fluorides. The semi-empirical and SCF potential curves are in reasonable agreement, and the calculated local mode frequency for Ca${\mathrm{F}}_2$: ${\mathrm{H}}^0$ agrees with the observed value.