Localized Vibrations of Atomic Hydrogen in CaF2

Abstract

The infrared (ir) absorption spectrum of Ca${\mathrm{F}}_2$ containing hydrogen has been measured over the range 590-2000 ${\mathrm{cm}}^{-1\mathrm{}}$. A strong, sharp line observed at 640±0.5 ${\mathrm{cm}}^{-1\mathrm{}}$ has been assigned to the localized mode of vibration associated with the interstitial neutral hydrogen atoms. The concentration of atomic hydrogen in the Ca${\mathrm{F}}_2$ has been determined using both ir absorption and ESR absorption techniques. The measured concentration of 3×${10}^{19}$/${\mathrm{cm}}^3$, together with the observed integrated absorption of the 640-${\mathrm{cm}}^{-1\mathrm{}}$ line of 73 ${\mathrm{cm}}^{-2\mathrm{}}$, indicates that the hydrogen-atom defect has an "apparent charge," as defined by Leigh and Szigeti, of 0.07 electrons. The observed localized-mode frequency has been compared with the result of an ab initio calculation of the interaction between the hydrogen defect and its eight fluoride neighbors. This calculation began with a Hartree-Fock-Roothaan self-consistent-field molecular-orbital calculation of the energy of an H${\mathrm{F}}^{-}$ molecule. A localized-mode frequency of 560 ${\mathrm{cm}}^{-1\mathrm{}}$ was obtained, in fair agreement with the observed frequency.