Dipolar Coupling and Molecular Vibrations in Crystals. IV. Frequency Shifts and Dipole Moment Derivatives

The internal vibrational modes of a dipole coupled crystal are discussed in terms of two models, a “back-ground polarization” model which differs from the transition moment dipole coupled “resonant mode” model in that the additional induced dipolar coupling due to electronic polarization is included. The transverse–longitudinal mode splittings as well as factor group splittings are discussed in terms of these two models. The contribution to the frequency shifts from nonresonant modes is calculated and the effect of dipolar coupling on the overtone frequencies is examined. Dipole moment derivatives and static crystal field frequencies of the ν3 doubly degenerate stretching mode are calculated for a few rhombohedral crystals.